Strain-Balanced Criteria for Multiple Quantum Well Structures and Its Signature in X-ray Rocking Curves

This paper examines the concept of strain balance in alternate tensile and compressively strained layers using classical elasticity theory and clarifies a number of issues associated with the definition of strain and misfit. The strain-balance criteria are derived from a zero average in-plane stress condition and compared against two commonly used thickness weighted models, based on strain and lattice parameter respectively. The zero-stress condition fully accounts for differences in the elastic properties of the layers, and establishes the true definition for a strain-balanced structure, within the confines of linear elastic theory. The validity of the thickness weighted models is discussed in the context of epitaxial growth tolerance, showing that for some device designs, the choice of strain-balance model is important for successful growth. The differences in the strain-balance models have consequences for characterization. For example, a comparison between simulated X-ray rocking curves from structures based on the zero-stress and thickness weighted lattice parameter shows that the coincidence of the zero-order satellite with the substrate Bragg peak does not correspond to the zero-stress situation, but approximates to the average lattice parameter method. The correct identification of a precisely strain-balanced structure requires agreement between experimentally measured and simulated X-ray rocking curves.