A generalized transport equation for ion implantation into infinite targets

In this paper a transport equation (TE) is derived which incorporates arbitrary distribution functions and a cut-off energy. Integral equations for the gas-like and liquid free-flight path length distribution models are both incorporated into the transport theory computer code KUBBIC using the two-parameter differential nuclear scattering cross section. Simulations for the ion As implanted into a-Si are compared with those performed using a parallel processor Monte Carlo (MC) code based on TRIM. Excellent agreement is obtained when using four versions of the liquid model, including use of the Biersack free-flight path extension formula and the time integral hard sphere approximation. In addition, the effects of varying the maximum impact parameter are investigated as is the effect of the ordering of nuclear and electronic interactions. The TE formalism and solver presented in this paper serve as a powerful tool for testing new approximations which may be incorporated into MC codes in order to improve computational efficiency.