A graphical method for estimating charge collected by diffusion from an ion track

The diffusion equation has some applications relevant to charge collection from ion tracks in silicon devices. This problem has been treated in the past for cases in which the entire upper surface can be represented as a sink for minority carriers. The present paper treats the case in which there are a number of disconnected upper junctions separated by reflective surfaces. Numerical results, presented as plots of charge-collection efficiency contours, are given for several device geometries. Such plots, combined with a simple superposition, provide charge-collection estimates for arbitrary track length, location, and direction. The mathematical theory applies to any geometry and can be used by the reader to obtain additional plots and/or analytical expressions. The diffusion coefficient can be an arbitrary function of carrier density.