Transient numerical simulation of sublimation growth of SiC bulk single crystals: modeling, finite volume method, results
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
2003
|
| Series: | Report / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 289 S. Ill., graph. Darst. |
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MARC
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| 100 | 1 | |a Philip, Peter |d 1971- |e Verfasser |0 (DE-588)124765084 |4 aut | |
| 245 | 1 | 0 | |a Transient numerical simulation of sublimation growth of SiC bulk single crystals |b modeling, finite volume method, results |c Peter Philip |
| 264 | 1 | |a Berlin |b Weierstraß-Institut für Angewandte Analysis und Stochastik |c 2003 | |
| 300 | |a XV, 289 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Report / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. |v 22 | |
| 502 | |a Zugl.: Berlin, Humboldt-Univ., Diss., 2003 | ||
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Record in the Search Index
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| adam_text |
CONTENTS
ABSTRACT
V
PREFACE
VII
FOREWORD
.
VII
ACKNOWLEDGMENTS
.
'
.
.
VII
CURRICULUM
VITAE
.
IX
ABBREVIATIONS
AND
NOTATION
.
X
1
INTRODUCTION
1
1.1
APPLICATION
AND
GROWTH
OF
SIC
BULK
SINGLE
CRYSTALS
.
1
1.2
SCOPE
AND
STRUCTURE
OF
THIS
WORK
.
5
1.2.1
MODELING
AND
SIMULATION
.
5
1.2.2
FINITE
VOLUME
METHOD
.
8
2
MODELING
10
2.1
MODEL
OF
THE
GAS
PHASE
.
10
2.1.1
GENERAL
BALANCE
AND
FIELD
EQUATIONS
.
10
2.1.2
SIMPLIFICATIONS
.
15
2.1.3
MATERIAL
LAWS
.
18
2.1.4
SIMPLIFICATIONS
ASSUMING
THE
GAS
CONSISTS
OF
ONE
CONSTITUENT
ONLY
.
19
2.2
HEAT
CONDUCTION
IN
SOLID
MATERIALS
.
20
2.3
INTERFACE,
BOUNDARY,
AND
INITIAL
CONDITIONS
.
21
2.4
MODEL
OF
DIFFUSE-GRAY
RADIATION
INCLUDING
SEMI-TRANSPARENCY
.
23
2.4.1
MODEL
ASSUMPTIONS
.
23
XII
CONTENTS
2.4.2
OPAQUE
CASE
.
24
2.4.3
AXISYMMETRIC
MODEL
.
26
2.4.4
SEMI-TRANSPARENT
CASE
.
28
2.5
MODELING
INDUCTION
HEATING
.
32
2.5.1
MODEL
ASSUMPTIONS
.
32
2.5.2
CONSEQUENCES
OF
MAXWELL
'
S
EQUATIONS
.
33
2.5.3
MAGNETIC
SCALAR
POTENTIAL
EQUATION
IN
INSULATORS
.
35
2.5.4
MAGNETIC
SCALAR
POTENTIAL
EQUATION
IN
CONDUCTORS
.
35
2.5.5
INTERFACE
AND
BOUNDARY
CONDITIONS
.
37
2.5.6
SINUSOIDAL
TIME
DEPENDENCE
.
37
2.5.7
PRESCRIBING
CURRENT,
VOLTAGE,
OR
POWER
.
40
3
FINITE
VOLUME
METHOD
45
3.1
THE
CONSIDERED
PROBLEM
CLASS
AND
SCOPE
OF
THE
TREATMENT
.
45
3.2
LITERATURE
REVIEW
.
51
3.3
THE
EVOLUTION
EQUATION
.
53
3.3.1
CONTINUOUS
SETTING
.
53
3.3.2
TIME
DISCRETIZATION
.
56
3.4
EVOLUTION
EQUATION
COMPLEXES
.
57
3.4.1
INTERFACE,
BOUNDARY,
AND
INITIAL
CONDITIONS
.
58
3.4.2
DOMAIN
COMPLEX
AND
EVOLUTION
EQUATION
COMPLEX
.
64
3.4.3
TIME
DISCRETIZATION
.
66
3.5
INTEGRAL
FORMULATION
.
72
3.5.1
POLYTOPE
DISCRETIZATION
OF
SPACE
DOMAINS
.
73
3.5.2
INTEGRAL
FORMULATION
OF
TIME-DISCRETE
EVOLUTION
EQUATIONS
.
73
3.5.3
USING
INTERFACE
CONDITIONS
TO
REPLACE
TERMS
INVOLVING
THE
FLUX
ACROSS
INTERFACES
.
78
3.6
CHANGE
OF
VARIABLES
.
86
3.6.1
COORDINATE
TRANSFORMATIONS
.
87
3.6.2
INTEGRAL
FORMULATION
.
89
3.6.3
WRITING
THE
DOMAINS
OF
INTEGRATION
AS
IMAGES
OF
THE
COORDINATE
TRANSFORMATION
.
91
3.6.4
CHANGE
OF
VARIABLES
.
94
CONTENTS
XIII
3.6.5
SYMMETRY
ASSUMPTIONS
AND
DIMENSION
REDUCTION
.
96
3.7
FINITE
VOLUME
DISCRETIZATION
AND
DISCRETE
A
PRIORI
ESTIMATES
.
101
3.7.1
OUTLINE
OF
DISCRETIZATION
STRATEGY
.
101
3.7.2
TERMS
INVOLVING
THE
TIME
STEP
.
106
3.7.3
TERMS
INVOLVING
INTERIOR
DIFFUSION
FLUX
.
106
3.7.4
TERMS
INVOLVING
INTERIOR
CONVECTION
FLUX;
UPWIND
.
112
3.7.5
TERMS
ON
OUTER
BOUNDARIES
.
117
3.7.6
TERMS
ON
INTERFACES
.
118
3.7.7
TERMS
INVOLVING
NONLOCAL
OPERATORS
.
121
3.7.8
EXAMPLE:
DISCRETIZATION
OF
NONLOCAL
RADIATION
TERMS
.
122
3.7.9
UPPER
BOUND
FOR
TERMS
ON
OUTER
BOUNDARIES
.
129
3.7.10
UPPER
BOUND
FOR
TERMS
ON
INTERFACES
.
132
3.7.11
SOURCE
AND
SINK
TERMS
.
137
3.7.12
SUMMARIZING
DEFINITIONS
.
138
3.7.13
DISCRETE
L-L
L
A
PRIORI
ESTIMATES
.
145
3.8
EXISTENCE
AND
UNIQUENESS
OF
A
DISCRETE
SOLUTION
.
149
3.8.1
EXISTENCE
OF
UNIQUE
FIXED
POINTS
.
150
3.8.2
A
ROOT
PROBLEM
.
152
3.8.3
DECOMPOSITION
OF
TERMS
INVOLVING
INTERIOR
DIFFUSION
FLUX
.
155
3.8.4
DECOMPOSITION
OF
INTERIOR
CONVECTION
FLUX
TERMS
.
161
3.8.5
DECOMPOSITION
OF
TERMS
ON
OUTER
BOUNDARIES
.
163
3.8.6
DECOMPOSITION
OF
TERMS
ON
INTERFACES
.
167
3.8.7
NONLOCAL
OPERATORS
.
175
3.8.8
DECOMPOSITION
OF
SOURCE
AND
SINK
TERMS
.
176
3.8.9
STATEMENT
AND
PROOF
OF
THE
THEOREM
.
178
3.8.10
EXAMPLE:
COUPLED
TRANSIENT
HEAT
EQUATIONS
.
188
3.9
PERSPECTIVES
ON
CONVERGENCE
.
192
4
NUMERICAL
RESULTS
194
4.1
GENERAL
SETTING
AND
METHODS
.
194
4.2
COMPILATION
OF
EQUATIONS
AND
PARAMETER
VALUES
USED
IN
SIMULATIONS
198
4.2.1
EQUATIONS
USED
IN
SIMULATIONS
.
198
XIV
CONTENTS
4.2.2
PARAMETERS
USED
IN
SIMULATIONS
.
199
4.3
TRANSIENT
NUMERICAL
INVESTIGATION
OF
CONTROL
PARAMETERS
AFFECTING
THE
TEMPERATURE
EVOLUTION
.
200
4.3.1
DESCRIPTION
OF
NUMERICAL
EXPERIMENTS
.
200
4.3.2
TEMPERATURE
EVOLUTION
AT
POINTS
OF
INTEREST
.
201
4.3.3
PHENOMENA
INACCESSIBLE
TO
DIRECT
MEASUREMENTS
.
205
4.3.4
EVOLUTION
OF
GLOBAL
DISTRIBUTION
OF
TEMPERATURE
AND
OF
HEAT
SOURCES
.
205
A
MATERIAL
DATA
210
A.L
GENERAL
PHYSICAL
CONSTANTS
.
210
A.
1.1
MOLECULAR
MASSES
.
210
A.
2
GAS
PHASE
.
210
A.
2.1
ARGON
.
210
A.
2.2
GENERAL
ESTIMATES
.
213
A.
3
SOLID
MATERIALS
.
214
A.
3.1
COPPER
.
214
A.
3.2
GRAPHITE
CRUCIBLE
.
215
A.
3.3
GRAPHITE
FELT
INSULATION
.
216
AJA
SIC
SOURCE
POWDER
.
218
A.
3.5
SIC
SINGLE
CRYSTAL
.
219
B
FORMULAS
AND
COMPUTATIONS
222
B.L
VECTORS,
TENSORS,
AND
DIFFERENTIAL
OPERATORS
.
222
B.2
BALANCE
AND
FIELD
EQUATIONS
.
224
B.2.1
SOME
IDENTITIES
.
224
B.2.
2
THE
BALANCE
EQUATIONS
IMPLY
THE
FIELD
EQUATIONS
.
225
B.2.
3
THE
FIELD
EQUATIONS
IMPLY
THE
BALANCE
EQUATIONS
.
227
B.2.
4
EQUATIONS
(2.1.11A),
(2.1.11B),
(2.1.3C)
ARE
EQUIVALENT
TO
EQUA
TIONS
(2.1.14A),
(2.1.14C),
(2.1.
14D)
.
228
B.2.
5
SIMPLIFICATIONS
.
228
B.3
CYLINDRICAL
COORDINATES
.
229
B.3.1
DEFINITION
AND
ELEMENTARY
PROPERTIES
.
229
CONTENTS
XV
B.3.2
GRAD,
DIV,
CURL
IN
CYLINDRICAL
COORDINATES
.
230
B.4
EXISTENCE
OF
A
MAGNETIC
SCALAR
POTENTIAL
.
230
C
MATHEMATICAL
BACKGROUND
MATERIAL
232
C.L
TOPOLOGY
.
232
C.L.L
ELEMENTARY
NOTIONS
.
232
C.L.
2
DOMAIN
INVARIANCE
.
233
C.2
NORMS
.
234
C.3
MATRIX
THEORY
.
234
C.4
AFFINE
GEOMETRY
.
235
C.4.1
AFFINE
SUBSPACES
.
235
C.4.
2
POLYHEDRAL
SETS
.
236
C.4.
3
VORONOI
DISCRETIZATION
.
239
C.5
GRAPH
THEORY
.
239
C.6
REGULARITY
NOTIONS
OF
FUNCTIONS
.
240
C.6.1
CONTINUOUS
DIFFERENTIABILITY
.
240
C.6.
2
MONOTONICITY
.
241
C.6.
3
VARIATION
.
241
C.7
SOME
SUBJECTS
IN
METRIC
SPACES
.
243
C.7.1
ELEMENTARY
NOTATION
.
243
C.7.
2
LIPSCHITZ
FUNCTIONS
.
244
C.7.
3
INVERSE
LIPSCHITZ
FUNCTIONS
.
246
C.7.4
CONTRACTING
MAPS
.
246
C.8
INTEGRATION
.
247
C.8.1
NOTATION
FOR
LEBESGUE
MEASURE
.
247
C.8.
2
INTEGRATION
THEOREMS
.
247
BIBLIOGRAPHY
249
LIST
OF
SYMBOLS
257
INDEX
276 |
| any_adam_object | 1 |
| author | Philip, Peter 1971- |
| author_GND | (DE-588)124765084 |
| author_facet | Philip, Peter 1971- |
| author_role | aut |
| author_sort | Philip, Peter 1971- |
| author_variant | p p pp |
| building | Verbundindex |
| bvnumber | BV017166626 |
| classification_rvk | SI 303 SK 950 |
| ctrlnum | (OCoLC)314147495 (DE-599)BVBBV017166626 |
| discipline | Mathematik |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV017166626 |
| illustrated | Illustrated |
| indexdate | 2024-08-17T00:41:04Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010349746 |
| oclc_num | 314147495 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-634 DE-11 DE-188 DE-83 |
| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-634 DE-11 DE-188 DE-83 |
| physical | XV, 289 S. Ill., graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Weierstraß-Institut für Angewandte Analysis und Stochastik |
| record_format | marc |
| series2 | Report / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. |
| spelling | Philip, Peter 1971- Verfasser (DE-588)124765084 aut Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results Peter Philip Berlin Weierstraß-Institut für Angewandte Analysis und Stochastik 2003 XV, 289 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Report / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. 22 Zugl.: Berlin, Humboldt-Univ., Diss., 2003 Gasphasenepitaxie (DE-588)4156040-1 gnd rswk-swf Direkte numerische Simulation (DE-588)4494453-6 gnd rswk-swf Kristallzüchtung (DE-588)4140616-3 gnd rswk-swf Siliciumcarbid (DE-588)4055009-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Siliciumcarbid (DE-588)4055009-6 s Kristallzüchtung (DE-588)4140616-3 s Gasphasenepitaxie (DE-588)4156040-1 s Direkte numerische Simulation (DE-588)4494453-6 s DE-604 Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. Report 22 (DE-604)BV009889758 22 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010349746&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Philip, Peter 1971- Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results Gasphasenepitaxie (DE-588)4156040-1 gnd Direkte numerische Simulation (DE-588)4494453-6 gnd Kristallzüchtung (DE-588)4140616-3 gnd Siliciumcarbid (DE-588)4055009-6 gnd |
| subject_GND | (DE-588)4156040-1 (DE-588)4494453-6 (DE-588)4140616-3 (DE-588)4055009-6 (DE-588)4113937-9 |
| title | Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results |
| title_auth | Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results |
| title_exact_search | Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results |
| title_full | Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results Peter Philip |
| title_fullStr | Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results Peter Philip |
| title_full_unstemmed | Transient numerical simulation of sublimation growth of SiC bulk single crystals modeling, finite volume method, results Peter Philip |
| title_short | Transient numerical simulation of sublimation growth of SiC bulk single crystals |
| title_sort | transient numerical simulation of sublimation growth of sic bulk single crystals modeling finite volume method results |
| title_sub | modeling, finite volume method, results |
| topic | Gasphasenepitaxie (DE-588)4156040-1 gnd Direkte numerische Simulation (DE-588)4494453-6 gnd Kristallzüchtung (DE-588)4140616-3 gnd Siliciumcarbid (DE-588)4055009-6 gnd |
| topic_facet | Gasphasenepitaxie Direkte numerische Simulation Kristallzüchtung Siliciumcarbid Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010349746&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009889758 |
| work_keys_str_mv | AT philippeter transientnumericalsimulationofsublimationgrowthofsicbulksinglecrystalsmodelingfinitevolumemethodresults |