Interdiffusion in Bilayered Pb/In Thin Films Studied by X-Ray Diffraction

An investigation of interdiffusion of bilayered Pb/In thin films was carried out using X-ray diffraction. To determine the interdiffusion coefficients \ ildeD in thin films, a conventional sectioning technique could not be used because of extremely short diffusion distances. A new, non-destructive technique was developed to determine \ ildeD values directly on the thin films with average grain sizes much larger than the film thicknesses. The \ ildeD values as low as 10−19 m2/s were determined in Pb-20 at%In films at a temperature range of 315 to 350 K. The present \ ildeD values were found to be in the range obtained by extrapolating to the low temperatures the \ ildeD values determined at high temperatures for Pb/In diffusion couples with single crystals. This indicates that in such large-grained films the volume diffusion through the Pb/In interface was the dominant mechanism. Using the present technique the effects of a monolayer thick oxide or 5 nm thick Au layer present at the Pb/In interface on the Pb/In interdiffusion could be detected. To determine the mobilities, the free energy ΔF of Pb–In system was calculated using a subregular solid solution approximation, where the interaction energies were determined by using the existing thermodynamic values. The mobilities M in the present system were determined from the measured \ ildeD values and calculated ΔF″ through a relation of \ ildeD=MΔF″ where ΔF″ is a second derivative of the free energy with respect to the In concentration.