Straggling in thin silicon detectors

Abstract

Experimental and theoretical data for dielectric functions, x-ray absorption coefficients, and generalized oscillator strengths needed for a description of the energy-loss spectrum of fast charged particles in solid silicon are given. Theories used to calculate spectra of total energy loss ("straggling spectra") are described. The convolution method is used to calculate straggling functions for thin silicon absorbers. They are compared with those obtained from other theories (Landau). For relativistic particles ($\ensuremath{\gamma}>100$), the Vavilov-Shulek theories give incorrect functions for absorbers of thicknesses $t<1$ mm. The conversion of energy-loss spectra into ionization spectra is discussed, and the latter are compared with experimental functions. Good agreement is found between calculated and observed functions for electrons, mesons, protons, and their antiparticles and for $\ensuremath{\alpha}$ particles. From this agreement, the error ($1\ensuremath{\sigma}$) of the theoretical values of the most probable energy loss ${\ensuremath{\Delta}}_{p}$ and the full width at half maximum, $w$, is estimated to be less than \ifmmode\pm\else\textpm\fi{}1%.