The photoelectric and Compton response to γ rays for a detector made from semi-insulating material (i.e., a monocrystalline semiconductor containing trapping centers) was calculated for the case of charge transport by one type of carrier (electron or hole), and also for the case of two-carrier transport (electron and hole) with each carrier having the same mean free path. Approximate expressions were then derived for the observable γ-ray efficiency of the detector as a function of material parameters for CdTe crystals used in the fabrication of surface barrier detectors; this efficiency is dependent upon temperature and electric field intensity for specified values of the carrier mobility-trapping time product and the threshold used in the recording of spectra. Spectra and values for efficiency were determined at room temperature for γ rays at energy values from 0.393 to 1.33 MeV, and also as a function of temperature over the range 24°to 68°C for γ rays from a 60Co source. The observations show behavior corresponding to a trap-limited response, and the presence of charge detrapping. © 1969 The American Institute of Physics.