Above Bandgap Hyperpolarization Mechanism in Isotopically Purified Silicon and Optimal Bayesian Experiment Design for $T_1$ Estimation

Abstract

This thesis is concerned with the mechanism underlying the above bandgap illumination Dynamic Nuclear Polarization (DNP) of phosphorus donors in isotopically purified silicon-28. Two proposed DNP models are introduced and compared. A series of NMR saturation experiments are performed in which modified buildup dynamics are observed when the saturation tone is applied at the bare phosphorus resonance. This effect is attributed to the phosphorus donor being ionized via the Auger process resulting in dynamics which are modelled as a set of coupled Bloch equations. The donor bound exciton capture and neutralization rates are extracted, and a paramagnetic shift of the bare phosphorus resonance is observed. These observed dynamics strongly imply the DNP mechanism is due to phononic modulation of the donor electron spatial wavefunction inducing cross-relaxation between the hyperfine coupled electron and nuclear spins.

The framework of Bayesian parameter estimation and its Sequential Monte Carlo(SMC) numerical implementation for continuous outcome probability distributions are introduced. Next, an introduction to Bayesian experiment design and its incorporation within the SMC framework is provided. A discussion of the computational challenges for continuous outcome distributions is given. To resolve these difficulties Monte Carlo Maximum Importance Sampling(MIS) numerical methods are developed which allow the evaluation of Bayesian experimental design heuristics such as the Bayes risk. These design strategies are applied to the problem of $T_1$ relaxation rate estimation with inversion recovery experiments. Experiments are optimized both respect to per-experiment performance and total experiment time. These techniques are shown to have substantial improvements over baseline methods. Furthermore, they compare favourably with previous frequentist experimental designs for IR experiments and demonstrate significant improvements.