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 Lₛ and collective resonance excitations Lᵣ to the stopping number L=Lₛ+Lᵣ in the sense that Lₛ=C+Lᵣ; the constant C grows with the gap width.