Mobility of Charge Carriers in Solids

the ratio of the drift velocity ν_dr to the electric field strength E:

μ = ν_dr/E

where the drift velocity is the velocity of the directed motion of conduction electrons and holes that is caused by the electric field. Different types of carriers in a substance have different mobilities. In anisotropic crystals each type of carrier has different mobilities for different directions of the field.

The quantity of μ is determined by the electron-scattering processes in the crystal. Scattering occurs at charged and neutral impurity particles and at defects in the crystal lattice; it can also be caused by phonons—that is, by thermal vibrations of the lattice. When a carrier emits or absorbs a phonon, it changes its quasimomentum and, consequently, its velocity. For this reason, μ changes markedly with temperature. When T ≥ 300°K, phonon scattering predominates. As the temperature is lowered, the probability of this process decreases, and scattering by charged impurities or defects becomes dominant. The probability of such scattering increases as the energy of the carriers decreases.

The average drift velocity ν̄_dr acquired in the period τ between two consecutive scattering events (the mean free time) is given by the expression

where e is the charge and m the effective mass of the carrier. Hence

The mobility of charge carriers in different substances varies over a broad range—from 10⁷ cm²/sec to 10^–3 cm²/sec (or even less) at T= 300°K. In an alternating electric field v̄_dr may not be in phase with the field strength E, and the mobility of the charge carriers is a function of the field’s frequency.