When I include an oxygen vacancy in SnO2 system a local state appears in the the middle of the forbidden gap. How can this affect the properties of my system? I am very new with the topic, I am just curious about it. Anyone can explain it to me or provide me with some easy to read bibliography?
Thanks in advance,
Luis
There is in principle nothing wrong with your observation, so long as you appropriately calculate the chemical potential so as to take proper account of the correct ensemble average of the number of electrons in your system at the given temperature. Incidentally, you do not specify your system and the adopted formalism. It is important to know how dilute the vacancies are, and, technically, what basis functions you are using -- whether your results are converged with respect to the adopted set of basis functions.
Adding to what has been said by Prof. Behnam: By definition localized states are allowed energy levels lying deep in the energy gap of the semiconductor material. It is o that the electron occupying such state are bound in the state and are not free to move. It is much like a trapped electron an a potential box with high potential wall. Or it i like an electron in as single atom or molecule. Conversely, in the extended state of the conduction band the electrons can move freely inside the band across the crystal. It is observed that impurities and geometrical defect such as vacancies can produce allowed energy states in the energy gap of the semiconductor as they disturb the periodic structure of the material. These states are localized and normally acts as a trap or recombination center.
You can search on the topic: impurities and defects in semiconductors.in the internet you will get many documents.
wish you success
For illustration purposes, it is useful to forget about bands and think about localized orbitals.
In a molecule (say SnO2), you have discrete electronic states. If you put many molecules together, you will get a bunch of same-energy states; if neighboring molecules interact, the energies will split up and you get a band. However, you can always go back and localize the states (Wannier functions) to get something that resembles approximately a localized typical band state.
Now if you have an oxygen vacancy, the neighboring atoms will have completely different excited states (crudely speaking: now you have the electronic structure of SnO). And that is what you see as a new state.
Regarding properties: Think of, say, conduction also in this localized basis as a hopping from one local orbital to another orbital, and you may get an intuitive grasp on what will happen. Right off the bat, I am lacking a good example.
It`s not an unusual situation, in DFT calculations, at last. The simplest explaining may be proposed as follows. In pure insulating crystal the atomic states (say, O-2p states) form the completely filled valence band. The presence of vacancy 1) makes the electron deficiency; 2) is a source of low-symmetry crystal field (LSF) which may split the degenerate atomic states forming the top of valence band - a) because the different atoms, say of oxygen (which were in equivalent positions in pure crystal) become to be NOT equivalent with respect to vacancy, b) because, for instance 2px,y,z orbitals of the given oxygen atom which were degenerate in pure crystal, become NOT degenerate being splitted by LSF. As a result, these states "segrerate" from the valence band and are shifted to the band gap of initial insulating crystal. Due to the electron deficiency the band of trhese states appears to be only partially filled.
As for the properties of the system, formally it tends to metallic conductivity and sometimes to formation of local magnetic moments in the vicinity of vacancy. However, the experiment, as for my knowledge, confirms that conclusion quite not always.
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