Two-dimensional ordering of self-assembled Ge islands on vicinal Si(001) surfaces with regular ripples

Two-dimensional ordering is achieved in a single layer of self-assembled Ge islands fabricated by molecular beam epitaxy on vicinal Si(001) surfaces with regular ripples caused by step bunching. The ripples with a typical period of about 120 nm lead to the long-range lineup of the Ge islands along their directions, while the strong repulsive interaction between the dense Ge islands determines their relative arrangement on different step bunches of a ripple. The ordering pattern can be tuned by the Ge coverage and the direction of the ripples. The ordering also helps to improve the size homogeneity of the Ge islands.