The photoelectric and Compton response to &ggr; 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 &ggr;‐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 &ggr; 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 &ggr; rays from a60Co source. The observations show behavior corresponding to a trap‐limited response, and the presence of charge detrapping.