We have studied a self-assembled growth technique to form ultra-low density InAs quantum dots on GaAs by molecular beam epitaxy. After growing a GaAs layer under a particular condition, we have deposited an InAs layer of far less than the critical thickness and performed an annealing process. By optimizing these process steps, the density of dots is successfully controlled over a wide range from 10 4 to 10 8 cm À2 , at which the average interdot distance gets as long as 100 m. Photoluminescence spectra of low dot density samples have shown discrete single-dot features even under a macroscopic optical excitation. These dots are found to be formed preferentially on GaAs mounds especially when the dot density is around 2:5 Â 10 5 cm À2 . #

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