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

TL;DR

The paper tackles the challenge of limited detector-grade HPGe yield by developing a data-driven framework that maps time-resolved CZ growth signals to the final detector-grade fraction using a BiLSTM with multi-head attention. It demonstrates robust predictive performance (MAE ≈ 2.27 percentage points) and provides interpretability via SHAP, identifying impurity concentration and growth dynamics as key yield drivers. The approach outperforms traditional baselines, offering a practical path toward predictive optimization and potential real-time closed-loop control to scale HPGe production for next-generation rare-event detectors. By outlining a multiscale vision that could integrate atomistic MD insights, the work sets the stage for physics-constrained, data-driven optimization of crystal growth.

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.

Figures (8)

• Figure 1: HPGe Crystal Growth Process
• Figure 2: Actual vs. predicted detector-grade percentages for the 48 crystals used in modeling, aggregated across all held-out test folds. Error bars represent $\pm 1$ standard deviation of the model predictions across repeated 5-fold cross-validation runs (five random seeds), reflecting model uncertainty rather than experimental measurement error.
• Figure 3: Error analysis of actual vs. predicted detector-grade percentage. (Left) Distribution of residuals. (Right) Prediction error as a function of actual detector-grade percentage, showing increased variance in sparsely sampled high-yield regions. Error bars represent $\pm 1$ standard deviation of the model prediction across repeated 5-fold cross-validation runs (five random seeds), reflecting model uncertainty rather than experimental measurement uncertainty.
• Figure 4: SHAP feature-importance analysis for the trained model. Features are ranked by their mean absolute SHAP value across all samples.
• Figure 5: Detailed SHAP summary plot for the BiLSTM--Attention model. Each point represents a prediction for a single crystal, colored by feature value (blue = low, red = high).