Ebook
Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures, 3rd EditionISBN: 9781119964759
564 pages
September 2011

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 !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 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. Jovanovíc
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 realisation
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. Ikoníc
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
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 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.