When it comes to the optical absorption spectroscopic studies of semiconductors, two physical parameters are majorly exploited - Bandgap (Eg) and Urbach energy (Eg).

There are certain models that researchers use for the fitting of experimentally obtained values in temperature dependent measurements.

One such model is Einstein single oscillator model, in which the temperature dependent (TD) data is fitted with the function:

EU(T) = E01 + E02/(exp(ThetaE/T) - 1)

where ThetaE is related to the Einstein temperature of the sample

a similar functional form for the bandgap is also used by the researchers for the fitting of temperature dependent bandgap:

Eg(T) = Eg(0) - aB(2 / (exp(Eph/kBT) - 1))

here, the Eph is usually discussed to be the effective phonon energy, and aB is related with the electron-phonon interaction strength.

I would like to discuss the resemblance between ThetaE and the term Eph/kB: are these two parameters appearing in the above models interchangeable? In case, we can not, it would be interesting to know the different origins of these parameters. Any information or reference in this regard will be helpful.

Because, in many literature, what one would observe is that when it comes to the Bandgap, Eph term is seen in the model, in contrary to the case of fitting the TD data of Urbach energy with taking ThetaE in the respective equation. Even though these models are inspired from the Einstein picture, which encompasses a single equivalent oscillation and the related temperature of its excitation, a disciplined notation is seen to be followed when it comes to the fitting of both the data (Eg(T) and Eu(T))