  The modeling of finite-extent semiconductor nanostructures that are embedded
in a host material requires the numerical treatment of the boundary in 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 efficient than the orbital-energy shift, in terms of the
elimination of nonphysical surface states in the middle of the gap. A
dangling-bond energy shift bigger than 5 eV efficiently eliminates all of the
mid-gap surface states and leads to interior states that are highly insensitive
to the change of the energy shift.
