Bayesian inference of high-purity germanium detector impurities based on capacitance measurements and machine-learning accelerated capacitance calculations

TL;DR

This paper introduces a Bayesian inference method utilizing machine learning and GPU-accelerated capacitance calculations to accurately determine impurity distributions in high-purity germanium detectors, improving understanding beyond limited manufacturer data.

Contribution

It presents a novel open-source Julia-based framework combining surrogate modeling, GPU acceleration, and Bayesian inference for impurity density estimation in germanium detectors.

Findings

Impurity density shows radial dependence in the tested detector.

Capacitance measurements can effectively infer impurity distributions.

The method enhances impurity characterization accuracy.

Abstract

The impurity density in high-purity germanium detectors is crucial to understand and simulate such detectors. However, the information about the impurities provided by the manufacturer, based on Hall effect measurements, is typically limited to a few locations and comes with a large uncertainty. As the voltage dependence of the capacitance matrix of a detector strongly depends on the impurity density distribution, capacitance measurements can provide a path to improve the knowledge on the impurities. The novel method presented here uses a machine-learned surrogate model, trained on precise GPU-accelerated capacitance calculations, to perform full Bayesian inference of impurity distribution parameters from capacitance measurements. All steps use open-source Julia software packages. Capacitances are calculated with SolidStateDetectors$.$jl, machine learning is done with Flux$.$jl and Bayesian inference performed using BAT$.$jl. The capacitance matrix of a detector and its dependence on the impurity density is explained and a capacitance bias-voltage scan of an n-type true-coaxial test detector is presented. The study indicates that the impurity density of the test detector also has a radial dependence.