Semiconductor Particle Detectors: A Reassessment of the Fano Factor Situation

The problems dealt with concern the production of electron-hole pairs in a semiconductor nuclear radiation sensor. The goal is to develop a semiphenomenological model capable of describing the present experimental situation from the standpoint of yield, variance and bandgap dependence. We proceed on the premise that ϵ, the average amount of radiation energy consumed per pair, can be accounted for by a sum of three contributions: the intrinsic bandgap (EG), optical phonon losses r(h ωR), and the residual kinetic energy (9/5)EG. Both the bandgap and the temperature dependence of pair-creation energies conform to this model and suggest that optical phonon losses remain essentially constant [0.5 ≤ r(hωR) ≤ 1.0 eV]. Fano-factor variations are found to reflect the relative weight of phonon losses [ϰ = r(hωR)/EG], but residual energy fluctuations govern the statistical behavior for ϰ2 ≲ 0.3; an application to Ge detectors yields good agreement with the best measurements available (F ≈ 0.13). Finally, it is shown that materials such as Si or CdTe (1.0 ≤ EG ≤ 1.5 eV) provide optimized media in terms of the "ultimate" resolution capability.