We have used an elementary statistical technique to derive a closed-form expression for the hole-tailing line shape produced by photoelectric absorption of monoenergetic radiation in a semiconductor X-ray/γ-ray detector. In the case of compound semiconductors, where the drift length for electrons is much greater than that for holes, the line shape is given by a type of power law, except for a small region very near the photopeak. This analytical result agrees well with Monte Carlo simulations and is used to extract approximate μτ products from a 57Co pulse height spectrum. We also present an expression for the maximum obtainable energy resolution of a semiconductor detector in the presence of leakage current noise and intrinsic statistical fluctuations as a function of material parameters, along with a chart of the optimal band gap as a function of temperature and photon energy. Based on these considerations, the optimal band gap for room-temperature operation is approximately 2.0 eV.