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Band Theory and Electronic Properties of Solids

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ISBN-10: 0198506449

ISBN-13: 9780198506447

Edition: 2001

Authors: John Singleton

List price: $74.00
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This latest text in the new Oxford Master Series in Physics provides a much need introduction to band theory and the electronic properties of materials. Written for students in physics and material science, the book takes a pedagogical approach to the subject through the extensive use of illustrations, examples and problem sets. The author draws on his extensive experience teaching band theory to provide the reader with a thorough understanding of the field. Considerable attention is paid to the vocabulary and quantum-mechanical training necessary to learn about the electronic, optical and structural properties of materials in science and technology. The text also offers several chapters on…    
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Book details

List price: $74.00
Copyright year: 2001
Publisher: Oxford University Press, Incorporated
Publication date: 10/24/2001
Binding: Paperback
Pages: 240
Size: 7.44" wide x 9.65" long x 0.55" tall
Weight: 0.946
Language: English

Metals: the Drude and Sommerfeld models
Introduction
What do we know about metals?
The Drude model
Assumptions
The relaxation-time approximation
The failure of the Drude model
Electronic heat capacity
Thermal conductivity and the Wiedemann-Franz ratio
Hall effect
Summary
The Sommerfeld model
The introduction of quantum mechanics
The Fermi-Dirac distribution function
The electronic density of states
The electronic density of states at E [approximate] E[subscript F]
The electronic heat capacity
Successes and failures of the Sommerfeld model
The quantum mechanics of particles in a periodic potential: Bloch's theorem
Introduction and health warning
Introducing the periodic potential
Born-von Karman boundary conditions
The Schrodinger equation in a periodic potential
Bloch's theorem
Electronic bandstructure
The nearly-free electron model
Introduction
Vanishing potential
Single electron energy state
Several degenerate energy levels
Two degenerate free-electron levels
Consequences of the nearly-free-electron model
The alkali metals
Elements with even numbers of valence electrons
More complex Fermi surface shapes
The tight-binding model
Introduction
Band arising from a single electronic level
Electronic wavefunctions
Simple crystal structure
The potential and Hamiltonian
General points about the formation of tight-binding bands
The group IA and IIA metals; the tight-binding model viewpoint
The Group IV elements
The transition metals
Some general points about bandstructure
Comparison of tight-binding and nearly-free-electron bandstructure
The importance of k
hk is not the momentum
Group velocity
The effective mass
The effective mass and the density of states
Summary of the properties of k
Scattering in the Bloch approach
Holes
Postscript
Semiconductors and Insulators
Introduction
Bandstructure of Si and Ge
General points
Heavy and light holes
Optical absorption
Constant energy surfaces in the conduction bands of Si and Ge
Bandstructure of the direct-gap III-V and II-VI semiconductors
Introduction
General points
Optical absorption and excitons
Excitons
Constant energy surfaces in direct-gap III-V semiconductors
Thermal population of bands in semiconductors
The law of mass action
The motion of the chemical potential
Intrinsic carrier density
Impurities and extrinsic carriers
Extrinsic carrier density
Degenerate semiconductors
Impurity bands
Is it a semiconductor or an insulator?
A note on photoconductivity
Bandstructure engineering
Introduction
Semiconductor alloys
Artificial structures
Growth of semiconductor multilayers
Substrate and buffer layer
Quantum wells
Optical properties of quantum wells
Use of quantum wells in opto-electronics
Superlattices
Type I and type II superlattices
Heterojunctions and modulation doping
The envelope-function approximation
Band engineering using organic molecules
Introduction
Molecular building blocks
Typical Fermi surfaces
A note on the effective dimensionality of Fermi-surface sections
Layered conducting oxides
The Peierls transition
Measurement of bandstructure
Introduction
Lorentz force and orbits
General considerations
The cyclotron frequency
Orbits on a Fermi surface
The introduction of quantum mechanics
Landau levels
Application of Bohr's correspondence principle to arbitrarily-shaped Fermi surfaces in a magnetic field
Quantisation of the orbit area
The electronic density of states in a magnetic field
Quantum oscillatory phenomena
Types of quantum oscillation
The de Haas-van Alphen effect
Other parameters which can be deduced from quantum oscillations
Magnetic breakdown
Cyclotron resonance
Cyclotron resonance in metals
Cyclotron resonance in semiconductors
Interband magneto-optics in semiconductors
Other techniques
Angle-resolved photoelectron spectroscopy (ARPES)
Electroreflectance spectroscopy
Some case studies
Copper
Recent controversy: Sr[subscript 2]RuO[subscript 4]
Studies of the Fermi surface of an organic molecular metal
Quasiparticles: interactions between electrons
Transport of heat and electricity in metals and semiconductors
A brief digression; life without scattering would be difficult!
Thermal and electrical conductivity of metals
Metals: the 'Kinetic theory' of electron transport
What do [tau subscript [sigma] and [tau subscript [kappa] represent?
Matthiessen's rule
Emission and absorption of phonons
What is the characteristic energy of the phonons involved?
Electron-phonon scattering at room temperature
Electron-phonon scattering at T [double less-than sign] [theta subscript D]
Departures from the low temperature [sigma] [proportional to] T[superscript -5] dependence
Very low temperatures and/or very dirty metals
Summary
Electron-electron scattering
Electrical conductivity of semiconductors
Temperature dependence of the carrier densities
The temperature dependence of the mobility
Disordered systems and hopping conduction
Thermally-activated hopping
Variable range hopping
Magnetoresistance in three-dimensional systems
Introduction
Hall effect with more than one type of carrier
General considerations
Hall effect in the presence of electrons and holes
A clue about the origins of magnetoresistance
Magnetoresistance in metals
The absence of magnetoresistance in the Sommerfeld model of metals
The presence of magnetoresistance in real metals
The use of magnetoresistance in finding the Fermi-surface shape
The magnetophonon effect
Magnetoresistance in two-dimensional systems and the quantum Hall effect
Introduction: two-dimensional systems
Two-dimensional Landau-level density of states
Resistivity and conductivity tensors for a two-dimensional system
Quantisation of the Hall resistivity
Localised and extended states
A further refinement- spin splitting
Summary
The fractional quantum Hall effect
More than one subband populated
Inhomogeneous and hot carrier distributions in semiconductors
Introduction: inhomogeneous carrier distributions
The excitation of minority carriers
Recombination
Diffusion and recombination
Drift, diffusion and the Einstein equations
Characterisation of minority carriers; the Shockley-Haynes experiment
Hot carrier effects and ballistic transport
Drift velocity saturation and the Gunn effect
Avalanching
A simple resonant tunnelling structure
Ballistic transport and the quantum point contact
Useful terminology in condensed matter physics
Introduction
Crystal
Lattice
Basis
Physical properties of crystals
Unit cell
Wigner-Seitz cell
Designation of directions
Designation of planes; Miller indices
Conventional or primitive?
The 14 Bravais lattices
Derivation of density of states in k-space
Introduction
Density of states
Reading
Derivation of distribution functions
Introduction
Bosons
Fermions
The Maxwell-Boltzmann distribution function
Mean energy and heat capacity of the classical gas
Phonons
Introduction
A simple model
Extension to three dimensions
The Debye model
Phonon number
Summary; the Debye temperature as a useful energy scale in solids
A note on the effect of dimensionality
The Bohr model of hydrogen
Introduction
Hydrogenic impurities
Excitons
Experimental considerations in measuring resistivity and Hall effect
Introduction
The four-wire method
Sample geometries
The van der Pauw method
Mobility spectrum analysis
The resistivity of layered samples
Canonical momentum
Superconductivity
Introduction
Pairing
Pairing and the Meissner effect
List of selected symbols
Solutions and additional hints for selected exercises
Index
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