  We developed a consistent mathematical model for isotropic crystal growth on
a substrate covered by the mask material with a periodic series of parallel
long trenches where the substrate is exposed to the vapor phase. Surface
diffusion and the flux of particles from vapor are assumed to be the main
mechanisms of growth. A geometrical approach to the motion of crystal surface
in two dimensions is adopted and nonlinear evolution equations are solved by a
finite-difference method. The model allows the direct computation of the
crystal surface shape, as well as the study of the effects due to mask regions
of effectively nonzero thickness. As in experiments, lateral overgrowth of
crystal onto the mask and enhanced growth in the region near the contact of the
crystal and the mask is found, as well as the comparable crystal shapes. The
growth rates in vertical and lateral directions are investigated.
