The emission energy from PL is coming higher than the indirect bandgap of the material? What can be interpreted from this? Is it possible to have a defect level along 'K axis in the band structure whose energy is higher than the CBM?
Is it about binding energy?
If so, then it is possible. The defect level can lie significantly below the top of the valence band. For example, we are faced with a situation where the intercalation of transition metals into titanium dichalcogenides leads to the formation of localized states below the top of the valence band. This level plays the role of an effective oxidizing agent, despite the fact that the metal is intercalated.
The CrxTiTe2 system is a good example. Here, the intercalation of Cr 3+ at a concentration of 1/3 and, therefore, the introduction of 1 electron for each titanium does not change the position of the Fermi level.
I am not sure, whether this information will be useful or not, but still I'm providing, as it has some relevance.
Moss–Burstein effect in doped semiconductors, is a concept where because of moderate defect-density, semiconductors achieve greater conductivity by a shift of the Fermi level towards conduction band for n-type materials and towards valence band for the p-type materials. In both cases, the optical gap increases a bit, although the electronic gap remains unaffected. In your case, this concept of Moss–Burstein shift may have some role. Have a look.
The position of a defect state can be anyway in energy, depending on the type and nature of the defect. Thus, my answer is that it is possible.
Interesting question. I agree with the previous answers that the defect may lie anywhere in energy (i.e. higher than CBM). However, I don't think that this transition is easily resolved using photoluminescence (but it depends on the sample temperature). Difficult to diagnose without the data.
I agree with Peter.
Transition of an electron from one energy level to another depends on many factors, e.g. selection rules, localization/delocalization of the orbitals, etc.
Therefore, it is not an easy job to solve this issue.
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