Modelling the upper yield point and the brittle–ductile transition of silicon wafers in three-point bend tests

Three-point bend tests carried out by Folk [R.H. Folk, The brittle to ductile transition in silicon: evidence of a criticaly yield event. PhD thesis, University of Pennsylvania (2000).] on initially dislocation-free specimens of semiconductor-grade single crystals of Si showed that, for a given strain rate, above a critical temperature, T c, and at a certain stress, a large load drop occurs upon yielding and the sample deforms plastically. Below T c specimens fail by brittle fracture after a small load drop, or at even lower temperatures without apparent prior plastic flow. This paper describes a simple dislocation model and computer simulation to explain the occurrence of a yield drop, the strain-rate dependence of T c and Folk's etch pit observations of the plastic zone. Good agreement is obtained between the temperature dependence of the upper yield stress and the strain-rate dependence of T c with the predictions of the model. These parameters are controlled by dislocation velocity.