Analysis of the Engulfment of a Foreign Particle By a Solidification Interface: A New Scaling for Flow and Interfacial Forces Involving SiC Particles during Silicon Crystal Growth

The engulfment of foreign particles during solidification has been studied for over 50 years, yet classical theories been unable to adequately describe the behavior of silicon carbide (SiC) particles during silicon crystal growth. The engulfment of these particles during the growth of multicrystaline silicon (mc-Si) remains a vexing problem for the production of high-quality, low-cost photovoltaic devices. In particular, carbon contamination of the melt, from the original silicon feed and via gas phase reaction and transport from hot furnace internals, leads to the formation of silicon carbide particles of 1-100 microns in diameter that may be engulfed during crystal growth. These particles are problematic for subsequent processing of solar cells, leading to issues of lower cell efficiency via the formation of dislocations and shunts, wafer breakage, sawing defects, and even saw wire breakage.

The engulfment of a micron-sized particle during solidification is determined by a balance of repulsive van der Waals forces between the particle surface and the solidification interface and drag forces arising from the flow around the particle and into a thin liquid gap between particle and interface, typically on the order of 10 nanometers in thickness. When drag forces overcome repulsive forces, the particle is engulfed, otherwise it is steadily pushed ahead of the advancing interface. Since drag increases with particle size and velocity, there exists a critical velocity at which a particle of a certain size is engulfed. However, drag forces are strongly dependent upon the shape of the solid-liquid interface as the particle approaches. Thus, the critical velocity is affected by significant and nonlinear interactions involving heat transfer, premelting, and Gibbs-Thomson phenomena.

In this presentation, we discuss a significant and previously unascertained interaction between particle-induced interface deflection (originating from the thermal conductivity of the SiC particle being larger than that of the surrounding silicon liquid) and curvature-induced changes in melting temperature arising from the Gibbs-Thomson effect. For a particular range of particle sizes, the Gibbs-Thomson effect flattens the deflected solidification interface, thereby reducing drag on the particle and increasing its critical velocity for engulfment. We show via numerical calculations and analytical reasoning that these effects give rise to a new scaling of the critical velocity to particle size as v_c ∼ R^−5/3, whereas all prior models have predicted either v_c ∼ R⁻¹ or v_c ∼ R^−4/3. This new scaling is needed to quantitatively describe the experimental observations for this system.

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This research was supported in part by NASA NNX10AR70G; no official endorsement should be inferred.