Mechanical stresses in (sub)monolayer epitaxial films

Abstract

We have studied stresses in thin Ge films growing on Si(001), in situ and in real time, with submonolayer sensitivity. As a result of the 4.3% lattice mismatch, Ge films develop a compressive stress in the 2D growth regime, which saturates when 3D growth sets in. These measurements give new insight in the interatomic forces that play a dominant role in establishing the growth mode and the generation of defects, and provide a new test for state-of-the-art total-energy calculations. PACS numbers: 62.20.Hg, 68.55.Gi The growth mode of a thin epitaxial film is controlled by two factors. A necessary condition for wetting of the substrate by the overlayer is that the surface free energy of the overlayer is lower than that of the substrate. In this case the overlayer will initially form a continuous film. In order to sustain this simple growth mode it is imperative that the lattice mismatch between substrate and overlayer is sufficiently small to prevent the buildup of significant stress in the overlayer. If the stress becomes too large, the overlayer may form islands and/or defects may be generated at the interface or throughout the epitaxial film.The relation between surface stress and surface structure has been studied experimentally by several authors, by varying the alloy composition of pseudomorphic epitaxial Ge/Si films on Si (111) (Refs. 1 and 2) or by applying an external stress to the sample, but direct measurements of surface stress have not been reported previously, to our knowledge. Theoretical calculations of surface stress for a number of adsorbate-induced 1 & 1 and J3 x J3 structures of the Si(111) surface were recently performed by Meade and Vanderbilt, but, again, no experimental observations of such surface stresses have been reported.Here we present a simple optical technique to determine stresses at surfaces and interfaces. This technique measures the bending of the substrate induced by the presence of surface stress and is sufficiently sensitive to detect stresses due to the adsorption of submonolayer quantities of adsorbates, in UHV and in real time. We believe that the technique, surface-stress-induced optical deflection (SSIOD), is a powerful tool to improve our understanding of the forces at work at surfaces and interfaces. Related techniques have been used to study stresses in thick films, but to our knowledge this is the first time that such techniques are used in UHV and in the (sub) monolayer regime.Briefly, if the stresses a~and a2 present in the front and back surfaces of the sample are not equal, the sample will bend in order to minimize the stored strain energy. The resulting radius of curvature R derived after Stoney is given by Et 6(1 -v) (cri -cr2) where t is the sample thickness, E is Young's modulus, and v is the Poisson ratio. ' The angular deflection of the sample, r, between two points separated by a distance d is given by r d/R. By measuring this deflection, the diA'erence cr~-a2 is obtained from Eq.(1).A schematic view of the setup is shown in Fig. 1. A thin sample is p...

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