We theoretically investigate elastic, piezoelectric and optical properties of wurtzite GaN QDs, having hexagonal pyramid-shape which are stacked in the multilayers.  We solve the boundary-value problem using the nonlinear theory of anisotropic hyperelasticity based upon the general strain measure.  Calculated strain field is used to determine piezoelectric polarization. The spontaneous polarization is taken into acccount. The distribution of the electrostatic potential is obtained by solving the Poisson equation while the electronic states are obtained by using 8x8 kˇp hamiltonian of the wurtzite crystal.
We perform calculations in two steps. First, we calculate the stress and strain distribution, the piezoelectric fields and the electrostatic potential for the sequence of five GaN/AlN QDs placed one on another in the direction of growth. Second, for the centrally located QD, we calculated electronic states. This procedure allows us to examine the correlations of strain and piezoelectric fields between QDs in the multilayers.
Calculations have been performed for structures having different height of QDs and different thickness of the AlN spacers. We observe that the magnitude of the strain in the plane perpendicular to the direction of growth increases in the QDs and decreases in the spacers with increase of the thickness of the spacer. Additionally, electric field in the QD increases with the increasing the distance between the dots which results in the variation of the energy emission on the thickness of AlN spacer. We predict that the energy emission for 4nm height QDs and separated by 10nm-thick AlN layers exhibits a red-shift as large as 200 meV comparing to the energy emission for the same QDs grown with the 5nm-thick AlN spacers.
 N. Gogneau, F. Fossard, E. Monroy, S. Monnoye, H. Mank, B. Daudin, Appl. Phys. Lett., 84, 4224, (2004)
 P. Dłużewski, G. Maciejewski, G. Jurczak, S. Kret, J.Y. Laval, Comp. Mat. Sci., 29, 379, (2004)