Quantum structures made of components with at least one dimension being at nanoscale, show great potential for future optoelectronic device applications. The elastic fields in quantum structures affect their physical and mechanical properties, and also play a significant role in their fabrication. Therefore, it is crucial that the induced elastic fields in quantum structures be modeled accurately and efficiently.
In Chapter II, a rigorous analysis on the elastic and electric fields in 2-dimensional quantum wire (QWR) structures is presented using the novel Green's functions and related boundary element method (BEM). The elastic and electric fields in embedded QWR structures for both the inclusion and inhomogeneity models are investigated. The electric field distribution in polygonal QWRs with different sides is also studied and it is found that the electric field in triangle and square QWRs can be very different to those in polygonal QWRs with sides larger than 4.
In Chapter III, a bimaterial BEM is developed for the calculation of the strain energy density and the relative strain energy in free-standing/embedded QWR structures. The required bimaterial Green's functions are derived in terms of the Stroh formalism. The boundary of the QWR is discretized with constant elements for which the involved Green's function kernels can be exactly integrated. We found that the magnitude of the relative strain energy increases with increasing depth of the QWR with respect to the surface of the substrate. Strain energy density inside the QWR is also plotted to show its close relation to the QWR shape.
In Chapter IV, an analytical method for calculating the 3-dimensional quantum dot (QD) induced elastic field in the half-space substrate is presented. The QD is assumed to be of any polyhedral shape, and its surface is approximated efficiently in terms of a number of flat triangles so that the Green's function kernels can be integrated analytically over the flat triangles. Numerical examples are presented for cubic, pyramidal, truncated pyramidal and point QDs in half-space substrate. The strain energy distribution on the surface of the substrate indicates clearly the strong influence of the QD shape and position on the induced strain energy. This long-range strain energy on the surface is the main source for controlling and modulating the overgrown QD pattern and size.
At last, a detailed theoretical calculation of the elastic and electric fields in and around nitride-based QDs which are buried in anisotropic half-space substrate is developed. Results are presented for a single dot as well as coupled dots. We consider in detail the case of AlN QDs in the shape of hexagonal truncated-pyramids. The calculated strain and piezoelectric potential distributions induced by a single QD are presented. Large piezoelectric potential can be observed in the structures. The results are compared to those of simplified model in which the QD is assumed to be a point. Very similar trends are observed. Strain and piezoelectric potential distributions induced by coupled QDs are also shown along line scans or on the surface.