Atomistic mesh generation for the simulation of nanoscale metal-oxide-semiconductor field-effect transistors.

We present a methodology for the finite-element discretization of nanoscaled semiconductor devices with atomic resolution. The meshing strategy is based on the use of patterns to decompose the unit cell of the underlying crystallographic structures producing unstructured tetrahedral meshes. The unit cells of the bulk semiconductors and, more importantly, of the interfaces between the substrate and the gate dielectric have been extracted from classical molecular dynamics and density functional theory simulations. A Monte Carlo approach has been then used to place the dopants in nodes of the crystal, replacing silicon atoms. The thus created "atomistic" meshes are used to simulate an ensemble of microscopically different double-gate Si metal-oxide-semiconductor field-effect transistors and the transition region at the Si/SiO_{2} interface. In addition, a methodology to approximate amorphous dielectrics is also presented.