The two-dimensional grid patterns on Si(001) in nanometer scale have been fabricated by holographic lithography and reactive ion etching, which can be used as a substrate for positioning Ge islands during self-assembled epitaxy to obtain an ordered Ge quantum dots matrix. By changing the configuration of the holographic lithography and the etching rate and time, we can control the grid period, the shape of the pattern cell, and the orientation of those shapes, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.