Two carrier temperatures non-equilibrium generalized Planck law for semiconductors

Planck's law of radiation describes the light emitted by a blackbody. This law has been generalized in the past for the case of a non-blackbody material having a quasi Fermi-level splitting: the lattice of the material and the carriers are then considered in an isothermal regime. Hot carrier spectroscopy deals with carriers out of the isothermal regime, as their respective temperatures (THe ≠ THh) are considered to be different than that of the lattice (_TL). Here we show that Fermi-Dirac distribution temperature for each type of carrier still determine an effective radiation temperature: an explicit relationship is given involving the effective masses. Moreover, we show how to determine, in principle with an additional approximation, the carrier temperatures (THe,THh) and the corresponding absolute electrochemical potentials from photoluminescence measurements.