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Nikolai Bart, Christian Dangel, Peter Zajac, Nikolai Spitzer, Julian Ritzmann, Marcel Schmidt, Hans-Georg Babin, Rüdiger Schott, Sascha René Valentin, Sven Scholz, Y. Wang, Ravitej Uppu, Daniel Najer, Matthias Christian Löbl, Natasha Tomm, Alisa Javadi, Nadia Olympia Antoniadis, Leonardo Midolo, Kai Müller, Richard Warburton, Peter Lodahl, Andreas D. Wieck, Jonathan J. Finley, Arne Ludwig

• Precise control of the properties of semiconductor quantum dots (QDs) is vital for creating novel devices for quantum photonics and advanced opto-electronics. Suitable low QD-densities for single QD devices and experiments are challenging to control during epitaxy and are typically found only in limited regions of the wafer. Here, we demonstrate how conventional molecular beam epitaxy (MBE) can be used to modulate the density of optically active QDs in one- and two- dimensional patterns, while still retaining excellent quality. We find that material thickness gradients during layer-by-layer growth result in surface roughness modulations across the whole wafer. Growth on such templates strongly influences the QD nucleation probability. We obtain density modulations between 1 and 10 QDs/\(\mu\)\(m^{2}\) and periods ranging from several millimeters down to at least a few hundred microns. This method is universal and expected to be applicable to a wide variety of different semiconductor material systems. We apply the method to enable growth of ultra-low noise QDs across an entire 3-inch semiconductor wafer.