Metal doping calculations?

This is a very complex problem,there is a lot to consider!!!!

The coefficient of partitioning k= Cs/Cl,Cs and Cl are the concentration of magazines on the solid and liquid side of the solid-liquid interface, respectively.

Let X be the proportion of the melt that has crystallized, assuming that the solution is always homogeneous, then

Cs=kCo(1-X)^(k-1)

where Co is the initial concentration of magazines in the melt.

The so-called p,n types you give have a parametric difference. It is better to check it. Here are the coefficients for common impurities:

Al 0.002

As 0.3

B 0.8

O 0.25

P 0.35

Sb 0.023

Because there is a viscous coefficient of adhesion of the solution, there will be a flow of material in a certain region close to the interface between liquid and solid. This region in the melt becomes the surface layer. So the coagulation coefficient k will be replaced by the effective coagulation coefficient ke:

ke=k/(k+(1-k)*e^(-Vb/D))

Which b is the effective thickness of the adherent layer, V is the pulling speed, and D is the diffusion coefficient of the impurity in the soluble semiconductor.

Then D can be derived from the resistivity relationship. You should be able to find this one.