Twinning mechanism at three-grain tri-junction during directional solidification of multi-crystalline silicon

Heterogeneous twinning during directional solidification of multi-crystalline silicon

“…The superscript 1w or 2w indicates the junction between G1 or G2 and the crucible wall. For silicon, is in the range of 0.45~0.5 J/m 2 at 1473 K as reported in the experiments by Otsuki [17]; here we again pick 0.4842 J/m 2 , which was a fitting parameter used previously [14]. Also, is the surface free energy of a {111} plane, and according to Hurle [16] the value is 0.257 J/m 2 .…”

“…2(b). Again, the nucleus is assumed to be a circular disc on the facet, as in Jain's model [14]. Therefore, the angles defined are based on the view angle normal to the facet, or the angles are normal to the facet.…”

“…The required volume and the surface area for the nucleus on the facet as shown in Fig. 2(c) can be calculated as explained in [14]. In Fig.…”

“…This model explained the nucleation and twinning mechanism at the solid-solid-liquid TJ (SSL-TJ) but was first applied to a 2D configuration. To further explain the more realistic situation of the three-grain tri-junctions (3GTJ) on the interface during ingot growth, Jain et al [14], further developed a three-dimensional model, referred as Jain's model. With the 3GTJ model, the twinning from certain grains during mc-Si growth experiments [15] was correctly predicted.…”

“…In this paper, we extend Jain's model [14] to the heterogeneous twinning. The cases involving the wall/grains, wall/gas/grain, and gas/grain junctions are modeled and discussed.…”