Heisenberg’s Uncertainty Principle and the Electron Statistics in Quantized Structures

This book highlights the importance of Electron Statistics (ES), which occupies a singular position in the arena of solid state sciences, in heavily doped (HD) nanostructures by applying Heisenberg’s Uncertainty Principle directly without using the complicated Density-of-States function approach as given in the literature. The materials considered are HD quantum confined nonlinear optical, III-V, II-VI, IV-VI, GaP, Ge, PtSb2, stressed materials, GaSb, Te, II-V, Bi2Te3, lead germanium telluride, zinc and cadmium diphosphides, and quantum confined III-V, IV-VI, II-VI and HgTe/CdTe super-lattices with graded interfaces and effective mass super-lattices. The presence of intense light waves in optoelectronics and strong electric field in nano-devices change the band structure of materials in fundamental ways, which have also been incorporated in the study of ES in HD quantized structures of optoelectronic compounds that control the studies of the HD quantum effect devices under strong fields. The influence of magnetic quantization, magneto size quantization, quantum wells, wires and dots, crossed electric and quantizing fields, intense electric field, and light waves on the ES in HD quantized structures and superlattices are discussed. The content of this book finds six different applications in the arena of nano-science and nanotechnology and the various ES dependent electronic quantities, namely the effective mass, the screening length, the Einstein relation and the elastic constants have been investigated. This book is useful for researchers, engineers and professionals in the fields of Applied Sciences, solid state and materials science, nano-science and technology, condensed matter physics, and allied fields, including courses in semiconductor nanostructures. ​ Preface References Acknowledgments Acknowledgment by Kamakhya Prasad Ghatak Acknowledgment by Madhuchhanda Mitra Acknowledgment by Arindam Biswas Contents About the Authors 1 The Heisenberg’s Uncertainty Principle (HUP) and the Electron Statistics (ES) in Heavily Doped (HD) Kane-type III-V and Opto-Electronic Materials in the Presence of Intense Radiation 1.1 Introduction 1.2 Mathematical Basis 1.2.1 The Bulk Compounds 1.2.2 The Magnetic Quantization 1.2.3 The Cross Fields Configuration 1.2.4 The Quantum Wells 1.2.5 The Doping Superlattices 1.2.6 The Quantum Dots 1.2.7 The Magneto-Size Quantization 1.2.8 The Nanowires 1.2.9 The Magneto Doping Superlattices 1.2.10 The Quantum Well Effective Mass Superlattices 1.2.11 The Nanowire Effective Mass Superlattices 1.2.12 The Quantum Dot Effective Mass Superlattices 1.2.13 The Magneto Effective Mass Superlattices 1.2.14 The Magneto Quantum Well Effective Mass Superlattices 1.2.15 The Quantum Well Superlattices with Graded Interfaces 1.2.16 The Nanowire Superlattices with Graded Interfaces 1.2.17 The Quantum dot Superlattices with Graded Interfaces 1.2.18 The Magneto Superlattices with Graded Interfaces 1.2.19 The Magneto Quantum Well Superlattices with Graded Interfaces 1.3 Few Related Applications 1.3.1 Introduction 1.3.2 Thermoelectric Power (G) 1.3.3 Experimental Determination of Debye Screening Length (DSL) 1.3.4 Experimental Determination of Diffusivity-Mobility Ratio 1.3.5 Experimental Determination of ΔC44 and ΔC456 1.3.6 Quantum Capacitance 1.4 Result and Discussions References 2 The HUP and the ES in HD Kane-Type III-V and Opto-Electronic Materials under Intense Electric Field 2.1 Introduction 2.2 Mathematical Basis 2.2.1 The Bulk Materials 2.2.2 The Magnetic Quantization 2.2.3 The Quantum Wells 2.2.4 The Nanowires 2.2.5 The Quantum Dots 2.2.6 The Magneto-Size Quantization 2.2.7 The Doping Superlattices 2.2.8 The Magneto Doping Superlattices 2.2.9 The Quantum Well Effective Mass Superlattices 2.2.10 The Magneto Effective Mass Superlattices 2.2.11 The Nanowire Effective Mass Superlattices 2.2.12 The Quantum Dot Effective Mass Superlattices 2.2.13 The Magneto Quantum Well Effective Mass Superlattices 2.2.14 The Quantum Well Superlattices with Graded Interfaces 2.2.15 The Nanowire Superlattices with Graded Interfaces 2.2.16 The Quantum dot Superlattices with Graded Interfaces 2.2.17 The Magneto Superlattices with Graded Interfaces 2.2.18 The Magneto Quantum Well Superlattices with Graded Interfaces 2.3 Result and Discussions References 3 The HUP and the ES in Quantum Wells (QWs) of HD Non-parabolic Materials 3.1 Introduction 3.2 Mathematical Basis 3.2.1 The Nonlinear Optical Materials 3.2.2 The III-V Materials 3.2.3 The II-VI Materials 3.2.4 The IV-VI Materials 3.2.5 The Stressed Kane-Type Materials 3.2.6 The Te 3.2.7 The Gallium Phosphide 3.2.8 The Platinum Antimonide 3.2.9 The Bismuth Telluride 3.2.10 The Germanium 3.2.11 The Gallium Antimonide 3.3 Result and Discussions References 4 The HUP and the ES in Nanowires of HD Non-parabolic Materials 4.1 Introduction 4.2 Mathematical Basis 4.2.1 The Nonlinear Optical Materials 4.2.2 The III-V Materials 4.2.3 The II-VI Materials 4.2.4 The IV-VI Materials 4.2.5 The Stressed Kane-Type Materials 4.2.6 The Te 4.2.7 The Gallium Phosphide 4.2.8 The Platinum Antimonide 4.2.9 The Bismuth Telluride 4.2.10 The Germanium 4.2.11 The Galium Antimonide 4.2.12 The HD II-V Materials 4.3 Result and Discussions References 5 The HUP and the ES in Quantum Dots (QDs) of HD Non-parabolic Materials 5.1 Introduction 5.2 Mathematical Basis 5.2.1 The Nonlinear Optical Materials 5.2.2 The III-V Materials 5.2.3 The II-VI Materials 5.2.4 The IV-VI Materials 5.2.5 The Stressed Kane-Type Materials 5.2.6 The Te 5.2.7 The Gallium Phosphide 5.2.8 The Platinum Antimonide 5.2.9 The Bismuth Telluride 5.2.10 The Germanium 5.2.11 The Gallium Antimonide 5.2.12 The II-V Materials 5.3 Summary and Conclusion References 6 The HUP and the ES in Doping Superlattices of HD Non-parabolic Semiconductors 6.1 Introduction 6.2 Mathematical Basis 6.2.1 The Nonlinear Optical Semiconductors 6.2.2 The III-V and Opto-Electronic Semiconductor 6.2.3 The II-VI Semiconductors 6.2.4 The IV-VI Semiconductors 6.2.5 The Stressed Kane-Type Semiconductors 6.3 Result and Discussions References 7 The HUP and the ES in Accumulation of Non-parabolic Semiconductors 7.1 Introduction 7.2 Mathematical Basis 7.2.1 The NonLinear Optical Semiconductors 7.2.2 The III-V and Opto-Electronic Materials 7.2.3 The II-VI Semiconductors 7.2.4 The IV-VI Semiconductors 7.2.5 The Stressed Kane-Type Materials 7.3 Results and Discussion References 8 The HUP and the ES in Heavily Doaped (HD) Non-parabolic Semiconductors Under Magnetic Quantization 8.1 Introduction 8.2 Mathematical Basis 8.2.1 The Nonlinear Optical Semiconductors 8.2.2 The III-V Semiconductors 8.2.3 The II-VI Semiconductors 8.2.4 The IV-VI Semiconductors 8.2.5 The Stressed Kane-Type Semiconductors 8.2.6 The Te 8.2.7 The Gallium Phosphide 8.2.8 The Platinum Antimonide 8.2.9 The Bismuth Telluride 8.2.10 The Germanium 8.2.11 The Gallium Antimonide 8.2.12 The II-V Materials 8.2.13 The Lead Germanium Telluride 8.3 Result and Discussions References 9 The HUP and the ES in HD Non-parabolic Semiconductors Under Cross-Fields Configuration 9.1 Introduction 9.2 Mathematical Basis 9.2.1 The Nonlinear Optical Semiconductors 9.2.2 The Kane-Type III-V Semiconductors 9.2.3 The II-VI Semiconductors 9.2.4 The IV-VI Semiconductors 9.2.5 The Stressed Kane-Type Semiconductors 9.3 Result and Discussion References 10 The HUP and the ES in Heavily Doped (HD) Non-parabolic Semiconductors Under Magneto-Size Quantization 10.1 Introduction 10.2 Mathematical Basis 10.2.1 The Nonlinear Optical Semiconductors 10.2.2 The III-V Semiconductors 10.2.3 The II-VI Semiconductors 10.2.4 The IV-VI Semiconductors 10.2.5 The Stressed Kane-Type Semiconductor 10.2.6 The Te 10.2.7 The Gallium Phosphide 10.2.8 The Platinum Antimonide 10.2.9 The Bismuth Telluride 10.2.10 The Germanium 10.2.11 The Gallium Antimonide 10.2.12 The II-V Materials 10.2.13 The Lead Germanium Telluride 10.3 Summary and Conclusion References 11 The HUP and the ES in Heavily Doped Non-parabolic Quantum Wells (HDQWs) Under Cross-Fields Configuration 11.1 Introduction 11.2 Mathematical Basis 11.2.1 The Nonlinear Optical Semiconductors 11.2.2 The Kane-Type III-V Semiconductors 11.2.3 The II-VI Semiconductors 11.2.4 The IV-VI Semiconductors 11.2.5 The Stressed Kane-Type Semiconductors 11.3 Summary and Conclusion References 12 The HUP and the ES in Doping Super Lattices of HD Non-parabolic Semiconductors Under Magnetic Quantization 12.1 Introduction 12.2 Mathematical Basis 12.2.1 The Nonlinear Optical Semiconductors 12.2.2 The Kane-Type III-V Semiconductors 12.2.3 The II-VI Semiconductors 12.2.4 The IV-VI Semiconductors 12.2.5 The Stressed Kane-Type Semiconductors 12.3 Result and Discussion References 13 The HUP and Magneto ES in Accumulation Layers 13.1 Introduction 13.2 Mathematical Basis 13.2.1 The Nonlinear Optical Semiconductors 13.2.2 The III-V and Opto-electronic Materials 13.2.3 The II-VI Semiconductors 13.2.4 The IV-VI Semiconductors 13.2.5 The Stressed Kane-Type Semiconductors 13.2.6 The Germanium 13.3 Summary and Conclusion References Material Index Subject Index