Charge collected by diffusion from an ion track under mixed boundary conditions

Charge-carrier diffusion from an ion track in a silicon substrate at least a few hundred microns thick is analyzed. The substrate upper surface is treated as reflective except for a small section, intended to represent a reverse-biased junction, which is treated as a sink. Total charge collected by the sink is calculated by assuming transport to be governed by an ambipolar diffusion equation with temporally constant and spatially uniform carrier lifetime and diffusion coefficient. Present results apply to a normally incident track but could easily be generalized to arbitrary track direction. The collected charge is found to depend on track length and on the electrostatic capacitance, rather than the area, of the sink. Theoretical predictions are compared to the results of a numerical simulation called the Poisson and Continuity Equation Solver (PISCES) for three cases and are found to agree within a factor of two in the worst case.