Pulse shape simulation for the reduced charge collection layer in p-type high-purity germanium detectors

TL;DR

This work presents a mechanistic, three-dimensional pulse-shape simulation of the reduced charge collection (RCC) surface layer in p-type HPGe detectors, implemented in SolidStateDetectors.jl. By modeling the RCC layer through lithium-diffusion impurity profiles, carrier mobilities, diffusion with self-repulsion, and depth-dependent trapping, the authors compute charge-collection efficiency and correct simulated spectra, enabling realistic surface-background studies. The method is validated against an analytical 1D model in a true-coaxial geometry and against experimental BEGe data, achieving good agreement and identifying an RCC-lifetime of around 800 ns as a key parameter for spectral fidelity. The framework provides a robust tool for understanding RCC-layer physics and for developing more effective pulse-shape discrimination in low-background experiments, with future work including depth-dependent lifetimes and extensions to other detector materials and geometries.

Abstract

$P$-type high-purity germanium (HPGe) detectors are widely used across many scientific domains, and current data analysis methods have served well in many use cases. However, applications like low-background experiments that search for rare physics, such as dark matter, neutrinoless double-beta decay, and coherent elastic neutrino-nucleus scattering, could profit a lot from a more detailed understanding of the detector response close to the surface. The outer $n^+$ electrode of the $p$-type HPGe detector forms a layer with reduced charge collection, and events originating here can be a critical background source in such experiments. If the difference in detector pulse shape between detector surface and bulk events is known, it can be used to identify and veto these background events. However, a faithful simulation of the detector response in this surface region is difficult and has not been available as a standard method so far. We present a novel three-dimensional pulse shape simulation method for this reduced charge collection (RCC) layer. We have implemented this method as a new feature in the open-source simulation package \emph{SolidStateDetectors.jl} and show a validation of the numerical simulation results with analytical calculations. An experimental study using a $p$-type HPGe detector also validates our approach. The current implementation supports $p$-type HPGe detectors of fairly arbitrary geometry, but is easily adaptable to $n$-type detectors by adjusting the impurity density profile of the layer. It should also be adaptable to other semiconductor materials in a straightforward fashion.

Figures (20)

• Figure 1: Schematic structure of the $n^+$ electrode of a $p$-type HPGe detector. From the surface inward, there are $n$-type neutral region (dark gray), $n$-type depleted region (light gray), and $p$-type depleted region (pink). The net impurity density profile, illustrated as a purple dashed line, crosses zero at the $p$-$n$ boundary. The region with non-zero electric field is marked with parallel dashed lines. The sensitive region (full charge collection) is marked with dotted area, and the left near-surface region is the RCC layer. FDD and FCCD are also marked.
• Figure 2: Donor (orange dashed), acceptor (green), and net (red) ionized impurity density profiles in the RCC layer with $N_a$ = 3$\times$10$^9$ cm$^{-3}$, $T_{\text{an}}$ = 623 K, $t_{\text{an}}$ = 18 min, and the saturated surface lithium concentration. The $p$-$n$ boundary is marked with a purple dashed line.
• Figure 3: Mobilities of electrons (black) and holes (red) in the RCC layer when adopting the IEEE standard value of hole mobility in the sensitive region (42000 cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$) and $T = 90$ K.
• Figure 4: Illustration of the CCE curve $f_\text{CCE}(x)$ and the step function $\Theta(x-\text{FCCD})$ with FCCD = 0.9 mm.
• Figure 5: Visualization of the simulated hypothetical true-coaxial HPGe detector geometry for the analytical validation.