N is proportional to the exp(-E/(KT)), i fit the PL curve and found that the tail of PL is matched well with a Gaussian curve instead of exp(-E/(KT)). so i cannot find the temperature and the carrier density relationship. only find the photon energy and the carrier density relationship.
if I want to add the temperature parameter, how should i do?
Let's assume you study photoluminescence in a direct bandgap bulk (3D) semiconductor. Then simple formulas for interband radiative recombination in parabolic band approximation suggest that radiation intensity at energy E is proportional to \sqrt{E-Eg}f_c(E1)f_v(E2), where Eg is a bandgap energy, E1 and E2 obey selection rules E1 = E2 + E, k1=k2, f_c and f_v are Fermi population numbers for electrons in the conduction band and holes in valence bands (heavy and light holes), respectively.
If the quasi-Fermi levels for electrons and holes are sufficiently far from E1 and E2 (meaning E1-Fn, Fh-E2 >> kT) intensity is proportional to \sqrt{E-Eg}exp(-E/kT).
In the highly doped material there would be departures from this law near the bandgap energy, and Casey-Stern approach with envelope matrix element should be adopted to treat the band formed by shallow dopants.
If your case is quantum well, the corrections to above formulas should be made.
Is this PL from a QW? At what temperature? If so, there are contributions from excitons and free carrier recombination. Each contribution can be approximated by a function as shown in the attached paper. If heavy hale and light holes are present each contribution/function is taken twice (one for HH, one for LH).with the corresponding parameters.
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