Equilibrium Lattice Relaxation and Misfit Dislocations in Continuously- and Step-Graded In_xGa_1-xAs/GaAs (001) and GaAs_1-yP_y/GaAs (001) Metamorphic Buffer Layers

The inclusion of metamorphic buffer layers (MBL) in the design of lattice-mismatched semiconductor heterostructures is important in enhancing reliability and performance of optical and electronic devices. These metamorphic buffer layers usually employ linear grading of composition, and materials including In_xGa_1-xAs and GaAs_1-yP_y have been used. Non-uniform and continuously graded profiles are beneficial for the design of partially-relaxed buffer layers because they reduce the threading dislocation density by allowing the distribution of the misfit dislocations throughout the metamorphic buffer layer, rather than concentrating them at the interface where substrate defects and tangling can pin dislocations or otherwise reduce their mobility as in the case of uniform compositional growth. In this work we considered heterostructures involving a linearly-graded (type A) or step-graded (type B) buffer layer grown on a GaAs (001) substrate. For each structure type we present minimum energy calculations and compare the cases of cation (Group III) and anion (Group V) grading. In addition, we studied the (i) average and surface in-plane strain and (ii) average misfit dislocation density for heterostructures with various thickness and compositional profile. Moreover, we show that differences in the elastic stiffness constants give rise to significantly different behavior in these two commonly-used buffer layer systems.