Scattering in semiconductor

1. Phonon or lattice vibration scattering
2. Ionized (dopant) impurity scattering
3. Scattering by neutral impurity atoms and defects
4. Carrier-Carrier scattering
5. Piezo electric scattering

Of these, (1) and (2) dominates. For most high speed devices where large carrier concentrations area not involved.

Where the mobility due to each scattering mechanism written separately, the overall mobility is

For Phonon or lattice vibration scattering,

C 11 = average longitudinal elastic constant of semiconductor, = the effectives mass of the carrier,

E ds = displacement of edge of the band per unit dilation of lattice, and T = the absolute temperature.

For lon scattering                                   

N 1 = ionized dopant or impurity density

= permittivity

Therefore overall mobility is

only for GaAs