Interaction of SiC particles with moving solid–liquid interface during directional solidification of silicon J. Friedrich a,n , C. Reimann a , T. Jauss b , A. Cröll b , T. Sorgenfrei b a Fraunhofer IISB, Erlangen, Germany b Crystallography – University of Freiburg, Freiburg, Germany article info Article history: Received 1 April 2016 Received in revised form 29 April 2016 Accepted 30 April 2016 Available online 2 May 2016 Keywords: A1: Directional solidification A2: Microgravity conditions B2: Semiconducting silicon Particle dynamics Liquid–solid interface structure abstract In this work, the interaction of SiC particles, having sizes of 7 mm to 300 mm, with the moving solid–liquid interface during directional solidification of silicon was experimentally and theoretically investigated. This included both convective and nearly diffusive conditions. In the nearly diffusive regime under mi- crogravity, the particles were incorporated at a lower growth velocity than in the convective regime under 1g conditions. The experimental data were compared to simple theoretical models allowing the calculation of the critical growth velocity for the incorporation of spherical particles in dependence of the particle size. It was found that the theoretical results could qualitatively explain the experimental ob- servations when a proper set of equations for the forces acting on the particle and of the material constants are chosen. It can be concluded that sedimentation of the particles due to gravity seems to play a role only for large particles. On the other hand, melt flow might cause a lift force which would push the particles away from the solid–liquid interface, and thus would result in higher critical growth velocities under convective conditions, e.g. due to buoyancy convection. Therefore, a contribution of the missing lift force under mg conditions could lead to the smaller critical growth velocity for particle incorporation that is observed under microgravity. & 2016 Elsevier B.V. All rights reserved. 1. Introduction It is well known that during directional solidification of mul- ticrystalline (mc) silicon SiC and Si 3 N 4 particles can be in- corporated into the growing silicon ingot [1–5]. These particles are formed when the solubility limit of C or N in liquid silicon is ex- ceeded [3]. These particles are transported through the melt and will interact with the moving solid–liquid interface where they may be incorporated into the silicon crystal. When such particles are present in the silicon ingot, they can lead to the small grained “grit” structure and the formation of dislocations [6], they can cause problems during the wire sawing process [7], and can act as shunts reducing the performance of the solar cells [8]. Therefore, the incorporation of these deleterious particles has to be avoided. It is known that the occurrence of such foreign phases in the solid silicon can be correlated to melt convection [3]. However, the interaction of particles with the moving crystallization front and their incorporation into solid silicon are not fully understood to- day. According to classical theories [9–20] a critical growth velo- city V c should exist which depends on the density, size, and morphology of the particle. Below V c a particle will be pushed in front of the growth interface, whereas above V c the particle will be captured and frozen into the growing crystal. This phenomenon of particle pushing and engulfment depends on the balance of dif- ferent forces acting on the particle in the vicinity of the interface, such as the interface, drag, lift, Magnus, or gravity force [18]. It has been theoretically shown that only mm-sized SiC parti- cles should be captured for typical growth velocities used in crystallization of mc silicon when only drag and interface forces are considered [21]. However, this result is in full contradiction to experimental observations that the particles detected in mc-sili- con are mm-sized [2–6]. Preliminary investigations, where SiC- particles were added to the silicon melt have shown that gravity and melt convection are most likely determining the particle transport under terrestrial conditions [4]. Depending on the size and density of the particles and on the convection intensity in the melt, they can either sink to the bottom of the melt or float on the melt surface. Since gravity affects melt flow, solute distribution, and sedimentation of the particles, microgravity offers an oppor- tunity to study particle transport and incorporation under nearly diffusive conditions. Therefore, the aim of this work was to get a better under- standing of the particle interaction with the moving solid–liquid interface during directional solidification of silicon under Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jcrysgro Journal of Crystal Growth http://dx.doi.org/10.1016/j.jcrysgro.2016.04.061 0022-0248/& 2016 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: jochen.friedrich@iisb.fraunhofer.de (J. Friedrich). Journal of Crystal Growth 447 (2016) 18–26