Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures, 3rd EditionISBN: 9780470770986
564 pages
February 2010

Description
Table of Contents
Acknowledgements.
About the author(s).
About the book.
Introduction.
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 Schrödinger’s equation.
2.1 The infinite well
2.2 Inplane 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 multiplewell systems
2.11 The asymmetric single quantum well
2.12 Addition of an electric field
2.13 The infinite superlattice
2.14 The single barrier
2.15 The double barrier
2.16 Extension to include electric field
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 Pöschl–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 electric field
3.12 Quantum confined Stark effect
3.13 Field–induced anticrossings
3.14 Symmetry and selection rules
3.15 The Heisenberg uncertainty principle
3.16 Extension to include band nonparabolicity
3.17 Poisson’s equation
3.18 Selfconsistent Schrödinger–Poisson solution
3.19 Computational implementation
3.20 Modulation doping
3.21 The highelectronmobility transistor
3.22 Band filling
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 δdoped 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 Twodimensional trial wave function
5.4 Threedimensional trial wave function
5.5 Variablesymmetry 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 nonparabolicity
5.10 Excited states
5.11 Application to spinflip 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 twodimensional and threedimensional limits
6.6 Excitons in single quantum wells
6.7 Excitons in multiple quantum wells
6.8 Stark Ladders
6.9 Selfconsistent effects
6.10 Spontaneous symmetry breaking
6.11 2s exciton
7 Strained quantum wells, V. D. Jovanovíć.
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 Simple models of quantum wires and dots.
8.1 Further confinement.
8.2 Schrödinger’s equation in quantum wires.
8.3 Infinitely deep rectangular wires.
8.4 Simple approximation to a finite rectangular wire.
8.5 Circular crosssection wire.
8.6 Quantum boxes.
8.7 Spherical quantum dots.
8.8 Nonzero angular momentum states.
8.9 Approaches to pyramidal dots.
8.10 Matrix approaches.
8.11 Finite difference expansions.
8.12 Density of states.
9 Quantum dots, M. Califano.
9.1 0dimensional systems and their experimental realization.
9.2 Cuboidal dots.
9.3 Dots of arbitrary shape.
9.4 Application to real problems.
9.5 A more complex model is not always a better model.
10 Carrier scattering.
10.1 Fermi’s Golden Rule.
10.2 Phonons.
10.3 Longitudinal optic phonon scattering of bulk carriers.
10.4 LO phonon scattering of twodimensional carriers.
10.5 Application to conduction subbands.
10.6 Averaging over carrier distributions.
10.7 Ratio of emission to absorption.
10.8 Screening of the LO phonon interaction.
10.9 Acoustic deformation potential scattering.
10.10 Application to conduction subbands.
10.11 Optical deformation potential scattering.
10.12 Confined and interface phonon modes.
10.13 Carrier–carrier scattering.
10.14 Addition of screening.
10.15 Averaging over an initial state population.
10.16 Intrasubband versus intersubband.
10.17 Thermalised distributions.
10.18 Augertype intersubband processes.
10.19 Asymmetric intrasubband processes.
10.20 Empirical relationships.
10.21 Carrier–photon scattering.
10.22 Carrier scattering in quantum wires and dots.
11 Electron transport.
11.1 Introduction.
11.2 Midinfrared quantum cascade lasers.
11.3 Realistic quantum cascade laser.
11.4 Rate equations.
11.5 Selfconsistent solution of the rate equations.
11.6 Calculation of the current density.
11.7 Phonon and carriercarrier scattering transport.
11.8 Electron temperature.
11.9 Calculation of the gain.
11.10 QCLs, QWIPs, QDIPs and other methods.
12 Optical properties of quantum wells, D. Indjin.
12.1 Intersubband absorption in quantum wells.
12.2 Boundbound transitions.
12.3 Boundfree transitions.
12.4 Fermi level.
12.5 Rectangular quantum well.
12.6 Intersubband optical nonlinearities.
12.7 Electric polarisation.
12.8 Intersubband second harmonic generation.
12.9 Maximization of resonant susceptibility.
13 Optical waveguides, C. A. Evans.
13.1 Introduction to optical waveguides.
13.2 Optical waveguide analysis.
13.3 Optical properties of materials.
13.4 Application to waveguides of laser devices.
14 Multiband envelope function (k.p) method, Z. Ikoníć.
14.1 Symmetry, basis states and band structure.
14.2 Valence band structure and the 6 × 6 Hamiltonian.
14.3 4 × 4 valence band Hamiltonian.
14.4 Complex band structure.
14.5 Blockdiagonalisation of the Hamiltonian.
14.6 The valence band in strained cubic semiconductors.
14.7 Hole subbands in heterostructures.
14.8 Valence band offset.
14.9 The layer (transfer matrix) method.
14.10 Quantum well subbands.
14.11 The influence of strain.
14.12 Strained quantum well subbands.
14.13 Direct numerical methods.
15 Empirical pseudopotential theory.
15.1 Principles and Approximations.
15.2 Elemental Band Structure Calculation.
15.3 Spin–orbit coupling.
15.4 Compound Semiconductors.
15.5 Charge densities.
15.6 Calculating the effective mass.
15.7 Alloys.
15.8 Atomic form factors.
15.9 Generalisation to a large basis.
15.10 Spin–orbit coupling within the large basis approach.
15.11 Computational implementation.
15.12 Deducing the parameters and application.
15.13 Isoelectronic impurities in bulk.
15.14 The electronic structure around point defects.
16 Microscopic electronic properties of heterostructures.
16.1 The superlattice unit cell.
16.2 Application of large basis method to superlattices.
16.3 Comparison with envelope–function approximation.
16.4 Inplane dispersion.
16.5 Interface coordination.
16.6 Strainlayered superlattices.
16.7 The superlattice as a perturbation.
16.8 Application to GaAs/AlAs superlattices.
16.9 Inclusion of remote bands.
16.10 The valence band.
16.11 Computational effort.
16.12 Superlattice dispersion and the interminiband laser.
16.13 Addition of electric field.
17 Application to quantum wires and dots.
17.1 Recent progress.
17.2 The quantumwire unit cell.
17.3 Confined states.
17.4 Vgrooved quantum wires.
17.5 Alongaxis dispersion.
17.6 Tiny quantum dots.
17.7 Pyramidal quantum dots.
17.8 Transport through dot arrays.
17.9 Antiwires and antidots.
Concluding Remarks.
Appendix A: Materials parameters.
References.
Topic Index.
Author Information
http://www.ee.leeds.ac.uk/homes/ph/
and always answers email. Currently he can be reached at:
p.harrison@leeds.ac.uk or p.harrison@physics.org
Paul is working on a wide variety of projects, most of which centre around exploiting quantum mechanics for the creation of novel optoelectronic devices, largely, but not exclusively, in semiconductor Quantum Wells, Wires and Dots. Uptodate information can be found on his web page. He is always looking for exceptionally wellqualified and motivated students to study for a PhD degree with himif interested, please don't hesitate to contact him.
Zoran Ikonic was Professor at the University of Belgrade and is now also a researcher in the IMP. His research interests and experience include the full width of semiconductor physics and optoelectronic devices, in particular, band structure calculations, strainlayered systems, carrier scattering theory, nonlinear optics, as well as conventional and quantum mechanical methods for device optimization.
Vladimir Jovanovic completed his PhD at the IMP on physical models of quantum well infrared photodetectors and quantum cascade lasers in GaN and GaAsbased materials for near, mid and farinfrared (terahertz) applications.
Marco Califano is a Royal Society University Research Fellow bas3ed in the IMP at Leeds whose main interests focus on atomistic Pseudopotential modelling of the electronic and optical properties of semiconductor nanostructures of different materials for applications in photovoltaics.
Craig A. Evans completed his PhD on the optical and thermal properties of quantum cascade lasers in the School of Electronic and Electrical Engineering, University of Leeds in 2008. He then worked as a Postdoctoral Research Assistant in the IMP working in the field of rareearth doped fibre lasers and integrated photonic device modelling and has now joined the staff of the school.
Dragan Indjin is an Academic Research Fellow in the IMP and has research interests in semiconductor nanostructures, nonlinear optics. quantum computing and spintronics.
New to This Edition
 New section devoted to electrical transport.
 Will contain three additional chapters: expansion of the work on quantum dots, on electromagnetic propagation and confinement in semiconductor heterostructures and nonlinear optical effects in quantum wells.
The Wiley Advantage
 Will address the theoretical aspects of the topic in detail.
 Will be a desktop reference book for the more experienced student/researcher.
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