Effect of piezoelectricity on critical thickness for misfit dislocation formation at InGaN/GaN interface

Abstract

An analytical study has been carried out to investigate the effect of piezoelectricity and spontaneous polarization on the critical thickness for misfit dislocation formation at the interface of InGaN/GaN layers. Two representative critical thickness prediction formulations given by Matthews (1974) and Freund (1987) have been generalized to include piezoelectricity and spontaneous polarization. Critical thicknesses have been calculated by using the generalized methods and presented for both c-plane and a-plane deposition in hexagonal crystal lattice. Numerical results of the critical thickness for an InGaN epitaxial film on a GaN substrate has been presented and discussed in terms of the indium concentration in the epitaxial layer, the line charge associated with the dislocation core, the spontaneous polarization along c-axis, and the piezoelectric constants of the InxGa(1-x)N film. Here, x stands for indium concentration. The indium concentration determines the misfit strain due to lattice mismatch between the InGaN film and GaN substrate. It is shown that the piezoelectricity and spontaneous polarizations have negligible effect on the critical thickness for the case of InGaN/GaN. Parametric studies were carried out by increasing the piezoelectric properties of the InxGa(1-x)N ten folds. It has been found that the enhanced piezoelectricity reduces the critical thickness so that it becomes easier to form the misfit dislocation. We have investigated the reason for the decrease in the critical thickness due to piezoelectricity by investigating the state of stress and internal energy of the film. Our study shows that the enhanced piezoelectric properties give rise to stiffening of the film which increases its elastic energy. This makes it favorable to form misfit dislocations by increasing the available energy for dislocation formation. It is also shown that spontaneous polarization along c-axis in the InGaN film decreases the critical thickness for c-growth orientation while it increases the critical thickness along a-growth orientation. This occurs because the internal energy of the film increases due to spontaneous polarization for c-growth orientation while it decreases for a-growth orientation. However, the increase or decrease in the critical thickness due to spontaneous polarization is very marginal. A line charge associated with dangling bonds along the dislocation core increases the critical thickness because it increases the required energy to form the dislocation.