Thermodynamic and kinetic study of solid state reactions in the Cu–Si system

Abstract

It has been shown that significant changes in the course of solid state reactions can be realized by decreasing length scale, temperature, or by varying parent microstructures. In the case of the formation of Cu3Si by interdiffusion of Cu and Si, previous research has shown that over a large temperature range reaction rates are determined by the rate of grain boundary diffusion of Cu through the growing Cu3Si phase. We have examined the effect of replacing crystalline Si with amorphous Si (a-Si) on these solid state reactions, as well as the effect of decreasing the temperatures and length scales of the reactions. Multilayered thin film diffusion couples of Cu and a-Si were prepared by sputter deposition, with most average composite stoichiometries close to that of the equilibrium phase Cu3Si. Layer thicknesses of the two materials were changed such that the modulation (sum of the thickness of one layer of Cu and a-Si), λ, varied between 5 and 160 nm. X-ray diffraction analysis and transmission electron microscopy analysis were used to identify phases present in as prepared and reacted diffusion couples. Complete reactions to form a single phase or mixtures of the three low temperature equilibrium silicides (Cu3Si, Cu15Si4, and Cu5Si) were observed. Upon initial heating of samples from room temperature, heat flow signals were observed with differential scanning calorimetry corresponding to the growth of Cu3Si. At higher temperatures (>525 K) and in the presence of excess Cu, the more Cu-rich silicides, Cu15Si, and Cu5Si formed. Based on differential scanning calorimetry results for samples with average stoichiometry of the phases Cu3Si and Cu5Si, enthalpies of formation of these compounds were measured. Considering the reaction of these phases forming from Cu and a-Si, the enthalpies were found to be −13.6±0.3 kJ/mol for Cu3Si and −10.5±0.6 kJ/mol for Cu5Si. The growth of Cu3Si was found to obey a parabolic growth law: x2=k2t, where x is the thickness of the growing silicide, k2 is the temperature dependent reaction constant, and t is the reaction time. Also, the form of the reaction constant, k2, was Arrhenius: k2=k0 exp(−Ea/kbT) with kb being Boltzmann’s constant and the prefactor, k0=1.5×10−3 cm2/s, and activation energy, Ea=0.98 eV. These results indicate a much slower reaction to form Cu3Si in thin film Cu/a-Si diffusion couples than indicated by previous researchers using mostly bulk samples of Cu and crystalline Si (x-Si).