A layer of HgCdTe (15) is epitaxially grown on a crystalline support (10). A single crystal CdTe substrate (5) is first epitaxially grown to a thickness of between 1 micron and 5 microns onto the support (10). Then a HgTe source (3) is spaced from the CdTe substrate (5) a distance of between 0.1 mm and 10 mm. The substrate (5) and source (3) are heated together in a thermally insulating, reusable ampoule (17) within a growth temperature range of between 500.degree. C. and 625.degree. C. for a growth time of between 5 minutes and 13 hours. In a first growth step embodiment, the source (3) and substrate (5) are non-isothermal. In a second growth step embodiment, the source (3) and substrate (5) are isothermal. Then an optional interdiffusion step is performed, in which the source (3) and substrate (5) are cooled within a temperature range of between 400.degree. C. and 500.degree. C. for a time of between 1 hour and 16 hours. Means are disclosed for preventing contamination of the reactants during HgTe (3) synthesis, and for polishing the finished HgCdTe layer (15).