HIGH-TEMPERATURE INELASTIC DEFORMATION DURING SHAPED CRYSTAL-GROWTH FROM THE MELT

We consider three models of high temperature inelastic deformation of a crystal during shaped growth from the melt for Czochralski growth and for EFG growth of sheets and tubes. The models are: elastic-perfectly plastic behavior, steady-state power law creep, and the Haasen-Sumino model which allows for the multiplication of dislocations. For the elastic-plastic model, the critical dislocation density is estimated below which simplified measures (based on thermoelastic calculations) for the dislocation density are valid. Such simplified estimates are improved and they involve a nonlinear dependence of the dislocation density on the excess of the thermoelastic stress over the crystal's yield stress. For the case of creep, non-dimensional quantities are derived which govern the contribution of creep to the total strain rate. These numbers are to be compared to non-dimensional numbers governing the contribution of the thermal strain rate. Typical material and growth data for Si and GaAs identify the importance of the prevailing length and thermoelastic stress levels in inducing creep. The analysis shows a marked difference in the stress and dislocation density levels for EFG growth of sheets versus tubes. For the Haasen-Sumino model, non-dimensional numbers are also derived which govern the rate of dislocation generation and the influence of dislocation back-stress due to dislocation build-up. These numbers are to be compared to unity. For EFG growth of tubes and sheets, the critical initial dislocation density was calculated. Above such critical density, creep effects become predominant. © 1990.