The rates of solid-phase epitaxy (SPE) in unstrained ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ alloys have been measured by time-resolved reflectivity for eight different alloy compositions, including both Si-rich and Ge-rich layers. Amorphous layers 300–400 nm thick were first formed in 8-μm-thick, relaxed, epitaxial ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ layers (0.02≤x≤0.87) by ion implantation of ${\mathrm{Si}}^{+}$. For each composition, the measured SPE rates spanned approximately two orders of magnitude. The alloy SPE rates are shown to be related to the regrowth rates of the two pure elements by a simple equation expressed in terms of the composition parameter x and having no adjustable parameters. The form of this equation implies that crystallization occurs by a serial attachment process at the amorphous-crystal interface and that the rate of attachment of each individual atom is determined by the identities of its four nearest neighbors. Such a process is consistent with the dangling-bond model proposed by Spaepen and Turnbull [in Laser-Solid Interactions and Laser Processing, edited by S. D. Ferris, H. J. Leamy, and J. M. Poate, AIP Conf. Proc. No. 50 (AIP, New York, 1979)] if the SPE rate is limited by the migration rate of dangling bonds rather than by their formation rate. Based on this analysis, an interpretation is proposed for the anomalously large activation energies that have been measured for SPE in some Si-rich compositions.

• Received 6 September 1994

DOI:https://doi.org/10.1103/PhysRevB.51.7762