Effect of rapid sample cooling on efficiency of multiple impurity-atom doping

Shallow and efficient doping of wide band-gap semiconductors has remained one of yet unresolved problems to date. A possible solution to this problem is doping with complexes of a few impurity atoms at a quasi-equilibrium state, which is introduced by controlled cooling of a sample after doping. In this work, (1) we first define a global and quasi-equilibria of our interest based on a simple thermodynamic model for a doped crystal, and then (2) we discuss how the cooling rate affects the probability of impurity-complex formation at a quasi-equilibrium as defined. Our main message is that one should design impurity complexes as small in size as possible which have as large a binding energy as possible. This is a required condition for complex designs when it is difficult to tune the cooling rate.