Creating perfectly ordered quantum dot arrays via self-assembly

Several applications involving quantum dots require perfect long-range ordered arrays. Unfortunately, self-assembly (the choice method to fabricate quantum dots) leads to patterns that, although short range ordered, exhibit defects equivalent to grain boundaries and dislocations on a large scale. We note that rotational invariance of film growth is one reason for formation of defects, and hence study an anisotropic model of quantum dot formation. However, nonlinear stability analysis shows that even in the extreme limit of anisotropy, square arrays whose orientations are in a finite range are linearly stable; consequently structures created in the film continue to have defects. Building on insights developed by the authors earlier on a simpler monolayer self-assembly model, we propose controlling the deposition through a mask to generate ordered quantum dots arrays. General principles to estimate geometrical characteristics of the mask are given. Numerical integration of the model shows that perfectly ordered square arrays of quantum dots can indeed be created using masked deposition.