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Formulation of mobile dislocation density in oxygen-precipitated silicon by crystal plasticity model

The relationship between mobile dislocation density and oxygen precipitation characteristics in Czochralski-grown silicon wafers has been investigated using the crystal plasticity model based on an extended Haasen–Alexander–Sumino model in combination with the experimental method. A formula of initial mobile dislocation density for oxygen-precipitated wafers has been deduced from the relationship obtained through the correlation of three-point bending test results and the simulation of a finite element model using the plasticity model. The formula obtained in this work indicates that the size of oxide precipitates has a dominant effect on the strength of precipitated wafers. It is also found from the formulation that the size of oxide precipitates responsible for dislocation slip is larger than about 200 nm, which is consistent with other studies. Analysis of the results also suggests a relationship between upper yield stress and the initial dislocation density which can be used as a tool to predict the yield stress of oxygen-precipitated silicon wafers.