A model for positron annihilation in multi-layer systems by solving the diffusion equation using different positron affinities

TL;DR

This paper introduces a new Python-based method for modeling positron diffusion and annihilation in multi-layer materials, improving analysis accuracy and reproducibility in defect characterization.

Contribution

It presents a novel Markov chain approach that incorporates material-specific parameters and is implemented in an accessible software tool for analyzing experimental data.

Findings

Accurate modeling of positron annihilation in layered systems.

Excellent agreement with experimental Doppler-Broadening Spectroscopy data.

Enhanced reproducibility of defect measurements across research groups.

Abstract

We present a method for solving the positron diffusion equation in multi-layer systems. Our approach incorporates material-specific implantation profiles, diffusion parameters, and positron affinities. It utilizes a Markov chain approach to model annihilation probabilities and provides fitting capabilities for experimental S (lineshape) parameter data. We have implemented this algorithm in Python and made it available for free under the name LIMPID. To demonstrate its performance, we analyze depth-resolved Doppler-Broadening Spectroscopy measurements of a Cu layer on a Si substrate, achieving excellent agreement with the experimental profiles. The LIMPID tool enhances the reproducibility and comparability of positron defect characterization measurements across different research groups.