Solubility of Flaws in Heavily-Doped Semiconductors

The solubility of a charged impurity in a semiconductor depends upon the Fermi level. This dependence may be understood in terms of a conceptual model in which an impurity is allowed to diffuse in a specimen containing a p-n junction, so that the Fermi level varies in respect to the band edges. If the impurity can exist in many states of charge (i. e. , is a "flaw"), then the concentration of flaws with charge r times the electronic charge varies as the rth power of the hole density. Summing the concentrations for the different states of charge gives the solubility and its dependence upon hole concentration, and, hence, Fermi level.