Electronic states in crystals of finite size: quantum confinement of Bloch waves
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2006
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Springer tracts in modern physics
212 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIV, 204 S. graph. Darst. |
| ISBN: | 0387263039 |
Internformat
MARC
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| 245 | 1 | 0 | |a Electronic states in crystals of finite size |b quantum confinement of Bloch waves |c Shang Yuan Ren |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Part I Why a Theory of Electronic States in Crystals of Finite
Size is Needed
1 Introduction 3
1.1 Electronic States Based on Translational Invariance 4
1.2 Energy Band Structure of Several Typical Crystals 6
1.3 Fundamental Difficulties of the Theory of the Electronic
States in Traditional Solid State Physics 8
1.4 The Effective Mass Approximation 10
1.5 Some Numerical Results 12
1.6 Subject of the Book and Main Findings 14
References 18
Part II One Dimensional Semi infinite Crystals and Finite
Crystals
2 Mathematical Basis 23
2.1 Elementary Theory and Two Basic Theorems 24
2.2 Floquet Theory 26
2.3 Discriminant and Linearly Independent Solutions 30
2.4 Basic Theory of the Schrodinger Equation in One
Dimensional Crystals 33
2.4.1 Two Different Eigenvalue Problems 34
2.4.2 The Function D(X) 35
2.5 Energy Band Structure of One Dimensional Crystals 39
2.6 Zeros of Solutions 43
References 47
3 Surface States in One Dimensional Semi infinite Crystals . 49
3.1 Basic Considerations 50
3.2 Two Relevant Theorems 52
3.3 Surface States in Ideal Semi infinite Crystals 54
3.4 Cases Where Vout Is Finite 57
3.5 Comparisons with Previous Work and Discussions 61
XII Contents
References 62
4 Electronic States in Ideal One Dimensional Crystals of
Finite Length 65
4.1 Basic Considerations 65
4.2 Two Types of Electronic States 66
4.3 r Dependent States 72
4.4 Electronic States in One Dimensional Finite Symmetric
Crystals 75
4.5 Comments on the Effective Mass Approximation 78
4.6 Comments on the Surface States 79
4.7 Two Other Comments 83
4.7.1 A Comment on the Formation of the Energy Bands... 83
4.7.2 A Comment on the Boundary Locations 84
4.8 Summary 84
References 85
Part III Low Dimensional Systems and Finite Crystals
5 Electronic States in Ideal Quantum Films 89
5.1 A Basic Theorem 90
5.2 Consequences of the Theorem 94
5.3 Basic Considerations on the Electronic States in an Ideal
Quantum Film 95
5.4 Stationary Bloch States 96
5.4.1 The Simplest Cases 96
5.4.2 More General Cases 98
5.5 r3 Dependent States 101
5.6 Several Practically More Interesting Films 102
5.6.1 (001) Films with a fee Bravais Lattice 102
5.6.2 (110) Films with a fee Bravais Lattice 103
5.6.3 (001) Films with a bec Bravais Lattice 105
5.6.4 (110) Films with a bec Bravais Lattice 105
5.7 Comparisons with Previous Numerical Results 106
5.7.1 Si (001) Films 106
5.7.2 Si (110) Films and GaAs (110) Films 108
5.8 Further Discussions 110
References 115
6 Electronic States in Ideal Quantum Wires 117
6.1 Basic Considerations 118
6.2 Further Quantum Confinement of ^n(fc, x; r3) 119
6.3 Further Quantum Confinement of i n,j3(k, x;t3) 123
Contents XIII
6.4 Quantum Wires of Crystals with a sc, tetr, or ortho Bravais
Lattice 127
6.5 fee Quantum Wires with (110) and (001) Surfaces 129
6.5.1 fee Quantum Wires Obtained from (001) Films
Further Confined by Two (110) Surfaces 130
6.5.2 fee Quantum Wires Obtained from (110) Films
Further Confined by Two (001) Surfaces 132
6.5.3 Results Obtained by Combining Sections 6.5.1 and 6.5.2134
6.6 fee Quantum Wires with (110) and (110) Surfaces 137
6.7 bee Quantum Wires with (001) and (010) Surfaces 138
6.8 Summary and Discussions 139
References 142
7 Electronic States in Ideal Finite Crystals or Quantum Dots 143
7.1 Basic Considerations 144
7.2 Further Quantum Confinement of i n{k,x; T2, T3) 144
7.3 Further Quantum Confinement of i)n,j3(k,x;T2,Ts) 148
7.4 Further Quantum Confinement of i/ nj2(fc,a;;T2,T3) 151
7.5 Further Quantum Confinement of Tpnj2j3(k,x;T2,T3) 154
7.6 Finite Crystals or Quantum Dots with a sc, tetr, or ortho
Bravais Lattice 158
7.7 fee Finite Crystals with (001), (110), and (110) Surfaces 160
7.8 bec Finite Crystals with (100), (010), and (001) Surfaces 163
7.9 Summary and Discussions 166
References 170
Part IV Epilogue
8 Concluding Remarks 173
8.1 Summary and Brief Discussions 173
8.2 Some Relevant Systems 178
8.2.1 Electronic States in Ideal Cavity Structures 178
8.2.2 Other Finite Periodic Systems, such as Finite
Photonic Crystals 179
8.3 Could a More General Theory Be Possible? 181
References 182
Part V Appendices
A Electronic States in One Dimensional Symmetric Finite
Crystals with a Finite Vout 185
References 190
XIV Contents
B Electronic States in Ideal Cavity Structures 191
B.I Electronic States in Ideal Cavity Structures of
One Dimensional Crystals 191
B.2 Electronic States in Ideal Two Dimensional Cavity
Structures of Three Dimensional Crystals 192
B.3 Electronic States in Ideal One Dimensional Cavity
Structures of Three Dimensional Crystals 194
B.3.1 Wire Cavities in Crystals with a sc, tetr, or ortho
Bravais Lattice 195
B.3.2 Wire Cavities with (001) and (110) Surfaces in fee
Crystals J. 196
B.3.3 Wire Cavities with (110) and (110) Surfaces in fee
Crystals 197
B.3.4 Wire Cavities with (010) and (001) Surfaces in bee
Crystals 197
B.4 Electronic States in Ideal Zero Dimensional Cavity
Structures of Three Dimensional Crystals 198
B.4.1 Dot Cavities in Crystals with a sc, tetr, or ortho
Bravais Lattice 199
B.4.2 Dot Cavities with (110), (110), and (001) Surfaces in
fee Crystals 200
B.4.3 Dot Cavities with (100), (010), and (001) Surfaces in
bee Crystals 201
Index 203
|
| adam_txt |
Contents
Part I Why a Theory of Electronic States in Crystals of Finite
Size is Needed
1 Introduction 3
1.1 Electronic States Based on Translational Invariance 4
1.2 Energy Band Structure of Several Typical Crystals 6
1.3 Fundamental Difficulties of the Theory of the Electronic
States in Traditional Solid State Physics 8
1.4 The Effective Mass Approximation 10
1.5 Some Numerical Results 12
1.6 Subject of the Book and Main Findings 14
References 18
Part II One Dimensional Semi infinite Crystals and Finite
Crystals
2 Mathematical Basis 23
2.1 Elementary Theory and Two Basic Theorems 24
2.2 Floquet Theory 26
2.3 Discriminant and Linearly Independent Solutions 30
2.4 Basic Theory of the Schrodinger Equation in One
Dimensional Crystals 33
2.4.1 Two Different Eigenvalue Problems 34
2.4.2 The Function D(X) 35
2.5 Energy Band Structure of One Dimensional Crystals 39
2.6 Zeros of Solutions 43
References 47
3 Surface States in One Dimensional Semi infinite Crystals . 49
3.1 Basic Considerations 50
3.2 Two Relevant Theorems 52
3.3 Surface States in Ideal Semi infinite Crystals 54
3.4 Cases Where Vout Is Finite 57
3.5 Comparisons with Previous Work and Discussions 61
XII Contents
References 62
4 Electronic States in Ideal One Dimensional Crystals of
Finite Length 65
4.1 Basic Considerations 65
4.2 Two Types of Electronic States 66
4.3 r Dependent States 72
4.4 Electronic States in One Dimensional Finite Symmetric
Crystals 75
4.5 Comments on the Effective Mass Approximation 78
4.6 Comments on the Surface States 79
4.7 Two Other Comments 83
4.7.1 A Comment on the Formation of the Energy Bands. 83
4.7.2 A Comment on the Boundary Locations 84
4.8 Summary 84
References 85
Part III Low Dimensional Systems and Finite Crystals
5 Electronic States in Ideal Quantum Films 89
5.1 A Basic Theorem 90
5.2 Consequences of the Theorem 94
5.3 Basic Considerations on the Electronic States in an Ideal
Quantum Film 95
5.4 Stationary Bloch States 96
5.4.1 The Simplest Cases 96
5.4.2 More General Cases 98
5.5 r3 Dependent States 101
5.6 Several Practically More Interesting Films 102
5.6.1 (001) Films with a fee Bravais Lattice 102
5.6.2 (110) Films with a fee Bravais Lattice 103
5.6.3 (001) Films with a bec Bravais Lattice 105
5.6.4 (110) Films with a bec Bravais Lattice 105
5.7 Comparisons with Previous Numerical Results 106
5.7.1 Si (001) Films 106
5.7.2 Si (110) Films and GaAs (110) Films 108
5.8 Further Discussions 110
References 115
6 Electronic States in Ideal Quantum Wires 117
6.1 Basic Considerations 118
6.2 Further Quantum Confinement of ^n(fc, x; r3) 119
6.3 Further Quantum Confinement of i n,j3(k, x;t3) 123
Contents XIII
6.4 Quantum Wires of Crystals with a sc, tetr, or ortho Bravais
Lattice 127
6.5 fee Quantum Wires with (110) and (001) Surfaces 129
6.5.1 fee Quantum Wires Obtained from (001) Films
Further Confined by Two (110) Surfaces 130
6.5.2 fee Quantum Wires Obtained from (110) Films
Further Confined by Two (001) Surfaces 132
6.5.3 Results Obtained by Combining Sections 6.5.1 and 6.5.2134
6.6 fee Quantum Wires with (110) and (110) Surfaces 137
6.7 bee Quantum Wires with (001) and (010) Surfaces 138
6.8 Summary and Discussions 139
References 142
7 Electronic States in Ideal Finite Crystals or Quantum Dots 143
7.1 Basic Considerations 144
7.2 Further Quantum Confinement of i n{k,x; T2, T3) 144
7.3 Further Quantum Confinement of i)n,j3(k,x;T2,Ts) 148
7.4 Further Quantum Confinement of i/ nj2(fc,a;;T2,T3) 151
7.5 Further Quantum Confinement of Tpnj2j3(k,x;T2,T3) 154
7.6 Finite Crystals or Quantum Dots with a sc, tetr, or ortho
Bravais Lattice 158
7.7 fee Finite Crystals with (001), (110), and (110) Surfaces 160
7.8 bec Finite Crystals with (100), (010), and (001) Surfaces 163
7.9 Summary and Discussions 166
References 170
Part IV Epilogue
8 Concluding Remarks 173
8.1 Summary and Brief Discussions 173
8.2 Some Relevant Systems 178
8.2.1 Electronic States in Ideal Cavity Structures 178
8.2.2 Other Finite Periodic Systems, such as Finite
Photonic Crystals 179
8.3 Could a More General Theory Be Possible? 181
References 182
Part V Appendices
A Electronic States in One Dimensional Symmetric Finite
Crystals with a Finite Vout 185
References 190
XIV Contents
B Electronic States in Ideal Cavity Structures 191
B.I Electronic States in Ideal Cavity Structures of
One Dimensional Crystals 191
B.2 Electronic States in Ideal Two Dimensional Cavity
Structures of Three Dimensional Crystals 192
B.3 Electronic States in Ideal One Dimensional Cavity
Structures of Three Dimensional Crystals 194
B.3.1 Wire Cavities in Crystals with a sc, tetr, or ortho
Bravais Lattice 195
B.3.2 Wire Cavities with (001) and (110) Surfaces in fee
Crystals J. 196
B.3.3 Wire Cavities with (110) and (110) Surfaces in fee
Crystals 197
B.3.4 Wire Cavities with (010) and (001) Surfaces in bee
Crystals 197
B.4 Electronic States in Ideal Zero Dimensional Cavity
Structures of Three Dimensional Crystals 198
B.4.1 Dot Cavities in Crystals with a sc, tetr, or ortho
Bravais Lattice 199
B.4.2 Dot Cavities with (110), (110), and (001) Surfaces in
fee Crystals 200
B.4.3 Dot Cavities with (100), (010), and (001) Surfaces in
bee Crystals 201
Index 203 |
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| id | DE-604.BV021258509 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:41:14Z |
| indexdate | 2024-07-09T20:34:03Z |
| institution | BVB |
| isbn | 0387263039 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014579777 |
| oclc_num | 62312759 |
| open_access_boolean | |
| owner | DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 DE-188 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 DE-188 |
| physical | XIV, 204 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Springer tracts in modern physics |
| series2 | Springer tracts in modern physics |
| spelling | Ren, Shang Yuan Verfasser aut Electronic states in crystals of finite size quantum confinement of Bloch waves Shang Yuan Ren 1. ed. New York [u.a.] Springer 2006 XIV, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer tracts in modern physics 212 Bloch-Funktion swd Cristaux - Propriétés électriques Cristaux - Propriétés électriques ram Eendimensionale systemen gtt Elektronenzustand swd Kristall swd Kristallen gtt Kritische verschijnselen gtt Kwantummechanica gtt Oppervlakken gtt Physique de l'état solide Physique de l'état solide ram Quantenmechanik swd Statistische mechanica gtt Tweedimensionale systemen gtt Vastestoffysica gtt Welle swd Crystals Electric properties Solid state physics Niederdimensionaler Festkörper (DE-588)4258975-7 gnd rswk-swf Elektronenstruktur (DE-588)4129531-6 gnd rswk-swf Kristall (DE-588)4033209-3 gnd rswk-swf Niederdimensionaler Festkörper (DE-588)4258975-7 s Kristall (DE-588)4033209-3 s Elektronenstruktur (DE-588)4129531-6 s DE-604 Springer tracts in modern physics 212 (DE-604)BV000000153 212 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2682754&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014579777&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 11 |
| spellingShingle | Ren, Shang Yuan Electronic states in crystals of finite size quantum confinement of Bloch waves Springer tracts in modern physics Bloch-Funktion swd Cristaux - Propriétés électriques Cristaux - Propriétés électriques ram Eendimensionale systemen gtt Elektronenzustand swd Kristall swd Kristallen gtt Kritische verschijnselen gtt Kwantummechanica gtt Oppervlakken gtt Physique de l'état solide Physique de l'état solide ram Quantenmechanik swd Statistische mechanica gtt Tweedimensionale systemen gtt Vastestoffysica gtt Welle swd Crystals Electric properties Solid state physics Niederdimensionaler Festkörper (DE-588)4258975-7 gnd Elektronenstruktur (DE-588)4129531-6 gnd Kristall (DE-588)4033209-3 gnd |
| subject_GND | (DE-588)4258975-7 (DE-588)4129531-6 (DE-588)4033209-3 |
| title | Electronic states in crystals of finite size quantum confinement of Bloch waves |
| title_auth | Electronic states in crystals of finite size quantum confinement of Bloch waves |
| title_exact_search | Electronic states in crystals of finite size quantum confinement of Bloch waves |
| title_exact_search_txtP | Electronic states in crystals of finite size quantum confinement of Bloch waves |
| title_full | Electronic states in crystals of finite size quantum confinement of Bloch waves Shang Yuan Ren |
| title_fullStr | Electronic states in crystals of finite size quantum confinement of Bloch waves Shang Yuan Ren |
| title_full_unstemmed | Electronic states in crystals of finite size quantum confinement of Bloch waves Shang Yuan Ren |
| title_short | Electronic states in crystals of finite size |
| title_sort | electronic states in crystals of finite size quantum confinement of bloch waves |
| title_sub | quantum confinement of Bloch waves |
| topic | Bloch-Funktion swd Cristaux - Propriétés électriques Cristaux - Propriétés électriques ram Eendimensionale systemen gtt Elektronenzustand swd Kristall swd Kristallen gtt Kritische verschijnselen gtt Kwantummechanica gtt Oppervlakken gtt Physique de l'état solide Physique de l'état solide ram Quantenmechanik swd Statistische mechanica gtt Tweedimensionale systemen gtt Vastestoffysica gtt Welle swd Crystals Electric properties Solid state physics Niederdimensionaler Festkörper (DE-588)4258975-7 gnd Elektronenstruktur (DE-588)4129531-6 gnd Kristall (DE-588)4033209-3 gnd |
| topic_facet | Bloch-Funktion Cristaux - Propriétés électriques Eendimensionale systemen Elektronenzustand Kristall Kristallen Kritische verschijnselen Kwantummechanica Oppervlakken Physique de l'état solide Quantenmechanik Statistische mechanica Tweedimensionale systemen Vastestoffysica Welle Crystals Electric properties Solid state physics Niederdimensionaler Festkörper Elektronenstruktur |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2682754&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014579777&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000153 |
| work_keys_str_mv | AT renshangyuan electronicstatesincrystalsoffinitesizequantumconfinementofblochwaves |