Wafer made from single crystal Gallium Arsenide (GaAs) are used as substrate materials in micro- and opto- electronic devices. During the various processes of manufacturing, the wafer are subjected to mechanical loads which may lead to fracture. The characterization of the fracture toughness of the wafer needs bending tests and a theoretical calculation of various stress distributions within the wafer. In this study we show that the nonlinear von K'arm'an theory may serve as an appropriate tool to calculate the stress distributions as functions of the external load, while the Kirchhoff theory has turned out to be completely inappropriate. Our main focus is devoted to (i) calculation of the contact area between the load sphere and the wafer, (ii) study of the influence of the anisotropic character of the material, (iii) study of the important geometric nonlinearity. Finally we compare the calculated and theoretical load-flexure relations in order to demonstrate the high accuracy of the von K'arm'an theory and its Finite Element implementation.

Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol. 897