Role of the density, density effect and mean excitation energy in solid-state detectors for small photon fields

Abstract

A number of recent publications on small photon beam dosimetry aim at contributing to the understanding of the response of solid-state detectors in small fields. Some of them assign the difference in response to the mass density, or to the electron density, of the sensitive detector material relative to that of water. This work analyses the role of the mass and electron density (), density effect (δ) and mean excitation energy (I-value) of some detector materials in a 6 MV photon beam of 0.5 cm radius, its rationale being that the response of a detector depends critically on the stopping-power ratio detector-to-water. The influence on the detector response of volume scaling by electron density, and of electron single and multiple scattering, is also investigated. Detector materials are water, diamond and silicon, and additional materials are included for consistency in the analysis. A detailed analysis on the () dependence of stopping-power ratios shows that the density effect δ depends both on the electron density and on the I-value of the medium, but not on the mass density ρ alone as is usually assumed. This leads to a double dependence of stopping-power ratios on the I-value and questions the adequacy of a ‘density perturbation factor’ or of common interpretations of detector response in terms of ρ alone. Differences in response can be described in terms of the variation of stopping power ratios detector-to-water, mainly due to different I-values and to a lesser extent to different values of electron density. It is found that at low energies the trend of Monte Carlo-calculated electron fluence spectra inside the detector materials depends solely on their I-values. No dependence on mass density or density effect alone is observed at any energy. The trend of restricted-cema ratios to water (as a substitute of absorbed dose ratios) follows that of stopping-power ratios at 1 MeV, the most probable energy of differential restricted-cema distributions in this study. It is concluded that the combined effect of the I-value and the dependence of δ on governs the restricted-cema values, and that neither ρ or a alone explain the different response of diverse detector materials. The results show that, for the small non-scaled and scaled volumes in this work, is practically constant and that in both cases the contribution of electron scattering to the restricted-cema values is about 2%.