Impact of the valley degree of freedom on the control of donor electrons near a Si/SiO_2 interface

TL;DR

This paper investigates how the valley degree of freedom influences the control of donor electrons near a Si/SiO2 interface, revealing complex energy level behaviors and implications for quantum manipulation.

Contribution

It provides a detailed analysis of valley compositions and energy level crossings in donor electrons influenced by electric fields and interface effects using a six-valley effective mass model.

Findings

Valley splitting occurs due to valley-orbit coupling at the interface.

Energy levels exhibit crossings and anti-crossings as the electric field varies.

The phase theta affects the symmetry and anti-crossing gaps of eigenstates.

Abstract

We analyze the valley composition of one electron bound to a shallow donor close to a Si/barrier interface as a function of an applied electric field. A full six-valley effective mass model Hamiltonian is adopted. For low fields, the electron ground state is essentially confined at the donor. At high fields the ground state is such that the electron is drawn to the interface, leaving the donor practically ionized. Valley splitting at the interface occurs due to the valley-orbit coupling, V_vo^I = |V_vo^I| e^{i theta}. At intermediate electric fields, close to a characteristic shuttling field, the electron states may constitute hybridized states with valley compositions different from the donor and the interface ground states. The full spectrum of energy levels shows crossings and anti-crossings as the field varies. The degree of level repulsion, thus the width of the anti-crossing gap, depends on the relative valley compositions, which vary with |V_vo^I|, theta and the interface-donor distance. We focus on the valley configurations of the states involved in the donor-interface tunneling process, given by the anti-crossing of the three lowest eigenstates. A sequence of two anti-crossings takes place and the complex phase theta affects the symmetries of the eigenstates and level anti-crossing gaps. We discuss the implications of our results on the practical manipulation of donor electrons in Si nanostructures.