Modeling the time-dependent growth of single-crystal fibers

Abstract

A model is developed to simulate time-dependent behavior in laser-heated miniature pedestal growth (LHPG) of single-crystal fibers. This process is meniscus controlled since the diameter of the growing fiber changes in response to variations between the equilibrium and the instantaneous contact angle at the melt/solidifying-solid interface. One of the operational problems associated with the LHPG technique is controlling diameter fluctuations in the growing fiber due to process perturbations. Smooth source feed and fiber pull rates, steady laser-heat input, and suppression of mechanical vibrations are necessary to achieve a constant fiber diameter. We derive a system of time-dependent, one-dimensional equations of motion and heat transfer as the leading order equations in an asymptotic expansion based upon the melt slenderness ratio (fiber radius/melt height). This system is solved numerically to predict the thermal profiles, mean positions of the melting and solidifying fronts, melt/gas interface, melt volume, and fiber diameter. System response to perturbations in the pull rates, thermal environment, and gravitational field is investigated.