Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

TL;DR

This study uses an effective mass theory approach to analyze how electric fields and interfaces influence the behavior of phosphorus donors in silicon, providing insights for quantum computer design.

Contribution

It introduces a variational method with deformed hydrogenic orbitals to model donor electrons under various experimental conditions in silicon-based quantum devices.

Findings

Donor electron density is highly sensitive to experimental parameters.

Resonance frequency varies significantly with gate voltage and device geometry.

Optimal device operation requires precise control of multiple parameters.

Abstract

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron was very sensitive to all the experimental variables studied in our work, and thus to optimise the operation of these devices it is necessary to control all parameters varied in this paper.