Control of the position and density of semiconductor quantum dots (QDs) is vital for a variety of emergent technologies, such as quantum photonics and advanced opto-electronic devices. However, established ordering methods typically call for ex-situ processing prior to growth that have a deleterious impact on the optical quality of nanostructures. Here, we apply a conventional epitaxial growth method - molecular beam epitaxy (MBE) - to achieve wafer scale positioning of optically active QDs with high reproducibility, tunable periodicity, and controlled density across an entire unpatterned 3-inch semiconductor wafer. Hereby, we exploit material thickness gradients across the wafer to modulate the QD nucleation probability and demonstrate how our approaches can be used to achieve strong periodic modulation of the local dot density tunable over length scales ranging from a few millimeters to at least a few hundred microns in one or two spatial directions. The methods are universal and are applicable to a wide variety of semiconductor material systems.
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