This paper reports on a detailed study of the development of the close space sublimation method, which has been widely used in the preparation of polycrystalline CdTe/CdS solar cells, as an epitaxial method for the growth of thick CdTe single crystal films over 200 lm on GaAs and Ge substrates for highenergy radiation detectors. The resulting microscopic growth phenomena in the process are also discussed in this paper. High-quality single crystalline CdTe thick films were prepared with x-ray rocking curves full width at half maximum (FWHM) values, which were $100 arcsec on Ge substrates and 300 arcsec on GaAs substrates. The quality of thick films on Ge(100) showed a substantial improvement with nucleation in a Te-rich growth environment. No Te inclusions in the CdTe films grown on GaAs(211)B and Ge(100) were observed with IR transmission imaging. Photoluminescence of CdTe/Ge shows a large reduction in the 1.44 eV defect energy bands compared with films grown on GaAs substrates. The film resistivity is on the order of 10 10 X cm, and the film displayed some sensitivity to alpha particles.