the band gap due to doping decreased (e.g., red shifted) to a certain minimum value (i.e., critical size) with decrease in particle size from an estimated bulk value. Further increasing in doping concentration results in decrease in particle size from the critical size (corresponding to band gap minimum) caused the band gap to increase (i.e., blue-shift). A plausible explanation for this change in band gap with respect to the size of the particle is that the bulk defects induce delocalization of molecular orbitals in the conduction band edge (e.g., LUMO) and create shallow/deep traps in electronic

energy, in turn causing the red-shift of the absorption spectra.

When crystalline size decreased below its size at the band gap

minimum, the traps shifted to higher energy, which resulted in

blue shifting of the absorption spectra.

Question is, how an increase in doping concentration shift the defect level to higher energy inside the band gap!

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