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We studied the stress field at the surface of GaAs capping layers of variable thicknesses burying InAs quantum dot arrays using the Finite Element method to solve numerically the equations of the elastic field. The aim is to determine the stress-determined favorable sites for dot nucleation. We show that: (i) depending on the cap thickness, dot distances, and array orientation, sudden transitions in the stress-strain fields occur, leading from a vertical alignment of the dots to an anti-aligned correlation. We find that just few determined positions are favorable for dot nucleation and exclude some other sites previously indicated as favorable in the literature; (ii) the critical thicknesses at which the switch between the vertical alignment and the anti-aligned positions occurs depend on the distance between the dots in a square array and on the ratio between the two different distances if the arrays are rectangular; (iii) the transitions occur within a few nanometer range of the capping layer thickness, and the elastic field undergoes large changes in its properties before and after the transition. This behavior has been revealed by a very accurate fit of the tangential stress field using appropriate fit functions. The fit and parameter functions allow to easily reproduce the stress field in different contexts and are useful in growth simulation models. The results suggest that by properly engineering the capping layer thicknesses in the layers of a stack, it is possible to obtain different three-dimensional quantum dot lattices starting from an initial fixed dot array. Our results are in agreement with the available experimental data.


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