Theory of atomic scale quantum dots in silicon: dangling bond quantum dots on silicon surface

TL;DR

This paper introduces Silicon-Qnano, a computational method for modeling atomic-scale quantum dots in silicon, specifically dangling bond quantum dots created on a passivated silicon surface, and analyzes their electronic properties.

Contribution

The paper develops a new computational tool combining DFT and tight-binding models to accurately simulate dangling bond quantum dots in silicon at an atomic scale.

Findings

Localized quantum dot states with energies in the silicon bandgap

Charged states of the quantum dot with up to two electrons

Calculated Coulomb charging energies for the quantum dot

Abstract

We present here a theory and a computational tool, Silicon-{\sc Qnano}, to describe atomic scale quantum dots in Silicon. The methodology is applied to model dangling bond quantum dots (DBQDs) created on a passivated H:Si-(100)-(2$\times$1) surface by removal of a Hydrogen atom. The electronic properties of DBQD are computed by embedding it in a computational box of Silicon atoms. The surfaces of the computational box were constructed by using DFT as implemented in {\sc Abinit} program. The top layer was reconstructed by the formation of Si dimers passivated with H atoms while the bottom layer remained unreconstructed and fully saturated with H atoms. The computational box Hamiltonian was approximated by a tight-binding (TB) Hamiltonian by expanding the electron wave functions as a Linear Combination of Atomic Orbitals and fitting the bandstructure to {\it ab-initio} results. The parametrized TB Hamiltonian was used to model large finite Si(100) boxes (slabs) with number of atoms exceeding present capabilities of {\it ab-initio} calculations. The removal of one hydrogen atom from the reconstructed surface resulted in a DBQD state with wave function strongly localized around the Si atom and energy in the silicon bandgap. The DBQD could be charged with zero, one and two electrons. The Coulomb matrix elements were calculated and the charging energy of a two electron complex in a DBQD obtained.