It is established that an array of silicon nanoislands is formed on the surface of a sapphire substrate at the initial stages of molecular beam epitaxy. Silicon islands formed at low temperatures of the substrate (below 650°C) exhibit a pyramidal shape, while the islands grown at T > 650° possess a dome shape. The maximum density of islands was 2 × 1011 cm−2, their lateral dimensions were within 20 nm, and their heights did not exceed 3 nm.