Thermal stresses in elastic multilayer systems

Thermal stresses in elastic multilayer systems have been previously modelled. However, because the displacement compatibility condition at interfaces between layers must be satisfied, the complexity in obtaining a closed-form solution increases with the number of layers in the system. As a result, existing analyses often adopt simplifications (e.g. assuming a constant elastic modulus throughout the system) to obtain closed-form solutions or are solved numerically by computer. The present study develops an analytical model, in which the complexity in obtaining a closed-form solution is independent of the number of layers and an exact closed-form solution can be concisely formulated. Specific results are calculated for elastic thermal stresses in (AlGa)As laser diodes, which consist of five layers. Also, the zero-order and the first-order approximations are formulated based on the exact closed-form solution, and their accuracy is examined. The acceptability of assuming a constant elastic modulus in the system in existing analyses is also discussed.