Convergent beam electron diffraction extinction distance measurements for quantitative analysis of Si 1− xGe x

Abstract

A new method to determine the concentration of germanium in Si 1− x Ge x single crystals is presented. It is based on extinction distance measurements by means of convergent beam electron diffraction (CBED). The two-beam condition CBED intensity oscillation (the so-called rocking curve) is measured for the 004 diffracted beam and compared with a numerical simulation. Using the two-beam dynamical diffraction approximation theory, this approach yields very precise values for both specimen thickness and effective extinction distance (Ultramicroscopy 87 (2001) 5). First a theoretical extinction distance ξ g ( x) for strain relaxed Si 1− x Ge x is calculated assuming a solid solution and using tabulated atomic scattering factors of silicon and germanium atoms. It is found that for single crystals ξ g ( x) decreases from 156 nm in pure silicon to 90 nm in pure germanium. Measurements on calibrated strain relaxed SiGe layers with variable germanium concentrations show an excellent agreement between experimental and calculated extinction distances ξ g ( x). As a consequence the experimental extinction distance ξ g ( x) becomes an indirect measure of the germanium concentration with a 1–2 at% sensitivity. The method turns out to be insensitive to strain as experimental ξ g ( x) values obtained on strained SiGe layers fit the theoretical extinction distance curve calculated for strain relaxed SiGe.