With the standard plane−parallel configuration of semiconductor detectors, good &ggr;−ray spectra can only be obtained when both electrons and holes are completely collected. We show by calculations (and experiments) that with contacts of hemispherical configuration one can obtain &ggr;−ray spectra of adequate resolution and with signal heights of nearly full amplitude even when only one type of carrier is collected. Experiments with CdTe detectors for which the &mgr;&tgr; product for electrons is about 103times that of the holes confirm these calculations. The adoption of hemispherical contacts thus widens the range of high−resistivity semiconductors potentially acceptable for &ggr;−ray detection at room temperature.