Investigation of strain relaxation of Ge_1-xSi_x epilayers on Ge(001) by high-resolution X-ray reciprocal space mapping

The evolution of strain relaxation of molecular-beam-epitaxy-grown Ge _1-xSi_x layered structures deposited on Ge(001) substrates was investigated by employing high-resolution X-ray reciprocal-space mapping. In contrast to the commonly investigated SiGe alloy layers on Si(001) substrates, in this case, the Ge_1-xSi_x alloy layers experience a bi-axial tensile strain due to the larger lattice constant of the Ge substrate, rather than a bi-axial compressive strain. The structures consist of a linearly graded Ge_1-xSi_x alloy buffer (B1), followed by an alloy buffer layer (B2) with constant Si content. For the four samples investigated, the grading rates of B1 were varied in the range 13.2-32.5% Si mu m ^-1, and the thicknesses were varied in the range 0.4-1.8 mu m. From our measurements, it turns out that the lower part of the graded buffer B1 close to the Ge(001) substrate is completely strain-relaxed, whereas the top part of the graded buffer and the uniform alloy buffer (B2) are only partly strain-relaxed, showing a linear increase in the in-plane strain towards the surface. In addition, the measured maximum in-plane strains at the surface depend on the grading rate of B1 as well as on the thickness of B2. These strains turn out to be much larger than those predicted by existing equilibrium theories for strain relaxation in epitaxial layers.