Quantum wells, wires and dots : theoretical and computational physics of semiconductor nanostructures /: theoretical and computational physics of semiconductor nanostructures. (2016)

• Record Type: Book
• Further Information: Note: Paul Harrison and Alex Valavanis.
• Authors: Harrison, P (Paul); Valavanis, Alex
• Contents: Dedication iii List of Contributors xiii Preface xv Acknowledgements xix Introduction xxiii References xxiv 1 Semiconductors and heterostructures 1 1.1 The mechanics of waves 1 1.2 Crystal structure 3 1.3 The effective mass approximation 5 1.4 Band theory 5 1.5 Heterojunctions 7 1.6 Heterostructures 7 1.7 The envelope function approximation 10 1.8 Band non-parabolicity 11 1.9 The reciprocal lattice 13 Exercises 16 References 17 2 Solutions to Schrödinger’s equation 19 2.1 The infinite well 19 2.2 In-plane dispersion 22 2.3 Extension to include band non-parabolicity 24 2.4 Density of states 26 2.4.1 Density-of-states effective mass 28 2.4.2 Two-dimensional systems 29 2.5 Subband populations 31 2.5.1 Populations in non-parabolic subbands 33 2.5.2 Calculation of quasi-Fermi energy 35 2.6 Thermalised distributions 36 2.7 Finite well with constant mass 37 2.7.1 Unbound states 43 2.7.2 Effective mass mismatch at heterojunctions 45 2.7.3 The infinite barrier height and mass limits 49 2.8 Extension to multiple-well systems 50 2.9 The asymmetric single quantum well 53 2.10 Addition of an electric field 54 2.11 The infinite superlattice 57 2.12 The single barrier 63 2.13 The double barrier 65 2.14 Extension to include electric field 71 2.15 Magnetic fields and Landau quantisation 72 2.16 In summary 74 Exercises 74 References 76 3 Numerical solutions 79 3.1 Bisection root-finding 79 3.2 Newton–Raphson root finding 81 3.3 Numerical differentiation 83 3.4 Discretised Schrödinger equation 84 3.5 Shooting method 84 3.6 Generalized initial conditions 86 3.7 Practical implementation of the shooting method 88 3.8 Heterojunction boundary conditions 90 3.9 Matrix solutions of the discretised Schrödinger equation 91 3.10 The parabolic potential well 94 3.11 The Pöschl–Teller potential hole 98 3.12 Convergence tests 98 3.13 Extension to variable effective mass 99 3.14 The double quantum well 103 3.15 Multiple quantum wells and finite superlattices 104 3.16 Addition of electric field 106 3.17 Extension to include variable permittivity 106 3.18 Quantum confined Stark effect 108 3.19 Field–induced anti-crossings 108 3.20 Symmetry and selection rules 110 3.21 The Heisenberg uncertainty principle 110 3.22 Extension to include band non-parabolicity 113 3.23 Poisson’s equation 114 3.24 Matrix solution of Poisson’s equation 118 3.25 Self-consistent Schrödinger–Poisson solution 119 3.26 Modulation doping 121 3.27 The high-electron-mobility transistor 122 3.28 Band filling 123 Exercises 124 References 125 4 Diffusion 127 4.1 Introduction 127 4.2 Theory 129 4.3 Boundary conditions 130 4.4 Convergence tests 131 4.5 Numerical stability 133 4.6 Constant diffusion coefficients 133 4.7 Concentration dependent diffusion coefficient 135 4.8 Depth dependent diffusion coefficient 136 4.9 Time dependent diffusion coefficient 138 4.10 δ-doped quantum wells 138 4.11 Extension to higher dimensions 141 Exercises 142 References 142 5 Impurities 145 5.1 Donors and acceptors in bulk material 145 5.2 Binding energy in a heterostructure 147 5.3 Two-dimensional trial wave function 152 5.4 Three-dimensional trial wave function 158 5.5 Variable-symmetry trial wave function 164 5.6 Inclusion of a central cell correction 170 5.7 Special considerations for acceptors 171 5.8 Effective mass and dielectric mismatch 172 5.9 Band non-parabolicity 173 5.10 Excited states 173 5.11 Application to spin-flip Raman spectroscopy 174 5.11.1 Diluted magnetic semiconductors 174 5.11.2 Spin-flip Raman spectroscopy 176 5.12 Alternative approach to excited impurity states 178 5.13 The ground state 180 5.14 Position dependence 181 5.15 Excited states 181 5.16 Impurity occupancy statistics 184 Exercises 188 References 189 6 Excitons 191 6.1 Excitons in bulk 191 6.2 Excitons in heterostructures 193 6.3 Exciton binding energies 193 6.4 1s exciton 198 6.5 The two-dimensional and three-dimensional limits 202 6.6 Excitons in single quantum wells 206 6.7 Excitons in multiple quantum wells 208 6.8 Stark ladders 210 6.9 Self-consistent effects 211 6.10 2s exciton 212 Exercises 214 References 215 7 Strained quantum wells 217 7.1 Stress and strain in bulk crystals 217 7.2 Strain in quantum wells 221 7.3 Critical thickness of layers 224 7.4 Strain balancing 226 7.5 Effect on the band profile of quantum wells 228 7.6 The piezoelectric effect 231 7.7 Induced piezoelectric fields in quantum wells 234 7.8 Effect of piezoelectric fields on quantum wells 236 Exercises 239 References 240 8 Simple models of quantum wires and dots 241 8.1 Further confinement 241 8.2 Schrödinger’s equation in quantum wires 243 8.3 Infinitely deep rectangular wires 245 8.4 Simple approximation to a finite rectangular wire 247 8.5 Circular cross-section wire 251 8.6 Quantum boxes 255 8.7 Spherical quantum dots 256 8.8 Non-zero angular momentum states 259 8.9 Approaches to pyramidal dots 262 8.10 Matrix approaches 263 8.11 Finite difference expansions 263 8.12 Density of states 265 Exercises 267 References 268 9 Quantum dots 269 9.1 0-dimensional systems and their experimental realization 269 9.2 Cuboidal dots 271 9.3 Dots of arbitrary shape 272 9.3.1 Convergence tests 277 9.3.2 Efficiency 279 9.3.3 Optimization 281 9.4 Application to real problems 282 9.4.1 InAs/GaAs self-assembled quantum dots 282 9.4.2 Working assumptions 282 9.4.3 Results 283 9.4.4 Concluding remarks 286 9.5 A more complex model is not always a better model 288 Exercises 289 References 290 10 Carrier scattering 293 10.1 Introduction 293 10.2 Fermi’s Golden Rule 294 10.3 Extension to sinusoidal perturbations 296 10.4 Averaging over two-dimensional carrier distributions 296 10.5 Phonons 298 10.6 Longitudinal optic phonon scattering of two-dimensional carriers 301 10.7 Application to conduction subbands 313 10.8 Mean intersubband LO phonon scattering rate 315 10.9 Ratio of emission to absorption 316 10.10 Screening of the LO phonon interaction 318 10.11 Acoustic deformation potential scattering 319 10.12 Application to conduction subbands 324 10.13 Optical deformation potential scattering 326 10.14 Confined and interface phonon modes 328 10.15 Carrier–carrier scattering 328 10.16 Addition of screening 336 10.17 Mean intersubband carrier–carrier scattering rate 337 10.18 Computational implementation 339 10.19 Intrasubband vers
• Edition: Fourth edition
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 537.6226; Quantum wells; Nanowires; Quantum dots
• Languages: English
• ISBNs: 9781118923344; 9781118923351
• Related ISBNs: 9781118923368
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.