Compositional and structural characterization of SixGe1− x alloys and heterostructures by high-resolution transmission electron microscopy

Abstract

A method is described for the quantitative characterization of coherent interfaces of strained Si/Si x Ge 1− x alloy multilayers by high-resolution transmission electron microscopy (HRTEM) in [110] and [100] crystal projections. The method uses systematic variations of the image contrast patterns with the local composition x for certain ranges of objective lens defoci Δƒ and specimen thicknesses t. From a detailed analysis of linear and non-linear beam interference contributions to the image intensity of 5- and 9-beam images in [110] projection and of 5-beam images in [100] projection, ranges of Δƒ and t were identified by Bloch-wave and multi-slice image simulations at 400 keV for which a quasi-linear functional relationship between the composition x and the first-order Fourier coefficients of the image intensity exists. Under such optimized conditions, the lattice images show a systematic reversal of the image contrast when x varies from 0 to 1. This contrast behaviour is found to be only weakly dependent on tetragonal lattice distortions and on Fresnel contrast contributions near the interfaces. For quantitative composition determination, a novel three-step algorithm is described, especially designed for the application to strained heterostructures. By this algorithm, compositions x can be determined locally with an accuracy of Δx≤±0.1. Positions of sharp Si/ Si x Ge 1− x interfaces can be determined with monolayer accuracy. Applications of the method to interface characterization of short-period Si m Ge n strained-layer superlattices and to Si/ Si x Ge 1− x quantum wells are presented.