A New Stain Analysis Model in Epitaxial Multilayer Systems

Abstract

A new strain analysis model, the so-called stress matched model, in an epitaxial multilayer system is proposed. The model makes it possible to know the strain, the stress, and the elastic strain energy in each epitaxial layer. Analytical formulas for the strain parameters in each epitaxial layer are derived under the assumptions that the substrate thickness is finite and the in-plane lattice constant is the same for all epitaxial layers for dislocation free growth. As an example, the model was applied to a 405 nm InGaN/GaN multiple-quantum-well (MQW) laser diode grown on a sapphire substrate in order to find the optimal material composition and thickness of epitaxially lateral grown Al(x)Ga(1-x)N template in view of the minimum average in-plane stress. The analysis result shows that an Al(x)Ga(1-x)N layer with an Al mole fraction of 0.06 and a thickness of 6 mu m is a good template for a laser. In fact, this layer structure coincides with the one that is experimentally optimized.