We start our analysis with a continuum three-dimensional axisymmetric model, accounting for complete selfconsistency of electromechanical fields. Although the techniques developed here, can be applied to other material heterostructures, all our examples in this paper are given for GaN/AlN nano-heterostructures. One of the reasons for that is an increasing range of current and potential applications of these nanostructures in optoelectronic devices. We consider in our examples a cylindrical GaN/AlN nano-heterostructure which allows us to reduce the original problem to a two-dimensional model. This reduction goes with a remark that albeit the wurtzite symmetry is not axisymmetric, Navier's equations do reflect axisymmetry [1].

We note also that recently the analysis of such nanostructures have been carried out in [2]. The analysis was selfconsistent in lattice mismatches, spontaneous polarization, piezoelectric effect, and strain and has been performed by employing a linear (static and dynamic) and nonlinear (static with electrostriction) electromechanical model framework developed there. However, it was restricted to the one-dimensional situation.

In spite of the belief that a combination of dimensional effects and electrostriction could lead to interesting new physics, the problem was lacking attention partly due to a sparse experimental information on electrostrictive tensor components in the nitrides. Here, due to the availability of experimental information on the electrostriction coefficient connecting the electric field along the z-direction with the strain component, our attention was drawn to only this component of electrostriction.

In order to deal with the inherent discontinuity of the physical parameters involved and the problem of lattice mismatch, the domain decomposition methodology has been employed for our numerical (nonlinear) analysis. Chebyshev pseudospectral methods have been used for discretization in each sub-domain. Our results demonstrate clear jumps in the electric field and strain distributions across the interface between the two materials, while the mechanical field and electric displacements exhibit a continuous pattern. The effect of electrostriction has been analyzed by comparison of the results with a linear model (without electrostriction). Finally, we demonstrate a significant difference in several key parameters of nanostructures, such as the electric field and strains, while analyzing them with our multidimensional model and previous one-dimensional models.

1

L. Lew Yan Voon, C. Galeriu, B. Lassen, M. Willatzen, R.V.N. Melnik, "Electronic structure of wurtzite quantum dots with cylindrical symmetry", Applied Physics Letters, 87 (4), 041906, 2005. doi:10.1063/1.2000329

2

M. Willatzen, B. Lassen, L. Lew Yan Voon, R.V.N. Melnik, "Dynamic coupling of piezoelectric effects, spontaneous polarization, and strain in lattice-mismatched semiconductor quantum-well heterostructures", Journal of Applied Physics, 100 (2), 024302, 2006. doi:10.1063/1.2214361

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