A theoretical model called the ''multibody model'' is developed for the composition dependence of the activation energy. The model that is based on the diffusion required of the recrystallization for the solid phase epitaxy does not involve any adjustable parameters and is shown to represent experimental data satisfactorily. For the Si 1Ϫx Ge x alloys that are of diamond structure, the most logical choice is the ''five-body model'' involving five atoms. The model is equally applicable to any other binary alloy.
The compensation effect, well known in catalytic reactions, is shown to apply equally well to the solid-phase epitaxial ͑SPE͒ growth of Si 1Ϫx Ge x alloys. A linear relationship exists between the logarithm of the pre-exponential factor and the activation energy of the SPE growth rate. This linear relationship, together with the activation energy obtained earlier, enables one to completely describe the growth rate of Si 1Ϫx Ge x alloys. The effect holds for both strained and unstrained SPE. The model is applicable to other binary alloys. © 1997 American Institute of Physics. ͓S0021-8979͑97͒03410-5͔Solid-phase epitaxial ͑SPE͒ growth of Si 1Ϫx Ge x alloys is of interest for possible applications of the alloy film is optical and electronic devices.1,2 A peculiar aspect of the SPE growth is that the activation energy is substantially larger than that for either pure silicon or germanium. A multibody model has been proposed to describe the composition (x) dependence of the activation energy that does not involve any adjustable parameter. 3This result on the activation energy suggests that a complete description of the SPE growth rate could be possible if the corresponding change of the pre-exponential factor with the activation energy is known. Often noted in the kinetics of catalytic reactions on a series of related catalysts is the compensation effect in which the logarithm of the preexponential factor of the rate is linearly related to the activation energy. [4][5][6] Since the change in the activation energy is with the composition for the same alloy, the compensation effect could apply to the SPE growth rate.The applicability of the compensation effect is clearly revealed in Fig. 1 where the logarithm of experimentally determined pre-exponential factor is plotted against the corresponding activation energy in the case of strained SPE growth. The data are from three different sources. 7-9Given the activation energy and the pre-exponential factor, the SPE growth rate can be written as follows:
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