Double-gated Isolated Vertically Aligned Carbon Nanofiber
Field Emission and Field Ionization Arrays
by
Liang-Yu Chen
B. S., Electrical Engineering and Computer Science,
University of Hawaii at Manoa, Aug. 2001
M. S., Electrical Engineering and Computer Science,
Massachusetts Institute of Technology, Feb. 2004
Submitted to the Department of Electrical Engineering and Computer Science
in Partial Fulfillment of The Requirements for the Degree of
Doctor of Philosophy
at the
Massachusetts Institute of Technology
May 2007
©2007 Massachusetts Institute of Technology
All rights reserved
Signature of Author............
.
Dep
....
..........
t ofeectrical Engineering and Computer Science
May 18, 2007
Certified by .............................
Profes sor
Accepted by...........
....
OF TECHNOLOGY
LI
..........
Arthur C. Smith
Chairman, Department Committee on Graduate Students
Department of Electrical Engineering and Computer Science
MASSACHUSETTS INSTITUTE
AUG 16 2007
.
Akintunde Ibitayo (Tayo) Akinwande
lectrical Engineering and Computer Science
Thesis Supervisor
I
AkRCHN Et
Doubled-gated Isolated Vertically Aligned Carbon Nanofiber
Field Emission and Field Ionization Arrays
by
Liang-Yu Chen
Submitted to the Department of Electrical Engineering and Computer Science
On May 18, 2007 in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
Abstract
Electron impact ionization (ElI) is used extensively in mass spectrometry for gas-phase
analytes. Due to the significant amount of fragmentation generated by ElI, the spectrum
is usually very noisy. In addition, the thermionic emission electron source used in ElI
has a slow response time and consumes large amount of power. To address these two
issues, double-gated vertically aligned carbon nanofiber (VACNF) field emission and
field ionization arrays have been developed. These arrays were characterized as field
ionizers, which could produce molecular ions without severe fragmentation; and as field
emitters, which act as an electron source with a fast response time and consume less
power than using thermionic emission.
Self-aligned double-gated isolated VACNF arrays, which were fabricated using a
photoresist-based planarization process, are reported. These arrays were designed such
that the tip electric field is maximized and the shielding effect from the neighboring tips
is minimized while the device is capable of handling large voltages during field emission
and field ionization. Two types of arrays were fabricated: (1) CNFs with tips in-plane
with the gate and (2) CNFs with tips 0.9pm below the gate. These arrays were
characterized as a field emitter and a low field emission turn-on voltage of 24V is
reported. These arrays were used as electron sources for ElI at pressures ranging from
5x10~6 to
x10-3
Torr. The ion current is linearly related to the product of the electron
current and the ambient pressure. Thus, the device could be used as a gas pressure sensor
in vacuum. Field ionization experiments were also conducted with double-gated VACNF
arrays. The field ionization turn-on voltage was reduced from about 10kV, typical of ungated ionizers, to 350V.
Thesis Supervisor: Akintunde ibitayo (Tayo) Akinwande
Title: Professor of Electrical Engineering and Computer Science
3
4
Acknowledgements
There are many people who have been helpful and supportive for my work and me along
this journey. Here, I would like to thank their contributions and express my appreciation.
I would like to thank my advisor, Tayo Akinwande, who guides and encourages me along
the way with patient and trust. He helps me build my knowledge and skills for my
research work almost from scratch. He has also set an excellent example for me to learn
from personally and professionally. I will always consider myself fortunate to be his
student.
I would also like to thank Professor Marty Schmidt and Professor Jesus del Alamo for
being my thesis committee members and giving me their comments and support.
I am fortunate to have many opportunities to work with our group members: John
Kymissis, Ching-yin Hong, Guobin Sha, Annie Wang, Luis Velasquez, Bosun Adeoti,
Kerry Cheung, Jeremy Walker, and Brian Mazzeo. Especially, I want to thank Ching-yin
for introducing me to the group, Guobin and Kerry for helping me with the simulation,
Luis for fabrication consultation, and Annie for moving and setting up the lab with me.
I am grateful to the entire MTL and NSL staff for their help. I especially want to thank
Donal Jamieson, Bob Bicchieri, Paul Tierney, Kurt Broderick, Bernard Alamariu, Jim
Daley, and Mark Mondol for helping me with different phases of my work.
I would like to express my appreciation to Dr. Ken Teo, Dr. Nalin Rupesinghe, and
Xiaozhi Wang from Department of Engineer at Cambridge University for their great help
on the synthesis of CNTs.
I would also like to thank my undergraduate research advisor, Professor Jung-Chih Chiao,
and my physic professor, Professor David Young for their encouragement and support. I
would like to thank them for always pushing me to succeed and to improve.
There are many friends I have met at MIT that made my Ph. D. life more than just
research work. I have enjoyed the company of Alice, Ling, Maggie, Hsin-Yu, Susan,
Allan, Baeian, Arthur, Hsin-Ni, Shihhsih, Dilan, Sybor, Rachael, Joyce, Cait, and Niamh.
Special thanks to Elana, who always gives me a hand whenever I need it, and Huankiat
who encourages, advices and companies me along the way. I am lucky to have friends
like them.
Finally, I have to give my thanks to my family. My parents' supports are essential in
getting me to where I am today. My sister, who companies me since my first day to this
world, has shared with me the ups and downs in my life.
5
6
Table of Contents
Abstract ......................................................................................
Acknowledgements ....................................................................
Table of Contents.......................................................................
List
...............................................................................
List of Tables ...........................................................................
3
5
7
11
17
1
19
Introduction..........................................................................
1.1
Background and Motivation - Mass Spectrometry (MS).............
1.1.1
The Importance of Mass Spectrometry ................................................
1.1.2
Key Elements of Mass Spectrometry ...................................................
1.1.3
The Importance of Ionization Methods ................................................
1.2
Statement of Problems.................................................................................
1.3
Objectives and Technical Approach.............................................................
1.4
Thesis Organization......................................................................................
2
19
19
20
21
22
23
24
Background of Ionization Methods for Gas-phase Analytes ..27
2.1
Background of Hard and Soft Ionization Methods.......................................
2.2
Hard Ionization - Electron Impact Ionization (EI)......................................
2.2.1
Electron Sources for Electron Impact Ionization - Field Emission.........
2.2.2
Electron Impact Ionization .................................................................
2.3
Soft Ionization............................................................................................
2.3.1
Chemical Ionization (CI).......................................................................
2.3.2
Field Ionization (FI) .............................................................................
2.4
Chapter Summary........................................................................................
27
29
29
34
37
37
38
43
3 Exploratory Characterizations of Silicon Field Emission Array
and Carbon Nanotubes Field Emission Device .........................
45
3.1
Silicon Field Emission Array ......................................................................
46
3.1.1
Device Description..............................................................................
46
3.1.2
Device Characterization ......................................................................
47
3.2
Carbon nanotube field emission device (Busek Device)..............................
52
3.2.1
Device Description..............................................................................
52
3.2.2
Device Characterization ......................................................................
52
3.3
Comparison between D-G silicon FEA and CNTs Field Emission Device and
Implications for Ionizer..........................................................................................
55
4 Design and Fabrication of Double-gated Isolated Vertically
Aligned Carbon Nanofiber (VACNF) Field Emission and Field
Ionization Arrays ......................................................................
59
4.1
Tip Material Selection and Carbon Nanofiber (CNF) Synthesis..................
4.1.1
Tip Material - Carbon Nanofiber ........................................................
4.1.2
Carbon Nanofiber Synthesis...............................................................
4.2
D evice D esign ............................................................................................
7
59
59
59
67
4.2.1
D evice Structure ...................................................................................
4.2.2
Device Structure Dimensions ...............................................................
4.3
D evice Fabrication .......................................................................................
4.3.1
Formation of 4 gm-Tall Isolated Vertically Aligned CNFs (VACNFs)...
4.3.2
Formation of the Gate Insulator and the Extraction Gate.....................
4.3.3
Formation of the Focus Insulator and the Focus Gate..........................
4.3.4
CNF Exposure and the Completed Device...........................................
4.4
C hapter Sum mary..........................................................................................
5
67
68
73
73
75
78
80
81
Field Emission Characterization...........................................83
84
5.1
Measurement Setup and Device Description................................................
5.2
Three-terminal IV Characterization ............................................................
86
5.2.1
Measurement and Analysis of Fowler-Nordheim Coefficients ............. 87
5.2.2
S-K Chart A nalysis...............................................................................
93
5.3
Four-terminal IV Characterization ...............................................................
97
5.3.1
M easurem ent Setup ...............................................................................
97
5.3.2
IV C haracterization ...............................................................................
98
5.3.3
Electron Trajectory Simulation ..............................................................
104
5.4
C hapter Summ ary...........................................................................................
106
6
Electron Impact Ionization (ElI) Characterization................107
Prior Work - Other Application: Ion Gauge ................................................
108
Electron Impact Ionization with Three-terminal Field Emission Electron Source
112
6.2.1
M easurem ent Setup ................................................................................
112
6.2.2
Electron Current Dependence.................................................................
113
6.2.3
Pressure D ependence..............................................................................
116
6.2.4
Change in S-K Chart After Three-terminal ElI...................................... 118
6.3
Electron Impact Ionization with Four-terminal Field Emission Electron Source
120
6.3.1
M easurem ent Setup ................................................................................
120
6.3.2
Protection of the CNF Tips from Ion Erosion by the Focus................... 121
6.3.3
Change in SK Chart After Four-terminal ElI.........................................
123
6.4
Comparison to Impact Ionization in Semiconductor......................................
125
127
6.5
C hapter Sum mary...........................................................................................
6.1
6.2
7
Field Ionization (FI) Characterization ...................................
7.1
7.2
7.3
7.4
M easurem ent setup.........................................................................................
Field Ionization Characterization ...................................................................
Ion Trajectory Simulation ..............................................................................
C hapter Sum mary...........................................................................................
129
129
130
139
141
8 Thesis Summary, Main Contributions, and Suggestions for
143
Future W ork ..............................................................................
8.1
8.2
8.3
T hesis summ ary..............................................................................................
M ain C ontributions ........................................................................................
Suggestions for Future work ..........................................................................
8
143
145
146
Appendix A. Process Flow of the Fabrication of Double-gated
vertically aligned CNT Field Emission and Field Ionization Array
.......................................
147
Appendix B. Details of Four-terminal Field Emission
149
Characterization ...........................................................................
Appendix C. Details of Three-terminal Electron Impact Ionization
. .... ..... ....
.... ....
......... .......... ... ... ....... ........ 150
Appendix D. Details of Three-terminal Electron Impact Ionization
..... . . ........ .152
.............. ........... ..... . . .................
Appendix E. Details of Three-terminal Field Ionization............154
Appendix F. Field Emitter Tip Simulation.................................155
Appendix G. Image effect in Field Ionization...........................158
R eferences....................................................................................161
9
10
List of Figures
Figure 1-1.
Diagram of a mass spectrometer.
Figure 2-1.
Mass spectrum for (a) hard ionization (b) soft ionization of 1-decanol
[2.1].
Figure 2-2.
Field emission process. (b is the work function [2.2].
Figure 2-3.
A structure of a double-gated field emission device with tip in-plane with
the gate.
Figure 2-4.
A schematic drawing of a Bayard-Alpert ion gauge [2.14].
Figure 2-5.
Total charge production (gross) cross sections for argon [2.11].
Figure 2-6.
(a) A diagram of describing the ionization energy of a gas molecule. (b)
A process of an electron in a free standing gas molecule that tunnels
through the coulomb potential in an external field. [2-24] (c) A process of
an electron that tunnels through the coulomb potential in an external field
when near a metal surface [2-24].
Figure 2-7.
A square potential well is used to approximate the potential of the gas
molecule.
The field ionization tunneling barrier is approximated as the
trapezoid shape between the CNF tip and the square potential well.
Figure 3-1.
SEM picture of a double-gated silicon FEA. A high aspect ratio of field
emitter is formed with an extraction gate slightly above the tip and a focus
gate is about 300nm above the top plane of the gate opening. Gate and
focus diameters are seen to be 358nm and 686nm respectively.
Figure 3-2.
The optical microscope photos of a completed double-gated silicon FEA
Figure 3-3.
The field emission IV data for a 50x50 double-gated FEA. (a) Anode
current vs. Gate voltage (VG) (b) FN plot: Ln(IANG 2 ) vS. 1NG-
Figure 3-4.
Illustration of the electron impact ionization experiment setup for a
double-gated silicon FEA.
VE
=
OV, VG= 0-70V, Vs = 200V, and V1 =
1100V.
Figure 3-5.
The double-gated silicon FEA electron impact ionization data. (a)
Pressure at 1x1O-6 Torr, (b) Pressure at 1x10-5 Torr, and (c) Pressure at
11
-
lxl04 Torr.
Figure 3-6.
The double-gated silicon FEA: a linear relationship between the
normalized ion current (iIis) and the pressure.
VG=56V.
(Ii/Is) vs.
Pressure
Figure 3-7.
(a) Photograph of a Carbon nanotube field emission device made by
Busek corporation (Top view). (b) A schematic drawing of the device and
the field emission setup (Side view).
Figure 3-8.
The field emission IV data for the CNTs field emission device. (a) Anode
current vs. Gate voltage (VG) (b) FN plot: Ln(IAVG2) vS.
Figure 3-9.
I/VG-
The illustration of the electron impact ionization experiment setup for
Busek CNT field emission device. VE=OV, VG=0-500V, Vs=600V and
VI=-l 100V.
Figure 3-10.
The electron impact ionization data of the CNTs field emission device.
(a) Pressure at 1x10-6 Torr, (b) Pressure at 1x10-5 Torr, and (c) Pressure at
lxlO~4 Torr.
Figure 3-11.
The CNTs field emission device: the linear relationship between the
normalized ion current (Li/Is) and the pressure. (Ii/Is) vs. Pressure
Figure 4-1.
The standard procedure of preparing the CNFs catalyst.
Figure 4-2.
SEMs of Ni nanoparticles with various initial Ni film thicknesses. The Ni
films were annealed at 750*C at 20 Torr of H2 for 15min [4.9].
Figure 4-3.
SEMs of CNFs with the diameters of Ni dots from (a) 100nm to (h)
800nm. The scale bar is 400nm long and the sample tilt was 400 [4.10].
Figure 4-4.
CNF stacked-cap structure. (a) A TEM picture shows that the graphene
planes are parallel to the facets of the Ni particles.
(b)-(e) shows the
schematic drawing of the PECVD CNF growth [4.13].
Figure 4-5.
Ni catalyst size: (a) 1[m in diameter and 5nm in thickness and (b) 3tm in
diameter and 5nm in thickness.
Figure 4-6.
CNFs were grown at 750'C for 30mins. Ni catalyst size: 3ptm in diameter
and 5nm in thickness.
Figure 4-7.
CNFs were grown at 725'C for 50mins. Ni catalyst size: 3[tm in diameter
and 5nm in thickness.
12
Figure 4-8.
A double-gated FEA having an extra electrode stacked above the
extraction gate for electron impact ionization and field ionization.
Figure 4-9.
(a) Electron impact ionization: The focus gate is biased at a lower voltage
than the gate to protect the tip from ion bombardment and also to focus
the electron beam. (b) Field ionization: The focus gate is based at a lower
voltage than the gate to focus the ions.
Figure 4-10.
The schematic drawing of the ideal complete device with dimension
details.
Figure 4-11.
The two models that are built in MATLAB with (a) the tip is in-plane with
the gate (b) the tip is 900nm below the gate.
sm tall single vertically aligned CNF.
Figure 4-12.
The process flow for fabricating a 4
Figure 4-13.
4 pm-tall single vertically-aligned CNF.
Figure 4-14.
Schematic drawing of the double-gated isolated VACNF FEA process
flow.
Figure 4-15.
(a) A single vertically aligned CNF covered by 1.4 pm of PECVD oxide.
(b) A 0.4 pm thick conformal layer of doped a-Si deposited on top of the
oxide as the extraction gate material.
Figure 4-16.
(a) A layer of photoresist was spun at a high speed, which automatically
planarized the photoresist surface. (b) The structure of the extraction gate.
Figure 4-17.
(a) Another layer of 1.4 pm thick PECVD oxide deposited on the
extraction gate. (b) Another 0.4 pm thick conformal layer of doped a-Si
deposited on top of the oxide as the focus gate material.
Figure 4-18.
(a) A layer of photoresist was spun at a high speed, which automatically
planarized the photoresist surface for making the focus gate.
(b) The
structure of the focus gate.
Figure 4-19.
(a) A 32 X 32 field emitter array with the gate and focus electrodes
labeled. (b) The SEM picture of the completed device.
Figure 5-1.
The photograph of the test station.
Figure 5-2.
(a) L10 - the tip is 900nm below the gate (b) L8 - the tip is in-plane with
the gate.
Figure 5-3.
The diagram of the three-terminal FE measurement setup.
13
Figure 5-4.
These IV sweeps were done in
IV sweeps for 32x32 arrays (VG=VF).
sequence. Gate voltage started at OV and increased to either 60V or 160V
depended on the devices. Once the highest gate voltage is attained, the
direction of the sequence is reversed with the gate voltage decreasing from
60V to OV. (a) Device LIsi (b) Device Ll0s3 (c) Device LlOs4, and (d)
Device L8s4.
Figure 5-5.
Repeatability of current readings for (a) Device L10si (b) Device L10s3
(c) Device LlOs4, and (d) Device L8s4.
Figure 5-6.
FN plots. The values of aF and bF can be extracted from the intercept
and the slope of the graph. (a) Device LIsi (b) Device Ll0s3 (c) Device
LlOs4, and (d) Device L8s4.
Figure 5-7.
Example of S-K chart and how to read it [5.15].
Figure 5-8.
S-K chart of (a) silicon FEAs and (b) CNF FEAs.
Figure 5-9.
S-K chart with silicon lxi array experimental data, and calculated FN
coefficients
with varying tip radius, effective emitting area, and
workfunction.
Figure 5-10.
S-K chart of both silicon (Si) and CNF (L8-L1O) arrays.
Figure 5-11.
A diagram of the four-terminal FE measurement setup.
Figure 5-12.
Four-terminal IV data for device LiOsi (a) The gate transfer characteristic
(IA
vs. IG at fixed VF) (b) The focus transfer characteristic (IA vs. IF at
fixed VG)
Figure 5-13.
Four-terminal IV data for device L8s4 (a) The gate transfer characteristic
(IA
vs. IG at fixed VF) (b) The focus transfer characteristic (IA vs. IF at
fixed VG)Figure 5-14.
Device LIsi (Tip below the gate): Total emission current vs. focus voltage
at fixed gate voltages. The PF and 1G are extracted based on equation 5.4.
Figure 5-15.
Device L8s4 (Tip in-plane with the gate): Total emission current vs. focus
voltage at fixed gate voltages.
The
1
F
and
PG
are extracted based on
equation 5.4.
Figure 5-16.
Total emission current, gate current, focus current, and anode current vs.
focus voltage for device L10si (Tip below the gate).
14
Figure 5-17.
Total emission current, gate current, focus current, and anode current vs.
focus voltage for device L8s4 (Tip in-plane with the gate).
Figure 5-18.
These two structures are identical with 1.7[im in extraction gate diameter
and 4ptm in focus gate diameter and the focus is 1 pim above the gate,
except (a) tip is 0.9pm below the gate (LiOsi) (b) Tip is in-plane with
gate (L8s4). VTip=OV, Vc=60V, and VF=30V.
Figure 6-1.
Schematic drawing of CNT-based ion gauge. is is the electron current, ig is
the grid current, and ii is the ion current [6.2].
Figure 6-2.
Schematic drawing of CNT-based ion gauge in the form of Bayard-Alpert
gauge [6.3].
Figure 6-3.
Schematic drawing of the Mo microtip Bayard-Alpert gauge by Baptist et
al. [6.4].
Figure 6-4.
Schematic drawing of Dong's ionization vacuum gauge setup [6.5].
Figure 6-5.
Schematic drawing of Huang's BA gauge setup with line-type CNT
cathode [6.6].
Figure 6-6.
The diagram of the three-terminal EII measurement setup.
Figure 6-7.
Double-gated CNF FE and FI array (LlOs3) electron impact ionization
data. (a) Pressure at 5x10-7 Torr, (b) Pressure at 5x10~6 Torr, (c) Pressure
at 5x10
Figure 6-8.
5
Torr, and (d) Pressure at 5x10~4 Torr.
Double-gated CNF FE and F array (L8s3) electron impact ionization
data. (a) Pressure at 5x10 7 Torr, (b) Pressure at 5x10- 6 Torr, (c) Pressure
at 5x10- 5 Torr, and (d) Pressure at 5x10~4 Torr.
Figure 6-9.
L1Os3 device: linear relationship between normalized ion current (li/Is)
and the pressure. (I,/Is) vs. Pressure.
Figure 6-10.
L8s3 device: linear relationship between normalized ion current (Ii/Is) and
the pressure. (I,/Is) vs. Pressure.
Figure 6-11.
FN coefficients of before and after EII for devices (a) LlOs3, and (b)
L8s3.
Figure 6-12.
The diagram of the four-terminal EII measurement setup.
Figure 6-13.
Focus current vs. Gate voltage for device LIOsi at 3x10-8 , 1xI0- 5 and
5x10-4 Torr. (a) VF=60V and (b) VF=30V.
15
Figure 6-14.
Focus current vs. Gate voltage for device L8s4 at 3x10-8, 1x10-5 and 5x10~
4 Torr.
Figure 6-15.
(a) VF=60V and (b) VF=30V.
FN coefficients of before and after ElI for devices L8s4 (Tip below the
gate).
Figure 7-1.
The diagram of the FI measurement setup.
Figure 7-2.
Three-terminal field emission characterization of the D-G vertically
aligned CNF arrays. VA=1 l0OV and Vnp=OV.
Figure 7-3.
EN plot of L6 device. aF and bF are extracted from the intercept and the
slope of the graph.
Figure 7-4.
The schematic drawing of the electron flow and the ion flow when the gas
molecules are ionization.
Figure 7-5.
Field ionization IV data of argon at 7.5x10~4 Torr. (a) abs(IION) vs. Time
(b) abs(IION) vs. VTip. VIoN= -1 100V and VG+F =OV-
Figure 7-6.
Three-terminal field emission characterization of the D-G vertically
aligned CNF arrays: LIOs 18. VA=llOOV and Vnp=OV.
Figure 7-7.
EN plot of Ll0s18 device. aF and bF are extracted from the intercept
and the slope of the graph.
Figure 7-8.
(a) Field ionization at 8.5x10~4 and 5.6x10~3 Torr: abs(IION) vs. Tip
voltage.
VION=
-1 100V and VG+F=OV. (b) Field ionization data of Device
LlOsl8 at 5.6x10- 3 and 8.5x10-4 Torr are plotted Ln(Ii) vs.
bF
Figure 7-9.
l/VG+F.
aH and
are extracted from the intercept and the slope of the graph.
(a) Field emission tunneling probability is approximated using the
triangular barrier.
(b)
Field ionization
tunneling probability
is
approximated using the trapezoid barrier.
Figure 7-10.
Field ionization barriers. The dash line is the trapezoid model and the
solid line represents the actual barrier. The actual barrier is lower than the
model barrier.
Figure 7-11.
Ion trajectory simulation results in Charged Particle Optics 3D software.
Tip is in-plane with the gate.
VT1p=500V, VG =0V
FION= -220V/mm. (a)
VG =VF=0V, (b) VF=IOOV, (c) VF=150V, (d) VF=20OV, (e) VF=225V.
16
List of Tables
Table 2-1.
Summary of electron impact ionization, chemical ionization and field
ionization.
Table 4-1.
Summary of the gate and focus field factor, and the ratio of
OF
/ OG
generated by the simulation when the device contains tips that are (a) inplane and (b) 900nm below the extraction gate. Other tip heights have been
included to illustrate the sensitivity to small variation.
Table 5-1.
Summary of the FN coefficients of four arrays.
Table 5-2.
Summary of
Table 5-3.
Summary of
eff,
a, and the estimated r values for all the arrays.
OF, OG,
and the ratio of
pFr[G from
3-terminal and 4-terminal
data.
Table 5-4.
Summary of the Matlab simulation results for different tip positions relative
to the gate.
Table 6-1.
The summary of the changes in FN coefficients before and after electron
impact ionization for L10s3, L8s3 and L8s4.
17
18
1
1.1
Introduction
Background and Motivation - Mass Spectrometry (MS)
1.1.1 The Importance of Mass Spectrometry
The mass spectrometer is an important research tool that played critical roles in many
significant scientific breakthroughs in the early 20 century, including the determination of
atomic masses and isotope compositions [1.1].
These accomplishments had great
impacts on the development of many scientific areas in their early stages. Today, mass
spectrometry has undergone countless improvements and is widely used in scientific
disciplines such as chemistry, biology, and geology [1.2-1.4].
As an example, adopting mass spectrometry in the petroleum industry has had a great
impact on the speed of analyzing samples [1.5]. Petroleum-related samples are highly
complex hydrocarbon mixtures and contain a wide range of species. In early 1940s, the
petroleum industry used fractional distillation and refractive index measurements to
separate and analyze those components. These methods required 200 hours or more to
complete an analysis.
After adopting mass spectrometry, the time to characterize a
sample has been dramatically reduced to just a few hours. In the pharmaceutical industry,
the improvement of MS sensitivity and speed has facilitated many areas of drug
discovery, including finding drug targets, and assessing drug efficacy and safety [1.6-1.8].
However, there is still a lot of room for improvement for MS technology, especially if it
were to be used in more diverse scientific fields where, currently, there are still numerous
limitations and difficulties. Some of these difficulties might be resolved by inventing a
new type of component in MS.
For example, the issue of ion production in the
biomolecular field was resolved by introducing new ionization methods. Some of the
other limitations of MS could be removed by integrating an ionizer that is compatible
with the analyzer for a specific type of analyte.
19
In this dissertation, the primary focus is to explore new ionization methods and develop a
smaller and lower-power ionizer for gas-phase analyte suitable for a portable MS and
micro gas analyzers. Before introducing the focus of this work, the basic concepts of
how MS works will be first introduced to provide a background for understanding MS
technology.
1.1.2 Key Elements of Mass Spectrometry
The basic operation of a MS consists of the following steps: the generation of ions from
the analyte by a suitable method, followed by the separation of the resultant ionized
species according to its mass-to-charge ratio (m/z), and then finally detecting those
separated species (as a function of m/z and abundance of the species). Typically, the mass
spectrometer would have three basic elements to accomplish these goals: an ionizer, a
mass analyzer, and a detector, as shown in Figure 1-1.
Mass Spectrometer
Gas
Gas
Inlet
-
Ionizer
Analyzer
Detector
.*
Cmue
Computer
Figure 1-1. Diagram of a mass spectrometer.
*
Ionizer: The material under analysis needs to be ionized by removing one or
more electrons from the outer shell of the atom or by attaching a ionized
species to it. The ions are accelerated by either an electrical or magnetic field
that keep the final energy of ions same. The ionization method to be used
depends on the type of material and the type of mass analyzer used in the
mass spectrometer.
20
"
Analyzer: The main function of the mass analyzer is to separate the ionized
species generated at the ionizer by their mass to charge ratios. For example,
the time-of-flight analyzer separates the ions by introducing the ions into a
straight analyzer tube first [1.9]. These ions have the same kinetic energy and
the length of the tube is known. Ions with different masses have different
velocities so they reach the detector located at the end of the analyzer tube at
different times. The lighter ions arrive earlier than the heavier ions at the
detector. Thus, the ions are mass separated.
* Detector: The detector records the current (signal) induced when ions impact
the detector screen. Abundances of each species are recorded and a mass
spectrum is produced. There are different types of the detectors. Examples
are the Faraday cup, electron multipliers, and focal plane detector [1.3]. The
sensing methods applied in these detectors and their sensitivities vary. Hence,
the selection of the detector depends on the design of the mass spectrometer
and the materials being analyzed. Amongst the detectors, the Faraday cup has
the simplest operation. Faraday cup is an ion collector, at which a current is
generated when an ion reaches. This current is proportional to the number of
the charges per ion and the number of ions. A high impedance resistor is
connected to the detector in order to allow for a voltage output as the detector
reading.
Currently, there are numerous types of mass spectrometers with various combinations of
ionization methods, analyzers and detectors.
With the wide selection range of mass
spectrometers, compounds from different scientific fields can be characterized with tools
specific to each need.
1.1.3 The Importance of Ionization Methods
There are various ionization methods for MS, such as electron impact, chemical
ionization, fast atom bombardment, electrospray ionization (ESI) and matrix-assisted
21
laser desorption/ionization (MALDI) [1.10-1.13]. The choice of ionization method for a
particular analyte depends on the analyte's physical state, volatility and thermal stability.
The type of analyzer used for the MS has to be taken into consideration in choosing the
ionization method.
In the early days of mass spectrometry, electron impact ionization and chemical
ionization were the only two ionization methods available. These methods are only
suitable for volatile analytes. This means that the analyte molecules must be in the gas
phase in order to be ionized, which is not applicable for the biological samples as
majority of the biological molecules are non-volatile and have large masses. The lack of
suitable ionization method for the biological sample therefore limited the application of
MS in the biomolecular field before the 1970s. After that, the development of
electrospray ionization (ESI), matrix-assisted laser desorption/ionization (MALDI), fast
atom bombardment (FAB), and field desorption (FD) [1.8-1.11] successfully resolved the
ion production problem. In addition, cascading ESI or MALDI with time-of-flight (TOF)
analyzer helps precisely determine the high molecular weight of biological compounds
[1.14, 1.15]. The development of the ionization methods, therefore, has a great impact in
the biomolecular field, allowing the utilization of the MS as an important tool for
biomolecular research.
1.2
Statement of Problems
The number and the intensity of the m/z peaks generated on the spectrum depend on the
ionization method used in mass spectrometry. Electron impact ionization is the most
common ionization method used in current mass spectrometry for gas-phase analytes
[1.3]. In this method, electrons are generated and accelerated to collide with the analyte
(i.e. the gas phase molecules). Electrons transfer energies to those gas molecules. During
collisions, gas molecules are ionized when energies gained are higher than the ionization
energy of the gas molecules.
However, this ionization method is very energetic and
destructive, leading to high degree of fragmentation of the gas molecules. Due to the
22
large amount of fragmentation, the spectrum generated is usually very noisy [1.5]. The
molecular ion peak is often missing when a large gas molecule is characterized (as larger
ions are often fragmented by this method). Thus it is hard to identify the molecular
specie and to determine its molecular weight. For the reasons stated above, there exists a
need to develop an ionization method, which can produce the molecular ions without
severe fragmentation.
In addition, the thermionic emission based electron sources are commonly used for
electron impact ionization. To emit electrons, a filament is heated by passing a high
current through the filament. Emission current density increases as temperature increases.
Heating the filament takes time, shortens the lifetime of the filament and consumes a lot
of power. In order to have an electron source with fast response time and low power
consumption, a new method of emitting electrons needs to be explored.
1.3
Objectives and Technical Approach
The objectives of this dissertation are: (1) to replace thermionic emission with field
emission in order to have an electron source with fast response time and low power
consumption for application to electron impact ionization, and (2) to explore a non
destructive ionization method such as field ionization (FI).
Field emission is identified as a good replacement for thermionic emission. In the field
emission process, which takes place at room temperature, electrons are emitted from a
sharp tip by an applied large electric field. The applied electric field bends the vacuum
level and reduces the barrier width between the tip and vacuum. When the barrier is
narrow enough, electrons tunnel through the barrier resulting in field emission. This
process is an instant source of electrons as the electric field that is applied and it
consumes less power than the thermionic emission.
23
For the second objective stated above, field ionization (FI) is being investigated as a nondestructive ionization method for gas-phase analytes. In field ionization, a strong electric
field is applied between the tip and the gas molecule. The applied electric field reduces
the barrier between the tip and the gas molecule, allowing an outermost electron of the
gas molecule to be extracted and absorbed by the tip [1.16, 1.17]. This process has no
vibration or electronic excitation, and is very promising for producing large molecular
ion (due to lower fragmentation when compared to EI). Using field ionization, fewer
fragment ions are generated and hence the spectrum is generally simpler and the
molecular ion peaks are preserved.
In this thesis, a double-gated isolated vertically-aligned carbon nanofiber (VACNF) field
emission and field ionization device will be explored.
This device will be used to
investigate electron impact ionization using field emission electron source and field
ionization for gas-phase analyte. The thesis will describe the design, fabrication and
characterization of the double-gated CNF FEA ans its application to electron impact
ionization and field ionization of gas-phase analytes.
1.4
Thesis Organization
The outline of this dissertation is as follow:
Chapter 2 of this dissertation compares the difference between the spectra produced by
hard ionization and soft ionization, and discusses the advantages and disadvantages of
these two techniques.
Next, the physics of field emission and the electron impact
ionization will be reviewed. Electron impact ionization will also be introduced as a hard
ionization technique.
Chemical ionization and field ionization will be introduced as soft
ionization techniques. The basic chemical reactions that occur in the chemical ionization
are reviewed, and models are presented to describe the fundamentals of field ionization in
both the high electric field and the low electric field limits.
24
In Chapter 3, a macro-scale electron emission device (CNT field emitter) and a microscale device (double-gated silicon field emission array) were characterized. Both devices
were characterized as field emitters first. Then, the emitted electrons from these devices
are used to demonstrate the electron impact ionization. These exploratory experiments
showed that it is possible to use field emission electron sources in electron impact
ionization. It also helped us to select the tip material that can resist ion erosion and
choose a structure that can lower the turn-on voltage for field emission and field
ionization.
In Chapter 4, we present the investigation of how the temperature, catalyst size, and
plasma time affect the CNF synthesis. The higher the temperature, the faster the growth
of CNFs. The larger the catalyst size is, the more CNFs grown at each site and the longer
the plasma time, the taller CNFs grow. We also present the design of the double-gated
isolated vertically aligned CNF (VACNF) array and use Matlab to simulate how the gate
and the focus contribute to the generation of the electric field at the tip. Lastly, we would
present the process steps for the fabrication of the device. The double-gated isolated
vertically aligned CNF arrays are fabricated by using (1) plasma enhanced chemical
vapor deposition (PECVD) to grow an isolated CNF, (2) photoresist planarization
technique to form self-aligned gates, and (3) buffered oxide etch (BOE) to etch the
insulator between CNF and two gates in order to expose the tip.
In Chapter 5, the double-gated isolated VACNF arrays are characterized as field emission
arrays (FEAs).
The gate and the focus are tied together to perform three-terminal
measurements and then the gate and focus are biased at different voltages to perform
four-terminal measurements.
Both the current-voltage characterization results of the
three-terminal and four-terminal measurements are presented and analyzed.
The FN
coefficients of the device are plotted in Seppen-Katamuki chart (SK chart) and compared
with the FN coefficients from double-gated silicon field emission arrays. This chapter
allows us to exam the performance of the arrays and the quality of the electron source
that are going to be used in electron impact ionization.
25
In Chapter 6, the gate and the focus are tied together to provide the field emission
electron source for the electron impact ionization.
Electron impact ionization
experiments were performed at different pressures and with different gate voltages to
study the relationships between the ion current, electron current and pressure. Then, the
gate and focus are biased at different voltages and electron impact ionization experiments
were conducted. We studied the effect of the focus on the "capture" or absorption of ions
with the objective of preventing the erosion of the emitters by the ions. The SK chart is
used here to investigate the effectiveness of the focus for protecting the tip.
In Chapter 7, the repeatability of the three-terminal current-voltage (I-V) field ionization
characterization is examined first. Next, the relationship between the pressure and the
ion current is investigated by performing the field ionization measurements at different
pressure.
The I-V data shows that the ion current increases as the chamber pressure
increases at a fixed gate voltage. The characterization results and analysis are reported.
Chapter 8 presents the summary of this thesis and suggestions for future work.
26
2 Background of Ionization Methods for Gas-phase
Analytes
2.1
Background of Hard and Soft Ionization Methods
Hard Ionization
Electron impact ionization (ElI) is the most representative method for hard ionization and
it is also the most popular and widely used technique in MS. In this process, electrons
are first accelerated to acquire energy, which is then transferred to a molecule during the
subsequent collision. In the ideal case, the molecule will only gain enough energy to
strip off a single electron, producing a molecular ion peak (M') in the spectrum. If the
molecule acquires excessive energy, it will dissociate and extensive fragmentation will
occur. The fragmentation not only can give us information about the structure of the
molecule, but also aid molecule identification. However, it is not desired for large or
complex molecules; the molecular ion peak might disappear and this restricts the
determination of the molecular weight.
Soft Ionization
Chemical ionization is one of the soft ionization methods. In the chemical ionization
process, gas molecules are ionized through ion-molecule reaction instead of electron
impact. To begin, reagent gas molecules (NH 3) are ionized. Then these reagent ions
transfer an electron, proton, or other charged species to the neutral gas molecules through
ion-molecule collisions. Through this process, the gas molecules are ionized. Different
reagent gases can be used to create different reagent ions. Ionizing gas molecules with
different reagent ions generates various fragments, which helps determine molecular
structure. This method produces less fragmentation than EII so that the spectrum is
generally cleaner and the molecular ion peak is easier to recognize. However, the gas
molecule often gains or loses a proton through the ion-molecule collisions, producing
either (M+l)* or (M-l)+ peaks in the spectrum. This can result in missing molecular ion
peak.
27
41
100
Base peak
CH3 (CHZ)sCH 2 OH
60-
i3
70
40
20(biL
80
60
40
Hard
Ionization
1358
112
91
CSH-
!1
100
120
160
140
m/z
(a)
141
CH3(CH 2)8 CH2OH
100 -
(M -
OH)
80 Base peak
Soft
Ionization
CH 3(CH 2)SCH
40 20 -
60
(M
70
84
80
98
100
m/Z
(b)
- 1),
157/
112
120
140
160
Figure 2-1. Mass spectrum for (a) hard ionization (b) soft ionization of 1-decanol [2.1].
The main difference between the spectra produced by hard ionization and soft ionization
is the cleanliness of the spectra, which depends on the amount of molecule fragmentation
generated during ionization.
For example, 1-decanol (CH 3(CH 2)8CH 2 OH) is a large
molecule that was analyzed by MS with two different ionization methods [2.1].
The
spectra produced by these two methods are shown in Figure 2-1 [2.1]. Figure 2-1 (a)
shows the spectra produced using electron impact ionization, which is a hard ionization
technique. In this figure, the molecular ion peak (at higher m/z) is missing and the
fragmentation of the molecule resulted in multiple peaks at lower m/z. Figure 2-1 (b)
shows the spectrum produced using chemical ionization, which is a soft ionization
method. This spectrum is cleaner, with less fragmentation, and an easier-to-recognize
molecular ion peak. Next, we are going to discuss the advantages and disadvantages of
both techniques.
28
2.2 Hard Ionization - Electron Impact Ionization (EI)
2.2.1 Electron Sources for Electron Impact Ionization - Field Emission
The ionization method for the majority of analyzers in MS is the electron impact
ionization, which uses a beam of electrons to collide with gas molecules. Traditionally,
thermionic emission, which uses of a heated filament to produce electrons, is the most
common way of generating electrons for MS using electron impact ionization. However,
thermionic emission has several disadvantages: slow switch-on time, large power
consumption, and lack of robustness. These disadvantages, however, could be eliminated
if thermionic emission is replaced by field emission.
The advantage of using a field emission electron source over a thermionic emission
electron source for electron impact ionization is that field emission occurs at room
temperature and does not require heating. In the field emission process, a voltage is
applied to a sharp tip to create a large electric field. This applied electric field bends the
vacuum level and thus narrows the energy barrier between the tip and the vacuum,
leading to electron tunneling, as shown in Figure 2-2. Electrons are emitted as soon as the
electric field is applied and consequently this process has a fast switch-on time. In the
thermionic emission process, the filament is heated using a high current supply. Then,
electrons with energy higher than the workfunction of the metal are ejected. Due to
thermal mass, the heating of the filament is not instantaneous, and the heat shortens the
lifetime of filament and consumes more power than field emission. Thus, this project
proposes electron impact ionization using field emission as an improved method over
thermionic emission.
29
M=
isia gim
-
-
-
- ----
----
-I--
a
--
Vacuum level, V(x>O)=O
/Vacuum level
-
bent by the
applied e-field
Image force lowering
Ef
x
Distance
~2nm
V(x>O)=-qFx
Vacuum
Metal
x=O
Figure 2-2. Field emission process. 4p is the work function [2.2].
The field emission process is described next. When an electric field applied at the
surface of the tip, the vacuum level is bent. When the field is large enough to reduce the
barrier to less than 2nm, electrons are field emitted from the tip. This process consists of
a flux of carriers to the surface (supply function) and transmission through a surface
barrier (transmission probability). Let N(Ex) be the supply function, where the electron
energy is normal to the surface (Ex), and D(Ex, F) be the transmission probability, where
F is the surface electric field. Then the current density J(F) is given by
Acm-2
J(F)= JN(E,)D(E,,F)dE,
N(Ex) depends on the density of states and the Fermi function.
probability
can be
approximated
(2.1)
The transmission
by using Wentzel-Kramers-Brillouim
(WKB)
approximation,
DwKB(EXF)=exp-2f
/!+
EF -Er -qF Jxj
30
(2.2)
-nm
where 4b is the workfunction of the tip material, EF is the Fermi level in the metal or
semiconductor, q is the electron charge, and x is the distance of the barrier width. After
the usual simplification and approximations, the Fowler-Nordheim (FN) equation,
equation (2.1), that describes the emission current density as a function of applied surface
field (F) can be reconstructed as below [2.3, 2.4]:
J(F)= AF 2
p
t 2(y)
_
F
A cm 2
v(Y)]
_
(2.3)
where A=1.56x10-6, B=6.87x10-7.
To take account the image charge effect, these
Nordheim elliptical functions, v(y)
(0.95-y 2 ) and t(y) ~1.1, are added in equation (2.3),
where y -
-
3.79x10-4
.
We can then rewrite the FN equation as
J(F)=
AxF
2
1.1x#b
[
j xexp xexp[[Bx1.44xi-l
L
0.95xBx3/2
F2.4)
(2.4)
By using the mean value approximation and assuming the emitter has a symmetrical cone
shape, Dvorson et. al derived that I = a')zRAJ(F), where r is the radius of the tip, J(F)
is the current density at the apex of the emitter tip as a function the applied electric field,
and a' is a non-dimensional constant with a value of
0.4 [2.5, 2.6]. Letting a = a'ar2 ,
the total emission current is proportional to the effective emitting area a, I = aJ(F). The
surface electric field F is related to the applied gate voltage VG through F =# x
where
s
VG ,
is the field factor. The ball in a sphere model is the simplest model, which
relates the field factor [ to the tip radius r and the radius of the extraction gate R.
However, it only gives, at best, a qualitative relationship between [ and r [2.7]:
f6= F/VG
I
=
(
(r
+
-
R
~ - where R>> r.
r
31
Substituting a= a'rR2 and F =#/xVG , the emission current for the single-gate field
emission array (FEA) can thus be expressed as
eA
ax
Bxl.44x10-7
xp
I(VG
2
X
G
)
XeXp -
0.95xBx 03/2
1.1x#
$0VG
(2.5)
_
According to FN equation, the emission current is exponentially dependent on the tip
radius. A small change in the tip radius will result in a huge change in emission current.
Consequently, by using the smaller tip radius and the larger electric field, the emission
current could be increased.
Model for Double-Gated Field Emission Structure
Figure 2-3 shows a double-gated field emission structure with tip in-plane with the
extraction gate. From the previous section, we know that the emission current depends on
the electrostatic field (F) at the tip surface. Thus, in the double-gated field emission
structure, the emission current depends on both the extraction gate and the focus bias
voltage, VG and VF. The field (F) at the tip surface can be related to VG and VF through
the gate field factor (PG) and the focus field factor (PF), respectively. Using superposition,
the tip apex field can be expressed as F = /GVG
+ /FVF.
Using the FN current equation
and assuming the effective emitting area is ci, then the emission current for the doublegate FEA (four-terminal FEA) is given by:
axA
I(VG,VF) =
$
x
1.xX eLl
Bxl.44x10- 7
1 x(Jv'GE/v+GGVGXexp
2
32
-
0.95 x B x 3/2
+/JFVF_ (2.6)
r
Focus
VF
Gate
VG
1Tip
4s
Figure 2-3. A structure of a double-gated field emission device with tip in-plane with the
gate.
An effective three-terminal FEA behavior is obtained from the double-gated FEAs if the
focus and the gate voltages are equal, i.e. VF = VG. The field factor
IeffVG =/GVG +/VF
= (G+
eff is
given by:
(2.7)
JF )VG
(2.8)
fieff = 8G + X
Thus, the current-voltage characteristic for the effective three-terminal FEA is given by
Bxl.44x10-7
axA
I(VG) =
-x
1.1xO
exp
X(fg VfG)
2
x exp -
0.95xBx 01 1 2
(2.9)
f
$,-gefVG
_
[V/cm]) and can
The ball-in-a-sphere is a very simplified electrostatic model (-=
r
provide us a rough relationship between fl and the tip radius. In prior work, double-gated
silicon FEAs were fabricated and characterized [2.8]. In that work, similar to M. Ding's
approach [2.9], a finite element model in Matlab was constructed to obtain a more
accurate effective field factor 8, = 38.3x10 5 [V/cm] when
(VF=VG)-
r0.753
same approach will be applied to deduce a more accurate form of
In this thesis, the
Peff as a function
of the
tip radius in the double-gated structure with the knowledge of the dimensions of the
device structure.
33
2.2.2 Electron Impact Ionization
Electron impact ionization, developed by A. J. Dempster at the University of Chicago, is
the original mass spectrometry ionization technique and is still the most widely used of
all ionization methods [2.10]. In addition to being used in MS, this ionization method is
also used in several vacuum technology applications such as the pressure gauge and the
residual gas analyzer [2.11-2.13].
Ion colector
GMi
Figure 2-4. A schematic drawing of a Bayard-Alpert ion gauge [2.14].
For example, the operation of the Bayard-Alpert ion gauge is based on ionizing gas
molecules using electron impact ionization. Figure 2-4 shows a schematic drawing of a
Bayard-Alpert ion gauge [2.14]. Depending on the specific design of this ion gauge, the
grid is biased at about 150V and the ion collector is biased about -30V. To operate, the
electrons are first generated and accelerated by the grid voltage. Then electrons oscillate
between the grid and the ion collector until they collide with gas molecules.
During
collisions, energy is transferred from the electrons to the gas molecules, removing
electrons from the gas molecules and resulting in the ionization of gas molecules. These
ionized gas molecules are then absorbed by the ion collector. The amount of the ion
current generated is proportional to the density of the gas molecules in the chamber. At a
fixed temperature, we can measure the chamber pressure by measuring the ion current.
34
However, this process is not desired when the chamber pressure is higher than 10-3 Toff.
This is because the mean free path of the gas molecules is less than 5cm for most of the
gases at pressures higher than 10-3 Torr and ion scatter occurs before reaching the ion
collector [2.12].
The lower limit of the ion gauge can operate depends on the x-ray
generated photo current [2.12,2.13].
An x-ray is generated when the electrons collide
with the grid. This x-ray then causes the photoemission from the ion collector, which
behaves as though ions have been absorbed by the ion collector, and contributes to the
ion current. This contribution is small compared to ion current generated at higher
pressure, but causes problem when the ion current is low at the lower pressure. Due to
this effect, the lower limit of operation of an ion gauge is generally in the range of about
10-9 Torr.
In the electron impact ionization process, in order to predict the ionization current (I(E))
and how it relates to the electron current (IE(E)) with incident energy E, we need to
identify three key parameters. These key parameters are the number density of neutral
molecules in the gas (p) [cm-3 ], the collision pathlength (L) [cm], and the total ionization
cross section (a(E)) [cm2]. The relationship between the ionization efficiency (I(E)IIE(E))
and these parameters is given below [2.15]:
I 1 (E)
IE (E)
=PpxLxaTt
0
(E)
(2.10)
The collision pathlength (L) is the distance between the electron source and the ion
collector, which is smaller than the mean free path [2.15, 2.16]. By using the ideal gas
law, given the gas pressure P [Torr] and the vacuum chamber temperature T [K], the
number density of the molecules p [cm-3 ] can be extracted [2.15].
n
P
P = n-= v kT
(2.11)
The total ionization cross section is a measure of the probability that a given ionization
process will occur when a molecule interacts with an electron. The total cross section can
also be seen as the sum of the partial cross sections. The total charge production cross
section (the total ionization cross section) is obtained as the weighted sum of the partial
35
cross sections and is sometimes called the gross ionization cross section, [2.15, 2.17,
2.18],
.
total = a+ + 2a.2+ +3U3
+4
+...
(2.12)
Under certain circumstance, a single ionization can be dominant, and then
arotal
can be
approximated as [2.15]
(2.13)
aTotal ~+
3
-Ar
1-I
10
100
1000
Energy (eV)
Figure 2-5. Total charge production (gross) cross sections for argon [2.17].
To eject the outermost electron of a molecule, the electron energy of an incident electron
must exceed the ionization potential of the gas molecule. Hence, the total cross section
increases with electron energy and maximizes when the incident electron has the same
speed as the orbital electron to be removed [2.19].
decreases the ionization cross section.
Further increase in electron energy
This is because the probability of ionization
depends on the polarizability of the gas molecule.
An incident electron will displace
electrons of the gas molecule with respect to the nucleus and the gas molecule becomes
an induced electric dipole. If the speed of an incident electron is too high, the interaction
time between the incident electron and electrons of the gas molecule shortens and the
induced electric dipole cannot be fully developed.
Therefore, the probability of
ionization decreases [2.20]. As shown in Figure 2-5 [2.17], the total cross section of
36
argon increases with electron energy initially. It peaks and subsequently decreases when
the electron energy is beyond the optimum value. Usually, for most gas molecules, the
peak of the ionization cross section falls in the order of 10-16 cm 2
In this thesis project, the electron beam will be generated by field emission and the
electron emission current can be calculated from the Fowler-Nordheim (FN) equation
[2.3, 2.4]. Thus, once the number density of molecules in the gas (p), the collision
pathlength (L), the total ionization cross section (3(E)), and the electron current (IE) are
known, the ionization current could be estimated by using equation (2.10).
2.3 Soft Ionization
2.3.1 Chemical Ionization (CI)
Munson and Field introduced a soft ionization method, chemical ionization (CI), which
can produce less fragmentation than electron impact ionization [2.21, 2.22]. Due to this
advantage, this technique is applied widely in MS to study the molecular structure and
determine molecular weight.
In chemical ionization, the gas molecules (neutral analyte) are ionized through ionmolecule reactions. Through these reactions, an electron, proton or other charge species
is transferred from reagent ions to the neutral analyte. To perform this process, the
chamber is filled with reagent gas molecules and the neutral analyte at a ratio between
103
and 104 . Thus, electrons collide with the reagent gas molecules exclusively to create
ions. In addition, the chamber is maintained at a pressure of 1 Torr so that reagent gas
ions created using electron impact have frequent ion-molecule collisions with the neutral
analyte.
The neutral analyte is ionized chemically and effectively through the ion-
molecule reactions [2.22, 2.23].
37
In CI, there are several different reaction pathways to form ions from a neutral analyte M.
Below are the most common five pathways [2.23]:
M + [BH]* -* [M+H]
+B ;
proton transfer
(2.14)
[M] + B -* [M-H]~ + [BH] ;
proton transfer
(2.15)
M + X+ -+ [M+X]+ ;
electrophilic addition
(2.16)
anion abstraction
(2.17)
charge exchange
(2.18)
M + X+ -+> [M-A]
M + X+6
-+
M**
+
++
AX;
+X;
These five chemical reactions show that the neutral analyte can be ionized by obtaining
or losing an electron, proton, or charged species through the ion-molecule collisions. The
proton transfer processes described in equations (2.14) and (2.15) are very common in
chemical ionization processes. Because of these processes, the molecular ion peak is
usually missing, and (M+1)+ or (M-1)+ peak is usually present in the spectrum.
Sometimes, the reagent ion or the ion fragmentation of the reagent attaches to the neutral
analyte, which is described in equation (2.16). For example, when ammonia is used as
reagent gas, the reagent ion (NH 4 +) can get attached to the neutral analyte (M), which
produces [M+NH 4 ]+. Despite this, the spectrum produced by chemical ionization is still
cleaner than the spectrum generated by electron impact ionization.
2.3.2 Field Ionization (FI)
Field ionization, which was first observed by W. Miller, can be considered as field
emission happening in reverse [2.24].
Instead of electrons tunneling from the tip to
vacuum under a high field (as in field emission), in field ionization, electrons tunnel from
the gas molecules into the tip, thereby ionizing the gas molecules. This new ionization
technique can broaden the capabilities of existing MS.
Different molecule species have different ionization energy I [eV]. The ionization energy
for a gas is analogous to the workfunction <P [eV] for a metal. This is the energy that is
required to remove the outermost electron from a gaseous atom, as shown in Figure 2-6
38
(a). Once a field is applied to a gas molecule, the electrostatic potential barrier of the
molecule is deformed. When the field is large enough, electrons can tunnel through a
finite barrier width and will have an increased probability to be ejected into vacuum.
This process is illustrated in Figure 2-6 (b) [2.25].
"Isolated"
el..
-Yacum
C
B
A
Isolated in an
Electrostatic Field
Near metal surface &
Electrostatic Field
Electron Tunneling
Electron Tunneling
EF
~2 nm
Metal
Tip
Molecule
Molecule
Molecule
Figure 2-6. (a) A diagram of describing the ionization energy of a gas molecule. (b) A
process of an electron in a free standing gas molecule that tunnels through the coulomb
potential in an external field. [2-25] (c) A process of an electron that tunnels through the
coulomb potential in an external field when near a metal surface [2-25].
If the molecules are close to a sharp tip, a lower field is needed for electron tunneling, as
shown in Figure 2-6 (c) [2.25].
Electrons at fixed energy levels in the molecule can
tunnel to empty allowed states in the sharp tip. At a fixed field F [V/A], there is a range
of distances for which ionization will occur to the tip. If the molecule is too close to the
tip, ionization would not occur due to the absence of empty states below the Fermi level
u [eV]. The energy of the electron in the gas molecules must be elevated above the
Fermi level of the tip material for electrons to tunnel into the tip. Thus, a minimum
distance X, [A] between the gas molecule and the tip is needed for field ionization to
occur. This critical distance X, is
Xc =
I- D
F(2.19)
39
If the molecule is too far from the tip, the barrier is too large for electrons to tunnel
through. Thus, the probability of tunneling through the barrier decreases with increasing
distance from the tip. This finite tunneling probability D of electrons tunneling through
the one-dimensional barrier can be calculated by using Wentxel-Kramers-Brillouin
(WKB) approximation [2.25, 2.26]. To calculate the tunneling probability, the potential
of the molecule is approximated to be a square potential well. When the molecule is near
a metal tip and an electric field (F) is applied, the square potential well is bent, as shown
in Figure 2-7. The trapezoid area formed between the metal tip and the molecule is used
to approximate the tunneling probability (D) as below,
D=exp -Bx
I
F
x C],
(2.20)
where B=6.8x10 7 [VeV-3 2cm-'], I is the ionization energy of the gas molecule [eV], and F
is the applied electric field [V/cm] and is related to the applied gate voltage
VG
through F =# x VG, where /8 is the field factor. Cim is the coefficient that takes account
of the image effect. The value of Cim falls into the range of 0.8312 and 0.9517. (See
Appendix G for image effect approximation).
Near CNF surface
A
I
f-I
1=15.75eV
EF
CNF
Tip
Molecule
Figure 2-7. A square potential well is used to approximate the potential of the gas molecule.
The field ionization tunneling barrier is approximated as the trapezoid shape between the
CNF tip and the square potential well.
40
The strength of the electric field, and the temperatures of both the tip and the gas
molecules can affect the ion current significantly. There are three cases that would result
in an ion generation event: when the electric field at the tip is (a) strong, (b) intermediate,
and (c) low.
Each case has its own mechanism of generating the current and the
intermediate field case is more complicated. Hence, only the two models for the strong
and low electric fields are discussed here.
When the electric field is sufficiently strong at the tip, all the molecules will be ionized in
the vicinity of the tip. The more gas molecules that are near the tip, the higher the ion
current is. This means that the ion current is limited by the supply of the gas molecules.
The supply function (n) is the number of molecules per unit time entering the ionization
zone, which is directly proportional to the pressure in the chamber (molecule density) and
is also related to the electric field at the tip. The molecule density (p) in the chamber is
described in equation (2.11) and can be used to approximate the number of molecules per
unit time entering the ionization zone. However, this number changes with field strength
and the type of the molecules. Some gas molecules possess a permanent dipole moment
due to the asymmetry, such as the water molecule.
For molecules with symmetrical
structures, a dipole moment could be induced in an electric field, such as oxygen and
nitrogen. In field ionization, the strong electric field at the tip polarizes gas molecules,
which attracts more gas molecules to the tip vicinity and increases the supply function.
In this thesis, argon molecules are used in the field ionization experiments. Thus, for
both the strong field case and the low field case, the polarization factor is negligible.
Hence, we can express the ion current in the strong field as below [2.25, 2.27],
Pv
I =qxn = qx--
(2.21)
kT
where q is the electron charge.
When the electric field is low, the gas molecules will not be ionized until they are very
close to the tip and, even then, only a portion of the gas molecules will be ionized. This
means that the rate of ionization is lower than the rate of gas molecules arriving at the tip.
So in the low electric field case, the ion current also depends on the number of molecules
41
near the tip (n' the supply function) but is limited by the lifetime of the molecules (r).
The ion current can be expressed as:
I, = qxn'/r
(2.22)
n' depends on the molecule density in the chamber (p) and the volume of the ionization
zone (v) and can be expressed as n'= p x v =
P
x v. The lifetime of the molecules (r) is
kT
directly related to the frequency (f) of an electron in the molecule arrives at the potential
barrier and the tunneling probability (D), described in equation (2.20). Hence, r =
1
JD
[2.24, 2.27]. We can then rewrite the ion current in equation (2.22) as below:
Ii = q x n'/r = q x
xvxfD
(2.23)
As indicated earlier, in the tunneling probability D, F is the applied electric field [V/cm]
and is related to the applied gate voltage VG through F =#B x VG, where fl is the field
factor. The higher the electric field, the higher the tunneling probability and the more
frequently an electron arrives at the potential barrier. In this case, the supply function n'
of the gas molecules still contributes to the ion current but the tunneling probability D
and the frequency f that an electron arrives at the barrier dominate the result, which is in
the order of 1015 to 1016 sec-1 [2.25, 2.27].
42
2.4 Chapter Summary
In this chapter, we discussed the advantages and the disadvantages of the hard ionization
and the soft ionization and Table 2-1 summarizes the different ionization methods
presented. We reviewed the theory of field emission and a model for field emission
electron source will be used in the electron impact ionization. This approach offers the
advantages of faster response time and consumes less power when compared with
thermionic emission of electrons. Compared to chemical ionization, field ionization is a
very promising soft ionization method of producing the molecular ion peak with less
fragmentation than CI.
In this dissertation, electron impact ionization using field
emission electron source and field ionization will be examined as the hard and soft
ionization techniques respectively using double-gated vertically aligned CNF field
emission and field ionization arrays.
Soft
Electron impact
ionization (ElI)
Chemical
ionization (CI)
or
hard Ionizing
ionization?
Agent
Hard
Energetic
electrons
Reagent
Soft
Fragmentation
M+
A lot
Weak or absent of
M peak
Most common ionz
or
most
common ions
gaseous ions
Fewer
(M+1)* and (M-l)*
Field ionization Soft
High electric Almost none
Prominent
M+
(FI)
field
I
peak
Table 2-1. Summary of electron impact ionization, chemical ionization and field ionization.
43
44
3 Exploratory Characterizations of Silicon Field
Emission Array and Carbon Nanotubes Field
Emission Device
There are many existing field emission devices with different structures. The choice of a
suitable device structure and the tip material for both electron impaction ionization and
field ionization plays a very critical role in device capability. Hence, we have conducted
exploratory experiments to give us a chance to evaluate and compare different device
structures and tip materials. There were three objectives we wanted to achieve in this set
of experiments. First, we wanted to gain an insight into make a choice between the micro
and macro devices. Secondly, we wanted to demonstrate that it is possible to ionize gas
molecules via electron impact ionization using field emission electron source. Thirdly,
we wanted to characterize and compare different devices to establish a baseline
performance. With that, we can then improve on the current devices by optimizing the
device design and by selecting a better tip material
Existing field emission devices can be divided into two categories based on their size:
micro-scale devices and macro-scale devices. In this chapter, the characterization of both
micro-scale and macro-scale devices will be described. The micro-scale device was
fabricated as double-gated field emission arrays (FEAs) with silicon tips, and was made
by the author at Microsystems Technology Laboratories. The macro-scale field emission
device, which uses carbon nanotubes (CNTs) as its tip, was made by Busek Corporation.
These two devices cover the two categories of field emission device structures and two
different tip materials.
Both devices were characterized as field emission devices,
showing their capability of generating field emission electrons. These electron sources
were then used to perform electron impact ionization experiments.
45
3.1
Silicon Field Emission Array
3.1.1 Device Description
The structure of the double-gated silicon FEAs is first introduced. This will help in the
design and interpretation of experimental data.
Figure 3-1 shows the scanning electron
microscope (SEM) of a double-gated silicon FEA. From the SEM photograph, we can
determine the dimensions of the structure. The emitter is a 3gm tall silicon tip with a tip
radius of 5nm and is placed 400nm below the extraction gate. The diameters of the
extraction gate and the focus gate are 0.4gm and 0.8pm respectively.
The vertical
separation between these two gates is 200nm. This double-gated silicon FEA structure is
similar to the device model we presented in Figure 2-3 with some changes of the
structure dimensions. Hence, the FN equations we obtained for the double-gated FEA
can be applied here. Figure 3-2 shows the optical microscope photograph of the top view of
the device with the extraction gate and the focus gate labeled.
Figure 3-1. SEM picture of a double-gated silicon FEA. A high aspect ratio of field emitter
is formed with an extraction gate slightly above the tip and a focus gate is about 300nm
above the top plane of the gate opening. The gate and focus diameters are seen to be 358nm
and 686nm respectively.
46
Figure 3-2. The optical microscope photos of the completed double-gated silicon FEA.
3.1.2 Device Characterization
Field Emission
For the field emission tests, a 50x50 FEA was used to perform three-terminal field emission
measurements. The three terminals are (a) the anode, which was a 1mm in diameter tungsten ball
biased at 1000V and positioned 5mm above the device, (2) the silicon emitter, which was biased
at OV, and (3) the gate, consisting of the focus and the extraction gate connected together. Each
of the terminals was connected to an individual measuring unit of the Keithley 237,
which simultaneously sourcing the voltage and measuring the current. The data was
taken by using a Labview program.
-201E-6! I1 E-7.
IA: Anode current
*uuu""
-22-24-
1-1
.U
1 E-8 1
10
-U
4)
0
C4
1 E-9 1
.l
1E-10 1
.
-j
1E-1l1
1E-12,
1E-13-
3
10
20
30
40
50
60
70
80
VG (V)
-26-
B
3
.60+I-0. 28
-28- bFN=-506. 29 +/-12 .3 9
aFN -
-30- R=-0.9885
SD=0.4696
-32- -u-LnAVG2
Linear Fit of Datal LnIAVG2
-1"
0.015 0.020 0.025 0.030 0.035
1NG (1N)
Figure 3-3. The field emission IV data for a 50x50 double-gated FEA. (a) Anode current vs.
Gate voltage (VG) (b) FN plot: Ln(IA/VG 2 ) vs. 1NG.
47
During field emission measurements, the anode voltage and the emitter voltage were
fixed, while the extraction gate voltage was swept from OV to 70V and then from 70V
back to OV. Field emission IV data is shown in Figure 3-3 (a). A thorough check was
done to proof that the IV data in Figure 3-30(a) is indeed the field emission current. The
field emission current follows the Fowler-Nordheim (FN) equation, which means that the
FN coefficients, ac
and
PFN,
can be extracted from the I-V data. In order to do that, we
simplify the FN equation, equation (2.9), to obtain the relation below:
I= a
V2 exp
(3.1)
FN
FN
G
VG
with
aFN -
'42
- 1.4
0-7)]
cAfxp[Bl44l
.001/2
0.95Bt
]
(3.2)
3 2
/
3
/ eff(3)
where A=1.54x10- 6, B=6.87x10 7. To analyze the IV data, we rewrite (3.1) as
ln(I /VG2)= naFN
(3.4)
bFN
VG
We can then plot the data as ln(IA/VG 2 ) vs l/VG to extract the FN coefficients. As a linear
relationship is shown in Figure 3-3(b), the FN coefficients (aF and bF) are simply the
intercept and the slope respectively. Using equation (3.3) and assume the workfunction
of the n-type Si is 4.05eV,
eff
can be calculated, which is 1.05x10- 6 V/cm. This also
suggests that the anode current we obtained is indeed the field emission current. From
the same test, it was shown that the turn-on voltage for our double-gated silicon FEA is
around 24V and it could achieve more than 1 [A when the extraction gate was biased at
70V.
48
Electron Impact Ionization
After demonstrating electron emission from the double-gated silicon FEA, an electron
impact ionization test was next performed in a argon ambient.
In this experiment,
another terminal, a screen anode, was added. This screen was made of an stainless steel
mesh grid, which has a transparency of 90%. This terminal is biased at about 200V. The
purpose of the screen anode is to accelerate the emitted electrons, allowing electrons to
collide with molecules within the zone between the ion collector and the screen anode.
After impact ionization, electrons are absorbed by the screen anode (the screen acts as an
anode) and the ions are repelled by the screen anode and absorbed by the ion collector.
The screen anode (VA) was biased at 200V and placed right above the double-gated FEA.
In this experiment, the emitter was still biased at OV, and the focus and gate were tied
together and was swept from OV to 70V to generate electrons. The ion collector (VI) was
biased at -1 IOOV to attract ions. Figure 3-4 illustrates the experiment setup.
Ion collector Vj= -11 OOV
Ion
I---
Neutral
Molecule
electron
M P
0* '+ Impact ionization region
- -----------------Screen anode VA=200V
*
Focus
Impact
Gate
VG=0~70V
Emitters VE=OV
Figure 3-4. Illustration of the electron impact ionization experiment setup for a doublegated silicon FEA. VE = OV, VG= 0-70V, Vs = 200V, and V, = -1100V.
49
1E-6
1E-6,
C
0
C)
-C
-UIs
1 E-7-
- absli
1E-7i
P=1 E-6 Torr
1E-81
1E-91
C
0
A
1E-10 1
1 E-9
U
IE-10
C
1E-11 1
S
1E-12 1
C)
C
0
1E-13- I
0
, . , I I . , . I
10 20 30 40 50
60
7
B
1E-11
IE-12
1E-13
V
s
absli
P=1E-5 Torr
1 E-8.
C)
C
0
---
0
10
20
30
40
50 60 70
V0M
VG (V)
1E-6C
+
C)
C
1 E-7.
absli
1E-8. P=1 E-4 Torr
1E-9
C
1E-10.
0
1 E-1 1
C
1E-12
1E-13
1E-13
o
1o
20
30
40
50
60
70
VG (V)
Figure 3-5. The double-gated silicon FEA electron impact ionization data. (a) Pressure at
1x1O' Torr, (b) Pressure at 1x10, 5 Torr, and (c) Pressure at 1x10 4 Torr.
A needle valve was used to introduce the Argon (Ar) gas into the ultra high vacuum
chamber, which normally stays at a pressure of about 10~8 Torr. This needle valve can
precisely control the amount of Ar flowing into the chamber and maintain the chamber
pressure at 1x10- 6, 1x10-5, and 1x10-4 Torr.
Figure 3-5 shows the electron impact
ionization data at different pressures: (a) lxlO~6 Torr, (b) 1x10-5 Torr, and (c) lxlO-4 Torr.
"Is" is the screen anode current, which is proportional to the emission current generated
by double-gated silicon FEAs and "absli" is the absolute value of the negative ion current,
which indicates the amount of ions generated. From the graph, we can observe that the
ion current increases with the emission current, and it is the case at all pressures tested.
In addition, at these three pressures, the electron current (Is) at any specific gate voltage
50
stayed the same value while the ion current increased as pressure increased. Hence, we
would explore the relationship between the ion current and the pressure next.
Ion Currents vs. Pressure
*B
Linear Fit of Datal B
eI-41E-4
0
|
1E-5
D-G Silicon FEA
R=0.9746
SD=0.1942
0.845x+0.075
0 1E-6
0
1E-6
1E-5
1E-4
Pressure [Torr]
Figure 3-6. The double-gated silicon FEA: a linear relationship between the normalized ion
current (Ii/Is) and the pressure. VG=56V. (Ii/Is) vs. Pressure
To see the relationship between the ion current (Ii), electron current (Is) and pressure, we
extracted the ion current and the electron current when the gate is biased at 50V from
Figure 3-5 (a), (b), and (c), and the result is plotted in Figure 3-6. In Figure 3-6, the ion
current is normalized with the electron current as the y-axis and pressure (in Torr) as the
x-axis. This graph shows that there is a linear relationship between the normalized ion
current and the pressure.
51
..
..
.......
3.2 Carbon nanotube field emission device (Busek Device)
3.2.1 Device Description
B
AL
l ElScreen
ElF-1
Gate
3-5mm
CNTs
Figure 3-7. (a) Photograph of a Carbon nanotube field emission device made by Busek
corporation (Top view). (b) A schematic drawing of the device and the field emission setup
(Side view).
The CNTs field emission device tested in this section is made by Busek corporation.
Figure 3-7 (a) is a photograph of the top view of the Busek CNT device and a schematic
drawing of the side view of the same device is shown in Figure 3-7 (b). Compared to the
double-gated silicon FEAs, this device is a macro device as its size is much larger. The
device was assembled manually. The carbon nanotubes were pasted with care at the
bottom of the device to form the emitters, and the stainless steel mesh (with 90%
transparency) was clamped on the top of the device with four screws as the extraction
gate. When the gate is biased at a high voltage, electrons can be extracted from carbon
nanotubes and they would pass through the stainless steel mesh gate.
3.2.2 Device Characterization
Field Emission
The test setup for the CNTs field emission device is similar to double-gated silicon FEAs.
For field emission measurements, the emitters (CNTs) and the anode were biased at OV
and 1 100V respectively, while the gate screen voltage was swept from OV to 500V and
then from 500V back to OV. Figure 3-8 (a) shows the field emission IV data of the CNTs
device. To ensure that the anode current was indeed the field emission current, the IV
52
data was fitted with FN equation (equation 3.4), and the FN coefficients were extracted,
as shown in Figure 3-8 (b). Using equation (3.3) and assume the workfunction of CNT is
4.8eV,
Peff
can be calculated, which is 1.68x10
5
V/cm. This confirms the capability of
field emitting electrons from the Busek device. Because this device is a macro device,
the distance between the gate (screen gate) and the emitters (CNTs) is large. This results
in a large turn-on voltage, 200V, as shown in Figure 3-8 (a). Nevertheless, we still
obtained a high emission current up to 1 pA by increasing the gate voltage up to 500V.
-241E-61
I
IA: Anode current|
."
1 E-7
.*
I-
I-
mU
..
-o
E.E.
1E-9 1
1E-101
0
1E-11
4 0 4
-40- Busek CNT
-36aFN -- 8.74"81
-38-
..-
.
1 E-1 21
"
*
Eu
100
"
bFN =-4076.22+/-254.45.
E
U..
~40- R=-0.901
mm
m
-42- SD=1.691
12
0
-32-34-
U
-
C)
U)
Linear Fit of buseckFEIA
-28-
E."...
*
1 E-8
U)
IA
--
-26-
200
300
400
0.002
500
0.003
VG (V)
0.004
0.005
1/ VG(1/V)
Figure 3-8. The field emission IV data for the CNTs field emission device. (a) Anode
current vs. Gate voltage (VG) (b) FN plot: Ln(IANG 2) vs. 1NG.
Electron Impact Ionization
Ion Collector=-1 1 OOV
neutral
electron
-------------->LO
impac~*
,
p
--
Ion
.
u um
-
4-
Screen Anode
Screen Gate
CNTs
Figure 3-9. The illustration of the electron impact ionization experiment setup for Busek
CNT field emission device. VE=OV, VG=0-500V, Vs=600V and V1=-1100V.
53
The setup for the electron impact ionization measurement is the same as the setup for
double-gated silicon FEA and instead of sweeping gate voltage from OV to 70 V, the gate
voltage was swept from OV to 500V.
Electron impact ionization data of CNTs device is plotted in Figure 3-10. In the figures,
electron emission current and ion current are plotted versus gate voltage at different
pressures (10-6, 10-5, and 10
4
Torr). We observed the same trends as in the double-gated
silicon FEA: (a) at a fixed pressure, ion current increases with electron current and (b) as
the pressure increases, ion current increases too.
1 E-5 1
C
0
0
S
1E-5
+-Is
1E-61
1 E-61 -.- absli
1E-71 P=1e-6 Torr
1E-81
1E-91
C
A
C
0
1E-10 1
C
C
L.
0
1 E-11
0
1 E-12 1
1 E-9.
B VI
1E-10.
1 E-1 1
C
1 E-13
4
-u-Is
-e - absli
1E-71 P=1 E-5 Torr
1E-8.
0
4A
0
100
200
300
400
50 o0
w
e
VG (M)
1E-121E-13.
1E-14
0
100
200
300
400
500
V0 (V)
1 E-5
1 E-6
C
0
1 E-71
Is
abshi
P=1E-4 Torr
I1E-9
1E-101
I-1
IE-11
1E-12
1E-13
I 1-1
0
100
200
300
400
500
VG (V)
Figure 3-10. The electron impact ionization data of the CNTs field emission device. (a)
Pressure at 1x10 Torr, (b) Pressure at 1x10 5 Torr, and (c) Pressure at 1x10 4 Torr.
54
Ion Currents vs. Pressure
To verify carefully the relationship between ion current and pressure, ion current and
electron currents were measured at pressures from 3x10-7 Torr to 1x10 4 Torr. The result
is plotted in Figure 3-11. In the figure, ion current is normalized by electron current and
plotted versus pressure. This agrees with what we observed in the double-gated silicon
FEA; i.e. normalized ion current is linearly related with pressure.
=
absIAIS
Linear Fit of Datal absIAIS
1E-4- R=0.9974
SD=0.06097
Y=0.99x+0.49
C
2 1E-5
C
1E-6
C
0
.1
E-6
1E-4
Pressure [Torr]
Figure 3-11. The CNTs field emission device: the linear relationship between the
normalized ion current (Ii/Is) and the pressure. (Ii/Is) vs. Pressure
3.3 Comparison between D-G silicon FEA and CNTs Field Emission
Device and Implications for Ionizer
In this chapter, we reported the characterization of electron emission and electron impact
ionization using the two devices in previous sections. For double-gated silicon FEAs, we
observed a low turn-on voltage of 24 V for field emission and the device achieved an
anode current of 1pA when the gate was biased at 70 V. This device is suitable for field
emission applications, such as flat panel display. However, it is not adequate for electron
55
impact ionization and field ionization. During electron impaction ionization experiments,
the silicon tip could be destroyed by ion back-bombardment [3.1]. During our electron
impact ionization experiments, several devices were destroyed due to ion bombardments.
It is not realistic to perform field ionization using this device due to limitations from the
device structure; the tip was 400nm below the gate and the gate opening was only 400nm
in diameter. With those dimensions, only limited number of gas molecules could gain the
access to the vicinity of the tip and be ionized. To confirm that, a field ionization
experiment was performed and no ion current was observed.
In the case of CNT field emission device, the large distance between CNTs and the gate
implies that the turn-on voltage for field emitting electrons will be high; in fact, the turnon voltage for the CNT device was measured to be 200V compared to 24V for silicon
FEAs. This device was still able to generate 1 [tA, but at a much higher gate voltage
(500V). This device is suitable for electron impact ionization because of the tip material.
The CNTs can be degraded but rarely be destroyed by ion bombardments [3.1]. However,
the large turn-on voltage makes this device unfavorable for the field ionization
experiment. To field ionize the gas molecules around the tip, an extremely high voltage
(-
1-2kV) is needed.
The objective of this thesis is to perform both electron impact ionization and field
ionization using the same device. Thus, the CNT is chosen to be the emitter material due
to its longer lifetime and its capability of withstanding ion bombardments. CNTs are
promising for electron field emitters, and several groups have worked on related topics.
Most papers reported that the turn-on electric field of CNTs ranged from 2 V/tm up to 30
V/tm for a diode structure field emission device. A diode type field emission device
typically places the anode about 125-250im away from the CNTs (cathodes). Hence, the
turn-on voltage ranges for such a device would range from 250V to 600V [3.1-3.9].
More recently, other groups have micro-fabricated individual extraction gates at each
emission site. This reduces the turn-on voltage to 9-65V [3.1, 3.10, 3.11]. Guillorn et al.
micro fabricated a double-gated CNT device. The self-aligned technique was used to
make the extraction gate while the photolithography was used to pattern the focus [3.12-
56
3.14]. When the gate and the focus were biased together during IV measurements, they
reported a turn-on voltage of 60V. When the gate and the focus were biased differently
for optical measurements, the electron beam width was successfully reduced. However,
the current was not specified in the optical measurement. Overall, gated micro-fabricated
CNTs FEAs have a lower turn-on voltage. Wang et al.'s report confirmed the
effectiveness of the gate [3.2, 3.3].
A micro fabricated gated CNT FEA was
characterized as a diode structure with the gate floating. With this setup, no anode
current was observed until the anode voltage reached 1000V.
Next, using the same
device, the anode and the CNTs were fixed at 500V and OV, respectively, the anode
current was observed when the gate voltage reached 50V.
According to these exploratory characterization experiments and the prior work in the
literature described earlier, we decided to design a CNF FEA, which is double-gated, for
both field emission and field ionization (shown in Figure 2-3). This device is suitable for
electron impact ionization. The low turn-on voltage allows the device to emit electrons at
a lower voltage. The focus (second gate) is biased at a lower voltage than the extraction
gate voltage to attract ions and reduce ion bombardment of the tip. For field ionization,
the turn-on voltage is reduced to a reasonable level due to the reduction of the distance
between the gate and the CNFs. The gate and focus apertures are large enough, allowing
the tip to be accessible to the gas molecules. In addition, the focus (second gate) can be
biased at a higher voltage than the extraction gate voltage for focusing the ion beam
[3.15].
57
58
4 Design and Fabrication of Double-gated Isolated
Vertically Aligned Carbon Nanofiber (VACNF)
Field Emission and Field Ionization Arrays
The goal of this project is to fabricate a device that is able to ionize gas molecules for
mass spectrometry using both electron impact ionization and field ionization methods.
This chapter will first describe the synthesis of carbon nanofibers and then present the
design of the device and finally a process for fabricating the device.
4.1
Tip Material Selection and Carbon Nanofiber (CNF) Synthesis
4.1.1 Tip Material - Carbon Nanofiber
As indicated in Chapter 3, carbon nanofibers are chosen to be the tip material. In the past
decade, carbon nanotubes/nanofibers (CNTs/CNFs) have been investigated for a wide
range of applications, including for use in field emission displays, transistors,
electromechanical sensors, and fuel cells [4.1-4.4]. The difference between CNTs and
CNFs is that CNTs have the tubular structures and the rest is CNFs.
Due to their
remarkably high electrical conductivity, carbon nanofibers have also generated a lot of
interest for applications in vacuum microelectronic devices [4.5-4.8]. In addition, due to
their unique physical structure: high aspect ratio with small diameters (in nano meters)
and relatively long lengths (in micro meters), carbon nanofibers can handle a large
electric field in order to field emit electrons and field ionizing gases. Thus, carbon
nanofibers are chosen to be the tip material for this reason precisely.
4.1.2 Carbon Nanofiber Synthesis
To grow vertically aligned CNFs, a plasma-enhanced chemical vapor deposition
(PECVD) machine is used. The CNFs used in this project were synthesized in a PECVD
59
machine at Cambridge University.
All the sample preparation was done at the
Massachusetts Institute of Technology's MTL, and the author flew to Cambridge
University in Cambridge, England to grow CNFs. There are many factors that affect the
growth of vertically aligned CNFs. These include the catalyst materials, the thickness
and size of the catalyst, the deposition temperature, the plasma exposure time, the applied
bias voltage, and the C2H2 :NH 3 gas-flow ratio. Here, we specifically investigated the
effects of growth temperature, catalyst size, and plasma exposure time while keeping the
remaining parameters fixed.
Sample Preparations
Figure 4-1 shows the standard procedure that was used to prepare a catalyst for growing
CNFs. First, a layer of negative photoresist (PR) was spun on an N-type silicon wafer
(Step A). Once the negative PR was patterned (Step B), a 4nm Ni dot, which serves as
the catalyst, was deposited using the electron beam evaporation (Step C). The NMP (1methyl-2-pyrrolidinone) was then heated up to 75*C to lift off unwanted Ni (Step D).
Silicon
Photoresist
Nickel
A
Coat a layer of negative
Photoresist on a n-type
wafer
Pattern the photoresist
C
a thin layer of Ni
=Deposit
(4nm)
D NLift
off the unwanted Ni
in NMP
Figure 4-1. The standard procedure for preparing the CNFs catalyst.
60
Standard Growth Conditions
The vertically aligned CNFs (VACNFs) were grown using a dc PECVD system on a
resistively heated graphite substrate stage, which allows for manipulation of the growth
temperature.
Before varying catalyst size, plasma time, and growth temperature, a
standard procedure was developed for synthesis of the CNFs. The PECVD chamber was
first pumped down to a base pressure of 10-2 Torr, and 200sccm of NH 3 and N2 were
introduced to maintain a chamber pressure of 20-30 Torr. The substrate temperature was
ramped up at 100*C/min until the substrate temperature reached 630C, then a 650V
plasma was turned on to anneal the Ni. At this step, the thin-film Ni catalyst dot
coalesced into nanoparticles, which later seeded the growth of CNFs. The thickness of
the Ni film controls the size of the nanoparticles, which later determines the structures of
the CNFs. Chhowalla et al. did a series of experiments to study the correlation between
the Ni film thickness and the size of the nanoparticles [4.9]. Figure 4-2 is a summary of
their experimental results. From the SEMs, we can clearly see that the size of the
nanoparticles varies in proportion to the thickness of the Ni film.
In addition to the
thickness of the film, the diameter of the Ni dots controls the number of nanoparticles
formed after the annealing. Teo et al. fixed the thickness of the Ni film (7nm) and varied
the diameter of the Ni dots to investigate the relationship between the diameter of the
dots and the number of CNFs produced by each dot [4.10]. The number of the CNFs
grown at each site is proportional to the diameter of the dot. SEM pictures in Figure 4-3
are from Teo et al.'s experiments [4.10].
After the nanoparticles are formed, 50 sCCm of C2 H2 , which serves as the carbon source
for growing the CNFs, is introduced when the substrate reaches the desired temperature.
Then Ni-C eutectic alloy is formed, which helps the carbon diffusion. The C2H2 then
decomposes at the nanoparticle surface, and the hydrogen and carbon dissolve into and
diffuse through the particle, finally to precipitate in the form of a CNF [4.11]. During the
growth, the nanoparticle is pushed upward and a metal cap is formed.
Once the
nanoparticle is completely covered by grapheme layers, the growth of the nanofiber stops.
During the growth, a-C is also deposited on the substrate surface, where Ni nanoparticles
are absent. The role of the NH3 is to etch a-C during the growth [4.12]. Thus, the ratio of
61
C2 H2 and NH 3 is fixed at 1:4 to prevent the presence of a-C on the substrate surface.
After the standard growth conditions were established, catalyst size, growth temperature,
and plasma time length were varied to optimize the synthesis of the CNFs [4.9].
A
schematic drawing of the CNF growth mechanism is shown in Figure 4-4 [4.13].
Figure 4-2. SEMs of Ni nanoparticles with various initial Ni film thicknesses. The Ni films
were annealed at 750 0C at 20 Torr of H2 for 15min [4.9].
62
Figure 4-3. SEMs of CNFs with the diameters of Ni dots from (a) 100nm to (h) 800nm. The
scale bar is 400nm long and the sample tilt was 400 [4.10].
63
a
NI
ac
Figure 4-4. CNF stacked-cap structure. (a) A TEM picture shows that the graphene planes
are parallel to the facets of the Ni particles. (b)-(e) shows the schematic drawing of the
PECVD CNF growth [4.13].
64
Figure 4-5. Ni catalyst size: (a) 1pm in diameter and 5nm in thickness and (b) 3pm in
diameter and 5nm in thickness.
Using the procedure described in Figure 4-1, Ni catalyst dots with the sizes of 1[tm and
3[tm in diameter and 4nm in thickness were fabricated. These catalyst dots were used to
study how the sizes of the catalyst dots affect CNF growth. Both samples were grown
using the standard conditions for 30mins at 725'C. The results are shown in Figure 4-5 (a)
and (b) for the i m- and 3[ m- diameter catalysts, respectively. We can clearly see that
for any given thickness of the Ni catalyst dots, the smaller the diameter of the dot, the
fewer CNFs that are grown. After the annealing, the catalyst dot breaks into smaller
nanoparticles, and each nanoparticle acts as a seed during CNF growth. This means that
each nanoparticle is capable of forming a CNF. Hence, the smaller the diameter of the
catalyst dot prior to annealing, the fewer nanoparticles that are generated, and the fewer
CNFs that are grown [4.10].
Next, the growth temperature was increased from 725*C to 750*C while the growth time
was fixed at 30mins. Figure 4-6 shows the structure of the CNFs synthesized using this
condition. Compared to Figure 4-5(b), we observe that temperature plays an important
role in the growth rate of CNFs. For a growth time of 30 minutes, CNFs are about 7ptm
tall at 725*C and about 19tm tall at 750*C.
Temperature increases the C2 H2
decomposition rate at the nanoparticle surface and also increases the rate at which the
hydrogen and carbon dissolve into the nanoparticle. The faster the hydrogen and carbon
precipitate, the faster the CNFs grow. Thus, the higher the temperature, the faster the
CNFs are grown.
65
Figure 4-6. CNFs were grown at 750'C for 30mins. Ni catalyst size: 3ttm in diameter and
5nm in thickness.
Figure 4-7. CNFs were grown at 725'C for 50mins. Ni catalyst size: 3ptm in diameter and
5nm in thickness.
Next, the effect of the plasma time was examined. To observe the effect, the temperature
was fixed at 725*C while the plasma time was increased to 50 minutes. The height of the
resulting CNFs was about 13[tm, as shown in Figure 4-7. These CNFs are much taller
than the CNFs shown in Figure 4-5 (b), which were grown using a plasma exposure of
only 30mins. Increasing the plasma time increases the CNF synthesis time, which results
in taller CNFs.
66
These CNF synthesis experiments demonstrate that catalyst size, growth temperature and
the plasma time are important factors for CNF synthesis. The smaller the catalyst size,
the fewer CNFs that are grown. The higher the growth temperature, the faster the CNFs
are grown. Lastly, the longer the plasma time, the taller the resulting CNFs. These
results show us how to synthesize 4ptm single vertically aligned CNFs.
4.2 Device Design
4.2.1 Device Structure
A double-gated field emission array (FEA) with an extra gate (focus gate) stacked above
the first gate (extraction gate) is the chosen device structure, as shown in Figure 4-8.
This structure is suitable for both electron impact ionization and field ionization of gas
molecules.
Anode
Focus
Gate
Emiffer
Figure 4-8. A double-gated FEA having an extra electrode stacked above the extraction
gate for electron impact ionization and field ionization.
67
A
-
-
Anode
I
I I
I
Screen
amm
,
Anode
,
~
Focus
F
Focus
Gate
Gate
Emitter
Emitter
(a) Electron Impact Ionization
(b) Field Ionization
Figure 4-9. (a) Electron impact ionization: The focus gate is biased at a lower voltage than
the gate to protect the tip from ion bombardment and also to focus the electron beam. (b)
Field ionization: The focus gate is based at a lower voltage than the gate to focus the ions.
In electron impact ionization, the focus gate can be biased at a lower voltage than the
extraction gate. This serves two purposes. One is to focus the electron beam. The other
is to attract and absorb ions generated between the focus gate and the screen to reduce the
chances of ions bombarding the tip, as shown in Figure 4-9 (a). In the field ionization
process, the focus gate can be biased at a higher voltage than the extraction gate to focus
the ion beam before the ions enter the MS analyzer, as shown in Figure 4-9 (b).
4.2.2 Device Structure Dimensions
In order to perform both electron impact ionization and field ionization using the same
double-gated CNF device, the design of the device structure focuses on two aspects. One
is to control the number of CNFs grown at each site to maximize the electrical field at
each CNF. The stronger the electrical field at the tip surface, the lower voltage is needed
to generate emission current for electron impaction ionization and ionize the gas
molecules for field ionization. The other is to have a thick insulator to sustain the high
voltage between gates and the tip during operation.
68
2.1
2.0
0.85
IL
4
.2
Tip height 4
1.4 oxide thickness
Unit: micron
Figure 4-10. The schematic drawing of the ideal complete device with dimension details.
2.4
Focus
Focus
9
Tip
Gate
A
Gate
B
Figure 4-11. The two models that are built in MATLAB with (a) the tip is in-plane with the
gate (b) the tip is 900nm below the gate.
Recent work in the literature has clearly shown that individual CNTs are excellent
electron field emitters; moreover, the closely packed arrays of CNFs will experience an
electric field shielding effect, and this shielding effect adversely affects the CNFs' field
emission characteristics [4.14, 4.15]. Teo et al. confirmed experimentally that patterned
69
arrays exhibit lower turn-on fields and better overall field emission characteristics as
compared to dense or sparse forests of "randomly" positioned vertically aligned CNFs.
To minimize the shielding effect, only a single CNF is grown on each site, and the CNFs
are spaced twice their height apart to reduce the electric field shielding effect from
adjacent CNFs. The number of CNFs per catalyst dot is controlled by the dot dimensions
[4.9 and 4.13]. The Ni catalyst disks must be 300nm or smaller in diameter to ensure the
growth of only a single CNF at each catalyst site. Hence the Ni dots are defined by
ebeam lithography to ensure that the dots are less than 300nm in diameter.
The device is designed to perform as a field emission array and a field ionization array,
which implies that when the device is used as a field ionization array, the insulators
between the gates and the tips have to sustain high extraction voltages. Thus, an insulator
with a high breakdown voltage is desired. Typically, the silicon dioxide layer is used as
the insulator between the tip, gate, and focus. The breakdown field of silicon dioxide is
107 Vcm' [4.16]; however, a more reasonable design value that accommodates surface
asperities is =106 Vcm-1. The oxide used here will be deposited by STSCVD in TRL and,
recently, Blaise Gassend (a MIT EECS Ph D student) conducted a series of breakdown
tests for all the available oxide materials at the MTL.
His results showed that the
minimum breakdown voltage of 1 im STSCVD oxide is greater than 750V. In order to
sustain voltages of about 1000V for the field ionization experiments, an oxide thickness
of 1.4 im is required between the CNF ground plane and the extraction gate and between
the extraction and focus gates. Assuming that the thickness of the extraction and focus
gates are each 0.4 gm, this implies that the CNFs should be 3.6 jim or taller. Hence, the
CNFs synthesized in this thesis are 4gm tall.
After the height of the tip and the thickness of the insulator were chosen, the vertical and
horizontal deposition rates of oxide were characterized to determine the ideal complete
device dimensions. The oxide deposited using STSCVD in the TRL is a conformal layer.
The horizontal and vertical deposition rates are 607nm to 1000nm, respectively. Hence,
when a 1.4gm oxide layer is deposited horizontally, a 0.85gm oxide layer is deposited
vertically. Figure 4-10 is a schematic drawing of the complete device. In this device, the
70
(1) tips are 4gm tall and in-plane with the extraction gate, (2) the gate and the focus
apertures are 0.85gm and 2.1gm, respectively, (3) the insulator between the silicon
substrate and the gate, as well as between the gates, is 1.4gm thick, and (4) the thickness
of both gates is 0.4gm (not specified in the drawing).
As was described in Chapter 2, to estimate the value of the gate field factor, focus field
factor, and effective field factor
a model with the dimensions specified in
(VF=VG),
Figure 4-10 was built in MATLAB using the finite element method (FEM) (courtesy of
Guobin Sha). This model is pictured in Figure 4-11 (a). In addition to this model, a
second MATLAB model was built, as shown in Figure 4-11 (b). This model was similar
in structure to the first, except for a distance of 900nm introduced between the tip and the
extraction gate. The purpose of these two MATLAB models was to determine how the
potential of the two gates affects the electric field generated at the tip. Therefore, for the
sake of simplicity, the focus gate simulated in the MATLAB was simplified to a
rectangular shape. As was described earlier, Ni disks that are 4nm thick and 250nm in
diameter grow isolated vertically aligned CNFs. A disk these dimensions has volume of
1.96x0 2 m3 , which, theoretically, would form a sphere with a radius of 36nm during the
annealing. Thus, the tip radius was assumed to be 36nm for the MATLAB simulation.
Table 4-1 summarizes the data generated from the simulation. The values of pF and OG,
and the ratio of OF /G are given for the scenarios in which tip was (a) in-plane and (b)
900nm below the extraction gate.
Tip 1000nm below the gate
Tip 900nm below the gate (LIOs1)
Tip 800nm below the gate
Tip 100nm below the gate
Tip in-plane with gate (L8s4)
Tip 100nm above the gate
Tip 200nm above the gate
EF [V/cm]
pG [V/cm]
8.47x103
1.12x10 4
1.48x10 4
8.74x10 4
3.07x10 5
1.29x10 5
1.52x10 5
pF /G
5.00x1O
4.97x10 5
4.93x10 5
4.15x10 5
1.19x10 6
3.68x10 5
3.41x10 5
0.017
0.023
0.030
0.210
0.272
0.351
0.447
Table 4-1. Summary of the gate and focus field factor, and the ratio of PF PG generated by
the simulation when the device contains tips that are (a) in-plane and (b) 900nm below the
extraction gate. Other tip heights have been included to illustrate the sensitivity to small
variation.
71
The table shows that the values for
pF and 1G are
similar for both models of the device.
In addition, it can be observed that when the tip is below the extraction gate, the ratio of
rF /
PG
is lower than when the tip is in-plane with the gate. This means that when the tip
is below the extraction gate, the focus gate has less effect on the tip. Also included in
Table 4.1 are values of 1F, PG and fF /G for other tip heights that are close to the two
nominal values to illustrate the sensitivity of pF, 03Gand F /
PG
to tip-height variation.
Using the same models, it is possible to deduce a more sophisticated form of
Oeff
as a
function of the tip radius in the double-gated structure. When the tip is in-plane with the
extraction gate and VF=VG,
04
Bff
r
extraction gate and VF=VG,
f47.5 X10
rr0.848
5
[V/cm].
When the tip is 900nm below the
[V/cm].
These two relationships are similar
but not the exactly same due to the different tip positions relative to the extraction gate.
72
4.3 Device Fabrication
In the previous chapter, we reported that self-aligned chemical mechanical polishing
(CMP) technique was used to fabricate the first gate of the double-gated vertically
aligned CNF (VACNF) FEA device by Guillorn et al. [4.17-4.19]. Photolithography was
used to define the second gate, which causes minor misalignment between the VACNF
and the center of the second gate. In our fabrication process, in order to ensure that the
CNF is at the center of both gates, both the extraction gate and focus gate were fabricated
using the self-aligned technique. In addition to the alignment improvement, the height of
the our CNFs is 4pm, compared to the 1gm CNF synthesized by Guillorn et al. The 4gm
tall CNF makes it possible to have a thicker insulator, which expands the voltage
operation range for the device.
4.3.1 Formation of 4 pm-Tall Isolated Vertically Aligned CNFs (VACNFs)
The process flow for fabricating 4 gm-tall isolated VACNFs is summarized in Figure 412. The CNF arrays have different sizes: 35x35, 100x100, and 206x366. The pitch of
the CNFs is 10 pim in order to create a reasonable array density resulting in little
interference between the CNFs.
The first step in fabricating CNFs was to define the Ni dot size on the silicon. Electron
beam lithography was used to carefully define a Ni dot size that is 250nm in diameter.
This ensured that only a single CNF would be grown at each site.
Specifically, the
photolithography step was as follows: (a) Hexamethyldisilazane (HMDS) vapor phase
application, (b) photoresist spin-coating, (c) soft bake (115
develop.
C), (d) expose, and (e)
4 nm of nickel (Ni) was then deposited using eBeam evaporation. This film
would later form the catalyst for growing CNFs. To eliminate excess Ni, the lift-off
process was performed using NMP (1-methyl-2-pyrrolidinone) as the solvent at 70'C.
This process created a Ni catalyst disk of 250nm with diameter and 5nm thickness.
73
PMMA
OP
Expose PMMA
(Ebeam lithogropghy)
Si substrate-
PMMA
-*
Si substrate-+
4mm
Develop
PMMA
Ni -+
PMMA
-*
Deposit Ni
(eBeam deposition)
Si substrateNi -Po
Lift off
Si substrate-l
Carbon nanofiber
(CNF)
Grow CNF
(PECVD)
Si substrate-+
Figure 4-12. The process flow for fabricating a 4 pm tall single vertically aligned CNF.
74
Figure 4-13. 4
stm-tall single
vertically-aligned CNF.
As stated in section 4.1.2 on carbon nanotube synthesis, CNF structure is strongly related
to the growth temperature and the length of plasma time. According to previous
synthesis experiments, at a growth temperature of 725'C, CNFs grow at a rate of 0.4pm
per min. To have a 4pm vertically aligned CNF, 10 minutes plasma time is required at
725'C. A recipe in which 200sccm of NH 3 and, 500sccm C2H2 are heated at 725'C for
10 minutes plasma time is used to grow 4pm vertically aligned CNFs. A SEM picture of
these vertically aligned CNF is shown is Figure 4-13.
4.3.2 Formation of the Gate Insulator and the Extraction Gate
A conformal layer of plasma enhanced chemical vapor deposition (PECVD) oxide was
deposited as the gate insulator to separate CNTs and the gate material (amorphous-Si).
The thickness of this oxide layer is 1.4gm and the diameter of the oxide pillar covering
the CNFs is 1.7gm, which defines the extraction gate diameter. A conformal layer of
75
PECVD doped amorphous-Si (a-Si) was deposited on top of the oxide to form a gate
electrode.
These two steps are shown in Figure 4-14 A-B and the corresponding
scanning electron microscope (SEM) pictures are shown in Figure 4-15.
The next three steps, shown in Figure 4-14 C-E, illustrate a novel technique developed by
the author and used twice in the process. This self-aligned technique was used to define
both gates. CNFs caused protrusions, which were much higher than the bottom of the
surface. To open the gate aperture, a layer of photoresist (PR) was spun at a high speed.
This process automatically planarized the PR surface without using CMP, as shown in
Figure 4-16 (a). When the PR was spun on the wafer, PR filled the gaps between the
protrusions, but did not cover the protrusions. This smooth PR layer defined the structure
of the gate aperture. Next, to open the gate aperture, an anisotropic silicon reactive ion
etch (RIE) was used to etch the a-Si. The tip position relative to the extraction gate is
related to the plasma time in RIE. The longer plasma time, the more the a-Si is etched.
This allowed the creation of a device that the tip is in-plane with the gate. When the
plasma time was shorter, less a-Si was etched. This created tips that were 900nm below
the gate.
In this thesis, these two types of device were made, and the device structures
are shown in Figure 4-11 (a) and (b). After the gate aperture was patterned by RIE, the
PR was the removed. This PR self-aligned technique offers a very fast, fairly uniform
and well-controlled planarization method of making the self-aligned gate, which can
replace the CMP technique that has been reported and used by L. Dvorson et. al, M. A.
Guillorn et. al, and L.-Y. Chen et. al [4.17-4.21].
after definition of the extraction gate.
76
Figure 4-16 (b) shows the structure
I
I
]
L
J
K
CNT
6 oLOxide
S6m
=
L
6a-Si
Photoresist
Figure 4-14. Schematic drawing of the double-gated isolated VACNF FEA process flow.
(a)
(b)
Figure 4-15. (a) A single vertically aligned CNF covered by 1.4 pum of PECVD oxide. (b) A
0.4 prm thick conformal layer of doped a-Si deposited on top of the oxide as the extraction
gate material.
77
(b)
(a)
speed, which automatically
Figure 4-16. (a) A layer of photoresist was spun at a high
gate.
planarized the photoresist surface. (b) The structure of the extraction
4.3.3 Formation of the Focus Insulator and the Focus Gate
to define the
The same steps (Steps A through E) presented in Figure 4-14 were repeated
layer of
focus insulator and the focus gate (Steps F through J). In step F, a conformal
focus gate using the
PECVD oxide was deposited to separate the extraction gate and the
A layer of PECVD a-Si was
same oxide thickness that was deposited earlier.
of these two steps are
subsequently deposited to form the focus gate (step G). The SEMs
shown in Figure 4-17.
by anisotropic
A layer of photoresist was spun at high speed again (step H) and followed
removed after the
silicon RIE to open the focus aperture (step I). The PR was then
Figure 4-18.
silicon was etched (step J). The SEMs of step H and I are shown in
78
. . ........
(a)
(b)
Figure 4-17. (a) Another layer of 1.4 pm thick PECVD oxide deposited on the extraction
gate. (b) Another 0.4 pm thick conformal layer of doped a-Si deposited on top of the oxide
as the focus gate material.
Figure 4-18. (a) A layer of photoresist was spun at a high speed, which automatically
planarized the photoresist surface for making the focus gate. (b) The structure of the focus
gate.
79
4.3.4 CNF Exposure and the Completed Device
The contact patterning of both the extraction gate and the focus gate were conducted at
the same time that the extraction gate aperture and the focus gate aperture were defined.
The last step of the fabrication process is to "release" the structure using a BOE etch.
This step removes the oxide between the focus electrode, gate electrode and the CNF
field emitter.
Figures 4-19 shows the optical micrograph and the SEM picture of the completed device.
Figure 4-19 (a) shows a 32 X 32 field emitter array with the gate and focus electrodes
labeled. Figure 4-19 (b) is the SEM of the device. The diameters of the extraction and
focus gates of this device are 1.7gm and 4.2gm respectively.
Figure 4-19. (a) A 32 X 32 field emitter array with the gate and focus electrodes labeled. (b)
The SEM picture of the completed device.
80
4.4 Chapter Summary
This chapter presented the design and fabrication of a double-gated isolated VACNF field
emission and field ionization arrays capable of field emission and field ionization. The
device was designed carefully to maximize the electric field generated at each tip and to
minimize the electrostatic shielding effected by neighboring tips. The device is capable
of handling a large breakdown voltage during field emission and field ionization
operations.
Two models of the device were built in Matlab in order to calculate the gate and focus
field factors. In one model, the tip and the gate were in-plane, whereas in the other model,
the tip was 900nm below the gate. The values of pG and PF were similar for both models
of the device; however, a difference occurred in the ratio of
OF/
PG. The ratio of
pF/
PG
was smaller for the model in which the tip was 900nm below the gate (0.02) than for the
model in which the tip was in-plane with the gate (0.26). In addition, the models of
eOff
as a function of the tip radius were deduced for both models of the device. When the tip
is in-plane with the extraction gate and VF=VG, ff =47.0 x10 5 [V/cm]. When the tip is
400nm below the extraction gate and VF=VG, /f
5 [V/cm].
= ef47.5x10
r0.848
r.
In the fabrication process, a 4pm-tall isolated VACNF was first grown using PECVD
method. The gates were then opened using the photoresist planarization technique, which
creates very uniform gate and focus apertures (1.7pm and 4.2pm, respectively) across the
silicon chip. This is also the first time that a double-gated self-aligned FEA with isolated
VACNFs has been fabricated and is reported in the literature.
81
82
5 Field Emission Characterization
Electron sources are widely used in a broad range of devices, including in field emitter
displays, power switches, field emission mass storage devices, mass spectrometers and
massively parallel electron-beam lithography [5.1-5.5].
Compared to thermionic
emission, field emission is an attractive way to extract electrons due to its high current
density, low operating temperature, efficient operation, virtually instant startup, and its
light weight [5.6]. Recently, various research groups have demonstrated that carbon
nanotubes/fibers (CNTs/CNFs) are promising field emission electron sources for a wide
range of applications. However, most of the CNT/CNF-based electron emission devices
that were reported have fairly large turn-on voltages due to the large distance between the
anode and the CNT/CNF cathodes. In this chapter, microfabricated double-gated isolated
VACNF field emission arrays (FEAs) are characterized described in Chapter 4. This
chapter begins by describing the equipment and procedures to measure field emission. In
sections 5.2 and 5.3, field emission results from single-gated FEAs (three-terminal FEAs),
and double-gated FEAs (four-terminal FEAs) are presented and discussed.
Lastly,
electron trajectory simulations are conducted in support of the four-terminal IV
characteristics.
83
...
..
.......
5.1 Measurement Setup and Device Description
Measurement Setup
Electrical characterization of the FEAs was conducted in an ultra-high vacuum (UHV)
chamber at a pressure of about 3x10-8 Torr or lower without bake-out, field forming, or
conditioning. Figure 5-1 is a photograph of the test station. The chamber on the right is
the loadlock, where samples can be loaded and unloaded. The main test chamber is on
the left. On top of the test chamber, a high-resolution camera magnifies the image of the
device's surface.
The device was probed with very sharp tungsten probes and the
backside of the wafer was contacted directly through the metallic stage, which was
always grounded. To eliminate vibrations that could potentially break the probe contacts,
the UHV chamber was mounted on a floating optical table. Triaxial cables were used for
all signals to minimize noise and interference. The instrumentation included five sourcemeasure units (Keithley 237), capable of simultaneously sourcing voltage and measuring
current. The Labview, a computer interface program, provided remote control of the
instrument and collected the data over the GPIB.
Figure 5-1. The photograph of the test station.
84
Device Description
The devices tested in this thesis are from two different pieces (L1O and L8); with
different geometries that were fabricated slightly different processes. In LbO, CNF tips
are 900nm below the gates (Figure 5-2 (a)), and in L8, CNF tips are in-plane with the
gates (Figure 5-2 (b)). This is because a longer plasma time was used to etch the gate
material in L8 than in L1b, which resulted in different relative positions of the tips with
respect to the gate. There are multiple arrays in each piece and different arrays from each
piece were tested and labeled as si or s2, for example. These differences in the relative
tip positions made it possible to analyze how devices with the tip in-plane with the gate
and devices with the tip 900nm below the gate behave when characterized for field
emission and electron impaction ionization.
Figure 5-2. (a) L10 - the tip is 900nm below the gate (b) L8 - the tip is in-plane with the
gate.
85
5.2 Three-terminal IV Characterization
There are four terminals in the device: the CNF emitter (cathode), the extraction gate, the
focus, and the anode.
When three-terminal field emission (FE) measurements were
performed, the extraction gate and the focus were always kept at a same voltage by a
Keithly 237. This ensured that there was no voltage difference between the gate and the
focus. The devices were probed on-wafer, and the emitter current
IE,
anode current IA
and gate current Ic were monitored. The diagram of the three-terminal characterization
setup is shown in Figure 5-3.
During this measurement, the FN coefficients were
extracted. These coefficients provide useful insight into the emission characteristics of
each device.
PC
Vacuum Chamber
Anode
I
Focus Drobe
Ground the substrate
G PIB
Kelthley 237
KeIthley 237
II
Kelthley 237
Figure 5-3. The diagram of the three-terminal FE measurement setup.
86
5.2.1 Measurement and Analysis of Fowler-Nordheim Coefficients
Field emission is a tunneling process. The potential barrier (workfunction, 4)) of the tip
deforms when a strong electric field is applied. This narrows the potential barrier, which
increases the electron tunneling probability.
Thus, the amount of current generated
depends strongly on the electric field at the tip and the workfunction of the tip. These
two factors determine the barrier width and the probability of the tunneling process.
It is common to observe fluctuations in the field emission current with time at a fixed
applied voltage. This temporal instability might be due to the changes in (D and 1. While
the device was characterized inside of a UHV chamber, conditions inside the test
chamber are never perfect. Gas molecules are present inside the chamber, which causes
the adsorption and desorption of molecules on the tip surface [5.7, 5.8]. The adsorption
or desorption of the molecules can alter the tips' work function or change the profile of
the tips' curvature, thereby changing the emission current. The goal of the experiments
presented in this chapter was not to study fluctuation or noise but simply to ensure that
the FE data was reproducible. For the measurements presented here, a series of 12 IV
sweeps, which consisted of a voltage increase immediately followed by a voltage
decrease, were performed in sequence. These repeated IV sweeps were used to ensure
that these measurements were reflective of each device's field emission behavior and
provide a guarantee against noise due to the adsorption and desorption of molecules on
the tip surface.
Figures 5-4 (a) through (d) show the data for the 32x32 arrays from both L8 (tips in-plane
with the gate) and LlO (tips below the gate).
Anode current is plotted on the y-axis,
while time is plotted on the x-axis. From the figures, it can be observed that device L8s4
has a higher maximum current than device LlO has. This could be attributed to several
possible effects: superiority of the L8 device structure, or the presence of more emitting
CNFs, or sharper CNFs on L8s4 in particular.
This data not only provides a more
accurate measurement of the FN coefficients but also implies that L8 and L10 could
87
perform differently under four-terminal measurement.
The same data are plotted
differently in Figure 5-5 (a) through (d) to illustrate the noise in the emission current (the
plot of current vs. gate voltage over time).
600.0n500.0n400.0n-
A
C
C
E 300.0n200.On-
ijijilli .
E 100.On-
4
0.01
0
200
400
600
800
0
C
400.0n350.0n 300.On
250.On
200.0n150.On
100.On.
50.0n
0.0
-50.On
LlOS31
0-I
B
LID
0
100 200 300 400 500 600
Time
1 .2p-
IAL
Time
2.5p-
s
-- IAL8s4
80.0n-
C
1.5p-
C
0
600.0n-
U
U)
400.0n
II-
2.0p-
0500-0n"
200.On
0.0
L
dlii
0.0*
0
200
400
600
800
1000
0.0
Time
200.0
400.0 600.0
Time
800.0
Figure 5-4. IV sweeps for 32x32 arrays (VG=VF). These IV sweeps were done in sequence.
Gate voltage started at OV and increased to either 60V or 160V depended on the devices.
Once the highest gate voltage is attained, the direction of the sequence is reversed with the
gate voltage decreasing from 60V to OV. (a) Device L10si (b) Device L10s3 (c) Device L10s4,
and (d) Device L8s4.
88
1E-7i
-
'
Lis
A
1 E-8 1
C
a)
1E-8
A
1 E-9
C
I
1E-10i
1 E-11 1
.I
"
1E-12 1
1'
11i*~-I.
;w.ill
B
1E-9
1E-10
a)
0
IA L10s
1E-7
IMF
.1j1I-'
.ill'
I.I"I
0
Eu
I
1E-11
C
1E-121
-I-
I ii
I
1E-1 O
1E-13
20
4
60
80
20 40 '6
160 10 140.
'A
L10s4
Ii
1 E-7
1 E-81
IE-10
1 E-7,
l
.1
1E-12
0
20
40
60
IA L8s4
I
1E-8-
""E
1 E-9,
I
1E-11
1E-13
C
"
I IIIIII
1 E-9.
a)
110 1010
1E-6,
1 E-6
U
k
V G(V)
VG (V)
V
6'101
0
1E-10
C
1 E-1 1
1E-12
80 100 120 140
.1:.
i
! ' ii'
00e
0 10
20
30
40
50
60
VG(
VG (V)
Figure 5-5. Repeatability of current readings for (a) Device L10si (b) Device LOs3 (c)
Device L1Os4, and (d) Device L8s4.
89
As indicated in Chapter 2, the effective field factor for the double-gated FEAs can be
expressed as
peff = fiG + hF to
3
simplify the FN equation. Below is the simplified FN
equation, first shown in Chapter 3, that is used to extract the FN coefficients: aF and bF.
I = aN V exp
___p___
a
= Q
be
=
1.10
exp
V
j
(5.1)
[B(1.44x1o-9
[
1
1j
O.95Bb 31
where A=1.54x10-6, B=6.87x10 7.
(5.2)
(5.3)
The Ln(IA/VG 2 ) vs l/VG can then be plotted to extract
the FN coefficients. Figures 5-6 (a) through (d) show the FN coefficients with the error
and standard deviation for all the arrays. In these figures, aF is the intercept and bF is
the slope of the FN plots.
R is a measure of the degree of linearity between two variables. An absolute value of R
near 1 indicates a high degree of correlation between x and y, whereas a value near 0
indicates a lack of correlation. A negative value of R indicates that y tends to decrease
when x increases [5.9]. The R, standard deviation, SD is a measure of the distribution of
a set of data with respect to its average value. The smaller the standard deviation is, the
closer the data points are. It can be seen from the FN plots that all the values of R in the
graphs are close to -I and that the standard deviations in each case are small. Also, it can
be observed that arrays containing the same piece (L10) have similar high values of bF,
(that is bF equals about 1400), while the value of bF of L8s4 is much less (bF=-417.49).
Table 5-1 summarizes the FN coefficients obtained for four arrays.
Once the bF and aN values were extracted, equations (5.2) and (5.3) were used to
calculate the effective field factor, Peff, and the effective emitting area, a, for each of the
arrays. In addition, the ball-in-a-sphere electrostatic model, which assumes that field
factor [=1/r, was used to estimate the tip radius from the slope of the FN (bF). To obtain
a more accurate estimate of the tip radii for the devices, two models built in MATLAB,
90
which were first introduced in Chapter 4, were used. When the tip is in-plane with the
[V/cm].
When the tip is 900nm below the
5
[V/cm].
extraction gate and VF=VG, 6eff = 47.5x10
r 0.848
The CNF workfunction is assumed
= 7.
extraction gate and VF=VG,
x10'
r
to be 5 eV [5.10]. Table-5-2 presents the values of eff and, a, and the estimated r, for
each of the arrays.
-24-
M
-26-
I
M
-28-
-30- a =-15.04+/-0.
-1
LlOs3
Linear Fit of FNL1Os3_LlOs3
-26-
-28-
-32-
*
-24-
.
-30-
b =-1375.43+/-15.81
-
SD=0.682
-34- R=-0.968
a LIOs1
-36- Linear Fit of FNL1Os1_L10s1
0.008
0.010
0.012
5-32- a
-1 7.004
-34- bN=-1445.46+-28.50
-34- SD=0.851
R=-0.939
0.014
0.006
0.008
C5
-20-
-24-26.
-28_1
"
-30-32-34- bFN=l1580.42+/-19.43
"a"
-36- SD=0.993
-38- R=-0.952
-40- * LlOs4
Linear Fit of FNL1Os4plotL10s4
-42-
0.008
0.010
0.012
I
0.010
0.012
1NG (iN)
1NG (1N)
=0
-5..
*
-22-
L8s4
Linear Fit of L8s4FN K
-24-
-26-28.
-30-
a =-14.43+-0.10
bN=-417.49+/-4.16
I
-32- SD=0.717
R=-0.968
-34-
0.014
0.02
ING (1IN)
0.03
0.04
1NG
Figure 5-6. FN plots. The values of aFN and bFN can be extracted from the intercept and the
slope of the graph. (a) Device LiOsi (b) Device LOs3 (c) Device LOs4, and (d) Device L8s4.
91
aF
SD
-15.04 0.15
0.682
0.968
bF
R
LiOsi
-1375.43±15.81
L1Os3
-1445.46±18.50
-17.00 ±0.25
0.851
-0.939
L1Os4
L8s4
-1580.42±19.43
-417.49±4.16
-13.40±0.20
-14.43±0.10
0.993
0.717
-0.952
-0.968
Table 5-1. Summary of the FN coefficients for four arrays.
Field
LiOsi
LlOs3
LlOs4
L8s4
factor Eff. emitting area (a) Esti. tip radius (r) Esti. tip radius (r)
(Peff)
(Matlab models)
(1/)
[nm]
[nm]
[nm2]
[V/cm]
5
5.31x10
446.95
13.2
18.85
5.05x10 5
69.53
14.1
19.81
5
4.62x10
7.32
15.6
21.66
1.75x10 6
75.79
3.2
5.72
Table 5-2. Summary of Peff, a, and the estimated r values for four arrays.
The data in Table 5-2 suggests that arrays on L10 have similar field factors, which results
in similar estimated tip radii. The estimated tip radii for arrays in L1O are about 14nm,
according to MATLAB model, and about 20nm, according to the ball-in-the-sphere
model.
This tip radius is less than the catalyst disks used to grow the CNFs.
As
described in Chapter 4, Ni disks with a thickness of 4nm and a diameter of 250nm were
used to grow isolated vertically aligned CNFs. Each disk had a volume of 1.96x10-22 M3 .
After annealing, these disks would theoretically form spheres with radii of 36nm. There
are several reasons why the radii of the CNFs are in reality smaller than 36nm. The Ni
disks were annealed at a high temperature to form Ni catalysts prior to growth of the
CNFs. During this process, silicon substrate could have reacted with Ni to form nickel
silicide, resulting in loss of Ni. Another possible explanation is that Ni was lost during
the CNT growth process.
V. I. Merkulov attributes the loss of catalysts to two main
mechanisms [5.11]. "First,a nanoparticlecan be continuously reduced in size down to
zero due to ion sputtering and/or dispersion of the catalyst material within the VACNC
during growth. A second mechanism is that a substantial upper part of the VACNC
becomes very thin as the catalyst particlesize decreases and breaks offfrom the VACNC
base due to intense ion sputtering that can occur at some distance away from the tip."
For the L8s4 array, the estimated tip radius was much smaller than the estimated tip
92
radius for the three arrays of devices on L1b. This suggests that there are tips that are
much smaller than the average tip radius and these tips with smaller radius dominate.
The reason for this is because field emission current strongly depends on the tip radius.
5.2.2 S-K Chart Analysis
Y. Gotoh et al. reported that the field emission property can be differentiated by means of
the plots of the intercepts (am) and the slopes of FN (bFN) [5.12]. The report showed that
even with different tip radii, different tip materials have clear differences in the
relationship of the intercepts (aN) and the slopes of FN (bF). They obtained an
empirical relation when the intercepts (am) are plotted on the x-axis and the slopes of FN
(bF) are plotted on the y-axis. This diagram provides a possible method for evaluating
the relative change or difference of work function among the emitters. Later, Y. Gotoh et
al. named this diagram "Seppen-Katamuki chart" or "S-K chart." In Japanese, Seppen
means intercept and Katamuki means slope [5.13, 5.14]].
Figure 5-7 [5.15] is an
example of a S-K chart and how to read it. The points which are located more toward to
the upper left corner of the graph have smaller tip radii than the points located at the
lower right corner. For the workfucntion of the materials, the points located at the upper
right corner have lower workfunction than the ones located at the lower left corner.
0
1
111
-I
-
(-2000
-
0
-2500
lower
work function
smaller
0L-1000 -- apex radius
-1500
-
*
-8
/
larger
apex radius
higher
work function
I
-3000
I 1
chart
-S-K
-500
-
I
I
-7
I
I
-6
I 1
-5
-4
Intercept of F-N plot
Figure 5-7. Example of S-K chart and how to read it [5.15].
93
-300-
zU
-350.
-400-
* Sil
* Si5
A silo
Z
v Si2O
.0u-
-800-
+ Si5O
z
0
0.
z
..
-450.
-1200*0
U-
".
E
*m
0
.2 -500CD
" L8s4
" L8s7
A L~s8
v L8s9
L10s4
-400-
.
Al
-19
-17
-18
-1600
0
-
U-2000-16
-14
-15
B
A
0
-26
-24
Intercept of FN plot ( a.)
-2
A
-20 -18
-16
-14
Intercept of FN plot (am)
Figure 5-8. S-K chart of (a) silicon FEAs and (b) CNF FEAs.
-400*
0
* U
n
IL
z
0%
U
.0
.
CL
-500-
M
U
0
0.
Si 1x1 experimental data
vary tip radius
V vary workfunction
*
*
0
-600
-19
-18
-17
Intercept of FN plot ( aFN)
Figure 5-9. S-K chart with silicon 1x1 array experimental data, and calculated FN
coefficients with varying tip radius, effective emitting area, and workfunction.
The author worked on the double-gated silicon FEAs as her master thesis, which
generated FN coefficients from various sizes of silicon arrays (lxi, 5x5, 10xlO, 20x20,
and 50x50 arrays). These FN coefficients of Si FEAs are plotted in Figure 5-8 (a) while
the FN coefficients we obtained for double-gated CNF FEAs are plotted in Figure 5-8 (b).
94
Silicon 1xi array is chosen to illustrate the SK chart explanation given by Y. Gotoh. The
Matlab model of the silicon double-gated FEA is described earlier, 8 = 38.3x101 [V/cm].
r0753
The average FN coefficients of this lxi array from the experimental data are aN=-18.14
and bFN is -469.62, which gives us the average tip radius of 9nm. When the n-type
silicon workfunction is fixed at 4.05eV, the calculated data points move from the right
lower corner to the left upper corner as tip radius varies from 7nm to 10nm (decrease in
the tip radius). Figure 5-9 shows the experimental and the calculated FN coefficients.
Next, shown in Figure 5-9, the workfunction is varied from 4.05eV to 3.9eV (decrease in
the workfunction) while the tip radius is fixed at 9nm and the point moves from the left
lower corner to right upper corner. This agrees with the explanation given by Y. Gotoh.
In addition, we can see that FN coefficients extracted from the experimental data of this
silicon lxi array varies, indicating that the silicon tip was changing its workfunction and
tip radius during the field emission experiments. It is a lxi array, which means that there
is only one silicon tip in the array, and these variations might due to the adsorption and
desorption of residual gas molecules at the tip.
In comparison, these variations are
smaller in the larger silicon arrays (10x10, 20x20, and 50x50 arrays), as shown in Figure
5-8 (a), due to the averaging effect. The S-K chart can serve as a tool to provide us a
rough idea of the difference of the workfunction between tip materials and the tip radius
among arrays.
In order to compare the silicon and CNF FN coefficients, Figure 5-8 (a) and (b) are
plotted together on the same S-K chart, as shown in Figure 5-10. In this figure, we can
see that silicon arrays are clustered together at the upper right corner while the CNF
arrays are dispersed at the lower right corner or lower center. This suggests us that
silicon arrays have more consistent workfunction and the tip radii than the CNF arrays.
This is a reasonable explanation. The workfunction for n- type silicon is 4.05 eV. For
CNF, the workfunction could vary from single-wall CNTs to multi-wall CNTs or from
thermal growth, to arc discharged growth, to PECVD growth. Even within PECVD
growth, there does still exist the variations of CNT workfunction.
95
Due to the tip
formation method for Si, silicon FEAs have more uniform radii ranging from 3.Onm to
5.3nm [5.16]. As indicated earlier, the CNF tip radius might vary due to the loss of the
Ni for various reasons resulting in a wide range of tip radii.
M
-400-
Si5
A
silo
v
Si2O
4
Si5O
L8s4
*
*
*
L8s7
L8s8
L8s9
LlOs4
*
z
.800.
0
-1200U.*
Sil
*
-,1600
(0
-2000-26 -24 -22 -20 -18 -16 -14 -12
Intercept of FN plot ( a
)
Figure 5-10. S-K chart of both silicon (Si) and CNF (L8-L1O) arrays.
96
5.3
Four-terminal IV Characterization
5.3.1 Measurement Setup
Four-terminal measurements were performed using a setup similar to that used for threeHowever, in the four-terminal measurements, the focus and
terminal measurements.
extraction gates were not biased at the same voltage
Instead, the focus was biased at a
lower voltage than the extraction gate to collimate the beam.
The diagram of the
measurement setup is in Figure 5-11.
UHV Chamber
Anode
GPIB
Focus
F
5
A
Gafte
Keithley 237Keithley 237-
F
Keithley 237~Ground the substratethey23
Figure 5-11. A diagram of the four-terminal FE measurement setup.
97
5.3.2 IV Characterization
As indicated earlier, the tip electric field depends on both extraction gate and the focus
gate for the double-gated FEA. Thus, using superposition, the tip apex field can be
expressed as F = fIGVG
+ / 3 FVF.
It was shown in Chapter 2, the four-terminal FN equation, which uses the FN current
equation and assumes the effective emitting area is a, the emission current is:
axA
I(VGVF
)
Bx1.44xlT10-
x ep
0.95x Bxf 3 /2
x#V
GV+FV
+ 6FVF)2 x expG-
X
(5.4)
Our goal is to investigate the influence of the extraction gate and the focus gate on the
emission current by extracting the gate field factor (pG) and the focus field factor (OF).
To accomplish this goal, we need to study the gate transfer characteristics and the focus
transfer characteristics of the device. The gate transfer characteristics show the variation
of the anode current as a function of gate voltage with focus voltage fixed. The focus
transfer characteristics show the variation of the anode current as a function of focus
voltage with gate voltage fixed.
Figure 5-12 (a) and Figure 5-13 (a) show the gate
transfer characteristics of device LIsi (Tips below the gate) and device L8s4 (Tips inplane with the gate).
Figure 5-12 (b) and Figure 5-13 (b) show the focus transfer
characteristics of device LIsi and device L8s4.
From Figure 5-12 and Figure 5-13, we observed that these two devices function
differently. Both Figure 5-12 (a) and (b) show that the anode current of device L10sI is
strongly dependent on the focus voltage. For instance, it is clear that, in the gate transfer
characteristic (Figure 5-12 (a)), there is still an anode current when the gate voltage is at
OV while the focus voltage is at 135V. This means that the influence of the focus gate on
the anode current or/and the electric field generated around the tip is higher than that of
the extraction gate. For device L8s4, we observe that the extraction gate and the focus
gate have the almost equal impact on the anode current or/and the electric field on the tip
98
since the gate transfer characteristic and the focus transfer characteristic of the device
L8s4 look alike.
1E-7
1E-7.
A
1E-8.
Z
1E-9.
~!!I--AZAR
1E-10.
0
1E-8
4C
" ov
I
C 1E-11.
1E-12
A
IF 1 -1 i
20
60
1E-11
g
1E-12
V 100V
+
*0
0
" 30V
~
-
."
1E-10
Focus voltage
EU.VV_
1E-9.
135V
0
20
10V
"
'.
.
1 00V
135V
A""*
i.
1E-13
40 60 80 100 120 140
Gate Voltage V (V)
Gate voltage
40
60
80
100 120 140
Focus Voltage VF (V)
Figure 5-12. Four-terminal IV data for device L10si (a) The gate transfer characteristic (IA
vs. IG at fixed VF) (b) The focus transfer characteristic (IA vs. F at a fixed VG)
1E-6-
1 E-61 E-7C
0
B
A
1 E-7
A
1 E-8.
V
4 a
1E-10- a
a
OC
C
4
.E "
L8s4
Focus Voltage
. 40V
* 50V
A 60V
"
1E-11-
,
0
20
30
40
50
"
viaU
L8s4
Gate voltage
* 40V
* 50V
A
60V
"
.
a
0 1E-11
.
1E-12
1E-13
10
A
1E-10
Ago
AAis.Eo
IeE9
89".
oI
*
1E-9-
I-1 9
AA
60
-
0
10
20
30
40
50
60
Focus Voltage VF (V)
Gate Voltage VG (V)
Figure 5-13. Four-terminal IV data for device L8s4 (a) The gate transfer characteristic (IA
vs. IG at fixed VF) (b) The focus transfer characteristic (IAvs. IF at a fixed VG)
To quantify this effect, we can extract the gate field factor (pG) and the focus field factor
(OF) by using equation (5.4). Anode current (IA), gate current (IG), and focus current (IF)
are added together to compute the total emission current. We fit the emission current to
equation (5.4) using Origin software package. There are several uncertainties that we
need to consider. The value of the tip workfunction (D fluctuates randomly with time and
the effective emitting area a is only an estimate that we obtained from the three-terminal
measurements.
This means that there is a dependence on the data set we chose. In
addition, there were variations in PG and OF of about 20% in L. Dvorson's work. Thus, L.
99
Dvorson suggested that instead of focusing on study the PG and the
field factors,
OF
OF,
the ratio of the
IOG is more stable and serves as a reliable estimate [5.17]. Figure 5-14
and Figure 5-15 show the fit of the LIsi and L8s4, respectively. The same two Matlab
models described in Figure 4-10 are used to estimate PG and OF. Table 5-3 summarizes
these parameter estimates.
1 E-5-
D-G CNT Li Os1
VG6
- VG6O
.5x1 0'V/cm
PG 6.8x1 OIcm
PF=
1E-6.
0
VG100
- --
0F
G
20
40
02
A-VG135
60
80
100 120
140
VF(V)
Figure 5-14. Device L10si (Tips below the gate): Total emission current vs. focus voltage at
fixed gate voltages. The PF and PG are extracted based on equation 5.4.
4 1 E-6
+
C,
oil
<1
E-7
1E-8
0
G=1
.Oxl 06V/Cm D-G CNT L8s4
VG40
P =2 .7 x10V/cm
02
F
EI1 E-9
-,
0
. PF /PG
U
, , - - ,10
20
30
--
VG50
7
40
VG60
50
60
VF(V)
Figure 5-15. Device L8s4 (Tip in-plane with the gate): Total emission current vs. focus
voltage at fixed gate voltages. The PF and PG are extracted based on equation 5.4.
100
4-TERMINAL DATA
$F
OG
[V/cm]
[V/cm]
6.8x10 5
OF/
Matlab Simulation
OF
OG
[V/cm]
[V/cm]
3G
OF/ OG
LIsi
1.51x10 4
0.02
1.12x104 4.97x10
0.02
0.26
1.01x10
0.26
3.07x10
1.19x10'
L8s4
2.71x10
Table 5-3. Summary of PF, PG, and the ratio of PF/PG from 3-terminal and 4-terminal data.
EF
Tip 1000mn below the gate
Tip 900nm below the gate (LIOs1)
Tip 800nm below the gate
Tip 100nm below the gate
Tip in-plane with gate (L8s4)
[V/cm]
pG
[V/cm]
OF
/G
8.47x103
1.12x10 4
1.48x10 4
5.00xlO
4.97x10 5
4.93x105
0.017
0.023
0.030
8.74x10 4
3.07x10 5
4.15x105
1.19x10 6
0.210
0.272
Tip 100nm above the gate
1.29x10 5
3.68x10 5
0.351
5
5
Tip 200nm above the gate
1.52x10
3.41x10
0.447
Table-5-4. Summary of the Matlab simulation results for different tip positions relative to
the gate.
L. Dvorson et al. [5.18] reported three types of double-gated silicon field emitters: (1)
1G
is 2.67 (Tip above the extraction gate); (2)
gate); and (3)
OF
/
OG
OF
OF/
/ 1G is 0.75 (Tip is slightly above the
is 0.16 (Tip is below the gate).
Dvorson observed that the
sF /
extraction gate shields the tip significantly from the focus gate on the device with
OG
is 0.16. The variation of the emission current at a given gate voltage as focus voltage
changes is small. Later, L.-Y. Chen et al. [5.16, 5.19] constructed three models of
double-gated FEAs with the same dimensions and only change the relative position to the
extraction gate using finite element method in MATLAB to quantify how pF and
1G
vary
with the relative position of tips and the gate. When tip is above the extraction gate,
pG is
1.415. When the tip is in-plane with the extraction gate,
the tip is lO0nm below the extraction gate,
OF
confirmed with the experimental data that when
OF
/ OG is 0.012.
pF is much
/G
OF/
is 0.632 and when
These simulations also
smaller than
OG,
focus has
less effect on the tip. From the fit data, summarized in Table 5-3, the ratio of OF /
OG
for
LIsi is 0.02 compared to 0.26 for L8s4 suggesting that the tip of LIsi is below the
extraction gate and the tip of L8s4 is closer to the extraction gate opening. The values of
@F and
1G
and the ratios of
OF
/ PG calculated from the Matlab simulation for both devices
are consistent with the experimental data. In addition, we simulated several models using
the same structure with different tip positions relative to the gate and the results are
101
summarized in Table5-4. As the tip position moving from below, in-plane, to above the
gate, the ratio of
pF /G
becomes larger. This means the focus has more effect on the tip
when the tip is higher. Both measured and calculated ratios agree with the SEMs shown
in Figure 5-2 (a) and (b) and are consistent with the results of by L. Dvorson et al. and L.Y. Chen et al [5.16, 5.18, 5.19].
However, there is an apparent discrepancy between the variations of anode current and
total emission current with respect to focus voltage for LiOsi. When the tip is below the
extraction gate, anode current is not expected to vary with focus voltage since it is
shielded by the extraction gate. As we observe in Figure 5-12 (b), there is large variation
of anode current of LIOsI as function of focus voltage but not in its total emission current
as shown in Figure 5-14. The reason for this is that, according to equation (5.1),
pF and
Gare the parameters that quantify the effectiveness of the both gates, which contribute
to the electric field on the tip. In other words, when
pF is less than
G, the focus gate has
less effect on generating electric field on the tip and the total emission current than the
extraction gate. This effect is observed from the total emission currents in Figure 5-14
for device L10s1. There is only a slight increase in the total emission current as focus
voltage varies. On the other hand, L8s4 in which
F / PG
is 0.2, focus voltage has an
equal/similar effect on the total emission current. Thus, in Figure 5-15, at fixed gate
voltage, the total emission current varies as focus voltage increases. This suggests that
and
G
equally affect the total emission current.
102
OF
1E-5
ONOMEMEMEMN
1E-6
AA="WMW
1E-7
V
A
1 E-8
lmV WV
1E-9
C
L1Os1
t-
VG=60V
* absIE
T IG
1E-11
LJ
1 E-1 1
1E-12
A
V
IE-13
-20O 6
40 '60
20O
IF
'IA
y
v
.a
80i 100 1201140
Focus Voltage VF (V)
Figure 5-16. Total emission current, gate current, focus current, and anode current vs.
focus voltage for device LiOsi (Tip below the gate).
1 E-5i
1 E-6 1
0016'
1 E-71
il
l-~
1 E-81
C
cc
V
1 E-9'
fT
1E-10
V
V
1E-11
V
1E-12,
1E-13-
0
IL8s4
VG=40V
N absitip
V
V
V
A
10
20 30 40
IG
IF
VIA
IA
I
50
60
Focus Voltage VF(
Figure 5-17. Total emission current, gate current, focus current, and anode current vs.
focus voltage for device L8s4 (Tip in-plane with the gate).
103
To investigate further how gate current, focus current and anode current contribute to the
total emission current, we plotted all the currents together for LIsi and L8s4 in Figure
5-16 and Figure 5-17, respectively. In Figure 5-16, we observe that gate current is almost
equal to the total emission current and the focus current varies with focus voltage. Both
gate current and focus current are much higher than the anode current.
This agrees
geometrically with the device structure of L10sl: tips are 0.9ptm below the gate. The
electrons are emitted along the tip radius at angles not in the axial direction, and will be
attracted to positively biased extraction gate once they are emitted. These two reasons
results in high gate current. As the focus voltage increases, more electrons are attracted
to the focus gate and causes the increase in focus current and hence the focus current
increases while the gate current decreases. The anode current increases also with the
increase in focus current. Compared to L8s4 in which the tip is almost in plane with gate,
once electrons are emitted from the tip, they are attracted to focus gate and results in
higher focus current. Also, anode current contributes larger portion in total emission
current in this case than when tip is below the gate. When the tips are below the gate,
most of the emitted electron are absorbed by both gates.
5.3.3 Electron Trajectory Simulation
To qualitatively see how relative position of tip and the extraction affect the electron
trajectory, we built models of L10sl and L8s4 geometries in Charged Particle Optics 3D
software (CPO-3DS) (courtesy of Kerry Cheung). These two models are identical except
tip is placed 0.9[tm below the extraction gate in Figure 5-18 (a) to represent device LIsl,
and in-plane with extraction gate in Figure 5-18 (b) to represent device L8s4. In the
model, tip, extraction gate, and focus gate are biased at OV, 60V, and 30V, respectively.
In Figure 5-18, we see that more electrons are absorbed by the extraction gate than the
focus when the tip is 0.9ptm below the extraction gate and all the emitted electrons bypass
the extraction gate and some are absorbed by focus while the tip is in-plane with the gate.
These simulations are consistent with our four-terminal IV data. When the tip is 0.9 m
104
below the extraction gate, the gate current is much larger than the focus current and when
the tip is in-plane with the gate, the focus current is larger than the gate current.
There is a discrepancy in the gate current between the simulation and the data when the
tip is in-plane with the gate. The simulation shows that when tip is in-plane with the gate,
there is no gate current but the gate current is observed in Figure 5-17. There are two
possible reasons. One reason is the gate current comes from the leakage current from the
focus gate through oxide layer when the focus voltage is small. If we look specifically at
the data, when VF=0V and VG=40V, the gate current is 1.9x10- 7 A and the focus current
is -1.98x10- 7 A. This shows that the gate current consists in part leakage current from
focus gate. The other reason is the simulation is an ideal model, which can only provide
us a rough idea of how the device behaves. When the gate voltage is higher, we can see
that the anode and the focus currents are almost the same. Both contribute to the total
emission current and are 2 orders magnitude larger than the gate current. This suggests
that the experimental data are not inconsistent with the simulation result.
/
/
~1
Focus
A
B
ip
ip
Figure 5-18. These two structures are identical with 1.7pm in extraction gate diameter and
4pm in focus gate diameter and the focus is 1pm above the gate, except (a) tip is 0.9pm
below the gate (L10s1) (b) Tip is in-plane with gate (L8s4). VTj,=OV, VG=60V, and VF=30V.
105
5.4 Chapter Summary
This chapter presented the IV characteristics of double-gated VACNF FEAs.
The extraction and focus gates were connected together in order to perform threeterminal characterization. The field emission characteristics for several arrays have been
reproducibly demonstrated. One of these devices achieved a turn-on voltage of 24V.
This data is representative of the FN parameters of the devices. An S-K chart was used to
assist in the comparison between the double-gated isolated VACNF FEAs and the
double-gated silicon FEAs with respect to the uniformity and relative magnitude of the
tip sharpness and the workfunction.
In this chapter, four-terminal field emission IV characteristics of double-gated VACNF
FEAs are reported and discussed for the first time in the literature. In four-terminal
characterization,
(5.1).
F and PG
The ratio of $F
/
are obtained by fitting the total emission current into equation
OG indicates the relative position of the tip with respect to the
extraction and focus gates.
Models of LiOsi and L8s4 geometries were built using
Charged Particle Optics 3D software to verify that the analysis done so far on distribution
of the anode current, gate current, focus current with respect to the different tip positions
relative to the extraction and focus gates is correct.
106
6 Electron Impact Ionization (ElI) Characterization
The goal for this project is to fabricate a device that can be used to ionize gas molecules
by both electron impact ionization (EII) and field ionization (FI) methods for the mass
spectrometry.
The previous chapter demonstrates that our double-gated isolated
vertically aligned carbon nanofiber
(VACNF)
devices can field-emit electrons
successfully with low turn on voltage. Depending on the relative positions of the tip and
the extract gate, anode currents react differently to focus bias. In this chapter, the emitted
electrons will be used for electron impact ionization of gas molecules. The device is first
used as a three-terminal electron source to perform electron impact ionization to ensure
that it follows the EI phenomena. Then the device is used as a four-terminal electron
source for electron impact ionization to demonstrate that the focus can protect the
emitters from ion erosion.
107
6.1
Prior Work - Other Application: Ion Gauge
We have discussed the advantages of using field emitted electrons to ionize the gas
molecules over the thermionic electron source for electron impact ionization in MS
applications in Chapter 1. An ion gauge is a device, which applies thermionic electron
source on ElI to measure the vacuum pressure. It has been used extensively in ultra high
vacuum (UHV) systems.
Similar to MS, the traditional ion gauge inherits the
disadvantages of thermionic emission: bulk, high power consumption, heat, light
generation and outgassing. These issues can be resolved by switching the electron source
to field emission.
Choi and co-workers reported an ion gauge using field emitted electrons from CNTs to
measure low pressure [6.1].
They used the screen printing method to make a triode
configuration CNT FEA (three-terminal FEA) with 2 cm x 2 cm area, as shown in Figure
6-1 [6.2]. Their ElI result shows that the chamber pressure and the ratio of the ionization
current and the CNT cathode current is not a linear relationship. Also, due to the largescale three-terminal structure, this device has large turn on voltage (180V) and the narrow
measurement range (1x10 4 to 1 Torr).
CNTs also suffer seriously from ion
bombardment. Choi et al. later improved their design by constructing the anode and the
grid similar in form to the Bayard-Alpert gauge, as shown in Figure 6-2 [6.3].
This
structure prevented ion bombardment of the CNTs but still did not improve the
measurement range. In summary, Choi et al. demonstrated that there is a correlation
among pressure, ion current, and electron current. They also showed that, without any
protection, tips are severely damaged by ion bombardment.
Baptist et al. replaced the tungsten filament in a classical Bayard-Aplert gauge with an
array of micro-fabricated molybdenum (Mo) tips, as shown in Figure 6-3 [6.4]. This Mo
microtip provided a more directional and instant field emission electron source than the
traditional thermionic emission electron source from the tungsten filament. Due to these
advantages, Baptist's setup not only increased the sensitivity of the ion gauge but also
could be operated in the fast-pulsed mode to protect the cathode at higher pressures.
108
Their result also demonstrated the linear relationship between the ion current and the
pressure from 1x10- 0 mbar to 1x10 3 mbar (7.5x10
Torr to 7.5x10~4 Torr). However, as
they mentioned in the report, there are two disadvantages of using Mo tips. One is that
the Mo tip is not suitable to operate in the temperature higher than 150*C and the other
that is Mo tip can be easily damaged in the higher pressure.
Dong et al. used the CNTs as the field emission tips to construct an ionization gauge as
shown in Figure 6-4 [6.5]. They reported that CNT field emitters offered a more stable
electron emission source than the metal field emitters. Their setup also obtained a linear
relationship between the ion current and the pressure. Inspired by Baptist and Dong,
Huang et al. constructed a Bayard-Alpert ionization gauge with CNT emitters. The CNT
field emitters were prepared on a stainless-steel rod and the gate was placed 0.65mm
away from the CNT emitters, as shown in Figure 6-5 [6.6].
The gate structure has
numerous 200pm round apertures with 50pm separation. Huang et al. also obtained the
linear relationship between the ion current and pressure and the sensitivity of their setup
was comparable to Dong's result but not as good as Baptist's result. To increase the
sensitivity, the number of electrons passing through the gate and transmitted to the impact
ionization zone needs to be increased.
Thus, Dong suggested that to increase the
sensitivity of the ion gauge, the structure of the gate needs to be changed.
Further,
reducing the distance between tips and the gate can lower the operation voltage.
In this chapter, a double-gated isolated vertically aligned CNT (VACNT) field emitter
array is used as the cathode to provide the field emission electron source for the electron
impact ionization. We will present a series of data to show the linear relationship among
pressure, ion current, and electron current and integrate a focus gate with our device to
protect the CNF emitters from erosion by ion bombardment.
109
Collector
.
Gas molecule-.
,
C-p
_-:
Ionized molecule
Ionization
V
GGdCr- :cOr
CNT
GlAss
is
Triode
Figure 6-1. Schematic drawing of CNT-based ion gauge. i is the electron current, ig is the
grid current, and i is the ion current [6.2].
Second Gid
.-
*=
Coaector
V 2 >O V
=
=
e
.
h
14
-
S4H
Ve<0 V
SCornd
-P=::=
.
!Limz
Cr Gri
F.G. Signal
f- 100 Hz
LI
urn
fl-FLfLptf-O V
Figure 6-2. Schematic drawing of CNT-based ion gauge in the form of Bayard-Alpert gauge
[6.3].
Ion collector
Microtips
cathode
+-
F-4~
~
I
ZO
-------7
I
Figure 6-3. Schematic drawing of the Mo microtip Bayard-Alpert gauge by Baptist et al.
[6.4].
110
4
m
2 5MM
CNT source
13 m
gauge anode
fII: : hole
focus plate
reflector
I
Ion colle(ctor
Figure 6-4. Schematic drawing of Dong's ionization vacuum gauge setup [6.5].
(b) (b)
Ion collector
Gate
Cathode,~
Grid
Figure 6-5. Schematic drawing of Huang's BA gauge setup with line-type CNT cathode
[6.6].
111
6.2 Electron Impact Ionization with Three-terminal Field Emission
Electron Source
6.2.1 Measurement Setup
The measurement setup for three-terminal EII, as shown in Figure 6-6, is similar to threeterminal field emission measurement. The extraction gate and the focus are tied together
to the same Keithley 237 while the emitter is biased at OV. A screen anode is placed
right above the device and is biased at a higher voltage than the gate voltage to accelerate
electrons before impact with gas molecules. The electron pass-through rate is 90%. The
ion collector is set at -1 100V to collect the ions generated by EII and repel electrons.
Vacuum
PC
Ion collector
GPIB
Screen
Kefthley 237
Focus
G
Keithley 237"'"
Keithley 237""
Ground the substrate
'I
""""""
Keithley 237
Figure 6-6. The diagram of the three-terminal ElI measurement setup.
112
6.2.2 Electron Current Dependence
In the ElI process, an electron source needs to be generated first and accelerated up to an
energy higher than the gas molecules' ionization energies. Ionization takes place when
these energetic electrons collide with gas molecules. As described earlier, the process
can be written as below,
I 1 (E)
=pxLxaTota (E)
(6.1)
IE(E)
where I1(E) is the ion current, IE(E) is the electron current, p is the molecule density in the
chamber, L is the collision pathlength, and T(E) is the total ionization cross section.
From this equation, we can see that the ion current depends on the number of electrons
and the density of the gas molecules in the chamber at fixed L and Y(E). In this section,
we are going to demonstrate this linear relationship by varying the electron current and
the chamber pressure. The gas is Argon. Two devices are tested: LlOs3 and L8s3.
Argon (Ar) is passed into the chamber by a needle valve, which can precisely control the
chamber pressure by the amount of Ar flowing into the chamber. The ion current (I1) and
the electron current (Is) are monitored and recorded while varying the extraction gate
voltage (VF=VG).
This experiment was run at different pressures: 5x10
7
Torr, 5x10- 6
Torr, 5x10-5 Torr, and 5x10 4 Torr. The IV data of ElI at different pressure are plotted in
Figure 6-7 (a), (b), (c), and (d), respectively for device LlOs3. We repeated the same
experiment with device L8s3 to show the repeatability of the Eli, and the data are plotted
in Figure 6-8 (a), (b), (c), and (d).
Electron currents and the molecular density, calculated using equation (2.11) at specific
pressures, are plugged into equation (6.1) to obtain the predicted ion currents (Ip). L is
0.5cm, which is the distance between the ion collector and the screen anode. According
to Figure 2-3, Y(E) for Are ranges from 2x10-16cm
113
2
to 3x10-16cm 2 with the colliding
electron energy varying from 40ev to 300eV [6.7]. The screen anode typically is biased
at 300V in our setup. Thus, 2x10-16cm 2 is chosen to be the value for a(E).
Using these parameters, these predicted ion currents are plotted with measured ion
currents in both Figure 6-7 and Figure 6-8. At 5x10-7 Torr, shown in Figure 6-7 (a) and
Figure 6-8 (a), the ion current is not observed because the ion current did not exceed the
noise floor of our measurement system, which is about
10-12
A. As the pressure reaches
5x10-6 Torr, for device LlOs3, the predicted ion current leveled with the noise floor of
our measurement system as shown in Figure 6-7 (b). Since device L8s3 generated a
higher electron current, the ion current is clearly observed and is in agreement with
predicted ion current as shown in Figure 6-8 (b). As the pressure increases further, we
can see that the ion currents increase with electron currents in Figure 6-7 (c) and (d), and
Figure 6-8 (c) and (d),
114
C
.2
2
L10s3
. 5E71s
1E-81 * 5E7i
g
-1 A 5E71p
1E-10' P=5E-7 Torr
1E-10
L
C
S*
AA A
AAA
AA A
AA
0
-c
AA
AAA
A
A
A
A
A A
LAA
A
A
9
A
AA
* I
1E-14,
A
)
1E-16,
i
0
20 40 60 80100 10140 160 180
V(G
V( ) (
L10s3
$
0
0.
C
a)
0
a)
C a)
* 5E51s
* 5E5Ii
* 5E5Ip
E
a)
a)
"
-....
..
. ." 1
1E-10j P=5E-5 Torr
.
I.:
1E-12
AAA
1 E-8-
C
a)
A
AAt
1E-10
0
C CL
0
a2
c 1E-12.
A A
AA*AA*
1E-141
C
a)
AAA
A
A
A
1E-14
A
0
C
0
1E-16
0
B
AAAAA
AA
20 40 60 80 100 12o140 160 180
1E-81
-
*A*A
E
AAA
-1
S1E-16i
*
1E-12 1
al.iE
1E-14 1
E
0.
"."h
*
.
1E-12 1
0
£
CL
U..".
OEMa
LlOs3
* 5E61s
* 5E6i
A
5E6Ip
P=5E-6 Torr
1E-8,
20 40 60
0
a)
80100120 140 160180
E
L10s3
* 5E41s
A 5E41p
5E4Ip
A
..:
* P=5E-4 Torr
* *
0 0 w
.*
AA
SAAAA
*
A A&A
E
A
a
A*
AAA,
OAA
AAA A
AAA
1 E-16.
0 20 40 60 80 100120140160 180
V(
V(G+F) (V)
(V)
(V)
Figure 6-7. Double-gated CNF FE and FI array (L10s3) electron impact ionization data. (a)
Pressure at 5x10 7 Torr, (b) Pressure at 5x10- Torr, (c) Pressure at 5x10-5 Torr, and (d)
Pressure at 5x10 4 Torr.
115
L8s3
N- SE61S
* 5E611
1 E-6
1E-6 L8s3
0 5E7S
5E7Ai
1E-8
A
5E7P
E
P=5E-7 Torr
1E-1O
..
0
WE-1
L1E-14
-00_AA
1E-12
15AA
1
cis4
1E-14
2
AU
1E-161E12
E
A
A-4
AA
d
50
1E-6
100
150
200
250 300
1E-8
A
L8s3
5E41S
*-
.AA.
04
00
*
= 1E-12
1E-12
L.
AA
A
00
At
-A
50
P=1 E-4 Torr
I E-10
AA
1E-14
A
A&
A445
iA
AA
o1E-8
5EI
E 4P
5E51P
A tk
150 20025030
100
50
1 EE-8 -
1E-10
S1E-14
A
0
1E-6
P=5E-5 Torr
0
A
_
L8s3
a 5E51S
E 9 SESIIH.
AhB
A
004
0
c
N2
1EcA
C~
5E61P
A
P=5E-6 Torr
1E-10 -
100
150
200
250
300
S
AI
A
A
A
IA
g
A
D
A
E-16
0
50
10160200
20
300
Figure 6-8. Double-gated CNF FE and FI array (L8s3) electron impact ionization data. (a)
Pressure at 5x10 7 Torr, (b) Pressure at 5x1O Torr, (c) Pressure at 5x10-5 Torr, and (d)
Pressure at 5x10 4 Torr.
6.2.3 Pressure Dependence
From Figure 6-7 and Figure 6-8, we observe that as pressure increases, ion current
increases. Further, to verify the linear relationship between pressure and the ion current,
ion currents and electrons were measured at different pressures from 5x10-6 to 1x10-3
Torr for both devices LlOs3 and L8s3. As shown in Figure 6-9 and Figure 6-10, the
linear relationship holds between pressure and the ratio of ion current and electron
current. Both R values of these two devices are very close to +1.
This indicates that the
pressure and the ratio of the ion current and electron current are highly correlated. The
standard deviation (SD) shows that all the data gathered tightly.
116
0.01-
0
1E-3
U) I-
*
L10s3
Linear Fit of LlOs3_LlOs3
y=0. 963x+0.75
SD 0.275
R=0 .955
U
.
I-i
0
I-=.
1 E-4
00
U
1 E-5
1E-4
1E-3
Pressure [Iog(Torr)]
Figure 6-9. LlOs3 device: linear relationship between normalized ion current (Ii/Is) and the
pressure. (11I1s) vs. Pressure
0.01
0
W
1 E-3
U
L8s3
Linear Fit of L8s3 L8s3
y=0.908x+0.79
SD=0.149
R=0.991
C
0
00
1E-4
1E-5
1E-4
1 E-3
Pressure [Iog(Torr)]
Figure 6-10. L8s3 device: linear relationship between normalized ion current (Ii/Is) and the
pressure. (Ii/Is) vs. Pressure
117
6.2.4 Change in S-K Chart After Three-terminal ElI
The focus gate and the extraction gate were tied together to perform three-terminal ElI
measurement, which means that the focus gate was not utilized for its protection function.
To quantify the degradation of the CNF emitters, three-terminal field emission
measurements were performed after three-terminal ElI to extract the FN coefficients, aN
and bF.
The new FN coefficients were then plotted with the old FN coefficients, which
were presented in Chapter 5. Figure 6-11 (a) and (b) show the FN coefficients before and
after the ElI experiments were performed for device LlOs3 and L8s3.
-1000
-1 200 -
1 0 0
EZ
1200-
z-14W0
LL
A
0
-1800-
*
0
B
B
0
.~
w -18000
*
Ll0s3before
LlOs3after
-22
-20
s
-14W0-
[160
-100
o
&-1600.
.
.
e%.
0
sbore
D
-18
-16
-14
0
L8s3after
-2000 1
t
-22
Intercept of FN plot ( aFN )
-21
rft I
-20
-19
-18
Intercept of FN plot ( aFN)
-17
Figure 6-11. FN coefficients of before and after EU for devices (a) LOs3, and (b) L8s3.
In the S-K chart, the data points located in upper left corner represent smaller tip radii
than the data points located in lower right corner and the data points located in upper
right corner represent lower workfunction than the data points located in lower left corner.
In Figure 6-11 (a), we can clearly see that, after EII, the data points move diagonally
from the lower right corner to upper left corner. This means that the tip profile changes
after ElI and the direction that data points move implies that the effective emitting area
and tip radii are reduced. For L1Os3, the electron currents after ElI are reduced from
lOnA to 1nA when the gate voltage is at 150V. The possible explanation is some of the
tips are destroyed during EII. Hence, the effective emitting area is reduced. However,
more evidence and analysis need to be obtained and done to support this argument.
118
Figure 6-11 (b) shows that the tip radii after ElI are not as stable as before ElI. This
might be due to the residue gas in the chamber, which causes the adsorption or desorption
of the gas molecules.
119
6.3 Electron Impact Ionization with Four-terminal Field Emission Electron
Source
6.3.1 Measurement Setup
The measurement setup for four-terminal ElI is similar to the setup for three-terminal ElI,
as shown in Figure 6-12. The only change is the extraction gate and the focus gate are
biased differently to test the effectiveness of the focus gate absorbing ions. The ion
collector is biased at -1 100V and the screen anode is biased at 200V.
PC
Vacuum
Ion collector
GPIB
Screen
Keithley 237
Focus
I
G
Keithley 237
Keithley 237
Ground the substrate
Keithley 237
Keithley 237
Figure 6-12. The diagram of the four-terminal ElI measurement setup.
120
6.3.2 Protection of the CNF Tips from Ion Erosion by the Focus
The previous section demonstrated that our devices are capable of using field emitted
electrons for electron impact ionization in the three-terminal setup. In this section, we are
going to examine if the focus gate serves as an ion absorber to protect the tips from ion
bombardment. In four-terminal EI measurements, the focus gate is kept at a constant
bias, while the extraction gate is swept through the operating range at different pressures.
Figure 6-13 and Figure 6-14 show the focus current of two different devices. In the first
device, the tip is below the extraction gate (LiOsi) and, in the second device, the tip is
close to the extraction gate (L8s4).
We began with all our ElI experiments at 3x10~8 Torr before Argon was introduced to the
chamber. This data gives us the baseline information so that we can use this data to
compare the data we obtained at 1x10-5 Torr and 5xlO Torr later. Figure 6-13 (a) and (b)
show us how focus current varies when the tip is below the extraction gate for device
LiOsi. Focus voltage was fixed at 60V and 30V, as shown in Figure 6-13 (a) and (b),
respectively, while extraction voltage swept from OV to 136V and then from 136V to OV
twice to show the repeatability.
When the focus voltage was biased at a fixed voltage, either at 60V or 30V, higher
chamber pressure resulted in lower focus current. As pressure went up, the ionization
rate increased due to the increase in the gas molecules' density in the chamber. This
means that more ions are created and absorbed by the focus gate. Due to the cancellation
between negative charges (electrons) and positive charges (ions), the focus current is
lower than the baseline focus current. Hence, higher pressure results in lower focus
current. This also suggests that the focus biased at a lower voltage than the extraction
gate can attract ions. In addition, in both Figure 6-13 and Figure 6-14, at a fixed pressure,
focus currents are reduced more when the focus voltage is biased at 30V than when
biased at 60V. This indicates that the focus gate biased at a lower voltage is more
effective at attracting ions.
121
1E-6
1E-7
1E-6i
*
6
a
,
*4
M
U
C
1E-7
LlOsl: VF=60V "
* 5E-4 Torr
U.
*
1E
*
O
0
1E-5 Torr
W
M
U.
0
A
3E-8 Torr
20 40 60
80
, . , .
I0
. ,
*
"..
1E-O
1E-11 Lis1: VF
. 5E-4 Torr
1E-12 o 1E-5 Torr
1E-13
A
0
160 120 140
B
3E-8Torr
20 40 60
VG (V)
80
100 120 140
VG M
Figure 6-13. Focus current vs. Gate voltage for device LiOsi at 3x10 4 , 1x10 5 and 5x10 4
Torr. (a) VF=60V and (b) VF=30V.
1E-6AAA*AA
e 5E-5 Torr
inX!111:1 '.
4 1.6uuuu
:;0
1E-7-
LUs4 VF;-40V
. 1E-4 Torr
1 E-6-
A
**
1 E-70
L.
S
U
L8s4: VF=50V
*
*
1E-8-
A
0
A
fd 20
40
30
3E-8 Toff
a
50
60
0
E"".
PO
I
0
U-
1E-4 Torr
5E-5 Torr
3E-8 Tor
A AE
*.
soh~~hh~h.::
s, oOmMeMa mM
M
1 E-8-
70
0
R
1'0 2
Va (V)
io 4b 50 6'70
V (V)
Figure 6-14. Focus current vs. Gate voltage for device L8s4 at 3x10 4 , 1x10 5 and 5x10 4 Torr.
(a) VF=60V and (b) VF=30V.
Device L8s4 provides us another opportunity to study how focus gate behaves when tip is
close to the extraction gate compare to tip is much below the gate (LiOsi). In both
Figure 6-13 (a) and (b), we can see that as pressure goes up, focus currents decreases.
Also, compared to Figure 6-14 (a) with VF=50V, the magnitude of decrease in focus
current is larger in Figure 6-14 (b) with VF=40V. This shows that focus voltage bias at a
lower voltage than gate voltage can attract ions and the lower focus voltage is, the more
ions are attracted to. This effect happens in both L10sI and L8s4
122
6.3.3 Change in SK Chart After Four-terminal ElI
After using the focus gate to protect the tips during the electron impact ionization, a
series of three-terminal field emission experiments was performed to extract the FN
coefficients.
The FN coefficients of before and after electron impact ionization are
plotted in Figure 6-15. The data points of FN coefficients still moved from lower right
corner to upper left corner. The change in direction is consistent with three-terminal
electron impact ionization results. This shows that the tips were still bombarded by the
ions.
-300ZL
-3500
0.
zLLU
%--4000U
0.
0
as-450-20
M
L8s4before
*
L8s4after
-19 -18 -17
M
-16
-15
-14
Intercept of FN plot ( aN )
Figure 6-15. FN coefficients of before and after EII for devices L8s4 (Tip below the gate).
To compare with the three-terminal results, the average FN coefficients values of before
and after EII for LlOs3, L8s3 and L8s4 are calculated and summarizes in Table 6-1. The
changes for L8s3 are the smallest among three devices. If we compare LlOs3 and L8s4,
the change in aN is smaller for LlOs3 and the change in bF is smaller for L8s4.
However, the change percentages are similar for both devices. With the limited data we
have, we cannot conclude that the tips are protected by the focus. To determine the
effectiveness of the focus gate by using SK chart, a more thorough and systematic
measurement need to be performed.
123
aFN
Before
3-term. ElI
4-term ElI
after
bFN
%change
Before
After
% change
L10s3
-17.11
-20.89
21.9%
-1433.42
-1144.8
25.2%
L8s3
-19.48
-19.20
3.7%
-1450.67
-1533.21
5.7%
L8s4
-14.43
-18.87
30.7%
-417.49
-317.67
23.9%
Table 6-1. The summary of the changes in FN coefficients before and after electron impact
ionization for LOs3, L8s3 and L8s4.
124
6.4 Comparison to Impact Ionization in Semiconductor
The mechanism of impact ionization in the semiconductor is similar to electron impact
ionization for gas. The electron or hole (carrier) is first accelerated in the large electric
field (E) so it acquires energy. When an electron with sufficient energy collides with the
lattice, an electron-hole pair is generated. Both the electron and the hole contribute to the
total generation rate so the rate is described as [6.8]:
G11= a IFh(drift|+ah|Fh(driftj
(6.2)
where ae is the impact ionization rate for electrons and
ah
is the impact ionization rate
for holes. They describe the average number of ionizations per unit length per carrier.
The Fe(drift) is the electron drift flux and Fh(drift) is the hole drift flux. They describe
the flux of the carrier that drifts in an electric field.
Let's look at only the electron carrier. ae depends strongly on the electric field (E) as
shown in equation (6.3) [6.8],
q, = Aexp -
ii
(6.3)
where Eli is the impact ionization threshold energy for a specific semiconductor material;
L is the mean free path, which is temperature-dependent; and A is the coefficient, which
slightly depends on Eu and E.
Let a, be the gain and a, = ae xr x v, where T is the carrier lifetime and v is the carrier
velocity.
We can rewrite equation (6.2) as the excess carrier flux, Fe(n), with the
contribution of the electron carriers,
F(drift |
IFe(nj|=Giixrxv=axzxvx|Fdrift=
(6.4)
Equation (6.4) shows that the excess carrier flux generated by electron impact ionization
is exponentially related to the electron drift flux through the gain, ae
125
Let Q be the collision rate for the electron impact ionization for gas and Q = p x a x L . p
is the number density of neutral molecules in the gas, o is the total ionization cross
section, and L is the collision pathlength. We can rewrite the ion current, equation (6.1),
as below,
Ii=pxaxLxIE =QXIE
(6.5)
The electron current (IE), which is used to collide electrons with the gas molecules, is
analogous to the flux of the carrier in the semiconductor. The more electrons or carriers
that participate in the impact ionization process, the more ions or electron-hole pairs that
are created. As shown in equation (6.4), the ion current (Ii) is related to the electron
current through the collision rate, Q, which depends strongly on the chamber pressure.
While the fundamental processes in ElI and semiconductor impact ionization are similar,
i.e. acceleration of a charged particle in an electric field and subsequent collision of the
energetic particle with neutral molecules (in a gas) or lattice atoms (in a semiconductor)
leading to ionization, there are still significant differences which manifest themselves in
the measurement of the ion current.
In ElI, the mean free path of the electron molecule collision is quite large and it is of the
order of the average distance between molecules, which is pressure dependent. Typically,
this distance is larger than the distance between the screen anode and the ion collector, i.e.
the dimensions of the ionization region. This implies that only one collision could occur
on the average during the electron trajectory through the ionization region. The collision
rate increases with pressure. Typically, the distance between the screen anode and the
collector plate is 5cm and, at lmTorr, the mean free path of most gasses is around 5cm.
If the pressure increases to 100mTorr, the distance between molecules decreases to
0.5mm implying that there would be multiple collisions for electrons with the gas
molecules in their trajectory through the collisions. This results in multiplication of the
collisions and a plasma which we have observed at high pressures.
In semiconductors on the other hand, the mean free path is quite low and it is of the order
of the electron/phonon collision path length. Typical number is of the order of 10nm
126
(5nm). Thus, in a typical device with dimensions of 10nm in the field region, there are
opportunities for multiple collisions, which result in avalanche multiplication (and gain).
6.5 Chapter Summary
In this chapter, we demonstrated the use of micro fabricated double-gated FEAs for
electron impact ionization. First, we used double-gated FEA as the three-terminal FE
device to show that the ion current varies with the electron current. Second, we obtained
a linear relationship between the pressure and the ratio of the ion current and the electron
current. Third, in the measurement range we tested, the device can be utilized as a
pressure sensor from 5x10~6 up to 1x 10-3 Torr. Lastly, four-terminal ElI measurement
shows that the focus gate can absorb ions when the focus voltage biased at a lower
voltage than the extraction gate. This is the first Ell device using the field emission
method that is integrated with a protecting gate. All the measurements reported here are
repeatable and work both when the tip is below the gate and when the tip is close to the
gate. Compared to Choi's devices, our device has a lower turn on voltage, covers a wider
ionization range and shows that the focus gate serves as a protecting gate.
In addition,
the electron impact ionization for gas and the impact ionization in semiconductor were
compared and the similarity between the fundamental processes is observed.
127
128
7 Field Ionization (FI) Characterization
7.1
Measurement setup
To operate the device in the field ionization mode, three Keithley 237 instruments are
used. One Keithley 237 is biased at -1 100V to collect ions (Ion Collector). The other is
connected to the CNFs (emitters). To maximize the electric field at the tip, we tied the
extraction gate and the focus gate together and connected them to the third Kiethley 237
(Extractor). The gas used is argon (Ar) and the chamber pressure is carefully controlled
by a needle valve. The schematic drawing of the FI measurement setup is shown in
Figure 7-1.
PC
Vacuum Chamber
Ion collector
G PIB
F2pobe
Gate prob a
Ground the substrate
IH
-h
Keflthley 237
Kethley 237
Figure 7-1. The diagram of the FT measurement setup.
129
7.2 Field Ionization Characterization
Traditionally, the emitters (anodes) used in the FI microscopy are carbon dendrites or
whiskers on a fine tungsten wire. The cathode or electrode is placed around 2mm away
from the emitters. Thus, a high voltage of 10-20 kV is applied to generate a large enough
electric field to ionize the gas molecules around the tips [7.1,7.2].
Recent works have
tried to lower the field ionization voltage. Edinger et al. used a tungsten single crystal
wire that was cooled to 20K to field ionize the gas molecules. They reported the currents
up to lOOnA with the biased voltage at about 10kV [7.3]. Salancon et al. prepared the tip
by etching a 100pm diameter polycrystalline W wire and obtained the current in the
lOnA range with few kV [7.4]. Riley et al. field ionized helium using carbon nanotubes
with 7.5kV [7.5].
In this project, we will use double-gated vertically aligned CNF arrays to field ionize the
gas. Instead of having the electrode placed 2mm away from the CNTs, the gate is
0.85gm from the CNTs and is able to generate a sufficient electric field to field ionize the
gas molecules at the tip with a lower voltage.
Field Emission
Before using double-gated isolated VACNF arrays as an FI device, the array was tested
as a three-terminal FE array, as shown in Figure 7-2. The gate voltage is swept from OV
to 1 1OV and from 1 OV to OV three times to ensure that the array functioned properly
and had potential to function as an FL device since a higher electric field is required for Fl.
This also allowed the extraction of the effective field factor, Peff.
130
..........................................
.....................................
..
Field Emission L6
- IA
1E-6.
1 E-7
1E-8
1E-9
""
1E-10"
ULM
1E-11
1E-12
I
0
20
40
60
80
100
120
Ve (V)
Figure 7-2. Three-terminal field emission characterization of the D-G vertically aligned
CNF arrays. VA=1100V and Vmw=OV.
-20-
LnIVG2
Linear Fit of L6FEFNpIot_LnIVG2
-22-24
-26
-28-
"
.0
,"M
-30 aN=-17.43+/-0.17
I
-32- bFN=- 5 02 .5 9+/-10.13
.
-34 SD=0.938
R=-0.955
-36
I
0.01
I
"
b
0.02
.
b3
0.03
1NG (1/V)
Figure 7-3. FN plot of L6 device. aFN and bFN are extracted from the intercept and the slope
of the graph.
Figure 7-3 shows the FN plots of the field emission data in Figure 7-2. After linearly
fitting the data, we obtain aN = -17.43 and bF=-502.59. These FN coefficients
correspond to the effective field factor of 1.45x 106 V/cm and the effective emitting area
of 5.46x 10-4 cm2. Using the model of the tip in-plane with the extraction gate,
=
7 O8x
[V/cm], the estimated tip radius is 4nm.
131
Field Ionization Repeatability
To perform the field ionization characterization, both gates were biased at OV, and the ion
collector was biased at -1100V and placed 5mm above the device while the emitters were
swept from OV to +700V then down to OV for 3 cycles to ensure repeatability.
The
chamber pressure constantly remained at 7.5x10 4 Torr during the measurement. This F
measurement setup was a reversed setup of the field emission setup. Instead of using an
electric field to emit electrons out of the tip, a strong electric field was generated to
extract electrons from the gas molecules close to the tip. Figure 7-4 shows the schematic
drawing of the flows of electrons and ions once the gas molecules were ionized. These
flows gave us a negative ion current and a positive tip current. The absolute value of the
ion current from F is plotted versus time in Figure 7-5 (a) and versus tip voltages in
Figure 7-5 (b). Both figures show good repeatability of the ion current from the device.
Figure 7-5 (b) shows that the ion current increases as the tip voltage increases. It also
shows that a high electric field is generated around the tip, the ionization zone around the
tip increases and the chance of the gas molecules at the tip vicinity getting ionized is
greater.
Ion collector= -1 100V
Neutral
Molecule
t
0
-
Ion
Electron
Focus=OV
Gate=OV
Tip= +700V
Figure 7-4. The schematic drawing of the electron flow and the ion flow when the gas
molecules are ionization.
132
250.0p-
Field Ionization L6 A
200.0p- I
abs(li)
200
OpField
B
1E-10-hFedlniainL
Ionization L6
abs(li)
150.0p
....
r-100.0pS50.Op.
0
.
--
c 1E-11;
.
00
-
.
1E-12-,
j
0.0
0
0
20 400 600 800 100012001400
Time
100 200300 400 500 600 700 800
VTIP (
Figure 7-5. Field ionization IV data of argon at 7.5x10-4 Torr. (a) abs(IIoN) vs. Time (b)
abs(IIoN) VS. VD,. VION= -1100V and VG+F =0V.
Field Ionization Pressure Dependence
After showing the repeatability and the tip voltage dependence of the F, we want to see
how the ion current changes at different pressures. Another device was characterized as a
three-terminal FE first to obtain the
In field emission characterization, the gate
eff.
voltage was swept from OV to 200V then back to OV for 6 times and the field emission IV characteristic of the device is shown in Figure 7-6. Next, the FN coefficients are
extracted with aN = 3.82 and bF=-1879.62, as indicated in Figure 7-7. This bFN
of 3.85x10 5 V/cm. A turn-on electric field
corresponds to the effective field factor (,e-ff)
(F 0a) of 1xO08 V/cm is required to field ionize a gas molecule and F is related to the
applied gate voltage VG through F =
#e
can be extracted from this equation V,, =
x VG . Then the field ionization turn-on voltage
F
Of
This suggests that the gate voltage must be
biased at 260V or higher to field ionize the gas molecules. Using the model of the tip is
900nm below the extraction gate,
Ie
= 47.5x10' [V/cm], the estimated tip radius is 19nm.
Af
.4
133
1E-7 Field Emissio n L10s18
M
IA
1E-8
1E-9
o r ""
b~
-0w
U
U
1E-11-
I II UU I
I
1E-12: I I U
U
ME
IIIIi'
El'
U
1E-13 .
0
100
50
150
200
VG (V)
Figure 7-6. Three-terminal field emission characterization of the D-G vertically aligned
CNF arrays: LOs8. VA=1100V and VTIp=OV.
C
-4-
Linear Fit of Datal_C
-6-8--C0%l
"i
-10
|
-12
aFN =3 .82+/0.2 0
-14-
bFN=-1 879.62+-29.84
-16
SD=0.870
R=-0.942
-10
0
0.008
0.006
0.010
1NG (1N)
Figure 7-7. FN plot of L1Os18 device. aFN and bFN are extracted from the intercept and the
slope of the graph.
134
Jr
L10s18 Field Ionization
1E-10. * 8.5x10 4 Torr
* 5.6x10e Torr
Z
0
1E-11 'p
r.
* 0
I
.0
1E-12
0
300
200
100
VG+F
%o.
**0. W
600
8.5 x10~4 Torr
5.6 x0-3 Torr
Lin ear fit of 8.5x10-4
3
Linn ear fit of 5.6x10
b 1=-4535.58
00 *
500
(\)
a=
4*5F355
0
1E-10
400
e
' oleo;
.
..-
Z
0...
--lE-11i
0
1 E-121
aF=-3.59
.
."E. .
b FI=-4028.74
0.0018
*
B
U
0.0019
0.0020
1NG+F (1"/)
Figure 7-8. (a) Field ionization at 8.5x10 4 and 5.6x10.3 Torr: abs(IIoN) vs. Tip voltage.
3
VION= -1100V and VG+F =OV. (b) Field ionization data of Device L1Os18 at 5.6x10. and
4
8.5x10- Torr are plotted Ln(Is) vs. l/VG+F. aFI and bFI are extracted from the intercept and
the slope of the graph.
135
Next, the field ionization experiments were performed at two different pressures, 8.5x10 4
and 5.6x10- 3 Torr, and the tip voltage was swept from OV to 570V then back to OV for 2
times at these two pressures. These two sets of F data are plotted in Figure 7-8 (a).
From the figure, we can see that ionization occurs around 400V and as the tip voltage
increases, ion current increases as the field increases for both pressures.
(More field
ionization data, which has turn-on voltage of 350V, are included in Appendix E.) The
turn-on voltages we observed from the experiments agree with our predicted turn-on
voltage, 260V or above. Compared to the field ionization turn-on voltages have been
reported (-10kV), the turn-on voltage using double-gated VACNF arrays is significantly
reduced. In addition, at a fixed tip voltage (Vnp is larger than 500V), ion current is
higher at 5.6x10- 3 Torr than at 8.5x10 4 Torr. At higher pressure, the gas molecules
density in the chamber is higher and the number of gas molecules that approach the
ionization zone increases. This relation results in higher ion current and it agrees with the
data shown in Figure 7-8 (a).
As described in Chapter 2, the ion current in the low field is shown below:
Ii =qxn'/r=qx xvBxD=qx -- xvxf xexp -Bx
kT
kT)
F
xC,,
(7.1)
where q is the electron charge, P is the chamber pressure and T is the chamber
temperature, k is the Boltzman constant, v is the volume of the ionization zone, f is the
frequency of an electron arrives at the barrier in the molecule, and D is the tunneling
probability. Cim is the image effect of the electron and is approximated to be around 0.92
(see Appendix G). We can rewrite the ion current similar to the form of the FN equation
as:
ln(I) =
bF
(7.2)
aFI
VG+F
where
bFI
aFI
=In qx
-
=0.92xBx
XvXf
and
.
eff
136
Ngr (NF surface
Vacuum level
AL
00
- 0
1=15.75eV
A
$=5eV
I
EF
CNF
Tip
CNF
Molecule
(B) Field Ionization
(A) Field Emission
Figure 7-9. (a) Field emission tunneling probabil ity is approximated using the triangular
barrier. (b) Field ionization tunneling probabili ty is approximated using the trapezoid
barrier.
AL
Near CNF surface
-- I*#
I
I
I
1=1 15.75eV
I
U
U-
EF
I
w
I
I
I
CNF
Tip
I
I
I
I
Molecul
e
Figure 7-10. Field ionization barriers. The dash line is the trapezoid model and the solid
line represents the actual barrier. The actual barrier is lower than the model barrier.
137
The field emission tunneling probability is associated with the triangular barrier, as
shown in Figure 7-9 (a). In field emission, bF = 0.95xBx
3 2
/
and bF is related to the
fleff
field emission tunneling probability.
In field ionization, the barrier between the CNF tip
and the molecule is approximated using the trapezoid shape, as shown in Figure 7-9 (b).
The potential of the molecule is assumed to be a square well shape, which covers more
barrier area than the actual barrier area as shown in Figure 7-11. Using trapezoid barrier
to approximate the tunneling probability is not a perfect model but could give us a close
approximation. Since the real barrier is actually lower than the model barrier, this gives
us bFI = 0.92xBx
=
8340.07
.
This value has larger value than the
fleff
experimental bH, which is 4535.58. The ratio of bH and bF is calculated and the value is
4.4, which is the upper bond of the ratio.
To extract aR and bH, In(I) vs.
l/VG+F
is plotted in Figure 7-8 (b). The values of bH are -
4535.58 and -4028.74 for P=5.6x10-3 and 8.5x10-4 Torr, respectively, and the bF that we
extracted from the field emission experiment is -1879.62.
The ratios of bH and bE from
the experimental data are 2.4 at 5.6x10~3 Torr and 2.14 at 8.5x10-4 Torr. These values are
within the upper bound of the ratio, which is 4.4. To improve the field ionization model
and obtain a more accurate ratio of bH and bE, a numerical model, which approximates
the potential of the gas molecule closer to the real case, is needed.
The ratio of two pressures is 6.6 (5.6x10-3/8.5x10~4 =6.6).
From the values of aR
extracted from the experimental data, we can deduce a similar ratio of 6.9. This shows
that aR contains the pressure information.
Using equation (7.2), we can calculate aH.
The tip radius is in the order of 20-30nm and the ionization takes place within the 20nm
above the tip. Assume only half of the sphere contributes to field ionization process, this
gives us the ionization volume of 2.05x10 22 m 3 . The frequency of a valence electron
strikes the potential barrier is 1016 sec- 1. At 5.6x10- 3 Torr, the calculated aH is -9.73
compare to the experimental
aH
is -1.66. At 8.5x10-4 Torr, the calculated
compare to the experimental aR is -3.59. The estimated values of are
138
aH
aH
is -11.62
different from
the experimental values. This could be that the predicted ionization volumes are not a
good guess.
7.3 Ion Trajectory Simulation
The purpose of having the second gate for the field ionization device is to focus the ion
beam for the next stage, for example, the analyzer, after using the first gate to generate
the ion molecules.
In other words, the second gate is acting as a lens and the ion
trajectory depends on the lens (focus gate) bias.
In this thesis, we built the model
according to the device we made with the tip in-plane with the extraction gate in Charged
Particle Optics 3D software (CPO-3DS) to simulate the ion trajectory (courtesy of Kerry
Cheung). In all the simulation models, the tip was biased at 500V and the extraction gate
was biased at OV. The ion collector had the field of -220V/mm, which was our FI setup.
The ion collector was placed at 5mm above the device and biased at -1 100V. Figure 711 shows the ion trajectories when the focus voltage is at (a) OV, (b) 100V, (c) 150V, (d)
200V, and (e) 225V.
When the focus voltage is the same as the gate voltage, there is no focusing effect, as
shown in Figure 7-11 (a).
The focusing effect becomes stronger as the focus bias
increases toward the ion potential. Figure 7-11 (b), (c), and (d) not only demonstrate the
focusing effect with respect to the focus bias but also suggest that we can tune the
optimal focused ion beam at the specific location with various focus gate biases. As
shown in Figure 7-11 (e), when the focus gate is biased at a large enough voltage, some
ions are repelled by the focus gate and return to the extraction gate.
139
VF=190V
Focus
VF=VG=OV
Gate
Tip
/
\
C
VF=150V
F
ID
I-
N
VG=OV
VTip=500V
'VTij =500V
140
E
VF=225V
VG=OV
VTip=500V
Figure 7-11. Ion trajectory simulation results in Charged Particle Optics 3D software. Tip is
in-plane with the gate. VTi,=500V, VG=0V FIoN= -220V/mm. (a) VG =VF =OV, (b) VF =100V,
(c) VF =150V, (d) VF=200V, (e) VF=225V
7.4 Chapter Summary
In this chapter, we successfully demonstrated the field ionization with micro-fabricated
double-gated CNF arrays.
Field ionization occurred at low voltages (below 700V)
compared to lOkV-2OkV used in the traditional FI device.
In addition, the turn-on
voltage of 400V is lower than turn-on voltages that have been reported in the literature.
The FI is repeatable and varies with tip voltages and the chamber pressures. An increase
in tip voltage or chamber pressure increases the ion current. Finally, we demonstrated the
effect of the focus gate by simulating the ion trajectory. As the focus bias increases, the
ion beam focuses more. By varying the focus bias, we can change the location of the
optimal focusing point of the ion beam.
141
142
8 Thesis Summary, Main Contributions, and
Suggestions for Future Work
8.1
Thesis summary
This work reported the design, fabrication, and characterization of double-gated vertically
aligned CNF arrays. The device was characterized in three areas with either a single gate
(VF=VG) or double gates (VF VG) for field emission (FE), electron impact ionization
(ElI), and field ionization (FI).
Before designing our device, two exploratory experiments were conducted on a microfabricated device (silicon FEAs) and a macro-fabricated device (Busek CNT FE) to
provide us some insights into tip material selections and device design. These two
exploratory experiments also facilitated our ability to foresee the success of the design
and estimate the performance of our device, including the field emission turn-on voltage
and the rough relationship among pressure, ion currents and electron currents.
CNF was selected as our tip material based on the exploratory experiments, and an
extensive work was done to synthesize CNF, which led to the growth of a 4 tm tall single
vertically aligned CNF at each site. A process for making CNF-based double-gated FE
and FI arrays was presented. In this process, the extraction gate and the out-of-plane
focus gate were fabricated with a novel photoresist planarization technique.
This
technique is a fast, uniform, self-aligned, and well-controlled planarization method,
which reduced process time from one month to one week. Two types of device were
fabricated: (1) tip in-plane with the extraction gate and (2) with tip 900nm below the
extraction gate. All devices were made using this process have gate and focus diameter
of 1.7m and 4.2tm, respectively.
For double-gated vertically aligned CNF arrays with the extraction and focus gates biased
at the same voltage, FN coefficients were extracted. Devices from the same piece (LlO)
143
have similar FN coefficients; bF was between -1375 and -1580 and aF was between 13.4 and -17 while the other array from the other piece (L8) had bF of -417 and
aFN of
14.43. Using the Matlab model, we obtained the tip radius of about 14.lnm for L1O and
3.2nm for L8. This suggested that in L8 sharper tips dominated. A comparison between
double-gated silicon FEAs and our device was made. It showed that the radius and the
workfunction of the silicon FEAs are more uniform and stable that of than the CNF FEAs.
Gate and focus transfer characteristics of double-gated vertically aligned FEAs were
measured. Devices from LIG and L8 showed different characteristics due to the relative
positions of the tip with respect to the extraction gate. Total emission currents for both
devices were computed and applied in the generalized FN equation to extract the values
of gate and focus field factors.
The details of gate currents, focus currents, anode
currents, and total emission currents were plotted together and the electron trajectory was
simulated to investigate the emission current distributions for these two different devices.
The most significant result of this work is demonstration of ionizing gas in both hard (ElI)
and soft (FI) modes, presented in Chapter 6 and Chapter 7. For ElI, we showed that the
ion current varies with electron current at a fixed pressure and the linear relationship
between pressure and the ratio between the ion current and the electron current. We also
demonstrated that the focus gate could serve as an ion absorber to protect the tip from ion
bombardment. The lower the focus voltage is, the more ions are absorbed. For Fl, we
reported field ionization current at a turn-on voltage (350V) lower than any reported in
the literature. We also demonstrated that the field ionization current varies with the
pressure.
144
8.2 Main Contributions
The main contributions of this thesis are summarized as follows:
*
We reported for the first time the fabrication of double-gated self-aligned field
emitter arrays with isolated VACNF.
*
We fabricated the double-gated isolated VACNF arrays with a novel photoresist
planarization technique. This process reduces the fabrication process time from
one month to one week.
*
We reported the lowest turn on voltage of 24V of a double-gated isolated VACNF
FEAs.
*
We demonstrated for the first time four-terminal field emission IV characteristics
of double-gated isolated VACNF FEAs.
*
We demonstrated for the first time the electron impact ionization using doublegated isolated VACNF FEAs. The result shows the linear relationship between
pressure and the ratio of electron current and the ion current.
* We utilized the double-gated isolated VACNF device as a pressure sensor. The
pressure range reported in this work covers from 5x10-6 up to
Ix10-3
Torr.
* We demonstrated for the first time that the focus gate of the double-gated isolated
VACNF array absorbs the ions with focus voltage biased at a lower voltage than
the extraction gate voltage to protect the tip from ion erosion.
* We reported the first field ionization data using double-gated CNF arrays and the
lowest turn-on voltage of 350V for field ionization in the literature.
145
8.3
Suggestions for Future work
A direct improvement of this work would be to re-design and re-fabricate the device to
have better performance. One of the purposes to have a micro-fabricated device in this
thesis was to have a low turn-on voltage for field emission and field ionization, which
depends on the gate aperture and the tip radius. Even though we have achieved the lower
turn-on voltages using some specific arrays than any reported in the literature, overall, the
turn-on voltages for most of the arrays were still high and could be reduced by modifying
the process in a couple of ways. First, the tips radius could be reduced by reducing the
diameter and the thickness of the Ni dots. Second, the gate aperture could be reduced by
decreasing the horizontal oxide deposition rate. In addition to lower the turn-on voltage,
the breakdown voltage of oxide could to be improved by densifying in oxygen.
Ultimately, the oxide should be able to sustain the high voltage for a long time for field
ionization and also be able to perform the four-terminal field ionization experiment.
On the characterization side, the measurement system could be calibrated to lower the
noise floor. This would greatly lower the turn-on voltage for field emission and field
ionization.
In electron impact ionization, the effectiveness of the focus gate for
protecting the tip from ion erosion could be investigate more carefully and systematically
by repeating the field emission and electron impact ionization experiments on more
devices. Another extension of this work is to show the soft ionization from the field
ionization.
To accomplish this, a vacuum chamber with an instrument that has the
function similar to MS or residual gas analyzer, but without an ionizer attached, needs to
be assembled. The field ionization study could be more complete with this result.
The original idea of this thesis was to develop new methods of ionizing gases for the
mass spectrometer. Currently, there are groups working on analyzers, detectors, and
pumps in micro-scale. After carefully selecting the compatible elements, a micro-MS can
be expected.
146
Appendix A. Process Flow of the Fabrication of Double-gated
vertically aligned CNT Field Emission and Field Ionization Array
Starting Wafers: 6" n-type Silicon prime wafers, <100> orientation
Process flow:
Step#
1
Lab
TRL
Machine
PMMA
Recipe
250nm
2
NSL
3
4
5
6
7
8
9
NSL
TRL
ICL
TRL
Cambridge
TRL
TRL
eBeam
Lithography
Photo Hood
eBeam
Die saw
Photo Hood
CNT
STSCVD
STSCVD
2:1 ISP:MIBK
Ni recipe
standard
NMP
725"C 10mins
LFSIO 16mins
Jendoped 72mins
10
TRL
HMDS
Recipe #5
11
TRL
Coater
12
13
14
15
16
17
18
TRL
TRL
TRL
TRL
TRL
TRL
TRL
Pre-bake oven
KS2
STS1
STS1
STSCVD
STSCVD
HMDS
19
TRL
Coater
20
21
22
23
24
TRL
TRL
TRL
TRL
TRL
Pre-bake oven
KS2
Asher
STS 1
STS1
6sec 500rpm,
7sec 750rpm,
30sec 3krpm
95"C, 30min
55 sec
Sidewell
02CLEAN 1 Imins
LFSIO 16mins
LFSIO 16mins
Recipe #5
6sec 500rpm,
7sec 750rpm,
30sec 3krpm
95*C, 30min
55 sec
10mins
Sidewell
02CLEAN 1 Imins
25
TRL
HMDS
Recipe #5
Description
250nm PMMA
Exposure
147
Develop, rinse + dry
Deposit 4nm Ni
Diasaw wafers into 2cmx2cm pieces
Lift off
Grow 4gm vertically aligned CNTs
Deposit 1.7gm of oxide
Deposit 0.5gm of doped a-Silicon
Flatten the PR to open first gate
Exposure, Mask #1: 1st -gate pattern
Etch a-Silicon (open 1 st gate)
Strip PR/Clean
Deposit 1.7gm of oxide
Deposit 0.5gm of doped a-Silicon
Flatten the PR to open second gate
Exposure, Mask #2: 2 -gate pattern
Strip some PR
Etch a-Silicon (open 2 nd gate)
Strip PR/Clean
Double-coated PR
26
TRL
Coater
27
TRL
Pre-bake oven
28
TRL
Coater
29
30
31
32
33
TRL
TRL
TRL
TRL
TRL
Pre-bake oven
KS2
Acid-Hood2
STS1
Acid-Hood2
6sec 500rpm,
7sec 750rpm,
30sec 3krpm
95"C, 20min
6sec 500rpm,
7sec 750rpm,
30sec 3krpm
95 C, 30min
500 sec
BOE 10mins
02CLEAN 25mins
BOE 4mins
148
_gate
pattern
Exposure, Mask #2: 2 "a
Etch Oxide above first contact pads
Strip PR/Clean
Exposure the CNTs
Appendix B. Details of Four-terminal Field Emission
Characterization
Device LIOsI
1 E-5 1
I
1 E-61
1 E-71
4
4
Y
1 E-8
V
ty
4)
I
1 E-91
U.
u.
*
.0.0
1E-10 1
V
.
.
*
,
V
V9g
,tvY,v,,vvv
*V 'e**V
00,
'WY
Li Os1:VF=30V
* IG:5E-4
* IF:5E-4
A
IG:1E-5
0
1 E-1 1
1E-12
0
1E-13
D
20
40
60
80
100 120 140
VG (V)
1E-6I
4
1
C)
o
*C
0
U-
L..
V
4 4
1 E-7
I
.YY
0
:Y
1 E-8
1 E-9i
E
++++"-
L8s4:VF=40
1E-101 N IG:1 EIF:1E-4
1E-11
IG:5E- 5
4
V
IF:5E-!
1E-12i
IG:3EIF:3E-E
II
4E1
4 Al
8
11
-10
0
10' 20
'MMIJO
AA
A
0 AA
A, AA
hA
30 40
50
VG (V)
149
IF:5E-5
+ IG:3E-8
** 0.0 :0 :0:
60 70
IF:3E-8
Appendix C. Details of Three-terminal Electron Impact Ionization
Device LIOs3
L1Os3
* 5E71s
* 5E71i
1E-81
I E-10
I:
*.::
5E71p
P=5E-7 Tor
A
ME-
L1Os3
1E-8,
:I
C
o
0= a
1E-10
1E- 10
*
1E6Ip
I2
1E-12,
*A
1E61s
1E6i
U..
."
..
P=1E-6 Torr
0~
1E-12
*
*
..
*A 16
*AAA
AAA
1E-14:
A
E
A
-1
I1E-1 61
A A
AA
A
A
A
Aa
AA
AA
A
AAA
AA
A
A
C
AA
1E-14,
AAA
AAA AAAA
AA
S1E-161
AA
hA
E
AA
AA
80 100 120 140 160 180
20 40 60
20 40 60 80 100 120 140 160 180
V(G+F) (V)
L1Os3
* 5E6Is
* 5E6Ii
1E-8,
A
1E-10
V(GF) (V)
"..
."E
*(
5E6Ip
U.
i
P=5E-6 Torr
L1Os3
M 1E51s
1E-8 1 . 1E511
1
A
1E5Ip
1E-10i P=1E-5 Torr
04
v 1E-12 1
1E-12
.'I
*A
A A
1E-14
hA
.
AA..
At'
At*U
0
1E-14
8o 1iO 160
140 1
w
so
80
E16
.
A
1E-16,
'o
A
0
A
20 40 60
150
3f
0 0
A
t
80 100 120 140160180
V
V(G
F) (V)
4
"A.
1
A
AA
1E-16 1
o *io4
El.
(V)
LlOs3
1 * 5E5Is
j- 1E-8 1 * 5E5i
A
5E5Ip
.(
1
8 1E-10 1 P=5E-5 Torr
LlOs3
. 1E41s
1 1E4i
A 1E41p
1E-10, P=1E-4 Torr
1
ang
.l
-I; 1E-12j
1E-14
a.Aa 03e
"A
. . A ..
.3'AaSat
AA
6
A
&A
AA
0
01 1E-16;
0
00
E
j
qs
A
:K.
A
A
a.
* .AA
asAA
E.K.
1E-14
~E
A
ee AAA
*
"A
.
-C
A
AA
a
.
*
*
1E-12,
0
A
A
1 j*
-
*1A a
*
*
*
I
.K.
1E-8-
--. A
A
A
A
A
tAA
1
1E-16,
0
_C
0 20 40 60 80 100 120 140 160 180
W
0 20 40 60
VG. (V)
L10s3
L10s3
* 5E41s
1E-8
1E-10:
on
O:.'
* P=5E-4 Torr
A
A
1E-10
1E-12
t
1
1a
1E-146
A
A A
*
.*0 *
. A
.
A
IA
*:
*AK
8A
A AA
1E-14
AAA
A
1E3Ip
.-
ait
..
sa
1
1E-12
:*,L
.
.A
1E3i
.P=1E-3 Torr
A
04
0
*
am 6
.
1E31s
.
1E-8'
* 5E411
5E41p
C
0
Ca
80 100 120 140 160 180
* i*
A
L
*
.*;
AALA
I 1E-1 6'
1 1 E-161
00
0 20 40 60 80 100 120 140 160 180
_*
t;
V(Gf) (V)
151
0
20 40 60 80 100 120 140 160180
V ()(V)
Appendix D. Details of Three-terminal Electron Impact Ionization
Device L8s3
1E-6
L8s3
*~
0-
04..
1E-6-
5E7AS
.
1 E-81 * 5E7Ii
* 5E71P
P=5E-7 Torr
lE-1lO 0
*
1E-12
U
0
W
:
0
1E61P
A
$
C
L8s3
* 1E61S
1E-8 1 * 1E6i
1E-10
P=1E-6 Torr
..
: 1E-12
A'
4 0-E
1E-14
AA4~A A
1E-16
50
)
L
V(GF):
E0
C.
R
200
250
300
-
AA
50
100
(V)
150
*
C 1E-10.
.
1E-12,
IA
250
300
A
50
100
150
200
250
A AA A
A
AA
wO
300
50
100
( )
V
150
V(V)
1E-6,
1E-6
So
L8s3
* SESIS
1E-8, * 5ES
A
5E51P
P=5E-5 Torr
1 E-10
C Cw
1E-8
L8s3
M1E41S
* 1E4Mi
A 1E41P
P=1 E-4 Torr
1E-1O
C
.u
1E-12
I1E-1 21
A A
A
A
1E-16
A
E
AAA~fi*ttA
A
0
300
I* ESIP
1E-14
1E-16
0J
250
S1E5P
P=1E-5 Torr"
a
A
1E-141
E 1E-14'
200
1E5IS
0.
1E-12
00
300
1E-8
C
L
S
250
1 E-6
P=5E-6 Torr
0
200
V(E (V)
1 E-6. L8s3
" 5E61S
* 5E611
1 E-8
*
5EP
1E-10
t.
1E-16
1
150
100
A
A
1E-14
50
A
100
AA
A
0
50
1E-16
150
V(G+F)
M1
200
250
300
_
100
150
V(+F (V)
152
200
1E-61 E-8.
C
0 C
1E-61
L8S3
" 5E41S%
m I1E31S
1E-8
5E41P
0
0
C
S
0
C
0
0
0
w
0-
1E-10. P=1 E-4 Tor
0
I
1E-14.
tA
A&
A
0Se
A
A
LAA
0
::.,w
A
I
E31P
P=1E-4 Torr
1E-10
E 1 E-12 1 i
CO@
1 E-12.
uI
1 E3Ii
A1
*5E4Ii
0
C
0
L8s3
1E-14i
mA:..A
j
*AA
Mu
6 O
10
10
200
20
0
300
V(r.F MV
50 100150
V(+F(VM
153
200
250
300
Appendix E. Details of Three-terminal Field Ionization
Device LIOs18
1E-10
L10s18 Field Ionization
8.5x1 04 Torr
1 E-11
Z
0
C3
1E-12O
0
100
200
300
400
500
400
500
VG+F (V)
1E-10-
L10s18 Field Ionization
* 5.6x1 0_ Torr
oaft%
z
.0 1E-11
1E-12
0
100
200
300
VG+F (\)
154
Appendix F. Field Emitter Tip Simulation
% Field Emitter Tip Simulation
% Guobin Sha
% modified from David Pflug
clear
% all in units of nm
apr=850;
%gate aperture outside tip nm
aprfocus=2100; %aperture of focus gate
roc=14;
%tip radius of curvature
hei=1400;
%gate height , i.e. oxide thickness
hei2=2200;
%height of verical gate
gap= 900;
%difference of tip height and the top of vertical gate. postive if tip is
below, negative if tip is above.
gap2=100; %difference of tip height and bottom of focus gate.
thi=2400;
%focus gate thickness
thi2=400;
%vertical gate thickness, can be changed, don't have to be same as focus
gate thickness anymore
the=88.57;
%cone base angle in degrees
%cone base angle in degrees
%the=88.57;
%the resuling beta are in voltage/cm
% the resulting graph is beta vs. angel of the tip.
% don't change anything below, don't change anything in coneleo2model
htip=hei+thi2+hei2; % tip height
apr2=(htip -hei)/tan(the * pi/180.0)+apr;
apr3=(htip-thi-hei) /tan(the *pi/180.0)+apr;
htip=htip-gap;
mr=2;
% mesh refinement, 0-3, 0 means coarse, 3 means very fine
wf=4.05;
Va=0;
155
Vg=1;
[p,e,t,ua,pg,eg,tg,ug]= coneleo2model(aprfocus, gap2,
apr3,apr2,apr,roc,hei2,hei,thi2,thi,the,htip,mr);
u=ug;
[ux,uy]=pdegrad(p,t,u);
uxn=pdeprtni(p,t,ux);
uyn=pdeprtni(p,t,uy);
sc=8; %segment of circle
theta=0:the*pi/(180*sc):the*pi/180;
xO=sin(theta)*roc; %starting point of trajectory
yO=cos(theta)*roc+(htip-roc);
for i= 1:size(uxn)
uen(i)=sqrt(uxn(i)*uxn(i)+uyn(i)*uyn(i));
end
for i=1:size(theta')
%pnt=[xO(i),yO(i)];
%[Ex(i),Ey(i)]=eatpt(pnt,p,t,ux,uy);
Ecircle(i)=tri2grid(p,t,uen,xO(i),yO(i));
end
plot(theta,Ecircle);
sprintf('beta gate=%f', Ecircle(1 )*10A7)
va=l; vg=0;
u=ua;
[ux,uy]=pdegrad(p,t,u);
uxn=pdeprtni(p,t,ux);
uyn=pdeprtni(p,t,uy);
sc=8; %segment of circle
theta=O:the*pi/(l 80*sc):the*pi/l 80;
xO=sin(theta)*roc; %starting point of trajectory
y0=cos(theta)*roc+(htip-roc);
for i=1:size(uxn)
uen(i)=sqrt(uxn(i)*uxn(i)+uyn(i)*uyn(i));
end
156
for i=1:size(theta')
%pnt=[xO(i),yO(i)];
%[Ex(i),Ey(i)]=eatpt(pnt,p,t,ux,uy);
Ecircle2(i)=tri2grid(p,t,uen,xO(i),yO(i));
end
plot(theta,Ecircle2);
sprintf('beta focusing gate=%f, Ecircle2(1)* 10A7)
157
Appendix G. Image effect in Field Ionization
The image effect of the electron lowers the tunneling barrier. In this appendix, four cases
of the image potential are discussed. Equation (G.1) describes the trapezoid barrier and
equation (G.2) describes the tunneling probability using the trapezoid barrier
approximation without taking into account of the image effect.
V(x)-E=q
+q
x
(G.1)
Xc
=exp
I
2mq
3
Gx
ex-Bp
F
F
'2
Next, four cases of different image potential are discussed using equation (G.3) with
replacing different Vimage functions.
2
T=exp -2
+
X
x+Vi,,gedxl
(G.3)
Case 1
Equation (G.4) describes the columbic potential of the image effect and equation (G.5)
describes the tunneling probability that takes account of the image effect using equation
(G.4). However, equation (G.5) is not possible to integrate. Thus, case 2, 3, and 4 are
presented to approximate the columbic potential image effect. Figure G. 1 shows these
four different cases and how close case 2, 3, and 4 can be approximated to case 1.
2
Vimagel
=
-q
T=exp -2
(G.4)
rnqX
x+V,,,,e dx
158
(G.5)
0-
7'
S-6
--
0
.
A-
-v-
-8
0
4
2
6
8
case
case
case
case
10
1
2 (phi)
3 (phi/2)
4 (phi/3)
12
14
Distance from the surface (Angstroms)
Figure G. 1. Four cases of the image effect. Case 1 is the coloumbic potential. Case 2, 3,
and 4 are approximate using triangular shapes.
Case 2
Equation (G.6) approximates the image effect from the surface to the minimal distance
(Xc) that the field ionization will take place using triangular shape. The base of the
triangular is the workfunction the CNF tip (4=5eV) and the height is the minimal
distance (Xc). This approximate gives us the upper bound of the image effect. Equation
(G.7) is the calculated tunneling probability, which lowered the trapezoid barrier by a
factor of 0.8312.
=
Vimage 2
xCx
(G.6)
-0
T2 =exp -2Jc
2q
IX
=
x+7
exp -B
-dx Q
F
(G.7)
Case 3
Case 3 is similar to case 2. Instead of using the workfunction of the CNF tip (4=5eV) as
the triangular base, 4/2 is used. Equation (G.8) describes the equation of this image
effect and Equation (G.9) represents the tunneling probability of case 2, which lowers the
159
trapezoid barrier by a factor of 0.9256. This factor is used in the thesis to approximate
the image effect.
Vimage3 =
2XC
T3=exp -2
x-
(G.8)
2
+
fc
x+Vimage3dx
x+V
dx)
2xI-O)JY2
)1/2(G.9)
expB
F2x(21-
)
2
Case 4
Similar to case 2 and 3, the base of the triangular is D/3, which give us the lower bound
of the image effect. Equation (G. 10) describes the equation of this image effect and
Equation (G. 11) represents the tunneling probability of case 2, which lowers the
trapezoid barrier by a factor of 0.9517.
Vimage4 =
3XC
x-
T4 =exp -2Jc
=exp -B
(G. 10)
3
Mq
0+
3x(I-#)[
F x(3I -2#)
x+V,,,ge 4
dx
(G.11)
(3
160
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