Twin-mediated Crystal Growth: an Enigma Resolved

Polycrystalline materials play a central role in everyday life, ranging from medical devices to airplane wings. The physical properties of the polycrystalline solid depend on the three-dimensional network of internal interfaces, i.e., the grain boundaries. In particular, polycrystalline Si (poly-Si) is widely used as the substrate of thin-film photovoltaic (PV) cells. To be commercially relevant, the efficiency of the poly-Si thin-film cells should reach 12% offered by other thin-film PV technologies1. However, the highest recorded efficiencies of the poly-Si thin-film cells are approx. 8–10%2,3, due to the high defect densities in the poly-Si thin films. Recombination at dislocations and grain boundaries adversely impact the performance of these devices1. For instance, the minority carrier lifetime depends on the character of the grain boundaries: coherent Σ3 (twin) boundaries are electrically inactive, while higher-order boundaries may be electrically active4,5. To clarify the nomenclature, in coincident site lattice (CSL) theory, Σm describes the “degree of fit” between two adjacent grains; the positive integer m is the reciprocal of the ratio of the coinciding sites to the total number of sites6. Thus, a fundamental understanding of the structure of polycrystalline materials during growth will provide the strategic link between solidification microstructure and underlying materials behavior. When group IV semiconductor crystals such as Si and Ge (point group m3m) precipitate from the melt, they form faceted crystals with {111} habit planes. {111} is the densely packed cleavage plane in the diamond cubic structure; it is now well established that {111} is both the low mobility7,8 and low energy9,10 orientation in such materials. The growth of faceted crystals requires large supersaturations in the melt unless there is some defect along the solid-liquid interface that facilitates the formation of new atomic layers, without the necessity of two-dimensional (2-D) nucleation on the {111} habit planes. Frank11,12 was the first to suggest that the steady-state growth of imperfect crystals is possible if there is a self-perpetuating step on the growth surfaces. These self-perpetuating steps result from two sources: (i) screw dislocations, which promote continuous spiral growth of atomic layers11, and (ii) twinned interfaces, which reduce the nucleation barrier by the line energy at the re-entrant groove13. Therefore, defective crystals can nucleate and grow rapidly with very little undercooling below the liquidus, compared to single crystals. The growth model of a twinned diamond cubic crystal was first proposed independently by Wagner, and by Hamilton and Seidensticker in 196014,15. We here review this twin-mediated growth mechanism, hereafter referred to as the WHS model. The central assumption of WHS theory is that nucleation of new layers takes place at the concave 141.06° re-entrant grooves that are caused by the intersection of the {111} Σ3 twin planes with the surface. According to simple bonding arguments, an atom adsorbed on the groove has four nearest neighbors, compared to three on a flat {111} plane16,17, and thus the groove may act as a preferential site for solute adsorption. A singly-twinned crystal contains three such re-entrant grooves along the 〈211〉 directions. Since nucleation readily occurs at the re-entrant grooves compared to the {111} surfaces, the crystal grows rapidly at the re-entrant grooves and a trigonal solid with 60° corners is obtained. Rapid growth is terminated at the time owing to the disappearance of the re-entrant groove, hence why a multiply twinned interface is needed for steady-state crystal growth. In other words, the solid is bounded by convex 218.94° ridge structures; since an adatom has only three nearest neighbors on either side of the ridge16, the ridges are not capable of continuous propagation. For a crystal with two parallel twin planes, as shown in Supplementary Fig. 1, rapid growth occurs at the 141.06° re-entrant corner (referred to as a type I corner15), similar to the crystal with one twin. When the nucleated layer propagates to the next twin, it forms a new re-entrant corner with an angle of 109.47° (referred to as a type II corner15). Like the type I corner site, the type II corner site is four-fold coordinated17. The type II corner is essential for the continuous propagation of the crystal interface because it relieves the shortage of nucleation sites caused by the formation of ridge structures. The important feature of the WHS model is that the type I corner does not disappear during growth, since it is regenerated by activity at the type II corner14,15. In addition, several authors16,18,19 suggest alternative growth mechanisms of a twinned interface involving the atomically rough {100} habit plane, but they disagree on the precise role of the {100} surface during microstructural evolution. In general, while it is widely accepted that at least two twin planes are needed for steady-state growth, the growth behavior of the twinned interface remains poorly understood due to the lack of in situ experimental evidence. Recently, Fujiwara and colleagues20,21,22,23 developed a 2-D in situ observation system to watch the growth of faceted Si dendrites. Based on this data, they proposed a growth mechanism of a doubly-twinned interface, hereby denoted as the F model and depicted in Supplementary Fig. 2. In their approach, triangular 60° corners (at the length-scale of the crystal) form at the growth tip, and the direction of the 60° corners changes during growth; this is made possible by the alternate formation and disappearance of type I corners at each of the two twin planes, in contrast to the WHS mechanism. Thus, according to the F model, type II corners play no role during growth20,21. While this model satisfactorily explains the observations of Fujiwara and colleagues, many open questions remain: namely, how do the experimental conditions (e.g., temperature, undercooling, and composition) influence the morphology of the twinned interface? To what extent is the F model applicable to other materials systems and solidification pathways? Furthermore, the studies conducted by Fujiwara and colleagues20,21,22,23 are limited to examing 2-D views of the material. While one can extract some qualitative information from these 2-D images, most kinetic models (e.g., solidification24, coarsening25, etc.) make predictions based upon a 3-D microstructure. To circumvent the above challenges, we probe the realtime interfacial dynamics during the growth of Si particles in an Al-Si-Cu liquid via 4-D (i.e., 3-D space plus time) synchrotron-based X-ray tomography (XRT). Our subsequent analysis of interfacial texture allows us to quantify unambiguously the habit plane and grain boundary orientations during growth, from which we validate with high precision the aforementioned twin-mediated growth mechanisms. To the best of our knowledge, this is the first time that time-dependent crystallographic information has been obtained from attenuation contrast XRT. We believe that this novel experiment and analysis method provide a unique approach for understanding crystal growth, and will have significant impacts on the processing of polycrystalline materials.