Theory of semiconductor response to charged particles

The wave-number- and frequency-dependent dielectric function of a semiconductor is derived and calculated in terms of a model consisting of an electron gas with an energy gap. From it are deduced, as a function of the gap width, (i) the screening of a point defect, (ii) the annihilation rate of positrons, and (iii) the stopping power for swift charged particles. A partition rule holds between the contributions of single-particle excitations L-x and collective resonance excitations L-r to the stopping number L = L-s + L-r in the sense that L-s = C +L-r; the constant C grows with the gap width.