Quasiclassical mobility for extrinsic semiconductors

A quasiclassical formulation for mobility in extrinsic semiconductors is presented based on scattering from ionized impurity atoms. Quantum theory enters the otherwise classical Chapman-Enskog expansion of the Boltzmann equation through incorporation of the Thomas-Fermi interaction potential together with the Bom approximation for evaluation of scattering integrals. The following expression results for mobility μ_i, (cgs):

$\text{μ}{}_{\mathrm{i}}\text{3}\text{2}\text{?}{}^2\text{n}{}_{\mathrm{s}}\text{e}{}^3\text{m}{}^1\text{2}\text{2}\text{k}{}_{\mathrm{B}}\text{T}\text{2φ}\text{3}\text{2}\text{1}\text{f(γ)}$

,

$\text{f(γ)=(1+γ)e}{}^{\mathrm{\gamma }}\text{E}{}_1\text{(γ)?1]}$

, where n_s is impurity concentration, m¹ is effective mass, E₁(γ) is the exponential integral, ? is dielectric constant and γ is dimensionless Thomas-Fermi energy. The structure of the dimensional factor in the preceding expression for μ_i agrees with previous expressions for this parameter.