Constitutive modeling of the effects of oxygen on the deformation behavior of silicon

A systematic theory is presented that models the effects of interstitial oxygen on the deformation behavior of silicon. The theory is based on calculation of the dependence of the dislocation velocity on the applied stress in the crystal and determination of the locking and unlocking stresses for dislocation motion. Internal stresses in the oxygen-hardened crystals are modeled by the superposition of the unlocking stress, a back stress due to the interaction between mobile dislocations, and an internal stress that arises from the interaction between a dislocation and the oxygen cloud around other dislocations. The initiation of dislocation multiplication is modeled as a two-step thermally activated process; the first step is the unlocking of the dislocation and the second step is the formation of jogs along the dislocation line. The coupled model for oxygen transport and dislocation motion is used to simulate crystal deformation in dynamic experiments and to reproduce stress-strain curves. The predictions of the initial stage of deformation are in good agreement with the experimental data of Yonenaga et al. [J. Applied Phys. 56, 2346 (1984)].