I've been trying to predict the theoretical annealing condition of a pure Ge thin film sputtered on Si substrate, the idea behind this process is to create a smooth composition gradient through the thin film while maintaining low threading dislocation density.
The interdiffusivity I found could be state as:
D(xGe)=310exp(-4.66eV/kT)exp(8.1×xGe)
With D being a function of concentration, no regular Fick's law solution could be put into use, I'd like to know that whether Fick's second law is solvable when I put the diffusivity above in the equation. Thank you.
In general, no, but there are likely solutions for some specific D(c) functions. If you have a theoretical c dependence or you write some function that has a shape suitable for your phenomenon, I would suggest working with numerical approximations. If you must have a function, use numerical solutions to get a profiles throughout the range of interest, then fit those to some function of your choice.
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