Abstract
Achieving periodicity and size uniformity of quantum dots is significant in improving the performance of quantum dot based devices. An efficient way to control the size and arrangement of quantum dots is to employ a patterned substrate in quantum dot growth. In this paper, the composition, position and shape transition of quantum dots are considered to obtain the minimum energy of the system. The least-energy principle is used here to estimate the critical size of the patterned substrate for single quantum dot growth. Numerical results are in good agreement with experiment, which can help one to control the arrangement of quantum dots by projection of the patterned substrate.
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