There is a method for forming a semiconductor nanostructure on a substrate. The method includes placing a substrate and a semiconductor material in a pulsed laser deposition chamber; selecting parameters including a fluence of a laser beam, a pressure P inside the chamber, a temperature T of the substrate, a distance d between the semiconductor material and the substrate, and a gas molecule diameter a₀ of a gas to be placed inside the chamber so that conditions for a Stranski-Krastanov nucleation are created; and applying the laser beam with the selected fluence to the semiconductor material to form a plume of the semiconductor material. The selected parameters determine the formation, from the plume, of (1) a nanolayer that covers the substrate, (2) a polycrystalline wetting layer over the nanolayer, and (3) a single-crystal nanofeature over the polycrystalline wetting layer, and the single-crystal nanofeature is grown free of any catalyst or seeding layer.