The pressure and temperature dependencies for vapor-liquid-solid (VLS) growth of Ge nanostructures on Si using chemical vapor deposition are reported. Gold nanodots self-assembled by evaporation on clean hydrogen-terminated and heated Si substrates are used to seed the liquid eutectic VLS growth. Digermane pressures are varied from 4x10(-5) to 1x10(-2) Torr and substrate temperatures from 400 to 600degreesC for heteroepitaxial growth on Si(111). Two types of nanostructures are identified, nanowires and nanopillars, with a transition from nanopillar growth to nanowire growth occurring with increasing pressure. Nanowires are characterized by rapid vertical growth, long-aspect-ratio structures, and linear dependence of the growth rate on pressure. At lower pressures a transition to nanopillars is observed; these exhibit both vertical and lateral growth with typical aspect ratios of 1:2. For Si(111) substrates nanowires grow epitaxially with their growth axis along the <111> direction. High-resolution transmission electron microscopy shows that the Ge nanowires are relaxed to their equilibrium lattice spacings a short distance from the Si substrate interface. (C) 2004 American Institute of Physics.