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

TL;DR

This paper investigates boundary conditions for finite semiconductor nanostructures embedded in a host material, comparing their effects on electronic states using empirical tight-binding models.

Contribution

It evaluates and compares three boundary conditions for modeling embedded nanostructures, identifying effective methods to eliminate nonphysical surface states.

Findings

Periodic boundary requires larger buffers for smooth boundaries.

Dangling-bond energy shift effectively removes mid-gap surface states.

A shift greater than 5 eV stabilizes interior states against boundary variations.

Abstract

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.