Thermodynamic Predictions of Phase Stability and Crystallization Temperature of Silicon-Based Amorphous Alloys
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THERMODYNAMIC PREDICTIONS OF PHASE STABILITY AND CRYSTALLIZATION TEMPERATURE OF SILICON-BASED AMORPHOUS ALLOYS J. R. A. Carlsson, X. -H. Li, S. F. Gong, and H. T. G. Hentzell Thin Film Division, Department of Physics and Measurement Technology, Link6ping University, S-58183 Link6ping, Sweden
ABSTRACT A thermodynamic calculation of Si-X alloys has been carried out, where X is any element from group III or V. Free-energy diagrams for those systems have been established. A comparison between thermodynamic predictions and experimental results is carried out for the Si-B and the Si-Sb alloys. It is found that the agreement between theory and experimental results for the freeenergy diagrams and for the crystallization temperature predictions are good. The model and the different features for the various elements are described in detail. I. INTRODUCTION Recently, the attention in microelectronics has been on amorphous Si-based amorphous alloys, since the amorphous alloys are found to have some interesting properties.1,2 Although many detailed studies on silicide formation 3,4 and silicide properties 5 ,6 have already been carried out, studies of the correlation between the thermodynamic properties and formation or stability of amorphous alloy have not been so common. Therefore, it is of interest to find a way to describe the formation energy of an amorphous alloy and to correlate it to e.g. the crystallization temperature. However, due to the complexity of disordered materials it is difficult to perform exact quantitative first-principle calculations, and therefore we have utilized a semi-empirical thermodynamic model 7 ,8 in order to calculate the heat of mixing and Gibbs free-energy diagram between two materials. In our previous work 8 we compared this model with experimental data and found that the model was able to explain rather well the experimental data. In this work we have modified the model in order to be able to calculate Gibbs free-energy diagram, not only for transition metal-based systems, but also for Si-based systems, and calculated the free-energies of the Si-X alloys. Moreover, a semi-empirical model for predicting the crystallization temperature7 is presented and compared with experimental data. II. CALCULATIONS OF GIBBS FREE-ENERGY The Gibbs free-energy, G, for a crystalline phase of a pure element at a temperature, T, can be calculated (assuming that a supercooled gas at 0 K has zero free-energy) from,
G = Ggas - AGso 0
(1)
where Ggas is the free-energy of the gas at the vapour temperature and AGsol is the free-energy change for the process of;9 transforming the gas to liquid, cooling the liquid, transforming the liquid to solid, and cooling the solid to T. The free-energy of the crystalline mixture between Si and X is just considered to be linear between the free-energies of the pure Si and the pure X element. Mat. Res. Soc. Symp. Proc. Vol. 297. ©1993 Materials Research Society
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The Gibbs free-energy of an amorphous phase of a pure element at a temperature T, can be calculated by using Eq.
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