Theory of shape stability in crystal growth from the melt

Abstract

A criterion is presented for the stability of the external shape of the crystal in crystal growth from the melt. The criterion takes cognizance of the finding that the constant cross-sectional growth of crystals by a meniscus-controlled process, such as Czochralski, floating-zone, and edge-defined film-fed growth (EFG), requires that the angle φ between the meniscus and the growth axis equal φ0 (a constant; for silicon, φ0=11°). Shape stability requires further that a change in crystal shape (whenever φ≠φ0) should be such that φ approaches φ0 again as a result of the shape change. The criterion is applied to the various melt-growth techniques; Czochralski growth is shown to be inherently unstable, whereas the usual floating zone techniques are shown to provide stability of the crystal shape. An application of the criterion is made to the EFG growth of various crystal shapes, with particular emphasis on EFG silicon ribbon growth, and the conditions under which shape stabilization is obtained in EFG are identified.