A group member doing QE DFT calculations argues that the band-gap of bulk TiO2 has decreased since a new energy level has been introduced within the band-gap of pure TiO2 following the introduction of an intrinsic defect. What would be a convincing argument to resolve this variation in opinion
In a semiconductor or insulator, the band gap is defined as the energy difference between the set of occupied electronic levels (valence band) and the set of unoccupied levels (conduction band) that lie higher in energy. The existence of such a gap is what distinguishes these solids from metals. If you introduce levels in the gap via e.g. intrinsic defects, indeed the energy required for an electron to be excited from the occupied levels in the valence band to an unoccupied level is reduced, but the band gap itself stays the same. Unless of course the level introduced by the defect somehow interacts with the conduction band, hence causing changes in the bulk of the system. An example of such a case is N in GaAs. Bottom line: the band gap is the energy difference between the valence band (continuum of occupied levels) and the conduction band (continuum of unoccupied levels).
Thank you Filip for taking time to provide that very informative suggestion. You could also help with some clarity on the difference between the terms fundamental band gap and optical band gap. A indication to appropriate literature (article or book) will be most welcome. Best wishes for 2015.
Hi!
Happy New Year.
I think we should note to three concepts:
1-Using DFT, one is able to calculate Kohn-Sham energy band gap which is ELUMO-EHOMO. When, you add impurity it is obvious that Eg changes.
2-Also one can calculate energy dispersion curve i.e., E(k) using DFT or TB method. E(k) shows direct/indirect bandgap and the value of Eg in each point such as Gamma, K, or Q-point. By adding impurity one is able to see new bands in E(k) and also deformation in E(k) and he/she can judge about the effect of impurity as n-type or p-type dopant.
3-Using TD-DFT, one is able to calculate singlet and triplet excited states, their occupation probability and the energy of photon which is necessary for excitation.
Therefore, we should specify what kinds of physics we want to study?
Best Regards
H.Simchi
A very good book: "Fundamentals of semiconductors" by Peter Yu and Manuel Cardona.
The differneve between the fundamental (electronic) band gap (Eg) and optical band gap is related to the binding energy of the electron and hole (exciton binding energy Ee) produced in the excitation by photons (hence the name optical band gap). A semiconductor can absorb a photon with energy Eg - Ee. In "regular" semiconductors (such as Si) Ee is very small and can be neglected for most purposes. In the case of e.g. organic semiconductors the situation can be very different and the optical band gap much smaller than the electronic/fundamental band gap.
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