Machine-Learning Optimization of Detector-Grade Yield in High-Purity Germanium Crystal Growth

TL;DR

This paper introduces a data-driven BiLSTM neural network model that predicts detector-grade yield in germanium crystal growth, helping optimize production and improve quality control in high-purity germanium manufacturing.

Contribution

The study develops an interpretable, predictive framework using BiLSTM with attention, linking in-process signals to detector quality to enhance yield in germanium crystal growth.

Findings

Impurity concentration and growth rate are key factors affecting yield.

The model accurately predicts detector-grade fraction from growth parameters.

SHAP analysis confirms known physical influences on crystal quality.

Abstract

High-purity germanium (HPGe) crystals underpin some of the most sensitive detectors used in fundamental physics and other high-resolution radiation-sensing applications. Despite their importance, the supply of detector-grade HPGe remains limited because achieving high yield in Czochralski growth (CZ) depends on tightly coupled, nonlinear processes, impurity incorporation, thermal gradients, and dynamic control settings that are largely mastered by only a handful of companies with decades of experience. Here we present a data-driven prediction framework based on a Bidirectional Long Short-Term Memory (BiLSTM) neural network with multi-head attention, trained on time-resolved growth parameters (e.g., heater power, pull rate, and impurity indicators) from 48 independent crystal runs. The model predicts the final detector-grade fraction for each growth and, using SHAP feature-importance analysis, identifies impurity concentration and growth rate as the dominant factors governing yield, consistent with empirical understanding. By providing a quantitative, interpretable link between in-process signals and post-growth detector quality, this framework offers a practical path toward improving yield, reducing dependence on trial-and-error tuning, and scaling HPGe production for next-generation rare-event detectors.