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We have derived an analytical formula for the temperature dependence of the photoluminescence (PL) intensity when the “negative” thermal quenching phenomenon is observed. The formula was examined using available experimental data for GaAs and ZnS, and the agreement of the results was quite good. It was confirmed quantitatively that the principal mechanism of negative thermal quenching is the thermal excitation of electrons to the initial state of the PL transition from the eigenstates with smaller energy eigenvalues. In addition, it was revealed that the real activation energy for the nonradiative recombination processes is given by ε + E ′ when the negative thermal quenching phenomenon is observed, where ε is the activation energy estimated simply from the apparent slope in the experimental data, and E ′ is the activation energy for the negative thermal quenching phenomenon.
Hajime Shibata (Sun,) studied this question.