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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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