In this paper, we investigated the heteroepitaxial germanium (Ge) growth on a nano-patterned Si substrate using a diblock copolymer self-patterning process, which provides approximate 10-nm-diameter holes and 20 nm distances in lateral scale. A 300-nm-thick pure Ge film was grown by solid source molecular beam epitaxy (MBE) and the epitaxial film was characterized by AFM, SEM, TEM, mu-Raman spectroscopy and etched pit dislocation (EPD) measurements. The results show that rms surface roughness was improved by 22.5% for the growth on nano-patterned templates and the epitaxial layer exhibited a fully relaxed single-crystalline structure. One-order reduction in etch pit density was achieved for the growth on the nano-patterned templates. (c) 2006 Elsevier B.V. All rights reserved.