Raman determination of layer stresses and strains for heterostructures and its application to the cubic SiC/Si system

Abstract

A set of formulas for Raman shifts of diamond and zinc‐blende semiconductors under a generalized axial stress are derived. The Raman shifts under hydrostatic pressure, uniaxial and biaxial stresses are only the special cases of the general formulas. Raman‐stress coefficients and mode parameters are introduced, by which the Raman shifts due to different kinds of applied stresses are related. By the analysis of known Raman data of cubic SiC (3C‐SiC) under hydrostatic pressures, one of the Raman‐stress coefficients is obtained and the existing elastic stiffness constants of 3C‐SiC are optimized. Unreliable data in the literature are pointed out and a choice of the best available data is made (C₁₁=5.4, C₁₂=1.8, and C₄₄=2.5×10¹² dyn/cm²). A series of chemical‐vapor‐deposited 3C‐SiC films on (100) Si with the film thicknesses between 4 and 17 μm are measured by Raman scattering. We propose a method for calculating the stress and strain in these SiC films. The stresses in 3C‐SiC on Si are in the range of 0.3–1.1 GPa and strains are on the order of 0.1%‐0.2%, which is a factor of 100 below the lattice mismatch between bulk 3C‐SiC and Si. Further discussion of the release of strain due to misfit dislocations and the effect of the buffer layer on the film stress is given. Our expressions and the method of the measurement of the stress and strain in heterostructures are quite general and may be used for other systems.