5. Surface Rate Calculation

The simulation of surface evolution requires the calculation of the surface velocity at every time step. For advanced models, the surface velocity depends on the particle transport. According to the surface kinetics model described in Section 2.3, the surface velocity ${V}$ is assumed to be a function of a certain number of surface rates ${R}_1,\ldots,{R}_{{N}_\text{R}}$ (2.25). This chapter is devoted to the calculation of these surface rates under the assumption of ballistic particle transport within the feature-scale region, as described by (2.14). Particles entering the feature-scale region through the source plane ${\mathcal {P}}$ follow the given arriving flux distribution ${\Gamma}_{\text{src}}$ . Particle reemission, modelled by the reemission probability function ${G}$ (2.15), must also be incorporated. In summary the problem states as follows:

• Given: ${\mathcal {S}}$ , ${\Gamma}_{\text{src}}$ for all ${\vec{x}}\in {\mathcal{P}}$ , and ${G}$ for all ${\vec{x}}\in{\mathcal{S}}$ .
• Required: ${R}_1,\ldots,{R}_{{N}_\text{R}}$ (in order to calculate ${V}$ ) for all ${\vec{x}}\in{\mathcal{S}}$ .

Two completely different approaches for solving this problem are presented in the following sections.