Thermoelectric Power in Nanostructured Materials (eBook)

Professor K. P. Ghatak is the First Recipient of the Degree of Doctor of Engineering of Jadavpur University in 1991 since the University inception in 1955 and in the same year he received the prestigious Indian National Science Academy award. He joined as Lecturer in the Institute of Radio Physics and Electronics of the University of Calcutta in 1983, Reader in the Department of Electronics and Telecommunication of Jadavpur University in 1987 and Professor in the Department of Electronic Science of the University of Calcutta in 1994 respectively. His present research interest is nanostructured science and technology. He is the principal co-author of more than 200 research papers on Semiconductor and Nanoscience in eminent peer-reviewed International Journals and more than 50 research papers in the Proceedings of the International Conferences held in USA and many of his papers are being cited many times. Professor Ghatak is the invited Speaker of SPIE, MRS, etc. and is the referee of different eminent Journals. He is the supervisor of more than 34 Ph.D candidates among which 24 have already been awarded their respective Ph.D degrees, 6 are working at present and 4 are writing their respective Ph.D. thesis in various aspects of materials and nanoscience and many of them are working as Professor, Reader and Lecturer in different Universities. He is the principal co-author of the two research monographs entitled "Einstein Relation in Compound Semiconductors and Their Nanostructures" Springer Series in Materials Science, Vol. 116, ISBN 978-3-540-79556-8 which is the first book on Einstein relation and contains many open research problems and "Photoemission from Optoelectronic materials and their nanostructures", which will be published from Springer, USA in 2009 and presently in the press as the first book solely devoted to Photoemission from nanostructured optoelectronic materials. The All Indian Council For Technical Education has selected the first Research & Development project in his life for the best project award in Electronics and second best research project award considering all the branches of Engineering for the year 2006. The present book is being written under the grant (8023/BOR/RID/RPS-95/2007-08) as sanctioned by the said Council in their reserach promotion scheme 2008. Dr. S. Bhattacharya obtained his M. Sc. Degree in Electronic Science of the University of Calcutta in 2003 and is presently working in the Centre for Electronics Design and Technology, Indian Institute of Science, Bangalore. His Ph. D. work involves the investigations of transport properties of different quantized structures under various external conditions. He is the co-author of the two aforementioned research monographs and 30 scientific research papers in different aspects of quantized structures in international peer-reviewed journals of high repute. His present research interests are the quantum effect devices and nonlinearities. He became the Invited Speaker at the XXIXth International Union of Radio Science, URSI.

Preface 8
Contents 16
List of Symbols 24
Part I Thermoelectric Power Under Large Magnetic Field in Quantum Confined Materials 29
1 Thermoelectric Power in Quantum Dots Under Large Magnetic Field 30
1.1 Introduction 30
1.2 Theoretical Background 34
1.2.1 Magnetothermopower in Quantum Dots of Nonlinear Optical Materials 34
1.2.2 Magnetothermopower in Quantum Dots of III–V Materials 38
1.2.2.1 The Three Band Model of Kane 38
1.2.2.2 The Two Band Model of Kane 39
1.2.2.3 The Model of Stillman et al. 39
1.2.2.4 The Model of Newson and Kurobe 40
1.2.2.5 The Model of Rossler 41
1.2.2.6 The Model of Palik et al. 43
1.2.2.7 The Model of Johnson and Dickey 44
1.2.2.8 The Model of Agafonov et al. 45
1.2.3 Magnetothermopower in Quantum Dotsof II–VI Materials 46
1.2.4 Magnetothermopower in Quantum Dots of n-Gallium Phosphide 47
1.2.5 Magnetothermopower in Quantum Dotsof n-Germanium 48
1.2.6 Magnetothermopower in Quantum Dots of Tellurium 50
1.2.7 Magnetothermopower in Quantum Dots of Graphite 52
1.2.8 Magnetothermopower in Quantum Dots of Platinum Antimonide 53
1.2.9 Magnetothermopower in Quantum Dots of Zerogap Materials 54
1.2.10 Magnetothermopower in Quantum Dotsof II–V Materials 55
1.2.11 Magnetothermopower in Quantum Dots of Gallium Antimonide 56
1.2.12 Magnetothermopower in Quantum Dots of Stressed Materials 60
1.2.13 Magnetothermopower in Quantum Dots of Bismuth 62
1.2.13.1 The McClure and Choi Model 62
1.2.13.2 The Hybrid Model 63
1.2.13.3 The Cohen Model 64
1.2.13.4 The Lax Model 65
1.2.13.5 Ellipsoidal Parabolic Model 65
1.2.14 Magnetothermopower in Quantum Dots of IV–VI Materials 66
1.2.15 Magnetothermopower in Quantum Dots of Lead Germanium Telluride 69
1.2.16 Magnetothermopower in Quantum Dots of Zinc and Cadmium Diphosphides 70
1.2.17 Magnetothermopower in Quantum Dots of Bismuth Telluride 71
1.2.18 Magnetothermopower in Quantum Dots of Antimony 72
1.3 Results and Discussion 74
1.4 Open Research Problems 97
References 114
2 Thermoelectric Power in Ultrathin Films and Quantum Wires Under Large Magnetic Field 122
2.1 Introduction 122
2.2 Theoretical Background 123
2.2.1 Magnetothermopower in Quantum-Confined Nonlinear Optical Materials 123
2.2.2 Magnetothermopower in Quantum-Confined Kane Type III–V Materials 126
2.2.2.1 The Three Band Model of Kane 126
2.2.2.2 The Two Band Model of Kane 127
2.2.3 Magnetothermopower in Quantum-Confined II–VI Materials 130
2.2.4 Magnetothermopower in Quantum-Confined Bismuth 132
2.2.4.1 The McClure and Choi Model 132
2.2.4.2 The Hybrid Model 134
2.2.4.3 The Cohen Model 136
2.2.4.4 The Lax Model 138
2.2.5 Magnetothermopower in Quantum-Confined IV–VI Materials 139
2.2.6 Magnetothermopower in Quantum-Confined Stressed Materials 143
2.2.7 Magnetothermopower in Carbon Nanotubes 144
2.3 Results and Discussion 146
2.4 Open Research Problems 161
References 169
3 Thermoelectric Power in Quantum Dot Superlattices Under Large Magnetic Field 172
3.1 Introduction 172
3.2 Theoretical Background 173
3.2.1 Magnetothermopower in III–V Quantum Dot Superlattices with Graded Interfaces 173
3.2.2 Magnetothermopower in II–VI Quantum Dot Superlattices with Graded Interfaces 176
3.2.3 Magnetothermopower in IV–VI Quantum Dot Superlattices with Graded Interfaces 178
3.2.4 Magnetothermopower in HgTe/CdTe Quantum Dot Superlattices with Graded Interfaces 182
3.2.5 Magnetothermopower in III–V Quantum Dot Effective Mass Superlattices 185
3.2.6 Magnetothermopower in II–VI Quantum Dot Effective Mass Superlattices 186
3.2.7 Magnetothermopower in IV–VI Quantum Dot Effective Mass Superlattices 187
3.2.8 Magnetothermopower in HgTe/CdTe Quantum Dot Effective Mass Superlattices 189
3.3 Results and Discussion 190
3.4 Open Research Problems 196
References 197
4 Thermoelectric Power in Quantum Wire Superlattices Under Large Magnetic Field 199
4.1 Introduction 199
4.2 Theoretical Background 199
4.2.1 Magnetothermopower in III–V Quantum Wire Superlattices with Graded Interfaces 199
4.2.2 Magnetothermopower in II–VI Quantum Wire Superlattices with Graded Interfaces 200
4.2.3 Magnetothermopower in IV–VI Quantum Wire Superlattices with Graded Interfaces 201
4.2.4 Magnetothermopower in HgTe/CdTe Quantum Wire Superlattices with Graded Interfaces 202
4.2.5 Magnetothermopower in III–V Quantum Wire Effective Mass Superlattices 203
4.2.6 Magnetothermopower in II–VI Quantum Wire Effective Mass Superlattices 204
4.2.7 Magnetothermopower in IV–VI Quantum Wire Effective Mass Superlattices 205
4.2.8 Magnetothermopower in HgTe/CdTe Quantum Wire Effective Mass Superlattices 206
4.3 Results and Discussion 207
4.4 Open Research Problem 213
References 213
Part II Thermoelectric Power Under Magnetic Quantization in Macro and Microelectronic Materials 214
5 Thermoelectric Power in Macroelectronic Materials Under Magnetic Quantization 215
5.1 Introduction 215
5.2 Theoretical Background 215
5.2.1 Magnetothermopower in Nonlinear Optical Materials 215
5.2.2 Magnetothermopower in Kane Type III–V Materials 217
5.2.3 Magnetothermopower in II–VI Materials 219
5.2.4 Magnetothermopower in Bismuth 220
5.2.4.1 The McClure and Choi model 220
5.2.4.2 The Cohen Model 221
5.2.4.3 The Lax Model 221
5.2.5 Magnetothermopower in IV–VI Materials 222
5.2.6 Magnetothermopower in Stressed Materials 222
5.3 Results and Discussion 223
5.4 Open Research Problems 235
References 236
6 Thermoelectric Power in Superlattices Under Magnetic Quantization 238
6.1 Introduction 238
6.2 Theoretical Background 238
6.2.1 Magnetothermopower in III–V Superlattices with Graded Interfaces 238
6.2.2 Magnetothermopower in II–VI Superlattices with Graded Interfaces 240
6.2.3 Magnetothermopower in IV–VI Superlattices with Graded Interfaces 241
6.2.4 Magnetothermopower in HgTe/CdTe Superlattices with Graded Interfaces 243
6.2.5 Magnetothermopower in III–V EffectiveMass Superlattices 244
6.2.6 Magnetothermopower in II–VI EffectiveMass Superlattices 245
6.2.7 Magnetothermopower in IV–VI EffectiveMass Superlattices 246
6.2.8 Magnetothermopower in HgTe/CdTe Effective Mass Superlattices 247
6.2.9 Magnetothermopower in III–V Quantum Well Superlattices with Graded Interfaces 248
6.2.10 Magnetothermopower in II–VI Quantum Well Superlattices with Graded Interfaces 249
6.2.11 Magnetothermopower in IV–VI Quantum Well Superlattices with Graded Interfaces 249
6.2.12 Magnetothermopower in HgTe/CdTe Quantum Well Superlattices with Graded Interfaces 250
6.2.13 Magnetothermopower in III–V Quantum Well-Effective Mass Superlattices 251
6.2.14 Magnetothermopower in II–VI Quantum Well-Effective Mass Superlattices 251
6.2.15 Magnetothermopower in IV–VI Quantum Well-Effective Mass Superlattices 252
6.2.16 Magnetothermopower in HgTe/CdTe Quantum Well-Effective Mass Superlattices 252
6.3 Results and Discussion 253
6.4 Open Research Problems 260
References 263
7 Thermoelectric Power in Ultrathin Films Under Magnetic Quantization 264
7.1 Introduction 264
7.2 Theoretical Background 264
7.2.1 Magnetothermopower in Ultrathin Films of Nonlinear Optical Materials 264
7.2.2 Magnetothermopower in Ultrathin Films of Kane Type III–V Materials 265
7.2.3 Magnetothermopower in Ultrathin Filmsof II–VI Materials 267
7.2.4 Magnetothermopower in Ultrathin Films of Bismuth 268
7.2.4.1 The McClure and Choi Model 268
7.2.4.2 The Cohen Model 268
7.2.4.3 The Lax Model 269
7.2.5 Magnetothermopower in Ultrathin Filmsof IV–VI Materials 270
7.2.6 Magnetothermopower in Ultrathin Films of Stressed Materials 270
7.3 Results and Discussion 270
7.4 Open Research Problems 276
References 279
Part III Thermoelectric Power Under Large Magnetic Field in Quantum Confined Optoelectronic Materials in the Presenceof Light Waves 280
8 Optothermoelectric Power in Ultrathin Films and Quantum Wires of Optoelectronic Materials Under Large Magnetic Field 281
8.1 Introduction 281
8.2 Theoretical Background 282
8.2.1 Optothermoelectric Power in Ultrathin Films of Optoelectronic Materials Under Large Magnetic Field 282
8.2.2 Optothermoelectric Power in Quantum Wires of Optoelectronic Materials Under Large Magnetic Field 294
8.3 Results and Discussion 296
8.4 Open Research Problem 313
References 316
9 Optothermoelectric Power in Quantum Dots of Optoelectronic Materials Under Large Magnetic Field 317
9.1 Introduction 317
9.2 Theoretical Background 317
9.2.1 Magnetothermopower in Quantum Dots of Optoelectronic Materials 317
9.3 Results and Discussion 318
9.4 Open Research Problem 321
Reference 321
10 Optothermoelectric Power in Quantum-Confined Semiconductor Superlattices 322
10.1 Introduction 322
10.2 Theoretical Background 322
10.2.1 Magnetothermopower in III–V Quantum Wire Effective Mass Superlattices 322
10.2.2 Magnetothermopower in III–V Quantum Dot Effective Mass Superlattices 324
10.2.3 Magnetothermopower in III–V Quantum Wire Superlattices with Graded Interfaces 324
10.2.4 Magnetothermopower in III–V Quantum DotSuperlattices with Graded Interfaces 326
10.3 Results and Discussion 327
10.4 Open Research Problems 333
Reference 336
Part IV Thermoelectric Power Under Magnetic Quantization in Macro and Micro-optoelectronic Materials in the Presence of Light Waves 337
11 Optothermoelectric Power in Macro-Optoelectronic Materials Under Magnetic Quantization 338
11.1 Introduction 338
11.2 Theoretical Background 338
11.2.1 Magnetothermopower in Optoelectronic Materials 338
11.3 Results and Discussion 340
11.4 Open Research Problem 351
Reference 351
12 Optothermoelectric Power in Ultrathin Films of Optoelectronic Materials Under Magnetic Quantization 352
12.1 Introduction 352
12.2 Theoretical Background 352
12.2.1 Magnetothermopower in Ultrathin Films of Optoelectronic Materials 352
12.3 Results and Discussion 353
12.4 Open Research Problem 357
Reference 357
13 Optothermoelectric Power in Superlattices of Optoelectronic Materials Under Magnetic Quantization 358
13.1 Introduction 358
13.2 Theoretical Background 358
13.2.1 Magnetothermopower in III–V Quantum Well-Effective Mass Superlattices 358
13.2.2 Magnetothermopower in III–V Quantum Well Superlattices with Graded Interfaces 360
13.3 Results and Discussion 362
13.4 Open Research Problems 365
References 367
14 Applications and Brief Review of Experimental Results 368
14.1 Introduction 368
14.2 Applications 368
14.2.1 Effective Electron Mass 368
14.2.2 Debye Screening Length 369
14.2.3 Carrier Contribution to the Elastic Constants 370
14.2.4 Diffusivity–Mobility Ratio 370
14.2.5 Diffusion Coefficient of the Minority Carriers 372
14.2.6 Nonlinear Optical Response 372
14.2.7 Third-Order Nonlinear Optical Susceptibility 372
14.2.8 Generalized Raman Gain 373
14.3 Brief Review of Experimental Works 373
14.3.1 Bulk Samples 373
14.3.2 Nanostructured Materials 377
14.4 Open Research Problem 381
References 381
15 Conclusion and Future Research 386
References 389
Appendix A 390
A.1 Nonlinear Optical Materials and Cd3As2 390
A.2 III–V Materials 391
A.2.1 Three Band Model of Kane 391
A.2.2 Two Band Model of Kane 391
A.2.3 Parabolic Energy Bands 392
A.2.4 The Model of Stillman Et al. 392
A.2.5 The Model of Palik Et al. 393
A.2.6 Model of Johnson and Dicley 393
A.3 n-Type Gallium Phosphide 394
A.4 II–VI Materials 395
A.5 Bismuth Telluride 395
A.6 Stressed Materials 395
A.7 IV–VI Semiconductors 396
A.7.1 Bangert and Kästner Model 396
A.7.2 Cohen Model 396
A.7.3 Dimmock Model 397
A.7.4 Foley and Langenberg Model 399
A.8 n-Ge 401
A.8.1 Model of Cardona Et al. 401
A.8.2 Model of Wang and Ressler 401
A.9 Platinum Antimonide 403
A.10 n-GaSb 404
A.11 n-Te 404
A.12 Bismuth 405
A.12.1 McClure and Choi Model 405
A.12.2 Hybrid Model 406
A.12.3 Lax Ellipsoidal Nonparabolic Model 407
A.12.4 Ellipsoidal Parabolic Model 407
A.13 Open Research Problem 407
Reference 407
Subject Index 408
Material Index 411