Introduction to Semiconductor Physics and Devices

I Fundamental Physics

1 Principles of Quantum Mechanics

1.1 Wave-particle duality . . . . . . . . . . . . . . . . . . . . . . . 9

1.2 Wavelength of a free particle in terms of its energy . . . . . . 11

1.3 Energy quantization . . . . . . . . . . . . . . . . . . . . . . . 12

1.4 Radiation spectrum of Hydrogen . . . . . . . . . . . . . . . . 13

1.5 The wave function . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6 The wave function of a free particle . . . . . . . . . . . . . . . 16

1.7 Schrödinger's equation . . . . . . . . . . . . . . . . . . . . . . 17

1.7.1 Time-dependent Schrödinger's equation . . . . . . . . . 17

1.7.2 Time-independent Schrödinger's equation . . . . . . . . 19

1.8 Probabilistic interpretation and collapse of the wave function . . . 19

1.9 The many-particle wave function . . . . . . . . . . . . . . . . 22

1.10 Electron states in a Hydrogen atom . . . . . . . . . . . . . . . 22

1.11 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.12 Degeneracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.13 Indistinguishability of quantum particles . . . . . . . . . . . . 24

1.14 Spin-statistics theorem . . . . . . . . . . . . . . . . . . . . . . 25

1.15 Pauli's exclusion principle . . . . . . . . . . . . . . . . . . . . 26

1.16 Appendix. A crash course in complex numbers . . . . . . . . . 26

2 Crystal Structure of Solids

2.1 Periodic table of elements . . . . . . . . . . . . . . . . . . . . 30

2.2 Chemical bonding . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.3 Atomic order in solids . . . . . . . . . . . . . . . . . . . . . . 33

2.4 Bravais lattices . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.5 Primitive unit cell . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6 Crystal basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.7 Volume density and atomic packing factor . . . . . . . . . . . 35

2.8 Basic cubic structures . . . . . . . . . . . . . . . . . . . . . . 36

2.9 Formation of diamond structure . . . . . . . . . . . . . . . . . 37

2.10 Miller indices . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.11 Miller indices for cubic structures . . . . . . . . . . . . . . . . 40

2.12 Imperfections and impurities in solids . . . . . . . . . . . . . . 41

3 Equilibrium Statistical Mechanics

3.1 Probability theory . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2 Microstates and macrostates . . . . . . . . . . . . . . . . . . . 45

3.3 Probabilistic description . . . . . . . . . . . . . . . . . . . . . 46

3.4 Thermodynamic equilibrium . . . . . . . . . . . . . . . . . . . 46

3.5 Postulate of equal a priori probabilities . . . . . . . . . . . . . 47

3.6 Grand canonical distribution . . . . . . . . . . . . . . . . . . . 48

3.7 Fermi-Dirac distribution . . . . . . . . . . . . . . . . . . . . . 50

3.8 Boltzmann approximation . . . . . . . . . . . . . . . . . . . . 52

3.9 Fermi energy at zero temperature . . . . . . . . . . . . . . . . 53

4 Band Theory of Solids

4.1 Electron states in a crystal lattice . . . . . . . . . . . . . . . . 55

4.2 Bloch's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Energy bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4 Conduction types of solids . . . . . . . . . . . . . . . . . . . . 59

4.4.1 Completely filled bands do not contribute to conductivity 59

4.4.2 Metals and semimetals . . . . . . . . . . . . . . . . . . 60

4.4.3 Dielectrics and semiconductors . . . . . . . . . . . . . 60

4.5 Conduction and valence