Influence of the doping element on the electron mobility in n-silicon

We present a theoretical approach to study the dependence of the electron mobility on the dopant species in $n$ -doped silicon under low electric fields. The electron charge distribution of the impurities is calculated by the Thomas–Fermi theory using the energy functional formulation. Ionized impurity scattering has been treated within the Born approximation. Our model accounts for degenerate statistics, dispersive screening and pair scattering, which become important in heavily doped semiconductors. The dielectric function is accurately approximated by a rational function. A new expression for the second Born amplitude of a Yukawa-like charge distribution is derived, which now depends on the atomic and electron numbers of the impurity ion. Monte Carlo simulations including all important scattering mechanism have been performed in the doping concentration range from ${10}^{15}$ to ${10}^{21}\hspace{0.17em}{\mathrm{cm}}^{\mathrm{-3}}.$ The agreement with experimental data is excellent. The results confirm the lower electron mobility in As-doped silicon in comparison to P-doped silicon.