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, ($\mathrm{ii}$) the annihilation rate of positrons, and ($\mathrm{iii}$) the stopping power for swift charged particles. A partition rule holds between the contributions of single-particle excitations $L_s$ 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.