Electronic structure boundary value problems without all of the atoms

A mixed atomistic/continuum technique, in the spirit of the quasicontinuum method, is formulated and used to solve boundary value problems in strained semiconductor structures in which the mechanical fields and the local electronic structure are fully coupled. The technique is implemented by means of a standard structural mechanics finite element package. Within each element in the mesh, tight binding calculations are made for mechanical properties based on the local electronic structure. The finite element program calculates equilibrium mechanical fields based on this atomistic constitutive information; the underlying electronic properties can then be extracted at the element level. The technique is demonstrated by examining several simple plane strain boundary value problems for coherently strained silicon.