Modeling the Effect of Operating Parameters on Oxygen Content in Czochralski Growth of Silicon

Abstract

A model has been developed for the calculation of the axial oxygen profile in Czochralski‐grown silicon crystals by extending the dynamic oxygen equilibrium model proposed by Carlberg, et al. (1). In this model the bulk of the melt is assumed to be well mixed and the transport of oxygen is described by mass transfer coefficients at the melt‐crystal, melt‐crucible, and melt‐gas interfaces. In the present work, boundary layer considerations are used to define the dependency of these transport coefficients on the operating parameters. The current model therefore provides a means of assessing the effect of operating variables on the crystal oxygen content. Parametric studies, varying one parameter at a time while keeping others constant, indicate that the oxygen content is strongly influenced by the crucible rotation rate and is relatively insensitive to crystal rotation. The crucible temperature has a strong effect on the oxygen content while the effect of wall heat flux is minor. The effect of uncertainties in the physical properties on the predicted oxygen content was also examined. The equilibrium segregation constant, oxygen diffusivity in the melt, and the thermocapillarity constant were found to be the most important properties affecting the model predictions of crystal oxygen content.