It has been hoped that high-Z semiconductors would offer efficient Â¿-ray detection at or near ambient temperatures with energy resolution significantly better than NaI (T1) scintillators. For use at X-ray energies, this goal has been achieved with both HgI2, CdTe, and GaAs detectors. However, at higher energies (~660 keV) all current detectors have one or more significant deficiencies in terms of attainable volume, charge collection efficiency, and polarization effects. Starting with first principles, all potential compounds which can be formed by the binary combination of elements from the periodic chart were considered as possible detector materials. A rank-ordered listing of the most promising materials for further development is given as well as an assessment of the prospects for future success.