Measuring Strain field of Multi-Component Material Systems Using X-Ray Bragg- Surface Diffraction

We investigated the strain field of the $\beta $-FeSi$_{2}$ semiconductor on a Si(001) substrate, where FeSi in a grain form coexists with $\beta$-FeSi$_{2}$ during the growth of $\beta $-FeSi$_{2}$. The lattice-parameter variations of silicon, $\beta $-FeSi$_{2}$, FeSi and the grain boundary were detected using x-ray Bragg-Surface Diffraction (BSD). With the penetration depth calculated by the dynamical theory of x-ray diffraction, the strain field versus depth of Si-substrate near the interface is determined with the resolution of 0.002 {\AA}. The largest strain detected is about 0.4{\%} up to 8$\sim$12 {\AA} below the interfaces.