Segregation Constant

 

 

It is also common to introduce dopant atoms into the melt so that a particular resistivity wafer can be made. To do this, one can simply weigh the melt, determine the number of impurity atoms that would be needed, and add that weight of impurity. The process is complicated, however, by the fact that impurities tend to segregate at solid/liquid interface.

 

Every impurity has a solid solubility in silicon and different equilibrium solubility in the melt. An equilibrium segregation coefficient k0 may be defined as

 

                             ko=CS/Cl

 

Where Cs and Cl are the equilibrium concentrations of the impurity in the solid and liquid near the interface, respectively. [2]

 

The distribution of an impurity in the grown crystal can be described mathematically by the normal freezing relation.

                  

                             CS = k0C0(1-X)k0-1

 

Where X is the fraction of the melt solidified, C0 is the initial melt concentration, Cs is the solid concentration, and k0 is the segregation coefficient.