 
PHY.K02UF Molecular and Solid State Physics  
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 xray diffraction.
Some common crystal 



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:
$$\text{electron concentration in the conduction band}\qquad n = N_c(T)\exp\left(\frac{\muE_c}{k_BT}\right)$$ $$\text{hole concentration in the valence band}\qquad p = N_v(T)\exp\left(\frac{E_v\mu}{k_BT}\right)$$ $$\text{law of mass action}\qquad n_i^2 = pn = N_c(T)N_v(T)\exp\left(\frac{E_g}{k_BT}\right)$$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, αSn, 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).
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:
ntype  ptype  
electron concentration  $n=N_dN_a$  $n=\frac{n_i^2}{N_aN_d}$ 
hole concentration  $p=\frac{n_i^2}{N_dN_a}$  $p=N_aN_d$ 
chemical potential  $\mu= E_c  k_BT \ln\left(\frac{N_c}{N_d  N_a}\right)$  $\mu= E_v + k_BT \ln\left(\frac{N_v}{N_a  N_d}\right)$ 
Reading
Kittel chapter 8: Semiconductor Crystals or R. Gross und A. Marx: Halbleiter
Properties 
Si  Ge  GaAs 
Bandgap E_{g}  $1.166\frac{4.73\times 10^{4}T^2}{T+636}$ 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) N_{c}  2.78 × 10^{25} m^{3}  1.04 × 10^{25} m^{3}  4.45 × 10^{23} m^{3} 
Effective density of states in valence band (300 K) N_{v}  9.84 × 10^{24} m^{3}  6.0 × 10^{24} m^{3}  7.72 × 10^{24} m^{3} 
Effective mass electrons  m_{l}^{*} = 0.98  m_{l}^{*} = 1.64  m^{*} = 0.067 
Effective mass holes  m_{lh}^{*} = 0.16  m_{lh}^{*} = 0.044  m_{lh}^{*} = 0.082 
Crystal structure  diamond  diamond  zincblende 
Density  2.328 g/cm³  5.3267 g/cm³  5.32 g/cm³ 
Atoms/m³  5.0 × 10^{28}  4.42 × 10^{28}  4.42 × 10^{28} 
More properties of semiconductors can be found at: NSM Archive  Physical Properties of Semiconductors.