Efficient Evaluation of Ionized-Impurity Scattering in Monte Carlo Transport Calculations

Abstract

Carrier scattering by ionized impurities is strongly anisotropic, and events with small scattering angles are highly preferred. On the Monte Carlo technique applied to semiconductor device modeling this behavior imposes several problems which are discussed. We present a method which reduces the amount of low-angle scattering very effectively. Instead of the anisotropic scattering mechanism an equivalent isotropic mechanism is defined which gives the same momentum relaxation time. Depending on doping concentration and carrier energy the equivalent scattering rate is up to four orders of magnitude lower. By analyzing the Boltzmann transport equation a condition is derived on which the use of the equivalent scattering model is justified. The equivalence of the anisotropic and the isotropic scattering models is also demonstrated empirically by means of Monte Carlo calculations. The plain Brooks-Herring model is employed as well as an improved model including momentum-dependent screening and coherent multi-potential scattering. An empirical correction to attenuate the peak of the scattering rate at low energies is presented, and the statistical screening model of Ridley is critically discussed.