**Quantum Physics of Semiconductor Materials and Devices by Debdeep Jena, ISBN-13: 978-0198856849**

[PDF eBook eTextbook]

- Publisher: Oxford University Press (August 26, 2022)
- Language: English
- 896 pages
- ISBN-10: 0198856849
- ISBN-13: 978-0198856849

**”Quantum Phenomena do not occur in a Hilbert space. They occur in a laboratory”. – Asher Peres**

Semiconductor physics is a laboratory to learn and discover the concepts of quantum mechanics and thermodynamics, condensed matter physics, and materials science, and the payoffs are almost immediate in the form of useful semiconductor devices. Debdeep Jena has had the opportunity to work on both sides of the fence – on the fundamental materials science and quantum physics of semiconductors, and in their applications in semiconductor electronic and photonic devices. In Quantum Physics of Semiconductors and Nanostructures, Jena uses this experience to make each topic as tangible and accessible as possible to students at all levels.

Consider the simplest physical processes that occur in semiconductors: electron or hole transport in bands and over barriers, collision of electrons with the atoms in the crystal, or when electrons and holes annihilate each other to produce a photon. The correct explanation of these processes require a quantum mechanical treatment. Any shortcuts lead to misconceptions that can take years to dispel, and sometimes become roadblocks towards a deeper understanding and appreciation of the richness of the subject. A typical introductory course on semiconductor physics would then require prerequisites of quantum mechanics, statistical physics and thermodynamics, materials science, and electromagnetism. Rarely would a student have all this background when (s)he takes a course of this nature in most universities. Jena’s work fills in these gaps and gives students the background and deeper understanding of the quantum physics of semiconductors and nanostructures.

**Table of Contents:**

Titlepage

Copyright

Dedication

Preface

Acknowledgement

Content

I Fundamentals

And off We Go!

Beyond belief

A brief history of semiconductors

Future

These boots are made for walking

Chapter summary section

Further reading

Exercises

Quantum Mechanics in a Nutshell

Planck’s photon energy quanta

Bohr’s electron energy quanta

Wave-particle duality

The wavefunction

Operators

States of definite momentum and location

States of definite energy: The Schrödinger equation

Time-dependent Schrödinger equation

Stationary states and time evolution

Quantum current

Fermions and bosons

Fermion and boson statistics

The Spin-statistics theorem

The Dirac equation and the birth of particles

Chapter summary section

Further reading

Exercises

Damned Lies and Statistics

Quantum statistics and entropy

The physics of equilibrium

Partition function for quantum systems

The Fermi–Dirac distribution

The Bose–Einstein distribution

Properties of the distribution functions

Quantum twist on thermodynamics

Meaning of equilibrium in semiconductor devices

Chapter summary section

Further reading

Exercises

Electrons in the Quantum World

In Schrödinger equation we trust

The free electron

Not so free: Particle on a ring

The electron steps into a higher dimension: 2D

Electrons in a 3D box

The particle in a box

The Dirac delta potential

The harmonic oscillator

The hydrogen atom

Chapter summary section

Further reading

Exercises

Red or Blue Pill: Befriending the Matrix

The expansion principle

Matrix mechanics

Matrices and algebraic functions

Properties of matrix eigenvlaues

Looking ahead

Chapter summary section

Further reading

Exercises

Secrets of the Classical Electron

Our ancestors knew metals

Discovery of the electron and its aftermath

Drude’s model explains Ohm’s law

Metals are shiny

Metals conduct heat

Icing on the cake: The Wiedemann–Franz law

All is not well

Chapter summary section

Further reading

Exercises

Quantum Mechanics in a Nutshell

Planck’s photon energy quanta

Bohr’s electron energy quanta

Wave-particle duality

The wavefunction

Operators

States of definite momentum and location

States of definite energy: The Schr¨odingerequ tion

Time-dependent Schr¨odinger equation

Stationary states and time evolution

Quantum current

Fermions and bosons

Fermion and boson statistics

The Spin-statistics theorem

The Dirac equation and the birth ofparticles

Chapter summary section

Further reading

Exercises

Damned Lies and Statistics

Quantum statistics and entropy

The physics of equilibrium

Partition function for quantum systems

The Fermi–Dirac distribution

The Bose–Einstein distribution

Properties of the distribution functions

Quantum twist on thermodynamics

Meaning of equilibrium in semiconductordevices

Chapter summary section

Further reading

Exercises

Electrons in the QuantumWorld

In Schr¨odinger equation we trust

The free electron

Not so free: Particle on a ring

The electron steps into a higherdimension: 2D

Electrons in a 3D box

The particle in a box

The Dirac delta potential

The harmonic oscillator

The hydrogen atom

Chapter summary section

Further reading

Exercises

Red or Blue Pill:Befriending the Matrix

The expansion principle

Matrix mechanics

Matrices and algebraic functions

Properties of matrix eigenvlaues

Looking ahead

Chapter summary section

Further reading

Exercises

Perturbations to the Electron’s Freedom

Degenerate perturbation theory

Non-degenerate perturbation theory

The Brillouin–Wigner perturbation results

Rayleigh–Schrödinger perturbation results

The Hellmann–Feynman theorem

Perturbation theory example

Chapter summary section

Further reading

Exercises

II Bands, Doping, and Heterostructures

Electrons in a Crystal Get Their Bands, Gaps, and Masses

The free–electron

Periodic perturbation

Bands, gaps, and effective masses

Non-degenerate perturbation theory

Glimpses of the Bloch theorem

Non-periodic potentials and scattering

Chapter summary section

Further reading

Exercises

Bloch Theorem, Bandstructure, and Quantum Currents

The Bloch theorem

Bloch theorem: aftermath

Real and reciprocal lattice, Brillouin zones

Velocity of Bloch states

Dynamics of Bloch states

Bloch wave velocity and ballistic current

Transport by Bloch waves with scattering

Energy (heat) current

Any current

Quantum Wiedemann–Franz law

Metals, semiconductors, semimetals and insulators

Chapter summary section

Further reading

Exercises

Crystal Clear: Bandstructure of the Empty Lattice

Diffraction as a sharp eye

Bragg diffraction condition

Broken symmetries and physical laws

Bravais lattices

Nearly free–electron bandstructure

Chapter summary section

Further reading

Exercises

Tight-Binding Bandstructure

Atoms, bonds, and molecules

Bandstructure of 1D, 2D, and 3D crystals

1D, 2D: nanotubes, graphene, BN, MX2

3D FCC: Si, GaAs

3D wurtzite: GaN, AlN, ZnO

Tight-binding to design new properties

Chapter summary section

Further reading

Exercises

k p Bandstructure

k p theory

Symmetry

Analytical model without spin

Non-parbolicity and sum rules

The Kane model with spin-orbit interaction

Chapter summary section

Further reading

Exercises

1, 2, 3 … : Pseudopotentials and Exact Bandstructure

The empire strikes back

Exact bandstructure of the Dirac comb potential

Tight-binding models emerge from Kronig–Penney

Point defects in Kronig–Penney models

Green’s functions from Kronig–Penney models

Pseudopotentials: what they are and why they work

Bandstructure of Si, Ge, and GaAs

Bandstructure of AlN, GaN, and InN

Pseudopotentials to DFT and beyond

Chapter summary section

Further reading

Exercises

Doping and Heterostructures: The Effective Mass Method

Effective mass approximation, envelope functions

3D, 2D, 1D, 0D: heterostructures

3D bulk bandstructure

Doped semiconductors

2D quantum wells

1D quantum wires

0D quantum dots

Finite barrier heights

Multilayers and superlattices

Wannier functions

Chapter summary section

Further reading

Exercises

Carrier Statistics and Energy Band Diagrams

Carrier statistics

EF is constant at thermal equilibrium

Metal-semiconductor Schottky junctions

p-n homojunctions

Heterojunctions

Energy band diagrams: Poisson+Schrödinger

Polarization-induced doping in heterostructures

Chapter summary section

Further reading

Exercises

Controlling Electron Traffic in the k-Space

Electron energies in semiconductors

Semiconductor statistics

Ballistic transport in semiconductors

Ballistic transport in non-uniform potentials/tunneling

Scattering of electrons by phonons, defects and photons

The Boltzmann transport equation

Current flow with scattering: drift and diffusion

Explicit calculations of scattering rates and mobility

Semiconductor electron energies for photonics

The optical joint density of states J()

Occupation of electron states for photonics

Absorption, and emission: spontaneous and stimulated

Chapter summary section

Further reading

Exercises

III Quantum Electronics with Semiconductors

Game of Modes: Quantized R, L, and C

Classical R, L, C circuits

Quantized conductance

Quantum capacitance

Kinetic inductance

Quantum R, L, C circuits

Negative R, L, and C

Chapter summary section

Further reading

Exercises

Junction Magic: Schottky, pn and Bipolar Transistors

Ballistic Schottky diodes

pn diodes: discovery

pn diodes: transport

Bipolar junction transistors

Deathniums!

Chapter summary section

Further reading

Exercises

Zeroes and Ones: The Ballistic Transistor

The MOS capacitor

The ballistic FET

Ballistic I-V characteristics

Quantum wire ballistic FET

The drift-diffusion FET

CMOS and HEMTs

Source/drain ohmic contacts

A brief history of FETs

Chapter summary section

Further reading

Exercises

Fermi’s Golden Rule

Fermi’s golden rule

Oscillating perturbations

Transitions to continuum

Kubo–Greenwood formula

Decoherence in qubits

Electron-electron scattering

Dyson series and diagrams

Zero-sum game: self energy

Chapter summary section

Further reading

Exercises

No Turning Back: The Boltzmann Transport Equation

Micro vs. macro

The Liouville theorem

Boltzmann transport equation

H-theorem and entropy

Equilibrium distribution

The RTA: time to relax!

One formula to rule them all

Electrical conductivity

Thermoelectric properties

Onsager relations

Conservation laws

Berry curvature correction

Limitations of the BTE

Chapter summary section

Further reading

Exercises

Taking the Heat: Phonons and Electron-Phonon Interactions

Phonon effects: A résumé

Phonon dispersions and DOS

Optical conductivity

Lyddane–Sachs–Teller equation

Acoustic wave devices

Thermal conductivity

Phonon number quantization

Electron-phonon interaction

Chapter summary section

Further reading

Exercises

Scattering, Mobility, and Velocity Saturation

Electron mobility: a résumé

Scattering mechanisms

Point defect scattering

Coulomb impurity scattering

Dipole scattering

Dislocation scattering

Alloy disorder scattering

Interface scattering

Phonon scattering

Experimental mobilities

High-field velocity saturation

Chapter summary section

Further reading

Exercises

Through the Barrier: Tunneling and Avalanches

Tunneling: a résumé

Single-barrier tunneling

WKB tunneling theory

WKB for semiconductors

Nordheim supply function

Fowler–Nordheim tunneling

Interband Zener tunneling

pn tunnel junctions in 1D, 2D, and 3D

NDR, backward diodes

Tunneling FETs

Resonant tunneling

Bardeen’s tunneling theory

Kubo formalism

Landau–Zener theory

Avalanche processes and impact ionization

Tail of the dragon

Chapter summary section

Further reading

Exercises

Running Circles: Quantum Magnetotransport

Magnetotransport: a résumé

Hall effect

Magnetoresistance

Nernst and Ettingshausen effects

Cyclotron resonance

Faraday rotation

Atoms: Bohr magneton and spin

Landau levels in solids

Shubnikov de Haas effect

The quantum Hall effect

Quantum Hall effect theories

Hierarchy of Hall effects

Chapter summary section

Further reading

Exercises

IV Quantum Photonics with Semiconductors

Let There Be Light: Maxwell Equations

Maxwell equations in vacuum

Light from Maxwell equations

Maxwell equations in (k, ) space

Maxwell equations in materials

Classical light-matter interaction

Kramers–Kronig relations

Accelerating charges radiate

Need for quantum theory of light

Chapter summary section

Further reading

Exercises

Light–Matter Interaction

Photonic effects: a résumé

Electron-photon matrix elements

Absorption spectra of semiconductors

Number of photons in light

Photon absorption rate

Equilibrium absorption coefficient

Quantum wells, wires, and dots

Critical points

Forbidden and indirect absorption

Exciton absorption

Franz–Keldysh effect

Intersubband absorption

Free carrier, and impurity absorption

Photoelectron spectroscopy

Chapter summary section

Further reading

Exercises

Heavenly Light: Solar Cells and Photodetectors

Solar sells and photodetectors: a résumé

Solar cells

Shockley–Ramo theorem

Photodetectors

Avalanche photodiodes

Quantum well infrared photodetectors

Electro-absorption modulators

Solar blind photodetectors

Chapter summary section

Further reading

Exercises

Reach for the Stars: Lasers and LEDs

Lasers and LEDs: a résumé

Einstein’s A and B coefficients

Semiconductor emission

Entropy of optical transitions

Gain and emission in bands

Spontaneous emission: LEDs

Stimulated emission: lasers

Double heterostructure lasers

Laser rate equations

Case study: blue laser diode

DFB, VCSELs and QCLs

Towards field quantization

Broadband field modes

Quantization of fields

Field quantization: aftermath

Quantized light-matter interaction

Fundamental optical processes

Einstein’s re-derivation of Planck’s law: back to 12!

Chapter summary section

Further reading

Exercises

Every End is a New Beginning

Smallest, fastest, brightest

Looking back and forward

Ferroelectric semiconductors

Ferromagnetic semiconductors

Multiferroic semiconductors

Superconducting semiconductors

Semiconductors for quantum communications

Semiconductors for quantum computation

Semiconductors for energy

Semiconductors for healthcare and agriculture

Semiconductors for space exploration

Social impact of semiconductors

Chapter summary section

Further reading

Exercises

Appendix

What is in the appendix?

Semiconductor Formulae

Physical properties of 3D and 2Dsemiconductors

References for the appendix

Physical constants

References

Index

* Debdeep Jena* is a Professor of Electrical and Computer Engineering and Materials Science and Engineering at Cornell University. His research and teaching interests are in the quantum physics, technology, and device applications of semiconductor and superconductor heterostructures such as III-V nitrides and oxides, and 2-dimensional crystals. He leads a research group that combines experiments and theory to investigate charge, heat, and spin transport in highly crystalline solids, and uses them to explore fundamental limits of electronic, photonic, and quantum devices. The research of this group has been published in approximately 300 papers, generated several patents, and recognized by international awards.

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