The equilibrium strain and misfit dislocation density profiles were calculated for hetero-epitaxial 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 y1 and another near the free surface of thickness h−yd, where h was the layer thickness. The intermediate region contained an exponentially tapered density of misfit dislocations. Approximate analytical models were proposed, for the strain and dislocation density profiles in exponentially graded Si1−xGex/Si (001), which could be used to calculate the effective stress and rate of lattice relaxation. The results of the work could be 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.

Equilibrium Strain and Dislocation Density in Exponentially Graded Si1-xGex/Si (001). B.Bertoli, D.Sidoti, S.Xhurxhi, T.Kujofsa, S.Cheruku, J.P.Correa, P.B.Rago, E.N.Suarez, F.C.Jain, J.E.Ayers: Journal of Applied Physics, 2010, 108[11], 113525