Boundary conditions for the electronic structure of finite-extent embedded semiconductor nanostructures

The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires a proper boundary treatment for a finite simulation domain. For the study of a self-assembled InAs dot embedded in GaAs, three kinds of boundary conditions are examined within the empirical tight-binding model: (i) the periodic boundary condition, (ii) raising the orbital energies of surface atoms, and (iii) raising the energies of dangling bonds at the surface. The periodic boundary condition requires a smooth boundary and consequently a larger GaAs buffer than the two nonperiodic boundary conditions. Between the nonperiodic conditions, the dangling-bond energy shift is more numerically efficient than the orbital-energy shift, in terms of the elimination of nonphysical surface states in the energy region of interest for interior states. A dangling-bond energy shift larger than 5 eV efficiently eliminates all of the surface states and leads to interior states that are highly insensitive to the choice of the energy shift.