Equilibrium strain and dislocation density in exponentially graded Si1-xGex/Si (001)

We have calculated the equilibrium strain and misfit dislocation density profiles for heteroepitaxial Si1-xGex/Si (001) with convex exponential grading of composition. A graded layer of this type exhibits two regions free from misfit dislocations, one near the interface of thickness y(1) and another near the free surface of thickness h-y(d), where h is the layer thickness. The intermediate region contains an exponentially tapered density of misfit dislocations. We report approximate analytical models for the strain and dislocation density profile in exponentially graded Si1-xGex/Si (001) which may be used to calculate the effective stress and rate of lattice relaxation. The results of this work are readily extended to other semiconductor material systems and may be applied to the design of exponentially graded buffer layers for metamorphic device structures including transistors and light emitting diodes. (c) 2010 American Institute of Physics. [doi: 10.1063/1.3514565]