Multi-scale and Multi-physics Modeling of Phosphorus Donor Qubits in Silicon

Abstract

Donor-based quantum computing in silicon has flourished in the last decade after the atomic precision placement of individual atoms has been demonstrated using Scanning Tunneling Microscope (STM) lithography. To facilitate effective design and characterization of the STM devices, predictive theoretical models are required that are multi-scale, multi-physics, self-consistent, and free of fitting parameters. The models need to capture quantum electronics at the nanoscale with corresponding electrostatics at nano- to micro-meter length scales. Here, we develop and apply such a framework involving atomistic tight-binding, non-linear Poisson, non-equilibrium Green’s function, and full configuration interaction (FCI) to investigate designs of STM devices for quantum computing. The methods are applied to investigate 1) electrical properties of semi-metallic degenerately doped phosphorus leads, 2) device electrostatics extending over multiple leads, gates, qubits, and SET regions, 3) current flow through atomically engineered tunnel barriers across leads/channels, 4) and long-range spin coupling between donor qubits. Each of these systems presents unique modeling challenges which we overcome in this thesis.

We compute the conduction properties of the STM leads atomistically as a function of their dimensions and predict the optimum width for better reproducibility in the experiments. We then combine the properties of these semi-metallic phosphorus structures to solve the electrostatics of the extended device regions including the leads, gates, and qubits. We find agreement with experimentally measured lever arms and charging energies, which provide insight into the electrical tunability of the devices. We use the device electrostatics to tune the nearest and non-nearest neighbor exchange couplings between phosphorus donor qubits, extending the FCI method to handle more electrons than previously considered. The simulations predict robust spin coupling to the third-nearest neighbors in a donor chain, with qubits spaced out by about 40 nm or more. Finally, we combine calculations of the extended device electrostatics with Green’s function method of quantum transport at low temperatures to describe the current flow between two leads as a function of their separation and obtain good agreement with the tunneling resistance measured in experiments. The methodology and the results lay a foundation to design more complex donor devices for scaling up the quantum processors.