We demonstrate, by both theory and experiment, the strain-induced self-orga
nized formation of "quantum platelets," monolayer-thick islands of finite d
imensions. They form at the early stage of heteroepitaxial growth on a. sub
strate with regularly spaced steps, and align along the steps. In the direc
tion perpendicular to substrate steps, the island position and spacing can
be preselected through substrate miscut. Along the steps, the island size a
nd density are controlled by self-organized growth.