Calculation of strain and piezoelectric effects in nanostructures.

This is a theoretical and computational study of strain and internal (spontaneous and piezoelectric) electrostatic fields in quantum wells and dots. The uncertainties in the values of elastic stiffness and piezoelectric properties of GaN and InN are discussed and the preferable route for estimating the piezoelectric tensor elements of an alloy is described. Fully electromechanically-coupled expressions for strain and internal field in single or multiple quantum wells are presented, and it is demonstrated that electromechanical coupling is a small effect in InGaN/GaN quantum wells. In simulations of various InGaN/GaN quantum well devices in the literature, the PZ tensor values of Shimada et al provide the best fit to experiment. A smooth In gradient in the growth direction of an InGaN/GaN quantum well is shown to have no appreciable effect on the emission energy. The usefulness of three recent numerical Green's function methods for calculating strain and internal field in Ill-nitride quantum dots is assessed, including that of Pan and Tonon; spontaneous polarisation is found to be more important than electromechanical coupling in these systems, so the Pan method is of limited use. Finally, to try to explain the fast rate of diffusion of C in Si, the method of Faux and Pearson is used to estimate the strain interaction energy between point defects in Si. Such energy is seen to be negligible compared to thermal energy. The energies conform with those from an atomistic simulation, and the sign of the energy depends on the orientation of the pair of defects