I am referring to calculated urbach energy at band gap edge for undoped and copper zno nanoparticles.
I need help in analyzing urbach energy obtained by transmission studies at near band edge
[A] If it does not come up to expectatiions, treat is as an unfruitful academic discussion without any prejudices . Some times , I have a lurking fear, yet the teacher in me compels me to put forth an idea. Once I had to listen sermons from a celebrated RG colleage to study more even in the eight decade of my life.
[B]Apply Tauc and Meneth :
α -------A/ hv[hv-Eg]^n
where A is a constant while n can have values ½,2,3/2 and 3 for allowed
direct, allowed indirect and forbidden direct and indirect transitions respectively.
[C]Now about URBACH TAIL AND URBACH ENERGY[EU or ∆E]
Plot a graph between[ ln(α )] and [hv] . May extrapolate if needed; slope gives Eo so that value of α becomes α0 and the following relation holds good:
α --------- α0 [exp(E/E0)]
where E is the photon enegy.
After having calculated Eo, we apply the relation
α=αo exp [(hv - Eo)/∆E]
or
α=αo exp [(hv - Eo)/EU]
where ∆E or EU is called the Urbach Energy or Urbach tail or Urbach width.
which can be calculated as all other parameters in the above relation are known.
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