Distribution of misfit dislocations and elastic mechanical stresses in metamorphic buffer InAlAs layers of various constructions

Here we report on computing of the distribution of the equilibrium misfit dislocation density $\rho(z)$ as well as the elastic strain $\varepsilon(z)$ along the grow direction for metamorphic buffer layer InAlAs/GaAs(001) with high In content ($x\le$ 0.87) and different design of composition profile: step-, linear- and convex-graded. For the computation, an approach based on the iterative finding the system total energy minimum have been used. It was shown, that the significant difference between different types of the buffer layer is observed for the $\rho(z)$ distribution rather than for $\varepsilon(z)$. In contrast to traditionally used step- and linear-graded metamorphic buffer layers, which are characterized by homogenous spreading of misfit dislocations, the main part of such dislocations in the convex-graded composition profile is concentrated at the bottom part of the buffer layer near to heterointerface InAlAs/GaAs, and the dislocation density drop by more than one order of magnitude along the layer thickness reaching near the surface the minimal value among the buffer types. Despite the fact, that the significant effect of interaction between misfit dislocations is not taken into account in the computation, the results obtained allowed one to determine the main features of the $\rho(z)$ and $\varepsilon(z)$ distributions in the different InAlAs metamorphic buffer layers, which were previously obtained experimentally. Thus, such an approach can be effectively utilized for the development of the metamorphic heterostructure based devices.