We demonstrate a self-assembling method for growing semiconductor quantum dots into ordered lattices. The quantum dot nucleation and positioning into lattices was achieved using a periodic subsurface stressor lattice. Three different two-dimensional (2D) square lattices are demonstrated. The unit cell dimensions, orientation, and the number of quantum dots in the basis are tunable. We find that the 2D lattice can be replicated at periodic intervals along the growth direction to form a three-dimensional (3D) lattice of quantum dots.
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