The Effects of Nuclear Radiation on Schottky Power Diodes and Power MOSFETs
Dissertation
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of
Philosophy in the Graduate School of The Ohio State University
By
Jonathan Andrew Kulisek, M.S.
Graduate Program in Nuclear Engineering
The Ohio State University
2010
Dissertation Committee:
Thomas E. Blue, Advisor
Don W. Miller
Tunc Aldemir
Copyright by
Jonathan Andrew Kulisek
2010
Abstract
NASA is exploring the potential use of nuclear reactors as power sources for
future space missions. These missions will require electrical components, consisting of
power circuits and semiconductor devices, to be placed in close vicinity to the reactor, in
the midst of a high neutron and gamma-ray radiation field. Therefore, the primary goal
of this research is to examine the effects of a mixed neutron and gamma-ray radiation
field on the static and dynamic electrical performance of power Schottky diodes and
power MOSFETs in order to support future design efforts of radiation-hard power
semiconductors and circuits.
In order to accomplish this, non-radiation hardened commercial power Si and
SiC Schottky power diodes, manufactured by International Rectifier and Cree,
respectively, were irradiated in the Ohio State University Research Reactor (OSURR),
and their degradation in electrical performance was observed using I-V characterization.
Key electrical performance parameters were extracted using least squares curve-fits of
the corresponding semiconductor physics model equations to the experimental data, and
these electrical performance parameters were used to model the diodes in PSpice. A
half-wave rectifier circuit containing Cree SiC Schottky diodes, rated for 5 A DC
forward current and 1200 V DC blocking voltage, was also tested and modeled in order
ii
to determine and analyze changes in overall circuit performance and diode power
dissipation as a function of radiation dose.
Also, electrical components will be exposed to charged particle radiation from
space, such as high energy protons in the Van Allen Radiation Belts surrounding earth.
Therefore, the results from this study, with respect to the Si and SiC Schottky power
diodes, were compared to results published by NASA, which had tested the same diode
models at the Indiana University Cyclotron Facility (IUCF) with a 203 MeV proton
beam. The comparison was made on the basis of displacement damage dose, calculated
with the aid of MCNPX 2.6.0, a charged particle transport code. From the results of the
calculation, it was determined that the response of both the Si and SiC diodes to the
OSURR neutron and gamma-ray radiation field could be used to predict the response of
the same diodes to the 203 MeV proton beam to a reasonable extent, relative to other
published studies employing the same model.
In addition, 100 V and 500 V power MOSFETs were irradiated in the OSURR,
and their degradation in electrical performance was observed using I-V characterization.
Changes in threshold voltage, transconductance parameter, and on-state resistance were
observed for both 100 V and 500 V MOSFETs and were attributed to radiation-induced
degradation of the SiO 2 gate, Si-SiO 2 interface, and n- drift layer.
Furthermore, diodes and MOSFETs were irradiated and tested in basic power
electronic circuits in order to determine the overall circuit response, as well as the
dynamic electrical performance characteristics of the diodes and MOSFETs as they are
switched from conducting (on) to non-conducting (off) states. All of the Schottky
diodes maintained their voltage-blocking capability in the tested circuits, despite
iii
substantial radiation-induced increases in series resistance. Also, as radiation dose
increased, an increase was observed in the turn-off delay times and turn-off times of the
MOSFETs coupled with a decrease in turn-on delay time, which caused an increase in
the output voltage in the buck and boost converters of which the MOSFETs were a part.
Furthermore, the power dissipation in the MOSFETs during conduction and the overvoltage turn-off transient increased as a function of radiation dose, while the power
dissipation during turn-on was essentially unaffected by the radiation.
iv
Acknowledgments
I would like to thank my advisor, Dr. Thomas Blue, for his intellectual support,
encouragement, and patience regarding this research project and the writing of this
dissertation. In addition, I would like to thank Dr. Donald Miller for his encouragement
and intellectual support for this research. Furthermore, I would like to express my
gratitude to Dr. Tunc Aldemir for being a member of my candidacy exam and
dissertation defense committees.
I would also wish to thank all present and past fellow students in Dr. Blue and
Dr. Miller’s research group who have been very helpful to me. I wish to thank Dr.
Behrooz Khorsandi for his knowledge and assistance with calculations regarding
material damage effects in Si and SiC and for his continuing encouragement throughout
my graduate studies. I would also like to thank Xia (Summer) Wang for inspiring me to
work hard.
NASA and the NRC provided the funding for this research, for which I am very
grateful. In addition, I would also like to acknowledge Dr. Rick Harris, Mr. Toby Mintz,
Mr. Marty Patton, and Dr. Bob Rohal for providing technical support and knowledge.
Furthermore, I would like to acknowledge the multitude of helpful discussions regarding
this research with Dr. Al Frasca, a consultant for this project.
v
Vita
2003……...………………………………………B.S. Computer Science & Engineering,
The Ohio State University
2006………….…………………………………..M.S. Nuclear Engineering,
The Ohio State University
2004 to 2010…………………….……………….Graduate Research Associate,
The Ohio State University
Publications
1. “Design and Preliminary Monte Carlo Calculations of an Active Compton Suppressed
LaBr 3 (Ce) Detector System for TRU Assay in Remote-Handled Wastes,” J. Kulisek, J.
Hartwell, M. McIlwain, R. P. Gardner, Nucl. Inst. And Meth. A, volume 580, issue 1, p. 226229 (2007).
2. “Trim Modeling of Displacement Damage in SiC for Monoenergetic Neutrons,” B. Khorsandi,
T.E. Blue, W. Windl, J. Kulisek, Journal ASTM Int. 3, 8 (2006).
Fields of Study
Major Field: Nuclear Engineering
vi
Table of Contents
Abstract…………………………………………………………………………………...ii
Acknowledgments………………………………………………………………………..v
Vita………………………………………………………………………………………vi
List of Tables…………………………………………………………………………....xii
List of Figures…………………………………………………………………………...xv
Chapter 1 : Introduction .......................................................................................................1
Chapter 2 : Nuclear Radiation Effects and Dosimetry ........................................................5
2.1
Displacement Damage .........................................................................................5
2.2
Ionization ...........................................................................................................10
2.3
Dosimetry for the OSURR Rabbit Facility........................................................14
2.3.1 Description of The Ohio State University Research Reactor (OSURR) ...........14
2.3.2 OSURR Rabbit Facility: Displacement Damage ..............................................16
2.3.2.1 Neutron-Induced Displacement Damage ..................................................17
2.3.2.2 Gamma-Induced Displacement Damage ...................................................21
2.3.3 Ionization Dosimetry........................................................................................25
2.3.3.1 Gamma-Ray-Induced Ionization ...............................................................25
2.3.3.2 Neutron-Induced Ionization .......................................................................26
vii
2.3.4 Conclusions for OSURR Dosimetry Calculations ............................................28
2.4
Dosimetry for the IUCF Proton Beam ...............................................................29
Chapter 3 : I-V Characterization Testing of Schottky Power Diodes ..............................34
3.1
Schottky Power Diode Background...................................................................36
3.2
Experimental Methodology ...............................................................................40
3.2.1 Experimental Apparatus ...................................................................................40
3.2.2 International Rectifier (IR) Si Schottky Power Diodes .....................................45
3.2.3 Cree SiC Schottky Power Diodes......................................................................46
3.2.4 Irradiation Procedure .......................................................................................47
3.2.4 I-V Characterization Procedure .......................................................................48
3.3
Diode Low-Injection, Forward-Biased I-V Characterization Results ...............49
3.4
MATLAB Curve-Fitting Analysis of Low-Injection, Forward-Bias Data ........51
3.5
Diode High-Injection, Forward-Biased I-V Characterization Results ..............55
3.6
MATLAB Curve-Fitting Analysis of High-Injection, Forward-Bias Data .......58
3.7
Reverse Bias I-V Characteristics of Si and SiC Schottky Power Diodes ..........61
3.8
Neutron-Proton Equivalency .............................................................................64
Chapter 4 : Functional Testing of Silicon Carbide Schottky Power Diodes: Half-Wave
Rectifiers ............................................................................................................................74
4.1
Experimental Methodology ...............................................................................74
4.1.1 Irradiation Procedure .......................................................................................75
viii
4.1.2 Pre- and Post-Irradiation I-V Characterization...............................................76
4.1.3 Functional Testing Apparatus and Procedure for Half-Wave Rectifier Circuits77
4.2
Results for I-V Characterization of CSD05120A Diodes..................................80
4.3
Results for Functional Testing of CSD05120A Diodes ....................................82
4.4
PSpice-Modeling of Half-Wave Rectifier .........................................................89
4.5
Analytical Model of Half-Wave Rectifier .........................................................92
4.6
Concluding Remarks on Functional Testing of Half-Wave Rectifiers ..............96
Chapter 5 : I-V CHARACTERIZATION TESTING OF POWER MOSFETS ...............98
5.1
Power MOSFET: Structure and Physics of Operation ......................................99
5.2
Experimental Methodology: Irradiation and I-V Characterization .................105
5.2.1 Power MOSFET Irradiations .........................................................................106
5.2.2 Power MOSFET I-V Characterization Testing ..............................................108
5.3
Determination of k and V TH : Results and Analysis:........................................110
5.4
Determination of R d from R ds(on) : Results and Analysis: ................................118
5.5
Background on Radiation Effects: Forward Breakdown and Leakage Current:126
5.6
Forward Breakdown and Leakage Current: Results and Analysis: .................127
5.7
Conclusions Regarding MOSFET I-V Characterization Testing ....................132
Chapter 6 : Functional Testing of Buck and Boost Converters………………….........133
6.1
Background on Operation of Buck and Boost Converters ..............................133
6.1.1 Background: Operation of Ideal Buck and Boost Converters ........................134
6.1.2 Background: Analytical Modeling of Non-Ideal Buck and Boost Converters136
6.1.2.1 Analytical Model of a Non-Ideal Buck Converter ...................................137
ix
6.1.2.2 Analytical Model of a Non-Ideal Boost Converter ..................................143
6.1.3 Background: Practical Swithing Behavior of Power MOSFETs....................147
6.2
Previous Work: Functional Testing of Buck and Boost Converters: ..............154
6.3
Experimental Setups and Procedures...............................................................158
6.3.1 Irradiation Procedure for Diodes and MOSFETs of Buck and Boost
Converters ................................................................................................................158
6.3.2 I-V Characterization Procedure for Diodes and MOSFETs ........................159
6.3.3 Functional Testing Setup and Procedure for Diodes and MOSFETs ...........160
6.3.3.1 Functional Test Procedure for Buck and Boost Converters: IRF1310N
MOSFET ..............................................................................................................166
6.3.3.2 Functional Test Procedure for Buck and Boost Converters: IRF840
MOSFET ..............................................................................................................166
6.4
I-V Characterization Results and Analysis for Schottky Power Diodes .........170
6.4.1 I-V Characterization Results and Analysis for Vishay IR40CTQ150PBF
Diodes ......................................................................................................................170
6.4.2 I-V Characterization Results and Analysis for Cree SiC Schottky Power
Diodes ......................................................................................................................175
6.5
Functional Testing Results for Buck Converter Containing IRF1310N
MOSFETs and IR40CQT150PBF Diodes ...................................................................178
6.5.1 Experiment I for Buck Converter containing IRF1310N MOSFETs and
IR40CTQ150PBF Diodes: 2 Months Post-Irradiation............................................178
6.5.2 Experiment II for Buck Converter containing IRF1310N MOSFETs and
IR40CTQ150PBF Diodes: 108 Days Post-Irradiation ...........................................187
6.6
Functional Testing Results for Boost Converter Containing IRF1310N
MOSFETs and IR40CQT150PBF Diodes: Two Months Post-Irradiation ..................205
6.7
Functional Testing Results for High-Voltage Buck Converter Containing
Vishay IRF840 MOSFETs and Cree CSD04060A Diodes: Two Months PostIrradiation ....................................................................................................................208
x
6.8
Conclusions......................................................................................................212
Chapter 7 : Mitigation of Radiation Effects ...................................................................215
7.1
Parallel Configuration ......................................................................................216
7.2
Isothermal Annealing of Cree SiC Schottky Diodes .......................................218
7.2.1 Irradiation Procedure .....................................................................................219
7.2.2 I-V Characterization Procedure .....................................................................220
7.2.3 Isothermal Anneal Procedure .........................................................................221
7.2.4 Isothermal Anneal Results and Discussion.....................................................222
7.3 I-V Characterization Testing of a Radiation-Hard MOSFET...............................225
7.3.1 Procedure........................................................................................................225
7.3.2 Results and Discussion ...................................................................................226
7.4
Conclusions......................................................................................................231
Chapter 8 : Conclusions and Future Work .....................................................................233
8.1
Conclusions......................................................................................................233
8.2
Future Work .....................................................................................................238
Appendix A: Analytical Buck Converter Model ............................................................246
Appendix B: Analytical Boost Converter Model ...........................................................249
xi
List of Tables
Table 2.1. Dosimetry results for OSURR .........................................................................29
Table 2.2. Htape results, showing contributions to nuclear scattering and damage energy
by inelastic scattering for pure Si. .............................................................................31
Table 2.3. Dosimetry results for the 203 MeV IUCF proton beam compared with Jun’s
results for 200 MeV protons. The NIEL for SiC was computed by applying
Equation 2.8 to the NIEL for Si and C. .....................................................................33
Table 3.1: The International Rectifier part numbers tested in this research project along
with their current and voltage ratings. The package voltage rating is the same as it
is for each individual leg. However, the current-rating for the package is double
that for each individual leg, since the package contains two diodes that can be wired
in parallel. ..................................................................................................................46
Table 3.2. The Cree SiC Schottky power diode part numbers tested in this research
project along with their current and voltage ratings. These diodes were packaged in
TO-220-2 packages, which contain only one diode per package. .............................47
Table 3.3. Results of curve fitting for forward-biased low-injection region for Cree
CSD04060A (4 A, 600 V) SiC Schottky power diodes.............................................53
Table 3.4: Results of curve fitting for forward-biased low-injection region for Cree
CSD10060A (10 A, 600 V) SiC Schottky power diodes...........................................53
Table 3.5: Results of curve fitting for the forward-biased low-injection region for Cree
CSD10120A (10 A, 1200 V) SiC Schottky power diodes.........................................54
Table 3.6 Results of curve fitting for the forward-biased low-injection region for IR
IR40CTQ150PBF (20 A, 150 V) Si Schottky power diodes. Only the average is
reported, since there was only one IR40CTQ150PBF diode in the sample. .............54
Table 3.7. Results of curve fitting for the forward-biased low-injection region for IR
IR43CTQ100 (20 A, 100 V) Si Schottky power diodes. ...........................................54
xii
Table 3.8. Results of curve fitting for the forward-biased low-injection region for IR
IR10CTQ150PBF (5 A, 150 V) Si Schottky power diodes. ......................................55
Table 3.9. Results of curve fitting for the forward-biased low-injection region for IR
IR60CTQ150PBF (30 A, 150 V) Si Schottky power diodes. ....................................55
Table 3.10. Reverse breakdown voltage and leakage current measurements of
IR40CTQ150PBF (20 A, 150 V) Si Schottky power diodes. ....................................63
Table 3.11. Reverse breakdown voltage and leakage current measurements of
IR43CTQ100 (20 A, 100 V) Si Schottky power diodes. ...........................................63
Table 3.12. Reverse breakdown voltage and leakage current measurements of
IR10CTQ150PBF (5 A, 150 V) Si Schottky power diodes. ......................................64
Table 3.13. Reverse breakdown voltage and leakage current measurements of
IR60CTQ150PBF (30 A, 150 V) Si Schottky power diodes. ....................................64
Table 3.14: Results of neutron-proton equivalency for Cree SiC Schottky power diodes.
The final result of the equivalency is represented by the ratio quantity in the rightmost column, explained further in the text. ...............................................................70
Table 3.15. Results of neutron-proton equivalency for IR Silicon Schottky power diodes
in terms of Φ eq,1MeV,Si . The final result of the equivalency is represented by the ratio
quantity in the right-most column..............................................................................72
Table 4.1. Correspondence between each group (sample) of three CSD05120A diodes
and the D d (MeV/g) to which it was exposed in the OSURR rabbit facility. ............76
Table 4.2. Results of curve fitting for forward-biased low-injection region for Cree
CSD05120A (5 A, 1200 V) SiC Schottky power diodes...........................................80
Table 5.1. Correspondence between each group (sample) of three IR IRF840 MOSFETs
and the Φ eq ,1MeV ,Si to which it was exposed in the OSURR rabbit facility............107
Table 5.2. Correspondence between each group (sample) of three Vishay IRF840
MOSFETs and the Φ eq ,1MeV ,Si and TID to which it was exposed in the OSURR
rabbit facility. ...........................................................................................................107
Table 5.3. Correspondence between each group (sample) of three IR IRF1310N
MOSFETs and the Φ eq ,1MeV ,Si and TID to which it was exposed in the OSURR
rabbit facility. ...........................................................................................................108
xiii
Table 6.1. Results of curve fitting for the forward-biased low-injection region for the
Vishay IR40CTQ150PBF (40 A, 100 V) Si Schottky power diodes used in
functional testing, for which the two diodes in the TO-220 package were wired in
parallel. ....................................................................................................................171
Table 6.2. Leakage current for a bias of VD=-80 V and breakdown voltage versus
Φ eq,1MeV , Si for the Vishay IR40CTQ150PBF (40 A, 100 V) Si Schottky power
diodes used in functional testing, for which the two diodes in the TO-220 package
were wired in parallel. .............................................................................................174
Table 6.3. Results of curve fitting for the forward-biased low-injection region for the
Cree CSD04060A (4 A, 600 V) SiC Schottky power diodes used in functional
testing. ......................................................................................................................175
Table 6.4 Leakage current for a bias of V D = -250 V and breakdown voltage versus
D d,SiC for the Cree CSD04060A SiC Schottky power diodes used in functional
testing.......................................................................................................................177
Table 6.5. MOSFET power dissipation results for the IRF1310N MOSFETs in the buck
converter of Figure 6.13, for an applied Vgate Duty Cycle of 25 %. ......................193
Table 6.6. As a function of load inductance, L: MOSFET power dissipation estimates
calculated using analytical buck converter model from section 6.1.2.1 for the
IRF1310N MOSFET and IR40CTQ150PBF diode pair irradiated to 3.7 Mrad(Si),
based on data from Experiment I, conducted 2 months post-irradiation. ................204
Table 6.7. Results for V o /V in versus radiation dose for the boost converter shown in
Figure 6.14 containing IRF1310N MOSFETs and IR40CTQ150PBF diodes, for an
applied V gate duty cycle of 25 %. Results obtained from the PSpice model and the
analytical boost converter model (section 6.1.2.2) are compared with those obtained
from the experiment. ................................................................................................207
Table 6.8. Results for V o /V in versus radiation dose for the boost converter shown in
Figure 6.14 containing IRF1310N MOSFETs and IR40CTQ150PBF diodes, for an
applied V gate duty cycle of 50 %. Results obtained from the analytical boost
converter model (section 6.1.2.2) are compared with those obtained from the
experiment. ..............................................................................................................207
Table 6.9. Dose and duty cycle at which Vishay IRF840 MOSFETs failed in the circuit
of Figure 6.15...........................................................................................................209
Table 7.1. Correspondence between Diode Labels and D d,SiC to which Cree
CSD10120A diodes were exposed. .........................................................................220
xiv
List of Figures
Figure 2.1. Effects of electrically active defects on the carrier transport properties of
semiconductors [7].......................................................................................................8
Figure 2.2. Short-term and long-term anneal processes in Si and Si devices at room
temperature [6]...........................................................................................................10
Figure 2.3. Process by which ionizing radiation induces trapped oxide charge and
interface traps at the Si/SiO2 interface [12] . ............................................................12
Figure 2.4. Top view of the Ohio State University Research Reactor (OSURR). ...........16
Figure 2.5. Neutron lethargy flux per kW in the OSURR rabbit facility, obtained from
the OSURR reactor staff….. ......................................................................................18
Figure 2.6. Generalized MCNPX model of TO-220 package, drawn to scale. The
semiconductor materials of interest in this study are Si and SiC. .............................19
Figure 2.7 MCNPX model of NASA experiments conducted at IUCF, using the TO-220
package model shown in Figure 2.6, and a perpendicularly incident proton beam, P.31
Figure 3.1. A schematic of a typical Schottky power diode. The p-n junction guard
rings are used to decrease the radius of curvature of the depletion region, which
occurs due to electric field crowding at the edges of this region, and thus increase
the breakdown voltage [46, Mohan]. .........................................................................37
Figure 3.2. Typical I-V characteristics of a power diode, after [46, Mohan]. ..................37
Figure 3.3: Block diagram of diode test apparatus ............................................................41
Figure 3.4. Photograph of one of the Experimental setups, containing the Keithley
Source Meters used to test the Si and SiC Schottky diodes. .....................................42
Figure 3.5. Front panel of LabView program used to control the Keithley 2410 and 2430
sourcemeters. .............................................................................................................45
xv
Figure 3.6. Unirradiated and post-irradiation low-injection, forward-biased I D vs. V D
curves of one of the three CSD04060A (4 A, 600 V) diodes tested in this study. For
the purpose of clarity, only the unirradiated curve and the irradiated curve
corresponding to the last measurement and thus highest dose received for this diode
are shown. The ideal, exponential portion of the I-V curve is circled in green........50
Figure 3.7. Unirradiated and post-irradiation low-injection, forward biased I D vs. V D
curves for one of the three IR10CTQ150PBF (5 A, 150 V) IR Si Schottky power
diodes tested in this study. For the purpose of clarity, only the unirradiated curve
and the irradiated curve corresponding to the last measurement and thus highest
dose received for this diode are shown. .....................................................................51
Figure 3.8. Unirradiated and post-irradiation high-injection, forward-biased I D vs. V D
curves of one of the three CSD10120A (10 A, 1200 V) diodes tested in this study.
These I-V curves are representative of the high-injection, forward-bias I-V curves
for all of the Cree SiC Schottky power diodes tested in this study. ..........................56
Figure 3.9. Unirradiated and post-irradiation high-injection, forward-biased I D vs. V D
curves of one of the three IR60CTQ150PBF (30 A, 150 V) IR Si Schottky power
diodes tested in this study. These I-V curves are representative of the highinjection, forward-bias I-V curves for all of the IR Si Schottky power diodes tested
in this study. ...............................................................................................................57
Figure 3.10. R s as a function of displacement damage dose in SiC, for the Cree SiC
Schottky power diodes tested in this study. Trend lines are included in order to
guide the eye. .............................................................................................................59
Figure 3.11. R s as a function of displacement damage dose in Si, for IR10CTQ150PBF
and IR40CTQ150PBF diodes. Only the average is reported for the
IR40CTQ150PBF diode, since only one IR40CTQ150PBF diode was tested. .........60
Figure 3.12. R s as a function of displacement damage dose in Si, for IR43CTQ100 and
IR60CTQ150PBF diodes. ..........................................................................................61
Figure 3.13. Reverse-bias I-V characteristics of an IR43CTQ100 (20 A, 100 V) Si
Schottky power diode as a function of φeq ,1MeV ,Si . ...................................................63
Figure 3.14. Graph of R s -1 versus D d in Si for representative, individual IR Silicon
Schottky diodes having part numbers 10CTQ150PBF (5 A, 150 V), 40CTQ150PBF
(20 A, 150 V), 60CTQ150PBF (30 A, 150 V), and 43CTQ100 (20 A, 100 V). .......66
Figure 3.15. Graph of R s -1 versus D d in SiC for representative, individual Cree SiC
Schottky power diodes having part numbers CSD10060A (10 A, 600V),
CSD10120A (10 A, 1200 V), and CSD04060A (4 A, 600 V). .................................67
xvi
Figure 4.1. Functional test apparatus for testing of half-wave rectifying circuits. ...........78
Figure 4.2. The half-wave rectifier circuit, containing a Cree SiC Schottky diode, which
is attached to the aluminum, water-chilled block, shown in the back of the
photograph. The transparent, plastic tubes at the bottom of the photograph contain
chilled water from the Opti-Temp chiller. .................................................................78
Figure 4.3. A schematic representation of the half-wave rectifier circuit shown in Figure
4.2. One CSD05120A diode was tested at a time, with 60 Hz sinusoidal, AC input
voltage of 240.4 Vp-p (170 Vrms). A 100 Ohm load, from the high resistive load
bank was used. Voltage and current markers are shown to indicate the voltage and
current measurements that were recorded by a Yokogawa Scopecorder, DL750. ....79
Figure 4.4. Yokogawa DL750 Scopecorder used for recording the voltage, current, and
temperature waveforms of the half-wave rectifying circuit, shown in Figure 4.2. ...79
Figure 4.5. Reverse bias I-V characteristics of a CSD0510120A diode, pre- and postirradiation. The leakage current has decreased as a result of the irradiation. ...........81
Figure 4.6. R s versus D d for Cree CSD05120A SiC Schottky power diodes as a function
of neutron-induced displacement damage dose. ........................................................82
Figure 4.7. Representative output voltage waveforms for three full cycles, over 100
Ohm load resistor, as a function of D d,SiC for half-wave rectifier circuits containing
CSD05120A diodes. The waveforms of three diodes, irradiated to different doses,
are shown. The D d,SiC values in this figure refer to the dose to which the
CSD05120A diodes were irradiated. The portion of the waveform labeled “Detail”
is shown enlarged in Figure 4.8. ................................................................................83
Figure 4.8 Portion of output voltage waveform labeled “Detail” in Figure 4.7. The
voltage over the load resistor decreases with increasing radiation dose, indicating a
larger voltage drop over the diode. As can be inferred from this graph, the output
voltage decreases slowly with respect to radiation dose for D d,SiC less than 1.4E11
(MeV/g), but increases rapidly with radiation dose for larger values of D d,SiC . ........84
Figure 4.9. Representative diode voltage and current waveforms, for 3 full cycles, for
half-wave rectifier circuits containing CSD05120A diodes. The portion of the
waveform labeled “Detail” is shown in .....................................................................85
Figure 4.10. Portion of diode current and voltage waveforms labeled “Detail” in Figure
4.9. As shown in there is very little leakage current for all levels of displacement
damage dose, as the diode current, I D , is nearly 0 for the non-conducting, voltageblocking portion of the cycle. The voltage drop over the diode increases very
slowly with increasing radiation dose for just over half of the total D d,SiC to which
the diodes were exposed, but then increases rapidly thereafter. ................................86
xvii
Figure 4.11. Diode power dissipation as a function of D d,SiC for Cree CSD05120A (5 A,
1200 V) diodes. ..........................................................................................................88
Figure 4.12. Power conversion efficiency vs D d,SiC of the half-wave rectifier containing
CSD05120A diodes. ..................................................................................................88
Figure 4.13. Forward-bias, low-injection I-V curve data versus the PSpice model for
this diode. The diode was irradiated to a D d,SiC of 2.3E11 (MeV/g). .......................89
Figure 4.14. Experimental, forward bias, high-injection I-V curve data compared to
PSpice models for representative, individual diodes from the unirradiated control
group, group #3 (irradiated to D d,SiC =1.4E11 (MeV/g)), and group #5 (irradiated to
D d,SiC =2.3E11 (MeV/g)), having an R s value closest to the mean for their respective
group. .........................................................................................................................90
Figure 4.15. Results from the PSpice simulation of the half-wave rectifier circuit are
compared to the experimental data for the voltage drop waveform of the diode,
when the diode is conducting current, for the same data shown Figure 4.10. PSpice
was used to model the diodes as they degraded as a function D D,SiC . .......................91
Figure 4.16. A Cree CSD05120A diode, irradiated to D d,SiC = 1.4E11 (MeV/g), fit to the
piece-wise linear diode model shown in Figure 3.2. V on is obtained by dividing the
intercept by the slope of the linear trend-line, and R on is obtained by calculating the
inverse slope of the trend-line. The value of R on , 0.26 Ohms, is very close to the
value of R s , 0.25 Ohms, obtained by fitting the data shown in this figure to
Equation 3.3. ..............................................................................................................92
Figure 4.17. Ron-1 versus D d,SiC (MeV/g) for the Cree CSD05120A diodes in this study.93
Figure 4.18. Half-wave rectifier containing the piece-wise linear model of a power
diode, shown in the dashed box. ................................................................................93
Figure 4.19. Diode power dissipation versus D d,SiC , for the experimental data of Figure
4.11, the PSpice simulations, and the analytical model described by Equations 4.24.4. .............................................................................................................................96
Figure 5.1. Schematic diagram of an n-channel MOSFET with built-in anti-parallel
diode. .......................................................................................................................100
Figure 5.2. I D versus V DS characteristic for an unirradiated IRF1310N power MOSFET.
The voltage drop across the channel, V CH , is equal to V DS minus V R , as indicated by
Equation 5.1. ............................................................................................................100
xviii
Figure 5.3. n-channel VDMOS structure containing primary contributions to on-state
resistance in power MOSFETs, namely R d and R channel , the drift and channel
resistances, respectively. ..........................................................................................101
Figure 5.4. TO-220 IC socket used for I-V Characterization of Power MOSFETs. ......109
Figure 5.5. I D 1/2 versus V GS curve for a Vishay IRF840 MOSFET, pre- and postirradiation. ................................................................................................................111
Figure 5.6. I DS versus V D for a Vishay IRF840 MOSFET, irradiated to Φ eq, Si, 1MeV =
5.1E13 (n/cm2). ........................................................................................................112
Figure 5.7. I DS versus V D for an IRF1310N MOSFET, irradiated to Φ eq, Si, 1MeV = 1.0E15
(n/cm2). ....................................................................................................................113
Figure 5.8. k versus TID in Si for IRF840 (8 A, 500 V) MOSFETs. .............................114
Figure 5.9. k versus TID in Si for IRF1310N (8 A, 500 V) MOSFETs. ........................114
Figure 5.10. V TH versus TID in Si for IRF840 (8 A, 500 V) and IRF1310 (42 A, 100 V)
MOSFETs. ...............................................................................................................116
Figure 5.11. Linear fits to the I D versus V DS characteristics for an IRF1310N MOSFET,
pre- and post-irradiation. .........................................................................................119
Figure 5.12. R ds(on) versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V)
MOSFETs. ...............................................................................................................119
Figure 5.13. R ds(on) versus Φ eq, Si, 1MeV for IR IRF1310N (42 A, 100 V) MOSFETs.......120
Figure 5.14. R d versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V) MOSFETs.
The results are nearly identical those shown in Figure 5.12, since, for the 500 V
MOSFETs, R d accounted for greater than 95 % of R ds(on) . ......................................121
Figure 5.15. R d and R ds(on) versus Φ eq, Si, 1MeV for IRF1310N (42 A, 100 V) MOSFETs.122
Figure 5.16. R d / R ds(on) (%) versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V)
MOSFETs. ...............................................................................................................123
Figure 5.17. R d -1 versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V) MOSFETs.125
Figure 5.18. R d / R ds(on) (%) versus Φ eq, Si, 1MeV for IRF1310N (42 A, 100 V) MOSFETs.125
Figure 5.19. I D versus V DS characteristics for Vishay IRF840 MOSFETs for V GS = 0. 128
xix
Figure 5.20. Drain Leakage Current, I D , versus TID for Vishay IRF840, 500 V
MOSFETs. ...............................................................................................................129
Figure 5.21. Drain Leakage Current, I D , versus TID for Vishay IRF1310N, 100 V
MOSFETs. ...............................................................................................................130
Figure 5.22. V 250μA versus TID for Vishay IRF1310N, 100 V MOSFETs. ...................131
Figure 5.23. Breakdown voltage versus TID for Vishay IRF1310N, 100 V MOSFETs.131
Figure 6.1. Buck converter with inductor, L, and capacitor, C. .....................................135
Figure 6.2. Boost converter with inductor, L, and capacitor, C. ....................................135
Figure 6.3. Schematic of a simplified model of a non-ideal buck converter. .................139
Figure 6.4. Schematic of a simplified model of a non-ideal boost converter. ................143
Figure 6.5. Equivalent circuit of a power MOSFET, in which the parasitic elements that
have the greatest affect on the switching behavior of the power MOSFET are shown
[60]...........................................................................................................................148
Figure 6.6. Switching waveforms of an IRF1310N (42 A, 100 V) MOSFET, operating
in a buck converter. Turn-on and Turn-off phases of the switching transient are
labeled (1) – (6) and are identified and described in the text. .................................149
Figure 6.7. This is the portion of the switching waveforms labeled “Detail” in Figure 6.6
for an IRF1310N (42 A, 100 V) MOSFET operating in a buck converter. Turn-on
and Turn-off phases of the switching transient are labeled (1) – (6) and are
identified and described in the text. .........................................................................150
Figure 6.8. The standard means to quantify power MOSFET switching performance as
listed on manufacturers’ datasheets will be used in this current study. ...................154
Figure 6.9 Functional test apparatus for testing buck and boost converters. ..................161
Figure 6.10. Filter used to reduce noise and smooth the signal from the waveform
generator. .................................................................................................................162
Figure 6.11. A MOSFET placed in a high-power TO-220 socket, mounted on a heatsink...........................................................................................................................165
Figure 6.12. MOSFET thermal pad coated with polysynthetic silver thermal compound.165
xx
Figure 6.13. A schematic for the buck converter circuit tested with the IRF1310N (42
A, 100 V) MOSFETs and the IR40CTQ150PBF (40 A, 150 V) Si ........................168
Figure 6.14. A schematic for the boost converter circuit tested with the IRF1310N (42
A, 100 V) MOSFETs and the IR40CTQ150PBF (40 A, 150 V) Si Schottky power
diodes. ......................................................................................................................168
Figure 6.15. A schematic of a buck converter circuit tested with an IRF840 (8 A, 500 V)
MOSFETs and a Cree CSD04060A (4 A, 600 V) SiC ...........................................169
Figure 6.16. R s versus Φ eq,1MeV,Si for the Vishay IR40CTQ150PBF diodes used in
functional testing, for which the two diodes in the TO-220 package were wired in
parallel. ....................................................................................................................172
Figure 6.17. Average voltage drop versus Φ eq,1MeV,Si for a diode current of 5 A and 10 A
for the Vishay IR40CTQ150PBF diodes used in functional testing, for which the
two diodes in the TO-220 package were wired in parallel. .....................................172
Figure 6.18. High-injection, forward bias curves for selected values of Φ eq,1MeV,Si for
Vishay IR40CTQ150PBF diodes that were functionally tested. .............................173
Figure 6.19. Reverse bias curves for selected values of Φ eq,1MeV,Si for Vishay
IR40CTQ150PBF diodes that were functionally tested. .........................................174
Figure 6.20. R s versus D d,SiC for the Cree CSD04060A diodes used in functional testing.176
Figure 6.21. High-injection, forward bias curves for selected values of D d,SiC for Cree
CSD04060A diodes that were functionally tested. ..................................................176
Figure 6.22. Reverse bias curves for selected values of D d,SiC for Cree CSD04060A
diodes that were functionally tested. .......................................................................177
Figure 6.23. Measured V o / V in versus TID in Si for the buck converter shown in Figure
6.13, and for applied gate drive signals, V gate , of various duty cycles. The duty
cycles of the applied gate signals are given in terms of %, shown to the right of
each curve. ...............................................................................................................180
Figure 6.24. Measured V o / V in versus applied V gate duty cycle for an unirradiated
MOSFET-diode pair, as well as a MOSFET-diode pair irradiated to a TID of 3.7
Mrad(Si), tested in the buck converter shown in Figure 6.13. ................................181
Figure 6.25. Efficiency, P out / P in , versus Φ eq,1 MeV,Si to which the IRF1310N MOSFETs
and IR40CTQ150PBF diodes of the buck converter circuit of Figure 6.13 were
exposed. ...................................................................................................................181
xxi
Figure 6.26. V DS and V GS waveforms for a Vgate signal having a duty cycle of 25 %,
measured using a Yokogawa DL750 ScopeCorder for various values of Φ eq,1 MeV,Si .
The item labeled “Detail” is shown more clearly in Figure 6.27. ...........................183
Figure 6.27. Portion of waveform labeled “Detail” in Figure 6.26, for selected dose
levels, for an applied V gate signal having a duty cycle of 25 %. ..............................184
Figure 6.28. IRF1310N MOSFET switching times versus TID as measured according to
the method shown in Figure 6.8, for the buck converter circuit of Figure 6.13, for a
V gate signal of 25 % duty cycle. ...............................................................................184
Figure 6.29. V o / V in for a V gate signal of 25 % versus TID, as shown for the
experimental data and the PSpice and analytical models. .......................................186
Figure 6.30. Inductor current for a V gate signal of 25 % for an IRF1310N MOSFET and
IR40CTQ50PBF diode pair irradiated to 1.2 Mrad(Si) (Φ eq,1MeV,Si = 7.3E13 n/cm2),
as shown for the experimental data and the PSpice and analytical models. ............187
Figure 6.31. V DS and I D waveforms for the IRF1310N MOSFET in the buck converter
circuit of Figure 6.13, 108 days post-irradiation, measured using a Yokogawa
DL750 ScopeCorder. ...............................................................................................189
Figure 6.32. MOSFET Turn-on portion of the V DS and I D waveforms shown in Figure
6.31. .........................................................................................................................190
Figure 6.33. MOSFET Turn-off portion of the V DS and I D waveforms shown in Figure
6.31. .........................................................................................................................190
Figure 6.34. Definitions and terms relating to MOSFET switching characteristics for a
buck-converter. ........................................................................................................191
Figure 6.35. P s,ton versus Vgate duty cycle for various levels of TID in Si. ..................193
Figure 6.36. P S,C versus V gate duty cycle for various levels of TID in Si. ......................194
Figure 6.37. P S,toff versus V gate duty cycle for various levels of TID in Si. ....................194
Figure 6.38. Diode power dissipation versus V gate duty cycle for various levels of TID in
Si. .............................................................................................................................195
Figure 6.39. MOSFET turn-on and turn-off, linearized waveforms for a circuit with a
clamped inductive load, after [60]. ..........................................................................197
xxii
Figure 6.40. P s,ton versus V gate duty cycle for various levels of TID in Si, comparing
analytical model from section 6.1.2.1 to experimental data from Experiment II,
conducted 108 days post-irradiation. .......................................................................198
Figure 6.41. P s,C versus V gate duty cycle for various levels of TID in Si, comparing
analytical model from section 6.1.2.1 to experimental data from Experiment II,
conducted 108 days post-irradiation. .......................................................................199
Figure 6.42. P s,toff versus V gate duty cycle for various levels of TID in Si, comparing
analytical model from section 6.1.2.1 to experimental data from Experiment II,
conducted 108 days post-irradiation. .......................................................................199
Figure 6.43. P s,total versus V gate duty cycle for various levels of TID in Si, comparing the
analytical model from section 6.1.2.1 to experimental data from Experiment II,
conducted 108 days post-irradiation. .......................................................................200
Figure 6.44. Buck converter analytical model (section 6.1.2.1) estimate for P s,ton versus
V gate duty cycle for various levels of TID in Si, based on data from Experiment I,
conducted 2 months post-irradiation. ......................................................................201
Figure 6.45. Buck converter analytical model (section 6.1.2.1) estimate for P s,C versus
V gate duty cycle for various levels of TID in Si, based on data from Experiment I,
conducted 2 months post-irradiation. ......................................................................202
Figure 6.46. Buck converter analytical model (section 6.1.2.1) estimate for P s,toff versus
V gate duty cycle for various levels of TID in Si, based on data from Experiment I,
conducted 2 months post-irradiation. ......................................................................202
Figure 6.47. Buck converter analytical model (section 6.1.2.1) estimate for P s,total versus
V gate duty cycle for various levels of TID in Si, based on data from Experiment I,
conducted 2 months post-irradiation. ......................................................................203
Figure 6.48. MOSFET conduction current, I D , as a function of load inductance, L,
calculated using the analytical buck converter model of section 6.1.2.1 for the
MOSFET and diode pair irradiated to 3.7 Mrad(Si), based on data from Experiment
I, conducted 2 months post-irradiation. The calculation is based on a V gate signal
having a duty ratio of 50 %......................................................................................204
Figure 6.49. V o / V in versus TID for V gate signals having various duty cycles, for the
boost converter of Figure 6.14. ................................................................................206
Figure 6.50. V o / V in versus V gate duty cycle for selected dose levels, for the boost
converter of Figure 6.14. .........................................................................................206
xxiii
Figure 6.51. Power conversion efficiency versus Φ eq,1MeV,Si for V gate signals having duty
cycles of 25 % and 50 %, for the boost converter of Figure 6.14. ..........................208
Figure 6.52. Voltage waveforms across the diode in the buck converter of Figure 6.15,
for one circuit containing an unirradiated diode and MOSFET and another
containing a highly irradiated diode and MOSFET. For these measurements, V gate
= 35 %. Corresponding waveforms for the MOSFETs tested with these diodes in
the same circuit are shown in Figure 6.53. ..............................................................210
Figure 6.53. Voltage waveforms across the MOSFET in the buck converter of Figure
6.15, for one circuit containing an unirradiated diode and MOSFET and another
containing a highly irradiated diode and MOSFET. For these measurements, V gate
= 35 %. Corresponding waveforms for the diodes tested with these diodes in the
same circuit are shown in Figure 6.52. ....................................................................211
Figure 6.54. Measured V o / V in versus TID in Si for the buck converter shown in Figure
6.15, and for applied gate drive signals, V gate , of various duty cycles. The duty
cycles of the applied gate signals are given in terms of %, shown to the right of
each curve. ...............................................................................................................212
Figure 7.1. Half-wave rectifier circuit containing a singe diode. ...................................216
Figure 7.2. Half-wave rectifier circuit containing three diodes in parallel. ....................217
Figure 7.3. Results for average power dissipation per diode as a function of D d,SiC for
Cree CSD05120A diodes in a half-wave rectifier circuit. The results from the
PSpice simulation are compared to the experimental results for a single diode.
Furthermore, PSpice results are shown for three diodes in parallel. .......................218
Figure 7.4. Minco CT137 digital temperature controllers, used for heating the
CSD10120A diodes. ................................................................................................221
Figure 7.5. CSD10120A diodes placed on an aluminum block, with heater and sense
wires from the MINCO CT137 digital temperature controller. ...............................222
Figure 7.6. High injection, forward I-V curve measurements for pre-irradiation, postirradiation, and post-anneal for various anneal times at 175 C, for a Cree
CSD10120A diode. This diode was irradiated to a displacement damage dose of
8.4E+11 (MeV/g) in SiC..........................................................................................224
Figure 7.7. The ratio quantity of ∆ (1 R S , A ) / ∆ (1 Rs ,0 ) versus Dd,SiC, as a function of
anneal time for an annealing temperature of 175 C. ∆ (1 R S , A ) / ∆ (1 Rs ,0 ) is a measure
of the amount of defects initially .............................................................................225
xxiv
Figure 7.8. I D versus V GS transfer characterstic for radiation-hard IRHM8450 MOSFET
versus radiation dose. V DS was held constant at 10 V. ...........................................227
Figure 7.9. I D versus V GS subthreshold characterstic for radiation-hard IRHM8450
MOSFET versus radiation dose. The drain and gate leads were shorted during
measurement, so that V GS = V DS . .............................................................................229
Figure 7.10. I D versus V DS forward breakdown and leakage characterstic for radiationhard IRHM8450 MOSFET versus radiation dose. The MOSFET was measured in
the cut-off regime, for which V GS = 0. .....................................................................230
Figure 7.11. I D versus V DS characterstic for radiation-hard IRHM8450 MOSFET versus
radiation dose. The MOSFET was measured with a constant applied gate-to-source
bias of V GS = 10. ......................................................................................................231
xxv
CHAPTER 1 : INTRODUCTION
NASA is exploring the potential use of nuclear reactors as power sources for
future missions. Some of the semiconductor devices, being part of the electrical power
system, may be required to be placed near the nuclear reactor. Therefore, in addition to
the effects on power semiconductors from cosmic radiation, such as high-energy protons
and electrons in the Van Allen Belts, the radiation effects of the intense neutron and
gamma-ray radiation field from the nuclear reactor must also be considered. In addition,
due to their availability, demonstrated reliability, and relatively low cost, non-radiation
hardened, commercial-of-the-shelf (COTS) parts are of interest to NASA.
In order to address these issues, one of the goals of this research is to examine the
effects of a mixed neutron and gamma-ray radiation field on the static electrical
characteristics of COTS power Schottky diodes and MOSFETs. By using I-V
characterization and analysis, the changes in basic electrical parameters as a function of
radiation dose, as well as the mechanisms by which these parameters change in a
radiation field, can be determined. As such electrical performance parameters are often
highly dependent on the manufacturer’s fabrication process, one of the objectives of I-V
characterization testing and analysis is to support the design effort for radiation-hard
semiconductor technology. Also, the results from the I-V characterization and analysis
of this study are compared to those of a previous study, for which the same Si and SiC
1
Schottky diode models were irradated with a 203 MeV proton beam [1,2], in order to
form a neutron-proton equivalency model. Such an equivalency model can be used to
reduce the time and cost associated with radiation hardness testing.
Another main goal of this research is to determine and analyze changes in the
dynamic electrical performance of COTS power Schottky diodes and MOSFETs, as well
as the overall performance of the circuits of which they are a part, as a function of mixed
neutron and gamma-ray radiation dose. This objective can be achieved using functional
testing, in which the unirradiated diodes and MOSFETs are tested in actual power
circuits. Also, by using electrical performance parameters, determined from I-V
characterization testing, as input for PSpice and analytical models, one can model the
circuits used in functional testing and thus compare the models with the experimental
data. Futhermore, the results from the PSpice modeling and functional testing can then
be analyzed in terms of changes of the key electrical performance parameters with
respect to radiation dose. Functional testing is necessary, since some semiconductor
dynamic characteristics, such as the turn-on and turn-off transients of a power MOSFET,
cannot be modeled with sufficient accuracy using the standard, built-in PSpice
semiconductor physics models. The overall purpose of this device and circuit modeling
is to aid in the future design of circuits intended for use in radiation fields.
In Chapter 2, a discussion of nuclear radiation effects on Si, SiC, and SiO 2 is
provided. Furthermore, dosimetry calculations are given in Chapter 2, which quantify
the energy deposited in Si, SiC, and SiO 2 from the neutron and gamma-ray radiation
field of the OSURR as well as the IUCF 203 MeV proton beam.
2
Chapter 3 contains the experimental procedure, results, and conclusions of the IV characterization testing of the Si and SiC Schottky power diodes. PSpice model
parameters are extracted from the I-V curves in order to determine the way in which the
diodes are degrading, as reflected in their electrical performance in the form of I-V
curves. Furthermore, in Chapter 3, the results from this experiment are compared, on the
basis of displacement damage dose, to the published results from the proton irradiation
testing conducted by NASA at the IUCF.
In Chapter 4, experimental procedures, results and conclusions regarding the
functional testing of half-wave rectifiers containing high voltage SiC Schottky power
diodes are discussed. PSpice analysis is included, in addition to an analytical model.
Chapter 5 provides background on power MOSFET technology, as well as I-V
characterization experimental procedures, results, and conclusions for the testing of
International Rectifier power MOSFETs IRF1310 (42 A, 100V) and IRF840 (8A,
500V). Furthermore, differences in radiation response between the 100 V and 500 V
MOSFETs are discussed, and PSpice model parameters are extracted from the I-V
curves.
In Chapter 6, the functional testing of DC-to-DC buck and boost converters
containing irradiated Si and SiC Schottky diodes and power MOSFETs is discussed.
The results obtained from these experiments are discussed in terms of radiation-induced
changes in their I-V characteristics and PSpice model parameters as discussed in Chapter
3 and Chapter 5. In addition, an analytical model of the buck and boost converters is
presented in order to quantify the effects of these changes in device electrical
performance parameters on the overall circuit.
3
Furthermore, in Chapter 7, we examine ways in which we can reduce radiationinduced damage in these devices. Also, Chapter 7 contains a discussion of some basic
circuit design techniques which can be employed to reduce the effects of radiation on
overall circuit performance.
Chapter 8 summarizes the dissertation and provides conclusions and suggestions
for future work. Chapter 8 highlights the important points and findings obtained by the
study, and suggests possible ways in which this research can be extended.
4
CHAPTER 2 : NUCLEAR RADIATION EFFECTS AND DOSIMETRY
Incident radiation loses energy in semiconductor and insulator materials,
affecting their electrical properties, by two primary mechanisms, which are the
displacement of atoms (displacement damage) and displacement of electrons from their
parent atoms (ionization). The main focus of Chapter 2 is to describe and quantify these
effects in the materials of interest in this study, namely Si, SiC, and SiO 2 for the OSURR
and IUCF radiation environments.
2.1
Displacement Damage
Radiation-induced displacement damage is of primary concern in
semiconductors, for which displacement of atoms from their lattice sites in the
semiconductor crystal can decrease the electrical conductivity of the semiconductor.
The process of nuclear radiation-induced displacement damage can be described as
follows [4,5].
First, an incident nuclear particle collides with and transfers energy to a lattice
atom, and the latter becomes a recoil atom. If sufficient energy is transferred to this
recoil atom, say above some threshold energy, E d , then this recoil atom will leave its
lattice site in the crystal, creating a vacancy at that site, and the recoil atom becomes an
interstitial, and thus a Frenkel defect is created. If the recoil atom has sufficient energy,
the recoil atom can in turn displace other atoms in the target material, and a defect
5
cascade is thus created. If the recoil has energy much greater than E d , then most of the
atomic displacements will occur within a small area, creating a cluster of defects.
Eventually, the displaced atoms lose sufficient energy to achieve thermal equilibrium
within the lattice. However, the thermal energy of the crystal is often sufficient to allow
the simple defects and defect clusters to migrate. Consequently, defects may
subsequently be annihilated by interstitial-vacancy recombination, form stable defects
with other lattice impurities or defects, or escape to a free surface [4].
Furthermore, the nature of the radiation-induced defects depends upon the mass,
energy, as well as charge of the radiation. For example, 1 MeV photons and electrons,
encountered in a typical thermal, light-water reactor such as the OSURR, produce
simple, isolated defects [6]. However, massive particles and energetic electrons, with
energies greater than approximately 5 MeV, are capable of transferring energies much
greater than E d to target recoil atoms, and therefore tend to produce a combination of
defects clusters as well as isolated defects [4]. Simple, isolated defects can introduce
energy levels within the forbidden energy band gap, and a sufficient number of such
defects generated uniformly throughout the semiconductor crystal may alter the Fermi
level, but not distort the shape of the conduction or valence band edges; in contrast,
defect clusters can cause large distortions in the shapes of the conduction and valence
band edges, as large amounts of charge are attracted to the large concentrations of
energy levels created in the band gap by such clusters [4]. Furthermore, defect clusters
tend to reduce the recombination lifetime of carriers much more effectively than simple
defects [7]. Neutrons are uncharged, and therefore interact with the strong, short-range
nuclear force, and are therefore capable of transferring a large amount of energy to target
6
recoil atoms. Protons and electrons may interact by Coulomb scattering due to longrange, Coulomb electrostatic forces. Furthermore, the energy transferred by Coulomb
scattering is dominated by ionization, and atomic displacements tend to be isolated [4].
However, highly energetic protons, such as those encountered in this study, may also
interact with the short-range, nuclear force to produce displacements. In Si, electron
radiation creates an acceptor level 0.4 eV above the valence band and a donor level 0.36
eV below the conduction band; whereas, neutron radiation creates an acceptor level at
0.56 eV (midgap) [8].
Ultimately, displacement damage affects the electrical properties of the
semiconductor by creating energy states within the energy band gap, which compete
with and disrupt the conduction process of free holes in the valence band and free
electrons in the conduction band. The ways in which electrically active defects affect
the conduction process are shown in Figure 2.1 [7]. Each of these effects, resulting from
displacement damage, is discussed by Srour [6]. Generation of electron-hole pairs can
occur from a defect level near midgap, as shown in Figure 2.1. The probability for
generation decreases exponentially as the defect energy is moved further from midgap.
Furthermore, generation dominates over capture primarily when the free-carrier
concentrations are much less than their thermal equilibrium values, such as in the
depletion region of a diode. Therefore, such defect generation centers contribute to
leakage currents in diodes. Another effect of displacement damage, shown in Figure 2.1,
is that of recombination, which, like generation, is primarily caused by a defect having
an energy level near midgap, since recombination requires the capture of one type of
carrier followed by another carrier of opposite charge. Recombination reduces the
7
number of free carriers, unlike generation which increases the number of free carriers.
Trapping, for which a carrier is trapped and later emitted back to its corresponding band,
occurs for shallow defect energy levels near the valence band or conduction band edge,
as shown in Figure 2.1. Carrier mobility, μ, is reduced by these shallow traps, which
effectively reduce the time the carriers spend in the conduction process [4]. Another
possible effect caused by displacement damage is that of doping compensation, shown in
Figure 2.1, in which defects, having energies deep within the band gap, essentially
compete with: 1) the conduction band for electrons from donor levels, or 2) the valence
band for holes from acceptors. Ultimately, doping compensation results in a reduction
of the equilibrium majority carrier concentration. Also shown in Figure 2.1 is the
process of tunneling, in which carriers tunnel through potential barriers with the aid of
defect energy levels. Increased tunneling current can increase the ideality coefficient, n,
of Schottky diodes [8].
Figure 2.1. Effects of electrically active defects on the carrier transport properties of semiconductors [7].
8
Furthermore, we note that annealing of displacement damage, which can lead to
at least partial recovery of electrical performance characteristics, occurs simultaneously
with displacement damage. For example, in Si at room temperature, following a burst of
fission neutrons from a pulsed reactor, carrier lifetime experiences a short-term anneal,
which can last up to approximately one hour after the burst, and the damage remaining
after this short term anneal process is termed “permanent damage” [6]. In addition, the
Si device experiences a long-term, slow-rate anneal process which may last up to
approximately one year [6]. A graphical representation of this process is shown in
Figure 2.2. In this study, we employ accelerated-life testing in that the irradiation times
are less than an hour; whereas, for example, the JIMO mission was planned to be for
approximately 8 years. However, we also perform ex-situ testing, and so it can be
expected that much of the damage has annealed from the time the devices are removed
from the radiation source to the time that they are tested. Therefore, the data presented
in this study can be regarded as slightly conservative with respect to post-irradiation,
pre-annealed displacement damage effects. It is important to note that, although
annealing in Si is possible at room temperature, the amount of annealing increases with
increasing temperature, as the thermal energy of the crystal increases, causing defects to
become more mobile.
9
Figure 2.2. Short-term and long-term anneal processes in Si and Si devices at room temperature [6].
2.2
Ionization
In semiconductors, ionizing radiation generates excess holes and electrons, which
eventually recombine directly, such as when an electron in the conduction band
recombines with a hole in the valence band, or indirectly, such as through a trap level
within the band gap. This process of electron-hole production and recombination causes
a transient increase in conductivity [4,5], and is useful in applications such as photodetectors and radiation detectors in general. It is described mathematically in Equation
2.1. In Equation 2.1, σ is the conductivity of the semiconductor, q is the charge of an
electron, µn and µ p are the electron and hole mobilities, respectively, and n and p are
the electron and hole concentrations, respectively. However, it should be noted that the
mobilities actually decrease due to the increase in carriers and the corresponding
increase in carrier-carrier scattering, but the decrease in these mobilities is typically
small, and therefore the mobilities are often assumed to be constant [5]. Unlike for the
case of nuclear detonations, which result in a burst of radiation, one can assume that for
10
nuclear reactors, such as those used for space propulsion systems, the radiation level is
essentially constant for long periods of time, and therefore transient effects, such as
excess-carrier generation from ionizing radiation, can generally be ignored [9].
Therefore, in this dissertation, we neglect the effect of ionization on semiconductor
materials, but it is important to note that ionization produced by heavy ions having high
linear energy transfer (LET), such as those associated with cosmic radiation, can induce
catastrophic single event effects in power devices, such as power MOSFETs [3, 10, 11].
=
δσ q ( µnδ n + µ pδ p )
2.1
Next, we consider effects caused by ionization in insulators. Although totalionizing-dose (TID) has been known to degrade the properties of Schottky diodes by
creating an increase in leakage currents and excess forward currents [12], as well as a
significant reduction in breakdown voltage [13], the data published by Harris for
irradiations at the IUCF, with 203 MeV protons, for the same diode models used in this
study, indicate a dominant effect of displacement-damage-induced carrier-removal [1,2].
Therefore, we focus on examining the effects of ionizing radiation on metal-oxidesemiconductor (MOS) structures. For the process leading to these effects, we refer to
Figure 2.3 and the discussion given by Oldham [14].
11
Figure 2.3. Process by which ionizing radiation induces trapped oxide charge and interface traps at the
Si/SiO2 interface [12] .
Referring to process (1) in Figure 2.3, an electron-hole pair in the SiO 2 gate is
first created by the ionizing radiation. The electron is quickly swept out of the oxide on
the order of picoseconds; however, within that time frame, some of the electrons and
holes recombine. The amount of recombination depends on the magnitude of the
electric field applied to the gate, as well as the type and energy of the ionizing radiation.
For example, for a higher applied gate voltage and thus electric field, more charge
escapes recombination and therefore the radiation effect is greater. Also, for the same
amount of dose, for higher LET radiation, more recombination of electron-hole pairs
will result, simply because they are generated more closely together, and therefore the
radiation-induced effect from the higher LET radiation will not be as pronounced for a
given absorbed dose.
12
Referring to process (2) in Figure 2.3, over a period of time ranging from
nanoseconds to seconds at room-temperature, for a positive gate bias, the holes hop
through the oxide to the Si/SiO 2 interface. Shown as process (3) in Figure 2.3, a fraction
of the holes will then become trapped at this Si/SiO 2 interface and cause a negative
voltage shift in threshold voltage of MOS devices. This effect can last from hours to
years. The amount of holes trapped at the Si/SiO 2 interface is very dependent on the
processing of the oxide; for example, in radiation-hardened MOS structures, having
much “cleaner” oxides with fewer hole traps, much fewer holes are trapped at this
interface, in general.
Lastly, we discuss process (4) in Figure 2.3, which is radiation-induced interface
traps within the Si band gap. Unlike the oxide trapped charge discussed in processes (1)
through (3) that cause a negative shift in threshold voltage, radiation-induced interface
traps can contribute either a positive or negative shift in threshold voltage, depending on
the Si Fermi level at the interface. For example, for p-channel MOSFETs, these
interface traps contribute a negative shift in threshold voltage, adding to the negative
shift induced by the trapped oxide charge. For n-channel MOSFETs, which is the case
for all of the MOSFETs tested in this study, the interface traps contribute a positive shift
in threshold voltage, countering the negative shift in threshold voltage induced by the
trapped oxide charge. The total shift in threshold voltage is simply the sum of the shifts
in threshold voltage caused by the trapped oxide charge and the radiation-induced
interface traps. These interface traps can occur during the irradiation and can even build
up tens of seconds to thousands of seconds post-irradiation. The amount of interface
traps also depends on the applied electric field as well as temperature. Essentially, the
13
radiation-induced interface traps are caused by the liberation of hydrogen ions in the
SiO 2 bulk by radiation-generated holes. The hydrogen ions then hop toward and interact
with dangling bonds at the Si/SiO 2 interface.
2.3
Dosimetry for the OSURR Rabbit Facility
The purpose of our dosimetry calculations with respect to the OSURR and IUCF
is to determine the types and amounts of energy deposition in the materials of interest, in
order to relate changes in electrical performance parameters to these radiation
environments. In this section, using MCNPX 2.6.0 [15], SRIM 2008[16], as well as
analytical calculations, we characterize the mixed neutron and gamma-ray radiation field
of the OSURR rabbit facility as well as the 203 MeV proton beam used at the IUCF by
NASA. This will aid in understanding the change in performance of the devices exposed
to the said radiation fields as well as form the basis of the neutron-proton equivalency
portion of our study. Also, it is important to note that the dosimetry calculations and
methods used in this study can be applied to a variety of different radiation
environments.
2.3.1 Description of The Ohio State University Research Reactor (OSURR)
The Ohio State University Research Reactor (OSURR) is a swimming pool-type
500 kW light water reactor with 19.5% enriched uranium silicide fuel rods seated in an
aluminum plenum. Figure 2.4 is a top view of the reactor showing the rabbit tube, the
facility that was used in this experiment. As shown in Figure 2.4, the rabbit tube
penetrates the reactor pool from the southwest corner of the reactor pool. It is 2 inches
14
in diameter. At its far end, it is tangent to the north face of the core. Among the various
reactor irradiation facilities, the rabbit facility was chosen for use because the interest of
this research is in the long term, stable, degradation of power semiconductor devices.
Consequently, it was not necessary to use a facility that would allow for the devices to
be monitored in real time, such as Beam Port 1. Also, the complicated equipment setup
involved with the need to monitor device degradation in real time was avoided. Among
the complications of the equipment setup for real time monitoring of device degradation
is the need for long sense leads. With our equipment setup for post irradiation testing,
we were able to make low current measurements, without leakage problems associated
with long sense leads.
15
Figure 2.4. Top view of the Ohio State University Research Reactor (OSURR).
2.3.2 OSURR Rabbit Facility: Displacement Damage
Both neutrons and energetic secondary electrons produced by gamma-rays
induce displacement damage in the OSURR rabbit facility, and a description of this
process is given in section 2.1. First, we mathematically define and discuss the
parameters that quantify the amount of displacement damage in a material. Then, we
16
discuss how these parameters are calculated for both neutrons and gamma-rays in the
OSURR rabbit facility and provide the results for the calculations.
2.3.2.1 Neutron-Induced Displacement Damage
The 1 MeV equivalent neutron fluence in Si, Φ eq ,1MeV ,Si , is a typical parameter
used for quantifying displacement damage in Si, and is defined by Equation 2.2 [17]:
∞
Φ eq ,1MeV ,Si
∫0 Φ ( E ) K D,Si ( E ) dE .
=
K D,1MeV ,Si
2.2
In Equation 2.2, K D,Si ( E ) are the displacement kerma factors for Si, and K D,1MeV ,Si is
the value of this function for a neutron energy, E, of 1 MeV. The values for K D,Si ( E ) ,
including the value for K D,1MeV ,Si , namely 95 (MeV-mb), are given in ASTM standard
E722-04. The neutron lethargy flux per kW, shown in Figure 2.5, was obtained from the
OSURR reactor staff using foil activation in conjunction with the SAND II spectrum
unfolding code [18].
The integral in Equation 2.2 was calculated with the aid of MCNPX 2.6.0, a
Monte Carlo transport code, and the ENDF/B-VI.6 libraries were used. That is, a
histogram source distribution consisting of the neutron group flux was simulated as an
isotropic surface source with a model of an industry standard TO-220 package, the
package for all of the devices used in this study, in the center of the spherical shell
source. The MCNPX model of the TO-220 package is shown in Figure 2.6, a package
for which Si was used as the semiconductor for the calculation of Φ eq ,1MeV ,Si . In the Si
within the TO-220 package model, a neutron flux tally, in conjunction with the dose17
energy and dose-function cards, having the ASTM standard E722-04 values
for K D,Si ( E ) , was then implemented in order to compute the integral in the numerator of
Equation 2.2. This integral, obtained from the Monte Carlo calculation,
Figure 2.5. Neutron lethargy flux per kW in the OSURR rabbit facility, obtained from the OSURR
reactor staff.
18
Figure 2.6. Generalized MCNPX model of TO-220 package, drawn to scale. The semiconductor
materials of interest in this study are Si and SiC.
was then divided by K D,1MeV ,Si as well as the cumulative neutron flux tallied in Si to
obtain the hardness parameter, H Si , defined by Equation 2.3:
∞
Φ eq ,1MeV ,Si
∫0 Φ ( E ) K D,Si ( E ) dE .
=
H Si =
∞
∞
∫ Φ ( E ) dE K D,1MeV ,Si ∫ Φ ( E ) dE
0
2.3
0
The hardness parameter was then multiplied by the cumulative flux in the OSURR rabbit
facility, obtained by integration, with respect to energy, over the measured spectrum, for
a reactor operating power of 450 kW, which was the nominal operating power used for
all of the irradiations for the experiments in this study. A value of 5.2 ×1011
n
was
cm 2 s
obtained for the 1 MeV equivalent neutron fluence rate, φeq ,1MeV ,Si . A value of
5.1×1011
n
was obtained by calculating φeq ,1MeV ,Si using Equation 2.2 directly, by
cm 2 s
simply multiplying the group flux values obtained from the OSURR reactor staff by the
19
corresponding ASTM values for K D,Si ( E ) , indicating that the other materials (SiO 2 and
Cu) in the TO-220 package do not significantly perturb the flux.
In addition, in order to compare the results from the characterization testing of
the Si and SiC Schottky power diodes to those obtained from 203 MeV proton beam
irradiations performed by NASA at the IUCF, a parameter, very closely related to
Φ eq ,1MeV ,Si , called the displacement damage dose, D d , is introduced. It is defined by
Equation 2.4:
Dd
=
∞
∫0
S NIEL ( E ) Φ ( E ) dE .
2.4
Referring to Equation 2.4, S NIEL ( E ) is the average displacement damage energy
released per unit mass and per unit fluence of incident particles having a kinetic energy
of E, and is defined for Si by Equation 2.5:
S NIEL ( E )
=
NA
NA
=
σ i L (Ti ) Ti
σ D,Si ( E ) .
∑
A i
A
2.5
In Equation 2.5, N A is Avogadro’s number, and A is the atomic weight of the material.
Furthermore, σ i ( E ) and Ti are the cross section and average recoil energy, respectively,
for the i’th reaction. Also, L(T i ) is the Lindhard [19] partition function applied to the
recoil energy, and is the fraction of the recoil energy going to displacement damage.
The summation
∑ σ i L (Ti ) Ti is simply the damage energy cross section, σ D,Si ( E ) .
The
i
Robinson [20] numerical approximation to the Lindhard partition function, implemented
in recent versions of NJOY [21], was applied in this study.
20
The neutron-induced D d was calculated for both Si and SiC using MCNPX 2.6.0
using the model described previously in this section. For the calculation of D d , the
neutron flux was tallied in the semiconductor cell, and the FM tally multiplier card was
applied. In particular, the damage energy cross sections from the ENDF/B-VI.6 libraries
for Si and C were specified on the FM tally multiplier card in MCNPX by using the
ENDF/B reaction number MT=444 [21-23], and the result of this tally was multiplied by
N A and divided by A, according to Equations 2.4 and 2.5. From these calculations, in the
OSURR rabbit facility for a reactor operating power of 450 kW, a D d rate of
1.1×109
MeV
MeV
was obtained for Si, and a D d rate of 1.2 ×109
was obtained for SiC.
g s
g s
It is important to note, that although this indicates that more displacement damage
energy is released in SiC relative to Si in the OSURR rabbit facility, in part due to the
lower scattering cross section of Si relative to C over a wide range of energies in the
neutron spectrum, the D d parameter, as well as all dose parameters presented in this
dissertation, do not account for material effects. For example, a study employing
molecular dynamics simulations concluded that radiation-induced material effects, such
molten zone formation, displacement cascade lifetimes, as well as defect clustering and
in-cascade amorphization are less severe in SiC than in Si on a per unit D d basis [24].
2.3.2.2 Gamma-Induced Displacement Damage
As discussed in section 2.1, gamma-ray interactions can produce energetic
electrons, which are capable of creating displacement damage through Coulomb
scattering. As mentioned in section 2.3.1, the OSURR is a swimming pool research
21
reactor. The average gamma-ray flux in a swimming pool reactor is typically on the
same order as the neutron flux [25]. For a swimming pool reactor operating at 1 MW,
the gamma-ray flux is about 5 ×1013
n
[25]. A Co-60 source is sometimes used to
cm 2  s
approximate the gamma-ray environment of a pool-type reactor [26]. In addition, for
computations, the average energy of 1.25 MeV for a Co-60 gamma-ray, which emits
both 1.17 MeV and 1.33 MeV gamma-rays, is assumed [27]. Also, since the
displacement damage from gamma-rays is due to secondary electrons, the NIEL value
for gamma-rays is computed by normalizing the NIEL for the secondary electrons by the
ratio of secondary electron flux, φe , to gamma-ray flux, φγ , as shown by Equation 2.6
[26]:
Sγ , NIEL ( E ) =
φe
S
(E)
φγ e, NIEL
2.6
In order to compute the values of σ D,Si ( E ) and σ D,C ( E ) , as required by
Equation 2.5, for Co-60 gamma-ray-induced secondary electrons, we applied the
McKinley-Feshback [29] numerical approximation to the Mott differential scattering
cross-section of relativistic electrons with nuclei [30], in the form given by Seitz and
Kohler [31], shown in Equation 2.7, using E d values of 21 eV for Si, and 35 eV for C
[32]:
e

 T
π be 2Tmax
T
2 T
dσ ( E , T=
1
−
+
− e
β
παβ
)


e
e
2
e
e
Tmax
4γ e 
 Tmax Tmax
where,
e
Tmax
=
(
)
2me E + 2me c 2 E
Mme c 2
  dT
  2 ,
  T
2
2.7
 me c 2 
2 Zq 2
,
, where Z is
b
=
1− 

e
2
2 2
m
c
E
+
m
c
β
 e

e
e
v
, β e= =
c
22
the atomic number of the target nucleus and q is the charge of an electron (elementary
1
Zq 2
Z
charge). In addition, γ e =
, and the fine structure constant=
.
α =
2
c 137.036
1− β
e
In addition, to calculate the electron group flux, as required by Equation 2.4, an
MCNPX simulation was performed, consisting of the MCNPX model described in
2.3.2.1, but with an average Co-60 gamma-ray energy of 1.25 MeV in the isotropic,
spherical-source distribution model. Finally, in order to calculate the 1.25 MeV gammaray NIEL, the calculated value for D d , induced by the secondary electrons, was divided
by the gamma-ray flux, that was tallied in the Si and C cells. For Si, a 1.25 MeV
gamma-ray NIEL of 1.98 ×10−7
value of 2.12 ×10−7
MeV cm 2
was calculated, in close agreement with the
g
MeV cm 2
, calculated by Summers, using aluminum shielding [33].
g
MeV cm 2
For carbon, we calculated a 1.25 MeV gamma-ray NIEL value of 2.57 ×10
.
g
−7
In order to determine the NIEL for compounds, Bragg’s rule is often applied to the
individual elements of the compound [32]. It has been specifically applied for NIEL
calculations in SiC [34], and is given by Equation 2.8:
S NIEL,Compound ( E ) = ∑ fi S NIEL,i ( E ) ,
2.8
i
where fi =
xi Ai
, and xi is the stoichiometric value of the i’th element in the
∑ i xi Ai
compound. Applying Equation 2.8 to the NIEL values for Si and C, the NIEL for 1.25
23
MeV gamma-rays in SiC equals 2.16 ×10−7
MeV cm 2
.
g
Multiplying the calculated NIEL values for Si and SiC of 1.98 ×10−7
MeV cm 2
g
MeV cm 2
n
and 2.16 ×10
, respectively, with the said gamma-ray flux of 5 ×1013
,
cm 2  s
g
−7
the D d rate due to 1.25 MeV gamma-rays, alone, for a 1 MW swimming pool reactor, is
approximately 1×107
MeV
for both Si and SiC. Therefore, the 1.25 MeV gamma-ray
g s
induced D d , for a 1 MW swimming pool reactor having a gamma dose rate of 200
MRad/hr [25], is more than two orders of magnitude lower than the calculated neutroninduced D d in the OSURR for both Si and SiC. The OSURR has a maximum operating
power of 450 kW, and a combined neutron and gamma-dose rate of 50 MRad/hr at the
periphery of the reactor core. Furthermore, from the discussion in section 2.1 of this
dissertation, secondary electrons having energies on the order of 1 MeV tend to produce
simple, isolated defects, which effect electrical properties to a lesser extent than defect
clusters produced by fast neutrons. Therefore, the contribution of gamma-rays to
displacement damage is assumed to be negligible in the OSURR rabbit facility compared
to neutron-induced displacement damage.
For comparion, others have computed Co-60 NIEL values for Si and SiC, using
other methods, assuming different surrounding materials, and assuming only Compton
interactions. For example, using his own Monte Carlo transport code, Akkerman [27]
obtained a NIEL of 1.07 ×10−7
MeV cm 2
for a 1.25 MeV Co-60 gamma-ray in Si, using
g
an equilibrium thickness of aluminum. Also, assuming aluminum shielding, Summers
24
[33] calculated the NIEL in Si due to secondary electrons from Co-60 gamma-rays, and
MeV cm 2
obtained a value of 1.308 ×10
. Multiplying the value obtained by Summers
g
−5
by
φe
= 0.018 tallied in our MCNPX simulation in Si, yields a value for the Co-60
φγ
gamma-ray NIEL of approximately 2.12 ×10−7
an n-type SiC NIEL value of 1.578 ×10−5
MeV cm 2
in Si. Onada [35] calculated
g
MeV cm 2
for secondary electrons, yielding a
g
MeV cm 2
for the Co-60 gamma-ray NIEL, after multiplying this
value of 2.80 ×10
g
−7
value by the ratio of
φe
= 0.018 determined from our MCNPX simulation for SiC.
φγ
2.3.3 Ionization Dosimetry
Both neutrons and gamma-rays are responsible for ionization in the OSURR
rabbit facility. A description of this process is given in section 2.2. This section
discusses how these parameters are calculated for both neutrons and gamma-rays in the
OSURR rabbit facility and provides the results for the calculations.
2.3.3.1 Gamma-Ray-Induced Ionization
The total ionizing dose, a quantity to which threshold voltage and
transconductance of a MOSFET are correlated, was measured in the beam port facility,
directly above and adjacent to the rabbit facility, using the paired-ion chamber method to
separate ionization induced by neutrons from ionization induced by gamma-rays [36].
25
The paired-ion chamber protocol that was followed was established for medical physics
applications and as such yielded the absorbed dose in tissue. The gamma-ray absorbed
dose in tissue was converted to the gamma-ray absorbed dose in Si for the purposes of
this dissertation. From the results of this experiment, a gamma-ray induced-TID rate of
10
krad ( Si )
s
was determined for operation at 450 kW.
In comparison, the TID rate in the OSURR Co-60 facility as of October 8, 2009,
is approximately 20
rad ( Si )
s
, approximately 500 times less than the TID rate in the
OSURR rabbit facility, for a reactor operating power of 450 kW. The Co-60 facility was
not used in this study, because it is known that ionizing radiation effects on MOSFET
devices are dependent on dose rate [37].
2.3.3.2 Neutron-Induced Ionization
As discussed in section 2.2, ionization effects are of primary significance in
insulators, such as the SiO 2 gate of a MOSFET. Neutrons indirectly ionize, primarily by
creating Si and O recoils in the SiO 2 gate [38]. Some studies have indicated that the
neutron contribution to ionizing dose and its effects are negligible in comparison to the
gamma-ray component of a reactor mixed-radiation field [39, 40]. However, Vaidya
[26] determined that neutrons, in a mixed-radiation field of a nuclear reactor, contribute
a noticeable amount to the degradation of MOSFET electrical performance parameters
that are sensitive to ionization (e.g. threshold voltage). Furthermore, Vaidya obtained
his experimental results using a swimming pool reactor having a thermal (E <= 0.625
26
eV) to fast (E >= 0.625 eV) neutron flux ratio of 3.2. The OSURR rabbit facility
neutron flux is very similar, with a thermal to fast neutron flux ratio of 3.3, obtained
from the neutron spectrum shown in Figure 2.5. Therefore, the goal of this section is to
quantify the neutron contribution to total ionizing dose (TID) in SiO 2 for the OSURR
rabbit facility.
In order to calculate the TID contribution to SiO 2 from neutrons in the rabbit
facility using MCNPX, a spherical surface source was modeled having a radius of 1 cm
and consisting of the neutron spectrum of the OSURR rabbit facility shown in Figure
2.5. The SiO 2 was modeled as a 1 mm × 1 mm × 1 mm cube at the center of the spherical
source. Also, the ENDF/B-VI.6 libraries for Si and O were used in addition to the +f6
collision heating tally and the flux multiplier damage tally, using the ENDF/B reaction
number MT=444 as discussed previously in section 2.3.2.1. A neutron flux tally was
also used in order to normalize the dose by fluence.
The result for neutron-induced TID was then calculated by subtracting the energy
deposited from displacement damage calculated using the damage tally from the total
energy deposited obtained from the +f6 collision heating tally. The TID was then
normalized by result of the neutron flux tally (f4). Then, the TID per unit fluence was
multiplied by the cumulative flux for the OSURR rabbit facility obtained from the
spectrum in Figure 2.5, and the result was converted to units of rad(Si)/s. A result of
64
rad ( SiO2 )
was obtained for neutron-induced TID in SiO 2 , which is less than 1 % of
s
the measured gamma-ray induced TID of 10
krad ( Si )
s
. Furthermore, Si and O recoils
are high LET radiation with respect to gamma-rays; therefore, per our discussion in
27
section 2.2, for the same ionizing dose, the gamma-rays should have greater effect on
MOS properties than neutrons, since electron-hole pairs generated further apart have less
chance of recombining, and consequently, greater probability of being trapped in the
oxide. Therefore, the effect of the contribution to TID in the MOSFET gate oxide from
neutrons is expected to be negligible compared to the effect of the contribution from
gamma-rays in the rabbit facility for a reactor operating power of 450 kW.
However, it is interesting to note that from this calculation, it was determined
that approximately 76 % of the energy lost by neutrons in the SiO 2 was due to
ionization, compared with 24 % lost to displacement damage. This result was also
obtained by calculating the Si and O primary knock-on (PKA) energies, positions, and
directions from the particle tracking (ptrac) file from MCNPX, and using them as input
for SRIM, as was done previously for SiC [41]. In essence, although over three quarters
of the energy lost by neutrons is in the form of ionization, neutrons account for less than
1 % of the TID in SiO 2 . However, they account for approximately 99 % of the
displacement damage in bulk Si and SiC.
2.3.4 Conclusions for OSURR Dosimetry Calculations
From the dosimetry calculations performed for the OSURR rabbit facility,
gamma-rays are primarily responsible for TID, and their contribution to bulk
displacement damage is negligible. Neutrons, on the other hand, create nearly all the
bulk displacement damage, but contribute very little to TID. The results, regarding the
dosimetry of the OSURR, are summarized in Table 2.1.
28
Dose Rate Parameter
Si
SiC
φeq,1MeV ,Si
5.2 ×1011
n
cm 2 s
D d
1.1×109
MeV
g s
TID
10
N/A
1.2 ×109
krad ( Si )
s
MeV
g s
N/A
Table 2.1. Dosimetry results for OSURR
2.4
Dosimetry for the IUCF Proton Beam
In addition we have also analyzed the 203 MeV proton beam of the IUCF with
respect to dosimetry, so that the data from this dissertation can be compared with those
from the NASA experiments [2], which were given in terms of proton fluence, on the
basis of D d . For this calculation, we used the method described by Jun [32,42], who
calculated and tabulated, as a function of energy, the nuclear contribution to the NIEL
for a number of individual elements, including Si and C, using a pencil proton beam as
the source, incident on a thin slab (0.1 cm) of the target material. In brief, the total
NIEL for high-energy protons can be partitioned into Coulomb and nuclear scattering, as
shown by Equation 2.9, written for an arbitrary material, mat:
S NIEL,mat ( E )
=
NA
(σ D,Coulomb + σ D, Nuclear ) .
A
2.9
MCNPX was used to calculate the nuclear scattering contribution to the NIEL.
The IUCF proton beam used for the NASA experiments, having a Gaussian energy
distribution with an average energy of 203 MeV and a full-width at half-max (FWHM)
29
value of 200 keV [43], was approximated in the MCNPX model using a histogram
source distribution. In addition, the TO-220 package was modeled as the target, and the
proton beam was perpendicularly incident, and covered the entire face of the TO-220
package, as shown in Figure 2.7. The MCNPX Bertini intra-nuclear cascade (INC)
model was applied [44]. The displacement damage energy was obtained using the
HTAPE3X code to post-process the history tape (histp) file generated by MCNPX. The
nuclear scattering contribution to the NIEL was then calculated by dividing this
displacement damage energy by the fluence tallied in the semiconductor.
In addition to the displacement damage energy, the HTAPE3X code also yields
the number of recoils (PKA’s) produced by elastic and inelastic scattering. The overall
average recoil (PKA) energy and the average recoils from elastic and inelastic process
are also calculated by HTAPE3X. Some of these parameters are shown in Table 2.2 for
pure Si. As shown in Table 2.2, nuclear inelastic scattering contributes significantly
more to displacement damage energy in Si than nuclear elastic scattering for the IUCF
203 MeV proton beam. The collision heating (+f6) was also tallied in MCNPX in order
to determine the total energy lost by the protons in the semiconductor.
The Coulomb damage energy cross section, σ D,Coulomb , was calculated using the
relativistic differential cross section in references [32] and [45], which is a simple
extension of the McKinley-Feshbach equation for relativistic electron scattering with
nuclei, used in section 2.3.2.2, for incident radiation of light nuclei, such as protons. The
relativistic
30
Figure 2.7 MCNPX model of NASA experiments conducted at IUCF, using the TO-220 package model
shown in Figure 2.6, and a perpendicularly incident proton beam, P.
% of Total Nuclear
Scattering Events
Due to Inelastic
Scattering
% of
Total Damage Energy Due to
Inelastic Scattering
58 %
73 %
Average
Recoil
Energy:
Inelastic
Scattering
Average
Recoil
Energy:
Elastic
Scattering
1084 keV
284 keV
Table 2.2. Htape results, showing contributions to nuclear scattering and damage energy by inelastic
scattering for pure Si.
damage cross section from Coulomb scattering was computed numerically by integrating
the right-hand side of Equation 2.10 [42]:
σ D,Coulomb = ∫
p
Tmax
Tdmat
where,
Si
Td
= 21 for Si and
C
Td
L (T )Tdσ ( E , T ) ,
2.10
=35 for C [32], and the maximum recoil energy,
given by Equation 2.11:
31
p
Tmax
, is
p
Tmax
=
(
2 E E + 2m p c 2
2
)
 mp 
2
1 +
 Mc + 2 E
M


.
2.11
In Equation 2.11, E is the incident proton energy, m p is the mass of the proton, and M is
the mass of the target nucleus. The differential cross section, dσ ( E , T ) , shown in
Equation 2.10, for a proton of energy E producing a recoil nucleus of energy T, is given
by Equation 2.12:
 T
π bp 2Tmax 
T
2 T
1
−
+
− p
dσ ( E , T =
β
παβ
)


p
p
2
p
p
4γ
Tmax
 Tmax Tmax

  dT
  2 ,
  T
2.12
2
v
where, β p= =
c
 mpc2 
2 z p Zq 2
, and bp =
, where z p is the atomic number of
1− 
 m p c 2 + E 
mpc2 β 2


the incident proton = 1, Z is the atomic number of the target nucleus, and q is the charge
of an electron (elementary charge). In addition, γ =
constant=
α
1
1 − β p2
, and the fine structure
Zq 2
Z
. An approximation for the average recoil energy, T , is
=
c 137.036
given by Equation 2.13:
 Tp

T ≈ Td  ln max − β p 2 + παβ p  ,


Td


2.13
It is interesting to note, that, from Coulomb scattering, although the maximum energies
transferred by a 203 MeV proton to a Si and C atom are 30 MeV and 60 MeV,
respectively, the average Si and C recoil energies are only 294 eV and 499 eV,
respectively. In contrast, using the method described in section 2.3.3.2 for neutrons [41],
32
the maximum recoil energies for Si and C are 814 keV and 2.1 MeV, respectively, and
the average Si and C recoil energies are 34 keV and 53 keV, respectively, in the OSURR
rabbit facility.
Also, in order to evaluate the relativistic Coulomb cross section, the average
proton energy absorbed in the SiO 2 layer, shown to the left of the semiconductor in
Figure 2.7, was calculated using SRIM, and this energy was subtracted from the average
energy of the IUCF proton beam (203 MeV) in order to estimate the average energy of
the protons, E, as they enter the semiconductor. From the SRIM calculation, this
average entry energy, E, was found to be 200 MeV, and was used as input to Equations
2.10-2.13, essentially approximating the IUCF proton beam as mono-energetic for this
computation. Coulomb scattering accounted for 23 % and 26 % of the total NIEL for Si
and SiC, respectively.
The results of the 203 MeV proton NIEL calculation, as well as those published
by Jun for 200 MeV protons in Si an C, are shown in Table 2.3. The results are not
surprising, in that the proton beam is sharply peaked around 203 MeV, and that from the
SRIM calculation, 203 MeV protons lose an average of approximately 3 MeV before
entering the semiconductor.
MCNPX
S NIEL,Si
S NIEL,C
S NIEL,SiC
Model
(MeV·cm2/g) (MeV·cm2/g) (MeV·cm2/g)
This study 1.91E-3
6.14E-4
1.52E-3
I. Jun [32] 1.88E-3
6.09E-4
1.50E-3
Table 2.3. Dosimetry results for the 203 MeV IUCF proton beam compared with Jun’s results for 200
MeV protons. The NIEL for SiC was computed by applying Equation 2.8 to the NIEL for Si and C.
33
CHAPTER 3 : I-V CHARACTERIZATION TESTING OF SCHOTTKY POWER
DIODES
Our purpose for radiation hardness testing of diodes that were tested by NASA at
the IUCF [1,2] by a high-energy proton beam is two-fold. First, the Si and SiC Schottky
power diodes exhibited a high level of resistance to high-energy proton radiation at the
IUCF; therefore, we want to test these diodes for radiation hardness in a mixed neutron
and gamma-ray radiation field. Second, we want to use this testing as an opportunity to
compare the diodes electrical performance based on displacement damage dose in order
to determine a neutron and proton equivalency model. Such an equivalency will provide
a level of confidence in the dosimetry of the OSURR and IUCF. Furthermore, this
equivalency will enable proton radiation degradation to be predicted from the data
presented in Chapter 3 with respect to a neutron and gamma-ray radiation field. As a
result, the time and financial cost associated with additional radiation hardness testing
can be reduced, provided that the performance of the diodes can be reasonably predicted
on the basis of displacement damage dose.
Diodes are the simplest form of semiconductor devices. They are made of either
a Schottky contact or a p-n junction, which is the building block of most semiconductor
devices. Furthermore, diodes have applications in a wide variety of circuits. They are
presently being used as radiation detectors. They are also used in power circuits, as
34
stand-alone switches, and in snubber circuits to protect more expensive semiconductor
devices. Therefore, the primary focus of this research is directed toward radiation
effects on diodes. Regarding applications, the effects on the performance of rectifying
circuits that are comprised of diodes will also be examined.
Evaluating circuit
performance as a function of diode degradation yields information on power constraints,
which arise from the need to meet thermal requirements for more resistive radiationdegraded devices, in which more than the nominal power is dissipated.
This research focuses on semiconductor devices made of Si and SiC. Si is
chosen as a material of interest, since it is so widely used; and SiC is chosen, given its
recent attention in the field of radiation hard electronics. SiC is known to have high
resistance to radiation damage and capability of operating at relatively high
temperatures, 700 C. Both of these characteristics can be attributed to a large band gap,
E g , compared to E g for other semiconductor materials.
Such characteristics are
extremely desirable, particularly on spacecraft, as this will reduce the necessary radiation
shielding and will allow for suitably low device temperatures to be more easily achieved
and maintained. Furthermore, due to the higher band gap, the critical electric field, E c ,
of 4H-SiC is roughly 10 times greater than that of Si. The breakdown voltage, V B , of a
one-sided junction, such as a Schottky diode, is inversely proportional to the dopant
density, N D , and directly proportional to ( Ec ) ; therefore, the SiC diode can have 100
2
times the dopant density of a Si diode, which enables SiC to have much lower on-state
resistances and greater resilience to displacement damage-induced carrier-removal
effects for the same breakdown voltage.
35
The focus of this study is on Schottky diodes, since they are majority carrier
devices and therefore not dependent on minority carrier lifetime, which is the most
sensitive parameter to radiation-induced displacement damage. Also, Schottky diodes
are generally more resistant to radiation-induced displacement damage than p-n junction
diodes, since the thermionic emission currents in Schottky diodes are much larger than
diffusion currents in p-n junction diodes [12]. The lower built-in potential of the
Schottky contact enables larger current densities, albeit at the cost of larger reverse
current and lower breakdown voltages [8]. In fact, Mohan states, as of 2003, that
Schottky diodes having breakdown voltages larger than 100 V – 200 V cannot be made
reliably [46]. This still appears to be the case for Si technology, as the Si Schottkies
used for this study all have breakdown voltages less than 200 V, the highest that could
be found for commercial-off-the-shelf Si Schottky power diodes. However, the SiC
Schottky diodes in this study have breakdown voltages ranging from 600 V – 1200 V.
3.1
Schottky Power Diode Background
A schematic of a Schottky power diode is shown in Figure 3.1, and the I-V
characteristics of a typical power diode, which is applicable for both Schottky and p-n
junction power diodes, are shown in Figure 3.2.
36
Figure 3.1. A schematic of a typical Schottky power diode. The p-n junction guard rings are used to
decrease the radius of curvature of the depletion region, which occurs due to electric field crowding at the
edges of this region, and thus increase the breakdown voltage [46, Mohan].
Figure 3.2. Typical I-V characteristics of a power diode, after [46, Mohan].
For an ideal Schottky junction, in which thermionic-emission is the dominant
current-conduction mechanism, and for which all of the voltage drop across the diode,
V D , can be assumed to occur across the metal-semiconductor junction, the diode current,
I D , can be expressed according to Equation 3.1 [8,47]:
37

 qV
=
I D I s exp  D
 nkT

 
 − 1 ,
 
3.1
where q is the elementary charge (1.602E-19 C), n is the ideality coefficient (1<= n<=
2), k is the Boltzmann constant (1.38E-23 J/K), T is the temperature (K), and the
saturation current, I s , is given by Equation 3.2:
 −qφB 
3.2
I s = A∗T 2 exp
.
 kT 
In Equation 3.2, φB is the Schottky barrier voltage, which is the difference between the
metal work function and the electron affinity of the semiconductor; furthermore, the A∗
term in Equation 3.2 is called the effective Richardson constant, and it is a function of
the effective mass of the majority carrier as well as tunneling and reflection [8]. When
thermionic emission is the dominant current conduction mechanism, n is closer to 1;
however, tunneling can induce an increase in both n and I s [8].
However, as shown in Figure 3.2, the I-V characteristics of power diodes are
quite linear for most of their forward-bias operating range. This linear effect in the highinjection forward bias operating condition is due to the series resistance, R S , of the
neutral semiconductor region outside the junction and depletion region, and is included
in Equation 3.3 in the rightmost term, V Rs = R s I D :
'
V
=
D
nkT  I D 
ln 1 +
 + RS I D
q
IS  

 VRS
3.3
VD
The V D term in Equation 3.3 is the ideal, low-injection forward bias Equation 3.1 solved
for V D . As shown by Equation 3.3, this V D term increases logarithmically with I D , at a
slower rate than the V Rs term, which increases linearly term with respect to I D . For an n-
38
type semiconductor, RS ∝ ρ , where ρ =
1
qµn n
, µn is the electron mobility, and n is the
electron (majority) free carrier concentration. Both µn and n are expected to decrease
with increasing radiation-induced displacement damage.
For instance, carrier mobility is reduced primarily by ionized impurity scattering,
such as an acceptor in an n-type semiconductor or a donor in a p-type semiconductor [4].
In an n-type material, for small changes in Fermi level, the mobility as a function of
radiation fluence can be expressed as Equation 3.4:
1
µn
=
1
µ LO
+
1
µ IO
+ Kµ Φ ,
Equation 3.4
where, µ LO and µ IO are the mobilities from lattice and impurity scattering, respectively,
and K µ is the mobility damage constant, which depends on the Fermi level, the
temperature, and type of irradiation [4].
However, for both the Si and SiC Schottky power diodes tested in this study, the
dominant effect observed by Harris was a reduction in n, or carrier removal when
exposed to the IUCF 203 MeV proton beam [1,2]. Also, for a neutron and protonradiation testing study of Si power MOSFETs, carrier removal was also determined to be
the primary culprit for increased on-state resistance [48]. One possible explanation for
this is that for all of the diodes used in the Harris studies that were also tested in this
study, the initial free carrier concentrations were on the order of 1015 cm-3 [49], and the
mobilities are fairly constant for impurity concentrations of less than ~ 1016 cm-3 for both
Si [50] and SiC [51]. Furthermore, Baliga states that the on-state resistance of power
MOSFETs, begins to increase when the radiation-induced defect concentration becomes
comparable to the drift layer doping concentration [52]. In n-type material, carrier
39
removal is a result of acceptor-type defects below the Fermi level, which capture
electrons from the conduction band [4]. For small changes in Fermi level, the electron
density can be related to the radiation fluence by Equation 3.5:
3.5
n = n0 − K n Φ , Equation
where n 0 is the initial, unirradiated electron carrier concentration and K n is the carrier
removal rate, which, like K µ , is dependent on Fermi level, temperature, and type of
radiation [4].
3.2
Experimental Methodology
In section 3.2, we discuss the experimental apparatus used to test the diodes. In
addition, the irradiation and I-V characterization (measurement) procedure is discussed
in this section. In order to obtain the best results possible with respect to comparison
between this data and the data obtained at the IUCF by NASA, the irradiation and I-V
characterization procedure used at the IUCF by NASA for proton radiation was followed
as closely as possible.
3.2.1 Experimental Apparatus
A block diagram showing the main components of one of the experimental
setups used to test the Si and SiC diodes is shown in Figure 3.3, and a photograph of this
setup is shown in Figure 3.4. The experimental setup shown in Figure 3.3 and Figure
3.4 was used to test the reverse bias I-V characteristics of the IR Si Schottky power
diodes, as well as the low-injection forward I-V characteristics of both the Si and SiC
diodes. The reverse bias I-V characteristics of the SiC Schottky power diodes were not
measured for this experiment, but some reverse bias I-V characteristics of Cree SiC
40
Schottky power diodes are presented in Chapter 4. In addition, the experimental setup in
Figure 3.3 and Figure 3.4 was used to measure the high-injection forward I-V
characteristics of the SiC diodes. Four-wire, Kelvin measurements were used for all I-V
characterization testing.
Diode to be tested
in TO-220 IC
socket
Keithley 2410
Tektronix 371B
High Power Curve
Tracer
source and
sense leads
HP laptop
computer with
LabView
USB cable
GPIB cable
Keithley 2430
Figure 3.3: Block diagram of diode test apparatus
41
Figure 3.4. Photograph of one of the Experimental setups, containing the Keithley Source Meters used to
test the Si and SiC Schottky diodes.
The Keithley 2410 Source Meter, shown in Figure 3.3 and Figure 3.4, is capable
of outputting up to 1100 V and up to 1 A of current with very little electrical noise, when
it is operated at and above the nano-amp range. This made the Keithley 2410 an ideal
instrument for measuring the reverse I-V curves and low currents for forward bias. The
latter attribute enabled precise I-V curve fits to the diode equation, Equation 3.1, for low
currents, where the effect of series resistance is negligible. However, the Keithley 2410
has a limitation, particularly with respect to high current measurements. That is, it
cannot provide more than 1 A of current; furthermore, it is not capable of pulsed
measurement. The latter limitation is a concern for high current measurements in that
the continuous application of voltage heats the device and thus alters the I-V
42
measurement, as indicated by equation 3.1. As the object of this research was power
diodes, which typically operate at currents from 1 A to 30 A in the forward direction, the
Keithley 2410 was inadequate for such measurements.
In order to measure the high forward injection of the SiC diodes, the Keithley
2430 was used. It has the ability of making pulsed measurements with a range of up to
10 A. Using pulsed measurements is important in order to prevent device heating, which
affects the I-V characteristics as shown by Equations 3.1 and 3.3. However, the 2430
alone is insufficient to accomplish our measurement goals, as poor noise rejection, with
noise in the milliamp range, prevents accurate low current measurements with the 2430.
As shown in Figure 3.3, the two Keithley sourcemeters were connected to one another
with a general parallel interface bus (GPIB) cable. As described in more detail below,
they were connected to a laptop computer with a USB cable.
A National Instruments GPIB-to-USB adapter was used to connect the USB port
of a desktop computer to the GPIB bus of the Keithley Source Meters. The desktop
computer had a Windows 2000 operating system with LabView 8.0 installed. The front
panel display of the LabView program that was used to control the Source Meters is
shown in Figure 3.5. As shown in the front panel display in Figure 3.5, a pulse width of
1 millisecond was used for measuring the forward I-V characteristics of the diodes, in
accordance with similar tests peformed by NASA. Also, as shown in the front panel
display, a voltage sweep is set, with the current through the device limited to 10 A. The
I-V curve of the diode being tested is also displayed.
Voltage sweeps for the low current measurements were taken with 5 mV steps,
and those for high current with 10 mV steps. The current was measured by the Keithley
43
sourcemeters at each of these steps in voltage, and the result was output to LabView
measurement files, which could then be imported and processed in a Microsoft Excel
spreadsheet. The forward direction yielded the information for the curve fitting analysis,
for the parameters n, I s , and R s .
Voltage sweeps were also taken in the reverse direction to characterize leakage
and breakdown. These voltage sweeps were taken in increments of -1 V until there was
evidence of device breakdown. Current was limited to 1 mA in the reverse direction for
all devices in order to avoid destruction of the device.
For measuring the forward bias, high-injection measurements of the IR silicon
Schottky power diodes, the high-power Tektronix 371B curve tracer, shown below the
the two Keithley Source Meters in Figure 3.4, was used. The curve tracer, like the
Keithley 2430 source meter, operates in pulsed mode, and so it can measure high
currents without heating the device. However, the Keithley 2430, as mentioned in
section 3.2.1, is limited at 10 A of current; therefore, the curve tracer was needed to
measure the I-V characteristics of the IR Si Schottky diodes, which have current ratings
ranging from 5 A to 30 A per individual diode. For the curve tracer, as well as for the
Keithley Source Meters, four-wire Kelvin measurements were implemented in order to
minimize cable effects.
44
Figure 3.5. Front panel of LabView program used to control the Keithley 2410 and 2430 sourcemeters.
3.2.2 International Rectifier (IR) Si Schottky Power Diodes
International Rectifier (IR) Si Schottky power diodes, having part numbers
10CTQ150PBF, 40CTQ150PBF, 60CTQ150PBF, and 43CTQ100, shown in Table 3.1,
were tested. The ‘PBF’ at the end of some of these part numbers indicate lead free
packaging. The presence or absence of lead is not expected to affect the results, since
lead does not activate much.
The International Rectifier Si Schottky diodes were packaged in TO-220AB
packages, which consist of 2 diodes in parallel. Each diode has its own anode, but they
share a common cathode. Following the procedure that was used for previous NASA
45
experiments conducted at the IUCF, only one of the diodes in each package was tested,
as it is assumed that both diodes in a package will behave similarly. Also, comparing
diodes from different packages is likely to yield more independent data and thus more
information about the variation in device performance from different diodes of the same
part number. The International Rectifier diodes that were tested are given in Table 3.1
along with the rated voltages and currents for each leg, or diode, of the package.
Part Number
Current Rating per Leg
(A)
Voltage Rating per Leg
(and Package)
(V)
43CTQ100
20
100
10CTQ150PBF
5
150
40CTQ150PBF
20
150
60CTQ150PBF
30
150
Table 3.1: The International Rectifier part numbers tested in this research project along with their current
and voltage ratings. The package voltage rating is the same as it is for each individual leg. However, the
current-rating for the package is double that for each individual leg, since the package contains two diodes
that can be wired in parallel.
3.2.3 Cree SiC Schottky Power Diodes
Also, some SiC Schottky diodes were of particular interest to NASA, having
withstood high amounts of 203 MeV proton radiation damage, over 1014 (p/cm2), in
experiments conducted at the IUCF [1]. The Cree SiC part numbers tested for this I-V
characterization study were the CSD04060A (4 A, 600V), CSD10060A (10 A, 600 V),
and CSD10120A (10 A, 1200 V).
46
The Cree SiC Schottky power diodes were packaged in TO-220-2 packages,
which contain only 1 diode per package. The Cree diodes that were tested are given in
Table 3.2 along with their corresponding voltage and current ratings. Comparing Table
3.1 and Table 3.2, the Cree SiC Schottky diodes have higher breakdown voltages than
the Si diodes. 4H-SiC has a higher electric field breakdown compared with Si, due to its
larger bandgap (E g ), so higher breakdown voltages are possible using 4H-SiC, as
discussed in more detail at the beginning of Chapter 3.
Current Rating
Voltage Rating
(A)
(V)
CSD04060A
4
600
CSD10060A
10
600
CSD10120A
10
1200
Part Number
Table 3.2. The Cree SiC Schottky power diode part numbers tested in this research project along with
their current and voltage ratings. These diodes were packaged in TO-220-2 packages, which contain only
one diode per package.
3.2.4 Irradiation Procedure
The rabbit facility of the Ohio State University Research Reactor (OSURR),
described in section 2.3.1, was used as the radiation source for all the radiation hardness
testing reported in this dissertation. Three of each diode part number were irradiated in
the rabbit facility. For irradiations in the rabbit facility, a pneumatic tube is used to
transport samples into a high flux region that is adjacent to the reactor core, shown in
Figure 2.4. In our application of the rabbit facility, a group of diodes, each having the
same part number, were placed inside a plastic bottle lined with cadmium to minimize
47
activation by thermal neutron absorption and the associated radiation hazard, since
thermal neutrons are expected to contribute negligible damage to the semiconductor
material. This irradiation procedure was repeated for each of the diode part numbers
listed in Table 3.1 and Table 3.2.
For all of the irradiations in the rabbit facility, the reactor was operated at a
nominal power of 450 kW. However, the data was recorded from the power monitor at
the OSURR, which records the actual, measured, reactor power for every dt = 0.1
seconds. The displacement damage dose rates for a reactor operating power of 450 kW
are given in Table 2.1 for both Si and SiC. Therefore, in order to determine D d for Si,
kW
9 MeV
for example, for which D d450
from Table 2.1, Equation 3.6 was used
, Si = 1.1× 10
g s
in order to calculate the cumulate dose. In Equation 3.6 t in and t out are the times that the
sample was placed in and taken out of the rabbit facility, respectively. Furthermore in
Equation 3.6, P(t) is the recorded power from the power monitor, in units of kW. This
procedure and calculation were performed for each of the irradiations in order to
determine the time-integrated quantities listed in Table 2.1.
Dd ,Si =
kW
D d450
, Si
tout
450 kW ∫t
P (t )dt
3.6
in
3.2.4 I-V Characterization Procedure
I-V characterization was conducted prior to irradiation and after each incremental
irradiation dose in the rabbit facility. Four-wire, Kelvin measurements were used for all
I-V measurements, in order to minimize cable effects associated with two-wire
48
measurements. As discussed in section 3.2.1, the Keithley 2410 was used for the lowinjection, forward bias I-V characterization of both the Si and SiC Schottky power
diodes, as well as for the reverse bias I-V characterization of the Si Schottky power
diodes. The Keithley 2430 was used for the high-injection forward bias I-V
characterization of the SiC Schottky power diodes. However, since some of the current
ratings of the Si diodes, as shown in Table 3.1 were higher than could be measured using
the Keithley 2430 Source Meter, which is limited to currents of 10 A or lower, the
Tektronix 371B curve tracer was required for high current measurements of the Si
Schottky diodes.
3.3
Diode Low-Injection, Forward-Biased I-V Characterization Results
Unirradiated and irradiated low-injection, forward-biased I-V curves of a Cree
SiC Schottky power diode, part number CSD04060A (4 A, 600V), are shown in Figure
3.6, in log-linear scale. Likewise, the unirradiated and irradiated low-injection, forwardbiased I-V curves of an IR10CTQ150PBF (5 A, 150V) IR Silicon Schottky power diode,
are shown together in Figure 3.7, in log-linear scale. For the purpose of clarity, only the
unirradiated curve and the irradiated curve corresponding to the last measurement and
thus highest dose received for this diode are shown in Figure 3.6 and Figure 3.7. The IV curves in Figure 3.6 and Figure 3.7, as mentioned in section 3.2.4, were measured
using the Keithley 2410, and are representative of all the unirradiated and irradiated lowinjection I-V curves of the Cree SiC Schottky and IR Si Schottky power diodes tested in
this study. That is, there is very little noticeable change in the low-injection, forwardbias I-V curves of all the SiC and Si Schottky power diodes, indicating that the metal49
semiconductor junction has not degraded, since for low-injection, forward-bias
operation, the diode voltage, V D , can be assumed to be dropped entirely across this
metal-semiconductor junction, as discussed in section 3.1.
Figure 3.6. Unirradiated and post-irradiation low-injection, forward-biased I D vs. V D curves of one of the
three CSD04060A (4 A, 600 V) diodes tested in this study. For the purpose of clarity, only the
unirradiated curve and the irradiated curve corresponding to the last measurement and thus highest dose
received for this diode are shown. The ideal, exponential portion of the I-V curve is circled in green.
50
Figure 3.7. Unirradiated and post-irradiation low-injection, forward biased I D vs. V D curves for one of the
three IR10CTQ150PBF (5 A, 150 V) IR Si Schottky power diodes tested in this study. For the purpose of
clarity, only the unirradiated curve and the irradiated curve corresponding to the last measurement and
thus highest dose received for this diode are shown.
Also, the linear portions of the I-V curves shown in Figure 3.6 and Figure 3.7 are
circled. These linear regions are a consequence of Equation 3.1, for which an
exponential dependence of I D on V D is represented by a straight line on a log-linear plot.
3.4
MATLAB Curve-Fitting Analysis of Low-Injection, Forward-Bias Data
As a first step in our quantitative analysis, Equation 3.1 was fit to the low-
injection, forward-bias I-V measurements made with the Keithley 2410, for the Si and
SiC Schottky power diodes, in order to determine the trend of n and I s as a function of
neutron dose. The non-linear least squares function in MATLAB 7.0 was used to fit the
low-injection data to Equation 3.1, and this non-linear least squares function requires
initial estimates for n and I s . From Equation 3.1, assuming the exponential is
sufficiently larger than 1, which is true for the linear regions in Figure 3.6 and Figure
51
 qV
3.7, I D ≈ I s exp  D
 nkT

 . Therefore, plotting ln(I D ) vs. V D will yield a straight line of

the form y = mx + b, where nestimate =
q
and I s ,estimate = exp ( b ) . These estimates for
mkT
n and I s were used as input to the MATLAB 7.0 least-squares curve-fitting function,
namely lsqcurvefit(), to determine more accurate values for n and I s , using Equation 3.1.
Results of the low-injection, forward-biased curve-fit for the Cree SiC power
diodes are shown in Tables 3.3-3.5. In addition, results for the forward-biased curve-fit
for the IR Si Schottky power diodes are shown in Tables 3.6-3.9. The values for the fit
parameters are reported in the form <value> ± σ; unless the standard deviation was 0
for the three diodes, in which case only the average was reported, which was the case for
some of the ideality coefficients. The exception to this was the data for part number
IR40CTQ150PBF, shown in
Table 3.15, for which there was only one diode, and therefore only the average is
reported. It should be noted that the value of σ that is reported is the sample standard
deviation and not the standard deviation of the mean. Generally, the curve fits were
quite good, with R2 values nearly equal to 1. The behaviors of n and I s generally give a
good indication of the material integrity of the junction, since in Equation 3.1, it is
assumed that the entire voltage drop across the diode is applied across its metalsemiconductor junction. As shown in Tables 3.3-3.9, the values for n and I s change very
little with respect to D d , indicating that the electrical properties of the metalsemiconductor junction (Schottky contact) are not changing with increasing
displacement damage, which is consistent with the I-V curves in Figure 3.6 and Figure
3.7. Furthermore, the values for I s for the Si diodes are much greater than those for the
52
SiC diodes. This is consistent with the discussion in the beginning of Chapter 3, relating
the disadvantage of Si Schottky diodes having relatively larger leakage currents, as a
result of having a bandgap approximately three times smaller than that of 4H-SiC.
D d (MeV/g) in SiC
0
6.5E+10
1.3E+11
1.9E+11
2.6E+11
n (unit-less)
1.030
1.031 ± 0.002
1.030 ± 0.003
1.031 ± 0.002
1.031 ± 0.002
I s (A)
(8 ± 1)E-17
(10 ± 2)E-17
(9 ± 1)E-17
(9.4 ± 0.9)E-17
(9 ± 2)E-17
Table 3.3. Results of curve fitting for forward-biased low-injection region for Cree CSD04060A (4 A,
600 V) SiC Schottky power diodes.
D d (MeV/g) in SiC
0.00E+00
9.7E+10
2.0E+11
2.9E+11
3.9E+11
4.9E+11
5.5E+11
6.2E+11
6.8E+11
7.5E+11
n (unit-less)
1.0309 ± 0.0008
1.024 ± 0.006
1.031 ± 0.001
1.027 ± 0.006
1.030
1.032 ± 0.001
1.030
1.02 ± 0.02
1.024 ± 0.006
1.027 ± 0.006
I s (A)
(2.4 ± 0.4)E-16
(2.0 ± 0.2)E-16
(2.5 ± 0.4)E-16
(2.3 ± 0.7)E-16
(2.3 ± 0.5)E-16
(2.4 ± 0.6)E-16
(2.2 ± 0.6)E-16
(2 ± 1)E-16
(1.8 ± 0.7)E-16
(1.8 ± 0.6)E-16
Table 3.4: Results of curve fitting for forward-biased low-injection region for Cree CSD10060A (10 A,
600 V) SiC Schottky power diodes.
53
D d (MeV/g) in SiC
0
9.7E+10
2.0E+11
2.9E+11
3.9E+11
4.9E+11
n (unit-less)
1.031 ± 0.001
1.028 ± 0.007
1.031 ± 0.002
1.032 ± 0.002
1.029 ± 0.006
1.028 ± 0.007
I s (A)
(3.0 ± 0.1)E-16
(2.8 ± 0.5)E-16
(3.0 ± 0.2)E-16
(3.0 ± 0.1)E-16
(2.7 ± 0.5)E-16
(2.5 ± 0.6)E-16
Table 3.5: Results of curve fitting for the forward-biased low-injection region for Cree CSD10120A (10
A, 1200 V) SiC Schottky power diodes.
D d (MeV/g) in Si φeq ,1MeV ,Si
0
1.6E+11
3.3E+11
4.9E+11
6.5E+11
8.1E+11
0
7.8E+13
1.6E+14
2.3E+14
3.1E+14
3.9E+14
n (unit-less) I s (A)
1.057
1.045
1.061
1.092
1.151
1.115
2.52E-07
1.62E-07
1.87E-07
2.64E-07
3.96E-07
2.78E-07
Table 3.6 Results of curve fitting for the forward-biased low-injection region for IR IR40CTQ150PBF (20
A, 150 V) Si Schottky power diodes. Only the average is reported, since there was only one
IR40CTQ150PBF diode in the sample.
D d (MeV/g) in Si φeq ,1MeV ,Si
n (unit-less)
I s (A)
0
1.6E+11
3.3E+11
4.9E+11
6.5E+11
8.1E+11
1.057 ± 0.008
1.035 ± 0.008
1.031 ± 0.001
1.038 ± 0.006
1.042 ± 0.003
1.047 ± 0.002
(3.1 ± 0.5)E-7
(1.9 ± 0.2)E-7
(1.83 ± 0.06)E-7
(2.1 ± 0.3)E-7
(2.1 ± 0.1)E-7
(2.23 ± 0.008)E-7
0
7.8E+13
1.6E+14
2.3E+14
3.1E+14
3.9E+14
Table 3.7. Results of curve fitting for the forward-biased low-injection region for IR IR43CTQ100 (20 A,
100 V) Si Schottky power diodes.
54
D d (MeV/g) in Si φeq ,1MeV ,Si
n (unit-less)
I s (A)
0.00E+00
8.3E+10
1.6E+11
2.5E+11
3.3E+11
4.1E+11
1.10 ± 0.03
1.095 ± 0.004
1.08 ± 0.03
1.09 ± 0.03
1.09 ± 0.01
1.12 ± 0.04
(3 ± 2)E-7
(2.2 ± 0.4)E-7
(2 ± 1)E-7
(2.1 ± 0.7)E-7
(2.2 ± 0.7)E-7
(3 ± 1)E-7
0.00E+00
3.9E+13
7.8E+13
1.2E+14
1.6E+14
2.0E+14
Table 3.8. Results of curve fitting for the forward-biased low-injection region for IR IR10CTQ150PBF (5
A, 150 V) Si Schottky power diodes.
D d (MeV/g) in Si
φeq,1MeV ,Si
n (unit-less)
I s (A)
0.00E+00
8.3E+10
1.6E+11
2.5E+11
3.3E+11
4.1E+11
0.00E+00
3.9E+13
7.8E+13
1.2E+14
1.6E+14
2.0E+14
1.09 ± 0.01
1.069 ± 0.002
1.090 ± 0.009
1.085 ± 0.009
1.10 ± 0.03
1.11 ± 0.02
(7.1 ± 0.3)E-7
(5.4 ± 0.4)E-7
(6.5 ± 0.9)E-7
(6 ± 1)E-7
(7 ± 2)E-7
(7.8 ± 0.7)E-7
Table 3.9. Results of curve fitting for the forward-biased low-injection region for IR IR60CTQ150PBF
(30 A, 150 V) Si Schottky power diodes.
3.5
Diode High-Injection, Forward-Biased I-V Characterization Results
Unirradiated and irradiated high-injection, forward-biased I-V curves of a Cree
SiC Schottky power diode, part number CSD10120A (10 A, 1200 V) are shown in
Figure 3.8. The high-injection I-V curves shown in Figure 3.8 are representative of all
the unirradiated and irradiated high-injection I-V curves of the SiC and Si Schottky
power diodes in this study. As discussed in section 3.1, for high-injection, forward-bias,
a portion of the total diode voltage is dropped across the neutral regions of the diode,
away from the depletion region. Therefore, Equation 3.3 applies, and the effects of R s
on the diode I-V curve cause the curve to deviate from the exponential behavior seen at
55
low-injection, and to become more linear at higher forward currents, as shown in Figure
3.2.
Figure 3.8. Unirradiated and post-irradiation high-injection, forward-biased I D vs. V D curves of one of
the three CSD10120A (10 A, 1200 V) diodes tested in this study. These I-V curves are representative of
the high-injection, forward-bias I-V curves for all of the Cree SiC Schottky power diodes tested in this
study.
Unirradiated and irradiated high-injection, forward-biased I-V curves of an IR Si
Schottky power diode, part number IR60CTQ150PBF (30 A, 150 V) are shown in
Figure 3.9. The high-injection I-V curves shown in Figure 3.9 are representative of all
the unirradiated and irradiated high-injection I-V curves of the Si Schottky power diodes
in this study. All of the International Rectifier Si Schottky diodes tested in this study
have two junction turn-ons [2], as shown by Figure 3.9. The first turn-on is the turn-on
of the Schottky contact, which occurs around 0.3 V. The second turn-on is the turn-on
of the p-n guard ring (shown in Figure 3.1), which occurs around 0.6 V to 0.7 V for the
56
unirradiated diode. This behavior can be easily seen by noting the change in slope
around 0.6 V in the high forward current I-V curve. These two junctions (Schottky
contact and p-n guard ring) are in parallel, and so the sum of the current through the
diode is the sum of the currents flowing through the two junctions. Since the two
junctions can be easily separated, due to their large threshold voltage difference, only the
Schottky region of the curve was fitted, so as to be able to relate the results that are
obtained here with the results of previous studies [2] of these particular diodes. The red,
dashed ellipse in Figure 3.9 indicates the portion of the I-V curve dominated by the
Schottky contact.
Figure 3.9. Unirradiated and post-irradiation high-injection, forward-biased I D vs. V D curves of one of
the three IR60CTQ150PBF (30 A, 150 V) IR Si Schottky power diodes tested in this study. These I-V
curves are representative of the high-injection, forward-bias I-V curves for all of the IR Si Schottky power
diodes tested in this study.
57
3.6
MATLAB Curve-Fitting Analysis of High-Injection, Forward-Bias Data
For the SiC diodes in this study, as the next step in our quantitative analysis,
Equation 3.3 was fit to the high-injection, forward-bias I-V measurements made with the
Keithley 2430, in order to determine the trend of R s as a function of neutron dose. The
non-linear least squares function in MATLAB 7.0 was used to fit the high-injection data
by first inserting the values for n and I s determined from the low-injection, least-squares
curve-fit analysis described in section 3.4, into Equation 3.3. For the initial estimate of
R s , to the MATLAB non-linear least squares function, R on was used, as shown in Figure
3.2. As shown in Figure 3.2, R on is simply the inverse slope of the high current region,
assuming a piece-wise linear model of the power diode. The non-linear least squares
function was then applied to Equation 3.3 using the high-injection forward-bias data in
order to determine a best estimate for R s , consistent with the analysis performed on the
IUCF proton data [1].
The results of R s versus displacement damage dose in SiC are shown in Figure
3.10 for the Cree SiC Schottky power diodes tested in this study. The error bars in
Figure 3.10 represent ± σ, where σ is the standard deviation of the sample containing 3
diodes of the same part number. As shown in Figure 3.10, the series resistance, R s ,
increases as a function of neutron-induced displacement damage dose in SiC for all three
diode models. These results are consistent with the discussion in section 3.1. That
is, RS ∝
1
qµn n
, and both the electron mobility, µn , and the electron carrier concentration,
n , are expected to decrease as a result of displacement damage, as discussed in section
2.1, by the processes given in Figure 2.1.
58
Figure 3.10. R s as a function of displacement damage dose in SiC, for the Cree SiC Schottky power
diodes tested in this study. Trend lines are included in order to guide the eye.
For the IR Si Schottky power diodes, the high-injection, forward-bias I-V
measurements made with the Tektronix 371B curve tracer were fit with Equation 3.3,
using the same method described for processing the forward-bias, high-injection data for
the Cree SiC Schottky power diodes. However, for the IR Si Schottky power diodes,
only the portion of the high-injection I-V curve dominated by the Schottky contact,
circled in red in Figure 3.9, was used, consistent with the analysis published by Harris
[2].
The results of R s versus displacement damage dose in Si are shown in Figure
3.11 and Figure 3.12 for the IR Si Schottky power diodes tested in this study. As shown
in Figure 3.11 and Figure 3.12, the series resistance, R s , increases as a function of
neutron-induced displacement damage dose in Si for all four Si Schottky diode models.
As shown in Figure 3.12, for the IR43CTQ100 diode, R s increases at a slower rate for
this diode than for the other diodes, most likely since it has a higher free carrier
59
concentration than the other Si diodes [49]. This can be viewed as a consequence of the
dopant density being inversely proportional to the breakdown voltage, as discussed in
the beginning of Chapter 3. A higher dopant density, in turn, generally leads to greater
radiation hardness, as the diode has more free carriers to spare.
Figure 3.11. R s as a function of displacement damage dose in Si, for IR10CTQ150PBF and
IR40CTQ150PBF diodes. Only the average is reported for the IR40CTQ150PBF diode, since only one
IR40CTQ150PBF diode was tested.
60
Figure 3.12. R s as a function of displacement damage dose in Si, for IR43CTQ100 and IR60CTQ150PBF
diodes.
3.7
Reverse Bias I-V Characteristics of Si and SiC Schottky Power Diodes
Although the reverse bias I-V characteristics of the Cree SiC Schottky power
diodes were not measured for this particular experiment, reverse bias I-V
characterization results are presented for CSD05120A (5 A, 1200V) Cree SiC Schottky
power diodes in Chapter 4. In short, the leakage currents of the SiC Schottky power
diodes were very low, and this was true for both unirradiated diodes as well as the most
highly irradiated diodes. Also, the breakdown voltage rating, V B , of the CSD05120A
diode is 1200 V, which is higher than can be measured using any of the equipment
available for this dissertation. No breakdown was observed for any of the unirradiated
and irradiated CSD05120A diodes, up to the maximum source voltage of the Keithley
2410 Source Meter, namely 1100 V.
61
In addition to the forward-bias I-V measurements made for the IR Silicon
Schottky barrier diodes, reverse-bias measurements were also made, using the Keithley
2410, which is suitable for high voltage (< = 1100 V) and low current measurements (<
= 1 A). A reverse-bias I-V curve for an IR43CTQ100 Si Schottky diode is shown in
Figure Figure 3.13, and is representative of all the Si Schottky diodes tested in this
research. In particular, the breakdown voltage, defined as the reverse-bias voltage at
which the reverse leakage current = 1 mA, decreases with increasing D d , but saturates at
a value above the manufacturer-rated breakdown voltage. Also, for all of the IR Si
Schottky diodes tested in this study, the reverse leakage currents, for an applied reverse
bias voltage of 90 % rated breakdown voltage, steadily increased with increasing D d , but
at a slow rate. Results for the breakdown voltages, as well as for the reverse leakage
currents measured at 90 % breakdown voltage, are given in Tables 3.10-3.13. The error
bars in Tables 3.10-3.13 represent ± σ, where σ is the sample standard deviation of the
sample containing 3 diodes of the same part number. However, only the average is
reported for the IR40CTQ150PBF, since only one diode of this part number was
available to test.
62
Figure 3.13. Reverse-bias I-V characteristics of an IR43CTQ100 (20 A, 100 V) Si Schottky power diode
as a function of φeq ,1MeV ,Si .
D d (MeV/g) in
Si
0
1.6E+11
3.3E+11
4.9E+11
6.5E+11
8.1E+11
φeq,1MeV ,Si
0
7.8E+13
1.6E+14
2.3E+14
3.1E+14
3.9E+14
Breakdown Votlage, V B ,
(V)
186
178
174
172
170
170
Reverse Leakge Current at 90%
V B (A)
1.60E-06
3.16E-06
5.47E-06
7.38E-06
9.28E-06
1.14E-05
Table 3.10. Reverse breakdown voltage and leakage current measurements of IR40CTQ150PBF (20 A,
150 V) Si Schottky power diodes.
D d (MeV/g) in
Si
0
1.6E+11
3.3E+11
4.9E+11
6.5E+11
8.1E+11
φeq,1MeV ,Si
0
7.8E+13
1.6E+14
2.3E+14
3.1E+14
3.9E+14
Breakdown Votlage,
V B , (V)
113 ± 1
108
104 ± 1
103 ± 1
103 ± 1
103 ± 1
Reverse Leakge Current at 90%
V B (A)
(2.7 ± 0.2)E-7
(3.7 ± 0.1)E-7
(5.1 ± 0.1)E-7
(6.6 ± 0.3)E-7
(8.2 ± 0.1)E-7
(1.03 ± 0.06)E-5
Table 3.11. Reverse breakdown voltage and leakage current measurements of IR43CTQ100 (20 A, 100 V)
Si Schottky power diodes.
63
D d (MeV/g) in
Si
0.00E+00
8.3E+10
1.6E+11
2.5E+11
3.3E+11
4.1E+11
φeq,1MeV ,Si
0.00E+00
3.9E+13
7.8E+13
1.2E+14
1.6E+14
2.0E+14
Breakdown Votlage,
V B , (V)
203 ± 4
196 ± 8
190 ± 9
187 ± 9
186 ± 9
186 ± 9
Reverse Leakge Current at 90%
V B (A)
(2.1 ± 0.8)E-7
(2.5 ± 0.5)E-7
(3.0 ± 0.6)E-7
(3.4 ± 0.6)E-7
(4.1 ± 0.8)E-7
(4.1 ± 0.6)E-7
Table 3.12. Reverse breakdown voltage and leakage current measurements of IR10CTQ150PBF (5 A, 150
V) Si Schottky power diodes.
D d (MeV/g) in
Si
0.00E+00
8.3E+10
1.6E+11
2.5E+11
3.3E+11
4.1E+11
φeq,1MeV ,Si
0.00E+00
3.9E+13
7.8E+13
1.2E+14
1.6E+14
2.0E+14
Breakdown Votlage,
V B , (V)
182 ± 2
179 ± 1
175 ± 1
173 ± 1
173 ± 1
173 ± 1
Reverse Leakge Current at 90%
V B (A)
(6.1 ± 0.7)E-7
(7.6 ± 0.3)E-7
(9.9 ± 0.4)E-7
(1.16 ± 0.08)E-5
(1.43 ± 0.06)E-7
(1.66 ± 0.09)E-7
Table 3.13. Reverse breakdown voltage and leakage current measurements of IR60CTQ150PBF (30 A,
150 V) Si Schottky power diodes.
3.8
Neutron-Proton Equivalency
From the discussion in section 3.1, and from the data and analysis published by
Harris for the IUCF proton irradiations [1,2,49], we expect the radiation-induced
increase in R s of these diodes, as shown in Figure 3.11 and Figure 3.12 to be primarily
due to carrier-removal from neutron-induced displacement damage. Also, we assume
that the displacement damage is sufficiently low that the Fermi level remains essentially
1
constant, such that Equation 3.5 applies. Since Rs ∝ ρ =
, as discussed in section
qµn n
64
3.1, substituting the expression for n as a function of neutron fluence (Ф n ), which is
proportional to displacement damage dose, we obtain Equation 3.7:
1 n0 − K n Φ n
,
=
Rs
C
3.7
where we denote K n as the carrier removal rate for the neutron spectrum in the OSURR
rabbit facility and C as a constant dependent on the geometry of the active area of the
device. Therefore, neglecting the effects of D d on μ, from Equation 3.7, a plot of
1
versus D d , which is proportional to Ф n , should yield a straight line having a slope
Rs
proportional to K n .
The results of
1
versus D d , for representative, individual diodes, are shown in
Rs
Figure 3.14 for the IR Si Schottky power diodes, and Figure 3.15 for the Cree SiC
Schottky power diodes. The good linear fits to the data, with respect to neutron-induced
D d , as shown by Figure 3.14 and Figure 3.15, indicate that the increase in series
resistance, R s , is due to carrier removal caused by neutron-induced displacement
damage. Furthermore, Figure 3.14 and Figure 3.15 also indicate that the increase in R s
of the Si and SiC diodes can be predicted using Equation 3.7. The slopes of the trendlines in Figure 3.14 and Figure 3.15 are proportional to K n , as shown by Equation 3.7.
65
Figure 3.14. Graph of R s -1 versus D d in Si for representative, individual IR Silicon Schottky diodes
having part numbers 10CTQ150PBF (5 A, 150 V), 40CTQ150PBF (20 A, 150 V), 60CTQ150PBF (30 A,
150 V), and 43CTQ100 (20 A, 100 V).
66
Figure 3.15. Graph of R s -1 versus D d in SiC for representative, individual Cree SiC Schottky power
diodes having part numbers CSD10060A (10 A, 600V), CSD10120A (10 A, 1200 V), and CSD04060A (4
A, 600 V).
In order to be able to predict the rate of degradation of the Schottky diodes in the
high-energy proton radiation field of the IUCF on the basis of D d for the neutron field,
Equation 3.8 should be satisfied [27]:
K n S NIEL, n
,
=
K p S NIEL, p
3.8
where, K p is the carrier removal rate in the proton radiation field, and S NIEL, n and S NIEL, p
are the effective NIEL values for the neutron and proton radiation fields, respectively.
Equation 3.8 indicates that if S NIEL, n and S NIEL, p are known, then K p can be determined
from K n , and vice versa. The values for S NIEL, p ,Si and S NIEL, p ,SiC obtained from this
67
study are listed in Table 2.3 as 1.91E-3 (MeV·cm2/g) and 1.52E-3 (MeV·cm2/g),
respectively. The cumulative flux in the OSURR rabbit facility, obtained by integrating
the energy-dependent neutron spectrum shown in Figure 2.5 with respect to energy, is
MeV
2.6E12 (n/cm2/s) at 450 kW. Therefore, dividing the values of D d ,Si = 1.1×109
g s
MeV
and D d ,SiC = 1.2 ×109
, listed in Table 2.1, by the cumulative flux in the OSURR
g s
rabbit facility yields effective values of S NIEL, n,Si = 4.2E-4 (MeV·cm2/g) and
S NIEL, n,SiC = 4.6E-4 (MeV·cm2/g). Therefore,
S NIEL, n,SiC
S NIEL, p , SiC
S NIEL, n,Si
S NIEL, p , Si
= 0.22 and
= 0.30 , meaning that on average and per unit fluence, neutrons in the
OSURR rabbit facility impart 22 % as much displacement damage energy in Si and 30
% as much displacement damage energy in SiC as the 203 MeV beam at the IUCF.
With respect to the Cree SiC Schottky power diode data from the IUCF proton
radiation studies, tabulated values for R s are given in [1] for part numbers CSD10120A
and CSD10060A. Furthermore, a graph of R s -1 for part number CSD04060A as a
function of proton fluence can be found in [49]. By performing a linear fit of R s -1 versus
proton fluence for the data found in [1], the slopes of the lines and therefore the values
of
Kp
C
, as shown in Equation 3.7, for each Cree SiC diode were obtained. The constant
C in Equation 3.7 is related to the geometry of the active area of the diode, and is
assumed to be different for diodes having different part numbers, but is expected to be
68
equal for diodes having the same part numbers. In addition, values of
Kn
for all of the
C
nine Cree SiC Schottky diodes were calculated from a linear fit of R s -1 versus cumulative
neutron fluence, Φ n , in the OSURR rabbit facility, which can be found by dividing the
D d values on the dependent-variable axis in Figure 3.15 by S NIEL, n,SiC .
The results for
the Cree SiC Schottky power diodes are reported separately for each part number in
Table 3.14, in the form of
Kn
C
Kn
± σ n,sample ,
C
Kn
K
C
= n , and
Kp
Kp
C
 S NIEL,n,SiC

 S NIEL, p ,SiC
K

 n, SiC 
 K p, SiC 




 ; where,
is the average of the slope of the linear fit of R s -1 versus Φ n among the three
diodes of each part number (sample), and σ n,sample is the standard deviation of
Kn
C
for the sample.
In particular, the final result of the neutron-proton equivalency is represented by
the ratio quantity in the right-most column of Table 3.14. Generically speaking, if this
ratio is close to unity, then Equation 3.8 is satisfied, which indicates that the surviving
fraction of interstitial-vacancy pairs is independent of PKA energy, and that the
remaining stable defects affect the carrier-removal rates to the same degree, regardless of
whether they originated from a sub-cascade or from an isolated interstitial-vacancy pair
[54]. On the other hand, if this ratio quantity is less than unity, then
( K n / S NIEL,n ) > ( K p / S NIEL, p ) , and therefore neutrons are expected to remove more
carriers than protons per D d . Conversely, if the ratio quantity in the right-most column
69
of Table 3.14 is greater than unity, then protons are expected to remove more carriers,
and thus increase R s to a greater extent than neutrons on a per unit D d basis.
Cree SiC Schottky
K n,SiC
Diode
C
± σ n,sample
K n,SiC
K p ,SiC
Part Number
(cm2/Ω)
CSD04060A
(4.9 ± 0.1)E-15
0.21
CSD10060A
(1.23 ± 0.08)E-14
0.19
CSD10120A
(1.06 ± 0.01)E-14
0.19
 S NIEL,n,SiC

 S NIEL, p ,SiC



 S NIEL,n,SiC

 S NIEL, p ,SiC
K

 n, SiC 
 K p, SiC 


1.5
0.30
1.6
1.6
Table 3.14: Results of neutron-proton equivalency for Cree SiC Schottky power diodes. The final result
of the equivalency is represented by the ratio quantity in the right-most column, explained further in the
text.
Pease [53] calculated and compared carrier-removal rates in Si for neutrons and
protons, by performing I-V characterization on irradiated Si power MOSFETs, and
reported his results with respect to neutron radiation in terms of φeq ,1MeV ,Si . In general,
the data obtained by Pease, in the form of
values of
MeV
S 1NIEL
,n, Si
S NIEL , p , Si
K n,1MeV ,Si
K p ,Si
, was in good agreement with the
calculated by Burke [45], where K n,1MeV ,Si is the carrier-removal
MeV
rate in Si for 1 MeV neutrons, and S 1NIEL
,n, Si is the NIEL value for 1 MeV neutrons.
However, at a proton energy of 175 MeV, the highest proton energy at which the
70



MOSFETs were irradiated, the experimental values of
MeV
S 1NIEL
,n, Si
S NIEL, p ,Si
K n,1MeV ,Si
K p ,Si
were lower than
by a factor of about two [53]. Therefore, we report the results of the neutron-
proton equivalency study for the IR Si Schottky power diodes in Table 3.15 on the basis
of φeq ,1MeV ,Si in order to extend the study by Pease to include experimental data with
respect to 200 MeV proton radiation. In order to accomplish this, the values of
K n,1MeV ,Si for this study were obtained by performing a linear fit of R s -1 versus
φeq,1MeV ,Si for the IR Si Schottky diode data. Furthermore, we use the value of
2.04 ×10
−3
MeV cm 2
for S NIEL,n,1MeV ,Si , as reported by Akkerman [27]. With respect
g
to the Si Schottky power diode data from the IUCF proton radiation studies, tabulated
values for R s are given in [2] for part numbers IR40CTQ150 and IR43CTQ100.
Furthermore, a graph of R s -1 for part numbers IR60CTQ150PBF and IR10CTQ150PBF
as a function of proton fluence can be found in [49].
71
K n,1MeV ,Si
IR Si Schottky Diode
Part Number
K n,1MeV ,Si
C
± σ n,sample
K p ,Si
MeV
S 1NIEL
,n, Si
S NIEL , p , Si
(cm2/Ω)
IR40CTQ150 PBF
IR43CTQ100
3.87E-14
1.2
(4.62 ± 0.05)E-14
0.95
MeV
 S 1NIEL

,n, Si


 S NIEL , p , Si 


K

 n,1MeV , Si 
 K p, Si 


0.91
1.1
1.1
IR60CTQ150PBF
(6.8 ± 0.5)E-14
1.6
0.68
IR10CTQ150PBF
(1.44 ± 0.02)E-14
1.3
0.85
Table 3.15. Results of neutron-proton equivalency for IR Silicon Schottky power diodes in terms of
Φ eq,1MeV,Si . The final result of the equivalency is represented by the ratio quantity in the right-most column.
In summary, the results of the neutron-proton equivalency with respect to carrierremoval in Si and SiC, for protons having energies of approximately 200 MeV, are
comparable to those from a previous study that compared neutron and proton carrier
removal rates for irradiations with fission neutrons and proton energies of and below 175
MeV [53], with regard to satisfying Equation 3.8. As demonstrated in Chapter 2, NIEL
can be calculated using differential cross sections and interaction kinematics, and does
not consider the microscopic properties of the displacement damage, such as the
interactions of defects following the initial atomic displacements.
With respect to the SiC power diodes, the ratio quantity in the right-most column
of Table 3.14 suggests that the protons from the 203 MeV proton beam are
approximately 1.6 times more effective in removing carriers in the SiC diodes as the
neutrons with the OSURR neutron spectrum per unit D d,SiC . This ratio quantity, for the
72
Si Schottky diodes, is closer to unity than for the SiC diodes, which can be seen
comparing the results for the SiC and Si diodes, shown in Table 3.14 and Table 3.15,
respectively. For the IR60CTQ150PBF diode, for which this ratio quantity is furthest
from unity among the IR Si Schottky diodes, σ n,sample is the greatest.
73
CHAPTER 4 : FUNCTIONAL TESTING OF SILICON CARBIDE SCHOTTKY
POWER DIODES: HALF-WAVE RECTIFIERS
In addition to I-V characterization testing, functional testing is also used in order
to test the SiC Schottky power diodes’ conduction and rectifying properties in an actual
power electronic circuit. From the I-V characterization testing in Chapter 3, it was
determined that the SiC Schottky power diodes show promise for high voltage
applications in mixed neutron and gamma-ray radiation fields, such as that encountered
in the proximity of a nuclear reactor, in that the electrical performance parameters
indicating the integrity of the Schottky contact, namely n and I s , changed very little as a
function of radiation dose. Therefore, the focus of this chapter is on the use of these SiC
Schottky diodes in a high-voltage, half-wave rectifying circuit. The half-wave rectifying
circuit is very simple, and the conduction and rectifying properties of the diode in the
circuit can be readily observed from voltage and current waveforms.
4.1
Experimental Methodology
From the I-V characterization study, it is evident that SiC Schottky power diodes
show promise for high-voltage applications in radiation environments; therefore, the
focus of this functional testing study is on diodes having high voltage-ratings. In
particular, a total of 18 diodes of part number CSD05120A (5 A, 1200 V) were used as
test subjects for this study.
74
4.1.1 Irradiation Procedure
All of the irradiations in this functional testing study were performed in the
OSURR rabbit facility. Prior to irradiation, the diodes, in groups of three, were covered
in cadmium and placed inside a polyethylene bottle. One group of three diodes
remained unirradiated in order to serve as the control group. All irradiations and
measurements were performed at room temperature, and the reactor was operated at a
nominal power of 450 kW, for a nominal displacement damage dose rate, in SiC, of
kW
9 MeV
, as shown in Table 2.1. Dosimetry was performed by
D d450
, SiC= 1.2 × 10
g s
integrating under the power monitor curve, as discussed in section 3.2.4, and shown by
Equation 3.6. Following irradiation, after an appropriate time, which allowed for the
radioactivity of the samples to decay to the point that the diodes could be safely handled,
the diodes were tested. For each group (sample) of three diodes, the corresponding
D d,SiC to which the group was irradiated in the OSURR rabbit facility are displayed in
Table 4.1 for part number CSD05120A.
75
CSD05120A Group
Dd ,SiC
(#)
(MeV/g)
Unirradiated Control
0
1
4.7E+10
2
9.3E+10
3
1.4E+11
4
1.9E+11
5
2.3E+11
Table 4.1. Correspondence between each group (sample) of three CSD05120A diodes and the D d
(MeV/g) to which it was exposed in the OSURR rabbit facility.
4.1.2 Pre- and Post-Irradiation I-V Characterization
In addition to the functional testing performed on the SiC diodes, I-V
characterization was also performed, in order to better analyze the performance of the
diodes as they operated in the half-wave rectifier circuit. I-V measurements were made
with two different instruments for forward and reverse bias diode conditions, using a
subset of the apparatus shown in Figure 3.3 and Figure 3.4. A Keithley 2410, being
well-suited for low current, high voltage measurements, was used to make I-V
measurements under conditions of reverse bias and for low injection, forward bias
conditions. A Keithley 2430, having the capability for operation for currents as large as
10 A, was used for high injection, forward bias measurements. For both Keithley
devices, each device lead was attached to two sets of wires, one for signal application
and the other for sense measurement. This I-V measurement setup enabled 4-wire
76
measurements, and thereby reduced the effects of the cables on the measurement results.
The I-V curves of the diodes were characterized at an ambient temperature of T = 20  C,
as measured by the Hewlett Packard 2802A thermometer.
4.1.3 Functional Testing Apparatus and Procedure for Half-Wave Rectifier Circuits
The functional testing apparatus used for testing the half-wave rectifying circuits
is shown in Figure 4.1. The half-wave rectifier circuit that was tested, using the
CSD05120A diode is shown in Figure 4.2, and the schematic of this circuit is shown in
Figure 4.3. For all tests, an input voltage consisting of an AC 60 Hz, 170 V rms voltage
source was used, from the California Instruments power supply. The diodes were
attached to a water-cooled, aluminum block while being tested. A thermocouple was
attached to the block as well as to the copper heat sink of the diode TO-220 package. An
Opti-Temp chiller was used to cool the water circulating through this aluminum block.
For functional testing of the CSD05120A diodes, a 100 Ohm load resistor was used, and
for the PID controller of the Opti-Temp chiller, a low set-point of 20.5  C and a high setpoint of 21.5  C were used. A Yokogawa DL750 ScopeCorder, used to record the
voltage, current, and temperature waveforms of the circuit, is shown in Figure 4.4. A
laptop computer was used to retrieve the waveform data from the Yokogawa
ScopeCorder. In addition, the thermal pads of the diodes were coated with Arctic
Silver® 5 high-density polysynthetic silver thermal compound (99.9% silver) in order to
improve thermal conductivity between the thermal pads of the diodes and the waterchilled, aluminum block.
77
Figure 4.1. Functional test apparatus for testing of half-wave rectifying circuits.
Figure 4.2. The half-wave rectifier circuit, containing a Cree SiC Schottky diode, which is attached to the
aluminum, water-chilled block, shown in the back of the photograph. The transparent, plastic tubes at the
bottom of the photograph contain chilled water from the Opti-Temp chiller.
78
V+
V+
V-
CSD05120A
V+
I
100 Ohms
V-
VAMPL = 240 Vp-p
FREQ = 60 Hz
V-
0
Figure 4.3. A schematic representation of the half-wave rectifier circuit shown in Figure 4.2. One
CSD05120A diode was tested at a time, with 60 Hz sinusoidal, AC input voltage of 240.4 Vp-p (170
Vrms). A 100 Ohm load, from the high resistive load bank was used. Voltage and current markers are
shown to indicate the voltage and current measurements that were recorded by a Yokogawa Scopecorder,
DL750.
Figure 4.4. Yokogawa DL750 Scopecorder used for recording the voltage, current, and temperature
waveforms of the half-wave rectifying circuit, shown in Figure 4.2.
79
4.2
Results for I-V Characterization of CSD05120A Diodes
The I-V curves were characterized using the analysis methods discussed in
sections 3.3 – 3.7 relating to the SiC diodes. Results for n and I s are given in
Table 4.2 for the CSD05120A diodes.
CSD05120A Group
Unirradiated Control
1
2
3
4
5
D d (MeV/g) in SiC n (unit-less)
1.034 ± 0.001
0
I s (A)
(5.3 ± 0.4)E-16
1.0313 ± 0.0007 (4.6 ± 0.1)E-16
4.7E+10
9.3E+10
1.04 ± 0.01
(6 ± 1)E-16
1.4E+11
1.036 ± 0.002
(5.0 ± 0.4)E-16
1.9E+11
1.045 ± 0.002
(4.7 ± 0.6)E-16
2.3E+11
1.059 ± 0.008
(6.5 ± 0.9)E-16
Table 4.2. Results of curve fitting for forward-biased low-injection region for Cree CSD05120A (5 A,
1200 V) SiC Schottky power diodes.
Representative reverse bias I-V characteristics, for the most highly irradiated
diodes in this study, are shown in Figure 4.5 for a CSD05120A diode. The leakage
current has decreased as a result of the irradiation, consistent with the IUCF proton study
[1]. Schottky contacts are, in general, very resistant to radiation-induced degradation
[55], and therefore, even for the most highly irradiated diodes in this study, for which the
forward-bias I-V characteristics were severely degraded, the reverse bias characteristics
actually improved with increasing radiation dose. The lack of degradation in the reverse
bias I-V characteristics, for very high reverse blocking voltages, is a major advantage for
high-voltage SiC Schottky power diodes.
80
Figure 4.5. Reverse bias I-V characteristics of a CSD0510120A diode, pre- and post-irradiation. The
leakage current has decreased as a result of the irradiation.
In addition, using the methods described in section 3.6, results for R s , extracted
from Equation 3.3 using the high-injection forward-bias data taken with the Keithley
SourceMeter 2430, are shown in Figure 4.6 for CSD05120A diodes as a function of
D d,SiC .
81
Figure 4.6. R s versus D d for Cree CSD05120A SiC Schottky power diodes as a function of neutroninduced displacement damage dose.
4.3
Results for Functional Testing of CSD05120A Diodes
Representative output voltage waveforms, measured over the 100 Ohm resistor,
shown in Figure 4.3, for the half-wave rectifier circuits containing the CSD05120A
diodes, are shown in Figure 4.7 for selected levels of D d,SiC . In particular, the voltage
waveforms in Figure 4.7 were measured over three full cycles, and are shown for diodes
having R s values closest to the mean R s of their respective sample. In Figure 4.7, the
“flat” portions of the output voltage waveforms over the load resistor represent the
portion of the cycle that the diode is blocking voltage, and thus current-flow. The top
portion of the output voltage waveforms labeled “Detail” in Figure 4.7, for when the
diodes are conducting current, is shown enlarged in Figure 4.8. All of the CSD05120A
diodes were tested in half-wave rectifier circuits in this study, but only results from
82
diodes having R s nearest to the average R s for their respective group, for selected values
of D d,SiC , are shown in the figures containing waveform data, for the purpose of clarity.
Figure 4.7. Representative output voltage waveforms for three full cycles, over 100 Ohm load resistor, as
a function of D d,SiC for half-wave rectifier circuits containing CSD05120A diodes. The waveforms of
three diodes, irradiated to different doses, are shown. The D d,SiC values in this figure refer to the dose to
which the CSD05120A diodes were irradiated. The portion of the waveform labeled “Detail” is shown
enlarged in Figure 4.8.
83
Figure 4.8 Portion of output voltage waveform labeled “Detail” in Figure 4.7. The voltage over the load
resistor decreases with increasing radiation dose, indicating a larger voltage drop over the diode. As can
be inferred from this graph, the output voltage decreases slowly with respect to radiation dose for D d,SiC
less than 1.4E11 (MeV/g), but increases rapidly with radiation dose for larger values of D d,SiC .
As shown in Figure 4.8, the voltage over the load resistor decreases as the diode
becomes increasingly resistive, due to radiation-induced displacement damage. In fact,
the results of Figure 4.8 are consistent with the results shown in Figure 4.6, in which the
series resistance, R s , of the diode increases very slowly up to a D d,SiC value of 1.4E11
(MeV/g), over half of the total radiation dose to which the diodes were exposed. For
values of D d,SiC larger than 1.4E11 (MeV/g), R s begins to increase rapidly with
increasing displacement damage dose, which, in turn, leads to a rapidly increasing
voltage drop over the diode.
To illustrate, the voltage and current waveforms over the CSD05120A diode in
the half-wave rectifying circuit are shown in Figure 4.9, over 3 full cycles of the AC
84
sinusoidal input voltage source. The waveforms shown in Figure 4.9 are for the same
three diodes of Figure 4.7 and Figure 4.8, having R s values closest to the mean value of
R s for their respective group (sample). The negative portion of the voltage waveform
corresponds to the portion of the cycle when the diode is blocking current flow.
The
diode current, I D , shown in Figure 4.9, is shown enlarged in Figure 4.10, along with the
portion of the voltage waveform corresponding to the time the diode is conducting. The
waveforms shown in Figure 4.10 are consistent with the initial, slow increase in R s up to
approximately D d,SiC = 1.4E11 (MeV/g), followed by a rapid increase in R s for larger
doses, as shown in Figure 4.6.
Figure 4.9. Representative diode voltage and current waveforms, for 3 full cycles, for half-wave rectifier
circuits containing CSD05120A diodes. The portion of the waveform labeled “Detail” is shown in
Figure 4.10. The diode current, I D , was positive when the diode was conducting current and 0, otherwise,
as shown more clearly in Figure 4.10.
85
Figure 4.10. Portion of diode current and voltage waveforms labeled “Detail” in Figure 4.9. As shown in
there is very little leakage current for all levels of displacement damage dose, as the diode current, I D , is
nearly 0 for the non-conducting, voltage-blocking portion of the cycle. The voltage drop over the diode
increases very slowly with increasing radiation dose for just over half of the total D d,SiC to which the
diodes were exposed, but then increases rapidly thereafter.
As shown in Figure 4.10, the voltage over the diodes rapidly increase with
increasing D d,SiC , but the current through the circuit, and thus diode, remains essentially
constant. The fact that the current remains essentially constant with increasing radiation
dose is not surprising. Although the diode series resistance, R s , for the diode irradiated
to D d,SiC = 2.3E11 (MeV/g) is approximately 14 times the value of R s for the
unirradiated diode shown in Figure 4.10, the series resistance for the diode irradiated to
D d,SiC =2.3E11 (MeV/g) is still only 1.6 Ohms, which is very small compared to the load
resistance of 100 Ohms in the tested circuit shown in Figure 4.3. Therefore, our primary
concern is with regard to increasing power dissipation in the diodes as a function of
86
D d,SiC . Accordingly, results for average power dissipation, P D,C , in the diodes as they are
conducting current in forward bias are shown in Figure 4.11 as a function of D d,SiC . The
average diode power dissipation, during the portion of the cycle for which the diodes
were forward-biased, was calculated over three full cycles each lasting
T = 16.67 seconds, as shown by Equation 4.1:
=
PD,C
1
3T
3T
∫ VD ( t ) I D ( t ) dt ,
forVD > 0 ,
4.1
0
where V D (t) and I D (t) are waveforms measured using the Yokogawa DL750. In
Equation 4.1, the power dissipation in the diode when it is in reverse bias is neglected.
The current probes, having a background noise level on the order of ~ 4 mA rms, could
not measure the low values of diode reverse leakage current, shown in Figure 4.5,
accurately. However, as shown in Figure 4.5, this reverse leakage current was very
small, and therefore the power dissipated by the diode in reverse bias was neglected. In
addition, the power conversion efficiency, defined as the average power dissipated over
the load resistor, P RL , divided by the average power delivered by the input voltage
source, P Vs , is shown in Figure 4.12, as a function of D d,SiC .
87
Figure 4.11. Diode power dissipation as a function of D d,SiC for Cree CSD05120A (5 A, 1200 V) diodes.
Figure 4.12. Power conversion efficiency vs D d,SiC of the half-wave rectifier containing CSD05120A
diodes.
88
4.4
PSpice-Modeling of Half-Wave Rectifier
Equation 3.3, with model parameters n, I s , and R s are essentially the physics
model PSpice employs to model the forward I-V characteristics of the diodes [47]. The
values of n, I S , and R s for individual diodes, obtained from I-V characterization and
shown in
Table 4.2 and Figure 4.6, were used as input to the PSpice diode model. By
default, PSpice assumes a temperature of T = 27  C [56], but this default temperature can
and was overridden in the model libraries of the devices as well as in the simulation
profile with the measured temperatures. The simulated I-V characteristics of the PSpice
model are compared with the measured I-V curves for select diodes in Figure 4.13 and
Figure 4.14 for low-injection and high injection forward bias, respectively.
Figure 4.13. Forward-bias, low-injection I-V curve data versus the PSpice model for this diode. The
diode was irradiated to a D d,SiC of 2.3E11 (MeV/g).
89
Figure 4.14. Experimental, forward bias, high-injection I-V curve data compared to PSpice models for
representative, individual diodes from the unirradiated control group, group #3 (irradiated to
D d,SiC =1.4E11 (MeV/g)), and group #5 (irradiated to D d,SiC =2.3E11 (MeV/g)), having an R s value closest
to the mean for their respective group.
As shown in Figure 4.15, the PSpice models are quite accurate in representing
the experimental data for the half-wave rectifier circuit for the unirradiated diode and the
diode irradiated to D d,SiC = 1.4E11 (MeV/g). An interesting deviation between the
PSpice model and experimental data can be observed in Figure 4.15, for the diode
irradiated to D d,SiC = 2.3E11 (MeV/g) as the voltage is rising and approaching
approximately 4 V. At this point, the experimental data becomes distorted and rises
above the PSpice simulated voltage waveform. This deviation is consistent with the
deviation between the measured I-V characteristics and the PSpice-simulated I-V
characteristics shown in Figure 4.14. Equation 3.1 and Equation 3.3, used in the curve90
fitting and PSpice model, are based on the assumption that the electron drift velocity, vdn ,
is proportional to the electric field strength, E, with μ n being the constant of
proportionality ( vdn = µn E) [8]. However, at moderate to high electric fields, the
electrons lose energy by emitting more phonons than they absorb, and therefore, their
drift velocity eventually saturates [8]. In essence, vdn can no longer be assumed linearly
dependent on the applied electric field, so that Equation 3.1 and Equation 3.3, and
therefore the PSpice model become increasingly inaccurate for high values of V D , as
shown in Figure 4.14.
Figure 4.15. Results from the PSpice simulation of the half-wave rectifier circuit are compared to the
experimental data for the voltage drop waveform of the diode, when the diode is conducting current, for
the same data shown Figure 4.10. PSpice was used to model the diodes as they degraded as a function
D D,SiC .
91
4.5
Analytical Model of Half-Wave Rectifier
Assuming the piece-wise linear model for the CSD05120A diodes, as shown in
Figure 3.2, an analytical model can be developed, and all of the voltages and currents
can be solved explicitly. The power diode can be modeled using a DC voltage source in
series with a resistor, where, from Figure 3.2, the DC voltage source has a magnitude of
V on , and R on is equal to the inverse slope of the linear portion of the I-V curve in the
forward-bias, high-level injection operation mode. An example of this model is shown
for one of the irradiated CSD05120A diodes in Figure 4.16, and a plot of 1 / R on versus
D d,SiC is shown in Figure 4.17. The value of V on was essentially 0.92 V for all
unirradiated and irradiated diodes. The half-wave rectifier circuit containing the piecewise linear model is shown in Figure 4.18.
Figure 4.16. A Cree CSD05120A diode, irradiated to D d,SiC = 1.4E11 (MeV/g), fit to the piece-wise linear
diode model shown in Figure 3.2. V on is obtained by dividing the intercept by the slope of the linear trendline, and R on is obtained by calculating the inverse slope of the trend-line. The value of R on , 0.26 Ohms, is
very close to the value of R s , 0.25 Ohms, obtained by fitting the data shown in this figure to Equation 3.3.
92
Figure 4.17. Ron-1 versus D d,SiC (MeV/g) for the Cree CSD05120A diodes in this study.
Figure 4.18. Half-wave rectifier containing the piece-wise linear model of a power diode, shown in the
dashed box.
93
The sinusoidal voltage source in Figure 4.18, V s , can be written as
 2π t 
Vs = Vrms 2 sin 
 , where T is the period of V s . Then, we calcalute the current, I,
 T 
for the portion of the input cycle for which the diode is forward biased, by dividing the
voltage over resistors R on and R L by the sum of these resistances. For the portion of the
input cycle that the diode is reverse biased, I is essentially 0, as shown in Figure 4.10, as
the diodes have very little leakage current in the reverse-bias condition; furthermore, this
leakage current tends to decrease slightly with increasing D d,SiC , as shown in the
measured I-V curves in Figure 4.5. Therefore, the expression for I, for when the diode is
forward-biased, is given by Equation 4.2:
I
Vrms 2 sin ( 2π t / T ) − Von

Ron + RL


for I > 0; 0 otherwise  .

4.2
The average power dissipation in the diode, P D , C , can then be calculated by summing
the power dissipated in R on and V on , as shown in Equation 4.3:
=
PD,C
1
T
∫0 ( I
T
2
)
Ron + IVon dt ,
4.3
where I is given by Equation 4.2.
For the Cree CSD05120A diodes tested in this study, V on was measured to be
slightly less than 1 V and remained essentially constant with respect to radiation dose,
and V rms = 170 V was applied, using the California Instruments power supply.
Furthermore, we note that R on << R L for even the most highly irradiated diodes (see
Figure 4.6). Therefore, from Equation 4.2, it is not surprising that the current remained
essentially constant as a function of radiation dose, as shown in Figure 4.10.
94
From the trend-line for 1 / R on versus D d,SiC , in Figure 4.17, R on can be estimated
as a function of D d,SiC using Equation 4.4, where D d,SiC is in units of MeV/g:
Ron =
(
1
)
7.94 − 3.20 ×10−11 Dd ,SiC
4.4
Furthermore, V on = 0.92 V for essentially all unirradiated and irradiated diodes, V rms =
170 V, and R L = 100 Ohms. Therefore, substituting these values into Equation 4.2 and
4.3, along with the expression for R on given in Equation 4.4, the analytical model is
compared with respect to P D , C in Figure 4.19, to the measured, experimental values, as
well as to the PSpice simulations. It is important to note that Equation 4.9 is not valid
for D d,SiC greater than approximately 2.4E11 (MeV/g). From Equations 4.2 and 4.3, the
analytical model predicts that the diode power dissipation will reach a maximum of
approximately 36 W for Ron ≈ 99 Ω , which is approximately equal to the load resistance
of 100 Ω.
95
Figure 4.19. Diode power dissipation versus D d,SiC , for the experimental data of Figure 4.11, the PSpice
simulations, and the analytical model described by Equations 4.2-4.4.
4.6
Concluding Remarks on Functional Testing of Half-Wave Rectifiers
Typically, recombination and generation centers, as shown in Figure 2.1, created
by radiation-induced displacement damage, severely degrade the electrical performance
of the p-n junction of high power Si p-n junction diodes. In particular, an increase in
generation centers leads to an increase in the leakage current of the p-n junction diode,
and an increase in recombination centers leads to an increase in V on (shown in Figure
3.2), as these recombination centers decrease the minority-carrier lifetime. The minority
carrier lifetime is the most sensitive parameter to displacement damage, and therefore
Schottky power diodes offer a distinct advantage, in that these diodes are majoritycarrier devices, and are therefore not sensitive to changes in minority-carrier lifetime. In
addition, SiC has a distinct advantage over Si in that the use of SiC enables the
96
production of Schottky diodes having reverse-bias blocking-voltages in excess of 1 kV
with negligible leakage currents.
97
CHAPTER 5 : I-V CHARACTERIZATION TESTING OF POWER MOSFETS
The vertical double diffused power MOSFET (VDMOSFET) is used extensively
in spacecraft power control and conversion applications [57]. However, there has been
little work done regarding mixed neutron and gamma-ray environments on power
MOSFETs [26,39,40,58]. Also, due to their availability, demonstrated reliability, and
relatively low cost, non-radiation hardened parts are of interest to NASA. For example,
all of the commercial, non-radiation parts purchased as part of this study cost less than
$5 (USD) a piece; whereas, currently, a rad-hard power MOSFET typically costs more
than $500 (USD) [59], which we have found to be true as well.
Therefore, the tests subjects of this mixed radiation field study were nonradiation hardened commercial power MOSFETs. The power MOSFETs in this study
were part numbers IRF840, rated at 8 A forward current (I D ) and 500 V forward
blocking voltage V (BR)DSS , and part number IRF1310N, manufactured by International
Rectifier, having part numbers IRF1310N and IRF840, rated at 42 A forward current and
100 V V (BR)DSS . Twenty-seven of the IRF840 MOSFETs were manufactured by Vishay,
and 9 of the IRF840 MOSFETs were manufactured by International Rectifier, for
purposes of comparison between MOSFETs of the same part number but different
manufacturers. All of the 30 IRF1310N MOSFETs were manufactured by International
Rectifier. The Vishay IRF840 power MOSFETs and International Rectifier IRF1310N
98
MOSFETs are the test subjects of the buck and boost converter testing in Chapter 6.
These MOSFETs were subjected to radiation hardness testing in the mixed neutron and
gamma-ray radiation field in the rabbit facility at the Ohio State University Research
Reactor (OSURR). Both the International Rectifier IRF840 and IRF1310N power
MOSFET models were also the subject of a single-event gate rupture (SEGR) study,
conducted by NASA scientists, using heavy ions as a radiation source [3].
5.1 Power MOSFET: Structure and Physics of Operation
The schematic symbol of the n-channel MOSFET, and its built-in, parasitic antiparallel diode, is shown in Figure 1. When operating in its normal, forward-biased state
(drain biased positive with respect to source), the MOSFET blocks current flow when
the voltage difference between the gate and source is less than some threshold value, V th ,
but conducts current from drain to source (I D ), as this difference becomes greater than
V th . One can infer from the anti-parallel diode in Figure 5.1 that the MOSFET cannot
block current flow when its source is biased positive with respect to its drain (reverse
bias).
Furthermore, forward I D versus V DS characteristic curves are shown in Figure
5.2, for an unirradiated IRF1310N power MOSFET. The triode (ohmic) and saturation
regions of the MOSFET I D versus V DS characteristic are shown in Figure 5.2, along with
the voltage drop, V R , across the n- drift epitaxial layer of the MOSFET, shown in Figure
5.3. When the MOSFET is in saturation, the conductive channel is pinched-off at the
drain end of the channel, and therefore I D is essentially independent of V DS in the
saturation region.
99
Figure 5.1. Schematic diagram of an n-channel MOSFET with built-in anti-parallel diode.
Figure 5.2. I D versus V DS characteristic for an unirradiated IRF1310N power MOSFET. The voltage
drop across the channel, V CH , is equal to V DS minus V R , as indicated by Equation 5.1.
A VDMOSFET cell is shown in Figure 5.3. A typical power MOSFET may
contain several thousands of these cells in parallel. Fortunately, the many I-V
characteristics of the power MOSFET can be analyzed by considering the MOSFET as
100
comprised of only one, large, effective cell. The total on-state resistance of the power
MOSFET (R ds(on) ) can be approximated by the sum of the channel resistance (R channel )
and the drift layer resistance (R d ), as indicated by Figure 5.3.
Figure 5.3. n-channel VDMOS structure containing primary contributions to on-state resistance in power
MOSFETs, namely R d and R channel , the drift and channel resistances, respectively.
Consequently, for operation in the triode region of the I D versus V DS
characteristic (applicable to the buck and boost converter circuits of Chapter 6), the total
voltage drop, V DS , from source to drain of the MOSFET, can be approximated by the
sum of the voltage drop across R channel and R d , as shown in Equation 5.1:
V=
DS VCH + VR ,
5.1
where, V CH is the voltage dropped across the channel, and V R is the volage dropped
across the drift region resistance, R D , in the n- epitaxial layer, the bulk n+ source and
substrate regions, and various other contacts, leads, and pins in the package [60]. V R is
101
linearly proportional to the drain current, I D , and for the high voltage MOSFETs used in
this study, the n- epitaxial layer is the major source of V R , especially for the 500 V
MOSFETs, which require a lower doped n- drift layer to support higher electric fields.
Therefore, VR ≈ I D ( Rd ) for the power MOSFETs in this study.
In order to formulate an expression for V CH , we consider two cases, which are
described in [60] and summarized here. The first case occurs for VCH ≈ 0 , for which we
can approximate the free-electron charge density, Q IL , as being uniform over the entire
length of the channel, such that Equation 5.2 applies:
=
QIL COX (VGS − VTH ) ,
5.2
where, C OX is the capacitance of the gate oxide, V GS is the applied gate-to-source bias,
and V TH is the threshold voltage, defined by Equation 5.3:
VTH =V fb + 2ψ B +
2ε si qN A ( 2ψ B )
Cox
,
5.3
where ε si is the Si permittivity ( 1.04E-12 F/cm), ψ B is the difference between the Fermi
level and intrinsic level in the Si, N A is the doping density of the p-type body region in
which the n-type channel is formed, and V fb is the flat-band voltage, given by Equation
5.4, for which φms is the difference between the metal and semiconductor work
functions, and Q ox is the equivalent oxide charge per unit area at the Si-SiO 2 interface
[61]:
VTH =V fb + 2ψ B +
2ε si qN A ( 2ψ B )
Cox
102
.
5.4
Furthermore, the small electric field along the length of the channel causes the electrons
within the channel to move with a drift velocity, v d , given by Equation 5.5:
=
vd µ=
n ( ECH ) µ n (VCH / L ) ,
5.5
where, L is the effective length of the channel. The total free-electron charge in the
channel is q n = Q IL WL, where W is the channel width, going into the page in Figure 5.1.
Then, it takes an average time t tr , for an electron to travel from source to drain along the
channel, given by Equation 5.6:
L
L2
5.6
=
vd µnVch
The drain current through the channel, I D , can therefore be expressed by Equation 5.7:
t=
tr
qn QILWL
.
5.7
=
ttr
ttr
Substitution of the expression for t tr in Equation 5.6 into Equation 5.7 yields Equation
I=
D
5.8:
ID =
µn
W
Cox (VGS − VTH )VCH =
k (VGS − VTH )VCH ,
L
5.8
W
Cox .
L
Therefore, for a small applied drain-to-source bias, V DS , R channel is given by Equation
5.9:
where, k, the device transconductance parameter, is defined by k = µn
Rchannel
=
VCH
1
.
=
ID
k (VGS − VTH )
5.9
Therefore, V DS is given by Equation 5.10:


1
VDS = VCH + VR = 
+ RD  I D .
 k (V − V )

GS
TH


103
5.10
However, for larger values of V CH , Q IL cannot be assumed uniform across the
channel, and therefore Equation 5.8 is not valid for this second case, which is also
described in [60], and summarized here. At the source end of the channel, Q IL is the
same level as Equation 5.2, as described by Equation 5.11, where Q IL (y) is the freeelectron charge density a distance ‘y’ from the source end of the channel:
=
QIL ( 0 ) COX (VGS − VTH ) .
5.11
However, at the drain end of the channel, QIL is lower than it is at the source by an
amount of COX VCH , so that QIL ( L ) is given by Equation 5.12:
QIL =
( L ) COX (VGS − VTH − VCH ) .
5.12
Taking the average of Equation 5.11 and 5.12 as the average surface charge density,
1

QIL , such that =
QIL COX  VGS − VTH − VCH
2


 , then the total free electron charge in the

channel, qn′ , is given by Equation 5.13:
1


5.13
qn′ CoxWL  VGS − VTH − VCH  .
=
2


q′
Therefore, since I D = n , I D can be written as in Equation 5.14:
ttr
1
W


Cox (VGS − VTH )VCH − VCH 2  ,
2
L


1


k (VGS − VTH )VCH − VCH 2  .
=
2


=
I D µn
5.14
Equation 5.14 is the Shichman-Hodges [62] MOSFET model and is implemented in
PSpice as the level 1 MOSFET physics model [47]. When V CH is increased to the point
such that the end of the channel, VGS − VCH =
VTH , then the channel is essentially
104
pinched-off at the drain end, and therefore, substituting VCH
= VGS − VTH into Equation
5.14 yields Equation 5.15, describing I D in the saturation state, as shown in Figure 5.2,
where I D becomes essentially independent of V DS :
=
ID
1
2
k (VGS − VTH ) .
2
As a consequence of Equation 5.15, a plot of
line with a slope of
5.15
I D versus VGS should yield a straight
k
k
and an intercept of −VTH
; whereby, V GS = V TH for I D = 0.
2
2
It should be noted, however, that Equation 5.15 is not valid for high values of
(VGS − VTH ) , as increased carrier-carrier scattering occurs in the channel as the number
of carriers in the channel increases as a result of increased V GS , thereby reducing
mobility and thus k. In other words, as increasingly more carrriers are drawn to the
channel by an increase in V GS , the carriers crowd and collide with each other,
causing µn , and therefore k, to decrease.
5.2 Experimental Methodology: Irradiation and I-V Characterization
The parts used in this study were commercial, un-radiation-hardened n-channel
power MOSFETs, manufactured by International Rectifier and Vishay. The part
numbers of these MOSFETs were IRF130N, rated at 100 V forward blocking voltage
(V (BR)DSS ) and 42 A continuous drain current (I D ), and IRF840, rated at V (BR)DSS = 500 V
and 8 A continuous I D . Nine of the IRF840 MOSFETs were manufactured by
International Rectifier (IR), and 27 of the IRF840 MOSFETs were manufactured by
Vishay. The IRF840 MOSFETs made by IR and Vishay are analyzed separately, and
105
then IRF840 MOSFETs of different manufactures are compared with one another. All
of the 30 IRF1310N MOSFETs of this study were manufactured by IR.
5.2.1 Power MOSFET Irradiations
Prior to irradiation, the power MOSFETs, in groups of three, were covered in
cadmium and placed inside a polyethylene bottle. For the Vishay IRF840 and
IRF1310N models, one group of three MOSFETs remained unirradiated in order to
serve as the control group; however, all of the IR IRF840 MOSFETs were irradiated,
since only 9 of these MOSFETs were available for this study (both pre- and postirradiation I-V curve measurements were made for all irradiated MOSFETs). For each
group of three Vishay IRF840 MOSFETs, three Cree CSD04060A SiC Schottky power
diodes were also placed inside the bottle and irradiated with the MOSFETs, for future
functional testing of buck and boost converters, which is discussed in Chapter 6.
Likewise, in preparation for future functional testing, a group of three Vishay
IR40CTQ150PBF Si Schottky diodes were placed inside the bottle and irradiated with
the IRF1310N MOSFETs. During all of the the irradiations, the source, drain, and gate
leads of the MOSFETs were shorted according to ASTM standard F110-993 [63] and the
procedure followed by Blackburn [39] for unbiased power MOSFET irradiations. All
irradiations and measurements were performed at room temperature, and the reactor was
operating at a nominal power of 450 kW. This power corresponds to φeq ,1MeV ,Si =
5.2 ×1011
krad ( Si )
n
and a TID rate of 10
, as shown in Table 2.1. Dosimetry was
2
s
cm s
performed by integrating under the power monitor curve, as discussed in section 3.2.4,
and shown by Equation 3.6. Following irradiation, after an appropriate time, which
106
allowed for the radioactivity of the samples to decay to the point that the MOSFETs
could be safely handled, the MOSFETs were tested. For each group (sample) of three
MOSFETs, the corresponding φeq ,1MeV ,Si and TID to which the group was irradiated in
the OSURR rabbit facility are displayed in Table 5.1, Table 5.2, and Table 5.3 for the IR
IRF840, Vishay IRF840, and IR IRF1310N power MOSFET models, respectively.
IR IRF840 Group
(#)
1
2
3
Φ eq ,1MeV ,Si
2
(n/cm )
2.1E+13
6.2E+13
1.0E+14
TID
(Mrad(Si))
0.4
1.1
1.8
Table 5.1. Correspondence between each group (sample) of three IR IRF840 MOSFETs and the
Φ eq ,1MeV ,Si to which it was exposed in the OSURR rabbit facility.
Vishay IRF840 Group
(#)
Unirradiated Control
1
2
3
4
5
6
7
8
Φ eq ,1MeV ,Si
2
(n/cm )
0
1.7E+13
3.4E+13
5.1E+13
6.2E+13
6.8E+13
7.7E+13
8.6E+13
1.0E+14
TID
(Mrad(Si))
0
0.3
0.6
0.9
1.1
1.2
1.3
1.4
1.8
Table 5.2. Correspondence between each group (sample) of three Vishay IRF840 MOSFETs and the
Φ eq ,1MeV ,Si and TID to which it was exposed in the OSURR rabbit facility.
107
IR IRF1310N Group
(#)
Φ eq ,1MeV ,Si
(n/cm2)
Unirradiated Control
1
2
3
4
5
6
7
8
9
0
3.6E+13
7.3E+13
1.1E+14
1.4E+14
1.8E+14
2.2E+14
5.0E+14
7.4E+14
1.0E+15
TID
(Mrad(Si))
0
0.6
1.2
1.8
2.5
3.1
3.7
8
13
17
Table 5.3. Correspondence between each group (sample) of three IR IRF1310N MOSFETs and the
Φ eq ,1MeV ,Si and TID to which it was exposed in the OSURR rabbit facility.
5.2.2 Power MOSFET I-V Characterization Testing
I-V characterization was conducted using the Tektronix 371B high power curve
tracer, shown below the two Keithley SourceMeters in Figure 3.4, prior to irradiation
and after each incremental irradiation dose in the rabbit facility. Four-wire, Kelvin
measurements were used for all I-V measurements, in order to minimize cable effects
associated with two-wire measurements. The Tektronix 371B was used to measure the
drain current versus applied drain-to-source bias (I D versus V DS ) and drain current versus
applied gate-to-source voltage (I D versus V GS ). The TO-220 IC socket used to
electrically connect the MOSFET leads to the curve tracer, is shown in Figure 5.4. As
shown in Figure 5.4, the drain and source leads of the MOSFET each have two wires
attached, one wire for the source signal, and the other wire for sense measurement.
For the I D versus V DS measurement, V GS was held constant at 10 V, and V DS was
swept from 0 V until I D reached the forward current rating for the MOSFET (42 A for
108
the IRF1310N MOSFET and 8 A for the IRF840 MOSFET). Although I D versus V DS
measurements were taken for a variety of values for V GS , only the I D versus V DS curve
corresponding to a value of V GS = 10 V is reported in this study, as 10 V was the gate
voltage used in the buck and boost converters, as discussed in Chapter 6. Only the triode
region of the I D versus V DS curve for V GS = 10 V was measured, since MOSFETs
operating in power converters, such as buck and boost converters typically operate in the
triode region, for which the MOSFET most resembles an ideal switch, with respect to
V GS .
Figure 5.4. TO-220 IC socket used for I-V Characterization of Power MOSFETs.
For the I D versus V GS measurement, V D was held constant at 10 V, and V GS was
swept from 0 V until I D reached the forward current rating for the MOSFET being
measured. V D was held constant at 10 V to ensure that the MOSFET was in saturation
mode, so that Equation 5.15 is applicable and could be used to determine V TH and k.
109
The forward-blocking I D versus V DS characteristics of the power MOSFETs were
also measured with the Keithley 2410 SourceMeter, shown in Figure 3.4, in order to
determine the change in drain leakage current as well as changes in breakdown voltage.
This measurement was accomplished by shorting the gate and source together, such that
V GS = 0 V, and sweeping V D to increasingly positive values, until I D reached 1 mA, at
which point breakdown was determined to have occurred.
5.3 Determination of k and V TH : Results and Analysis:
The threshold voltage, V TH , and transconductance parameter, k, were determined
by performing a least squares curve-fit of the I D versus V GS data to Equation 5.15. For
this, the MATLAB non-linear, least-squares curve-fit function was applied, using the I D
versus V GS data as input along with initial estimates for V TH and k. The initial estimates
for V TH and k, which MATLAB requires as input to the built-in non-linear, least-squares
curve-fit function, were determined by performing a linear, least-squares curve-fit of the
data in the form of
I D versus V GS to a straight line, in the form of =
I D mVGS + b ,
where VTH ,estimate =
−b
and
m
kestimate
= m , as indicated by Equation 5.15 and
2
discussed at the end of section 5.1. An example of linear fits to the I D versus V GS
measured characteristics are shown in Figure 5.5, for a Vishay IRF840 MOSFET, before
and after irradiation. Note that the irradiated curve in Figure 5.5 saturates at
approximately V GS = 3 V. An explanation for this effect is shown in Figure 5.6, for
which an applied V DS bias of +10 V is no longer sufficient to force the MOSFET into
saturation for V GS > 3 V for Φ eq,Si,1MeV = 5.1E13 (n/cm2); therefore, Equation 5.15 is not
110
valid there. Also, at lower currents, for both unirradiated and irradiated MOSFETs, the
I D versus V GS characteristic deviates from linearity. In this low-current region of the
I D versus V GS curve, the MOSFET is operating in the so-called subthreshold regime,
and I D is exponentially dependent on V GS ; therefore, Equation 5.15 does not apply in the
subthreshold region of the I D versus V GS curve.
Figure 5.5. I D 1/2 versus V GS curve for a Vishay IRF840 MOSFET, pre- and post-irradiation.
111
Figure 5.6. I DS versus V D for a Vishay IRF840 MOSFET, irradiated to Φ eq, Si, 1MeV = 5.1E13 (n/cm2).
Furthermore, groups 7, 8, and 9 of the IRF1310N MOSFETs were irradiated to
an extent that their I-V characteristics could not be modeled accurately using Equation
5.15, since for these groups, I D was not constant with respect to V DS as Equation 5.15
requires, as shown in Figure 5.7. Therefore, curve-fit results are not reported for groups
7, 8, and 9 of the IRF1310N MOSFETs.
112
Figure 5.7. I DS versus V D for an IRF1310N MOSFET, irradiated to Φ eq, Si, 1MeV = 1.0E15 (n/cm2).
The curve-fit results for k are shown in Figure 5.8 for Vishay and IR IRF840 (8
A, 500 V) MOSFETs and in Figure 5.9 for the IRF1310N (42 A, 100 V) MOSFETs. In
general, k, being proportional to the carrier mobility in the channel, μ n , decreases with
increasing ionizing dose and thus increasing radiation-induced interface traps, shown as
item (4) in Figure 2.3. In fact, Sexton [64] determined that the carrier mobility, μ, is
correlates strongly with N it , the density of interface trapped charge, and does not depend
to first order on the density of oxide trapped charge, N ot ; furthermore, an empirical
relation between μ and N it is given by Equation 5.16, where μ 0 is the pre-irradiation
carrier mobility, and α is an experimentally determined constant, dependent on the
surface impurity concentration [65]:
µ=
µ0
1 + α ( ∆Nit )
.
5.16
113
Figure 5.8. k versus TID in Si for IRF840 (8 A, 500 V) MOSFETs.
Figure 5.9. k versus TID in Si for IRF1310N (8 A, 500 V) MOSFETs.
114
The results for V TH are shown in Figure 5.10, for both the IRF1310N and IRF840
MOSFETs, from which some interesting observations can be made: 1) For the
IRF1310N MOSFET, V TH decreased sharply for a cumulative dose of less than 1 Mrad
(Si), but then remained fairly constant for the remainder of the experiment, for a total
cumulative dose in excess of 3 Mrad (Si). This saturation in threshold voltage shift at
high dose levels has been previously observed in MOSFETs, and was attributed to
increased electron-hole recombination for low applied electric fields in the oxide [66].
Also, at high doses, an increasing number of the finite hole traps at the Si/SiO 2 interface
are filled [66]; 2) The results for the change in V TH for both of the 500 V IRF840
MOSFET models are significantly different from those observed for the 100 V IRF1310
MOSFET. That is, for the IR 500 V MOSFET, V TH becomes negative for TID less than
2 Mrad (Si), and for the Vishay 500 V MOSFET, V TH drops below 1 V for TID less than
2 Mrad (Si), but does not become negative.
It is important to note that, in addition to being temperature and time-dependent,
radiation-induced oxide trapped charge, as well as radiation-induced interface traps are
highly dependent on the processing (manufacturing) of the oxide [14]; furthermore,
manufacturers may even alter their fabrication process while a device is still
commercially available, which is one of the disadvantages of testing and using COTS
devices [7]. The IR840 MOSFETs manufactured by IR were purchased as part of the
JIMO radiation hardness testing, and IR no longer produces these MOSFETs, as of the
time this dissertation is written. The results in Figure 5.10 suggest that the Vishay
115
IRF840 MOSFETs have oxides containing fewer oxide traps, and are therefore more
radiation-hard than the IR IRF840 MOSFETs.
Figure 5.10. V TH versus TID in Si for IRF840 (8 A, 500 V) and IRF1310 (42 A, 100 V) MOSFETs.
In general, for MOSFETs with higher forward-blocking voltage rating, the gate
oxide thicknesses must be greater in order to support greater electric fields across the
oxide. However, the shift in the threshold voltage is proportional to the square of the
gate oxide thickness [14], and so the observed large shift in the threshold voltage for the
500 V MOSFET is not surprising. In particular, the proportionality of ΔV TH on the
square of the oxide thickness, t ox , follows from Q = CV , where Q is proportional to t ox ,
and C is proportional to t ox -1 [14].
116
In addition, ΔV TH is dependent on both oxide trapped charge, as well as radiationinduced interface traps, such that ∆VTH = ∆Vot + ∆Vit , where ∆Vot is the change in
threshold voltage due to trapped oxide charge, and results in a negative shift of VTH , due
to the positive, trapped holes in the oxide [11]. However, the sign of ∆Vit , depends on
the position of the Fermi-level at the Si surface at inversion [14], and for n-channel
MOSFETs, ∆Vit contributes a positive shift of V TH , countering the negative shift due to
∆Vot . The process contributing to ∆Vit depends on the diffusion of hydrogen to the
Si/SiO 2 interface, and has a very different time scale than the process of trapped oxide
charge contributing to ∆Vot . In fact, at low dose rates, comparable to those encountered
in natural space, the V TH of n-channel MOSFETs may actually increase above its preirradiated value [11]. However, in our case, the TID rate is very high in the OSURR
rabbit facility, 10 krad(Si) / s, in comparison to the dose rate encountered in natural
space (0.012 rad/s [67]), and therefore, as shown by Figure 5.10, ∆VTH is predominantly
negative with respect to TID for the MOSFETs tested in this study.
Furthermore, it should be noted that oxide trapped charge and radiation-induced
interface traps are also electric-field dependent, and that the leads of the MOSFETs were
shorted during the irradiations in the rabbit facility. It is expected that both the 100 V
and 500 V MOSFETs would degrade to greater extents with respect to both threshold
voltage and transconductance for an applied positive gate-to-source voltage during
irradiation, as this would result in greater positive trapped charge in the oxide as well as
radiation-induced interface traps, due to the increase in the amount of electrons and
holes that would escape recombination [68]. However, it was determined in a study [68]
117
that V DS has very little to no effect on ΔV TH ; on the other hand, applying a constant DC
bias of V GS = +10 V resulted in a greater shift in ΔV TH than for switching V GS from +10
V to – 10 V at 100 kHz [68]. Therefore, it is expected that ionizing radiation will affect
ΔV TH of the power MOSFETs to an extent dependent on the duty cycle and frequency of
the applied V GS bias.
5.4 Determination of R d from R ds(on) : Results and Analysis:
The full on-state resistance of the MOSFET, R ds(on) , can be determined by
inspection from Equation 5.10, and is given in Equation 5.17:


1
+ RD  ,
Rds( on ) ≈ 
 k (V − V )

GS
TH


5.17
such that VDS = Rds( on ) I D , in the linear portion of the triode region of the I D versus V DS
characteristic. Therefore, R ds(on) was determined by performing a linear fit of the I D
versus V DS data, for the linear portion of the triode region, to Equation 5.17 in order to
determine R ds(on) . An example of this calculation is shown in Figure 5.11, which shows
the linear region of the I DS versus V D characteristic, of an IRF1310N MOSFET, pre- and
post-irradiation, for which R ds(on) ~ 39 mΩ and 54 mΩ, respectively. Results for R ds(on)
as a function of Φ eq ,1MeV ,Si are shown for the IRF840 and IRF1310N MOSFETs in
Figure 5.12 and Figure 5.13.
118
Figure 5.11. Linear fits to the I D versus V DS characteristics for an IRF1310N MOSFET, pre- and postirradiation.
Figure 5.12. R ds(on) versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V) MOSFETs.
119
Figure 5.13. R ds(on) versus Φ eq, Si, 1MeV for IR IRF1310N (42 A, 100 V) MOSFETs.
In addition, the resistance of the low-doped drift region of the MOSFETs, R d ,
shown in Figure 5.2, was determined by subtracting the channel resistance,
Rchannel =
1
, from the R ds(on) , given in Equation 5.17. V TH and k were
k (VGS − VTH )
determined from the I D versus V GS characterization, as described in section 5.3, and a
constant value of V GS = +10 V was applied to the MOSFET for the I D versus V DS
measurements. Results for R d as a function of Φ eq ,1MeV ,Si are shown in Figure 5.14 and
Figure 5.15 for IRF840 and IRF1310N MOSFETs, respectively. In addition, in Figure
5.15, R ds(on) is compared with R d as a function of Φ eq ,1MeV ,Si .
120
Figure 5.14. R d versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V) MOSFETs. The results are
nearly identical those shown in Figure 5.12, since, for the 500 V MOSFETs, R d accounted for greater than
95 % of R ds(on) .
121
Figure 5.15. R d and R ds(on) versus Φ eq, Si, 1MeV for IRF1310N (42 A, 100 V) MOSFETs.
Comparing the results for the IRF840 MOSFETs with respect to R ds(on) and R d ,
shown in Figure 5.12 and Figure 5.14, the figures are nearly identical. This is not
surprising, since in a typical 500 V MOSFET, R d accounts for 97 % of R ds(on) [69]. This
is essentially true for the IRF840, 500 V MOSFETs tested in this study, as shown in
Figure 5.16; furthermore, R d increased as a percentage of R ds(on) with
increasing Φ eq ,1MeV ,Si , as shown in Figure 5.16. In addition, 1 / R d is plotted as a
function of Φ eq ,1MeV ,Si and fit to a straight line in Figure 5.17, as was done for Si and
SiC Schottky power diodes in Chapters 3 and 4. From the results shown in Figure 5.16,
for the IRF840 MOSFETs, it is evident that the large increase in R ds(on) with
increasing Φ eq ,1MeV ,Si is due primarily to the increase in R d , most likely as a result of
122
carrier-removal in the n- drift epitaxial region, as indicated by the linear relationship
between 1 / R d and Φ eq ,1MeV ,Si , described mathermatically in Equation 3.7, and shown
in Figure 5.17.
Figure 5.16. R d / R ds(on) (%) versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V) MOSFETs.
In addition, the results for R d as a percentage of R ds(on) as a function of
Φ eq ,1MeV ,Si , for the 100 V IRF1310N MOSFETs, for Φ eq ,1MeV ,Si less than 2.2E14
(n/cm2), are shown in Figure 5.18. In comparison, R d accounts for approximately 70 %
of R ds(on) for a typical 150 V MOSFET [69]. For the IRF1310N MOSFETs, as shown in
Figure 5.18, R d decreased as a percentage of R ds(on) with increasing Φ eq ,1MeV ,Si . This
result was in contrast to the IRF840 MOSFETs, for which R d increased as a percentage
123
of R ds(on) with increasing Φ eq ,1MeV ,Si , as shown in Figure 5.16. Furthermore, from
Figure 5.15, it is evident for the IRF1310N MOSFETs that R d is essentially constant as a
function of Φ eq ,1MeV ,Si , for Φ eq ,1MeV ,Si less than 2.2E14 (n/cm2), even though R ds(on) is
increasing. Therefore, for the IRF1310N MOSFETs, for Φ eq ,1MeV ,Si less than 2.2E14
(n/cm2), the increase in R ds(on) as a function of Φ eq ,1MeV ,Si is due to the increase in
R channel , due to decreased mobility in the conductive channel, and therefore decreased k.
Furthermore, from Figure 5.9, k, and therefore, μ n , appear to saturate at the TID
corresponding to Φ eq ,1MeV ,Si = 2.2E14 (n/cm2). This results in a saturation of R channel at
this dose level. However, from Figure 5.13, R ds(on) increases rapidly with respect to
increasing Φ eq ,1MeV ,Si beyond Φ eq ,1MeV ,Si = 2.2E14 (n/cm2), suggesting that for these
high dose levels, carrier-removal in the n- epitaxial drift layer, from neutron-induced
displacement damage is primarily responsible for the increase in R ds(on) beyond
Φ eq ,1MeV ,Si = 2.2E14 (n/cm2). An explanation for this result is that the R d increases
significantly only when the neutron-induced, deep level traps begin to compensate the
donors in the drift region, raising its resistivity [52]; furthermore, this only happens
when the deep trap-level concentration approaches the doping level of the epitaxial drift
layer [52]. Furthermore, MOSFETs having lower breakdown voltages have drift regions
that are more heavily doped; therefore, the rapid increase of R ds(on) associated with
neutron-induced displacement damage does not occur until much high dose levels for the
100 V MOSFETs compared to the 500 V MOSFETs in this study.
124
Figure 5.17. R d -1 versus Φ eq, Si, 1MeV for IR and Vishay IRF840 (8 A, 500 V) MOSFETs.
Figure 5.18. R d / R ds(on) (%) versus Φ eq, Si, 1MeV for IRF1310N (42 A, 100 V) MOSFETs.
125
5.5 Background on Radiation Effects: Forward Breakdown and Leakage Current:
In addition, as discussed in section 5.2.2, the forward leakage current and
breakdown voltage of the Vishay IRF840 and IR IRF1310N MOSFETs were measured
pre- and post-irradiation. An increase in leakage current results in increased power
dissipation when the MOSFET is off.
In particular, the radiation-induced off-state leakage current in power MOSFETs
was studied extensively in [57]; although, neither the IRF840 nor the IRF1310N
MOSFETs were tested in that study, for which all of the tested power MOSFETs had
voltage ratings of 100 V and less. Also, in [57], it was observed that the leakage current
of most of the tested MOSFETs increased substantially with increasing ionizing dose
and was due to surface rather than bulk effects. In particular, radiation-induced leakage
in n-channel MOSFETs is associated with negative shifts in threshold voltage, as
radiation-induced, positive trapped oxide charge induces conductive channels in the ptype body region, so that substantial current may flow even with V GS = 0 [57,70].
Therefore, it is expected that the 500 V MOSFETs tested in this study will exhibit larger
leakage current increases than the 100 V MOSFETs, as well as the lower-voltage-rated
MOSFETs tested in [57] due to the larger t ox required for higher voltage MOSFETs,
coupled with the proportionality of oxide trapped charge on t ox 2 [14], as discussed in
section 5.3.
Furthermore, ionizing radiation can reduce the forward breakdown voltage of
power MOSFETs by inducing oxide trapped charge as well as generating traps at the SiSiO 2 interface [71]. In particular, the positive, trapped oxide charge acts to reduce the
radius of curvature of the depletion region of the pn- junction of n-channel MOSFETs,
126
shown in Figure 5.3, and therefore reduce the breakdown voltage [71]. In addition, the
reduction in breakdown voltage of n-channel MOSFETs was observed to be greater for
MOSFETs having high breakdown voltages [71]. This is reasonable, given that nchannel MOSFETs having higher voltage ratings require thicker oxides, and the amount
of trapped oxide charge is proportional to the square of the oxide thickness [14].
5.6 Forward Breakdown and Leakage Current: Results and Analysis:
Unirradiated and irradiated I DS versus V D characteristics for V GS = 0 are shown
in Figure 5.19 for representative Vishay IRF840, 500 V MOSFETs. For this
measurement, the MOSFETs in group 8, irradiated to Ф eq,1MeV,Si = 1.0E14 (n/cm2), had
leakage currents in excess of 1 mA after post-irradiation. We define the breakdown
voltage, arbitrarily, as the value of V DS , for V GS = 0 V, at which the leakage current, I D ,
reaches 1 mA, to be consistent with previous work [71]. As shown in Figure 5.19, the
leakage current increases dramatically, over several orders of magnitude, in accordance
with previous studies [57]. Also, the average leakage current as a function of TID at 250
V, half the rated-breakdown voltage, is shown in Figure 5.20 for the Vishay IRF840, 500
V MOSFETs. Comparing Figure 5.10 and Figure 5.20, the trends in V TH and leakage are
mirror images of each other. This is consistent with our previous discussion, in that
surface effects, such as trapped oxide charge and radiation-induced interface traps are
responsible for changes in both V TH and leakage current.
However, surprisingly, the breakdown voltage, as shown in Figure 5.19, changes
very little with respect to dose, contrary to previous results in literature for high voltage
MOSFETs [71]. Furthermore, all but one of the irradiated MOSFETs, with the
127
exception of group 8, irradiated to Ф eq,1MeV,Si = 1.0E14 (n/cm2), maintained breakdown
voltages in excess of their manufacturer-rated breakdown voltage of 500 V postirradiation.
Figure 5.19. I D versus V DS characteristics for Vishay IRF840 MOSFETs for V GS = 0.
128
Figure 5.20. Drain Leakage Current, I D , versus TID for Vishay IRF840, 500 V MOSFETs.
In addition, the average leakage current of IRF1310N MOSFETs, for an applied
V DS of 80V, as a function of TID, is shown in Figure 5.21. As shown in Figure 5.21, the
leakage current increases at a continually lower rate with increasing TID up to 4 Mrad
(Si), but then rapidly increases for higher values of TID. The leveling-off of the leakage
current at slightly less than TID = 4 Mrad(Si) is consistent with the saturation of V TH for
these MOSFETs with respect to TID, as shown in Figure 5.10, for TID less than 4
Mrad(Si). The value of V GS measured at I D = 250 μA, V250 µ A , is shown as a function of
TID in Figure 5.22. As shown in Figure 5.22, the value of V250 µ A for TID greater than 4
Mrad(Si) decreases at a much slower rate than for TID less than 4 Mrad(Si), indicating a
sharp decrease in the rate at which holes are being trapped at the Si/SiO 2 interface.
V250 µ A is reported on IR’s datasheet for the IRF1310N MOSFET as the gate threshold
129
voltage, VGS (th ) . To obtain V250 µ A , the Keithley 2410 SourceMeter was used, and the
procedure on the IRF1310N datasheet was followed in that the gate and drain of the
MOSFET were shorted together (V DS =V GS ) and swept positive. Therefore, the increase
in leakage current for TID greater than 4 Mrad(Si) may be due to radiation-induced
generation centers near the pn- body-drain junction, as a result of displacement damage.
As shown in Figure 5.23, the breakdown voltage of the IRF1310N MOSFETs
decreased as a result of irradiation. This is consistent with the results from a previous
study [71], for which the breakdown voltage of n-channel MOSFETs decreased as a
function of TID and was attributed to the increase in radiation-induced trapped oxide
charge. This positive oxide charge decreases the radius of curvature of the depletion
region in n-channel MOSFETs, which in turn decreases the breakdown voltage.
Figure 5.21. Drain Leakage Current, I D , versus TID for Vishay IRF1310N, 100 V MOSFETs.
130
Figure 5.22. V 250μA versus TID for Vishay IRF1310N, 100 V MOSFETs.
Figure 5.23. Breakdown voltage versus TID for Vishay IRF1310N, 100 V MOSFETs.
131
5.7 Conclusions Regarding MOSFET I-V Characterization Testing
For both the IRF1310N (42 A, 100 V) and IRF840 (8 A, 500 V) power
MOSFETs, V TH and k decrease as a result of oxide trapped charge and radiation-induced
interface traps. The degradation is worse for the 500 V MOSFETs, which can be
attributed to the greater oxide thickness as well as lower doping of the n- epitaxial drift
region required to support the higher breakdown voltage.
The on-state resistance, R ds(on) , also increased as a result of irradiation for both
the IRF1310N and IRF840 power MOSFET models. For the IRF840 MOSFET, the
increase in R ds(on) is dominated by the increase in R d , which can be attributed to
radiation-induced displacement damage in the n- drift layer. However, for the
IRF1310N MOSFET, the increase in R ds(on) is dominated by the increase in R channel as a
result of decreased mobility in the conductive channel from radiation-induced interface
traps, for TID less than 4 Mrad(Si). For TID greater than 4 Mrad(Si), corresponding to
Φ eq ,1MeV ,Si greater than 2.2E14 (n/cm2), the rapid increase in R ds(on) with respect to
radiation dose can be attributed to radiation-induced displacement damage.
In addition, with respect to the I D versus V DS characterization testing with V GS =
0 V, the leakage currents for both the IRF1310N and IRF840 MOSFETs increased
dramatically from the exposure to the mixed neutron and gamma-ray radiation field,
primarily as a result of positive, trapped oxide charge. In addition, the breakdown
voltage of the IRF1310N MOSFETs decreased, albeit much less dramatically than the
leakage current, with increasing radiation dose. However, surprisingly, the breakdown
voltage of the IRF840 MOSFETs remained essentially unchanged with increasing
radiation dose, as indicated by Figure 5.19.
132
CHAPTER 6 : FUNCTIONAL TESTING OF BUCK AND BOOST CONVERTERS
In this chapter, we present the results from functional testing of buck and boost
converters, using Si and SiC Schottky power diodes as well the Vishay IRF840 (8 A,
500 V) and IR IRF1310N (42 A, 100 V) power MOSFETs that were characterized in
Chapter 5. The performance of the buck and boost converters are modeled in this
chapter using the results with respect to changes in performance parameters as a function
of radiation dose, from the I-V characterization analysis performed in Chapter 3 and
Chapter 5 for the Schottky power diodes and power MOSFETs, respectively. The
testing and analysis for the buck and boost converter circuits are performed for
continuous conduction mode only, in which case the inductor current is greater than zero
for the entire MOSFET switching cycle.
6.1 Background on Operation of Buck and Boost Converters
In section 6.1, we provide background on the operation of buck and boost
converters. First, a description of the operation of ideal buck and boost converters is
presented. Then, a description of the operation of non-ideal buck and boost converters is
presented. Furthermore, the details of the non-ideal switching characteristics of the
MOSFET are described.
133
6.1.1 Background: Operation of Ideal Buck and Boost Converters
In this section, we analyze the buck and boost converters in the ideal case, in
which the diode and MOSFET are ideal switches, in order to describe the basic operation
of the converters. We define an ideal switch as being able to switch instantaneously,
conducts no current when in the off-state (infinite resistance), and has no voltage drop
when in the on-state (infinite conductance). Therefore, an ideal switch absorbs no power.
A buck converter is shown in Figure 6.1, which is analyzed as follows,
considering the MOSFET and diode as ideal switches. In steady state, the time-average
voltage across the inductor is zero. Referring to Figure 6.1, during the time the MOSFET
is in the on-state and thus conducting current, the integral of the inductor voltage over
time is (Vin − Vo ) ton , where t on is the time in which the MOSFET is on during its
switching cycle. When the MOSFET is off, the integral of the inductor voltage over time
−Vo (Ts − ton ) , where T=
is ( 0 − Vo )(Ts − ton ) =
s ton + toff is the period of the MOSFET
switching cycle. Since the time-average voltage across the inductor is zero in steady state
operation, (Vin − Vo ) ton − Vo (Ts − ton ) =
0 . Therefore, in continuous conduction mode
 ton 
(CCM) operation,
=
Vo =
 Vin DVin , where D is the duty ratio, or duty cycle of the
T
 s 
MOSFET. The duty ratio, D, is the fraction of the switching period, T S , that the
t 
MOSFET is on and conducting current, defined mathematically as D =  on  .
 Ts 
134
MOSFET
L
1
2
+
Vin
RL
Vgate
Diode
C
Vo
-
Figure 6.1. Buck converter with inductor, L, and capacitor, C.
A boost converter is shown in Figure 6.2, which is analyzed as follows,
considering the MOSFET and diode as ideal switches. In steady state, the time-average
voltage across the inductor is zero. Referring to Figure 6.2, during the time the
MOSFET is in the on-state and thus conducting current, the integral of the inductor
voltage over time is Vinton . When the MOSFET is off, the integral of the inductor
voltage over time is (Vin − Vo )(Ts − ton ) . Setting the time-average voltage over the
0 . Therefore,
inductor to zero yields Vinton + (Vin − Vo )(Ts − ton ) =


 1 
1 
 Vin 
Vo V=
=
in 
.
 1 − ton 
 1− D 
 T 
s 

1
L
Diode
2
+
Vin
MOSFET
C
Vo
Vgate
Figure 6.2. Boost converter with inductor, L, and capacitor, C.
135
RL
6.1.2 Background: Analytical Modeling of Non-Ideal Buck and Boost Converters
In this section, we analyze the buck and boost converters in the non-ideal case, in
which case the diode and MOSFET have non-zero on-state resistances. Furthermore, the
buck and boost converter circuits are assumed to be operating in continuous conduction
mode. This analysis is intended to aid in interpreting the performance results of the
circuits containing irradiated diodes and MOSFETs and provide a means to estimate the
the power dissipation in the MOSFET and diode with respect to radiation dose. We
refer to the term ‘power dissipation’ as power dissipated by the MOSFET and diode in
the form of heat.
It should be noted that in our analytical models, for the sake of simplicity, we
assume that the MOSFET and diode can switch instantaneously. Although this is not a
gross assumption for the Si and SiC Schottky diodes used in this study, in reality, the
MOSFET cannot switch instantaneously when the V gate signal from the waveform
generator is applied. We investigate the practical switching behavior of the MOSFET in
section 6.1.3. The power dissipation associated with switching a controllable
semiconductor switch, in general, is directly proportional to the switching frequency, f s ,
as well as the length of the time required to switch the semiconductor on and off [46].
On-state conduction power loss is directly proportional to the duty cycle.
The simplified, non-ideal diode model that is used to analyze the behavior of the
non-ideal buck and boost converters is that of the large signal diode model, for which the
I-V characteristics are shown in Figure 3.2. Furthermore, the circuit-equivalent of the
large-signal diode model is shown dashed-in within the half-wave rectifier circuit of
Figure 4.18. The large-signal diode model consists of a DC voltage source, V on ,
136
representing the forward-voltage drop of the diode, in series with a resistor, R on ,
representing the on-state resistance of the diode, which is approximately equal to R s . As
shown in Figure 4.17 for the Cree CSD05120A SiC Schottky power diodes, V on remains
essentially constant with dose, but R on is expected to increase with radiation-induced
displacement damage.
The simplified, non-ideal MOSFET model that is used in this dissertation to
analyze the behavior of the non-ideal buck and boost converters consists of a single
resistor, having a value of R ds(on) , the on-state resistance of the MOSFET. As shown by
Equation 5.17 in section 5.4, for power MOSFETs of at least moderately high voltagerating, R ds(on) consists primarily of R d , the drift layer resistance, and R channel , the
resistance of the conductive channel formed in the body region of the MOSFET. An
expression for R channel is shown in Equation 5.9. From the MOSFET I-V
characterization results presented in Chapter 5, it was shown that R d increases with
radiation-induced displacement damage, and the rapid increase in R d occurs for lower
values of Φ eq,1MeV,Si, for the 500 V MOSFETs than for the 100 V MOSFETs, as
MOSFETs having larger breakdown voltage ratings typically require lower doping in the
drift layer of the MOSFET. For the 100 V MOSFETs, for Φ eq,1MeV,Si of 2.2E14 (n/cm2)
and lower, the main contribution to the increase observed in R ds(on) was determined to be
R channel , from ionizing radiation-induced reduction of channel mobility.
6.1.2.1 Analytical Model of a Non-Ideal Buck Converter
A non-ideal model of the buck converter is shown in Figure 6.3, with non-ideal
models of the MOSFET, diode, and inductor shown dashed-in. A non-ideal inductor
137
consists of an ideal inductor in series with a DC resistance, R DCR . The inductor R DCR
typically increases with increasing inductance and is often comparable in magnitude to
R on and R ds(on) , as was the case in this current study. For instance, for the testing of the
Vishay IRF840 MOSFETs and Cree CSD04060A diodes in the buck converter of Figure
6.15, a value of 212 mΩ was measured for the R DCR of the 1 mH inductor, using a 4-wire
Kelvin measurement with the Keithley 2410 SourceMeter. Furthermore, for the buck
and boost converter circuits shown in Figure 6.13 and Figure 6.14, containing the
IRF1310N MOSFETs and IR40CTQ150PBF diodes, a value of 13.7 mΩ was measured
for the effective R DCR of the two 100 μH inductors in parallel. The ESR resistance of the
capacitor decreases with increasing size of the capacitor; therefore, due to the large size
of the capacitors used in this study, and also for convience of modeling, the ESR
resistance is neglected in this analysis, and the capacitors are considered ideal. In
addition, the leakage currents of the MOSFET and diode are neglected in the analysis.
Furthermore, in our analysis, we consider V o as constant, since for the converters used in
this study, and for commercial DC-to-DC converters in general, the ripple voltage in the
load capacitor is typically very small compared to the average output voltage, V o . For
instance, in switch-mode power supplies, the percentage ripple in the output voltage is
typically specified to be less than 1 % [46]. Furthermore, in a previous study [72], the
output voltage ripple was specified to be 2.2 % and 2.7 % for the boost and buck
converters, respectively. Thefore, we assume V o to be constant, which allows the use of
first-order differential equations to model the buck and boost converter circuits.
138
1
2
Rds(on)
R_DCR
L
1
2
MOSFET
+
Ron
Vin
C
Von
Vo
RL
2
Vdc
iL
Diode
1
-
0
Figure 6.3. Schematic of a simplified model of a non-ideal buck converter.
For the non-ideal buck converter shown in Figure 6.3, we base our analysis on
the current flowing through the inductor, i L , for the case when the MOSFET is
conducting and the diode is off ( 0 < t <
D
), and then for the case when the diode is
fs
conducting after the MOSFET has been switched off (
switching frequency of the MOSFET ( f s =
D
1
). Here, f s is the
<t <
fs
fs
1
). Once the inductor current is known, the
Ts
on-state power dissipation in the MOSFET and diode can be determined.
When the MOSFET is switched on in the circuit of Figure 6.3, the diode must be
off (open circuit). Therefore, applying Kirchoff’s voltage law (KVL) for this case yields
Equation 6.1:
Vin − iL,on Rds( on ) − iL,on RDCR − L
diL,on
dt
−=
Vo 0, 0 < t <
D
. 6.1
fs
Solving Equation 6.1 for i L,on yields Equation 6.2, for some constant A:
139
(
)
− R

ds( on ) + RDCR
Vin − Vo
D

=
+ Aexp
iL,on ( t )
t  , 0 < t < .


Rds( on ) + RDCR
L
fs


6.2
Now, we consider the case when the MOSFET has been switched off (opencircuit), and the diode is therefore conducting. Applying KVL for this case yields
Equation 6.3:
−Von − iL,off Ron − iL,off RDCR − L
diL,off
dt
D
1
<t < .
fs
fs
=
− Vo 0,
6.3
Solving Equation 6.3 for i L,off yields Equation 6.4, for some constant B:
iL,off ( t )
=
− (Von + Vo )
Ron + RDCR
 − ( Ron + RDCR ) 
+ Bexp 
t  ,
L


D
1
<t < .
fs
fs
6.4
Next, in order to develop the boundary conditions, we note that the current
through an inductor must be continuous and cannot change instanteously. Therefore, our
boundary conditions, which can be applied to Equations 6.2 and 6.4 in order to obtain
the constants A and B, are given in Equations 6.5 and 6.6:


D
D
iL,on=
t =
 iL,off=
t
,
fs 
fs 


6.5

iL,on (=
t 0=
) iL,off =t

6.6
1
fs

.

Furthermore, as the capacitor is assumed to be sufficiently large such that V o is constant,
V o , and therefore i L , can now be solved by equating the average inductor current through
the load resistor, R L , to V o / R L , as expressed in Equation 6.7, where i L,on (t) and i L,off (t)
are given by Equations 6.2 and 6.4, respectively:
140
fs ∫
 0
D / fs
Vo
.
6.7
iL,off ( t ) dt  =
 R
D / fs
L
iL,on ( t ) dt + ∫
1/ f s
The average on-state power dissipation in the MOSFET, during conduction, can be
calculated according to Equation 6.8:
PS ,C = Rds( on )  f s  ∫
D / fs
0
iL,on ( t )  dt .
2
6.8
Furthermore, the average power dissipation in the diode, during conduction, can be
calculated according to Equation 6.9:
2
1/ f s
1/ f
iL,off ( t )  dt + Von ∫ s iL,off ( t ) dt  . 6.9
=
PD,C f s  Ron ∫


D
f
D
/
/ fs
s


We emphasize that Equation 6.8 accounts only for power dissipation when the
MOSFET is fully on. In reality, the MOSFET will also dissipate power in the form of
heat during the time that it is switched on and off. The power dissipated during
switching is investigated later in this chapter.
The solutions of the equations in this section were obtained analytically and
coded in MATLAB, and the MATLAB code for this calculation is given in the
Appendix of this dissertation. Comparisons with PSpice simulations and experimental
data are given later in this chapter.
In addition, in order to better understand how and to what extent the parasitic
resistances introduced into the buck converter circuit by the non-ideal MOSFET and
diode affect the operation of the circuit as a whole, we consider the simplest case, in
which the inductor is also very large, such that there is very little ripple in the inductor
current (
∆iL
≈ 0 ). In such a case, we can assume that the inductor current, i L , is purely
iL
141
DC. Furthermore, for simplicity, we neglect the power dissipation of the MOSFET for
the time when it is being switched on and off. Consequently, energy balance yields
Equations 6.10 – 6.11:
Pin = DVin ( iL )
6.10
=
Pout D ( iL ) Rds ( on ) + (1 − D) ( iL ) Ron + (1 − D) ( iL )Von + ( iL ) RDCR + ( iL ) RL
2
2
2
Equating P in with P out , and noting that iL =
2
6.11
Vo
, the following simple expression,
RL
given as Equation 6.12, can be obtained for V o / V in :
V 
D + (1 − D )  on 
Vo
 Vin 
.
=
Vin  DRds ( on ) + (1 − D ) Ron + RDCR 
1 +

RL


6.12
In Equation 6.12, as we may expect, we see that the effect of the parasitic elements on
the buck converter depends on the portion of the cycle that the parasitic element is
conducting current. Furthermore, as long as the parasitic resistances are small in
comparison with the load resistance, R L , and the diode turn-on voltage is small in
comparison with the input voltage, V in , the ratio of V o / V in will remain fairly constant
with radiation-induced displacement damage. This was true for the converters tested in
this dissertation, even after the diodes and MOSFETs had been irradiated to a Φ eq,1MeV,Si
of 1.0E14 (n/cm2) and greater.
Furthermore, the efficiency of this buck converter can be determined by taking
the ratio of the power distributed to the load resistor, ( iL ) RL to the total power delivered
2
by the source. Re-arranging terms, and noting that P in = P out and Vo = iL RL , the
142
expression in Equation 6.13 can be obtained for the efficiency of the buck converter,
PRL
namely
Pin
:
PRL PRL
= =
Pin Pout
1
DRds ( on ) + (1 − D ) Ron + RDCR
V
1 + on (1 − D ) +
Vo
RL
.
6.13
6.1.2.2 Analytical Model of a Non-Ideal Boost Converter
A non-ideal model of the boost converter is shown in Figure 6.4, with non-ideal,
large signal models of the MOSFET, diode, and inductor shown dashed-in. As in the
case for the analysis of the buck converter in section 6.1.2.1, we assume V o to be
essentially constant. As in the case of the non-ideal buck converter analyzed in section
6.1.2.1, for the sake of simplicity, we assume that the MOSFET can switch
instantaneously.
1
2
L
2
R_DCR
1
Von
Ron
+
Diode
2
iL
1
Vin
MOSFET
Rds(on)
Vo
C
-
0
Figure 6.4. Schematic of a simplified model of a non-ideal boost converter.
143
RL
For the analysis of the non-ideal boost converter, we proceed by finding an
expression for the inductor current, i L , for the case when the MOSFET is on and the
diode is off. Applying Kirchoff’s voltage law (KVL) for this case yields Equation 6.14,
noting that t on = D / f s and T s = 1 / f s :
Vin − L
diL,on
dt
− iL,on RDCR − iL,on Rds( on
=
) 0, 0 < t <
D
.
fs
6.14
Solving Equation 6.14 for i L,on yields Equation 6.15, for some constant K:
(
)
− R

ds( on ) + RDCR
Vin
D


=
+ K exp
iL,on ( t )
t , 0 < t < .


Rds( on ) + RDCR
L
fs


6.15
Now, we consider the case when the MOSFET has been switched off (opencircuit), and the diode is therefore conducting. Applying KVL for this case yields
Equation 6.16:
Vin − L
diL,off
dt
− iL,off RDCR − Von − iL,off Ron =
− Vo 0,
D
1
<t < .
fs
fs
6.16
Solving Equation 6.16 for i L,off yields Equation 6.17, for some constant J:
=
iL,off ( t )
 − ( Ron + RDCR ) 
Vin − (Von + Vo )
t  ,
+ J exp 
Ron + RDCR
L


1
D
.
<t <
fs
fs
6.17
Furthermore, noting that the inductor current must be continuous, and therefore applying
the boundary conditions of Equation 6.5 and Equation 6.6, yields the solution for
constants K and J, shown in the matrix equation of Equation 6.18:
−1
 K   Vin − (Von + Vo ) Vin   exp ( −α ⋅ ton / L ) − exp ( − β ⋅ ton / L )  1
,
=
−


  
− exp ( − β ⋅ Ts / L )  1
1
β
α 
J  
144
6.18
where
=
α Rds( on ) + RDCR and =
β Ron + RDCR .
Now, we must find V o . Since the average inductor current is not continuously
supplying the load, we cannot use the same approach as was used in the case of the buck
converter, namely Equation 6.7. However, we can use the concept of charge-balance of
the capacitor over one input cycle. That is, in order to satisfy steady-state conditions, the
charge that the capacitor receives from the inductor ripple current when the MOSFET is
conducting current ( 0 < t <
D
) must be discharged through R L during the time interval
fs
when the MOSFET is off (
D
1
). Therefore, Equation 6.19 can be used to
<t <
fs
fs
deterimine V o for the non-ideal boost converter of Figure 6.4:
 Vo   D 
=

 
 RL   f s 
 V   1− D 
.
fs 
∫D / f iL,off ( t )dt −  RoL  
1/ f s
s
6.19
The power dissipation in the MOSFET and diode, during on-state conduction, can then
be calculated according to Equation 6.8 and Equation 6.9, respectively. The solutions of
the equations in this section were obtained analytically and coded in MATLAB, and the
MATLAB code for this calculation is given in the Appendix of this dissertation.
In addition, in order to gain better insight as to how and to what extent the
parasitic resistances introduced into the boost converter circuit by the non-ideal
MOSFET and diode affect the operation of the circuit as a whole, we consider the
simplest case, in which the inductor is also very large, such that there is very little ripple
in the inductor current (
∆iL
≈ 0 ). Therefore, in this case, we can assume that the
iL
145
inductor current, i L , is purely DC. Furthermore, we neglect the power dissipation in the
MOSFET as it is switched. Consequently, energy balance yields Equations 6.20 – 6.21:
Pin = Vin ( iL )
=
Pout
( iL )
2
6.20
RDCR + D ( iL ) Rds ( on ) + (1 − D) ( iL )Von + (1 − D) ( iL ) Ron +
2
2
Vo 2
RL
6.21
In addition, we note that the load resistor and capacitor as a system receive all of their
energy for the entire period of the cycle, T s , during the portion of the cycle that the
MOSFET is off. Therefore, energy balance for the load resistor and capacitor as a
system yields Equation 6.22:
V2
RL
o
.
(1 − D )VoiL =
6.22
Therefore, from Equation 6.22, iL =
Vo
, which we then substitute into Equations
RL (1 − D )
6.20 and 6.21 and solve for V o / V in , as given in Equation 6.23:
Vo
=
Vin
1− D +
V 
1 − (1 − D )  on 
 Vin 
.
RDCR + DRds( on ) + Ron (1 − D )
RL (1 − D )
Furthermore, the efficiency,
PRL PRL
=
=
Pin Pout
6.23
PRL
Pin
, for the boost converter is given in Equation 6.24:
1
1+
RDCR + DRds( on ) + (1 − D ) Ron
RL (1 − D )
146
2
6.24
+
Von
Vo
6.1.3 Background: Practical Swithing Behavior of Power MOSFETs
A practical MOSFET cannot switch immediately when a voltage is applied
between its gate and source leads. In particular, the MOSFET has various parasitic
inductances and capacitances which affect its switching behavior. These parasitic
capacitances, as well as the source-lead and drain-lead inductances, are shown in the
MOSFET equivalent circuit of Figure 6.5, given in [60]. In an n-channel MOSFET, the
gate-source capacitance (C GS ) is formed by the gate electrode, the gate SiO 2 layer as
well as the depletion layer that forms at the Si-SiO 2 interface, and the n+ source region.
Also, the gate-drain capacitance (C GD ) is formed by the gate electrode, the depletion
layer in the n- region, and the drain. The drain-source capacitance (C DS ) is then formed
by the source, the depletion region in the n- layer, and the drain. C GD plays a major role
in the switching behavior of power MOSFETs, and gives rise to plateau regions in the
V GS waveforms that are very distinct and observable for the buck and boost converters
containing the IRF1310N MOSFETs.
147
Figure 6.5. Equivalent circuit of a power MOSFET, in which the parasitic elements that have the greatest
affect on the switching behavior of the power MOSFET are shown [60].
The details of the switching behavior of the power MOSFET are fairly
complicated and are dependent on the circuit of which the MOSFET is a part. A detailed
analysis of the transient switching behavior of power MOSFETs can be found in [60];
however, we will focus on those aspects of the switching process most relevant to this
dissertation, especially those that are affected by radiation in order to interpret the results
from the functional testing. In this dissertation, we refer to the gate drive voltage signal
originating from the waveform generator as V gate . In addition, we refer to the bias
between the actual gate and source ends of the MOSFET channel as V G’S’ . Furthermore,
we refer to the discussions in [46,60], as they apply to the MOSFET switching
characteristics for a diode-clamped inductive load, which is essentially a step-down
(buck) converter [46].
148
The switching waveforms of an IRF1310N MOSFET, operating in the buck
converter circuit of Figure 6.13, are shown in Figure 6.6. The waveforms in Figure 6.6
were recorded using two different Yokogawa DL750 Scopecorders. The MOSFET V GS
curve shown in Figure 6.6 was recorded on a separated ScopeCorder than the V DS and I D
curves. Therefore, in Figure 6.6, the V GS waveform was positioned on the same timescale as the V DS and I D curves by using the measurement from the LeCroy Wavesurfer
424 oscilloscope, which measured the V DS and V GS waveforms simultaneously, on the
same time-scale. The portion of the waveforms labeled “Detail” in Figure 6.6 is shown
more clearly in Figure 6.7.
Figure 6.6. Switching waveforms of an IRF1310N (42 A, 100 V) MOSFET, operating in a buck
converter. Turn-on and Turn-off phases of the switching transient are labeled (1) – (6) and are identified
and described in the text.
149
Figure 6.7. This is the portion of the switching waveforms labeled “Detail” in Figure 6.6 for an
IRF1310N (42 A, 100 V) MOSFET operating in a buck converter. Turn-on and Turn-off phases of the
switching transient are labeled (1) – (6) and are identified and described in the text.
Referring to Figure 6.7, in phase (1) of the MOSFET turn-on process, when the
V gate signal from the waveform generator is applied, V G’S’ begins to increase in a manner
max
described by Equation 6.25, where Vgate
is the maximum value of the voltage signal
from the waveform generator (10 V in our testing), and the amplitude of V gate is assumed
max
to be Vgate
, as this was the case for our functional testing:
max
1 − exp ( −t / τ G )  .
VG ' S=' Vgate
6.25
In Equation 6.25, τ G =
( RS + RG )( CG ' S ' + CG ' D ' ) , where R S is the effective resistance
between the waveform generator output and the gate lead of the MOSFET. In Equation
6.25, setting V G’S’ equal to the MOSFET threshold voltage, V TH , and solving for t yields
the turn-on delay time, t d(on) , given by Equation 6.26:
150
(
)
max
max
=
− VTH  .
td ( on ) τ G ln Vgate
/ Vgate


6.26
Note that according to Equation 6.26, reductions in V TH , such as that caused by ionizing
radiation, have the potential to reduce the MOSFET turn-on delay time.
max
While still in phase (1), at a time t d(on) after Vgate = Vgate
, the MOSFET drain
current, I D , begins to rise. When V G’S’ reaches a value of V TH + I 0 /g fs , the MOSFET is
able to support the full inductor current, I 0 , and the MOSFET drain-to-source voltage,
V DS , begins to decrease. The term g fs is the MOSFET transconductance, for which
 ∂I D 
[60].
g fs = 

 ∂VG ' S ' VDS =constant
In our functional testing, we operate the MOSFET in the Ohmic region, such that the
conductive channel is not pinched-off at the drain end. In this condition g fs is given by
Equation 6.27 [60], where we have previously defined the device transconductance
parameter, k, in Chapter 5:
=
g fs k (VG ' S ' − VTH ) .
6.27
At this point, referring to Figure 6.7, the MOSFET enters phase (2) of the turn-on
process. When I D = I 0 , V D begins to decrease as C GD continues to charge. The large
voltage spike in the V G’S’ waveform is likely due to the change in current across the
source inductance, L s , shown in the MOSFET equivalent circuit in Figure 6.5 [60].
When V DS drops to its minimum value, the MOSFET enters phase (3) of the turn-on
process as V G’S’ resumes its rise to V gate in a manner described by Equation 6.25, at
which point the turn-on transient has essentially ended.
151
As for the turn-off process, referring to Figure 6.7, the MOSFET enters phase (4)
when V gate drops to its minimum value, which is 0 V in our case. This change in V gate
max
causes V GS to decrease exponentially from Vgate
to V TH + I 0 /g fs in a manner described
by Equation 6.28:
max
=
VG ' S ' Vgate
exp ( −t / τ G ) .
6.28
The time for this decrease in V G’S’ to occur is the turn-off delay time, t d(off) , and can be
calculated by substituting V TH + I 0 /g fs for V G’S’ in Equation 6.28 and solving for t.
Therefore, t d(off) is given by Equation 6.29:
(
)
max
=
td ( off ) τ G ln Vgate
/ VTH + I 0 / g fs  .


6.29
Note that according to Equation 6.29, a decrease in V TH , such as that caused by ionizing
radiation, has the potential to increase t d(off) .
During phase (5), V G’S’ and I D remain constant as V DS increases and C GD
discharges, as shown in Figure 6.7. The time required for V DS to increase to V in during
this phase is given by Equation 6.30 [60]:
tVDS ,rise ≈
{
Vin CD ' S ' + 1 + g fs ( RS + RG )  CG ' D '
I 0 + g fsVTH
}.
6.30
However, it should be noted that the rise in V DS is not truly linear, since C GD is
discharging during this time [60].
When V DS reaches V in , in the case of the buck converter [46], the MOSFET
enters phase (6) as shown in Figure 6.7, when V G’S’ and the drain current, I D , begin to
decrease. When V G’S’ decreases to V TH , I D falls to 0, and the turn-off transient is
essentially complete [46]. We also note that in phase (6), as shown in Figure 6.6, V DS
152
increases beyond V in , which is slightly greater than 80 V for this circuit, while I D
decreases. V DS then returns to V in after I D decreases to 0. This feature of the V DS
waveform is due to the voltage spike across the parasitic inductance at the drain end of
the MOSFET as a result of the fall in drain current as described in [74].
For simplicity, as well as to follow standard procedure, the measurement shown
in Figure 6.8 will be used in order to quantify the switching performance of the
MOSFETs as a function of radiation dose. This measurement is standard, in that it is
used on manufacturers’ datasheets for power MOSFETs in order to quantify switching
performance [60]. In Figure 6.8, the turn-on delay time (t d(on) ) is the time required for
V DS to decrease to 90 % of its maximum value after V GS increases to 10 % of its
maximum value. The rise time, t r , is the time that it takes V DS to decrease from 90 % to
10 % of its maximum value. Also, for turn-off, t d(off) is the time it takes for V DS to
increase to 10 % of its maximum value after V GS decreases to 90 % of its maximum
value. Furthermore, t f , the fall time, is the time required for V DS to increase from 10 %
to 90 % of its maximum value during the turn-off transient.
153
Figure 6.8. The standard means to quantify power MOSFET switching performance as listed on
manufacturers’ datasheets will be used in this current study.
6.2 Previous Work: Functional Testing of Buck and Boost Converters:
No previous work regarding functional testing of buck and boost converters in
neutron and gamma-ray mixed radiation fields has been found. However, two studies
were found regarding total ionizing dose (TID) on the performance of buck and boost
converters [72,73].
In [72], IRF150 MOSFETs (100 V, 38 A) were tested in buck and boost
converters, and this study is briefly summarized here, highlighting aspects relevant to the
study for this dissertation research. In [72], the boost converter was supplied with an
input voltage (V in ) of 6 V, and the buck converter was supplied with an input voltage of
15 V. For both the boost and buck conveters, an 85 kHz square wave was applied across
the gate and source of the IRF150 MOSFETs, and the MOSFETs were switched
between saturation (on) and cut-off (off) states. Load resistances of 1.2 kΩ and 50 Ω
were used in the boost and buck converter circuit topologies, respectively. In addition,
unlike in [73], the MOSFETs were irradiated, with an ARACOR x-ray source, under the
154
three bias conditions. That is, for the first bias condition, the MOSFETs were irradiated
with V GS = 0 V. For the second bias condition, the MOSFETs were irradiated with V GS
> 0. For the third bias condition, the MOSFETs were irradiated as they operated in the
buck and boost converters, with an 85 kHz square wave applied to the gate and source of
the MOSFETs. From these various bias conditions during irradiation, it was determined
that the largest negative shift in V TH occurred for the case for which V GS > 0, as would
be expected, since this would result in more electron-hole pairs escaping recombination.
In addition, for the most realistic case in terms of MOSFET gate-bias conditions, for
which the 85 kHz square wave was applied to the MOSFET gate and source during
irradiation, the negative shift in V TH was much less drastic than the for the case for
which a constant positive gate-to-source bias was applied, but only slightly more
negative than for the case in which V GS = 0. For a TID of 70 krad(Si), the boost
converter output voltage, across the load resistor, fell to 0 V, as the MOSFET gate signal
was not low enough to turn off the irradiated MOSFET, having a severely reduce V TH ,
and therefore the output resistor was shorted. However, the output voltage of the buck
converter remained constant for the highest TID used in the study (~ 100 krad);
although, the efficiency of the buck converter decreased steadily with increasing TID.
In [73], irradiated Motorola IRF 440 power MOSFETs were tested in buck and
boost converters, and the study is briefly summarized here, highlighting aspects relevant
to the study for this dissertation research. In [73], the MOSFET was switched between
saturation, shown in Figure 5.2, and cut-off (V GS < V TH ). Furthermore, in [73], the
MOSFETs were irradiated at dose rate of 2 rad(Si)/s with a 60Co source, and a gate
voltage of +9 V was applied while the MOSFETs were irradiated.
155
For the buck
converter, the output voltage, V o , and MOSFET drain current (I D ) in the off-state,
remained fairly constant for TID less than 60 krad(Si), but rapidly increased for TID
greater than 60 krad (Si), as the threshold voltage of the MOSFET became too low in
order for the V GS signal to turn the MOSFET off. For the boost converter, the MOSFET
drain current in the off-state remained fairly constant for TID less than 40 krad(Si), but
then rapidly increased for TID greater the 40 krad(Si), as V TH of the MOSFET became
too low, as a result of ionizing radiation, in order for the V GS signal to turn the MOSFET
off. Accordingly, for a TID of 40 krad(Si) and greater, V o of the boost converter fell as
the output load resistor (R L ) became shorted, since the MOSFET could not be turned off
by the applied V GS signal. It is important to note for this previous work, for both the
boost and buck converters, an input voltage (V in ) of 6 V was used, and the MOSFET was
switched at 100 kHz. The highest radiation dose used for this previous study was 80
krad(Si), using a 60Co source.
The current study, for this dissertation research, differs from these previous
studies [72,73] in several respects, such as radiation source. For instance, in the current
study, both the diode and the MOSFET in the converters of Figure 6.1 and Figure 6.2
were irradiated, and the radiation source was the mixed neutron and gamma-ray
radiation field of the OSURR rabbit facility. Therefore, neutron-induced displacement
damage was not an issue in those previous studies. Furthermore, in [72,73] , the highest
TID used was on the order of ~ 100 krad(Si); whereas, in the current study, the Vishay
IRF840, 500 V MOSFETs were irradiated to a TID of greater than 1 Mrad(Si) and
Φ eq,1MeV,Si as high as 1.0E14 (n/cm2), and the IRF1310N, 100 V MOSFETs were
irradiated to a TID of greater than 15 Mrad(Si) and Φ eq,1MeV,Si as high as 1.0E15 (n/cm2).
156
Also, in the current study, much different values were used for V in and V gate ,
shown in Figure 6.1 and Figure 6.2, than in the previous two studies [72,73]. For
instance, for the current study, much higher voltages, comparable to the manufacturerrated voltages for the devices, were used for V in than in [72,73]. For instance, for the
buck converter, V in = 80 V for the 100 V MOSFET, and V in = 250 V for the 500 V
MOSFET. Furthermore, in the current study, V gate was switched between 0 and +10 V,
which was sufficiently high to put the MOSFETs into the linear region of the triode
(Ohmic) portion of the I D versus V DS characteristic, shown in Figure 5.2. This is
significant for a radiation field consisting of neutrons in addition to gamma-rays, since
operation in the triode region allows one to directly correlate the effects of R ds(on) on
MOSFET and converter performance, and as was reported in Chapter 5, neutron-induced
displacement damage has a great effect on R ds(on) .
Furthermore, in [72,73], only the output voltage and power conversion efficiency
of the converters were reported, the only exception being in [73], which also reported the
MOSFET drain current as a function of TID. In the current study, in addition to the
power conversion efficiencies and output voltages of the buck and boost converters, the
voltage and current waveforms over all of the leads of the MOSFET and diode are
measured and analyzed.
In addition, in the previous studies of [72,73], the threshold voltages of the
MOSFETs decreased to such an extent, as a result of ionizing radiation, that the gate
drive circuitry could not turn the MOSFETs completely off. At this point, the converters
were said to have failed. Since the post-irradiation values of V TH for all of the Vishay
IRF840 and IRF1310N MOSFETs were greater than 0, as discussed in Chapter 5, the
157
minimum of the V gate signal was sufficient to turn each of the MOSFETs off. Therefore,
the failure mode of concern in this study is that due to thermal breakdown of the power
MOSFETs, in which the power dissipation in the MOSFET becomes sufficiently large as
to destroy the body-drain p-n junction within the MOSFET structure. When this occurs,
a short circuit exists between the drain and source leads rendering the MOSFET
completely useless.
6.3 Experimental Setups and Procedures
For this study, a number of experimental setups and procedures were used. The
Vishay IRF840 (8 A, 500 V) MOSFETs, characterized in Chapter 5, were functionally
tested in the circuits of Figure 6.1 and Figure 6.2 along with Cree CSD04060A (4 A,
600V) SiC Schottky power diodes. In addition, the IR IRF1310N (42 A, 100 V)
MOSFETs, also characterized in Chapter 5, were tested in the circuits of Figure 6.1 and
Figure 6.2 along with Vishay IR40CTQ150PBF (40 A, 150 V) Si Schottky power
diodes, which are characterized in this chapter. For example, I-V characterization with
the experimental apparatus of Figure 3.4 was used in order to characterize the DC static
performance of the MOSFETs and diodes, as well as to extract electrical performance
parameters from physics models. Also, the circuits and equipment used to measure the
various voltage and current waveforms in the circuits are described in this section.
6.3.1 Irradiation Procedure for Diodes and MOSFETs of Buck and Boost Converters
The irradiation procedure used for the diodes and MOSFETs of the buck and
boost converters tested in the current study is described in section 5.2.1 and summarized
in this section. The leads of the diodes were left floating, and the leads of the MOSFETs
158
were shorted according to ASTM standard F110-993 [63], as each sample of three
diodes and three MOSFETs were irradiated inside of a Cd-lined bottle in the OSURR
rabbit facility, as the reactor operated at nominal power of 450 kW, corresponding to
φeq ,1MeV =
5.2 ×1011 n / cm 2 s and a TID rate of 10 krad ( Si ) / s . For each group of three
, Si
Vishay IRF840 MOSFETs, three Cree CSD04060A SiC Schottky power diodes were
also placed inside the Cd-lined bottle and irradiated with the MOSFETs in the OSURR
rabbit facility. The values for Φ eq,1 MeV,Si and TID corresponding to each group is given
in Table 5.2. Likewise, in preparation for functional testing, a group of three Vishay
IR40CTQ150PBF Si Schottky diodes were placed inside the Cd-lined bottle and
irradiated with the IRF1310N MOSFETs in the OSURR rabbit facility. The values for
Φ eq,1 MeV,Si and TID corresponding to each group is given in Table 5.3.
6.3.2 I-V Characterization Procedure for Diodes and MOSFETs
The Cree SiC Schottky power diodes, part number CD04060A and Vishay
IR40CTQ150PBF Si Schottky power diodes were characterized using the apparatus
shown in Figure 3.4. The I-V characterization for the Cree SiC CSD04060A Schottky
diodes were performed according to the procedure described in section 3.2.4, using the
Keithley 2410 Sourcemeter for low current, high voltage measurements. For
characterizing the I-V characteristics of the Vishay IR40CTQ150PBF Si Schottky
diodes, the same procedure was used as described for the IR Si Schottky diodes in
section 3.2.4. That is, for the Si Schottky diodes tested in this study, the Keithley 2410
Sourcemeter was used for high voltage, low current measurements, and the Tektronix
371B high-power curve tracer was used for forward-bias, high-injection I-V
159
characterization. For the Vishay Si Schottky diodes used for functional testing, the two
diodes in each TO-220 package were wired in parallel and characterized. The Vishay Si
Schottky diodes in each package were characterized and functionally tested, wired in
parallel, since their combined current rating in the package, 40 A, matched closely to the
current rating of the IRF1310N MOSFETs (42 A), with which they were functionally
tested in the circuits of Figure 6.1 and Figure 6.2.
Furthermore, the I-V characterization procedure for the Vishay IRF840 and IR
IRF1310N MOSFETs is described in section 5.2.2. In particular, the Vishay IRF840 and
IR IRF1310N MOSFETs characterized and analyzed in Chapter 5 are the same
MOSFETs used for the functional testing reported in this chapter.
6.3.3 Functional Testing Setup and Procedure for Diodes and MOSFETs
An overall view of the functional testing apparatus used for testing the buck and
boost converters is shown in Figure 6.9. Shown in Figure 6.9 are the following items,
labeled (1) – (6):
(1) Agilent 33210A arbitrary waveform generator
(2) LeCroy WaveSurfer oscilloscope, model 424
(3) (3a) and (3b): Two Yokogawa DL750 Scopecorders
(4) High power and low resistance Avtron load bank
(5) Circuit under test (CUT)
(6) Yokogawa current probe, model 701930
160
Figure 6.9 Functional test apparatus for testing buck and boost converters.
The Sorensen DC power supply, model DCR 300-33T, rated at 300 V and 33 A,
used to supply the input voltage for the buck and boost converters, is not shown in
Figure 6.9. In order to reduce noise and smooth the signal from the DC power supply, a
30 mH choke was placed between the high and low voltage wires of the DC power
supply.
The Agilent 33210A arbitrary waveform generator was used to provide the
pulsed gate signal, V gate , to the MOSFET, as shown in Figure 6.1 and Figure 6.2. In
order to reduce noise and smooth the signal, a 30 mH choke was placed between the
high and low voltage wires of the waveform generator. In addition, a 10 nF capacitor
161
was placed between the high and low voltage wires of the waveform generator, on the
output of the 30 mH choke, as shown in Figure 6.10.
Figure 6.10. Filter used to reduce noise and smooth the signal from the waveform generator.
The LeCroy WaveSurfer oscilloscope, model 424 was used to measure the V GS
and V DS waveforms of the MOSFET, as well as the diode voltage drop waveform for the
buck and boost converters containing the IRF1310N (42 A, 100 V) MOSFET and
IR40CTQ150PBF Si Schottky diode. The LeCroy oscilloscope provided the capability
of measuring the MOSFET and diode voltage waveforms with a timing resolution of 1
Giga-samples per second (1 data-point every 1 ns). Therefore, the switching of the
MOSFET could be measured and analyzed with 100 times the precision of the
162
Yokogawa DL750 ScopeCorders, for which the highest time resolution was 10 Megasamples per second (1 data-point every 100 ns). The LeCroy oscilloscope was only used
for the circuits containing the 100 V MOSFETs and 150 V diodes, since the voltages
used in the circuits containing the 500 V MOSFETs and 600 V diodes were too high to
be measured using the LeCroy oscilloscope.
The two Yokogawa DL750 Scopecorders, labeled (3a) and (3b) in Figure 6.9,
were used for measuring various voltage and current waveforms in the buck and boost
converter circuits, as well as the temperatures of the TO-220 heat sinks on which the
MOSFETs and diodes were mounted. For instance, the ScopeCorder labeled (3a) in
Figure 6.9 was used to measure V in and V o , as well as the temperatures of the TO-220
heat sinks on which the MOSFETs and diodes were mounted. Furthermore, the
ScopeCorder labeled (3b) in Figure 6.9 was used to measure the V GS and V DS waveforms
of the MOSFET and the voltage drop waveform of the diode. All of the voltage
waveforms measured with the Yokogawa ScopeCorders were measured using sense
wires connected to the Yokogawa 701250, 12-bit isolation module, which had a sample
rate of 1 data-point per 100 nanoseconds (10 MS/s). In addition, the Scopecorders were
used to measure the current flowing out of the MOSFET source lead, the current flowing
into the anode lead of the diode, as well as the currents flowing through the inductor and
load capacitor. With the exception of the second experiment conducted for a buck
converter, comprised of IRF1310N MOSFET and IR40CTQ150PBF diode, the currents
were measured using the Yokogawa current probe, model 701930, labeled (6) in Figure
6.9, attached to the Yokogawa 70251, 16-bit isolation module, which had a sample rate
of 1 data-point per microsecond (1 MS/s). For the second experiment conducted for the
163
buck converter containing a IRF1310N MOSFET and a IR40CTQ150PBF diode, the
current probes used to measure the current flowing through the source lead of the
MOSFET as well as into the anode lead of the diode were attached to the Yokogawa
701250, 12-bit isolation module, which has ten times the time resolution of the
Yokogawa 70251 isolation module.
The MOSFETs and diodes were connected to the circuits through high-power
TO-220 sockets, as shown in Figure 6.11. Furthermore, as shown in Figure 6.11 the
MOSFETs and diodes were mounted on TO-220 heat sinks. Before mounting the
MOSFETs and diodes on the heat sinks, the thermal pads of the MOSFETs and diodes
were coated with Arctic Silver® 5 high-density polysynthetic silver thermal compound
(99.9% silver), as shown in Figure 6.12, in order to improve thermal conductivity
between the thermal pads of the semiconductor devices and the TO-220 heat sinks.
164
Figure 6.11. A MOSFET placed in a high-power TO-220 socket, mounted on a heat-sink.
Figure 6.12. MOSFET thermal pad coated with polysynthetic silver thermal compound.
165
6.3.3.1 Functional Test Procedure for Buck and Boost Converters: IRF1310N MOSFET
A schematic for the buck converter circuit tested with the IRF1310N (42 A, 100
V) MOSFETs and the IR40CTQ150PBF (40 A, 150 V) Si Schottky power diodes is
shown in Figure 6.13. The schematic for the boost converter, using the IRF1310N
MOSFET and IR40CTQ150PBD diode is shown in Figure 6.14. For both circuits, the
waveform generator provided a 50 kHz square pulse with 20 ns rise and fall times, and
was switched between 0 V and 10 V. The duty cycle of the square pulse was swept from
20 % to 50 % in 5 % increments, with measurements being taken at each of the 5 %
intervals. The two diodes in the IR40CTQ150PBF TO-220 package were wired in
parallel to achieve the full package rating of 40 A. For the buck converter, the load
resistance, R L , consisted of two 10 Ω resistors from the load bank wired in parallel, for
an effective load resistance of R L = 5 Ω. For the boost converter, R L consisted of 20 Ω
of resistance from the load bank.
For the functional testing, the IRF1310N MOSFET having a value for R ds(on)
closest to the average in its group, irradiated to the same dose, was tested with an
IR40CTQ150PBF diode having a forward voltage drop at 5 A closest to the average in
its group, irradiated to the same dose.
6.3.3.2 Functional Test Procedure for Buck and Boost Converters: IRF840 MOSFET
For the IRF840 MOSFETs and CSD04060A diodes, a buck converter, having an
input voltage of 250 V and a load resistance of 40 Ohms, was tested, as shown in Figure
6.15. The waveform generator provided a 50 kHz square pulse with 20 ns rise and fall
times, and was switched between 0 V and 10 V. The duty cycle of the square pulse was
166
swept from 20 % to 50 % in 5 % increments, and waveform measurements were
recorded after each duty cycle increment of 5 %. For each level of dose, the IRF840
MOSFET having a value for R ds(on) closest to the average in its group was tested with a
CSD04060A diode having a value of R s closest to the average in its group.
167
L2
100uH
2
1
M1
IRF1310N
2
1
Vin
80V
C1
1 mF
D1
IR40CTQ150PBF
Vgate
TF = 20 ns
PW = 10 us
PER = 20 us
V1 = 0 V
TR = 20 ns
V2 = 10 V
L1
100 uH
C2
1 mF
D2
RL
10 Ohms
RL1
10 Ohms
Figure 6.13. A schematic for the buck converter circuit tested with the IRF1310N (42 A, 100 V) MOSFETs and the IR40CTQ150PBF (40 A, 150 V)
Si Schottky power diodes.
L2
100uH
1
2
1
2
D1
IR40CTQ150PBF
L1
100 uH
Vin
40V
C1
1 mF
D2
Vgate
TF = 20 ns
PW = 10 us
PER = 20 us
V1 = 0 V
TR = 20 ns
V2 = 10 V
M1
IRF1310N
C2
1 mF
RL
20 Ohms
Figure 6.14. A schematic for the boost converter circuit tested with the IRF1310N (42 A, 100 V) MOSFETs and the IR40CTQ150PBF (40 A, 150 V)
Si Schottky power diodes.
168
M1
IRF840
L1
1
2
1 mH
Vin
250V
C1
470 uF
Vgate
TF = 20 ns
PW = 10 us
PER = 20 us
V1 = 0 V
TR = 20 ns
V2 = 10 V
D1
CSD04060
C2
470 uF
RL1
40 Ohms
Figure 6.15. A schematic of a buck converter circuit tested with an IRF840 (8 A, 500 V) MOSFETs and a Cree CSD04060A (4 A, 600 V) SiC
Schottky power diode. In this circuit, V in = 250 V and R L = 40 Ohms.
169
6.4 I-V Characterization Results and Analysis for Schottky Power Diodes
The I-V characterization procedure, results, and analysis for the Vishay IRF840
and IR IRF1310N power MOSFETs used in the functional testing of the buck and boost
converters are given in Chapter 5. The I-V characterization results for the Vishay
IR40CTQ150PBF and the Cree CSD04060A diodes that were functionally tested are
given in section 6.4.1 and section 6.4.2, respectively. I-V characterization results are
only reported for the Vishay IR40CTQ150PBF diodes having a voltage drop (V D ) at a
current of 5 A (I D = 5 A) closest to the average of their respective sample with which
they were irradiated, and these were the only IR40CTQ150PBF diodes functionally
tested in boost and buck converters. Similarly, I-V characterization results are only
reported for the Cree CSD04060A SiC Schottky power diodes having a value of R S
closest to the average of their respective sample with which they were irradiated, and
these were the only CSD04060A diodes functionally tested in boost and buck converters.
6.4.1 I-V Characterization Results and Analysis for Vishay IR40CTQ150PBF Diodes
Results for the IR40CTQ150PBF diodes, for the low-injection curve-fit of the IV data to Equation 3.1, are shown in Table 6.1, for which the two diodes in the TO-220
package were wired in parallel for the measurement. Only parameters for the diodes
used in functional testing are reported in Table 6.1. At φeq ,1MeV ,Si greater than 5.0E14
(n/cm2), the resistance of the neutral regions became sufficiently large that the lowinjection and high-injection regions of the forward-bias I-V curve could not be
distinguished.
170
φeq,1MeV ,Si
0
3.6E+13
7.3E+13
1.1E+14
1.4E+14
1.8E+14
2.2E+14
5.0E+14
7.4E+14
1.0E+15
n (unit-less) I s (A)
1.06
1.05
1.06
1.06
1.06
1.07
1.07
1.15
-
7.5E-7
6.2E-7
6.1E-7
5.8E-7
6.2E-7
6.6E-7
6.6E-7
1.0E-6
-
Table 6.1. Results of curve fitting for the forward-biased low-injection region for the Vishay
IR40CTQ150PBF (40 A, 100 V) Si Schottky power diodes used in functional testing, for which the two
diodes in the TO-220 package were wired in parallel.
Results for the IR40CTQ150PBF diodes, for the high-injection curve-fit of the IV data for the extraction of R s are shown in Figure 6.16 and Table 6.1, for which the two
diodes in the TO-220 package were wired in parallel for the measurement.
For φeq ,1MeV ,Si greater than 2.2E14 (n/cm2), the I-V curves became sufficiently distorted
such that R s could not be extracted from the I-V curve data. The voltage drop at 5 A and
10 A as a function of φeq ,1MeV ,Si is shown in Figure 6.17 for the IR40CTQ150PBF
diodes, for all values of φeq ,1MeV ,Si . High-injection forward bias I-V curves for these
diodes for selected values of φeq ,1MeV ,Si are shown in Figure 6.18.
171
Figure 6.16. R s versus Φ eq,1MeV,Si for the Vishay IR40CTQ150PBF diodes used in functional testing, for
which the two diodes in the TO-220 package were wired in parallel.
Figure 6.17. Average voltage drop versus Φ eq,1MeV,Si for a diode current of 5 A and 10 A for the Vishay
IR40CTQ150PBF diodes used in functional testing, for which the two diodes in the TO-220 package were
wired in parallel.
172
Figure 6.18. High-injection, forward bias curves for selected values of Φ eq,1MeV,Si for Vishay
IR40CTQ150PBF diodes that were functionally tested.
In addition, the reverse-bias I-V characteristics of the Vishay IR40CTQ150PBF
diodes were also measured, and reverse-bias I-V curves for selected values of
φeq,1MeV ,Si are shown in Figure 6.19. As shown, the leakage current increases by
approximately 1 order of magnitude from φeq ,1MeV ,Si = 0 (n/cm2) to φeq ,1MeV ,Si = 1.0E15
(n/cm2). Furthermore, the breakdown voltage, which we arbitrarily define as the reverse
bias voltage at which the diode leakage current equals 1 mA, remained fairly unchanged
and above the manufacturer-rated breakdown voltage of 150 V for all of the Vishay
IR40CTQ150PBF diodes irradiated. The leakage current at 80 V and the breakdown
voltage are shown in Table 6.2 as a function of Φ eq ,1MeV ,Si .
173
Figure 6.19. Reverse bias curves for selected values of Φ eq,1MeV,Si for Vishay IR40CTQ150PBF diodes
that were functionally tested.
φeq,1MeV ,Si
0
3.6E+13
7.3E+13
1.1E+14
1.4E+14
1.8E+14
2.2E+14
5.0E+14
7.4E+14
1.0E+15
I D at V D = -80 V Breakdown Voltage
(A)
(V)
2.4E-6
192
3.2E-6
188
4.4E-6
188
4.6E-6
186
6.8E-6
180
8.1E-6
187
8.5E-6
185
1.5E-5
185
1.8E-5
184
2.2E-5
189
Table 6.2. Leakage current for a bias of VD=-80 V and breakdown voltage versus Φ eq,1MeV , Si for the
Vishay IR40CTQ150PBF (40 A, 100 V) Si Schottky power diodes used in functional testing, for which
the two diodes in the TO-220 package were wired in parallel.
174
6.4.2 I-V Characterization Results and Analysis for Cree SiC Schottky Power Diodes
Results for the low-injection curve-fit of the I-V data to Equation 3.1 are shown
in Table 6.3, for the Cree CSD04060A SiC Schottky power diodes, used in this
functional testing study. Only parameters for the diodes used in functional testing are
reported in Table 6.3.
D d (MeV/g) in SiC n (unit-less)
0.0E+00
1.045
3.8E+10
1.057
7.7E+10
1.049
1.2E+11
1.067
1.4E+11
1.066
1.5E+11
1.058
1.8E+11
1.054
1.9E+11
1.064
2.3E+11
1.075
I s (A)
4.02E-16
5.06E-16
4.99E-16
5.73E-16
6.17E-16
4.21E-16
5.32E-16
4.40E-16
1.10E-15
Table 6.3. Results of curve fitting for the forward-biased low-injection region for the Cree CSD04060A
(4 A, 600 V) SiC Schottky power diodes used in functional testing.
The results for R s versus D d,SiC for the Cree CSD04060A diodes, used in the
functional testing, are shown in Figure 6.20 for the high-injection curve-fit of the I-V
data to Equation 3.3. High-injection forward bias I-V curves for these diodes for
selected values of D d,SiC are shown in Figure 6.21.
In addition, the reverse-bias I-V characteristics of the Cree CSD04060A diodes
were also measured, and reverse-bias I-V curves for selected values of D d,SiC are shown
in Figure 6.22. The leakage current at 250 V and the breakdown voltage are shown in
Table 6.4 as a function of D d,SiC .
175
Figure 6.20. R s versus D d,SiC for the Cree CSD04060A diodes used in functional testing.
Figure 6.21. High-injection, forward bias curves for selected values of D d,SiC for Cree CSD04060A
diodes that were functionally tested.
176
Figure 6.22. Reverse bias curves for selected values of D d,SiC for Cree CSD04060A diodes that were
functionally tested.
D d (MeV/g) in SiC
0.0E+00
3.8E+10
7.7E+10
1.2E+11
1.4E+11
1.5E+11
1.8E+11
1.9E+11
2.3E+11
I D at V D = -250 V Breakdown Voltage
(A)
(V)
4.0E-10
887
2.0E-09
790
1.2E-09
791
7.3E-10
755
4.2E-09
862
8.3E-10
834
3.5E-09
877
7.6E-10
877
4.4E-09
828
Table 6.4 Leakage current for a bias of V D = -250 V and breakdown voltage versus D d,SiC for the Cree
CSD04060A SiC Schottky power diodes used in functional testing
177
6.5 Functional Testing Results for Buck Converter Containing IRF1310N MOSFETs
and IR40CQT150PBF Diodes
Two experiments were conducted for the buck converter containing IRF1310N
MOSFETs and IR40CTQ150PBF diodes. The first experiment, refered to as Experiment
I, was conducted approximately 2 months post-irradiation. For Experiment I, the current
probes measuring the current flowing out of the MOSFET source lead and into the diode
anode lead were measured attached to the Yokogawa 70251 isolation module, which has
a timing resolution of 1 sample per microsecond (1 MS/s). Although this sample rate
was sufficient for measuring input and output power over V in and the load resistor, this
sample rate was not fast enough to capture the switching characteristics of the MOSFET
and diode. Therefore, a second experiment, referred to as Experiment II, conducted 108
days post-irradiation, was conducted in order to measure the power dissipation during
switching, by attaching the Yokogawa current probes to the Yokogawa 70250 isolation
module, which as a sample rate of 1 sample per 100 ns, or (10 MS/s).
6.5.1 Experiment I for Buck Converter containing IRF1310N MOSFETs and
IR40CTQ150PBF Diodes: 2 Months Post-Irradiation
In the circuit of Figure 6.13, using the Yokogawa DL750 ScopeCorder labeled
(3a) in Figure 6.9, V o was measured directly over R L , consisting of the two 10 Ω load
bank resistors wired in parallel, and V in was measured directly over the input capacitor in
parallel with V in (high voltage DC power supply). Results for V o / V in versus TID in Si
for applied gate drive signals (V gate ) having duty cycles ranging from 20 % - 50 % are
178
shown in Figure 6.23, for the buck converter circuit of Figure 6.13. As shown in Figure
6.23, the values of V o / V in for each duty cycle were higher for all of the buck converter
circuits containing irradiated MOSFETs and diodes than for the buck converter
containing unirradiated devices. Furthermore, for the buck converter circuits with
irradiated MOSFETs and diodes, V o / V in for each duty cycle of V gate remained fairly
constant as a function of TID. The results for V o / V in versus duty cycle of V gate are
shown in
Figure 6.24 for the unirradiated diode and MOSFET, as well as for the diode and
MOSFET irradiated to a TID of approximately 3.7 Mrad(Si). The MOSFET and diode
irradiated to a value of Φ eq,1MeV,Si = 5.0E+14 (n/cm2) failed for a V gate duty cycle of 40
%, and the MOSFET and diode irradiated to Φ eq,1MeV,Si = 7.4E+14 (n/cm2) failed when a
V gate having a duty cycle of 30 % was applied. Failure is defined in terms of the
MOSFET as a short between the drain and source leads of the MOSFET, essentially
rendering the MOSFET useless.
The results for efficiency, in terms of P out / P in , are shown in Figure 6.25 for the
buck converter circuit of Figure 6.13. For this calculation, as the V in and V o were nearly
pure DC, P out was calculated according to Equation 6.31, where <V o > is the average of
the measured voltage waveform over R L . Also, R L is the measured load resistance of
4.964 Ohms, obtained with a 4-wire Kelvin measurement using a Hewlett Packard
3458A multimeter. Furthermore, P in was approximated according to Equation 6.32,
where <V in > is the average of the measured voltage waveform over the input capacitor,
which was essentially pure DC, in parallel with the DC power supply. In addition, in
Equation 6.32, the input current, <I in >, is the average of the current measured flowing
179
out of the source lead of the MOSFET, which was measured on a different Yokogawa
DL750 ScopeCorder than V in .
Pout =
< Vo > 2
RL
6.31
Pin = < Vin >< I in >
6.32
Figure 6.23. Measured V o / V in versus TID in Si for the buck converter shown in Figure 6.13, and for
applied gate drive signals, V gate , of various duty cycles. The duty cycles of the applied gate signals are
given in terms of %, shown to the right of each curve.
180
Figure 6.24. Measured V o / V in versus applied V gate duty cycle for an unirradiated MOSFET-diode pair,
as well as a MOSFET-diode pair irradiated to a TID of 3.7 Mrad(Si), tested in the buck converter shown in
Figure 6.13.
Figure 6.25. Efficiency, P out / P in , versus Φ eq,1 MeV,Si to which the IRF1310N MOSFETs and
IR40CTQ150PBF diodes of the buck converter circuit of Figure 6.13 were exposed.
181
The higher values of V o / V in for each duty cycle of V gate for the buck converter
circuits containing irradiated MOSFETs and diodes can be attributed to radiationinduced changes in the switching behavior of the MOSFET. This radiation-induced
effect is illustrated in Figure 6.26, in which the waveforms for V GS and V DS are shown
for a circuit containing an unirradiated diode and MOSFET and for a circuit containing a
diode and MOSFET irradiated to a Φ eq,1MeV,Si of 3.6E13 (n/cm2). The waveforms in
Figure 6.26 were measured for a waveform generator-applied V gate signal having a duty
cycle of 25%, measured using the Yokogawa DL750 ScopeCorder labeled (3b) in Figure
6.9. As shown in Figure 6.26, the low portion of the V DS waveform, for when V GS is
high, is wider for the irradiated diode and MOSFET. Therefore, as a result of
irradiation, the effective duty cycle of the MOSFET has increased for the same applied
V gate signal from the waveform generator. The portion of Figure 6.26 labeled “Detail” is
shown more clearly in Figure 6.27. As shown in Figure 6.24, irradiation has caused the
effective duty cycle to expand noticeably.
The results for the MOSFET switching times, according to the method shown in
Figure 6.8, are plotted in Figure 6.28 for a duty cycle of 25 %. The switching times in
Figure 6.28 were measured using the data obtained from the LeCroy oscilloscope, which
has a time resolution of 1 GS/s (1 sample per nanosecond).
As shown in Figure 6.28, t d(on) decreases sharply for the lowest TID value and
then remains fairly constant up to a TID of less than 4 Mrad(Si). This trend follows the
results for V TH as a function of TID for these IRF1310N MOSFETs, as presented in
Chapter 5. From Equation 6.26, a decrease in V TH has a potential to reduce t d(on) simply
because less time is required for V GS to increase to a lower value of V TH .
182
Figure 6.26. V DS and V GS waveforms for a Vgate signal having a duty cycle of 25 %, measured using a
Yokogawa DL750 ScopeCorder for various values of Φ eq,1 MeV,Si . The item labeled “Detail” is shown
more clearly in Figure 6.27.
Furthermore, according to the results shown in Figure 6.28, t d(off) increases as a
function of TID. The initial increase in t d(off) , for a TID of 0.6 Mrad (Si), may also be
attributed to the reduction of V TH , as a longer time is required for V GS to decrease to a
voltage sufficiently low to turn the MOSFET off, as indicated in Figure 6.27.
183
Figure 6.27. Portion of waveform labeled “Detail” in Figure 6.26, for selected dose levels, for an applied
V gate signal having a duty cycle of 25 %.
Figure 6.28. IRF1310N MOSFET switching times versus TID as measured according to the method
shown in Figure 6.8, for the buck converter circuit of Figure 6.13, for a V gate signal of 25 % duty cycle.
184
A PSpice model, in addition to the analytical model described in section 6.1.2.1,
was used to model the buck converter circuit shown in Figure 6.13. For the PSpice
model, the values of n, I s , and R s obtained from the I-V characterization of the
IR40CTQ150PBF diodes, as presented in section 6.4.1, were used as input for the
PSpice diode model. In addition, for the PSpice model, the values of V TH , k, and R D
obtained from the I-V characterization of these MOSFETs, presented in Chapter 5, were
used as input for the PSpice level-1 MOSFET physics model. In both the PSpice and
analytical models, the duty ratio of the MOSFET gate signal was modeled using the
experimentally determined effective duty cycle, Deff =
ton,eff
Ts
. For the purpose of
modeling, we arbitrarily define the time that the MOSFET is on, t on,eff , as the time
elapsed from when V DS falls to 10 % of V in at turn-on to the time that V DS increases to 10
% of V in at turn-off, as measured using the LeCroy oscilloscope. During this time, as
shown in Figure 6.6 and Figure 6.7, the MOSFET is conducting the full current passing
through the inductor, i L .
In Figure 6.29, for the buck converter of Figure 6.13, and for an applied V gate
signal of 25 %, experimental data in terms of V o / V in are compared with a PSpice model
of the circuit, as well as the analytical buck converter model developed in section
6.1.2.1. For TID > 4 Mrad(Si), only results for the analytical model and experimental
data are given, as the MOSFET and diode I-V characteristics were degraded to such an
extent such that they could not be modeled using the PSpice physics models. In
addition, the inductor current, for a V gate signal of 25 %, is shown in Figure 6.30 for the
185
experimental data as well as the analytical and PSpice model of the buck converter of
Figure 6.13, for one switching cycle.
Figure 6.29. V o / V in for a V gate signal of 25 % versus TID, as shown for the experimental data and the
PSpice and analytical models.
It should be noted that, from the results of Experiment I, neither the data from
this experiment, the PSpice model, nor the analytical buck converter model of section
6.1.2.1 are sufficient to explain the failure of the IRF1310N MOSFETs irradiated to TID
values greater than 4 Mrad(Si).
Therefore, a second experiment, Experiment II, was
conducted 108 days post-irradiation, in order to measure the MOSFET power dissipation
during switching, using higher time-resolution for measuring the current.
186
Figure 6.30. Inductor current for a V gate signal of 25 % for an IRF1310N MOSFET and IR40CTQ50PBF
diode pair irradiated to 1.2 Mrad(Si) (Φ eq,1MeV,Si = 7.3E13 n/cm2), as shown for the experimental data and
the PSpice and analytical models.
6.5.2 Experiment II for Buck Converter containing IRF1310N MOSFETs and
IR40CTQ150PBF Diodes: 108 Days Post-Irradiation
Experiment II was conducted using the same MOSFET and diode pairs in the
same buck converter circuit of Figure 6.13 as Experiment I, approximately 47 days after
Experiment I, and therefore 108 days post-irradiation. After this period of time, the
MOSFET and diodes had annealed to some extent as determined by additional I-V
characterization measurement.
However, unlike the first experiment, for this experiment, the current probes
were attached to the Yokogawa 701250, 12-bit isolation module, which had a sample
rate of 1 data-point per 100 nanoseconds (10 MS/s). Therefore, with this setup, the
187
power dissipation in the MOSFET during the turn-on and turn-off switching transients
could be measured.
To illustrate, the V DS and I D waveforms of unirradiated and irradiated IRF1310N
MOSFETs, for this experiment, conducted 108 days post-irradiation, are shown in
Figure 6.31. The irradiated MOSFETs were irradiated to a TID in Si of approximately 4
Mrad(Si). Note that in Figure 6.31, the initial drop in V DS at turn-on coincides with the
rise of I D for both the unirradiated and irradiated MOSFETs. Also, the spike in the V DS
waveform concides with the fall of I D for both the irradiated and unirradiated
MOSFETs. This spike in V DS is a known effect for circuits of this type [60,74] and is
caused by the parasitic inductance on the drain, high-voltage side of the MOSFET [74].
Note that this voltage spike is also present in the V DS waveforms of Figure 6.26 from the
first IRF1310N buck converter experiment, and appears to lengthen in time duration
with respect to radiation dose. Referring to Figure 6.31, as the voltage across an
inductor, in general, is governed by V = L
di
, it is reasonable that this voltage seen in the
dt
V DS waveforms of the unirradiated and irradiated MOSFETs disappears, and V DS falls to
the value of V in ~ 80 V as I D falls to 0. These V DS and I D waveform characteristics were
essentially universal for all MOSFETs and applied V gate duty cycles used in this
experiment. The MOSFET turn-on and turn-off portions of the waveforms shown in
Figure 6.31 are shown more clearly in Figure 6.32 and Figure 6.33, respectively.
188
Figure 6.31. V DS and I D waveforms for the IRF1310N MOSFET in the buck converter circuit of Figure
6.13, 108 days post-irradiation, measured using a Yokogawa DL750 ScopeCorder.
With the better timing resolution in the current measurement, the power
dissipation contributed by the switching transients could be measured. In order that this
analysis can then be applied to the first buck converter experiment for which the current
could not be measured with sufficient timing precision, we base the time definitions
relating to the duration of the switching transients on the behavior of V DS .
189
Figure 6.32. MOSFET Turn-on portion of the V DS and I D waveforms shown in Figure 6.31.
Figure 6.33. MOSFET Turn-off portion of the V DS and I D waveforms shown in Figure 6.31.
190
For instance, we define the beginning of the turn-on transient as the time at
which V DS drops to 5 % below V in . Furthermore, we define the time at which V DS drops
to 5 % above V in at the end of the V DS turn-off spike as the end of the turn-off transient.
In addition, we then define the end of the turn-on transient as the time at which V DS falls
to 10 % of V in at turn-on; also, we define the beginning of the turn-off transient as the
time at which V DS rises to 10 % of V in at turn-off. Therefore, we maintain the definition
of on-state conduction from the previous experiment and analysis as being the time
during which V DS is less than 10 % of V in . In this dissertation, we follow the notation in
[46] for the duration of the turn-on and turn-off transients. In this dissertation, the
duration of the turn-on transient is referred to as t c(on) , and the duration of the turn-off
transient is referred to as t c(off) . These definitions and terms are illustrated in Figure
6.34, using the measured V DS and I D waveforms for an unirradiated MOSFET and diode,
for a V gate duty cycle of 35 %.
Figure 6.34. Definitions and terms relating to MOSFET switching characteristics for a buck-converter.
191
Referring to Figure 6.34, we define P S,ton , P S,C , and P S,toff as the power dissipated
by the MOSFET during the turn-on, on-state conduction, and turn-off portions of the
switching cycle, respectively. The quantities P S,ton , P S,C , and P S,toff are time-averaged
quantities over the switching cycle. Results with respect to MOSFET power dissipation
are shown for the buck converter experiment for the IRF1310N MOSFETs in
Table 6.5, for an applied V gate signal duty cycle of 25 %. As the MOSFETs
irradiated to a TID greater than 4 Mrad(Si) were destroyed during the first experiment,
only the results for TID less than 4 Mrad(Si) are shown. From the results in
Table 6.5, the power dissipation during the turn-off transient dominates the total
power dissipated by the MOSFET, accounting for approximately 90 % of the total power
dissipation. In addition, the results for power dissipated versus duty cycle for TID levels
of 0, 0.6 Mrad (Si), and 3.7 Mrad (Si) are shown in Figure 6.35, Figure 6.36, and
Figure 6.37, for P S,ton , P S,C , and P S,toff respectively. In addition, the power
dissipation in the diode is given in Figure 6.38.
192
TID (Mrad(Si)) P S,ton (W) P S,C (W) P S,toff (W)
0
1.5
~0
12.6
0.6
1.4
0.1
17.3
1.2
1.6
0.1
19.1
1.8
1.5
0.2
18.7
2.5
1.1
~0
18.4
3.1
1.3
0.2
18.4
3.7
1.4
0.1
18.5
Table 6.5. MOSFET power dissipation results for the IRF1310N MOSFETs in the buck converter of
Figure 6.13, for an applied Vgate Duty Cycle of 25 %.
Figure 6.35. P s,ton versus Vgate duty cycle for various levels of TID in Si.
193
Figure 6.36. P S,C versus V gate duty cycle for various levels of TID in Si.
Figure 6.37. P S,toff versus V gate duty cycle for various levels of TID in Si.
194
Figure 6.38. Diode power dissipation versus V gate duty cycle for various levels of TID in Si.
It can be seen in Figure 6.37 that the turn-off transient is the major contributor to
power dissipation in the MOSFET buck converter circuit of Figure 6.13, and increases
with TID in Si as well as duty cycle. Furthermore, the power dissipated during on-state
conduction, P S,C also increases with TID in Si and duty cycle. The major contributor to
P S,C is expected to be the MOSFET on-state resistance, R ds(on) . For the IRF1310N
MOSFETs irradiated to TID levels of 3.7 Mrad(Si), which corresponds to Φ eq,1MeV,Si =
2.2E+14 n/cm2 in the OSURR rabbit facility, the major contributor to R ds(on) was
determined to be reduced electron mobility in the conductive channel, as discussed in
Chapter 5. It is interesting to note, however, that the the power dissipated in the
MOSFETs during turn-on decreased slightly with increasing TID. One explanation for
this effect is the decrease in t d(on) with increasing TID in addition to the fairly constant
195
trend of t r with respect to TID, as shown in Figure 6.28 for Experiment I. The increase
in power dissipation for P S,ton , P S,C , and P S,toff for increasing duty cycle is due to the fact
that the current is larger for higher duty cycles.
In a clamped-inductive load, using the notation of this dissertation for the timeduration of the turn-on and turn-off transients, the energy dissipated in the MOSFET
1
during turn-on, E on , can be approximated by Eon ≈ Vin I 0tc (on ) , where I 0 is the inductor
2
current [60]. Likewise, the energy dissipated in the MOSFET during turn-off, Eoff , can
1
be approximated by Eoff ≈ Vin I 0tc (off ) [60]. Therefore, by extension, the power
2
dissipated during turn-on, P S,ton , can be approximated by Equation 6.33, and the power
during turn-off, P S,toff , can be approximated by Equation 6.34, where f s is the MOSFET
switching frequency:
1
PS=
f s Er ≈ Vin I 0 f s tc( on )
,ton
2
6.33
1
PS=
f s E f ≈ Vin I 0 f s tc( off )
,toff
2
6.34
Equations 6.33 and 6.34 are based on the linearized approximation of Figure 6.39.
Therefore, we added this approximation to the analytical model for a non-ideal buck
converter derived in section 6.1.2.1 in order to calculate P S,ton and P S,toff . Furthermore,
in this modified analytical model, we replace I 0 with the value of the MOSFET current
at the end of turn-on in Equation 6.33, and we also replace I 0 with the value of the
MOSFET current at the on-set of turn-off in Equation 6.34, since in the experiment, the
196
MOSFET current was not constant and had a substantial ripple component, as shown in
Figure 6.31.
ID
I0
t
0
VDS
Vin
t
0
E
Eoff
Eon
0
tc(off)
t
tc(on)
Figure 6.39. MOSFET turn-on and turn-off, linearized waveforms for a circuit with a clamped inductive
load, after [60].
Comparisons between the experimental data and the analytical model, for P S,ton ,
P S,C , P S,toff , and PS ,total ≈ PS ,ton + PS ,C + PS ,toff are shown in Figure 6.40, Figure 6.41,
Figure 6.42, and Figure 6.43, respectively.
The results shown in Figure 6.40 indicate
that P S,ton is relatively insensitive to radiation dose. However, from the results shown in
Figure 6.41 and Figure 6.42, P S,C and P S,toff are sensitive to radiation dose. From the
MOSFET I-V characterization results from Chapter 5, the R ds(on) of the IRF1310N
MOSFET increased as a result of decreased electron mobility in the conductive channel,
which increases on-state power dissipation. Also, as shown in Figure 6.28, the voltage
spike in V DS at turn-off increases in time-duration, indicating that the current is taking
197
longer to fall to 0. An increase in the time required for the current to fall to 0 when V DS
is high results in an increase in the power dissipation at turn-off. From these figures, it is
apparent that P S,toff is the primary contributor to total power dissipation in the MOSFET.
Figure 6.40. P s,ton versus V gate duty cycle for various levels of TID in Si, comparing analytical model
from section 6.1.2.1 to experimental data from Experiment II, conducted 108 days post-irradiation.
198
Figure 6.41. P s,C versus V gate duty cycle for various levels of TID in Si, comparing analytical model from
section 6.1.2.1 to experimental data from Experiment II, conducted 108 days post-irradiation.
Figure 6.42. P s,toff versus V gate duty cycle for various levels of TID in Si, comparing analytical model
from section 6.1.2.1 to experimental data from Experiment II, conducted 108 days post-irradiation.
199
Figure 6.43. P s,total versus V gate duty cycle for various levels of TID in Si, comparing the analytical model
from section 6.1.2.1 to experimental data from Experiment II, conducted 108 days post-irradiation.
Although the current could not be measured with sufficient time resolution
necessary to experimentally determine the power dissipation in the MOSFET for the
setup in Experiment I, the analytical model can be used to estimate P S,ton and P S,toff for
Experiment I, since it was determined from Experiment II that the rise and fall of the
current can be predicted based on the fall and rise of V DS , as shown in Figure 6.34.
Results for the calculated estimates of power dissipation in the MOSFET for Experiment
I, using the analytical buck converter model derived in section 6.1.2.1, are shown in
Figure 6.44, Figure 6.45, Figure 6.46, and Figure 6.47 for P S,ton , P S,C , P S,toff , and P S,total ,
respectively.
The results for P S,total , shown in Figure 6.47, still do not determine the cause of
failure for the MOSFETs irradiated to dose levels of approximately 8 Mrad(Si) and 13
Mrad(Si), as the maximum power dissipation specified on IR’s datasheet for this
200
MOSFET is 160 W for a junction temperature of 25 degrees Celsius. However, it should
be noted that the temperature of the MOSFET heat sink could not be measured
accurately during the experiment using the thermocouples attached to the Yokogawa
DL750 ScopeCorder, and that a linear derating factor of 1.1 W/oC is specified on the
datasheet. Since the most highly irradiated MOSFETs failed as higher duty cycles were
applied, the failure of these MOSFETs is attributed to thermal breakdown of the p-n
junction formed by the p-type body and n- drain region of the MOSFET.
Figure 6.44. Buck converter analytical model (section 6.1.2.1) estimate for P s,ton versus V gate duty cycle
for various levels of TID in Si, based on data from Experiment I, conducted 2 months post-irradiation.
201
Figure 6.45. Buck converter analytical model (section 6.1.2.1) estimate for P s,C versus V gate duty cycle for
various levels of TID in Si, based on data from Experiment I, conducted 2 months post-irradiation.
Figure 6.46. Buck converter analytical model (section 6.1.2.1) estimate for P s,toff versus V gate duty cycle
for various levels of TID in Si, based on data from Experiment I, conducted 2 months post-irradiation.
202
Figure 6.47. Buck converter analytical model (section 6.1.2.1) estimate for P s,total versus V gate duty cycle
for various levels of TID in Si, based on data from Experiment I, conducted 2 months post-irradiation.
From the results with respect to MOSFET power dissipation from Experiment I
and II, it was determined that P S,toff was the major contributor to the total power
dissipation in the MOSFET, and P S,toff increases with radiation dose, as shown in Figure
6.42 and Figure 6.46. One way to reduce P S,toff is to reduce the current at turn-off, I 0 .
This can be accomplished by simply increasing the load inductance, L, in the buck
converter circuit, since this, in turn, leads to a decrease in the ripple component of the
current, noting that the voltage across an ideal inductor, VL = L
di
. This reduction in the
dt
ripple component of the current and the resulting reduction of the MOSFET conduction
current at turn-off, calculated using the analytical buck converter model described in
section 6.1.2.1, are shown in Figure 6.48 as the load inductance is increased from the 50
μH equivalent load inductance used in Experiment I and Experiment II. As shown in
203
Table 6.6, for an applied V gate signal having a duty ratio of 50 %, the increase in load
inductance from 50 μH to 200 μH for the MOSFET and diode pair irradiated to 3.7
Mrad(Si) results in a decrease in total power dissipation, P S,total , by nearly 16 %.
Figure 6.48. MOSFET conduction current, I D , as a function of load inductance, L, calculated using the
analytical buck converter model of section 6.1.2.1 for the MOSFET and diode pair irradiated to 3.7
Mrad(Si), based on data from Experiment I, conducted 2 months post-irradiation. The calculation is based
on a V gate signal having a duty ratio of 50 %.
L (μH) P S,ton (W) P S,C (W) P S,toff (W) P S,total (W)
50
4.9
2.0
50
57
100
7.3
1.9
42
51
150
8.1
1.8
39
49
200
8.5
1.8
38
48
Table 6.6. As a function of load inductance, L: MOSFET power dissipation estimates calculated using
analytical buck converter model from section 6.1.2.1 for the IRF1310N MOSFET and IR40CTQ150PBF
diode pair irradiated to 3.7 Mrad(Si), based on data from Experiment I, conducted 2 months postirradiation.
204
6.6 Functional Testing Results for Boost Converter Containing IRF1310N MOSFETs
and IR40CQT150PBF Diodes: Two Months Post-Irradiation
In the circuit of Figure 6.14, using the Yokogawa DL750 ScopeCorder labeled
(3a) in Figure 6.9, V o was measured directly over R L , consisting of a 20 Ω load bank
resistor, and V in was measured directly over the input capacitor in parallel with V in (high
voltage DC power supply). Results for V o / V in versus TID in Si for applied gate drive
signals (V gate ) having duty cycles ranging from 20 % - 50 % are shown in Figure 6.49,
for the boost converter circuit of Figure 6.14. Also, V o / V in results for the PSpice
model as well as the analytical boost converter model, derived in section 6.1.2.2 are
compared with the values obtained from the experiment in Table 6.7 for an applied
Vgate duty cycle of 25 %. Results are shown for the experimental data and analytical
model in Table 6.8 for an applied V gate duty cycle 50 %.
The results for efficiency, in terms of P out / P in , are shown in Figure 6.51 for the
boost converter circuit of Figure 6.14. For this calculation, as the V in and V o were nearly
pure DC, P out was calculated according to Equation 6.31, where <V o > is the average of
the measured voltage waveform over R L . Also, R L is the measured load resistance of
19.756 Ohms, obtained with a 4-wire Kelvin measurement using a Hewlett Packard
3458A multimeter. Furthermore, P in was calculated according to Equation 6.32, where
<V in > is the average of the measured voltage waveform over the input capacitor, in
parallel with the DC power supply. In addition, in Equation 6.32, the input current,
<I in >, is the average of the current flowing into the two 100 μH inductors wired in
parallel.
205
Figure 6.49. V o / V in versus TID for V gate signals having various duty cycles, for the boost converter of
Figure 6.14.
Figure 6.50. V o / V in versus V gate duty cycle for selected dose levels, for the boost converter of Figure
6.14.
206
TID (Mrad(Si)) Φeq,1MeV,Si (n/cm2) Experiment PSpice Analytical Model
0.0
0.0E+00
1.33
1.34
1.32
0.6
3.6E+13
1.36
1.36
1.34
1.2
7.2E+13
1.36
1.35
1.35
1.8
1.1E+14
1.36
1.35
1.35
2.5
1.4E+14
1.37
1.36
1.36
3.1
1.8E+14
1.37
1.36
1.36
3.7
2.2E+14
1.38
1.36
1.36
Table 6.7. Results for V o /V in versus radiation dose for the boost converter shown in Figure 6.14
containing IRF1310N MOSFETs and IR40CTQ150PBF diodes, for an applied V gate duty cycle of 25 %.
Results obtained from the PSpice model and the analytical boost converter model (section 6.1.2.2) are
compared with those obtained from the experiment.
TID (Mrad(Si)) Φeq,1MeV,Si (n/cm2) Experiment Analytical Model
0.0
0.0E+00
1.93
1.93
0.6
3.6E+13
1.99
1.99
1.2
7.2E+13
2.00
1.98
1.8
1.1E+14
2.01
1.98
2.5
1.4E+14
2.02
2.00
3.1
1.8E+14
2.02
2.02
3.7
2.2E+14
2.02
2.02
Table 6.8. Results for V o /V in versus radiation dose for the boost converter shown in Figure 6.14
containing IRF1310N MOSFETs and IR40CTQ150PBF diodes, for an applied V gate duty cycle of 50 %.
Results obtained from the analytical boost converter model (section 6.1.2.2) are compared with those
obtained from the experiment.
207
Figure 6.51. Power conversion efficiency versus Φ eq,1MeV,Si for V gate signals having duty cycles of 25 %
and 50 %, for the boost converter of Figure 6.14.
6.7 Functional Testing Results for High-Voltage Buck Converter Containing Vishay
IRF840 MOSFETs and Cree CSD04060A Diodes: Two Months Post-Irradiation
In addition, a buck converter, containing a Vishay IRF840 (8 A, 500 V) power
MOSFET and a Cree CSD04060A (4 A, 600 V) SiC Schottky power diode, shown in
Figure 6.15 with a V in of 250 V, was tested. For each pair, consisting of a MOSFET and
diode irradiated to the same dose in the OSURR rabbit facility, the circuit was tested,
with the duty cycle of V gate swept, in 5 % increments, from 20 % to 50 %, or until the
MOSFET in the circuit failed. In the context of this dissertation, failure of the MOSFET
means that the drain and source of the MOSFET shorted together, rendering the
MOSFET useless.
208
Φ eq,1MeV,Si (n/cm2) TID (Mrad(Si)) Duty Cycle at Failure (%)
6.2E13
1.1
40
8.6E13
1.4
50
1.0E14
1.8
40
Table 6.9. Dose and duty cycle at which Vishay IRF840 MOSFETs failed in the circuit of Figure 6.15.
As the radiation-induced increase in R s for even the most highly irradiated Cree
CSD04060A diodes was less than 100 mΩ, as shown in Figure 6.20, there was very little
change in voltage drop across the diode as a function of radiation dose, as shown in
Figure 6.52. However, as R ds(on) for the Vishay IRF840 MOSFET increased by over a
factor of four for a Φ eq,1MeV,Si of 1.0E14 (n/cm2), as shown in Figure 5.12, the voltage
drop over the MOSFET, V DS , increased significantly with dose, as shown in Figure 6.53.
Note that in Figure 6.52, the irradiated diode is conducting for a shorter portion
of the input cycle for the same duty cycle of applied V gate . This is consistent with the
waveforms of the MOSFET shown in Figure 6.53, for which the irradiated MOSFET is
conducting for a longer portion of the input cycle for the same duty cycle of applied
V gate . Therefore, the duty cycle of the MOSFET has increased as a result of irradiation,
similar to the effect observed for the buck and boost converters containing the
IRF1310N MOSFETs discussed in section 6.5 and 6.6. Results for V o / V in versus TID
in Si for applied gate drive signals (V gate ) having duty cycles ranging from 20 % - 50 %
are shown in Figure 6.54, for the buck converter circuit of Figure 6.15.
209
Figure 6.52. Voltage waveforms across the diode in the buck converter of Figure 6.15, for one circuit
containing an unirradiated diode and MOSFET and another containing a highly irradiated diode and
MOSFET. For these measurements, V gate = 35 %. Corresponding waveforms for the MOSFETs tested
with these diodes in the same circuit are shown in
Figure 6.53.
210
Figure 6.53. Voltage waveforms across the MOSFET in the buck converter of Figure 6.15, for one circuit
containing an unirradiated diode and MOSFET and another containing a highly irradiated diode and
MOSFET. For these measurements, V gate = 35 %. Corresponding waveforms for the diodes tested with
these diodes in the same circuit are shown in
Figure 6.52.
211
Figure 6.54. Measured V o / V in versus TID in Si for the buck converter shown in Figure 6.15, and for
applied gate drive signals, V gate , of various duty cycles. The duty cycles of the applied gate signals are
given in terms of %, shown to the right of each curve.
6.8 Conclusions
In conclusion, the output voltage of all of the buck and boost converter circuits
tested in this chapter increased sharply, then increased at a slower rate as a function of
radiation dose. This is similar to the trend observed for results for the MOSFETs with
respect to threshold voltage, transconductance, and leakage currents as a function of
radiation dose, presented in Chapter 5. The increase in output voltage of the buck and
boost converter circuits is attributed to the decrease in MOSFET threshold voltage with
increasing radiation dose, as a decrease in threshold voltage decreases t d(on) and increases
t d(off) . This decrease in t d(on) and t d(off) leads to an increase in the effective duty cycle of
the MOSFET, for the same gate signal applied by the waveform generator. The increase
in effective duty cycle, in turn, leads to an increase in output voltage in both the buck
212
and boost converters. Practically speaking, this is not viewed as a major problem, since,
in general, a feedback and control system would likely be used to automatically control
the signal to the MOSFET gate and reduce the applied V gate duty cycle to compensate for
the radiation-induced increase in output voltage.
However, a greater concern is the increased power dissipation in the MOSFETs
as a function of radiation dose. Increased power dissipation may eventually lead to
thermal breakdown and therefore total destruction of the MOSFET. Power dissipation
during the turn-off switching transient, P S,toff , was observed to be the major component
of total power dissipation for the IRF1310N MOSFETs tested in this study. The
increase in P S,toff with radiation dose is attributed to the longer times it takes for the
MOSFET drain current to fall to 0 after V DS has increased above the input voltage, V in ,
at turn-off. One way to decrease P S,toff is to increase the load inductance, and therefore
minimize the MOSFET drain current during the turn-off transient.
The 500 V MOSFETs, part number IRF840, failed at much lower dose levels
than the 100 V, IRF1310N MOSFETs, for which none failed for Φ eq,1MeV,Si less than 2.2
E14 (n/cm2), corresponding to a TID of approximately 3.7 Mrad(Si). This can be
attributed to the higher sensitivity of higher-rated voltage MOSFETs to radiation, due to
their having thicker gate oxides and a lower-doped n- drift layer to support the higher
breakdown voltage. As discussed in Chapter 5, MOSFETs having thicker gate oxides
are more susceptible to gate oxide charging effects, such as reduced threshold voltage
and transconductance, as well as increased leakage currents. Furthermore, a lowerdoped n- drift layer, typically required by higher-voltage rated MOSFETs, leads to
increased sensitivity to radiation-induced displacement damage effects, such as an
213
increase in on-state resistance. This increase in on-state resistance leads to higher
voltage drops, and thus on-state power dissipation, during the portion of the switching
cycle that the MOSFET is fully on.
In all of the circuits tested, the diodes had little effect on circuit performance,
even for the most highly irradiated diodes. Furthermore, unlike the most highly
irradiated MOSFETs tested, all of the IR40CTQ150PBF and Cree CSD04060A diodes
in this study remained operational after functional testing.
214
CHAPTER 7 : MITIGATION OF RADIATION EFFECTS
From the functional testing and analysis of the half-wave rectifier and DC-toDC buck and boost converters, the main concern is the integrity of the semiconductor
device. Therefore, in this chapter, we discuss ways in which to mitigitate the effects of
radiation on device properties, using the results and conclusions from previous chapters.
For example, we have discussed how the high band gap of SiC enables it to be
used in Schottky power diodes, having high breakdown voltages, low leakage currents,
and increased radiation-tolerance. Furthermore, the only degradation observed for the
SiC Schottky power diodes was an increase in R s , and thus on-state resistance. An
increase in R s in turn leads to higher power dissipation in the diode, which may
eventually lead to destruction of the diode. One way in which the power dissipation for
a Schottky diode can be decreased with respect to radiation dose is simply to add more
diodes in parallel, so that the current, and therefore the power dissipation, is shared
among the diodes. MOSFETs can also be easily paralled [46].
Furthermore, higher operating temperatures may be beneficial in harsh radiation
environments, in the form of thermal annealing. Therefore, in this chapter, we present
the results of an isothermal annealing experiment, in which Cree SiC Schottky power
diodes were annealed, post-irradiation, for various times at 175 C.
215
For example, we discussed in Chapter 6 how increasing the load inductance in a
buck converter can reduce the power dissipation in the MOSFET during the turn-off
transient by simply reducing the ripple in the current. In this chapter, we will present IV characterization results of a rad-hard, 500 V MOSFET.
7.1 Parallel Configuration
In order to determine the effects of parallel configuration in circuit topologies
with respect to power dissipation in semiconductor devices, we revisit the half-wave
rectifier circuits tested in Chapter 4, containing the irradiated Cree CSD05120A (5 A,
1200 V) diodes. A schematic of this half-wave rectifier is shown in Figure 7.1. A halfwave rectifier circuit containing three Cree CSD05120A in parallel is shown in Figure
7.2.
D1
CSD05120
100
VAMPL = 240.4
FREQ = 60
0
Figure 7.1. Half-wave rectifier circuit containing a singe diode.
216
D1
CSD05120
D2
CSD05120
D3
100
VAMPL = 240.4
CSD05120
FREQ = 60
0
Figure 7.2. Half-wave rectifier circuit containing three diodes in parallel.
For the single diode configuration, PSpice simulations were performed for
circuits containing the diode having a value of R s nearest to the mean in its
corresponding group of three CSD05120A diodes irradiated to the same dose. In Figure
7.3, the results for average power dissipation in forward bias are compared against the
experimental data for these same diodes, measured using the Yokogawa DL750
Scopecorder. Also, PSpice simulations were performed for the circuit of Figure 7.2,
containing all three diodes from each group, irradiated to the same dose level. The
results from the PSpice simulations for the three diodes in parallel are also shown in
Figure 7.3, for comparison. From Figure 7.3, the PSpice simulation predicts that the
parallel configuration can significantly reduce the average power dissipation per diode
for each dose level.
217
Figure 7.3. Results for average power dissipation per diode as a function of D d,SiC for Cree CSD05120A
diodes in a half-wave rectifier circuit. The results from the PSpice simulation are compared to the
experimental results for a single diode. Furthermore, PSpice results are shown for three diodes in parallel.
7.2 Isothermal Annealing of Cree SiC Schottky Diodes
The objective of this isothermal annealing experiment is to determine the effect
of elevated temperature on the operational performance of semiconductors in a nuclear
radiation field. Generally, as a crystal is heated to a certain temperature, defects may be
mobilized, and therefore their positions (or even their existence), may be altered as a
result. These changes may be a result of vacancy-interstitial recombination, diffusion of
mobile defects to drains, or various other mechanisms. As irradiation induces changes in
a semiconductor’s structure, the electrical properties of the semiconductor may be
altered as well. The structural and electrical properties of the semiconductor may be
restored, or at least partially restored, to their pre-irradiation condition, in a process
218
(such as heating) in which case the damage is described as having been “annealed.”
Recent studies on thermal annealing in SiC indicate that low temperature annealing,
even within the operating temperature limit of the commercial Cree SiC Schottky diodes,
rated at 175 C, is possible [75]. Therefore, one of the aims of this research was to
determine if, and to what extent, operating these diodes at the upper limit of their rated
temperature will improve their performance in a nuclear radiation field.
Isothermal annealing experiments were performed on Cree CSD10120A, (10 A,
1200 V) SiC Schottky diodes that had been irradiated in the OSURR. As the purpose of
the isothermal annealing procedure was to determine the effects of elevated temperature
on the electrical performance of the diodes as they are operating within their rated limits,
all of the diodes were annealed at a constant temperature of 175 C, which is the
manufacturer-rated operating junction and storage temperature of these diodes. In
particular, the goal of the isothermal anneal study was to determine the effects of
annealing with respect to time at a constant temperature, as well as the effects of
annealing with respect to neutron dose.
7.2.1 Irradiation Procedure
Fifteen Cree CSD10120A diodes were irradiated in the rabbit facility, in groups
of three. The diodes, in groups of three, were covered in cadmium and placed inside a
polyethylene bottle. One group of three diodes remained unirradiated in order to serve
as the control group. All irradiations and measurements were performed at room
temperature. Following irradiation, after an appropriate time, which allowed for the
219
radioactivity of the samples to decay to the point that the diodes could be safely handled,
the diodes were tested.
The diodes were labeled and irradiated to various neutron fluences at a nominal
power of 450 kW (for a D d rate in SiC of 1.2 ×109
MeV
), in groups of three. Table 7.1
g s
presents a list of the diode labels along with the D d,SiC to which the diodes were
irradiated.
Diode Label #
1,2,3
4,5,6
7,8,9
10,11,12
13,14,15
16,17,18
D d,SiC (MeV/g)
0
1.4E+11
2.8E+11
3.5E+11
7.8E+11
8.4E+11
Table 7.1. Correspondence between Diode Labels and D d,SiC to which Cree CSD10120A diodes were
exposed.
7.2.2 I-V Characterization Procedure
I-V measurements were made with two different instruments for forward and
reverse bias diode conditions. A Keithley 2410, being well-suited for low current, high
voltage measurements, was used to make I-V measurements under conditions of reverse
bias and for low injection, forward bias conditions. A Keithley 2430, having the
capability for operation for currents as large as 10 A, was used for high injection,
forward bias measurements. For both Keithley devices, each device lead was attached to
two sets of wires, one for signal application and the other for sense measurement. This
I-V measurement setup enabled 4-wire measurements, and thereby reduced the effects of
the cables on the measurement results. The I-V characterization setup is shown in
Figure 3.4.
220
7.2.3 Isothermal Anneal Procedure
The CSD10120A diodes were heated with a MINCO CT137 digital temperature
controller, shown in Figure 7.4. The diodes were placed metal (heat sink) side down,
three at a time, on top of aluminum blocks to which the heating and temperature sensor
elements of the digital temperature controller were wired, as shown in Figure 7.5. For
the isothermal annealing experiment with the CSD10120A diodes, in the interest of
determining the transient anneal characteristics, the diodes were annealed in 7 time
increments, for a total of 7 cumulative anneal times, ranging in powers of 2 from 1 to a
total of 64 minutes. The I-V curve measurement of each diode was made after each
annealing increment.
Figure 7.4. Minco CT137 digital temperature controllers, used for heating the CSD10120A diodes.
221
Figure 7.5. CSD10120A diodes placed on an aluminum block, with heater and sense wires from the
MINCO CT137 digital temperature controller.
7.2.4 Isothermal Anneal Results and Discussion
The I-V curves were fit to Equation 3.1 and Equation 3.2 to determine n, I s , and
R s . As discussed in section 3.8,
1 n0 − K n Φ n
, as given by Equation 3.7.
=
Rs
C
Furthermore, we refer to Ru = C / n0 as the series resistance of the diode pre-irradiation.
The difference between 1/R u and 1/R s is independent of the initial dopant density, which
is useful in reducing the effects arising from variations in the manufacturing process in
an analysis of the effects of radiation on the diode’s series resistance. Forming the
difference between 1/R u and 1/R s results in Equation 7.1:
∆(1/ R) =
1/ Ru − 1/ Rs =
KnΦ n / C .
7.1
Furthermore, we refer to R s,0 as the series resistance of the diode post-irradiation but preanneal, and we refer to R s,A as the series resistance of the diode post-irradation and post-
222
anneal. Substituting R s,0 and R s,A into Equation 7.1 for R s yields ∆(1/ Rs ,0 ) and
∆(1/ Rs , A ) , respectively.
Some results from the isothermal anneal are shown in Figure 7.6. It can be seen
in the figure that the resistance decreases sharply for the first few minutes of anneal.
Figure 7.7 illustrates the results of the isothermal anneal, in terms of
∆ (1 R S , A ) / ∆ (1 Rs ,0 ) versus anneal time at a temperature of 175 C, for the CSD10120A
diodes. This ratio quantity is related to the fraction of radiation-induced defects, initially
created, which remain after the thermal anneal. For example, if R s,A = R s,0 , then all of
the defects initially induced by the radiation remain after the anneal. On the other hand,
if the thermal anneal is able to reduce R s,A to the unirradiated series resistance, R u , then
∆(1/ Rs ,0 ) , and thus ∆ (1 R S , A ) / ∆ (1 Rs ,0 ) would both equal 0.
As shown in Figure 7.7, this ratio decreased sharply within the first 8 minutes of
annealing, then decreased at a slower rate with respect to time. The trends are not as
smooth for the lower doses, due to higher measurement variations for these diodes. In
general, the measurement uncertainties ranged between 2% and 2.5% for the most highly
irradiated diodes, and 10% for the lowest irradiated diodes. The results of the isothermal
anneal, in terms of ∆ (1 R S , A ) / ∆ (1 Rs ,0 ) versus dose, after a total cumulative anneal time
of 64 minutes at a temperature of 175 C, for the CSD10120A diodes, are shown in
Figure 7.7Figure 7.7. The ratio of ∆ (1 R S , A ) / ∆ (1 Rs ,0 ) increases with increasing neutron
dose, suggesting that more stable defect clusters are formed with increasing neutron
fluence, which require a higher temperature to anneal than was used in this experiment.
223
Figure 7.6. High injection, forward I-V curve measurements for pre-irradiation, post-irradiation, and
post-anneal for various anneal times at 175 C, for a Cree CSD10120A diode. This diode was irradiated to
a displacement damage dose of 8.4E+11 (MeV/g) in SiC.
From the results of the isothermal annealing study with respect to the Cree SiC
Schottky diodes, it is evident that noticeable recovery, in terms of decreased series
resistance, R s , can be achieved by thermal anneal at even a relatively low temperature of
175 C. Furthermore, this decrease in series resistance, with respect to isothermal anneal
time, exhibits a smooth and predictable trend. Also, at higher neutron fluences, it is
clear from these results that more stable damage is created, as an increasing fraction of
defects remain after the anneal for the more highly irradiated diodes.
224
(
) ( )
∆ (1 R S , A ) / ∆ (1 Rs ,0 ) is a measure of the amount of defects initially
Figure 7.7. The ratio quantity of ∆ 1 R S , A / ∆ 1 Rs ,0 versus Dd,SiC, as a function of anneal time for an
annealing temperature of 175 C.
induced by radiation that remain post-anneal.
7.3 I-V Characterization Testing of a Radiation-Hard MOSFET
In this section, we describe the I-V characterization testing and results for a
radiation-hard MOSFET, manufactured by International Rectifier (IR), part number
IRHM8450, rated at 500 V forward blocking voltage and 11 A forward current.
7.3.1 Procedure
Similarly to all the irradiations reported in this dissertation, the IRHM8450
MOSFET was irradiated in the rabbit facility, in a Cd-lined bottle. The reactor was
n 

operated at a nominal power of 450 kW  φeq ,1MeV =
5.2 ×1011 2  . I-V
, Si
cm s 

225
characterization was performed after each successive radiation dose, using the Tektronix
371B CurveTracer, shown in Figure 3.4, to measure the transfer I D versus V GS
characteristics, as well as the I D versus V DS characteristics, for V GS > 0. Furthermore,
the Keithley 2410 Sourcemeter, also shown in Figure 3.4, was used to measure the I D
versus V DS forward breakdown and leakage characteristics (with V GS = 0 V) as well as
the subthreshold I D versus V DS characteristics.
7.3.2 Results and Discussion
Results for the I D versus V GS transfer characteristic, for V DS held constant at 10
V, for the radiation-hardened IRHM8450 MOSFET are shown in Figure 7.8, as a
function of radiation dose. The I D versus V GS curves shown in Figure 7.8 were
measured using the Tektronix 371B CurveTracer. Notice that in Figure 7.8 that there is
no shift in the I D versus V GS characteristic, contrary to the results observed for the
IRF840, un-radiation hardened MOSFET shown in Figure 5.5. The results shown in
Figure 7.8 indicate very little oxide trapped charge as a function of increasing radiation
dose.
226
Figure 7.8. I D versus V GS transfer characterstic for radiation-hard IRHM8450 MOSFET versus radiation
dose. V DS was held constant at 10 V.
Furthermore, results are shown in Figure 7.9 for the subthreshold I D versus V GS
characteristic, measured using the Keithley 2410 SourceMeter, with the drain and gate
shorted so that V GS = V DS . Note that the curves in Figure 7.9 appear linear on the semilog graph. In the subthreshold region, for which V GS < 0, the drain current varies
exponentially with applied V GS . The slope of the line on the semi-log graph is
proportional to a parameter known as the subthreshold swing, denoted ‘S’. The
parameter ‘S’ is defined mathematically in Equation 7.2 [8]:
S = ln(10)
dVG
.
d (ln I D )
7.2
Furthermore, it can be shown [8] that changes in interface trap density, ΔD it , can be
related to changes in ΔS by Equation 7.3:
227
=
∆Dit
Cox
∆S
kT ln(10)
7.3
Therefore, since ΔS is proportional to the reciprocal of the slopes of the I-V curves
shown in Figure 7.9, ΔD it is proportional to the change in the reciprocal of the slopes of
the I-V curves shown in Figure 7.9. As shown in Figure 7.9, the slope of the I D versus
V GS subthreshold characteristics changes little as a function of radiation dose for the
radiation-hard MOSFET. Therefore, we can conclude that little radiation-induced
interface trap charge occurred as the MOSFET was irradiated.
The results shown in Figure 7.8, as well as Figure 7.9, indicate that the radiationhard MOSFET has a very clean, radiation-hard oxide. Figure 7.8 indicates that the gate
oxide contains very few hole traps at the interface. Furthermore, Figure 7.9 indicates
that the gate oxide also has little hydrogen contamination; since, as discussed earlier, the
radiation-induced transport of hydrogen in the gate oxide to the Si-SiO 2 interface is
considered to be the cause of radiation-induced interface traps [14].
228
Figure 7.9. I D versus V GS subthreshold characterstic for radiation-hard IRHM8450 MOSFET versus
radiation dose. The drain and gate leads were shorted during measurement, so that V GS = V DS .
Furthermore, the breakdown and leakage characteristics of the radiation-hard
MOSFET are shown in Figure 7.10. This measurement was taken with the Keithley
2410 SourceMeter by shorting the gate and source leads together so that V GS = 0 V,
essentially forcing the MOSFET into cut-off mode. Note that the breakdown voltage
and leakage current changes little with radiation dose compared to the 500 V, unradiation hard IRF840 MOSFET, shown in Figure 5.19 and Figure 5.20.
229
Figure 7.10. I D versus V DS forward breakdown and leakage characterstic for radiation-hard IRHM8450
MOSFET versus radiation dose. The MOSFET was measured in the cut-off regime, for which V GS = 0.
In addition, the results for the I D versus V DS characteristic, for a constant applied
gate-to-source bias of V GS = 10 V are shown in Figure 7.11, as a function of radiation
dose. Note that from the I D versus V DS characteristics shown in Figure 7.11 that
although the radiation-hard MOSFET is radiation-hard with respect to gate oxide trapped
charge and radiation-induced interface trapped charge, the radiation-hard MOSFET is
sensitive to radiation-induced displacement damage, as was the case for the un-radiation
hardened IRF840 MOSFETs. The large increase in resistance observed for the
radiation-hard MOSFET in Figure 7.11 indicates bulk displacement damage effects in
the n- drift layer, as was observed for the IRF840 MOSFETs, for comparable dose levels.
230
Figure 7.11. I D versus V DS characterstic for radiation-hard IRHM8450 MOSFET versus radiation dose.
The MOSFET was measured with a constant applied gate-to-source bias of V GS = 10.
7.4 Conclusions
From the results in this chapter, PSpice simulations of the Cree CSD05120A
diodes in half-wave rectifier circuits predict that the power dissipation in the diodes,
which increases with R S and thus radiation-induced displacement damage, can be
appreciably reduced by adding diodes in parallel. The parallel configuration allows the
diodes to share the current and thus considerably reduce power dissipation in the diodes.
Furthermore, results from the isothermal anneal experiment in this chapter
indicate that SiC can be annealed at the manufacturer-rated temperature of 175 C for the
Cree SiC Schottky diodes. The thermal anneal is significant to the extent that recovery
can be observed in the forward, high-injection I-V characteristics of the diodes.
231
In addition, the irradiation and I-V characterization results for a 500 V, radiation
hard MOSFET are presented in this chapter. From the results of this experiment, the
radiation-hard MOSFET is very resistant to radiation-induced oxide trapped charge and
radiation-induced interface trapped charge, as was evident from the negligible shift in
the I D versus V GS transfer curve, as well as the relatively small change in slope of the
subthreshold I D versus V GS curve with respect to radiation dose. Consequently, very
little change with respect to radiation dose is expected for electrical performance
parameters dependent on the integrity of the gate oxide, such as the threshold voltage,
transconductance, forward leakage current, and breakdown voltage. However, the
radiation-hard MOSFET is susceptible to radiation-induced bulk displacement damage
effects, such as on-state resistance. Therefore, on-state conduction losses may increase
significantly for the radiation-hard MOSFET with increasing displacement damage dose.
232
CHAPTER 8 : CONCLUSIONS AND FUTURE WORK
8.1 Conclusions
In conclusion, modern power Si and SiC Schottky diodes were irradiated in a
mixed neutron and gamma-ray radiation field, and the I-V curves of the diodes were
measured and fit to the equations governing the thermionic emission model. From this
analysis, key electrical performance parameters, such as ideality coefficient (n),
saturation current (I s ), and series resistance, R s , were determined as a function of
radiation dose. From these results, it was determined that the Si and SiC Schottky power
diodes are very tolerant to radiation-induced displacement damage, owing to the
Schottky contact. This was evident in the form of little change, with respect to
displacement damage dose, observed in the reverse bias I-V characteristics, such as
leakage current and breakdown voltage. Furthermore, little change was observed in the
forward turn-on voltage in both the Si and SiC Schottky power diodes. Therefore, the IV characterization results indicate that for voltage-blocking requirements of 150 V or
less, the Si Schottky diodes are sufficient, but the SiC Schottky power diodes are
required for higher-voltage applications. In fact, the high band gap of SiC makes it an
ideal choice for high-voltage applications in radiation fields relative to high-voltage p-n
233
diodes, which quickly degrade in a neutron radiation field due to severe radiationinduced reductions in minority-carrier lifetime [1-2,49]. Recovery in the I-V
characteristics of CSD10120A (10 A, 1200 V) SiC Schottky power diodes could be
observed by annealing these diodes at their manufacturer-rated temperature of 175 C.
With respect to neutron and proton equivalency, the results from the diode I-V
characterization testing were used to extend previous work [48], which compared fission
neutron and proton carrier-removal rates in Si for proton energies ranging up to 175
MeV. In this previous work, for a proton energy of 175 MeV, a discrepancy of
approximately 2 was reported between the proton and neutron carrier-removal rates in Si
and the ratio of the corresponding NIEL values [48]. From comparing the results from
the current study to a previous study which irradiated the same diode models with a 203
MeV proton beam [1-2,49], it was determined that the ratio of the neutron and proton
carrier-removal rates in both Si and SiC were well within a factor of 2 of the ratio of the
NIEL values. In addition, from the current study, it was determined that, in Si, the
neutrons in the OSURR rabbit facility remove carriers at the same rate as the 203 MeV
proton beam, per unit D d . However, in SiC, the 203 MeV proton beam removes
approximately 1.6 times as many carriers as the neutrons in the OSURR rabbit facility,
per unit D d .
Functional testing results were also presented for high-voltage, half-wave
rectifiers containing unirradiated and irradiated Cree SiC Schottky power diode, part
number CSD05120A, rated at 5 A and 1200 V. From the results of this functional
testing, it was determined that the increase in series resistance of the diodes, with respect
to radiatiation dose, had little effect on overall circuit performance, as the series
234
resistance remained small compared to the load resistance, and the turn-on voltage
remained essentially constant and small compared to the input voltage. However, a
noticeable increase in power dissipation in the diodes was observed for increasing
radiation dose, owing to the fact that their series resistances increased dramatically, but
the current remained fairly constant. PSpice and analytical models were in excellent
agreement with the experimental results in terms of diode voltage drop and power
dissipated by the diode during forward-bias conduction. Furthermore, deviations of the
experimental data from the PSpice and analytical models at the highest dose level were
consistent with the I-V curve analysis, and can be attributed to high electric field effects,
namely non-constant mobility with respect to electric field strength at high applied
forward bias. From additional PSpice simulations, the power dissipated per diode can be
significantly reduced, especially for high D d , by simply wiring diodes in parallel and
thereby reducing the amount of current flowing through each individual diode.
In addition, modern 100 V and 500 V power MOSFETs were characterized with
respect to their I-V characteristics as a function of mixed neutron and gamma-ray
radiation dose in the OSURR rabbit facility. For both the 100 V and 500 V MOSFETs,
the threshold voltage and transconductance decreased sharply for the lowest doses to
which the MOSFETs were exposed, but then decreased more slowly for the 500 V
MOSFETs, and remained essentially constant for the 100 V MOSFETs, for higher
radiation dose. This can be attributed to the finite number of hole traps at the Si-SiO 2
interface coupled with the fact that the leads of the MOSFETs were shorted during
irradiation. Furthermore, radiation-induced displacement damage increases in the drift
layer R d resistance were found to be primarily responsible for the increases in on-state
235
resistance of the 500 V MOSFETs with respect to radiation dose. However, reduced
electron-mobility in the conductive channel, resulting in an increase in R channel , was
deemed primarily responsible for the modest increase observed with respect to on-state
resistance for the 100 V MOSFETs for doses less than approximately 4 Mrad(Si), or a
Φ eq,1MeV,Si of 2.2E14 n/cm2. However, for larger doses, the rapid increase in the on-state
resistance of the 100 V MOSFETs with respect to dose is attributed to radiation-induced
displacement damage in the n- drift layer. Furthemore, both the leakage currents of the
100 V and 500 V MOSFETs increased drastically as a function of radiation dose. In
addition, the breakdown voltages of the 100 V MOSFETs decreased slightly as a
function of radiation dose, but the breakdown voltages of the 500 V MOSFETs remained
relatively unchanged as a function of radiation dose.
In addition, a radiation-hard, 500 V MOSFET was irradiated in the OSURR
rabbit facility, and its I-V characteristics were measured pre-irradiation, as well as
immediately after each successive radiation dose. The radiation-hard MOSFET was
found to be very resistant with respect to gate oxide trapped charge and radiationinduced interfrace traps. However, the radiation-hard MOSFET exhibited a
susceptibility to increased on-state resistance of comparable magnitude to the unradiation hardened 500 V MOSFETs tested in this study.
Also, unirradiated and irradiated Vishay IR40CTQ150PBF (40 A, 150 V) Si
Schottky diodes were tested in buck and boost converters along with unirradiated and
irradiated IR IRF1310N (42 A, 100 V) power MOSFETs. Previous studies regarding
buck and boost DC-to-DC converters have focused solely on overall circuit performance
parameters, such as V o /V in and efficiency (η) versus ionizing radiation dose [72-73].
236
However, in the current study, in addition to these overall circuit performance
parameters, the voltage and current waveforms over the MOSFET and diode were
recorded and analyzed, and therefore the effect of the radiation on the transient
switching characteristics of the MOSFET could be investigated. For both the buck and
boost converters containing irradiated MOSFETs and diodes, a noticeable increase in
output voltage was observed relative to the buck and boost converters containing
unirradiated MOSFETs and diodes. This increase can be attributed to a decrease in turnon delay time as well as an increase in turn-off delay time of the MOSFET, due to a
reduction in threshold voltage from radiation-induced trapped oxide charge. These
changes in delay times both served to increase the effective duty cycle of the MOSFET,
and thereby increase the output voltage, for the same applied gate signal. However, of
greater concern was the large power dissipation during the turn-off transient of the
MOSFET, which increased dramatically as a function of radiation dose, as the drain
current required a longer time to fall to 0 after V DS rose above V in in the buck converter.
One way in which the power dissipation during turn-off can be reduced is by using a
larger load inductance, thereby decreasing the ripple in the current, and therefore
decreasing the current in the MOSFET at the on-set of the turn-off transient, as
calculated using an analytical model.
Also, unirradiated and irradiated Vishay 500 V MOSFETs were tested with Cree
CSD04060A diodes. A dramatic increase in on-state voltage drop for increasing
radiation dose was observed in the V DS waveforms of the 500 V MOSFETs, owing to
their increased on-state resistance.
237
8.2 Future Work
There are many ways in which this research can be expanded. For example, for
the neutron and proton-equivalency model, more robust computational materials
modeling can be employed to account for the microscopic nature and evolution of
defects within SiC for protons having energies greater than 100 MeV, for which nuclear
scattering effects are important.
Also, with respect to the radiation hardness testing of power MOSFETs, both for
I-V characterization and functional testing, it is desirable to test the MOSFETs in-situ, as
the MOSFETs are irradiated, under the more realistic conditions of switched V GS bias.
The performance of the MOSFETs is expected to be worse for the condition of switched
V GS bias relative to zero V GS bias in terms of reductions in threshold voltage and
transconductance.
Furthermore, it is desirable to model the switching characteristics of the power
MOSFET in PSpice and be able to account for changes in the model parameters as the
MOSFET is irradiated, as determined in this dissertation. One such power MOSFET
model on which to build can be found in [76].
238
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245
Appendix A: Analytical Buck Converter Model
246
% Start of input parameters
RL = 4.964;
% load resistance (Ohms)
fs = 50e3; % MOSFET switching frequency
Ts = 1/fs; % Period of switching cycle (s)
Rdcr = 0.0137; % inductor effective DCR resistance (Ohms)
L = 50e-6; % load inductor value (H)
Rdson = 1/18.712; %Rdson for piece-wise linear model of MOSFET
Von = 25.98/39.014;
%Von for piece-wise linear model of diode
Ron = 1/39.014;
%Ron for piece-wise linear model of diode
Vin = 79.3; % Vin (Volts)
t_c_on = 5.14e-7;
%length of MOSFET turn-on transient
(seconds)
ton = 7.47e-6;
% length of on-state conduction
t_c_off = 1.84e-6;
% length of MOSFET turn-off transient
(seconds)
D = ton*fs;
% MOSFET duty cycle
% End of input parameters
alpha = Ron + Rdcr;
Beta = Rdson + Rdcr;
v = alpha / L;
y = Beta / L;
% Solve for Periodic Boundary Conditions ...
M = [exp(-y*ton) -exp(-v*ton)
1
-exp(-v*Ts)];
Msol = inv(M)*[1;1];
q = Msol(1,1);
r = Msol(2,1);
% Now Solve for Vo
VoMult = 1/RL - (1/Ts)*(-ton/Beta + (ton-Ts)/alpha + (1/Beta 1/alpha)*((q/y)*(1-exp(-y*ton))+ ...
(r/v)*(exp(-v*ton)-exp(-v*Ts))));
RHS = (1/Ts)*(ton*Vin/Beta + (ton-Ts)*Von/alpha - (Vin/Beta +
Von/alpha)*((q/y)*(1-exp(-y*ton))+ ...
(r/v)*(exp(-v*ton)-exp(-v*Ts))));
Vo = RHS / VoMult;
% We can now solve for the inductor current
BoundaryConditionRHS = -((Vin-Vo)/Beta+(Von+Vo)/alpha);
A = q*BoundaryConditionRHS;
B = r*BoundaryConditionRHS;
247
t = [0:1e-7:ton];
t(length(t))=ton;
toff = [ton:1e-7:Ts];
toff(length(toff))=Ts;
i_L_on = (Vin-Vo)/Beta + A.*exp(-y.*t);
< t < D/fs
i_L_off = -(Von+Vo)/alpha + B.*exp(-v.*toff);
D/fs < t < 1/fs
% inductor current, 0
% inductor current,
PscMOSFET = (Rdson/Ts)*( ((Vin-Vo)/Beta)^2*ton + (2*(VinVo)*L/Beta^2)*A*(1-exp(-Beta*ton/L))+ ...
(A^2*L/(2*Beta))*(1-exp(2*Beta*ton/L)));
PstonMOSFET = fs*t_c_on*0.5*i_L_on(1)*Vin;
PstoffMOSFET = fs*t_c_off*0.5*i_L_on(length(i_L_on))*Vin;
PtotalMOSFET = PscMOSFET + PstonMOSFET + PstoffMOSFET;
Integral_i_L_off_sq = (-(Von+Vo)/alpha)^2*(Ts-ton) - ...
(2*B*L/(alpha^2))*(-(Von+Vo))*(exp(-alpha*Ts/L)-exp(alpha*ton/L)) - ...
(B^2*L/(2*alpha))*(exp(-2*alpha*Ts/L)-exp(-2*alpha*ton/L));
Integral_i_L_off = (-(Von+Vo)/alpha)*(Ts-ton) - (B*L/alpha)*(exp(alpha*Ts/L)-exp(-alpha*ton/L));
PdiodeCond = (1/Ts)*(Ron*Integral_i_L_off_sq +
Von*Integral_i_L_off);
plot(t,i_L_on);
hold on;
plot(toff,i_L_off);
248
Appendix B: Analytical Boost Converter Model
249
% Start of input parameters
RL = 19.756;
% load resistance (Ohms)
fs = 50e3; % MOSFET switching frequency = 50 kHz
Ts = 1/fs; % Period of switching cycle (s)
L = 50e-6; % load inductor = 1 mH
Rdcr = 0.0137; % Two 100 uH inductor in parallel: DCR = 0.0137
Ohms;
Vin = 39.3; % Vin
Rdson = 1/23.383; %Rdson for piece-wise linear model of MOSFET
Von = 7.4807/19.494;
%Von for piece-wise linear model of diode
Ron = 1/9.494;
%Ron for piece-wise linear model of diode
ton = 5.36e-6;
% End of input parameters
D = ton*fs;
% MOSFET duty cycle
%Note this notation is reversed from Buck converter analysis...
alpha = Rdson + Rdcr;
Beta = Ron + Rdcr;
% Solve for Periodic Boundary Conditions ...
M = [exp(-alpha*ton/L) -exp(-Beta*ton/L)
1
-exp(-Beta*Ts/L)];
Msol = inv(M)*[1;1];
a = Msol(1,1);
b = Msol(2,1);
% Now Solve for Vo
VoMult = Ts/RL + (Ts-ton)/Beta + (L*b/(Beta^2))*(exp(-Beta*ton/L)exp(-Beta*Ts/L));
RHS = (Vin-Von)*(Ts-ton)/Beta + (L*b/Beta)*((Vin-Von)/BetaVin/alpha)*(exp(-Beta*ton/L)-exp(-Beta*Ts/L));
Vo = RHS / VoMult;
% We can now solve for the inductor current
BoundaryConditionRHS = (Vin-(Von+Vo))/Beta - Vin/alpha;
K = BoundaryConditionRHS*a;
J = BoundaryConditionRHS*b;
t = [0:1e-7:ton];
t(length(t))=ton;
toff = [ton:1e-7:Ts];
toff(length(toff))=Ts;
i_L_on = Vin/alpha + K.*exp(-alpha.*t./L);
% inductor
current, 0 < t < D/fs
i_L_off = (Vin-(Von+Vo))/Beta + J.*exp(-Beta.*toff./L); % inductor
current, D/fs < t < 1/fs
Pmosfet = (Rdson/Ts)*( (Vin/alpha)^2*ton + (2*Vin*L/alpha^2)*K*(1exp(-alpha*ton/L))+ ...
250
(K^2*L/(2*alpha))*(1-exp(-2*alpha*ton/L)));
Integral_i_L_off_sq = ((Vin-(Von+Vo))/Beta)^2*(Ts-ton) - ...
(2*J*L/(Beta^2))*(Vin-(Von+Vo))*(exp(-Beta*Ts/L)-exp(Beta*ton/L)) - ...
(J^2*L/(2*Beta))*(exp(-2*Beta*Ts/L)-exp(-2*Beta*ton/L));
Integral_i_L_off = ((Vin-(Von+Vo))/Beta)*(Ts-ton) (J*L/Beta)*(exp(-Beta*Ts/L)-exp(-Beta*ton/L));
Pdiode = (1/Ts)*(Ron*Integral_i_L_off_sq + Von*Integral_i_L_off);
plot(t,i_L_on);
hold on;
plot(toff,i_L_off);
251