Differential analysis of the free-charge-carrier concentration in semiconductors containing localized levels with negative electronic correlation energy

The concentration of single carriers and carrier pairs bound to localized levels with negative and positive electronic correlation energy $U$ is calculated for a semiconductor as a function of the Fermi energy. It is shown how the stability of the Fermi energy against variations of the doping level depends on the sign of the correlation energy. From this one obtains a new experimental criterion for associating a given kind of doubly charged defect with the negative-$U$ property.