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.

Crystal Shape Stability in Meniscus-Controlled Growth Processes

“…(13) Qualitatively, the above condition implies that, if a change in crystal dimension t occurs (i. e., whenever C{J ;o! CfJo), the meniscus angle C{J should approach C{Jo again as a result of the shape change in order for the crystal shape to be stable [20,21].…”

“…In the portions of the curves where as/a(t/2) <0, it is found that acp/at <0. Shape stability in the growth of rod-shaped crystals (or at the ribbon edges) is thus seen to be conditional; it requires that the edgedefining die radius should not exceed approximately twice the radius of the crystal (or the radius of curvature at the ribbon edge) [20,21].…”

“…An approximation [21] to the problem is to consider a crystal of radius t/2 growing from a die shaper of radius t d /2 (cf . Fig.…”

Stability of Crystallization in Edge-Defined Film-Fed Growth from the Melt

“…The pressure may be produced by an appropriate level of the melt. By dipping an edge-definer, shaped as a slab with a cylindrical or conical hole, into the melt it is possible to achieve successively the boundary conditions of anchoring at the lower circumference of the edge-definer, wetting of the walls, or anchoring at the upper circumference [8,16,17]. …”

A Review of the Automation of the Czochralski Crystal Growth Process

“…Surek's initial stability analysis was only of the capillary problem, i.e., for the meniscus region [49]. He came to the conclusion that the capillary system is unstable.…”