A predictive model for plastic relaxation in (0001)-oriented wurtzite thin films and heterostructures

In this work, we present an experimental and theoretical study of the process of plastic strain relaxation of (0001)-oriented wurtzite heterostructures. By means of transmission electron microscopy and atomic force microscopy, we show that plastic relaxation of tensile strained Al_xGa_1-xN/GaN heterostructures proceeds predominantly by nucleation of a-type misfit dislocations in the $13⟨112¯0⟩|0001$ slip-system driven by a three-dimensional surface morphology, either due to island growth or due to cracking of the layer. Based on our experimental results, we derive a quantitative model for the dislocation nucleation process. With the shear stress gradients at the nucleation sites of a-type misfit dislocations obtained by the finite element method, we calculate the critical thickness for plastic relaxation of strained wurtzite films and heterostructures as dependent on the surface morphology. The crucial role of the growth mode of the film on the strain relaxation process and the resulting consequences is discussed in the paper.