The growth of Ge on (110) and (111) oriented Si substrates is of great interest to enhance the mobility of both holes and electrons in complementary metal oxide semiconductor transistors. However, the quality of thick, relaxed Ge layers grown epitaxially on these surfaces is usually much lower than similar layers grown on (100) Si, resulting in both higher defect densities (i.e. threading dislocations and stacking faults) and rougher surfaces. In this work we have investigated the growth of Ge layers on (110) and (111) Si substrates by reduced-pressure chemical vapour deposition using a two temperature process. We have found that the combination of suppressing the Ge seed layer roughness and high temperature post-growth annealing can reduce the rms surface roughness of (110) Ge layers to below 2 nm and the threading dislocation density to below 1 x 10(7) cm(-2). Thick (111) Ge layers were found to exhibit a very high density of stacking faults, that could not be reduced by post-growth annealing and a higher rms surface roughness of around 12 nm, which was limited by the Ge seed layer. (C) 2011 Elsevier B.V. All rights reserved.