A methodology for mesh generation with nodes placed on the atomic positions of the structure is presented. The meshing strategy is based on the use of patterns to decompose a unit cell of the target crystal into tetrahedra. The mesh generation procedure has been applied to crystalline Si and SiO
(α-quartz) as well as to their interface. The constructed meshes have been consequently randomly populated by dopants using Monte Carlo approach. The dopants are replacing silicon atom in nodes of the crystal. The ‘atomistic’ mesh populated with random discrete dopants has been used to simulate an ensemble of microscopically different double gate MOSFETs in order to demonstrate the functionality of the meshing methodology.