The heteroepitaxial growth in self-assembled quantum dot multilayers is investigated using kinetic Monte Carlo simulations and a quantitative comparison with experiment is included. We study the self-organization effect in the PbSe/PbEuTe͑111͒ semiconductor system. For this purpose we developed an efficient kinetic Monte Carlo model enabling us to simulate multilayers consisting of tens of periods with hundreds of threedimensional islands. We corroborate that the lateral and vertical-dot correlations are caused mainly by the strain field induced by buried dots. A progressive self-ordering from period to period in a growing multilayer is clearly illustrated. We also reproduced all three experimentally observed dot arrangements in the PbSe/ PbEuTe͑111͒ superlattices inclusive of two abrupt transitions between them. Moreover, we achieved a good quantitative agreement with the experimentally measured dependence of lateral-dot distance on spacer-layer thickness. The advantages and shortcomings of our model are analyzed in detail.

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