Strain relaxation at the 3C-SiC/Si interface: Raman scattering experiments

Using micro-Raman spectroscopy we have investigated both the residual strain and strain relaxation effect in the heteroepitaxial 3C-SiC/Si system. To get quantitative results, we have developed a theory of inhomogeneous shift and broadening for optical phonons, which takes into account the phonon interaction with the static strain fluctuations. We solved Dyson's equation for the averaged phonon Green's function and studied the solution for a small momentum transfer near the top of the phonon branches. The Raman scattering cross section is then calculated, including both disorder and the spatial dependence of the average strain with distance from the interface. It is shown that two regimes of short- and long-range disorder, with different line shapes, can be observed. In the case of the short-range disorder, a phonon can change its momentum (in the scattering process due to strain fluctuations) in a range which is larger than the value determined by the phonon width. The opposite case corresponds to the long-range disorder. We have also considered the case of an anisotropic (two-dimensional-like) disorder which can be viewed as a set of columns perpendicular to the heterointerface. The results of our investigations show that all three regimes should have macroscopic scales. Comparing in great detail the experimental results with the theory, we have obtained a very good agreement in both cases of the singlet (LO) and doublet (TO) modes, including the cases where the lattice mismatch-induced splitting is observed. Finally we have found, from the change in coupling constant plotted versus distance from the interface, that the mean-squared strain relaxes in the bulk of our epitaxial samples according to an approximate z^-1 dependence.