The stress and strain induced by a lattice mismatch between an epilayer and its substrate are known to control most of physical properties valuable for (opto)-electronic components. In good conditions of epitaxy and when no extended defects are seen, thin layers are considered as perfect, i.e. homogeneous and monocrystalline. This result is based on crystalline perfection of the structure: i) a sharp interface corresponding to a change of the chemical composition on one atomic plane; ii) an ideal film where all the deposited atoms take a strained position according to the elasticity theory. Within these conditions, the classical model is well established with applied strain fields directly defined by the continuity of the atomic planes through the interface. From this approach, below the critical thickness, 10 nm for 1% lattice mismatch, an epilayer is considered as perfectly strained. This representation need to be verified experimentally. Classical methods of the strain field analysis are performed by diffraction techniques and the stress field is deduced from the strain using the standard elasticity theory. The Transmission Electron Microscope (TEM) is a tool well adapted for this evaluation.
In this presentation the epitaxial strain field has been determined on X-HREM micrographs using numerical moire technique and on plan view sample using the conventional moire method. Good results are obtained for relaxed systems with misfit dislocations.
A new method of analysis of stress in epitaxial structures is described. It has been developed for determining the stress induced by a lattice mismatch in specimens such as Ga0.8In0.2As/(001)GaAs (about 1% lattice mismatch with a critical thickness of about 10 nm). Specimens prepared for plan view TEM observations appear to be bent with a radius of several tens of ľm for a substrate thickness ts of about 0.1 to 0.3 μm, an epilayer thickness tl of 10 nm. In these conditions the ratio tl/ts, which varies between 0.04 to 0.1, agrees well for determining the stress from the experimental measurement of the radius of curvature R and the Stoney formula corrected for high value of tl/ts. The measured misfit stress is 1 GPa, about 30% lower than the theoretical stress for the pseudomorphic structure.
The conventional representation of pseudomorphic systems based on Vegard law and the homogeneity of the materials will be discussed. In the case of ternary compounds, many physical and chemical phenomena (segregation, heterogeneous nucleation, ...) are activated during the first stages of epitaxial growth. They create a transition zone where both the crystalline structure and the chemical composition are heterogeneous. This heterogeneity is a direct manifestation of relaxation of the misfit stress and constitutes a failure as far as the concept of the critical thickness based on the crystalline perfection of the substrate, the epitaxial layer and their interface is concerned.