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Selective nitridation of silicon substrates using microwave nitrogen plasma

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SELECTIVE NITRIDATION OF SILICON SUBSTRATES USING
MICROWAVE NITROGEN PLASMA
By
Shashank Sharma
B.Tech, Osmania University. Hyderabad. India. 1998
A thesis
Submitted to the Faculty o f the
Graduate School o f the University o f Louisville
In Partial Fulfillment o f the Requirements
for the Degree o f
Master o f Science
Department o f Chemical Engineering
University o f Louisville
Louisville, Kentucky
August 2000
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SELECTIVE NITRIDATION OF SILICON SUBSTRATES USING
MICROWAVE NITROGEN PLASMA
By
Shashank Sharma
B.Tech, O sm ania University, Hyderabad, India, 1998
A Thesis Approved on
12 , 2 0 0 0
(Date)
by the following Reading Committee:
f —f- k~
£
Dr. M ahendra K. Sunkara (Thesis Director)
Dr. Robert W. Cohn (Thesis Co-director)
Dr. Raul Miranda
Dr. Kevin M. Walsh
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ACKNOWLDEGEMENTS
The author gratefully acknowledges support and encouragement provided by his
thesis adv isor. Dr. M ahendra Sunkara. The author appreciates the help o f Mark Crain and
Dr. Sergei Lyukyutov for valuable suggestions and for helping him obtain the oxide
patterns (photolithographic and AFM written oxide lines). The author appreciates the
time o f Dr. Robert Cohn. Dr. Kevin Walsh, and Dr. Raul Miranda for reviewing this
work and participating in the final oral examination. He would also like to thank Dr.
Donald M. Wheeler o f NASA Glenn Research Center for helping him obtain the XPS
analysis o f the nitrided samples. The author would like to express his thanks to Dr. M.
Meyyappan for providing the SAMPR simulation package and various suggestions
regarding nitrogen plasma modeling at low pressures.
The author would finally like to express his thanks to his parents and sisters for
their endless support, encouragement and blessings.
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ABSTRACT
Nanometer scale features on silicon find applications in a variety o f electronic,
optical
and optoelectronic
devices and
nanoelectromechanical
systems.
Current
lithographic techniques for producing structures in the nanometer regime either have not
yet been shown to yield high aspect ratio structures needed in certain applications and are
limited by the mask thickness and characteristics.
In this thesis, a novel process is proposed and developed, which makes use o f
silicon nitride as an etch mask for fabrication o f micro- and nanometer size structures on
silicon. In this technique, an oxide patterned silicon substrate is nitrided using microwave
generated nitrogen plasma. Upon subsequent selective wet chemical etching, a
complementary pattern on silicon surface is obtained. The direct nitridation using atomic
nitrogen produced the necessary wet-chemical etch selectivity between silicon nitride,
oxide and the nitrided oxide. Etch characteristics o f the nitride and oxy-nitride are
studied. Silicon nitride etch rate decreases with increasing microwave power, pressure
and for longer nitridation. Silicon oxide etch rate does not change significantly upon
direct nitridation. Composition o f the nitrides is determined using X-ray photoelectron
spectroscopy (XPS). XPS analysis shows incorporation o f fractional amounts o f nitrogen
into silicon and silicon oxide substrates, which is also supported by a simplified
thermodynamic analysis. Silicon nitride is found to be thicker than the oxy-nitride for a
particular set o f process conditions. Thus the starting oxide thickness is found to be
critical in obtaining the selective etching.
Direct nitridation for producing silicon nitride and silicon oxy-nitride is also o f
interest for producing thin dielectric films for nanometer scale ULSI circuits.
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TABLE OF CONTENTS
PAGE
A CK N O W LED G EM EN TS......................................................................................................... iii
ABSTRACT.....................................................................................................................................iv
LIST OF TA BLES......................................................................................................................... vii
LIST OF FIGURES......................................................................................................................viii
LIST OF ABBREVIATIONS........................................................................................................ x
NOM ENCLATURE....................................................................................................................... xi
CHAPTER
1. IN TR O D U C TIO N ....................................................................................................... 1
2.
BACKGROUND........................................................................................................ 5
A. Micro- and Nanoscale Structures on S ilico n ..............................................5
B. Silicon Nitride and O xy-nitride...................................................................7
C. Synthesis and and Processing-property Relationships o f Silicon
Nitride and Oxy-nitride Film s.................................................................... 10
3.
EX PER IM EN TA L..................................................................................................15
A. Microwave Chemical Vapor Deposition Reactor................................... 15
B. Etch Rate Measurements..............................................................................17
1. White Light Interferometer (WYKO Surface Profiler)................... 19
1.1. PSI Mode..........................................................................................19
1.2. VS I Mode......................................................................................... 21
C. Compositional Analysis using X-Ray Photoelectron Spectroscopy ..24
1. Depth Profiling using X P S .................................................................. 26
1.1. Angular variation............................................................................27
1.2. Application to silicon nitride films..............................................28
4.
RESULTS AND DISCUSSIONS.........................................................................29
A.
B.
C.
D.
E.
Thermodynamic Analysis...........................................................................29
Nitridation Kinetics......................................................................................32
Micro- and Nanoscale Structures on Silicon........................................... 36
Nitride and Oxy-nitride Etch Studies....................................................... 37
Compositional Analysis Using X-Ray Photoelectron Spectroscopy..43
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F. Short Time Scale W et Chemical Etching o f Silicon/Silicon
oxide/Silicon nitride f o r ............................................................................ 47
5. CONCLUSIONS.........................................................................................................59
6 . RECOMMENDATIONS.......................................................................................... 60
LIST OF REFERENCES........................................................................................................... 61
APPENDICES
A. Low PressureNitrogen Plasma Modeling................................................67
VITA............................................................................................................................................. 88
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LIST OF TABLES
TABLE
PAGE
2.1.
Silicon nitride and oxy-nitride properties and pertinent applications........................10
2.2.
Undesirable nitride film properties associated with various growth methods......... 14
3.1.
Range o f PSI and VSI modes in WYKO profiler system ...........................................23
3.2.
Vertical resolution o f PSI and VSI modes....................................................................24
4.1.
Summary o f results o f low-pressure nitrogen plasma modeling using SAMPR...42
4.2.
Silicon oxide etch rates for different time scales o f etching......................................52
A -1.
Summary o f various equations used by SAMPR in order to model
low-pressure nitrogen plasm a...................................................................................... 6 8
A-2.
A summary of results from SAM PR.............................................................................71
A-3.
A summary of the results from CHEMK.IN/AURORA.............................................77
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LIST OF FIGURES
FIGURE
PAGE
1. Proposed process scheme for patterning silicon substrates......................................... 4
2. Typical photolithographic process to pattern nitride on silicon................................. 6
3. Experimental setup............................................................................................................16
4. Silicon nitride etching setup........................................................................................... 18
5. An interference microscope [35]................................................................................... 20
6.
VSI algorithm [35]............................................................................................................22
7. Block diagram o f a photoelectron spectrometer [36].................................................25
8.
Variation o f G ibbs’ free energy change o f silicon nitride formation
reaction with tem perature............................................................................................... 31
9. Variation o f G ibbs’ free energy change o f silicon oxy-nitride formation
Reaction with tem perature..............................................................................................32
10. (a) A photolithographically microscale oxide pattern on blank Si
nitrided and selectively wet chemically etched using a 30 %
aqueous KOH solution tp result in a nitride pattern (b)............................................ 36
11. (a) An SPM written oxide line on blank Si, nitrided and anisotropically
selectively wet chem ically etched using a 30 % aqueous KOH solution
to result in a trench (b).....................................................................................................37
12.
Variation o f etch step height with etch duration for a silicon substrate
nitrided at 550 W microwave power, 30 torr pressure for 1 hour........................... 39
13. Variation o f etch step height with etch duration for a silicon oxide
substrate nitrided at 550 W microwave power, 30 torr pressure for 1 h o u r
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40
14. Etch rate variation with various process param eters.................................................41
15. N Is spectra o f the nitride surface before sputtering.................................................44
16. N Is spectra at various nitride depths.......................................................................... 44
17. A typical XPS depth profile, showing the variation o f N atomic percentage
with depth fo ra silicon substrate nitrided at 550 W microwave power,
30 torr pressure for 3 hours.............................................................................................45
18. A typical XPS depth profile, showing the variation o f N atomic percentage
with depth for a silicon oxide substrate nitrided at 550 W microwave power,
30 torr pressure for 3 hours.............................................................................................. 46
19. (a) Top view o f the silicon oxide surface after 2.5 seconds o f wet-chemical
etch.
(b) Two-dimensional WYKO line profile in X-coordinates.
(c) Two-dimensional WYK.0 line profile in X-coordinates.
(d) Three-dimensional representation o f the etched surface in (a)............................48
20. (a) Top view o f the silicon oxide surface after 40 seconds o f
wet-chemical etch.
(b) Two-dimensional WYKO line profile in X-coordinates.
(c) Two-dimensional WYKO line profile in X-coordinates......................................50
21. (a) Etch step height variation with etch time for scales o f
up to 1 m inute................................................................................................................... 51
(b) Etch step height variation with etch time for long time scales of
up to 6 hours..................................................................................................................... 51
22. Substrate surface with a spherical roughness m ound.................................................53
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LIST OF ABBREVIATIONS
AFM
Atomic Force Microscopy
SPM
Scanning Probe Microscopy
XPS
X-Ray Photoelectron Spectroscopy
STM
Scanning Tunneling Microscopy
CVD
Chemical Vapor Deposition
PECVD
Plasma Enhanced Chemical Vapor Deposition
uv
Ultra-Violet
ECR
Electron Cyclotron Resonance
PSI
Phase Shift Interferometry
VSI
Vertical-Scanning Interferometry
PZT
Piezoelectric Transducer
IMFP
Inelastic Mean Free Path
SAMPR
Simple Analysis of Materials Processing Reactors
MWCVD
Microwave Chemical Vapor Deposition
N2V
Vibrationally excited nitrogen molecule
N2E
Electronically excited nitrogen molecule
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NOMENCLATURE
Eg (d):
Band gap as a function o f size o f silicon nanodots (eV)
c:
Dielectric constant
G (P. T):
G ibbs' free energy o f a species as a function o f temperature and pressure
(J/Mol)
P:
Pressure (atm)
T:
Temperature (K)
AG:
G ibbs’ free energy change o f a reaction (J/Mol)
W \:
Flux o f species N (MoI/cm:sec)
CN:
Concentration o f species N (M ol/cnr5)
ps,:
Bulk molar density o f silicon (Mol/cm3)
D:
Diffusivity o f species N (cm 2/sec)
A:
Surface area (cm2)
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CHAPTER 1
INTRODUCTION
As electronic device dimensions reduce to the nanometer regime, the spectrum o f
choices o f materials, which can be used for a particular application, gets narrower. The
processes and the materials used in semiconductor device fabrication need to be
modified, as the material properties change significantly with size. Nanometer scale
features on and o f silicon have found application in a variety o f semiconductor devices
such as nanoelectromechanical systems (NEMS) [1-3]. In order to attain high integration
density in devices, patterning o f materials in the nano- regime is important. When
electrons are confined in extremely small regions o f a semiconductor material, such as
silicon, they behave in different m anner than in bulk crystal. Porous silicon represents a
good exam ple o f a material, which shows visible photoluminescence at room
temperature, and thus can be used in light emitting devices [4], Restricting the motion o f
carriers can cause a material to transform from indirect to direct band gap structure with
higher band gap.
This makes nanoscale silicon structures very suitable for certain
optoelectronic applications. The band gap has been shown to vary with the size o f silicon
nanodots [5] as shown below.
Eg (d) = 1.167 + 88.34/d 1 37 (eV)
(1.1)
where, d is the diameter o f silicon nanodots.
Silicon nanostructures also find applications in single electron transistors [6 ],
Non-periodic arrangement o f high aspect ratio, sub-micron scale structures have been
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suggested for fabrication o f multi-passband integrated optical filters [7]. The proposed
gratings require high aspect ratio nanoscale structures. However, lithographic techniques
and processes for producing structures in the nanometer regime are extremely limited and
are currently a subject o f research. Recent efforts to produce nanometer scale structures
are detailed below.
Nano-scale structures have been fabricated by evaporating metal through holes in
a masking material such as silicon nitride [8 ], Fabrication o f gold nano-structures on
silicon has been reported [9]. Several lithography techniques have been developed in the
past few years to pattern silicon surfaces in the nanometer regime including the use o f
electron beams and proximal probes (such as SPM) combined with wet chemical etching
o f silicon [ 10 ], use o f metastable atoms to form oxide resists on hydrogen-passivated
silicon [ 11 ], irradiation o f amorphous silicon with infrared free electron lasers [ 12 ],
m olecular beam epitaxy [13], laser annealing [14] and a laser direct- write process [15].
Although molecular beam epitaxy, laser direct-write and laser annealing techniques have
been shown to fabricate nanoscale structures, they are yet to be shown to produce high
aspect ratio structures on silicon. An important step in obtaining nanostructures is
achieving nanoscale etch mask pattern.
Traditionally, silicon oxide has been used as a masking material for the
fabrication o f microscale structures on silicon. The starting oxide dimensions limit the
dimensions o f the resulting structures. To fabricate smaller dimension structures, the
oxide pattern dimensions have to be reduced. Oxide lines as small as 20 nm wide have
been written by AFM [16]. The oxide line width and line resolution can be adjusted, but
the oxide lines beyond a few nanometers thick cannot be produced by AFM lithography.
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Oxide masking lines o f only about 2 nm thickness have been written. In applications
requiring high aspect ratio structures such as non-periodic grating in multi passband
filters, the issues o f anisotropy and o f oxide holding up to wet chemical etching become
important. Silicon nitride acts as a better etch mask for certain specific etchants, but it is
very difficult to pattern a nitride in the nanometer regime using the direct patterning
techniques such as photolithography due to excellent etch resistance o f the nitride. Apart
from having excellent etch resistance properties, silicon nitride with its suitable dielectric
constant, can perform as a better gate dielectric than silicon oxide in nanometer scale
ultra large-scale integrated circuits because o f the need for thinner dielectric films. SixNy
offers a broad range o f refractive index depending upon the stoichiometry, making it an
extremely useful material for a variety o f optical device applications [17],
Taking advantage o f better etch resistance characteristics o f silicon nitride over
oxide/nitrided-oxide. we propose a direct nitridation scheme, in combination with AFM
probe based lithography, to fabricate nanosize structures on silicon surface. In this
process, as shown in Figure I, an oxide-patterned silicon surface is nitrided using a
microwave generated nitrogen plasma. The nitrided surface is then selectively wet
chemically etched to result in a complementary pattern. The dimensions o f the resultant
pattern are dependent on the starting oxide pattern dimensions.
Unlike thermal process, the silicon nitridation in this technique is a nonthermal
one. In this process, the nitrogen species N+, N, N i+, etc., penetrate the surface with
enough energy, breaking the bonds in the silicon substrate through coilisions and forming
stable Si-N bonds. The activation is provided by plasma (high-energy state) instead o f
thermal means. This work focuses on the feasibility o f the concept of introducing a
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nitridation step in the nanolithography scheme in order to produce nanoscale patterns on
silicon. Specifically, the nitridation process is investigated in detail in terms o f etch and
compositional characteristics o f the resultant nitride and oxy-nitride films.
Resist
Mask
S iO
Positive Resist
S iO
Nitrided
Pattern
Microwave
Plasma direct
Nitridation
\
S iO
Complementary
Pattern
Wet
Chemical
Etching
Figure 1. Proposed process scheme for patterning silicon substrates.
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CHAPTER 2
BACKGROUND
Material properties change significantly with the dimensions o f a structure. As the
device dimensions move into the nanometer regime, selectivity o f a material for a
particular application becomes a significant issue. The lithographic processes to produce
structures and materials in the nanometer regime are currently being researched. In this
chapter a review o f the state o f the art in fabrication o f nanometer scale structures on
silicon and in silicon nitridation processes for various device applications is presented.
A. Micro- and Nano-scale Structures
Conventional micro-fabrication uses a process called photolithography to transfer
patterns on silicon surface [18]. Photolithography works on the principles
of
photoengraving. As shown in Figure 2. in this technique, patterns are first transferred
from a mask to a light sensitive material called photoresist.
The pattern is then transferred from the photoresist to the barrier material on the
wafer surface using wet/dry chemical etching. The resultant patterns are limited by the
thickness, uniformity and quality of the barrier material film. Patterning also depends on
the size o f the starting pattern, which is usually in the micro-scale regime. This technique
has been widely used to fabricate integrated circuits and microelectromechanical systems
(MEMS) containing patterns o f barrier and dielectric materials.
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Resist
Mask
SiN
Positive Resist
SiN
\
SiN
Figure 2. Typical Photolithographic process to pattern nitride on silicon.
The patterning o f materials in the nanometer regime is o f great interest for future
lithography in order to attain higher integration density for semiconductor devices and to
fabricate devices with an entirely new set o f functionalities due to change in material
properties at sm aller size. Nano-scale structures have been fabricated by evaporating
metal through holes in a masking material such as silicon nitride [8 ]. Fabrication o f gold
nano-structures on silicon has been reported [9]. Pure gold STM tips were used to form
gold nano-structures using a field-assisted atom-transfer mechanism. In order to cause
gold emission from the tip, the positive or negative voltage pulses were applied to the
gold tip where it was within the tunneling regime.
Several lithography techniques have been developed in past few years to pattern
silicon surfaces in the nanometer regime, which include the use o f electron beams and
proximal probes (such as SPM). Silicon nanostructures o f high aspect ratios have been
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fabricated by scanning probe lithography combined with aqueous KOH orientationdependent etching o f H-passivated (110) silicon surface [10]. Use o f metastable atoms to
form oxide resists on hydrogen-passivated silicon has been demonstrated as a
nanolithography technique [II]. Silicon nanostructures such as porous silicon and
nanofibers have been fabricated by irradiation o f amorphous silicon with infrared free
electron lasers [12]. Silicon on calcium difluoride and CaFi on silicon is a model system
for growth o f epitaxial semiconductor/insulator structures. Nanometer-size silicon
structures have been grown on CaF^ [19], Silicon nanostructures have been grown by
molecular beam epitaxy using micro-shadow masks [13]. Laser annealing has been used
to pattern a silicon surface with arrays o f nanometer size stripes and dots [14], A laser
direct-write process has been used to fabricate nanoscale silicon structures [15]. Atomic
force microscopy has emerged as a powerful nano-lithography tool. In AFM lithography,
feedback control works independently o f the patterning mechanism, when an electric
field or current is applied for patterning. Thus AFM can be used to process a wide range
o f materials. Resist material is a key issue in AFM lithography. AFM patterning has
been proposed as a technique to fabricate multi-passband integrated optical filters [7],
B. Silicon Nitride and Oxynitride
Silicon nitride is an industrially important material, which has been widely used
in silicon-based microelectronic devices as passivation layers, insulating barriers in thin
film transistors, and diffusion barriers in multilayer devices [20]. Silicon nitride films are
usually obtained as amorphous, but it can also be obtained in two hexagonal crystalline
forms, alpha and beta, the latter being the high-temperature form. An irreversible phase
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transformation from alpha to beta occurs at 1600 °C. Silicon nitride has many unique
electrical, optical, mechanical and chemical properties. It has a density o f 3.18 g/cm3, a
melting point o f 1900 °C, a low thermal expansion (2.5 ppm /°C over the range o f 0-100
°C) and a thermal conductivity o f 0.45 W/cm°C at 25 °C. Silicon nitride is an electric
insulator with a resistivity o f 10 14 ohm-cm at 20 °C [21]. It has an attractive feature that
the diffusivity o f various impurities in it — in particular, that o f sodium- is much lower
than in silicon dioxide. Thus surface field-effect transistors made with silicon nitride
would be less susceptible to the ionic contamination problem than those made with
silicon dioxide [22]. To achieve high levels o f integration and speed in nanoscale
ultalarge-scale integrated circuits, ultrathin SiC>2 gate dielectrics o f ~2-3 nm thick are
required. To reduce the problem o f direct tunneling, as in the case o f ultrathin SiOz,
physically thicker insulators with higher dielectric constants are more favorable as the
gate dielectrics [23], Also, in the case o f oxide dielectrics, there is a problem o f boron
penetration from the heavily doped p "r - polysilicon gate through the underlying gate
oxide and into the channel region o f the p-M OS transistor, which leads to a decrease in
the subthreshold slope, an increase in the flatband potential and a possible source-drain
short circuit [24], It can also generate defects due to interaction with hot carriers that
reduces the device reliability. Therefore, silicon nitride and silicon oxy-nitride thin films
are particularly interesting for the ultra-thin dielectric applications. Their characteristics
do not degrade significantly during high-energy processes (e.g., ion implantation, plasma
etching). Higher density, low leakage current, high breakdown strength, and low interface
density make silicon nitride even more appropriate for VLSI technology [25].
Stoichiometric silicon nitride (SisN.*) oxidizes slowly, about 50 times slower than Si
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when using wet oxidation at i 100° C. Therefore, it is often used as a mask against 0 2
diffusion during the local oxidation o f silicon (LOCOS) process [21], The SixNv - Si
system provides a large available range o f refractive indices, from 3.6 for silicon to 1.97
for stoichiometric silicon nitride, making it useful for optical device applications [17],
Because o f suitable refractive index, silicon nitride can also be used in improving
efficiency o f polysilicon solar cells and photovoltaic devices [26]. Silicon nitride films
have found recent applications as membranes for x-ray lithography masks, where good
optical and mechanical properties are desired [27],
Silicon oxy-nitride possesses an interesting property o f low absorption losses in
the visible and near infrared wavelength range, making it an extremely useful material for
applications in various integrated optical devices [28]. Oxy-nitrides possess several
properties superior to those o f conventional thermal oxides (S i0 2). Nitrogen “doping”
reduces hot-electron-induced degradation. The dielectric constant of the oxy-nitride
increases linearly with the percentage of nitrogen from e (S i0 2) = 3.8 to e (SijNj) = 7.8
[19], Table 2.1 shows a summary o f various properties o f silicon nitride and oxy-nitride
films, which make them useful in certain specific applications.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Table 2.1
Silicon nitride and oxy-nitride properties and pertinent applications
|
Property
Application
Silicon nitride
I
Dielectric characteristics
Nanometer scale ULSI fabrication
!i
Refractive index
Impurity diffusion barrier
Optical devices, solar cells, photovoltaic
devices
Thin film transistors, multilaver devices
Oxygen diffusion barrier
LOCOS process
1
1
!
Silicon oxy-nitride
Dielectric characteristics
Nanometer scale ULSI fabrication
Low absorption losses in visible-near
infrared wavelength range
Integrated optical devices
C. Synthesis and Processing-property Relationships of Silicon Nitride and Oxy­
nitride Films
Silicon Nitride films have been synthesized by various methods and investigated
by several authors. These methods include a plasma-enhanced technique or chemical
vapor deposition or a combination o f these techniques. Irradiation o f silicon with nitrogen
ions from nitrogen plasma has been shown to form a thin, continuous amorphous nitride
layer. The target temperature was less than 600 K, resulting in the amorphization o f the
nitride. For high implant doses, a layer o f voids was observed in the center o f the
amorphous layer [29]. Very thin silicon nitride films (SixNy) are desired in ULSI circuits.
For the growth o f such a very thin layer, direct thermal nitridation of silicon has been
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widely studied, where a nitrogen containing gas such as ammonia decomposes to form
nitride on the silicon surface. Also, SixNy deposition using the Si source gas, for e.g.,
SiH 4 in addition to ammonia has been studied by using chemical vapor deposition. High
growth temperatures (800-1200 -C) required for these processes often induce undesired
processes such as dopant diffusion, providing limitations in ULSI device fabrication.
Therefore, formation o f SixNv at low temperature is strongly desired. Surface nitridation
technique based on gas-decomposition reaction by catalytic CVD has been studied. In
this catalytic CVD method, deposition gases (NH3. etc.) are decomposed by catalytic
cracking reactions at a heated catalyzer placed near the substrates so that films are
deposited at low temperature without help from plasm a or photochemical excitation. The
surface could be contaminated with tungsten. Also, there was a considerable am ount o f O
(approx. 30%) found in the films [30], The conventional plasma-enhanced chemical
vapor deposition technique for depositing nitride films at a low temperature involves the
reaction o f a combination o f gases such as silane. ammonia, nitrogen, etc. in glow
discharge plasma. Because o f the large amount o f trapped hydrogen, S ixN\, films
deposited by PECVD generally exhibit a lower density and refractive index and a higher
etch rate. The entrapped hydrogen is evolved on subsequent thermal treatments, which
causes the degradation o f films. In addition, the SiH and NH bonded groups generate
localized states, which act as deep traps or recombination centers resulting in a poor gate
insulator for memory applications [31].
The growth parameters greatly influence the microstructure o f the films
deposited. This dependence o f nitride properties on process parameters has been studied
with respect to the dielectric properties. It has been observed that electron hopping
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conduction is the dominant conduction mechanism for the uniform and dense SixNy films
[32], Studies have been done to investigate the silicon surface passivation characteristics
o f PECVD silicon nitride. A higher substrate temperature provides more energy to the
radicals on the surface and thus increases their desorption. Therefore higher temperature
reduces the deposition rate and improves the silicon/silicon nitride interface quality,
hence better surface passivation [33]. Nitride growth has also been reported by ion-beam
sputtering. But due to variable sputter yield, control o f film composition is difficult.
Hydrogen terminated silicon surfaces have been shown to convert to nitrogen-terminated
surfaces
using
dimethylhydrazine
(DMH)
as
the
nitridation
agent
[34],
Dimethylhydrazine was used because o f its high chemical reactivity, which permits
nitridation at low temperatures. Carbon contamination from DMH limits the temperature
range over which, nitridation could be carried out. Electronic properties o f thin SijN j
films grown on silicon in a nitrogen glow discharge have been investigated [35]. The
activation energy for growth has been reported to be 0.3 ± 0 .1 2 eV. These ultra-thin
(thickness< 100
A)
films have an average breakdown field of 10-12 M V/cm. Recently
nanometer scale SijN.; rods have been shown to be synthesized using carbon nanotubes as
templates. The diameters are in the same range as the starting carbon nanotube diameters.
The nanorods were formed through the reaction o f carbon nanotubes with Si-SiOi
powder mixture in nitrogen atmosphere. According to the suggested mechanism o f
formation, SiO gas forms through the reduction o f silica.
SiOz(s) + Si(s) -> 2SiO{g)
12
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(2.1)
The generated SiO gas and nitrogen react with carbon nanotubes. In a Si-C-N-O
system, following reactions are suggested to be responsible for the formation o f silicon
nitride and oxynitride nanorods [36].
3*SfO(g) + 3C (j) +-2 N , (g) -> Si}N 4(s) + 3CO(g)
2SiO(g) + C(s) + Ar,(g) -► Si2N zO(s) + CO(g)
Stoichiometric silicon nitride films free o f hydrogen, oxygen, argon and heavy
metals have been synthesized using a low voltage reactive ion-plating process, with
carbon as a substrate [37], Atomic scale incorporation of nitrogen in oxide layers can be
achieved by oxidation o f silicon in N 2O environments. But this kind o f nitridation has to
be carried out at high temperatures. Studies have been done to investigate nitridation o f
silicon dioxide layers using plasma technique, for e.g, NH 3 plasma, N 2 plasma, and
plasma created by electron impact (applying high voltage to a filament). A high amount
of nitrogen was found in the oxide layers [38]. Table 2.2 shows undesirable nitride film
characteristics associated with various growth techniques. Due to these process related
undesirable film properties, silicon nitridation has been a focus o f research.
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Table 2.2
Undesirable nitride film properties associated with various growth methods
Synthesis method
Film characteristics
•
Ion implantation
Amorphous, high amounts o f voids
!
Chemical vapor deposition
High growth temperatures
Catalytic chemical vapor deposition
Surface contamination, oxygen
incorporation
Less stable, lower density and refractive
index, higher etch rates
Less control over film composition and
thickness
Carbon contamination
i
!
i
Plasma enhanced chemical vapor
deposition
Ion beam sputtering
j
!
Direct nitridation using
Dimethylhydrazine
As described above, various lithographic techniques have been developed to
fabricate micro- and nano scale structures on silicon. Nanometer scale mask and higher
etch selectivity are required in order to pattern a silicon surface with high aspect ratio
structures. Compared to silicon oxide as an etch mask, silicon nitride can provide much
better etch resistance and flexibility with respect to the dimensions o f the desired
structures. However, according to our knowledge, a process for producing nanoscale etch
mask based on silicon nitride has not been reported in the literature.
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CHAPTER3
EXPERIMENTAL
A typical photolithographic process sequence for patterning nitride etch-masks is
shown in Figure 2. A thin nitride film followed by a photoresist (positive or negative) is
deposited on a blank silicon surface. According to the desired nitride pattern, the surface
is exposed to UV radiation using a radiation sensitive mask. Then the surface is wet/dry
etched to result in a nitride pattern.
The process proposed in this thesis is different from the conventional scheme, i.e..
a direct nitridation process step is inserted prior to wet/dry etching step. The nitridation
experiments were done in an ASTeX model 5010 bell ja r reactor chamber equipped with
an ASTeX model 2115 1500 W microwave power generator.
A. Microwave Chemical Vapor Deposition Reactor
Plasma is defined as a continuum, which is partially ionized and which has equal
number densities o f electrons and ions, thus maintaining charge neutrality at each point in
the field. Microwaves at 2.45 GHz are used to ionize the nitrogen gas phase into
electrons, ions (N"\
N \ N?’, etc.), excited molecules (N , [N], etc.), and radicals (N).
The electrons can be more easily accelerated to high energy levels with temperatures o f
5000 K or greater. Since electrons are much lighter than other gas phase species, the bulk
gas phase temperature is less than electron temperature. The electrons collide w ith the gas
molecules, which results in dissociation and generation o f reactive chemical species
providing activation for subsequent reactions on the substrate surface. The m icrowave
nitrogen plasma nitridation o f silicon substrates has advantages in terms o f better control
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on the nitridation process parameters, stability over longer times, and scalability for
larger substrates.
The nitridation experiments were done in an ASTeX model 5010 bell ja r reactor
chamber equipped with an ASTeX model 2115 1500 W microwave pow er generator.
Figure 3 shows a schematic o f the reactor.
Tuners
Waveguide
Ji,
Microwave
Outer metal
perforated
casing
Power
Quartz Bell
~
jar
Plasma
Silicon
Exhaust
Inlet gas
Figure 3. Experimental Setup.
At this point in time, there is no provision for substrate heating and biasing or
langmuir probe to measure the plasma density and fluxes o f nitrogen species reaching the
silicon substrate. Graphite blocks were used as the substrate stage. The plasma ball sits
right on top o f the silicon substrate, unlike the ECR plasma setup, where there is a
separation o f about 15 cm between the substrate and the plasma producing region.
Various nitridation process parameters were varied to study the variation o f
nitride etch rates, quality and thickness with these parameters, for e.g., microwave power,
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pressure, etc. Nitridation was performed at pressures o f 30, 50 and 100 torrs: microwave
powers o f 550, 650, 900 and 1100 W and for 1 and 3 hours. Hydrogen was introduced in
small proportions to stabilize the nitrogen plasma and to increase the plasma temperature
(hydrogen recombination is more energetic). There were attempts made to measure the
absolute temperature using a K-type thermocouple. But due to insufficient contact
between the thermocouple and the backside o f the substrate stage and substantial
thickness o f the substrate stage, erroneous readings were observed and thus are not
reported in the thesis. The nitrided substrates are selectively wet chemically etched to
result in a complementary pattern on the silicon surface.
B. Etch Rate Measurements
To study etch rate characteristics o f the nitrides on silicon and silicon oxide, blank
surfaces were directly nitrided separately using microwave nitrogen plasma. Before
nitridation. the blank p-type (100) silicon surfaces were cleaned using a 50% HF solution
and ultra-sonicated to remove any extraneous dirt particles. After nitridation. etch rate
measurements were done. A nitrided blank silicon surface was etched using a 30 % (by
weight) K.OH solution at ~70 °C. The nitrided surface was partially dipped into the
etchant solution as shown in Figure 4.
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30 % aqueous KOH
solution
Nitrided blank
* 0
Hot plate
Enlarged side view
Figure 4. Silicon Nitride etching setup.
Due to etching, a step was created depending on the duration o f etch. Etch step
height was measured using a white light interferometer (WYKO NT 2000). This is a noncontact type o f profilometer. The minimum depth resolution o f this instrument is 3 A. PSI
(Phase Shift Interferometry) mode was used in the etch step height measurements, as
when the etching was performed at short time scales, the etch step height values were in
the order o f single and double- digit nanometers. The PSI mode has a minimum vertical
resolution o f 3 A and it is more sensitive to the surface roughness. Hence etch steps for
short etch durations could be measured without any instrumentation limitation. But as the
etching continued into longer time scales, the surface roughness decreased and at the
same time the etch step height increased to hundreds o f nanometers. Etch step heights in
such magnitudes were measured using the VSI (Vertical Scanning Interferometry) mode.
Step height was plotted as a function o f etch-duration.
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1. White Light Interferometer (WYKO Surface Profiler) [39]
The WYKO surface profiler systems are non-contact optical profilers that use two
technologies to measure a wide range o f surface heights. Phase-shifting interferometry
(PSI) mode allows measuring smooth surfaces, while vertical-scanning interferometry
(VSI) mode allows to profile rough surfaces and steps.
1.1. PSI Mode
In phase-shifting interferometry. a white light beam
is filtered and an
interferometer beam-splitter reflects half o f the incident beam to the reference surface
within the interferometer. The beams reflected from the test surface and the reference
surface recombine to form interference fringes. These fringes are the alternating light and
dark bands seen when the surface is in focus. Figure 5 shows an interference microscope.
During the measurement, a piezoelectric transducer (PZT) linearly moves the
reference surface a small, known amount to cause a phase shift between the objective and
reference beams. The system records the intensity o f the resulting interference pattern at
many different relative phase shifts, and then converts the intensity to wavefront (phase)
data by integrating the intensity data. The phase data are processed to remove phase
ambiguities between adjacent pixels, and the relative surface height can be calculated
from the phase data using
/»(.*,y ) = ^ - ^ ( j r , v)
4/T
Where /. is the wavelength o f the source beam, and <Kx,y) is the phase data.
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(3 .1 )
Digitized intensity data
Detector array
Neutral density
Light
source
PZT Transducer
Aperture stop
Microscope objective
F i e l d stop
Mirau interferometer
Reference surface
Beam splitter
Test
surface
Figure 5. An Interference Microscope [35|.
This technique for resolving surface heights is reliable when the fringe pattern is
sufficiently sampled. When the surface-height difference between adjacent measurement
points is greater than a /4 , height errors in multiples o f a /2 may be introduced and the
wavefront
cannot be correctly reconstructed. Therefore, conventional phase-shift
interferometry is limited to fairly smooth, continuous surfaces. To resolve rougher
surfaces, WYKO surface profilers use vertical-scanning interferometry techniques.
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1.2. VS I Mode
The basic interferometric principles are sim ilar to those in PSI mode. But in VSI
mode, the white light source is not filtered, and the system measures the degree o f fringe
modulation, or coherence, instead o f the phase o f the interference fringes.
In vertical-scanning interferometry. a white-light beam passes through a
microscope objective to the sample surface. A beam splitter reflects half o f the incident
beam to the reference surface. The beams reflected from the sample and the reference
surface recombine at the beam splitter to form interference fringes.
During the measurement, the reference arm containing the interferometric
objective moves vertically to scan the surface at varying heights. A linearized
piezoelectric transducer precisely controls the motion. Because white light has a short
coherence length, interference fringes are present only over a very shallow depth for each
focus position. Fringe contrast at a single sample point reaches a peak. The fringe
contrast, or modulation, increases as the sample is translated into focus, then falls as it is
translated past focus. The system scans through focus (starting above focus) at evenly
spaced intervals as the camera captures frames o f interference data. As the system scans
downward, an interference signal for each point on the surface is recorded. The system
uses a series o f advanced computer algorithms to demodulate the envelope o f the fringe
signal. Finally the vertical position corresponding to the peak o f the interference signal is
extracted for each point on the surface. A block diagram o f the algorithm used in VSI is
shown in Figure 6 .
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I(z)
Square-
DC
law
Subtract
A(z)
Lowpass
filter
Peak
detector
Surface height
Figure 6. VSI algorithm (35|.
The light for both techniques originates from a white-light source; however, it is
filtered during PSI measurements to produce red light at a nominal wavelength o f 632
nm. The light is not filtered during VSI measurements. White light has a short coherence
length. Thus, the fringe contrast is highest at best focus but falls o ff rapidly as focus is
lost. A white light source works best for VSI because the technique depends on a high
modulation at a precise focus point. If white light is used during a PSI measurement, a
single high-contrast fringe (the zero order fringe) would fill most or all o f the array when
the fringes are annulled. Because the contrast drops off rapidly on either side o f this
fringe, the intensity modulation would be slow in some regions when phase shifting
occurs. A red-light source works best for PSI because it has longer coherence length than
white light. High-contrast fringes are present through a larger depth o f focus. This
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increases the accuracy o f measurements, especially when the objective has a short depth
o f focus o r the sample has tilt that cannot be removed easily.
In VSI, the arm holding the magnification objective actually moves through focus
in a controlled manner. The detector measures the modulation corresponding to every
focus point on the surface as the objective moves vertically. Before the measurement, the
objective is focussed. After starting the measurement, the system scans downward a
specific amount. The measurement takes a few seconds. In PSI, the objective does not
move through focus. During the measurement, the PZT causes a slight shift between the
reference and sample beams. The measurement is very quick.
To increase the resolution o f the measurement beyond the sampling interval, a
curve-fitting interpolation technique is used. With this algorithm, the surface height
resolution is approximately 3 nm rms for a single measurement on a smooth, highly
reflective sample. For resolving surfaces smoother than this. PSI is used. Only the range
of the PZT to perform the translation through focus limits the range o f heights that VSI
can profile. For WYKO profilers, the range is upto 500 pm. Ranges o f the two modes in
the WYKO profiler system are shown in Table 3.1.
Table 3.1
Range of PSI and VSI modes in WYKO profiler system
Mode
Range
PSI
160 nm
VSI
500 pm
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Resolution refers to the smallest distance the WYKO surface profilers can
accurately measure. Resolution values for VSI and PSI modes are listed in Table 3.2.
Table 3.2
Vertical resolution of PSI and VSI modes
Mode
Single
Multiple measurements
measurement
(averaged)
PSI
3A
3A
VSI
3 nm
< 1 nm
C. Compositional Analysis using X-Ray Photoelectron Spectroscopy [40|
When a material is exposed to electromagnetic radiation o f sufficiently high
energy, the emission o f electrons is observed. This phenomenon is called photoelectric
effect. If the sample is irradiated with monochromatic photons o f frequency v,
hv = Ik + Ek
(3.2)
Where. Ik is the binding energy o f the kIh species o f electron in the material and Ek
is the kinetic energy o f the ejected electron. A high energy photon, with hv significantly
in excess o f the threshold energy hvQ. may be capable, in separate one photon/one
electron photoionization events, o f ionizing different species o f electrons having various
ionization energies Ik < hv. One photon may eject a very loosely bound electron,
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imparting to it a high kinetic energy, while another (o f same energy) might instead ionize
a more tightly bound species o f electron and produce a photoelectron o f lower kinetic
energy. Since the energy levels occupied by electrons are quantized, the photoelectrons
have a kinetic energy distribution n(E). consisting o f a series o f discrete bands, that
essentially reflects ‘shell’ form o f the electronic structure o f the sample. The
experimental determination o f n(E) by a kinetic energy analysis o f the photoelectrons
constitutes photoelectron spectroscopy. A block diagram o f a photoelectron spectrometer
(PES) is shown in Figure 7.
Sample Inlet
System
Electron
Ionization
Analyzer
Detector
Chamber
Pumping
System
Recording
Figure 7. Block Diagram o f a photoelectron spectrometer [36|.
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Source
Electrons have only a very short mean free path within a gas before they are
inelastically scattered by the bound electrons o f atom s they encounter. So. to exam ine the
photoelectrons, it is essential to contrive a high vacuum pathway from the ionization
region, where they are produced, through the analyzer to the detector. Electrons travelling
through a material have a relatively high probability o f experiencing inelastic collisions
with locally bound electrons, as a result o f which they suffer energy loss. These inelastic
scattering processes affect photoelectrons and, if they occur frequently, the flux o f
photoelectrons emerging from the sample is much attenuated. The effect is not very
important in gas phase PES but, in solids, where atomic densities are much higher, it
proves to be o f great significance. Whereas the exciting photons penetrate deeply into the
solid sample, the photoelectrons can escape from only very short depths within the
surface. The mean escape depth o f electrons from a material is dependent on their kinetic
energy. The degree o f resolution achievable with a given PE spectrometer is limited by
the resolving power, R=E/AE, o f its analyzer system.
Ejection o f photoelectrons is a very direct way o f obtaining information,
characteristics o f atoms. If high enough excitation energy is provided, core level spectra
can be obtained for all elements in the periodic table except H and He and the determ ined
binding energies o f these core levels are sufficiently unique for their unambiguous
identification. Mg K a (1253.6 eV) and A1 K a (1486.6 eV) X-rays satisfy this
requirement and are commonly used excitation sources.
I . Deplh profiling using XPS
Electron scattering accounts for the surface sensitivity o f electron spectroscopy
for chemical analysis (ESCA) and the total photoelectron scattering coefficient, Sj is
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inversely related to the inelastic mean free path (IM FP) or ‘escape depth’,
a ..
The exact
definition o f IMFP leads to the equation
I tl = I J l - e - 1 *)
Where
(3.3)
is the ESCA peak intensity from a layer o f material o f thickness d and
I r that from a ‘infinitely’ thick layer for electrons o f IMFP=a. Thus 63, 87 and 95% o f
the total peak intensity derive from depths equal to k, 2/. and 3>. respectively. Hence, to a
reasonable approximation the depth of material actually sampled is given by 3X. The ratio
lo/'Is increases exponentially with the overlayer thickness, where I0 and Is are peak
intensities from components o f a substrate and overlayer respectively. Thus this effect
can be used to study the structure o f overlayers.
1.1. Angular Variation
The potential value o f varying the angle o f electron emission, or ‘take-off angle’
(0) in ESCA experiments was first demonstrated by Frazer et al [41] who showed that a
surface sensitivity (surface:volume signal ratio) enhancement o f ca. 10 could be achieved
at low 0. In the ideal case the signal intensity from the top monolayer actually increases
as 0 decreases. Modification o f eqn.3.3 takes this effect into account.
/ , = / x ( \ - e - j ; i 'n0)
(3.4)
The form o f curves o f absolute intensities is not reliable and for quantitative
analysis, only ratio curves can be used, i.e, it is essential to follow relative changes in
peak intensity. Because XPS has a low effective sampling depth, it is particularly
sensitive to the cleanliness o f the surface.
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1.2. Application to silicon nitride films
Assuming that a uniform layer of SixNy forms on Si with an abrupt interface, the
ratio o f Si 2p intensities from the nitride and Si layers, R (0), can be expressed as
D.a*
K\u ) —
7*-v
•v s ,( ^ A \ )-^5,, v (2p)-[l - exp(-c/0 /(✓.,, v (2p)cos#)J
——---------n
" ’r
r
—■
{ s S E s,-2 P - 6 )
-V s . ( S i ) ' /'-si(2/J)[ l —exp(—
c/, /(As ( 2p) cos #)]-exp[-</0 /(/.', cos#)]
( E * ' 2 P - d '>
i
,
(3-4)
Where NSj(SixNy)/NSj(Si0) is the ratio o f moles per unit volume o f Si in SixNy to Si
in Si. or 3 Vmoi(Si)/Vmoi(SixNv), where Vmo| is the corresponding molecular volume,
/.si(2p), -2 6 A, is the inelastic mean free path (IMFP) o f Si 2p photoelectrons in Si and
/.’si(2/?) and A.sixN>(2p) are - 30 A for Si 2p photoelectrons in SixNy from Si-Si and Si-N
bonds, respectively [15].
The XPS analysis done in this work was not truly angle-resolved usually meaning
I (0) data. In the analysis performed in this work, the angle o f emission o f the analyzed
electrons was well defined, i.e, it was normal to the surface plus or minus 6 degrees. The
x-ray source had an A1 anode and was not monochromatized. The depth profiles were
obtained by Ar-ion etching the surface for successively longer times and analyzing after
each etch.
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CHAPTER 4
RESULTS AND DISCUSSIONS
The process developed in this work involves direct nitridation o f an oxidepatterned silicon surface using microwave nitrogen plasma. The nitrided pattern upon
subsequent wet chemical etching, results in a pattern reversal. In this chapter, a
thermodynamic analysis is performed to determine the feasibility o f this process. Etch
selectivity between the nitride and the oxy-nitride is studied by determining the etch
characteristics o f the nitrides. This process is shown to produce micro- and nanoscale
structures on silicon surface. Various parameters affecting the process are identified.
Compositional analysis o f the nitrides using XPS is also discussed.
A. Thermodynamic Analysis
Although the plasma nitridation is a non-equilibrium process, a thermodynamic analysis
is done to determine the feasibility o f this process and the nature of the nitrides grown
under these temperatures. The following two formation reactions are considered
xSi + vvV -► S/'JV
SiO, + (2 - P ) N -► SiO,iVr
(4.1)
Feasibility o f each process is governed by the G ibbs’ free energy change. G ibbs’ free
energy change o f the two reactions was calculated as a function o f temperature.
The Gibbs' free energy G (P, T) o f a species as a function o f pressure P and temperature
T is given by equation 4.2.
29
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
For solid species, the G variation with pressure was neglected. And the gas phase
was assumed to be an ideal gas so that.
hence eqn. (4.2) becomes
p
(4.4)
(4.5)
Using the Gibbs’ free energy data for individual species obtained from JANAF
[42], the Gibbs’ free energy change for above two reactions is plotted as a function o f
temperature as shown in Figure 8 . For thermodynamic feasibility, the G ibbs’ free energy
change o f these reactions must be negative. It can be seen that only the formation of
SixNv is feasible over the whole temperature range (where x and y are fractions). The
G ibbs’ free energy change o f the formation reaction shows a decrease over the
30
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
temperature range. AG for the formation o f stoichiometric silicon nitride is positive over
the whole temperature range, indicating the non-feasibility o f formation o f Si3N4 under
these conditions. The formation o f oxynitride was also found to be thermodynamically
feasible over a specific temperature range as shown in Figure 9.
1.E+06 1.E+06 Si3N#
8.E+05 -
♦
♦
6.E+05 U
<
4.E+05
2.E+05
SiXNy
0.E+00
500
-2.E+05 -
1000
000
1500
2500
i
T(K)
i
0.E+00
0
♦
T(K)
1000
2000
3000
-1 .E+04
Figure 8. Variation of Gibbs’ free energy change o f silicon nitride formation
reaction with temperature.
31
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
Thus the nitrides are suggested to be non-stoichiometric, for e.g., SixNy and
SiOnNp. where x, y and p are fractions. It was also observed that the variation o f G ibbs’
free energy change o f formation reaction o f SixNy is different for different values o f x and
y-
0
500
1000
40000
T (K)
1500
2000
2500
SiXNy
% -4 0 0 0 0
O
< -8 0 0 0 0 -
-120000
■
SiOpN
-
-160000
Figure 9. Variation of Gibbs’ free energy change of silicon oxynitride formation
reaction with temperature.
B. Nitridation Kinetics
The nitridation mechanism is sim ilar to thermal oxidation. Expansion occurs upon
silicon nitridation. As the nitride grows, nitrogen species have to pass through thicker and
denser nitride material. Thus the growth rate decreases with time.
32
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e rm is s io n .
To find the rate o f diffusion o f species N to the silicon surface, we apply a
differential N mole balance over the increment Az located somewhere between z=0 and
z=L. where L is the nitride thickness at a particular time (as shown below)
Z=0
Silicon
Nitride
Az
Silicon
The mole balance on N between z and z+Az is
WvAl
z-
W n-A|
=0
(4.6)
Where. A is the wafer area (constant). Therefore,
dWs
d:
=
(4.7)
0
But.
d:
Where. C \ is the concentration o f species N at a particular z.
Hence eq. (4.7) becomes
33
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
(4.8)
This second order differential equation can be solved using the following
boundary conditions
At z=0. C \ = Cso
At z=L. C \ = C \ l
Therefore, the concentration profile becomes
C
^ V -C
^ VQ _
C \ L - C^ VO ~ L
(4.10)
And.
w\-
=- j ( cSL- c S0)
If we carry out a mole balance on silicon,
A _ d (A -L Psi)
dt
dL rs”
=> — = —
dt p Si
34
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
(4.12)
(4.13)
Where, rsi” is the rate o f reaction o f silicon, psi is the bulk molar density o f silicon.
Assuming that at the silicon-silicon nitride interface, the N flux is proportional to the N
concentration. That is.
Ws = kCSi
XL
^
kC XL
(4-14)
~
^
(Cv,
C vo,
-r
(4.15)
vt " kL
+ 1
D
DC JO
W, =
•'
D
L+
k
DC AO
dL
dt
L+
Ps,
D
(4.16)
Integration yields.
Lr +
DL
DC JO
k
Ps,
L~ + AL —Bt
Or
(4.17)
Where, A=D/k and B=DCAo/psi
Thus the kinetics o f the nitride growth suggests that the nitride thickness increases
with time initially and for further nitridation, it increases with square root o f time, i.e., the
35
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
nitride growth rate decreases over the course o f nitridation. The final thickness is limited
by the concentration o f the nitrogen plasma species diffusing into silicon.
C.
Micro- and Nanoscale Structures on Silicon
The nitridation scheme developed in this work produces microscale and nanoscale
structures on silicon surface, which presents a novel alternative for various applications
involving such structures and nitrides. In this process, we can convert an oxide pattern on
silicon into a silicon nitride/silicon oxy-nitride pattern. Depending on the etch selectivity,
micro- and nanoscale trenches can be fabricated on silicon surface. A micro-scale oxide
pattern shown in Figure 10 (a) was reversed to yield in a pattern shown in Figure 10 (b).
Similarly an oxide line written by AFM was nitrided and selectively etched w ith a 30 %
aqueous K.OH solution to result in a trench as shown in Figure 11.
Figure 10. (a) A photolithographically microscale oxide pattern on blank Si nitrided
and selectively wet etched using a 30 % aqueous KOH solution to result in a nitride
pattern (b).
36
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 11. (a) An SPM written oxide line on blank Si, nitrided and anisotropically
selectively wet etched using a 30 % aqueous KOH solution to result in a trench (b).
The primary reason for oxide pattern reversal is the difference in the etch
characteristics o f silicon nitride and the oxy-nitride with KOH as an etchant. The etch
selectivity is defined as the ratio o f etch rates. This etch selectivity is highly dependent on
the nitridation process parameters and starting oxide quality and thickness.
D. Nitride and Oxy- nitride Etch Studies
The etch characteristics o f the nitrides formed on blank Si and SiO i (the nitride
and the oxy-nitride) were determined as a function o f nitridation process parameters. The
etch selectivity is defined as the ratio o f nitride and oxy-nitride/silicon etch rates. A blank
silicon substrate was nitrided and the etch rate with a 30 % aqueous solution o f KOH was
determined. To determine the etch rate, the nitrided silicon sample was partially dipped
in the etchant. Etching results in a step on the surface, height o f which depends on the
duration o f etching. A typical plot of nitride etch step height as a function o f etch time is
37
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
shown in Figure 12. Nitridation o f this particular sample was performed at 550 W
microwave power. 30 torr pressure for 1 hour.
The etching was performed at very short time scales, starting from 2 seconds. The
etch step height obtained with such short time etching was on the order o f single digit
nanometers. The white light interferometer used for measurement purposes was able to
measure such small features. For short time scales o f etching, there was no definitive etch
interface observed. In these time scales, etching reduced the surface roughness. Thus for
short time scales on the order o f <10 sec, the difference between the surface roughness
between the etched and unetched regions was taken as etch step value. It was observed
that the surface roughness reduces with etching. The etch step height increases linearly
with etch duration. Slope o f this linear variation gives the etch rate. The nitride etches at a
rate about ten times less than blank silicon. But as etching continues, nitride is depleted
and after a certain breakthrough time, as the silicon gets exposed to the etchant, the
surface starts etching at approximately the same rate as bare silicon. Thus, the
breakthrough depth also gives an indication about the nitride thickness. Figure 13 shows
a similar plot for nitrided oxide and the reference oxide. It can be seen that the silicon
oxide etch rate does not change much upon nitridation and also silicon nitride etches
about twice as slow as the oxy-nitride, yielding an etch selectivity o f about 2 and also
causing a nitrided oxide-patterned silicon surface to result in a reversed pattern upon wet
chemical etching. The etch selectivity is highly dependent upon the nitridation parameters
as it will be seen in the discussion further.
38
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
▲ Bare Si
450 -
♦
SiN - short time
s c a le etching
• SiN - long time
s c a le etching
^ L i n e a r (Bare Si)
400
350 -
y = 9.93x - 6.37
Linear (SiN - short
tim e sc a le etching)
Linear (SiN - long
tim e sc a le etching)
300 -
i
e
.s
250 -
st
200
-
y = 9.77x - 133.41
100
50 -
__y = 1.3 7 x - 1.27
20
Estimated
Nitride
30
40
50
Etch Time (sec)
Thickness
Figure 12. Variation of etch step height with etch duration for a silicon substrate
nitrided at §50 W microwave power, 30 torr pressure for 1 hour.
39
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
80 70
S i0 2 N
Bare
SiOc
60 -
y = 1,69x - 0 .4 5
y = 1 .6 9 x - 0 .3 3
i 50 -
"
cn
30
20
-
= 1 .9 x + 0 .1 5
0
0
10
20
30
40
50
Etch Time (sec)
Figure 13. Variation of etch step height with etch duration for a silicon oxide
substrate nitrided at 550 VV microwave power, 30 torr pressure for I hour.
Process parameters were varied to study the effect on the nitride quality and the
etch rate variation. Figure 14 shows the effect o f microwave power, pressure and
nitridation duration on the etch characteristics of nitrided silicon.
40
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
—
5 0 torr, 3 hr
3 0 torr, 1 hr
1 Hr
▲ 5 0 torr. 1 hr
3 0 torr, 3 hr
1 0 0 torr, 1 hr
Increasing
Pressure ▼
S3
S6
1 0 0 torr, 3 hr
0.4
400
600
800
1000
1200
Microwave Power (W)
Figure 14. Etch rate variation with various process parameters.
It can be seen that the nitride etch rate decreases with increasing microwave
power (i.e., increasing temperature) and pressure. Nitride etch rate also shows a drop for
nitrides obtained for longer nitridation runs. Etch rate decreases more with nitridation
duration than it does with increasing pressure. Etch rate variation with process parameters
can be explained on the basis o f varying magnitudes o f nitrogen species incorporation
into silicon. Low nitrogen plasma is modeled using SAMPR. Steady state composition o f
the plasma is determined. The actual modeling procedure is explained in APPENDIX A.
The results from the modeling are shown in Table 4.1.
41
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
Table 4.1
Summary of results of low-pressure nitrogen plasma modeling using SAMPR
Power 50 W
Power 250 W
Pressure, mTorr
Pressure, mTorr
N2+
N+
Mole Fraction
0.7981
0.89142
o
I Gas phase species
j
N2
1
j
N
40
o
10
Mole Fraction
0.511344
0.3336069
0.09378394
0.030664
0.2628131
0.0014769
0.000266469
0.01708923
j
0.36778469 j
i
0.005647811
5.35875E-08 8.62976E-08
3.07246E-08
l.l 1346E-07
N2V
0.0301223
0.05074615
0.007517449
0.05784593
N2E
0.07504978
0.0266406
0.1841469
0.2294044
' '
v' ■■■' ■ T
Gas temperature, K.
602.88537
579.66
940.25
1666.31
Electron Temp., eV
3.906
2.36
14.68
4.686
The plasma is modeled at pressures in millitorrs. much lower than the operating
pressures used in this work. But a general idea can be gathered that as the microwave
power is increased, the steady state mole fraction o f species N increases. Increasing the
pressure decreases the N mole fraction, but it increases the overall gas density, still
increasing nitrogen species incorporation. It was observed that the nitride etch rate shows
a greater drop with increasing process parameters, than the oxy-nitride etch rate.
42
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
E. Compositional Analysis Using X-Ray Photoelectron Spectroscopy
The composition o f the nitrides was also determined using angle-resolved XPS
(although Auger electron spectroscopy has a similar resolution with respect to
composition, it involves depletion o f first few angstroms o f the nitride).
Oxide thickness plays an important role in the fabrication o f micro- and nanoscale
structures using this process. With a very thin starting oxide for an oxide thickness less
than 10 nm, nitrogen species penetrate through the oxide and form silicon nitride beneath
the oxy-nitride, m aking the selective etching difficult. For a thicker starting oxide for an
oxide thickness greater than 30 nm, the oxide gets exposed to the etchant after the oxy­
nitride gets etched away. A difference in the etch rates o f silicon nitride and the oxide by
a factor o f about 2 makes selective etching very difficult. Figure 15 shows the N Is XPS
spectrum o f the nitride surface before sputtering. It can be seen that the peak binding
energy is about 398.5 eV. Figure 16 shows all the N Is spectra from a silicon sample
nitrided for 3 hours with 550 W o f microwave power at 30 torr pressure. The largest peak
is obtained from as prepared surface (before sputtering) and is at a higher binding energy
than the others obtained at various nitride depths.
43
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
5500 5 000 4500 i
e 400 0 V
3500
3000
2500 387
397
392
402
407
412!
Kinetic Energy, eV
Figure 15. N Is spectra of the nitride surface before sputtering.
5000
4500
<n 4000
8
3500
3000
2500
390
392
394
396
398
400
402
404
406
Kinetic Energy
Figure 16. N Is spectra at various nitride depths.
44
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
408
410
The reason for this shift could be some charging effect or some sort o f N-O
functionality on the surface. A typical XPS depth profile o f the same nitrided silicon
sample is shown in Figure 17.
100 -
80 -
60 -
Oxygen
Nitrogen
C arb on
Silicon
10 s
0
5
10
15
20
Depth (nm)
Figure 17. A typical XPS depth profile, showing the variation of N atomic
percentage with depth for a silicon substrate nitrided at 550 W microwave power,
30 torr pressure for 3 hours.
There was a considerable amount o f oxygen found throughout the nitride profile.
It is suspected that oxygen got incorporated in the time between nitridation and the
analysis (approximately 30 days). N concentration at the surface was found to be 8
atomic %, which dropped to zero at approximately 15 nm. The N Is binding energy was
45
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
found to be 397.9 eV. The value for stoichiometric silicon nitride is 397.4 eV [43].
Hence. N is present in the form of a nitride with O existing
mainly as a diffused
independent species. The bulk phase diagram o f the Si-N-O system has been studied, and
it has been found that the nitride and the oxide never coexist under equilibrium
conditions. They are always separated by the oxy-nitride [44], Hence a favorable
thermodynamics stability o f the oxide accounts for O incorporation in the nitride films.
Figure 18 shows the XPS depth
profile curve for a nitrided silicon
nitridation was performed at 550 W,
30 torr pressure for 3 hours.
100 -
"9
O
E
o
<
surface.The
•O x y g e n
90 -
- N itrogen
80 -
• C arbon
70 -
•S ilico n
♦
60 ♦ 50 40 30 ^
20 10 0 *=
0
3
4
Depth/nm
Figure 18. XPS depth profile, showing the variation o f N atomic percentage with
depth for a silicon oxide substrate nitrided at 550 W microwave power, 30 torr
pressure for 3 hours.
46
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
It can be seen that for a particular set o f process conditions, silicon nitride is
thicker than the silicon oxy-nitride. with less am ount o f nitrogen incorporation into the
oxide surface than in silicon. Nitridation was also performed on a (110) cut p-type Si. It
was found that the nitrides were thinner than those obtained with a (100) cut Si. The
amount o f nitrogen incorporation was more than that in (100) silicon. It was seen that the
nitride etch rate was less than the etch rate o f the nitride on (100) silicon. Further
experiments are needed to study the use o f ( 1 10) cut silicon as the starting silicon
substrate, to fabricate micro-scale and nanoscale structures on silicon. ( 1 10)-cut silicon
surfaces offer certain advantages such as obtaining near vertical trench walls after wet
etching.
F. Short Time Scale Wet Chemical Etching of Silicon/Silicon oxide/Silicon nitride
The nitride etch characteristics were determined by etching nitrided silicon
substrates with a 30 % aqueous KOH solution for varying lengths o f time. Etching was
also performed at very short time scales on the order o f < 50 sec. The etching behavior
and rate at which the material etches for such short etch time scales might be different
from those for long time etching. In this section thermally grown silicon oxide etching
results for short time scale etching are discussed and compared with the values obtained
for long time scale etching.
Silicon oxide substrate was etched using a 30 % (by weight) aqueous KOH
solution at 70 °C. The etch time scales were varied from 2-10 sec, to I-10 min. and to 1-6
hrs. The short time scale etching was performed, by dipping an oxide surface partially
47
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
into the etchant solution. The etching resulted in a nanometer scale step, height o f which
was measured using a white light interferometer. The minimum depth resolution o f this
instrument is 3
A.
Figure 19 (a) shows a 2-dimensional WYKO surface profile o f silicon
oxide after about 2.5 seconds of partial etching. The average step height was determined
by averaging the surface roughness on either sides o f the etch demarcation. A clearer
picture o f the etch step can be seen in the 3-dimensional surface profile (figure 19 d).
UqfL
X Profile
Nanoscale
x 0 635 m m
Im agin g
Facility
— ■•/*'''■f*s\
;
j
(b)
0 0
0 2
0 ■*
00
33
to
Y Profile
?:
(a)
*h// V \
v
(
A
t
'
'
r
\
i
i j
V
t £
(C)
Figure 19. (a) Top view of the silicon oxide surface after 2.5 seconds o f wet-chemical
etch, (b) Two-dimensional WYKO line profile in X-coordinates. (c) Twodimensional WYKO line profile in X-coordinates. (d) Three-dimensional
representation of the etched surface in (a)
48
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
1
(d)
Figure 19 (Continued)
Figure 20 shows a 2-dimensional WYKO surface profile o f silicon oxide after
about 1 minute o f partial etching. The average step height was determined by averaging
the surface roughness on either sides o f the etch demarcation. Figure 21 (a) shows the
etch step height variation with etch time for short etch time scales. The slope o f the linear
variation gives the etch rate. After short time etching, the oxide surface was etched for
longer durations by dipping the whole surface in the etchant bath at 70 °C. The etched
depth o f oxide was determined by taking the difference between the oxide thicknesses
before and after etching. The oxide thickness was determined using FILM ETRIX. The
longest etch time was 6 hrs. Figure 21 (b) shows the etch depth variation with etch time
for longer time scales.
49
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
UqfL
X Profile
Nanoscat*
X. 0 619 mm
im a g in g
Facility
fi
-H
-
|M
^
v
•
-- -------------
\
■a
Y 0 043 um
i
I
"Vj'
F '
&----------,-- --- --- —,----------- -------- -----------------
(b)
00
02
0 *
OS
03
to
1 ;
Y Profile
x.
555 4 um
(a)
(c)
Figure 20. (a) Top view of the silicon oxide surface after 40 seconds of wet-chemical
etch, (b) Two-dimensional WYKO line profile in X-coordinates. (c) Twodimensional WYKO line profile in X-coordinates.
50
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
80
70
E 60
c
y = 1 .6 8 9 6 x -0.3303
R2 = 0.9998 ^
O) 50
'55
z 40
Q.
OJ
CO 30
LU
20
10
0
0
10
30
20
40
50
20000
25000
Etch time (sec)
(a)
300
250
1 200
.c
1-150
Q
a 100
in
50
0
0
5000
10000
15000
Etch time (sec)
(b)
Figure 21. (a) Etch step height variation with etch time for scales of up to 1 minute,
(b) Etch step height variation with etch time for long time scales of up to 6 hours.
51
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
A summary o f silicon oxide etch study is shown in Table 2. It shows the decrease
in the oxide etch rate with etch time. The study yields three different etch rates with
decreasing magnitudes with longer etch time scales.
Table 4.2
Silicon oxide etch rates for different time scales of etching
!
Etch Time scale
Etch Rate,' nm/sec
Up to 1 minute
1.69
1 min-5 minute
0.043
6min-6 hrs
0.009
The bulk silicon oxide etch rate reported in literature is approximately 0.028
nm/sec [44]. It can be seen that the short etch time scale etch rate values determined are
on the orders o f magnitude higher than the reported longer time scale etch rate value.
The results shown in Table 2 are significant outcomes o f this study. For nanoscale
lithography involving wet chemical etching, short time scale etching becomes significant.
The reported etch rate values remain no longer valid for short time scale etching. For
example, an empirical relation giving etch rate o f silicon oxide as a function o f etchant
concentration and temperature has been reported as [45]
R = 2.2 x 1CF Wr(l .5 x 1O'4 W 215 + I)e x p - (0.795 + 6 x 10 '6 fF 25) / k (T + 273)
52
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohib ited w ith o u t p e r m is s io n .
(4.18)
Where R is the etch rate in microns per hour, W is the weight % o f KOH in water, k is
Boltzm ann’s constant o f 8.617x10'' eV/K. and T is temperature in degrees Celsius.
It can be seen that the activation barrier is proportional to KOH concentration.
Hence the lower the etchant concentration, the lower the activation barrier, and hence
higher the resistance due to diffusion.
Assuming that the etching reaction is mass transport limited, a theoretical model
is developed to estimate the effect o f nanometer scale roughness on the etch rates, in
order to explain the observed discrepancy in measured etch rates and the reported values
a theoretical analysis is developed. It is assumed that the surface roughness consists o f
small mounds, which are spherical in curvature, with a radius R and a solid angle o fQ .
The center o f the imaginary sphere is considered as the reference level for the analysis.
Consider the substrate surface with roughness mound as shown in Figure 22.
z=L
Q/2
z=0
Figure 21. Substrate surface with a spherical roughness mound.
L is the distance o f the reference level from the surface. £ represents the surface
roughness. Here, only one mound out o f a number o f roughness mounds will be
considered, and the theoretical etch rates will be determined.
53
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
The etchant species diffuse from the bulk etchant solution, and react at the
substrate surface. The etch products diffuse back into the bulk solution. Under mass
transport limitation regime, the chemical reaction offers minimal (or zero) resistance to
etching. Hence the reactant species concentration at the substrate surface is zero.
To study how the radius o f the imaginary sphere changes with time, the rate o f
out-diffusion o f etched product species from the substrate surface is determined. Next, a
mole balance on the substrate material is carried out. Since diffusion is the dominant
mechanism, a mass transfer boundary layer gets developed over which the concentration
o f etched species drops from the surface concentration, C As to 0 in the bulk etchant
solution.
Using the spherical coordinate system, a mole balance over the increment Ar
located somewhere between r=R and r=R+5, can be written as
[rate in] —[rate out] + [rate o f generation] = [rate o f accumulation]
W.r4
m-\I r
1
tr
ir-Ar
=0
d ( r 2WAr)
=0
dr
(4.19)
(4.20)
Assuming that for every mole o f species A, which diffuse into the boundary layer,
one mole o f etch products diffuse out, that is equimolar counter diffusion.
54
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Therefore,
W,. = - d *C a
dr
dr
, dCs
dr
(4.21)
=
0
(4.22)
The boundary conditions are.
At r=R+5. CA=0
r=R. C\= C..\s
Solving the above equation,
r
•)
- C« R R + S - I
c*
(4.23)
And.
IVAr = De
C /?(/? + <5)
r'S
(4.24)
Carrying out an overall balance on the substrate material,
xR’p .1/
r ’ 4xR- =-
(4.25)
dt
Where, Pm is the molar density o f the substrate material
55
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Therefore,
dR
. .
—
=
rM
1P\r
dt
(4.26)
The rate o f disappearance o f substrate material is equal to the flux o f etchant species to
the etchant-substrate interface:
- r 1/” = - W ArA \ r = R = D
C as(R + S)
RS
(4.27)
Therefore.
d R = D Cm (R + S)
dt
R p uS
dR_
=a ( /? + S )
dt
R
dR
5'
= a H---dt
R
(4.28)
Where.
a = 0£*
Pu<5
And dR/dt is the etch rate in nm/sec. From the above equation, it is evident that the radius
o f the imaginary sphere increases with time at a decreasing rate.
56
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
For planar portion o f the surface, the etch rate can be shown as constant under
mass transfer lim ited etching as shown below.
dL
— =-a
dt
(4.29)
Thus the planar portion etches at a constant rate, which is (1+5/R) a tim e less than the
rate at which the rougher part, i.e, the spherical mound etches.
The surface roughness,
s = R -L
The rate o f change o f surface roughness can be represented as
d s _ dR dL_
dt
dt
dt
de
=a 2 +
dt
R
(4.30)
Hence, it can be seen that the surface roughness reduces with tim e at a rate on the
order o f 5/R times the etch rate o f the smoother portion o f the surface. The rate at which
the surface roughness reduces increases over the course o f etching, until the radius o f the
surface roughness mound reduces to zero.
Upon doing an order o f magnitude analysis with boundary layer thickness on the
order o f microns, it was found that the short time scale etch rate represented by de/dt was
about 10 - 1000 times more than the longer etch time scales, dL/dt, with a boundary layer
thickness in the order o f microns. For the boundary layer thickness to be in the order o f
57
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
microns, etched product concentration has to be between 10"4 and 10° MoI/mJ with the
diffusion coefficient between I O'9 and I0‘8 m2/s. These etched product concentration
values are estimated using the short time scale etch rate values. These values seem
realistic as the etched product concentration is expected to be very low in the mass
transfer boundary1 layer. The diffusion coefficient values are o f the same order o f
magnitude as those for some o f the common aqueous solutions. Thus the experimentally
observed etch rate values for short time scale etching agree with the theoretical values
obtained as a function o f surface roughness.
58
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n pro hibited w ith o u t p e r m is s io n .
CHAPTER 5
CONCLUSIONS
A novel nitridation process is demonstrated for the fabrication o f nanoscale and
microscale structures on silicon substrates. In this process, the oxide patterned silicon
substrates are nitrided using microwave nitrogen plasma, which upon subsequent wet
chemical etching, result in complementary patterns on the silicon surface.
The direct nitridation using atomic nitrogen produced the necessary etch
selectivity, defined as the ratio o f etch rates, for wet chemical etching o f patterned silicon
substrates to result in micro- and nanoscale structures.
• The etch selectivity between silicon nitride and silicon was 10 or more.
• Silicon nitride etches about twice as slow as the oxynitride.
The etch selectivity depends on the nitridation process parameters.
•
It was found that the silicon nitride etch rate decreases with increasing microwave
power, pressure and for longer nitridation runs.
•
The oxynitride etch rate does not show as much significant variation with process
parameters.
X-ray
photoelectron
spectroscopy
analysis
shows
fractional
nitrogen
incorporation into silicon and silicon oxide substrates, which was also supported by a
simplified thermodynamic analysis. The resulting nitride was found to be thicker than the
oxy-nitride for a particular set o f process conditions. However, there was a significant
amount of oxygen incorporation into the nitride films, over a period o f time.
It was found that the starting oxide thickness is a critical factor for obtaining silicon
nitride etch mask pattern.
59
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
CHAPTER 6
RECOMMENDATIONS
Despite the success o f direct nitridation process used to fabricate micro- and
nanoscale structures on p-type (100) silicon surface, the following suggestions are made
in order to further understand and develop this technique.
1. Experiments can be performed on (110) and (111) cut silicon substrates.
2. RF bias can be applied to the silicon substrate in order to increase the flux of
nitrogen plasma species reaching and diffusing into the surface.
3. There should be a provision to measure the absolute temperature to understand the
direct variation o f nitride quality and etch rates.
4. A quick set o f nitridation experiments can be done in ECR plasma CVD reactor to
observe the growth o f nitride. Unlike in the MWCVD reactor, ECR CVD operates
at much lower pressures and temperatures with a provision for increasing the
nitrogen species flux reaching the surface.
5. Dry etching as well as wet etching studies using other common etchants such as
Buffered Oxide Etch (BOE) can be performed to optimize the perform ance o f this
technique to produce high aspect ratio structures.
6. Detailed studies can be done to understand the effect o f nitridation parameters
upon selective etching. Higher magnitude o f selectivity in etching result in almost
vertical and high aspect ratio features on silicon.
60
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
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F.S-S,
Wu, C-L, Chou,
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23. Chien, F.S-S, Chang, J-W, Lin, S-W, Chou, Y-C. Chen, T.T.. Gwo. S.. Chao. T-S,
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28. De Ridder. R.M., Worhoff, K., Driessen, A., Lambeck. P.V., "Silicon oxy-nitride
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29. Ensinger, W„ Volz, K... Schrag, G., Stritzker. B., Rauschenback, B., "Form ation of
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30. Izumi, A., Matsumura, H., "Low-temperature nitridation of silicon surface using
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34. Takami. S.. Egashira. Y., Honma, I., Komiyama, H., “Monolayer nitridation o f
silicon surfaces by a dry chemical process using dimethylhydrazine or ammonia”.
Appl. Phys. Lett. 66 (12), p. 1527 (20 March 1995).
35. Paloura, E.C., Lagowski, J., Gatos, H.C., “Growth and electronic properties o f thin
SisNj films grown on Si in a nitrogen glow discharge”, J. Appl. Phys. 69 (7). p. 3995
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40. Briggs. D., Handbook o f X-Ray and Ultraviolet Photoelectron Spectroscopy, p. 153,
Heyden. London, 1978.
41. Frazer, W.A., Florio, J.V., Delgass, W.N.,
Robertson, W.D., Surf. Sci. 36, p.661
(1973).
42. Janaf Thermochemical Data, J. Phys. Chem. Ref. Data, 14, Suppl. 1, 1985.
65
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43. Moulder, J.F., Stickle, W.F., Sobol, P.E., Bomben, K.D., Handbook o f X-ray
Photoelectron Spectroscopy, Jill Chastain, ed. (1992, Perkin Elm er Corp. Physical
Electronics Div, Eden Prairie, MN).
44. Gusev, E.V.. Lu, H-C, Garfimkel. E.L., Gustafsson, T.. Green, M.L., “Growth and
characterization o f ultrathin nitrided silicon oxide films”. IBM J. Res. Develop. 43
(3). p.265 (May 1999).
45. Rai-Chowdhury,
P.,
Handbook
of
Microlithography,
M icromachining
and
Microfabrication: Handbook o f Microlithography (Materials and Devices Series, 1),
February 1997, fnspec/'IEE. p. 57.
46. Meyyappan, M., Govindan, T.R.. SAMPR: A computer code for simple analysis o f
materials processing reactors, NASA Research Publication 1402, April 1997.
47. Meeks. E., Larson, R.S., Vosen. S.R.. Shon, J.W., "Modeling Chemical Downstream
Etch Systems for N F3/02 Mixtures". Journal o f the Electrochemical Society 144. p.
357 (1997).
66
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
APPENDIX A
Lou Pressure Nitrogen Plasma Modeling
In the nitridation scheme proposed in this thesis, the nitrogen species N+, N. N?".
etc.. penetrate the surface with enough energy; break the bonds in the silicon substrate
through collisions, forming stable silicon nitride. A Langmuir probe can be employed in
order to physically determine the fluxes o f these nitrogen species in the gas phase
reaching the substrate surface. Presently, there is no provision for a Langmuir probe in
the microwave CVD reactor used for nitridation. But theoretically, nitrogen plasma can
be modeled to yield the plasma composition and various other parameters such as the gas
and electron temperature.
There have been efforts to model nitrogen plasma at low pressures. A computer
code for simple analysis o f materials processing reactors (SAM PR) has been developed
by Dr. Meyyappan et al. at NASA. Ames [46].
SAMPR has been developed for the analysis o f plasma and non-plasma processes
used in semiconductor processing. The model involves mass and energy (gas and plasma)
balance. This code represents a zero-dimensional analysis, in which the balance equations
are reactor volume-averaged. The reactor contents are assumed to be perfectly mixed as
in continuous stirred tank reactors used in chemical industry. The SAM PR code yields
volume-averaged electron density, electron temperature, and radical and ion
concentrations at various reactor parameters. A summary o f the equation solved by
SAMPR is shown in Table A 1.
67
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Table A-1
Summary of various equations used by SAMPR in order to model low
pressure nitrogen plasma
Equation
<*.>•,,. -.1-,) + VM, 2 +
/
AM ,£
k
\
I
1
1
i
(q k I - One, AP,
-i
^
- r ,) -
,ff>,+0.5fc£)=0
!
i
Description
Species Mass Conservation
Where, the subscript in denotes
inlet conditions. I is the total no. o f
neutral and ionic species, yi is the
mass fraction o f species i: pi is the
mass density o f species i M j is the
molecular weight: R,j is the molar
homogenous reaction rate o f
species i in the reaction j; Sjk is the
molar heterogenous reaction rate o f
species i in surface reaction k.
Electron Energy Balance
Where, Q is the flow rate, is the
electron mean thermal energy. IV is
Avagadro number. R^j is rate o f
electron impact reaction j, Hj is the
corresponding threshold energy, m
is mixture-averaged mass, vci is the
elastic collision frequency, and Tc
is the electron wall flux.
i
P Vc p
d'
= (me p Tg ) m
3( m c / m )v w
Gas Energy Balance
Where, cp is the mixture specific
heat, / j , is the species enthalpy per
unit mass, vce is the charge
exchange collision frequency, T+ is
ion temperature, U is the overall
heat transfer coefficient, and Ta is
the ambient temperature. This
equation represents sensible heat
associated with gas inflow and
outflow, heat gain through electrongas elastic collisions, heat gain
from charge exchange collisions
with ions, heat o f all other chemical
reactions and the heat losses.
me p Tg +
^k ( T t - Tg ) +
v „ V n . 3 / 2 k ( T , - T g)
+ l ' Y . h ; M . T . R .i - U A i T s - T J
t
/
68
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
SAMPR is used in order to determine the steady state conditions o f low-pressure
nitrogen plasma. The gas and electron energy equations are also solved to yield the gas
and electron temperatures.
The logical variables ESOLVE and TSOLVE are set to TRUE in order to solve
the energy equations. The reactor pressure is specified in milli-torrs. The module has not
yet been tested for higher-pressure reactor systems. The inlet flow rates o f all the species
have to be specified. The reactor parameters such as length, diameter, etc.. also have to be
specified. Deposition power to the plasma has to be input. Various heat losses taking
place in the reactor system play important role in the determination of the steady state
conditions. The thermodynamic data for the nitrogen plasma species was obtained from
JANAF [42],
The original SAMPR code could not solve for the gas and electron temperatures,
as dummy thermodynamic data was input. This feature was activated by putting in the
thermo-chemical property data fit coefficients obtained from Meeks et al [47], Some o f
the data was obtained from the thermodynamic database included in CHEMKIN package.
The chemical reaction rate data was obtained from the SAMPR data files provided by Dr.
Meyyappan. Following chemical reaction set was used in the theoretical analysis.
1.
2.
j.
4.
5.
6.
7.
8.
9.
10.
N + N + M > N 2 + M a = 2.61 e 15
N2 + e- > N2+ + 2 e- eth=15.6
N2 + e- > 2 N + e- eth=12.0
N2 + e- > N+ + N + 2 e- eth=18.5
N2 + e- > N2V + e- eth=0.29
N2 + e- > N2V + e- eth=0.59
N2 + e- > N2V + e- eth=0.88
N2 + e- > N2V + e- eth= 1.17
N2 + e- > N2V + e- eth =1.47
N2 + e- > N2V + e- eth=1.76
69
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p roh ibited w ith o u t p e r m is s io n .
11. N2 + e- > N2V + e12. N2 + e- > N2V + e13. N2 + e- > N2E + e14. N2 + e- > N2E + e15. N2 + e- > N2E + e16. N2 + e- > N2E + e17. N2 + e- > N2E + eIS. N2 + e -> N 2 E + e19. N2 + e- > N2E + e20. N2 + e- > N2E + e21. N2 + e- > N2E + e22. N2 + e - > N2E + e23. N2 + e - > N2E + e24. N2 + e - > N2E + e25. N2 + e - > N2E + e-
eth=2.06
eth=2.35
eth=6.17
eth=7.0
eth=7.35
eth=7.36
eth=7.8
eth=8.16
eth=8.4
eth=8.55
eth=8.89
eth = ll.0 3
eth=11.88
eth=12.25
eth= l3.0
Where N 2E and NNv are the electronically and vibrationally excited species
respectively, eth is related to threshold energy to compute energy loss after each inelastic
collision. Various parameters used in the iterative solution o f the differential equations
were also input. Pressure and microwave input power was changed to see the effect on
steady state plasma composition.
A summary o f results is shown in Table A.2.
As the pressure increases, molecular nitrogen increases as the recombination
reactions increase with pressure. But as the microwave pow er is increased molecular
dissociation takes over. Also, molecular ionization reduces with increasing pressure,
evident by a decrease in N 2+- Rate o f molecular ionization is many magnitudes more than
that o f atomic ionization. But as the pressure increases, atomic ionization increases.
Increasing pressure increases vibrational excitation, but at the same time reduces the
electronic excitation. Electronic excitation increases with pressure at higher microwave
powers. Gas and electron temperatures also reduce with increasing pressure.
70
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Table A-2
A Summary of results from SAMPR
|
P ow er 50 W
P ow er 2 5 0 W
P ressu re, mTorr
P r essu re, mTorr
|
10
10
40
40
i
M ole Fraction
;G as p h a s e s p e c ie s
M ole Fraction
:
0.7981
0 .8 9 1 4 2
0 .5 1 1 3 4 4
0 .3 3 3 6 0 6 9
0 .0 9 3 7 8 3 9 4
0 .0 3 0 6 6 4
0 .2 6 2 8 1 3 1
0 .3 6 7 7 8 4 6 9
N2+
0 .0 0 1 4 7 6 9
0 .0 0 0 2 6 6 4 6 9
0 .0 1 7 0 8 9 2 3
0 .0 0 5 6 4 7 8 1 1
N+
5 .3 5 8 7 5 E -0 8
8 .6 2 9 7 6 E -0 8
3 .0 7 2 4 6 E -0 8
1 .1 1 3 4 6 E -0 7
N2V
0 .0 3 0 1 2 2 3
0 .0 5 0 7 4 6 1 5
0 .0 0 7 5 1 7 4 4 9
0 .0 5 7 8 4 5 9 3
N 2E
0 .0 7 5 0 4 9 7 8
0 .0 2 6 6 4 0 6
0 .1 8 4 1 4 6 9
0 .2 2 9 4 0 4 4
1
N2
:
!
,
N
i
: \ ’ "
G a s tem peratu re, K
E lectron T em p ., eV
6 0 2 .8 8 5 3 7
5 7 9 .6 6
9 4 0 .2 5
1 666.31
3 .9 0 6
2 .3 6
1 4 .6 8
4 .6 8 6
As the microwave power is increased, molecular nitrogen decreases as the
molecular ionization increases as evident by an increase in the N;T mole fraction.
M olecular dissociation increases, raising the N mole fraction. Also, the atomic ionization
is suppressed by the molecular ionization. But it increases as the pressure is increased.
Increasing microwave power increases electronic excitation, at the same time reducing
the vibrational excitation. Gas and electron temperatures increase with increasing
microwave power. The absolute values o f the gas temperatures seem high compared to
those observed physically. SAMPR does not take into account heat losses to the
surroundings, resulting in higher temperature readings. It also does not consider the
71
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
interaction o f gas phase species and the surface. There are no surface species specified in
the input file. It was seen that as the pressure is increased the gas temperature decreases.
This may be due to the fact that at high pressures the exothermic reactions in the reaction
set are suppressed and the endothermic reactions take over. Increasing the microwave
power increases the electron temperature due the increase in electron impact reactions.
A sample SAMPR output file is shown at the end o f this discussion.
To get a more realistic idea o f the gas and electron temperatures, AURORA
module o f the CHEMKIN software package was used to model the low-pressure nitrogen
plasma. This module solves various material and energy balance equations similar to
those solved in SAMPR. The AURORA module accounts for the finite rate elementary
reactions both in the gas phase and on the surface. The reactor model assumed in this
program is that o f a perfectly stirred reactor (PSR). The model combines surface
reactions and neutral chemistry and also the electron impact reactions along with global
plasma modeling approach. The approach includes mass and energy balances. The energy
balance includes both gas and electron energy balances taking into account various
energy losses in the system. The program considers both the gas phase and surface
kinetics. In AURORA, keywords ENRG and ENGE are used. In this case, the modules
solve for steady states at constant input power instead o f constant temperature (as in the
case o f TGIV keyword). Initial estimates o f the gas temperature, ion temperature (which
is assumed to be equal to the gas temperature), electron temperature, surface temperature
(assumed to be same as the gas temperature), have to be specified. The reactor pressure is
specified in millitorrs. This module also has not yet been tested for higher-pressure
reactor systems. The inlet flow rates o f all the species have to be specified. The reactor
72
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
parameters such as volume, diameter, etc., also have to be specified. Deposition power to
the plasma has to be input. Various heat losses taking place in the reactor system play
important role in the determination o f the steady state conditions.
AURORA requires information about the gas and surface phase species and
chemistry. Chemkin and surface linking files are needed to execute the AURORA
program successfully.
The thermodynamic data is taken from the thermodynamic
database included in the CHEMKIN package. Following reaction chemistry set was used
for the modeling.
A
b
N + N + M = N2 + M
I.414E-32
0.
E + N2 = > N 2 + E
1.0099E-03 -1.0949E+00
EXCI/ 0.02/
E + N2 = > N 2 + E
5.1699E-13 6.1113E-01
N2 Vibrational Excitation
EXCI/ 0.29/
E + N2 = > N 2+ E
5.9840E-01 -1.7665E+00
N2 Vibrational Excitation
EXCI/ 0.29/
E + N2 = > N 2 + E
2.573IE-01 -1.7326E+00
N2 Vibrational Excitation
EXCI/ 0.59/
E + N2 = > N 2 + E
4.4889E-01 -1.8499E+00
N2 Vibrational Excitation
EXCI/ 0.88/
E + N2 => N2 + E
6.5681E-02 -1.6467E+00
N2 Vibrational Excitation
EXCI/ 1.17/
E + N2 = > N 2 + E
8.1622E-02 -1.6959E+00
N2 Vibrational Excitation
EXCI/ 1.47/
E + N2 => N2 + E
2.0737E+00 -2.0502E+00
N2 Vibrational Excitation
EXCI/ 1.76/
E + N2= > N 2 + E
1.4520E+01 -2.3412E+00
N2 Vibrational Excitation
EXCI/ 2.06/
E + N2 = > N 2 + E
7.2326E-01 -2.0862E+00
N2 Vibrational Excitation
e
0.
1.7337E+04
5.3449E+03
2.1980E+04
2.2322E+04
2.2634E+04
2.3254E+04
2.3667E+04
2.5621E+04
2.7118E+04
2.7851 E+04
73
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n pro hibited w ith o u t p e r m is s io n .
E X C I/2.35/
E + N t => N t + E
N: Excitation
E X C I/6 .17/
E + N; => N2 + E
N: excitation
EXCI/ 7.00/
E + Nt => NN + E
N2 excitation
EXCI/ 7.35/
E + N 2 => N 2 + E
N 2 excitation
EXCI/ 7.36/
E + N2 => N2 + E
N'2 excitation
EXCI/ 7.80/
E + N 2 —-> N 2 + E
N'2 excitation
EXCI/ 8.16/
E + NN => NN +■ E
N 2 excitation
EXCI/ 8.40/
E + N2 => N: + E
N'2 excitation
EXCI/ 8.55/
E + N2 => N2 + E
N 2 excitation
EXCE 8.89/
E + N 2 =-> N 2 ■+■E
NN excitation
EXCL/11.03/
E + N2 => N: + E
N 2 excitation
EXCI/11.88/
E + N 2 =-> N 2 ■+■E
N2 excitation
EX CI/12.25/
E + N2 => N: + E
N2 excitation
EXCI/13.00/
E + N2 => N2+ + 2E
5.6495E-21
2.1658E+00 2.9055E+04
7.4823E-21
2.2745E+00 3.1907E+04
2.6692E-19 2.0594E+00 3.3573E+04
4.8449E-21
2.4I58E+00 3.23 32E+04
1.2157E-21
2.4398E+00 3.5358E+04
9.7236E-22 2.4598E+00 3.6081 E+04
9.1888E-22
2.4457E+00 3.7463 E+04
3.5894E-22 2.6305E+00 3.7012E+04
5.1845E-21
2.3116E+00 4.0490E+04
2.8765E-27 3.8281E+00 3.7962E+04
6.0906E-33
4.5247E+00 3.5432E+04
3.4764E-32
4.5557E+00 3.7072E+04
2.0173E-34
5.2876E+00 3.6200E+04
2.5615E-43
7.0658E+00 3.1481 E+04
n 2 io n iz a t io n
E + N => N + E
N excitation 4p-3s
EXCI/I0.33/
4.5735E-24 2.9872E+00 4.5365E+04
74
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
E + N => N + E
N excitation 4p-2p4
EXCI/'10.92/
E + N => N + E
N excitation 2D0-2p3
EX C I/2.38/
E + N => N + E
N excitation 2P0-2p3
EXCI/ 3.57/
E + N => N + E
N excitation 2P-3p
EXCI/10.68/
E + N => N + E
N excitation 2S0-3p
EXCI/11.60/
E + N => N + E
N excitation 4D0-3p
EXCI/11.75/
E + N => N + E
N excitation 4P0-3p
EXCI/11.84/
E + N => N + E
N excitation 4S0-3p
EXCI/11.99/
E + N => N + E
N excitation 2D0-3p
EXCI/12.00/
E + N => N + E
N excitation 2PO-3p
EXCI/12.12/
E + N => N + E
N excitation 2p-3d
EXCI/12.97/
E + N => N + E
N excitation 4F-3d
EXCI/12.98/
E + N => N + E
N excitation 2F-3d
EXCI/12.99/
E + N => N + E
N excitation 4F-3d
EXCI/12.99/
E + N => N + E
N excitation 4D-3d
EXCI/I3.01/
E + N => N + E
3.1169E-30 4.3697E+00 3.3085E+04
6.6I20E-02 -I.I422E + 00 2.5550E+04
3.866IE-03 -1.0324E+00 3.4755E+04
2.2374E-2I
2.3442E+00 5.0639E+04
2.4480E-29 4.0041E+00 3.7084E+04
4.235IE-31
4.2666E+00 3.6427E+04
1.8714E-35 5.2822E+00 3.4I68E+04
4.5728E-30 4.0970E+00 3.7647E+04
9.7994E-31 4.1875E+00 3.7772E+04
2.I845E-30 4.2142E+00 3.8395E+04
2.59I6E-32 4.5913E+00 3.9470E+04
1.0292E-33 4.7754E+00 3.8617E+04
7.8858E-33 4.5971 E+00 3.9485E+04
3.9622E-38 5.7953E+00 3.6229E+04
1.4103E-33 4.7450E+00 3.9233E+04
I.0584E-32 4.5682E+00 4.0117E+04
75
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
N excitation 2D-3d
EXCI/13.03/
E + N => N + E
N excitation 4p-ns
EXCI/13.70/
E + N => N + + 2E
N IONIZATION
I.2475E-39 6.0655E+00 3.8618E+04
5.1110E-37 5.7818E+00 4.7602E+04
A summary o f the results from CHEMKIN modeling is shown in Table A.3. The
steady state gas species densities and other steady state properties calculated from
CHEMKIN and SAMPR are significantly different. It can be seen that the reaction
chemistry set used by SAMPR and CHEMKIN are different. CHEMKIN does not
recognize the vibrationally and electronically excited species whereas these are
considered in SAMPR. Also, certain reactions such as reaction # 3 and 4 are not
considered in CHEMKIN modeling. This affects the solution o f various mass balance
equations. Also, in CHEMKIN dataset, there are atomic excitation reactions, included
which account for a significant difference in the steady state mole fractions given out by
the two modules. The gas and electron temperatures given by CHEMKIN are close to
physical observation. In SAMPR surface reactions are not considered whereas
CHEMKIN module considers surface reactions.
76
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
Table A-3
A summary of the results from CHEMKIN/AURORA
Power 50 W
j
1
Pressure, mTorr
Pressure, mTorr
10
40
o
|
i
!1
Power 250 W
o
j Gas phase species
|
j
Mole Fraction
Mole Fraction
N2
0.999844429 0.99998688
N
1.55571E-20
1.80798E-19 1.48784E-20 2.75441 E-20
N2+
0.000155571
1.31198E-05 0.002436605 8.93958E-05
N+
8.6665E-21
1.51998E-19 8.01061E-19
1.57815E-20
N2V
*
*
*
*
N2E
*
*
*
*
■ y
0.99512679
0.999821208
'
Gas temperature, K 335.79
309.3
901.3
375.24
Electron Temp., eV 3.48
2.82
4.58
2.97
This theoretical analysis was done at low pressures in the range o f tens o f
millitorrs. At such low pressures, the reactions taking place in the gas phase are
essentially the electron-species impact reactions, resulting in ionization and excitation
(vibrational and electronic) as shown above in the chemical reaction set. The pressure
dependence o f the reaction rate data is also not explored. At higher pressures, the gas
phase reaction chemistry changes, and some other reactions become significant. These
77
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
reactions include atom-molecule, molecular dissociation, recombination, ion-atom, ionmolecular. ion-ion reactions. And hence there will be a larger reaction chem istry set
required to model such plasma. Also, at higher pressures the assumption o f a perfectly
stirred tank reactor has to be evaluated critically, and it might lose the validity at certain
high pressures.
A S am p le S A M PR O u tp u t File
SAMPR
SIMPLE ANALYSIS OF MATERIALS PROCESSING
REACTORS
VERSION 2 .1 October 30. 1997
SREAD1
plasma = .true.,
esolve = .true.,
tsolve = .true..
SEND
SREAD2
igeom = 2.
radius = 1.25.
cleng = 10.0,
nw f = 0 .
warea = 0.0,
nrwall = 1.
SEND
SREADS
press = 10.0.
power = 50.0,
tempgas = 350.0,
tempwl = 350.0,
tem pw f = 350.0,
tinlt = 300.0,
eldens = 2.0el 1, eltemp = 2.0, eltin = 0.0,
SEND
SREAD4
ecinp(l) = 3, ecfq( 1) = 7.08el9,
78
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
chexcr(3) = 6.0e-15,
thcon = 5.0e-5,
glcorr = .true.,
SEND
SREAD5
p\vall(2) = 1.0e-l. asurf( 1.2) = 0.5,
p\vall(3) = 1.0,
asurf( 1.3) = 1.0.
pwall(4) = 1.0.
asurf(2.4) = 1.0,
pwall(5) = 1.0,
asurf( 1.5)= 1.0,
pwall(6) = 1.0,
asurf( 1,6) = 1.0,
SEND
SREAD6
nt = 1000000. dtmin = 1.0e4 . dt = 1.0e4. dtmax = 1,0e4.
dtfac(7) = I.0e6,I.0e6.
gues\vf( 1) = 0.9,0.50e-1,1.0e-3.1,0e-3.1,0e-2.1.0e-2.
SEND
SREAD7
isscnt = 500,
SEND
SPECIES MW
FLOW
DBASE
N2
28.0
100.0
input
N
14.0
0.0
input
28.0
0.0
N2+
input
N+
14.0
0.0
input
N2V
28.0
input
0.0
N2E
28.0
0.0
input
END
SJANAFNL
aispec( 1,1.1) = 2.99.
aispec( 1,2,1) = 3.29,
aispec( 1.1.2) = 2.45,
aispec( 1,2.2) = 2.50,
aispec( 1.1.3) = 3.59,
aispec( 1.2.3) = 3.78.
aispec( 1.1.4) = 2.51.
aispecf 1,2,4) = 2.80,
aispec( 1,1,5) = 2.5,
aispec( 1,2.5) = 2.5,
aispec( 1,1,6) = 2.5,
aispec( 1.2.6) = 2.5,
aisp ec(2 ,l,l) = .Ole-2,
aispec(2,2,1) = ,0825e-2,
aispec(2.1,2) = 1.07e-4,
aispec(2,2,2) = -.0218e-3,
aispec(2,l,3) = 2.53e-4,
aispec(2,2,3) = -2.06e-3,
79
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
aispec(2,l,4) = 3.46e-6,
aispec(2,2,4) = -1,45e-3,
aispec(l,l,5) = 2.5,
aispec(3.1,1) = -.056e-6,
aispec(3,2,1) = -.0 8 14e-5,
aispec(3,l,2) = -,0747e-6,
aispec(3.2,2) = ,0542e-6,
aispec(3,l,3) = 1.85e-7,
aispec(3,2.3) = 4.76e-6,
aispec(3.1.4) = -1,59e-8,
aispec(3.2,4) = 2.77e-6.
aispec(4,l,l) = -,0923e-10,
aispec(4,2.1) = -,0948e-9,
aispec(4.1,2) = .0188e-9,
aispec(4,2.2) = -,0565e-9,
aispec(4.1,3) = -4.55e-11,
aispec( 4.2.3) = -3.16e-9.
aispec(4.1.4) = 7.25e-12,
aispec(4,2,4) = -2.40e-9,
aispec(5,l.l) = ,158e-14,
aispec(5,2,l) = ,0413e-l 1,
aispec(5,1,2) = -. 10 3 e-14,
aispec(5.2,2) = ,021e-12,
aispec(5.1.3) = 3.27e-15.
aispec(5.2.3) = 6.71e-13,
aispec(5.1.4) = -6.45e-16,
aispec(5.2.4) = 7.81 e - 13,
aispec(6,1.1) = -.0835e4,
aispec(6,2,1) = -. 101 e4.
aispec(6,l,2) = .056 le6,
aispec(6,2,2) = .056 le6,
aispec(6,l,3) = 1.8e5,
aispec(6,2,3) = 1.81 e5,
aispec(6,l,4) = 2.26e5,
aispec(6.2.4) = 2.26e5,
aispec(7,I,I) = -.136el,
aispec(7,2,l) = -3.29,
aispec(7,l,2) = 4.45,
aispec(7,2,2) = 4.17,
aispec(7,l,3) = 3.1,
aispec(7,2,3) = 2.69,
aispec(7,l,4) = 4.93,
aispec(7.2,4) = 3.58,
SEND
REACTIONS
N + N + M > N2 + M : ir=2 a = 2.61 e 15
80
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
N2 + e > N2+ + 2e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2+ie=l
eth=15.6
N2 + e > 2N + e
:ir=3 input=/sw/home/shashank/sampr/runtest/n2-n ie=l eth=12.0
N2 + e > N+ + N + 2e :ir= 1 a = 1.Oe-13 ie= 1 eth= 18.5
N2 + e > N2V + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2vl ie=l eth=0.29
N2 + e > N2V + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2v2 ie= l eth=0.59
N2 + e > N2V + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2v3 ie= l eth=0.88
N2 + e > N2V + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2v4 ie= l eth= 1. 17
N2 + e > N2V + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2v5 ie=l eth=1.47
N2 + e > N2V + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2v6 ie=l eth=L76
N2 + e > N2V + e :ir=3 input=/s\v/home/shashank/sampr/runtest/n2-n2v7 ie=l eth=2.06
N2 + e > N2V + e :ir=3 input=/sw/horne/shashank/sampr/runtest/n2-n2v8 ie=l eth=2.35
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2el ie=l eth= 6.17
N'2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e2 ie=l eth=7.0
N'2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e3 ie=l eth=7.35
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e4 ie= l eth=7.36
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e5 ie=l eth=7.8
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e6 ie=I eth=8.16
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e7 ie= l eth=8.4
N2 + e > N2E + e :ir=3 input=/s\v/home/shashank/sampr/runtest/n2-n2e8 ie=l eth=8.55
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2e9 ie=l eth=8.89
N2 + e > N2E + e :ir=3 input=/s\v/home/shashank/sampr/runtest/n2-n2el0 ie=l
eth=l 1.03
N2 + e > N2E + e :ir=3 input=/s\v/home/shashank/sampr/runtestyn2-n2el 1 ie= l
eth=l 1.88
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/nintest/n2-n2el2 ie=l
eth= 12.25
N2 + e > N2E + e :ir=3 input=/sw/home/shashank/sampr/runtest/n2-n2el3 ie=I
eth=13.0
END
SPECIES INFORMATION
NO. SPECIES SYMBOL MOLEC. WT. REF. MASS FRAC
SOURCE CHARGE
H298(cal/mole)
1 N2
7.897115E-01
2 N
1.129506E+05
3 N2+
3.617762E+05
4 N+
4.506327E+05
5 N2V
I.481060E+03
28.000
14.000
28.000
14.000
28.000
1-000000E+00
0.000000E+00
O.OOOOOOE+OO
O.OOOOOOE+OO
1.OOOOOOE+02
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO
REF. FLOW
INPUT
INPUT
INPUT
INPUT
INPUT
81
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e rm is s io n .
0
0
1
1
0
DATA
6 N2E
28.000 O.OOOOOOE+OO O.OOOOOOE+OO
1.481060E+03
REACTION RATE COEFFICIENTS
K(T) = A T**B EXP(-C/T)
2J
IR
I
2
J
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
2
j
j
1
j
j
j
j
j
j
j
3
3
j
j
j
j
j
j
j
j
->
j
j
j
j
A
B
2.6100E+15
0.0000E+00
O.OOOOE+OO
1.0000E-13
0.0000E+00
0.0000E+00
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
O.OOOOE+OO
C
IE
0
ETH
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
INPUT
0
1
I
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
O.OOOOOE+OO
1.56000E + 01
1.20000E+01
1.85000E+01
2.90000E-0!
5.90000E-01
8.80000E-01
1. 17000E+00
1.47000E+00
1.76000E+00
2.06000E+00
2.35000E+00
6 .17000E+00
7.00000E+00
7.35000E+00
7.36000E+00
7.80000E+00
8 . 16000E+00
8.40000E+00
8.55000E+00
8.89000E+00
1.10300E+01
1.18800E+01
1.22500E+01
1.30000E+01
LIST OF CHEMICAL REACTIONS
REACTION
I
2
j
4
5
6
7
8
9
2.0 N
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
+
+
+
+
+
+
+
+
+
M
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
—
e
e
e
e
e
e
e
e
—
—
—
—
—
—
—
—
>
>
>
>
>
>
>
>
>
1.0 N2
1.0 N2+
2.0 N
1.0 N
1.0 N2V
1.0 N2V
1.0 N2V
1.0 N2V
1.0 N2V
+
+
+
+
+
+
+
+
+
M
2.0 e
1.0 e
1.0 N+
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
82
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
2.0 e
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
1.0 N2
I.0 N 2
1.0 N2
1.0 N2
I.0 N 2
1.0 N2
1.0 N2
TIME STEP NO. =
IEQ
SOLUTION
1
8.38655E-01
2
4.92754E-02
J
1.55200E-03
4
2.81556E-08
5
3.16533E-02
6
7.88644E-02
7
2.00962E+00
8
3.90638E-01
ELEC. DENSITY =
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
—>
1.0 N 2V
1.0 N 2V
1.0 N 2V
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
1.0 N2E
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
1.0 e
500
TIME = 5.00000E+06
DT = 1.00000E+04
MAX CHANGE
RESIDUAL
-4.9154 IE -10
2.20684E-09
1.79276E-10
3.05013E-10
8.50334E-12
3.20784E-10
2.96296E-17
2.2042 IE -15
7.39475E-12
1.11313E-10
2.96366E-10
1.46972E-09
2.28782E-09
2.06841 E-07
1.28944E-09
5.12893 E-08
2.1320326E+1 1
TIME STEP NO. 600 TIME = 6.00000E+06 DT = 1.00000E+04
IEQ
SOLUTION
MAX CHANGE
RESIDUAL
1
8.38655E-01
9.5247 IE -11
-2.12147E-11
2
7.73765E-12
4.92754E-02
1.31645E-11
J
1.55200E-03
3.67002E-13
I.38450E-11
4
2.81556E-08
1.27885E-18
9.5I349E-17
5
3 .16533E-02
3.19235E-13
4.80457E-I2
6
7.88644E-02
1.279I2E-11
6.34334E-11
7
2.00962E+00
8.92724E-09
9.87419E-11
8
3.90638E-01
2.21364E-09
5.56522E-11
********* STEADY STATE REACHED *********
INLET CONDITIONS
SPECIES
N2
MASS FRACTION
0.1000000E+01
MOLE FRACTION
0.1OOOOOOE+01
83
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
2
3
4
5
6
N
N2+
N+
N2V
N2E
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO O.OOOOOOOE+OO
O.OOOOOOOE+OO O.OOOOOOOE+OO
INITIAL TOTAL N U M B ER DENSITY = 3.2187999E+14 cm**-3
INITIAL GAS D EN SITY = 1.4963705E-08 gm /cm **3
MASS IN FLOW = 2.0832096E-03 gm/s
GAS PHASE RA TE CONSTANTS
REACTION #
FO R W A R D
REVERSE
1
6.2552 723 E+05
O.OOOOOOOE+OO
2
4 .19 10605E+02
O.OOOOOOOE+OO
3
5.7211220E+02
O.OOOOOOOE+OO
4
2 .1320327E-02
O.OOOOOOOE+OO
5
I.23I0773E+02
O.OOOOOOOE+OO
6
3.0872678E+02
O.OOOOOOOE+OO
7
2.0138878E+02
O.OOOOOOOE+OO
8
1.4199095 E+02
O.OOOOOOOE+OO
9
1.14353II E+02
O.OOOOOOOE+OO
10
I.0240675E+02
O.OOOOOOOE+OO
11
5.6953001E+01
O.OOOOOOOE+OO
12
2.7105142E+01
O.OOOOOOOE+OO
13
2.1762627E+01
O.OOOOOOOE+OO
14
9.2109549E+01
O.OOOOOOOE+OO
15
2.7244240E+02
O.OOOOOOOE+OO
16
2.8350239E+02
O.OOOOOOOE+OO
17
8.8086352E+01
O.OOOOOOOE+OO
18
8.3305246E+01
O.OOOOOOOE+OO
19
6.5533081E+01
O.OOOOOOOE+OO
20
2.4477634E+02
O.OOOOOOOE+OO
21
7.8285454E+01
O.OOOOOOOE+OO
22
6.I375687E+02
O.OOOOOOOE+OO
23
4.0648044E+00
O.OOOOOOOE+OO
24
2.8883234E+01
O.OOOOOOOE+OO
25
8.0442800E+02
O.OOOOOOOE+OO
FINAL REACTION RATES gmmole cm**-3 s**-l
REACTION #
1
2
3
4
FORWARD
REVERSE
NET
3.1601998E-16
8.0164394E-08
1.0943061 E-07
4.0780398E-12
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
3.1601998E-16
8.0164394E-08
1.0943061 E-07
4.0780398E-12
84
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohib ited w ith o u t p e r m is s io n .
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
2.3547397E-08
5.9051630E-08
3.8520584E-08
2.7159280E-08
2.1872860E-08
1.9587822E-08
1.0893670E-08
5.1845286E-09
4.1626405E-09
1.7618229E-08
5.2111346E-08
5.4226842E-08
1.6848693 E-08
1.5934188 E-08
1.2534822E-08
4.6819528E-08
1.4974029E-08
1.1739618E-07
7.774943 5E -10
5.5246327E-09
1.5386675E-07
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
2.3547397E-08
5.9051630E-08
3.8520584E-08
2.7159280E-08
2.1872860E-08
1.9587822E-08
1.0893670E-08
5.1845286E-09
4.1626405E-09
1.7618229E-08
5.2111346E-08
5.4226842E-08
1.6848693E-08
1.5934188E-08
1.2534822E-08
4.6819528E-08
1.4974029E-08
1.1739618E-07
7.7749435E -10
5.5246327E-09
1.5386675E-07
o
o
o
o
o
m
+
o
o
WALL COLLISION RATE CONSTANTS cm s**-l
1.8188378E+03
3.6666926E+05
5.1854863 E+05
1.2861125 E+04
1.2861125 E+04
RATE CONSTANTS FOR WAFER REACTIONS cm s**-l
O.OOOOOOOE+OO
0.0000000E+00
O.OOOOOOOE+OO
O.OOOOOOOE+OO
O.OOOOOOOE+OO
0.0000000E+00
FINAL REACTOR RESULTS
<4
SPECIES
1
2
3
4
5
6
N2
N
N2+
N+
N2V
N2E
MASS FRACTION
MOLE FRACTION
0.8386549E+00
0.492 753 7E-01
0 .1551997E-02
0.2815559E-07
0.3165334E-01
0.7886436E-01
0.7980900E+00
0.9378394E-0I
0.1476929E-02
0.5358746E-07
0.3012230E-01
0.7504978E-01
85
R e p r o d u c e d with p e r m i s s io n of th e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
SUM OF MASS FRACTION CHECK = 1.000000
OUTFLOW fN seem FOR CASCADING
SPECIES
N2
N
N2+
N+
N2V
N2E
MW
28.00
14.00
28.00
14.00
28.00
28.00
FLOW
104.31
12.26
0.19
0.00
3.94
9.81
DBASE
INPUT
INPUT
INPUT
INPUT
INPUT
INPUT
ELECTRON OUTFLOW = 1.9304390E-01 seem
TOTAL OUTFLOW RATE = I.3070157E+02 seem
FINAL TOTAL NUMBER DENSITY = 1.4435059E+I4 cm**-3
FINAL GAS DENSITY = 6.3860503E-09 gm/cm**3
MASS OUT FLOW = 2.0832096E-03 gm/s
FINAL SPECIES NUMBER DENSITY cm**-3
N2
1.1520477E+I4
N
1.3537767E+13
N2+
2.1319554E+11
N+
7.7353819E+06
N2V
4.3481723E+12
N2E
1.0833480E+13
GAS TEMEPERATURE = 6.028853 7E+02 deg. K
VARIOUS GAS ENERGY PROCESSES. cal.s**-l
SENSIBLE HEAT INFLOW
HEAT GAIN - ELASTIC COLLISIONS
HEAT GAIN - CHARGE EXCHANGE
VOLUMETRIC HEAT ADDITION
WALL HEATING
TOTAL HEAT INFLOW INTO SYSTEM
=
=
=
=
=
=
0.I536895E+00
0.3252108E+00
0.2718050E-01
O.OOOOOOOE+OO
O.OOOOOOOE+OO
0.5060808E+00
SENSIBLE HEAT OUTFLOW
HEAT LOSS TO AMBIENT
HEAT OF REACTIONS
TOTAL HEAT OUTFLOW FROM SYSTEM
= 0 .3 105994E+00
= 0.1954815E+00
= -0.4475486E-08
= 0.5060808E+00
ELECTRON DENSITY
ELECTRON TEMPERATURE
VP minus VF
= 2.1320327E+11 cm**
= 3.9063772E+00 eV
= 2.1654657E+01 Volts
86
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
APPLIED POWER DISTRIBUTION, fraction
INELASTIC COLLISION LOSS
ELASTIC COLLISION LOSS
ELECTRON ENERGY OUTFLOW
AMBIPOLAR WALL LOSS
ION POWER DEPOSITION
=
=
=
=
=
0.7546
0.0272
0.0013
0.0575
0.1594
87
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n p ro hibited w ith o u t p e r m is s io n .
VITA
The author, Shashank Sharma was born on April 19, 1977. in New Delhi, India.
In September 1994, he joined College o f Technology, Osmania University, Hyderabad.
India, one o f the most reputed chemical engineering program s in India. He received his
Bachelor o f Technology degree majoring in chemical engineering in June 1998.
In August 1998, he joined the graduate chemical engineering program at the
University o f Louisville, under the guidance o f Dr. M ahendra K. Sunkara. The author is a
member o f the American Institute o f Chemical Engineers, the Materials Research
Society, the American Vacuum Society and Phi Kappa Phi National All University
Honor Society.
88
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n p rohibited w ith o u t p e r m is s io n .
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