Hi all!
In semiconductors and insulators, photoelectron spectroscopy (PES) and inverse photoemission spectroscopy (IPES) are often used to probe the occupied and unoccupied electronic states, respectively. Basically, PES gives a picture of the valence bands, which lie below the Fermi level EF, while IPES shows the distribution of the conduction bands above EF. The empty bands sometimes extend to several 10s of eV above EF, for example here in NiO, where they find states up to ~20eV: Article Electronic structure of epitaxial thin NiO(100) films grown ...
On the other hand, there is the concept of the electronic vacuum level, which gives the energy necessary to remove an electron from the solid. Typically, this level is only a few eV above EF (for NiO, Evac-EF ~ 5eV or so).
This is the aspect I have difficulties with. If I only need a few eV to remove an electron from the solid, how does it make sense that there are unoccupied states in the solid even far above that energy? Wouldn't they be unstable somehow? But if so, why are they detectable by IPES? Or am I getting something wrong about the vacuum level concept?
This may be a bit of a stupid question -- I'm not an expert on PES/IPES, but I have been thinking about this for a while and couldn't find anything even remotely close to an answer.
Thank you for your input,
Robert
Hi,
You are right, there are two different concepts to be distingished:
A. Energy levels ''belonging'' to the solid. These are:
1. Higher lying energy levels of a solid which are sometimes several 10's of eV > than the bottom or similarly several 10's of eV lower than the top of the valence band.
2. Under normal conditions and temperatures, allowed (CB and VB) are occupied only few 100's of meV above lowest CB or VB extrema.
3. Under high energy excitations the electrons (or holes) can populate for a short wile higher energy unstable states (states short lifetime).
However in all these three cases the electrons are ''inside'' the solid. They cannot escape out of the solid.
B. The vacuum level has the meaning of ''ionization'' level: the energy required for an electron (or hole) originating from a fundamental state of the solid (e.g.bottom of the CB or VB) to escape the attractive potential of the solid and then move freely in the vacuum.
Sometimes this energy is called electron affinity.
It has nothing to deal with higher lying energy levels. Electrons on higher energy levels of a solid are not free to move in the vacuum; they are accupying for a short lifetime a highly unstable energy level belonging to the solid.
It has to deal with the ability of the lowest fundamental to get ionized with a free electron.
I hope this make it clear for you
Best regards
Professor A. Kadri
Hi Robert Karsthof, I hope you are doing well. Abderrahmane Kadri is correct, but more simply put, you are calculating properties within an infinite Bloch-like crystal. You should calculate surface states or isolated atoms, if you want to calculate vacuum ionization.
For example, in DFT, when you are approximating an infinite crystal, you can space one direction out with empty vacuum by at least 15-20 Angstroms to approximate a surface. Also, there is a software called Atomic, which calculates LSDA energy bands of isolated atoms. There, you will find I think what you are looking for. It's tough software to find, but I think I have the source code around here somewhere if you need it.
Thank you Abderrahmane Kadri and John Emil Petersen III for your input! So I may have mixed the concept of the vacuum level, which is a surface property, with that of higher conduction bands, a bulk property. I think I can get behind that. Although the question is, what happens to the conduction bands when you get close to the surface? Do they simply.... stop to exist? Move down in energy? What does the unoccupied energy landscape between EF and Evac look like to an electron very close to the surface?
I'm not really looking for doing any calculations myself; this is just something I've been pondering about for ages!
Hi Robert Karsthof , and John Emil Petersen III ,
Thanks for feedback,
Indeed near to a surface or interface, bulk energy bands will change in energy by the band bending effect due to depopulation of bulk bands by processes as carrier diffusion (through interface) or carrier trapping at surface or interface defect centers,....
Now, the electrons are definitly subjected to quantum mechanics (Q.M) rules. They can experience a transition only and only if they can fulfill Q.M selection rules, and the energy requirement is not the only one. There are at least two other requirements: the transition must be allowed (either in 1st approximation or in 2d approximation) and there should be symmetry compatibility between initial and final states as well as with the symmetry of excitating perturbation.
Therefore, the electron knows exactly what to do :
1. to go to higher bulk bands,
2. to go to surface or interface,
3. or to go to vacuum leve as in heterostructures starting from metal-semiconductor contact as in Schottky diode, or in heterojunctions, or in heterostructure, or in superlattices, and so on...
I advise you reading this excellent paper by Herbert Krömer in his Nobel Prize (shared with Zhores Alferov) lecture in 2002 entitled ''Teaching electrons new tricks''
Article Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks
I hope you'l enjoy
Best regards,
Professor A. Kadri
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