Self-organized InAs quantum dots (QDs) were grown on patterned GaAs substrates. A 2.5-ML-thick InAs grown on self-organized GaAs nano-wire surfaces showed QD formation with a very low density of 1.5 x 10(8) cm(-2). The self-organized GaAs nano-wires were grown under low V/III ratio, and nano-wires were parallel to the [1 1 0] direction. On the other hand, the 2.5-ML-thick InAs on smooth (0 0 1) GaAs surfaces formed QDs with a density of 4.4 x 10(9) cm(-2). We grew these low density InAs QDs on patterned GaAs, which had small A-planes. The InAs QDs were formed only on the small A-plane, which was positioned at the boundary between the square-patterned and planar areas. Except for the A-planes, no InAs QD formation was observed in a relatively large area. These results indicate that the combination of GaAs nano-wires and pattern substrates with small A-planes can produce InAs QDs at desired areas. (c) 2006 Elsevier B.V. All rights reserved.