Thermal Transport for Applications in Micro/Nanomachining

Front Cover
Springer Science & Business Media, Jul 19, 2008 - Science - 231 pages

Beginning with an overview of nanomachining, this monograph introduces the relevant concepts from solid-state physics, thermodynamics, and lattice structures. It then covers modeling of thermal transport at the nanoscale and details simulations of different processes relevant to nanomachining. The final chapter summarizes the important points and discusses directions for future work to improve the modeling of nanomachining.

 

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Contents

Introduction
1
11 Motivation for Building Small
3
12 Nanopatterning Approaches
4
13 ElectronBeam Processing
5
14 MicroNanomachining with Electrons
7
15 Outline of the Monograph
12
Transport Equations
14
Electrons Photons and Phonons
16
522 Computational Grid
109
523 ElectronBeam Monte Carlo Simulation
111
524 Auxiliary Heating Using Laser Beam
112
525 Fourier Heat Conduction
114
526 Modeling Melting and Evaporation
121
527 Computational Parameters for MicroNanomaching Scenario
122
5210 Comments
125
53 Sequential Patterning Using Electron Beam
126

22 Classification of Transport Models
18
23 Time and Length Scales
19
24 Boltzmann Transport Equation
20
241 RelaxationTime Approximation
22
25 Intensity Form of Boltzmann Transport Equation
24
252 Radiative Transfer Equation
27
253 Phonon Radiative Transport Equation
29
254 Electron Transport Equation
30
26 Moments of Boltzmann Transport Equation
31
261 Continuity or Conservation of Number of Particles
32
262 Conservation of Momentum
34
263 Conservation of Energy
36
264 Conservation of Heat Flux
38
27 Macroscale Thermal Conduction
39
28 MicroNanoscale Thermal Conduction
41
282 DualPhase Lag Model
43
283 ElectronPhonon Hydrodynamic Equations
45
29 Nanoscale Thermal Conduction
51
210 Thermal Radiation at Nanoscales
52
211 Comments
53
Modeling of Transport Equations via MC Methods
57
31 Cumulative Probability Distribution Function
60
32 Building a CPDF Table for a MC Method
61
33 Monte Carlo Simulation for ParticleBeam Transport
62
331 Setting up Computational Grid
63
333 Simulation Steps
64
334 Incident Beam Profiles
66
335 Direction of Propagation
67
336 Distance of Interaction
68
337 Attenuation of Energy
69
34 Monte Carlo Simulation for Thermal Conduction by Electrons
70
341 Initial Electron Distributions
72
342 Launching of Electrons
73
344 PseudoTemperature Calculations
74
345 Scattering of Electrons
75
35 Monte Carlo Simulation for Phonon Conduction
76
352 Launching and Tracing Phonons
78
355 Boundary Conditions
79
36 Normalization of the Statistical Results
80
Modeling of eBeam Transport
81
42 Elastic Scattering of an Electron by an Atom
82
421 Rutherford Cross Section
84
422 Mott Cross Section
87
The Bethe Theory
94
The Dielectric Theory
96
45 Electron Reflection and Refraction at a Surface
100
46 Monte Carlo Simulation Results and Verifications
101
47 Comments
102
Thermal Conduction Coupled with eBeam Transport
105
52 Thermal Conduction due to Single ElectronBeam Heating
107
532 Computational Methodology
127
533 Computational Parameters
129
535 Comments
133
TwoTemperature Model Coupled with eBeam Transport
135
62 Problem Description and Assumptions
137
63 ElectronBeam Monte Carlo Simulation
138
64 Results and Discussions
139
642 TwoTemperature Model Predictions
140
65 Comments
145
Thermal Conduction with Electron FlowBallistic Behavior
146
71 ElectronPhonon Hydrodynamic Modeling
148
712 Physical Domain and Boundary Conditions
150
713 Thermophysical Properties for the Simulation
152
714 Results and Discussions
154
72 Thermal Conduction by Electrons via Monte Carlo Method
156
721 Electron Band Structure
159
723 ElectronPhonon Scattering
161
724 Monte Carlo Simulation Results
163
725 Remarks on Electron Conduction Simulations
165
73 Comments
166
Parallel Computations for TwoTemperature Model
167
82 Parallelization of the TTM for MicroNanomachining
169
83 Parallel Computing Resources
170
84 Implementation of Parallelization
171
85 Parallel Computing Experiment
176
86 Parallel Computing Using Parabolic Two Step PTS Model
180
87 Parallel Computing Including an Electron Beam
181
88 Comments
182
Molecular Dynamics Simulations
185
91 Overview of Molecular Dynamics
186
911 Interatomic Potential
187
912 Time Integration of the Equations of Motion
190
913 Molecular Dynamics in Different Ensembles
191
921 Equipartition Theorem and the Virial
192
923 Velocity Autocorrelation Function and Density of States
193
924 Phonon Spectral Densities
194
93 Molecular Dynamics Codes
195
931 Bulk Simulations
196
932 Surface Simulations
197
94 Coupling of MD with Monte Carlo Method
199
95 Simulations of Electron Heating
201
96 Comments
202
Concluding Remarks
204
Derivation of Matrix for the Fourier Conduction Law
209
Simplified ElectronPhonon Hydrodynamic Equations
213
Thermophysical Properties
219
References
221
Index
229
Copyright

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Page 224 - Monte Carlo Modeling for Electron Microscopy and Microanalysis», Oxford University Press, 1995.
Page 228 - W. Zhu, C. Bower, O. Zhou, G Kochanski, S Jin, Appl. Phys. Lett. 75, 873-5 (1999).