A pure semiconductor is a material with poor electrical conductivity. However the conductivity can be increased by order of magnitude by the addition of a small concentration of dopant atoms or by applying an electric field. Semiconductors are important for computation, communication, power electronics, solar cells, lighting, and display technologies.

For semiconductors, the chemical potential lies in a band gap and the band gap is less than about 3 eV. To calculate the properties of a semiconductor, first the crystal structure must be determined. This can be done by x-ray diffraction.

Some common crystal  structures for semiconductors

Diamond  C, Si, Ge, α-Sn

Zincblende  GaAs, InP, GaP, InAs, AlAs

Wurzite  ZnO, GaN, AlN, CdSe

• Electron states in a semiconductor
  

  You should be able to look at a bandstructure diagram for a semiconductor and be able to identify the conduction band, the valence band, the energy gap, whether the semiconductor is direct or in direct, and to be able to determine the effective masses of electrons and holes.

  Some example electronic bandstructures are: Si, GaAs, GaN, GaP, Ge, InAs, 6H SiC.

  Some calculated electron density of states: Si diamond, GaN, 6H SiC, GaAs, GaP, Ge, InAs.

  Many propertities of semiconductors related to the electron density of states can be calcuated using the Boltzmann approximation. There is also a table summarizing the thermodynamic properties of semiconductors in the Boltzmann approximation.

  Important results of the Boltzmann approximation are:

  $$\text{electron concentration in the conduction band}\qquad n = N_c(T)\exp\left(\frac{\mu-E_c}{k_BT}\right)$$ $$\text{hole concentration in the valence band}\qquad p = N_v(T)\exp\left(\frac{E_v-\mu}{k_BT}\right)$$ $$\text{law of mass action}\qquad n_i^2 = pn = N_c(T)N_v(T)\exp\left(\frac{-E_g}{k_BT}\right)$$
• Phonon states
  

  From the change in energy as a function of lattice constant, an effective spring constant between the atoms can be determined and this can be used to calculate the phonon dispersion relation and the phonon density of states. The phonon density of states can be used to calculate the phonon contribution to the thermodynamic properties. At room temperature, the phonon contribution to the thermodynamic properties usually dominates over the electron contribution of semiconductors.

  Phonon densities of states: Si, α-Sn, ZnO (rocksalt), ZnO (zincblende), ZnO (wurtzite).

  From the phonon densities of states, the following properties can be calculated: Energy spectral density u(ω,T), Internal energy density u(T), Specific heat c_v(T), Helmholtz free energy density f(T), Entropy density s(T).

• Intrinsic semiconductors are undoped.
  $$\text{carrier densities}\qquad n = p = \sqrt{N_cN_v}\exp\left(\frac{-E_g}{2k_BT}\right)$$ $$\text{chemical potential}\qquad\mu = \frac{E_c+E_v}{2}+\frac{k_BT}{2}\ln \left(\frac{N_v}{N_c}\right)$$
• Extrinsic semiconductors are have been doped with a donor concentration $N_d$ or an acceptor concentration $N_a$ or they have been doped with both donors and acceptors.
  

  The temperature dependence of the carriers concentrations of extrinsic semiconductors can be divided into three regimes: freeze out, the extrinsic regime, and the intrinsic regime.

  In the extrinsic regime:

  	n-type	p-type
  electron concentration	$n=N_d-N_a$	$n=\frac{n_i^2}{N_a-N_d}$
  hole concentration	$p=\frac{n_i^2}{N_d-N_a}$	$p=N_a-N_d$
  chemical potential	$\mu= E_c - k_BT \ln\left(\frac{N_c}{N_d - N_a}\right)$	$\mu= E_v + k_BT \ln\left(\frac{N_v}{N_a - N_d}\right)$

  
  
• You should able to describe what a pn-junction is and how a light emitting diode and a solar cell work.

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Reading
Kittel chapter 8: Semiconductor Crystals or R. Gross und A. Marx: Halbleiter

Properties	Si	Ge	GaAs
Bandgap Eg	$1.166-\frac{4.73\times 10^{-4}T^2}{T+636}$ eV (indirect)	$0.7437-\frac{4.77\times 10^{-4}T^2}{T+235}$ eV (indirect)	$1.519-\frac{5.41\times 10^{-4}T^2}{T+204}$ eV (direct)
Effective density of states in conduction band (300 K) Nc	2.78 × 1025 m-3	1.04 × 1025 m-3	4.45 × 1023 m-3
Effective density of states in valence band (300 K) Nv	9.84 × 1024 m-3	6.0 × 1024 m-3	7.72 × 1024 m-3
Effective mass electrons m*/m0	ml* = 0.98 mt* = 0.19	ml* = 1.64 mt* = 0.082	m* = 0.067
Effective mass holes m*/m0	mlh* = 0.16 mhh* = 0.49	mlh* = 0.044 mhh* = 0.28	mlh* = 0.082 mhh* = 0.45
Crystal structure	diamond	diamond	zincblende
Density	2.328 g/cm³	5.3267 g/cm³	5.32 g/cm³
Atoms/m³	5.0 × 1028	4.42 × 1028	4.42 × 1028

More properties of semiconductors can be found at: NSM Archive - Physical Properties of Semiconductors.

More Resources
• Semiconductor materials: Silicon, SiC 4H
• Semiconductors in Wikipedia: Si, Ge, GaAs, GaN, InP