This is a multidisciplinary thesis research in semiconductor quantum dot (QD) field and includes two parts. On one hand, the strain-induced local electronic band edges in single QD are studied using a kp description of the electronic eigenstates coupled with the induced lattice strain as calculated using the continuum mechanics (CM) description. In the CM method, the misfit-lattice induced strain can be reduced to an analytical expression that is straightforward to evaluate numerically. Different from most previous analyses for QDs in infinite spaces, QDs are assumed to have different shapes and lattice orientations located in half-space substrates which more realistically describe experimental situations in most instances. The band edges within the cubic and pyramidal InAs QDs embedded in GaAs substrates are predicted with the six-band kp basis approach. Comparison between the strain-induced local band edge based on the approximate method and exact method shows that the approximate method could result in substantial error near the interface region of the QD. The strain-induced band edges along the bottom center line of the QD can differ by a factor of two between the two approaches. Furthermore, the effect of the free surface on the strain-induced band edges is studied by varying the depth of the buried QD. When the QD is moved away from the surface, the band edges converge in a consistent way to the infinite space solution. Comparison with available experimental results validates our exact model within the half-space substrate and shows the importance of treating the surface in a theoretically rigorous way. On the other hand, once we have achieved our study for a particular QD, the next logical and natural step is to fabricate consistent QDs with uniform size and distribution. The multilayer structure (superlattice) which is governed mainly by the distribution of the long-range elastic strain energy, is an effective route for improving the uniformity of QDs. Based on the rigorous strain energy calculation, a scaling behavior on the dimensionless lateral (horizontal) spacer versus vertical spacer (xdist/b versus hdist/h) for multilayer quantum dots (QDs) distribution is proposed and four typical correlation regimes-aligned correlation, transition zone, antialigned correlation and non-correlation, are predicted via varying the dimensionless parameters. It is shown that the prediction matches well with available experimental data for semiconductors with low elastic anisotropy (A< 2), and holds a shift in hdist/h for those with high elastic anisotropy (A≥ 2). The calculation also shows that a decreasing rate on strain energy density contributes to the enlargement of nucleation domain in vertical aligned correlated multilayer QD array.