Simulation of crucible-free growth of monocrystalline silicon fibres for mirror suspension in gravitational-wave detectors

Abstract

Monocrystalline silicon fibres are a promising candidate to support the test mass needed in gravitational-wave detectors. Stringent requirements on material purity and fibre diameter underscore the imperative for crucible-free crystal growth methods, such as Pedestal and Floating Zone techniques. We developed a multiphysics numerical model that simulates the coupling between electromagnetism, heat transfer, fluid flow and phase boundaries for these techniques within the same mathematical framework, which facilitates direct comparisons of both growth techniques. Model validation was addressed using experimental measurements and other simulation tools, and satisfactory agreement was obtained. Our findings indicate that electromagnetic forces are the primary mechanism responsible for stirring the molten silicon at small crystal diameters. The resulting fluid velocity develops slightly transient behaviour, although this has little impact on the phase boundary shapes. The understanding of the growth process enabled by the model will facilitate future optimization of crystal quality and diameter stability.