A monte Carlo based development of a cavity theory for solid state detectors irradiated in electron beams

Recent Monte Carlo simulations have shown that the assumption in the small cavity theory (and the extension of the small cavity theory by Spencer-Attix) that the cavity does not perturb the electron fluence is seriously flawed. For depths beyond d_max not only is there a significant difference between the energy spectra in the medium and in the solid cavity material but there is also a significant difference in the number of low-energy electrons which cannot travel across the solid cavity and hence deposit their dose in it (i.e. stopper electrons whose residual range is less than the cavity thickness). The number of these low-energy electrons that are not able to travel across the solid state cavity increases with depth and effective thickness of the detector. This also invalidates the assumption in the small cavity theory that most of the dose deposited in a small cavity is delivered by crossers. Based on Monte Carlo simulations, a new cavity theory for solid state detectors irradiated in electron beams has been proposed as: D_med(p) = D̄_det(p) × S_med,det^S-A × γ(p)^e × S^T where D_med(p) is the dose to the medium at point p, D̄_det(p) is the average detector dose to the same point, S_med,det^S-A is the Spencer-Attix mass collision stopping power ratio of the medium to the detector material, γ(P)^e is the electron fluence perturbation correction factor and S^T is a stopper-to-crosser correction factor to correct for the dependence of the stopper-to-crosser ratio on depth and the effective cavity size. Monte Carlo simulations have been computed for all the terms in this equation. The new cavity theory has been tested against the Spencer-Attix cavity equation as the small cavity limiting case and also Monte Carlo simulations.