Semiconductor Device Modeling
and Characterization – EE5342
Lecture 37 – Spring 2011
Professor Ronald L. Carter
ronc@uta.edu
http://www.uta.edu/ronc/
SPICE mosfet Model
Instance
CARM*, Ch. 4, p. 290
M
MOSFET
General Form
M<nam e> < drain node> <gate node> < source node>
+ <bulk /subs trate node> <model nam e>
+ [L=< value>] [W=< value> ]
L = Ch. L. [m]
+ [AD= <value>] [AS= <value>]
W = Ch. W. [m]
+ [PD= <value>] [PS= <value>]
+ [NRD=< value>] [NRS=<value>] AD = Drain A [m2]
+ [NRG=<v alue>] [NRB= <value>] AS = Source A[m2]
+ [M= <value>]
Examples
NRD, NRS = D and
S diff in squares
M1 14 2 13 0 PNOM
L=25u W=12u
M13 15 3 0 0 PSTRONG
M = device multiplier
M16 17 3 0 0 PSTRONG M=2
©rlc L37M28 0 2 100 100 NWEAK L=33u W=12u
04May2011
CARM*, Ch. 4, p. 99
Model Forms
.MODEL <model name> NMOS [model parameters]
.MODEL <model name> PMOS [model parameters]
As shown in Figure 11, the MOSFET is modeled as an intrinsic MOSFET with ohmic resistances
in series with the drain, source, gate, and bulk (substrate). There is also a shunt resistance
(RDS) in parallel with the drain-source channel.
[L=<value>] [W=<value>] cannot be used in conjunction with Monte Carlo analysis .
The simulator provides four MOSFET device models, which differ in the formulation of the I-V
characteristic. The LEVEL parameter selects between di fferent models :
LEVEL=1
LEVEL=2
LEVEL=3
LEVEL=4
LEVEL=5
LEVEL=6
is the Shichman-Hodges model (see reference [1])
is a geometry-based, analytic model (see reference [2])
is a semi-empirical, short-channel model (see reference [2])
is the BSIM model (see reference [3])
is the BSIM3 model (see reference [7] Version 1.0)
is the BSIM3 model (see reference [7] Version 2.0)
L and W are the channel length and width, and are decreased to get the effective channel length
and width. L and W can be specified in the device, model, or .OPTIONS statements. The value
in the device statement supersedes the value in the model statement, which supersedes the
value in the .OPTIONS statement.
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SPICE mosfet
model levels
• Level 1 is the Schichman-Hodges
model
• Level 2 is a geometry-based,
analytical model
• Level 3 is a semi-empirical, shortchannel model
• Level 4 is the BSIM1 model
• Level 5 is the BSIM2 model, etc.
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SPICE Parameters
Level 1 - 3 (Static)
Param. Parameter Description
Def.
Typ.
Units
1
1
V
VTO
Zero-bias Vthresh
KP
Transconductance
GAMMA
Body-effect par.
0.0
0.35
V^1/2
PHI
Surface inversion pot.
0.6
0.65
V
0.0
0.02
1/V
LAMBDA Channel-length mod.
2.E-05 3.E-05
A/V^2
TOX
Thin oxide thickness
NSUB
Substrate doping
0.0
1.E+15
cm^-3
NSS
Surface state density
0.0
1.E+10
cm^-2
LD
Lateral diffusion
0.0
8.E-05
m
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1.E-07 1.E-07
m
SPICE Parameters
Level 1 - 3 (Static)
Param. Parameter Description
Def.
Typ.
1
1
600
700
Units
TPG
Type of gate material*
UO
Surface mobility
IS
Bulk jctn. sat. curr.
JS
Bulk jctn. sat. curr. dens.
PB
Bulk junction potential
0.8
0.75
V
RD
Drain ohmic resistance
0
10
Ohms
RS
Source ohmic resistance
0
10
Ohms
RSH
S/D sheet ohmic res.
0
10
Ohms/sq
1.E-14 1.E-15
cm^2/V-s
A
A/m^2
* 0 = aluminum gate, 1 = silicon gate opposite substrate type,
2 = silicon gate same as substrate.
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SPICE Parameters
Level 1 - 3 (Q & N)
Param. Parameter Description
Def.
Typ.
Units
0
1.E-09
Fd/m^2
CJ
Zero-bias bulk cap./A
MJ
Bulk jctn. grading coeff.
0.5
0.5
CJSW
Zero-bias perimeter C/l
0
1.E-09
MJSW
Per. C grading coeff.
0.5
0.5
FC
For.-bias cap. coeff.
0.5
0.5
CGBO
Gate-bulk overlap C/L
0
2.E-10
Fd/m
CGDO
Gate-drain overlap C/L
0
4.E-11
Fd/m
CGSO
G-S overlap C/L
0
4.E-11
Fd/m
AF
Flicker-noise exp.
1
1.2
KF
Flicker-noise coeff.
0.0
1.E-26
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Fd/m
Level 1 Static Const.
For Device Equations
Vfb = -TPG*EG/2 -Vt*ln(NSUB/ni)
- q*NSS*TOX/eOx
VTO = as given, or
= Vfb + PHI + GAMMA*sqrt(PHI)
KP = as given, or
= UO*eOx/TOX
CAPS are spice pars., technological
constants are lower case
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Level 1 Static Const.
For Device Equations
b = KP*[W/(L-2*LD)] = 2*K, K not spice
GAMMA = as given, or
= TOX*sqrt(2*eSi*q*NSUB)/eOx
2*phiP = PHI = as given, or
= 2*Vt*ln(NSUB/ni)
ISD = as given, or = JS*AD
ISS = as given, or = JS*AS
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Level 1 Static
Device Equations
vgs < VTH, ids = 0
VTH < vds + VTH < vgs,
id = KP*[W/(L-2*LD)]*[vgs-VTH-vds/2]
*vds*(1 + LAMBDA*vds)
VTH < vgs < vds + VTH,
id = KP/2*[W/(L-2*LD)]*(vgs - VTH)^2
*(1 + LAMBDA*vds)
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SPICE Parameters
Level 2
Param. Parameter Description
Def.
Typ.
1
5
NEFF
Total channel chg coeff.
UCRIT
Critical E-field for mob.
UEXP
Expon. coeff. for mob.
0
0.1
UTRA
Transverse field coeff.
0
0.5
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1.E+04 1.E+04
Units
V/cm
SPICE Parameters
Level 2 & 3
Param. Parameter Description
Def.
Typ.
Units
NFS
Surface-fast state dens.
0.0
1.E+10
cm^-2
XJ
Metallurgical jctn. depth
0.0
1.E-06
m
VMAX
Max. drift v of carr.
0.0
5.E+04
m/s
XQC
Coeff. of ch. Q share
0.0
0.4
DELTA
Width eff. on Vthresh
0.0
1.0
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Level 2 Static
Device Equations
Accounts for variation of channel
potential for 0 < y < L
For vds < vds,sat = vgs - Vfb - PHI
+ g2*[1-sqrt(1+2(vgs-Vfb-vbs)/g2]
id,ohmic = [b/(1-LAMBDA*vds)]
*[vgs - Vfb - PHI - vds/2]*vds
-2g[vds+PHI-vbs)1.5-(PHI-vbs)1.5]/3
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Level 2 Static
Device Eqs. (cont.)
For vds > vds,sat
id = id,sat/(1-LAMBDA*vds)
where id,sat = id,ohmic(vds,sat)
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Level 2 Static
Device Eqs. (cont.)
Mobility variation
KP’ =
KP*[(esi/eox)*UCRIT*TOX
/(vgs-VTH-UTRA*vds)]UEXP
This replaces KP in all other formulae.
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SPICE Parameters
Level 3
Param. Parameter Description
Def.
Typ.
KAPPA
Saturation field factor
0.2
1.0
ETA
Stat. feedbk on Vthresh
0.0
1.0
THETA
Mobility modulation
0.0
0.05
DELTA
Width eff. on Vthresh
0.0
1.0
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Units
1/V
BJT Self-heating
• Self heating of the transistor is
proportional to the power dissipated.
• Temperature Rise = ΔT = Rth ∙Power
• The VBIC model was developed to simulate
the BJT such that the device temperature
tracked power dissipation in real time.
• Other circuit simulators which
accommodate thermal resistance are
– HICUM
– MEXTRAM
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Rth Estimation for a Small Diode-isolated
BJT Device
VBE=0.87 V and VCE=20 V, RTH = 341
C/W
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VBIC Model Highlights
dt
tl
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Self-heating effects
included
Improved Early effect
modeling
Quasi-saturation
modeling
Parasitic substrate
transistor modeling
Parasitic fixed (oxide)
capacitance
modeling
An avalanche
multiplication model
included
Base current is
decoupled from
collector current
2-D Isotherm Plot- Lines Connecting
Points of Equal Temperature
2-D Isotherm plots for a structure scaled to be the
same as the P10 1X2X1 device.
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Thermal Model of a SiGe HBT
• The structure of a typical SiGe HBT (Heterojunction Bipolar
Transistor) [1]
Oxide
• The Electrical circuit topology (Cauer network) for the
thermal analogy model
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2
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SILICON
•A silicon structure can be sub-divided
into several silicon slabs.
•Each section contributes to the total
Rth and Cth of the structure. If each
section is of equal volume, their
individual Rth and Cth should be equal in
value.
•To correspond to uniform heat flow,
each section can be represented by a
thermal resistance and half the total
capacitance on each node of the
resistor.
Cth
SILICON
One Dimensional Heat Flow in
Silicon
HEAT
AMBIENT
Rth
Cth
2
The Distributed Nature of the Heat Flow
•The corresponding CTh /2 capacitors are aggregated at
each node.
•Note that the “ambient end” CTh /2 is short-circuited.
•The distributed equivalent circuit analogy simulation is
obtained from the following network.
Rth
n
Cth
2n
Rth
n
Cth
n
Cth
n
Rth = Total Thermal resistance for the silicon structure
Cth= Total Thermal capacitance of the silicon structure
n = number of sections
A=area
t= thickness
cp= thermal capacitance
kp= thermal conductance
ρ=density
©rlc L3704May2011
Rth
n
Rth
n
Cth
n
t
k A
p
Cth  ρ  c  t  A
p
Rth 
Comparison of Circuit Analogy to Davinci Simulation
of the Heat Flow
Considering a silicon structure of size 3.7umx2.5um x10um
Rth 
t
 6989  Cth  ρ  c  t  A  18.2n  Tau  Rth  Cth  1.26u
p
k A
p
Dividing the structure into 10 sections.
Rth
Cth
where i=1,2,3…n,
Rth 
 Cth 
n= number of sections
i
i
n
n
Dotted line=Davinci simulation measurement
Solid line = equivalent circuit simulation
©rlc L3704May2011
Approximating the Distributed Circuit
With a Single Pole Model
•Converting the 10
element distributed
model to a 1 pole model:
RTotal=Rth at ‘dc’
ΔQTotal =(cp)(ρ)Tavg
For total heat
consumption. n
Rth 1 pole    Rthi  Rth
i 1
Rth
n
Cth
2n
©rlc L3704May2011
Cth
n
Rth
n
Cth
n
Heat stored
corresponds to charge
stored for the
equivalent circuit.
n
V1pole  C1pole   Vi  Ci
i1
For n  , the limit is
C1pole
CTh

2
Rth
n
Cth
n
Rth
n
Comparison of Circuit Analogy to Davinci
Simulation for Heat Flow
RTh(W/K)
1.E+04
1.E+03
30um slab davinci
30um slab circuit simulation
20um slab davinci
20um slab simulation
1.E+02
10um slab davinci
10um slab simulation
1.E+01
1.E-08
©rlc L3704May2011
1.E-07
1.E-06
1.E-05
Time
1.E-04
1.E-03
(cont’d)
Rth(k/W)
1.E+04
1.E+03
1.E+02
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
Time
Results from equivalent circuit simulations
Results from Davinci Simulation
Results from device measurement Foster network
Results from device measurement Cauer network
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Top of the tub
Top of the oxide
Top of the wafer
Circuit used for simulations
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dt for VBIC-R1.5 model
• Model: VBIC-R1.5.
• “selft” flag set to
1.
• No optimization
done.
• No external
circuit connected.
• Rth=5.8E+0
• Cth=96E-12
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VBIC-R1.5 Y11 plot (standard data)
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VBIC-R1.5 Y11 plot (standard data)
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VBIC-R1.2 Y11 plot (optimized data)
• For optimized data refer
slide “Model Parameters”.
• Circuit used is shown in
“Circuit for Y parameters
(optimized data)” slide.
fc
Τ
fc1= 2E3
7.962E-05
fc2=
9.25E4
1.721E-06
fc3= 3.2E6
4.976E-08
Fc4=2E3
7.962E-05
Fc5=1E5
1.592E-06
Fc6=4E6
3.981E-08
fc7= 2E3
7.962E-05
fc8= 1E5
1.592E-06
fc9=4E6
3.981E-08
©rlc L3704May2011
Spreadsheet for Calculating the Rth and Cth
• Calculations mentioned in the previous slides have been
implemented in an Excel spreadsheet.
• The Cauer to Foster network transformation is done.

Fig. 7. Electrical equivalent Cauer network of the HBT
Fig. 8. Electrical equivalent Foster network of the HBT
• The spreadsheet takes the dimensions of different
layers of the devices and gives corresponding Cauer and
Foster network values. This enables the calculation of
time constants which can be converted into a single
pole. The characteristic times for the Foster network
appear on a impulse response plot.
©rlc L3704May2011
Effect of Rth on current feedback
op-amp settling time
500
500
W
W
-
vOUT
+
100 W
vIN = 1 V P-P, t
= 200 m-sec
Offset  
©rlc L3704May2011
vOUT ,max   vOUT t 
AvIN,max 
Current Feedback Op Amp Data
(LMH6704) Switching Offset
Thermal switching offset as %
of Vp
1.00% cfoa model  0.39%  e  t / 13.4  0.16%  e  t / 3.3
y = 0.0039e-0.0749x
Offset = .39%
Tau = 13.4 u-sec
0.10%
y = 0.0055e-0.1416x
Offset = 0.16%
Tau = 7.1 u-sec
Tau 
0.01%
©rlc L3704May2011
0
5
0.16%
 3.3
0.55% / 7.7  0.39% / 13.4
10
15
20
25
Time after switching (u-sec)
30
LMH6550 impulse thermal
characteristics
• LeCroy sampling oscilloscope (1MW input
mode)
• Maximum averaging (10000)
• Input nominally +/- 1V with 50 micro-sec
period and 50% duty cycle.
• Fractional Gain Error = FGE
vOUT (t)
FGE 
©rlc L3704May2011
vOUT ,max
vIN (t)
vIN,max
1
vIN Rising Response
1.2
10.00%
vIN
1.0
0.8
FGE
vOUT
0.6
0.4
0.2
1.00%
y = 0.0362e-111568x
R2 = 0.9707,
Tau = 9 micro-sec
0.0
0.0E+00
©rlc L3704May2011
5.0E-06
1.0E-05
1.5E-05
0.10%
2.0E-05
vIN Falling Response
0
10.00%
-0.2
vOUT
-0.4
y = 0.0373e-148345x
R2 = 0.9257
Tau = 6.7 micro-sec
-0.6
1.00%
-0.8
-1
-1.2
0.0E+00
©rlc L3704May2011
FGE
vIN
5.0E-06
1.0E-05
1.5E-05
0.10%
2.0E-05
Current Feedback Op-Amp (CFOA) with
Simple Current Mirror (CM) Bias
VCC
Q3
Q4(stk2pnp-cm)
Q9
Q10
Q17
Q7(stk3-npn-bf)
200 μA
+1 V
Q6
Q14
VEE
VP
VCC
VEE
Z
VN
Q5
-1 V
Q 15
RF
Q13
Q8(stk3-pnp-bf)
Q1
Q2
Q11
VO
VCC
Q12
Q 16
Q18
sup
VEE
©rlc L3704May2011
STICK1
STICK2
STICK3
STICK4
STICK5
STICK6
Large-signal Output Voltage Transient
Analysis for CFOA with Simple CM Biasing
Voltage (mV)
-968
High-to-Low area x1
High-to-Low area x8
-970
TT=-5311 mV
-972
-974
TT=-789 mV
-976
-978
0
5
10
15
20
25
30
35
40
45
Time (ms)
Voltage (mV)
1028
1026
Low-to-High area x1
Low-to-High area x8
TT=5313 mV
1024
1022
TT=789 mV
1020
0
©rlc L3704May2011
5
10
15
20
25
Time (ms)
30
35
40
45
Hypothesis: The Thermal Tail is a Linear Superposition
of the Contribution from each Individual Circuit Stick
• The contribution of individual transistor to the total
thermal tail.
• Used six stick classifications according to transistor type
and functionality.
i.e. Q10stk3-pnp-bf and Q11stk4-npn-cm
• Enabled the self-heating effect in the stick of interest
and disabled the self-heating effect of the remaining
transistors.
• Simulated the contribution of each individual stick.
• The total thermal tail simulated is essentially the sum of
the individual thermal tail contributions of each circuit
stick.
©rlc L3704May2011
The Hypothesis Supported
Area x1
Thermal Tail (uV/V)
©rlc L3704May2011
Area x8
High-to-Low
Low-to-High
High-to-Low
Low-to-High
stk2-npn-bf (Q5)
-822
842
-124
128
stk2-pnp-bf (Q6)
-727
712
-101
98
stk2-npn-cm (Q2)
-89
91
-11
12
stk2-pnp-cm (Q4)
-91
89
-10
9
stk3-npn-bf (Q7)
-877
850
-111
106
stk3-pnp-bf (Q8)
-783
808
-111
115
stk4-npn-cm (Q12)
-1213
1217
-172
173
stk4-pnp-cm (Q10)
-1075
1073
-159
158
stk5-npn-bf(Q13)
13
-13
2
-2
stk5-pnp-bf(Q14)
-4
4
-1
1
stk5-npn-cm(Q18)
16
-15
2
-2
stk5-pnp-cm(Q17)
-5
2
0
0
stk6-npn-bf(Q15)
0
1
0
0
stk6-pnp-bf(Q16)
-1
0
0
0
added total
-5658
5661
-796
796
simulated total
-5311
5313
-789
789
References
•
•
•
•
•
Fujiang Lin, et al, “Extraction Of VBIC Model for SiGe
HBTs Made Easy by Going Through Gummel-Poon Model”,
from
http://eesof.tm.agilent.com/pdf/VBIC_Model_Extractio
n.pdf
http://www.fht-esslingen.de/institute/iafgp/neu/VBIC/
Avanti Star-spice User Manual, 04, 2001.
Affirma Spectre Circuit Simulator Device Model
Equations
Zweidinger, D.T.; Fox, R.M., et al, “Equivalent circuit
modeling of static substrate thermal coupling using
VCVS representation”, Solid-State Circuits, IEEE
Journal of , Volume: 2 Issue: 9 , Sept. 2002, Page(s):
1198 -1206
©rlc L3704May2011
Thermal Analogy References
[1] I.Z. Mitrovic , O. Buiu, S. Hall, D.M. Bagnall and P. Ashburn “Review
of SiGe HBTs on SOI”, Solid State Electronics, Sept. 2005, Vol.
49, pp. 1556-1567.
[2] Masana, F. N., “A New Approach to the Dynamic Thermal Modeling
of Semiconductor Packages”, Microelectron. Reliab., 41, 2001, pp.
901–912.
[3] Richard C. Joy and E. S. Schlig, “Thermal Properties of Very Fast
Transistors”, IEEE Trans. ED, ED-1 7. No. 8, August 1970, pp. 586599.
[4] Kevin Bastin, “Analysis and Modeling of self heating in SiGe HBTs” ,
Aug. 2009, Masters Thesis, UTA.
[5] Rinaldi, N., “On the Modeling of the Transient Thermal Behavior of
Semiconductor Devices”, IEEE Trans-ED, Volume: 48 , Issue: 12 ,
Dec. 2001; Pages:2796 – 2802.
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Simulation … References
•
•
[1] E. Castro, S. Coco, A. Laudani, L. LO Nigro and G. Pollicino, “A New Tool For Bipolar
Transistor Characterization Based on HICUM”, Communications to SIMAI Congress,
ISSN 1827-9015, Vol. 2, 2007.
[2] K. Bastin, “Analysis And Modeling of Self Heating in Silicon Germanium
Heterojunction Bipolar Transistors”, Thesis report, The University of Texas at
Arlington, August 2009.
©rlc L3704May2011
AICR Team at University of Texas
Arlington - Electrical Engineering
Earlier Contributors
Current
• Ronald L. Carter,
Professor
• W. Alan Davis, Associate
Professor
• Howard T. Russell, Senior
Lecturer
• Ardasheir Rahman1
• Xuesong Xie3
• Arun Thomas-Karingada2
• Sharath Patil2
• Valay Shah2
©rlc L3704May2011
•
•
•
•
•
•
Kevin Bastin, MS
Abhijit Chaugule, MS
Daewoo Kim, PhD
Anurag Lakhlani, MS
Zheng Li, PhD
Kamal Sinha, PhD
1PhD
Student
2MS Student
3Post-doctoral Associate
References
• CARM = Circuit Analysis Reference Manual,
MicroSim Corporation, Irvine, CA, 1995.
• M&A = Semiconductor Device Modeling with
SPICE, 2nd ed., by Paolo Antognetti and Giuseppe
Massobrio, McGraw-Hill, New York, 1993.
• **M&K = Device Electronics for Integrated
Circuits, 2nd ed., by Richard S. Muller and
Theodore I. Kamins, John Wiley and Sons, New
York, 1986.
• *Semiconductor Physics and Devices, by Donald A.
Neamen, Irwin, Chicago, 1997
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