Multi-Dimensional Charge Diffusion–Collection Model in Semiconductor Devices Subjected to Single Ionizing Particles

Analytical modeling of charge collection is essential for predicting single-event effects in integrated circuits subjected to radiation. This work proposes a unified model of charge collection by diffusion in semiconductors in one, two, and three dimensions, accounting for recombination effects. We derive exact expressions for the carrier density, diffusion current, and collected charge using the solution of the diffusion equation for a point source. We formulate the collected charge using Bessel functions, which allow for a more general and fully analytical description of the problem. The model emphasizes the role of geometry by explicitly accounting for the dimensionality of the problem. It also establishes that, for any dimension, the collected current peaks before the carrier density does. We also propose analytical expressions for the collection efficiency and the recombination factor, with simplified forms in the absence of recombination. A minimal Python implementation is provided to facilitate the practical application of the model. Finally, we outline how to use the proposed model to perform realistic simulations of single events and relate the results to the soft error rate of a given device.