Density of states, localized states.

[physiagy]

Hi All!

I am doing my Masters project on III-V Nitrides, my question is really a basic one.

What are the localized states and what is meant by localization energy and degree of localization, also that excitons are localized to the tail state?

Could you please give me an answer and guide me to useful references.

Thanks All!

 

[citw]

Essentially, we think of electrons in solids as (relatively speaking) extended/delocalized or localized. Electrons in a lattice that can be described by Bloch functions are relatively extended -- that is to say the extension of the wavefunction spreads over many lattice constants (the electron is extended over a relatively large region of real space). Delocalized impurities can be described using the "effective mass" ("hydrogenic") approximation, where we treat the problem of the ionized impurity like a hydrogen atom. This gives us hydrogenic impurity wavefunctions and energy levels. Usually these impurities are shallow (close to either the conduction or valence band edge). Delocalized/extended states are primarily determined by the long range Coulomb interaction.

On the other hand, localized states are determined by a short range (often referred to as the central cell) potential. The extension of these localized states is generally on the order of a lattice constant (i.e., the electrons are localized to a small region of space). Unlike delocalized/extended states, these states are more difficult to describe mathematically, because the short range potential can be tricky to deal with and the wavefunctions can't be described by Bloch functions (Bloch functions require extension in real space and localization in momentum (k) space). Also unlike extended states, localized impurities often (BUT NOT ALWAYS!) have "deep" energy levels (far from the conduction or valence band edges).

Importantly, don't believe when someone says "delocalized = shallow, localized = deep" when it comes to impurities. The important thing to understand is that delocalized/extended states are primarily determined by the long range potential (sometimes treated with a small contribution from the short range potential, known as the "central cell correction"), while localized states are primarily determined by the short range potential (often referred to as the "central cell" potential.

I find this topic incredibly interesting, but I also think it is not well understood (and often misunderstood). I've had to read an incredible amount of material just to get meaningful insight on this topic. I'll see if I can't find some of my old references.

 

[physiagy]

Thank you very much

Dear citw
Thank you very much for your detailed explanation, that was really helpful.