Constitutive modeling of the effects of oxygen on the deformation behavior of silicon
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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)].
I. INTRODUCTION The presence of impurities is known to play crucial roles in establishing the properties of most semiconductor materials. Electrically active impurities significantly affect the electrical characteristics of the intrinsic semiconductor and these effects have been extensively studied.1'2 The mechanical properties of semiconductor crystals are affected by both electrically active and inactive impurities, because of the interactions between impurities and dislocations3"5 which result in acceleration, retardation, and even immobilization of dislocations. These changes in dislocation dynamics significantly affect the plastic deformation of the material caused by an applied stress.6 In silicon, the most important substrate material for electronic devices, impurities generally interrupt the motion of dislocations that move at low velocities under low applied stresses and thus improve the mechanical strength of the material.6 The role of the interaction between an impurity and a dislocation has become extremely important in a variety of semiconductor materials processes. For example, impurities are added to the melt in the bulk melt growth of III-V compound semiconductors, e.g., GaAs and InP, to lower the dislocation density or even to produce dislocation-free materials.7'8 In the processing of initially dislocation-free silicon wafers, a low oxygen content results in warpage of wafers under thermal cycling.6 In spite of the tremendous technological importance of the effects of impurities on the mechanical properties of crystalline semiconductors, theoretical understanding J. Mater. Res., Vol. 6, No. 11, Nov 1991
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of such effects is still limited. The development of constitutive theories that describe the effects of impurities on defect dynamics and on continuum mechanical properties of the material is a diffic
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