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

Abstract

We present a theory and a computational tool, Silicon-Qnano, describing atomic scale quantum dots in silicon. The developed methodology is applied to model dangling bond quantum dots (DBQDs) created on a passivated H:Si-(100)-(2 × 1) surface by removing a hydrogen atom. The electronic properties of the DBQD are computed by embedding it in a computational box of silicon atoms. The surfaces of the computational box were constructed by using density functional theory as implemented in the Abinit package. 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 linear combinations of atomic orbitals and fitting the bandstructure to 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 ab-initio calculations. The removal of one hydrogen atom from the reconstructed surface resulted in a DBQD state with a wave function strongly localized around the Si atom and the 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.