58 magnitude of the arsenic ﬂux. The total amount of Ga deposited was 10.0 monolayers (MLs), corresponding to the amount of Ga necessary for 10.0 MLs of GaAs growth. A Ga deposition rate of 1.0 ML/s was selected by separately observing RHEED oscillations during the growth of GaAs. To minimize the system’s energy, the deposited liquid Ga forms nano droplets. In particular, by form- ing nano-droplets the surface to vacuum and interface to the Al0.3Ga0.7As layer, can be minimized, thereby minimizing the system’s energy. The atomic force microscopic (AFM) image in Fig. 1a reveals that the Ga droplets have an average lateral size of ~125 nm, a height of ~32 nm, and a number density of ~2.3 per square micrometer. In forming the droplets we have observed that the substrate temperature is a signiﬁcant parameter for the tuning of droplet density. For Fig. 1 (a) AFM image of Ga droplets. (b) AFM image of QD pairs formed after 45 s annealing under arsenic ﬂux Nanoscale Res Lett (2006) 1:57–61 example, the density of droplets increases by a factor of six for the same amount of Ga, but deposited at the lower temperature [7] of 380 C as opposed to 550 C. We also observed that the size of the droplets could be tuned by controlling the total amount of Ga deposited at a ﬁxed temperature. Figure 1b shows an AFM image of the surface nanostructures that are transformed from the Ga droplets after 45 s of annealing while under an arsenic ﬂux of 4.2 · 10–5 Torr. Remarkably, every Ga droplet turns into a QD pair sitting on a 3 nm hill of GaAs. The average separation between two QDs in a pair is about 130 nm, comparable with the original lateral size of Ga droplets. The tips of two QDs are about 4 nm above the GaAs hill. It is important to note that these results are observed at a substrate temperature of 550 C which is signiﬁcantly higher than previously reported droplet- related experiments (growth temperatures of 200 C or lower) [4–6]. Traditional droplet epitaxy has used low temperatures in an effort to directly crystallize the Ga droplets into GaAs without material redistribution. On the other hand, in our approach we used high-tem- perature to encourage material redistribution. In this way we can fabricate novel semiconductor nanostruc- tures by taking advantage of the shape instability of Ga droplets during the transformation into GaAs dots. The crystallization of Ga droplets proceeds at a much faster rate at high temperature so that surface pro- cesses on the GaAs surface can play a more important role in the shape evolution of the GaAs nanostructure. In particular, the GaAs forms more quickly then it can diffuse away from the droplet. With surface tension removed, the droplet collapses down the center of the droplet pushing material away from the center while restricted by diffusion. Gradually this leaves a smaller and smaller Ga droplet on the GaAs surface acting as a source for forming GaAs diffusing outward, forming ridges and center-holed shaped nanostructures. In particular, Fig. 2 shows an AFM image of the outcome at high temperature. The AFM image shows that the Ga droplets have fully crystallized after only 1-s of annealing at 550 C and surface nanostructures shaped like square-holed round coins are immediately observed. Similar shaped nanostructures have been observed for droplet epitaxy performed at 380 C but with a much longer 45-s annealing and signiﬁcantly lower arsenic ﬂux [7]. The holed nanostructures are observed to sit on GaAs hills due to the high As ﬂux and corresponding diffusion limited Ga transport. This is conﬁrmed since by lowering the arsenic ﬂux, two- dimensional (2D) growth of GaAs is enhanced and the hills are observed to disappear. As we pointed out