Quantum Wells, Wires and Dots Second Edition by Paul Harrison
(Theoretical and Computational Physics of Semiconductor Nanostructures)
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Quantum Wells, Wires and Dots Second Edition written by
by Paul Harrison , The University of Leeds, UK.
This book is aimed at providing all of the essential information, both theoretical and computational, in order that the reader can, starting from essentially nothing, understand how the electronic, optical and transport properties of semiconductor heterostructures are calculated. However, perhaps more importantly, starting from this low common denominator, this text is designed to lead the reader through a series of simple example theoretical and computational implementations, and slowly build from solid foundations, to a level where the reader can begin to initiate theoretical investigations or explanations of their own.
Quantum Wells, Wires and Dots Second Edition written by
by Paul Harrison
cover the following topics.
1 Semiconductors and heterostructures
1.1 The mechanics of waves
1.2 Crystal structure
1.3 The effective mass approximation
1.4 Band theory
1.5 Heterojunctions
1.6 Heterostructures
1.7 The envelope function approximation
1.8 The reciprocal lattice
2 Solutions to Schrodinger's equation
2.1 The infinite well
2.2 In-plane dispersion
2.3 Density of states
2.4 Subband populations
2.5 Finite well with constant mass
2.6 Effective mass mismatch at heterojunctions
2.7 The infinite barrier height and mass limits
2.8 Hermiticity and the kinetic energy operator
2.9 Alternative kinetic energy operators
2.10 Extension to multiple-well systems
2.11 The asymmetric single quantum well
2.12 Addition of an electricfield
2.13 The infinite superlattice
2.14 The single barrier
2.15 The double barrier
2.16 Extension to include electricfield
2.17 Magnetic fields and Landau quantisation
2.18 In summary
3 Numerical solutions
3.1 Shooting method
3.2 Generalised initial conditions
3.3 Practical implementation of the shooting method
3.4 Heterojunction boundary conditions
3.5 The parabolic potential well
3.6 The Poschl-Teller potential hole
3.7 Convergence tests
3.8 Extension to variable effective mass
3.9 The double quantum well
3.10 Multiple quantum wells and finite superlattices
3.11 Addition of electricfield
3.12 Quantum confined Stark effect
3.13 Field-induced anti-crossings
3.14 Symmetry and selection rules
3.15 The Heisenberg uncertainty principle
3.16 Extension to include band non-parabolicity
3.17 Poisson's equation
3.18 Self-consistent Schrodinger-Poisson solution
3.19 Computational implementation
3.20 Modulation doping
3.21 The high-electron-mobility transistor
3.22 Bandfilling
4 Diffusion
4.1 Introduction
4.2 Theory
4.3 Boundary conditions
4.4 Convergence tests
4.5 Constant diffusion coefficients
4.6 Concentration dependent diffusion coefficient
4.7 Depth dependent diffusion coefficient
4.8 Time dependent diffusion coefficient
4.9 d-doped quantum wells
4.10 Extension to higher dimensions
5 Impurities
5.1 Donors and acceptors in bulk material
5.2 Binding energy in a heterostructure
5.3 Two-dimensional trial wave function
5.4 Three-dimensional trial wave function
5.5 Variable-symmetry trial wave function
5.6 Inclusion of a central cell correction
5.7 Special considerations for acceptors
5.8 Effective mass and dielectric mismatch
5.9 Band non-parabolicity
5.10 Excited states
5.11 Application to spin-flip Raman spectroscopy
5.11.1 Diluted magnetic semiconductors
5.11.2 Spin-flip Raman spectroscopy
5.12 Alternative approach to excited impurity states
5.13 The ground state
5.14 Position dependence
5.15 Excited States
5.16 Impurity occupancy statistics
6 Excitons
6.1 Excitons in bulk
6.2 Excitons in heterostructures
6.3 Exciton binding energies
6.4 1s exciton
6.5 The two-dimensional and three-dimensional limits
6.6 Excitons in single quantum wells
6.7 Excitons in multiple quantum wells
6.8 Stark Ladders
6.9 Self-consistent effects
6.10 Spontaneous symmetry breaking
6.11 2s exciton
7 Strained quantum wells, V. D. Jovanovic
7.1 Stress and strain in bulk crystals
7.2 Strain in quantum wells
7.3 Strain balancing
7.4 Effect on the band profile of quantum wells
7.5 The piezoelectric effect
7.6 Induced piezoelectric fields in quantum wells
7.7 Effect of piezoelectric fields on quantum wells
8 Quantum wires and dots
8.1 Further confinement
8.2 Schrodinger's equation in quantum wires
8.3 Infinitely deep rectangular wires
8.4 Simple approximation to a finite rectangular wire
8.5 Circular cross-section wire
8.6 Quantum boxes
8.7 Spherical quantum dots
8.8 Non-zero angular momentum states
8.9 Approaches to pyramidal dots
8.10 Matrix approaches
8.11 Finite difference expansions
8.12 Density of states
9 Carrier scattering
9.1 Fermi's Golden Rule
9.2 Phonons
9.3 Longitudinal optic phonon scattering of bulk carriers
9.4 LO phonon scattering of two-dimensional carriers
9.5 Application to conduction subbands
9.6 Averaging over carrier distributions
9.7 Ratio of emission to absorption
9.8 Screening of the LO phonon interaction
9.9 Acoustic deformation potential scattering
9.10 Application to conduction subbands
9.11 Optical deformation potential scattering
9.12 Confined and interface phonon modes
9.13 Carrier–carrier scattering
9.14 Addition of screening
9.15 Averaging over an initial state population
9.16 Intrasubband versus intersubband
9.17 Thermalised distributions
9.18 Auger-type intersubband processes
9.19 Asymmetric intrasubband processes
9.20 Empirical relationships
9.21 Carrier-photon scattering
9.22 Quantum cascade lasers
9.23 Carrier scattering in quantum wires and dots
10 Multiband envelope function (k.p) method, Z. Ikonic
10.1 Symmetry, basis states and band structure 345
10.2 Valence band structure and the 6 x 6 Hamiltonian •
10.3 4x4 valence band Hamiltonian
10.4 Complex band structure
10.5 Block-diagonalisation of the Hamiltonian
10.6 The valence band in strained cubic semiconductors
10.7 Hole subbands in heterostructures
10.8 Valence band offset
10.9 The layer (transfer matrix) method
10.10 Quantum well subbands
10.11 The influence of strain
10.12 Strained quantum well subbands
10.13 Direct numerical methods
11 Empirical pseudopotential theory
11.1 Principles and Approximations
11.2 Elemental Band Structure Calculation
11.3 Spin-orbit coupling
11.4 Compound Semiconductors
11.5 Charge densities
11.6 Calculating the effective mass
11.7 Alloys
11.8 Atomic form factors
11.9 Generalisation to a large basis
11.10 Spin-orbit coupling within the large basis approach 396
11.11 Computational implementation
11.12 Deducing the parameters and application
11.13 Isoelectronic impurities in bulk
11.14 The electronic structure around point defects
12 Microscopic electronic properties of heterostructures
12.1 The superlattice unit cell
12.2 Application of large basis method to superlattices
12.3 Comparison with envelope-function approximation
12.4 In-plane dispersion
12.5 Interface coordination
12.6 Strain-layered superlattices
12.7 The superlattice as a perturbation
12.8 Application to GaAs/AlAs superlattices
12.9 Inclusion of remote bands
12.10 The valence band
12.11 Computational effort
12.12 Superlattice dispersion and the interminiband laser
12.13 Addition of electricfield
13 Application to quantum wires and dots
13.1 Recent progress
13.2 The quantum-wire unit cell
13.3 Confined states
13.4 V-grooved quantum wires
13.5 Along-axis dispersion
13.6 Tiny quantum dots
13.7 Pyramidal quantum dots
13.8 Transport through dot arrays
13.9 Anti-wires and anti-dots
Concluding Remarks
Appendix A: Materials parameters
References
Topic Index
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