Photoelectric Effect & Metals: Overview

[Umabel]

Hi all. This is my first post.

I'm a little eluded by this question given to me...

"What does the photoeffect (photo-electric effect) tell about electrons bound in metals"

It seems a bit too trivial to me. I'm tempted to just say that since the work function is proportional to how "bounded" the electrons are to the metal, bounded electrons will not be ejected compared to the metal's free electrons. Therefore, bound electrons will not transfer energy in the metal.

Do I even make sense, maybe I'm missing something else? I was also working on phonons in the same assignment, but if there is a relation to the photoeffect besides energy transfer, I can't see it.

 

[Astronuc]

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c5

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c3

The photo-electric effect indicates that electrons are bound with certain energies within atoms. This is shown by using light of different frequencies until photoelectrons are emitted from the element.

Phonons are related to the motion of atoms in a crystal. What can one say about the binding energy of electrons in the atom and the binding of energy of atoms in a crystal lattice?

 

[Umabel]

What can one say about the binding energy of electrons in the atom and the binding of energy of atoms in a crystal lattice?

Does binding energy of atoms in a crystal lattice refer to the energy of the phonons?

If so, I guess I can say comparing the binding energys of the atoms in the lattice to the electrons in the atoms will depend on the state of the electrons. I expect bound electrons to have much higher binding energy than the atoms, and the free electrons to have the same (or very close to it) binding energy.

Anyways, Thanks for the reply.

 

[ZapperZ]

1. Phonons do not affect the energy spectrum in a standard photoelectric effect.

2. The "binding energy" of atoms are no longer relevant in a metal. The conduction electrons are only weakly affected by the ions in the lattice via the perioding potential. Other than that, the atoms have lost their individual identity. The conduction band occurs due to a collective effect of the overlap of all the valence electrons.

3. The "binding" of the conduction electrons (which are the electrons that participate in a typical photoelectric effect experiments) to the metal manifests itself via the work function. The work function exists due to the inherent surface effects and image potential. No phonons here.

4. Only in very high resolution angle-resolved photoemission spectroscopy would one begin to notice the many-body effects and possible coupling of the photoelectron with a "bosonic collective" such as phonons. The current debate on the origin of the "kink" near the Fermi energy in the spectroscopy of high-Tc superconductor is one such example.

Zz.

 

[Gokul43201]

Hi all. This is my first post.
I'm a little eluded by this question given to me...
"What does the photoeffect (photo-electric effect) tell about electrons bound in metals"
It seems a bit too trivial to me. I'm tempted to just say that since the work function is proportional to how "bounded" the electrons are to the metal, bounded electrons will not be ejected compared to the metal's free electrons. Therefore, bound electrons will not transfer energy in the metal.
Do I even make sense, maybe I'm missing something else? I was also working on phonons in the same assignment, but if there is a relation to the photoeffect besides energy transfer, I can't see it.

I think you may be confusing two different processes here :

1. The typical photoelectric effect excites only conduction (or "free") electrons (from the Fermi energy to the Vacuum energy - this difference is the work function of the metal). There is not enough energy in the photons to significantly excite bound (inner shell) electrons. This, however, happens with ...

2. X-ray photoelectron spectroscopy - where the X-ray photons have sufficient energy to excite core (inner) electrons to the vacuum state. This is known as core emission.

 

[Pieter Kuiper]

I'm a little eluded by this question given to me...
"What does the photoeffect (photo-electric effect) tell about electrons bound in metals"
...
I was also working on phonons in the same assignment, but if there is a relation to the photoeffect besides energy transfer, I can't see it.

Maybe the answer is that (angle-resolved) photoemission gives information about the dispersion relations of electrons in a crystal (the dependence of the electron energy on its wave vector).

 

[ZapperZ]

Maybe the answer is that (angle-resolved) photoemission gives information about the dispersion relations of electrons in a crystal (the dependence of the electron energy on its wave vector).

However, the dispersion relation that you get is the dispersion relation for a free electron gas. So that doesn't tell you anything about the electron's interaction with the crystal, at least not directly. It is only when you examine the self-energy part of what is known as the spectral function (which is related to the imaginary part of the single-particle Green's function), that you can extract the scattering rates. Even then, the phonon influence is very small when compared with scattering off impurities.

In any case, I highly doubt that the OP is even remotely connected to ARPES. When something invokes the name of "photoelectric effect", it tends to be the very primitive version of the photoemission phenomenon.

Zz.

 

[Pieter Kuiper]

However, the dispersion relation that you get is the dispersion relation for a free electron gas. So that doesn't tell you anything about the electron's interaction with the crystal, at least not directly.

That is not correct. The whole point of doing ARPES nowadays is measuring real dispersion relations and Fermi vectors, and comparison with detailed band structure calculations, not just the free-electron model.

In any case, I highly doubt that the OP is even remotely connected to ARPES. When something invokes the name of "photoelectric effect", it tends to be the very primitive version of the photoemission phenomenon.

The OP mentioned phonons, and probably read about dispersion relations of phonons, maybe also about inelastic neutron scattering. In connection with dispersion relations, also ARPES may come in.

 

[ZapperZ]

That is not correct. The whole point of doing ARPES nowadays is measuring real dispersion relations and Fermi vectors, and comparison with detailed band structure calculations, not just the free-electron model.

But the gross dispersion that you do get is the free electron model. I have said earlier that only in very high resolution do you get the deviation from such a model via the "kink" very close to the Fermi energy. This is the many-body effects of the electron-electron interaction. And this occurs with about 60 MeV of the Fermi energy. But other than that, it is the typical Fermi-liquid model (see, for example, Valla et al. on the surface state ARPES of Mo(110))

The OP mentioned phonons, and probably read about dispersion relations of phonons, maybe also about inelastic neutron scattering. In that connection, also ARPES may come in.

Again, you do not see any phonon effects until you actually do a rigorous analysis of the spectral function. The brodening of the energy or momentum distribution curves comes from 3 sources: electron-electron scattering, electron-phonon scattering, and electron-impurity scattering. It takes quite an effort to actually get the electron-phonon scattering. You have to know what the phonon spectrum is first, either from First Principle, or from a different source, because you have to know the cut-off Debye energy for that particular material.

This is all still fresh in my head because I had to referee a paper last week exactly on this done on a "model metal", TiSe. This isn't something you get simply from the dispersion relation, which gives you the parabolic relationship that is expected for a metal.

Zz.

 

[Pieter Kuiper]

Again, you do not see any phonon effects until you actually do a rigorous analysis of the spectral function.

I am not talking about phonon effects in ARPES or about phonon scattering rates.
I am talking about the gross features of electron bands, which can be measured by ARPES. Examples are diamond and silicon, which are not free-electron like.

In the attached image file, the green lines is the theoretical band structure of diamond. There are clear gaps at zone boundaries, due to electron interaction with the lattic (Bragg reflection).
Source: http://www.als.lbl.gov/als/science/sci_archive/diamond.html

 

[ZapperZ]

I am not talking about phonon effects in ARPES or about phonon scattering rates.
I am talking about the gross features of electron bands, which can be measured by ARPES. Examples are diamond and silicon, which are not free-electron like.

In the attached image file, the green lines is the theoretical band structure of diamond. There are clear gaps at zone boundaries, due to electron interaction with the lattic (Bragg reflection).
Source: http://www.als.lbl.gov/als/science/sci_archive/diamond.html

Eh? But I was talking about METALS.

It would be silly for me to go on and on about free electrons if I wasn't referring to metal cathodes. I clearly mentioned in the beginning that the standard photoeletric effect are normally done on metals, not on insulators or semiconductors. My emphasis on the "model metal" should have indicated to you that this is what I was discussing.

Now, having said that, can you tell me how, by looking at the dispersion from all those bands, that you can actually get any info of phonons in those material?

Zz.

 

[Pieter Kuiper]

Diamond was just an example that I knew a decorative picture of. But of course one can also look at metals - nickel or vanadium or tungsten or graphite or whatever. Many bands there are not free-electron-like.

Photoemission can tell us the dispersion relations of the electrons bound in metals. I still think that this is a possible answer to the Original Poster's question. I would like to hear if he found my comment helpful.

ZapperZ seems to be quite an expert on electron-phonon effects in photoemission. I am sure he can explain that much better than what I can.

 

[ZapperZ]

Diamond was just an example that I knew a decorative picture of. But of course one can also look at metals - nickel or vanadium or tungsten or graphite or whatever. Many bands there are not free-electron-like.

And for many of them, the standard BAND STRUCTURE calculation fails, and fails miserably also. So how is that relevant? Remember, you claim that you can detect phonons from just the dispersion relation. I dispute that from the standard metal arguments. I didn't realize that we were invoking exotic metals and non-fermi liquid features.

Photoemission can tell us the dispersion relations of the electrons. I still think that this is a possible answer to the Original Poster's question. I would like to hear if he found my comment helpful.

Well, all you need to do is point to me a specific paper in which they used JUST the dispersion relation to arrive at the phonon spectrum. That would seal the deal. Band structure calculation cannot do that. Band structure calculation requires the coordination number, i.e. where all the ions are, and then invoke maybe the tight-binding model to come up with all the relevant bands. Invoking phonons into this AND then trying to see its effect from photoemission dispersion is highly dubious considering till about 6 years ago, energy resolution of a typical ARPES experiment is larger than 30 meV!

ZapperZ seems to be an expert on electron-phonon effects in photoemission. I am sure he can explain that much better than what I can.

Doing ARPES was my postdoc project, and I did it on some of the most exotic materials being studied, from 2D mott insulators to 1D luttinger liquid material that could show spin-charge separation. In fact, my avatar is a raw data from from an ARPES measurement. So I know all about non-standard behavior that clearly deviates from the simple free-electron or Fermi Liquid model. Never ever did I use the dispersion curves, be it on standard metals all the way to exotic compound, to get the phonon structure. I don't even know how! My "proof" to support my argument is that if we can detect phonons THAT easily, everyone would have done it. It would be silly for paper after paper to painfully extract the spectral lines, then analyze the self-energy from the broadened quasiparticle peaks, and then try to extract the phonon contribution. Why didn't they just look at the dispersion if such a thing is possible?

Zz.

 

[Pieter Kuiper]

Remember, you claim that you can detect phonons from just the dispersion relation.

I cannot remember having claimed such a thing.

 

[ZapperZ]

I cannot remember having claimed such a thing.

The OP asked:

I'm a little eluded by this question given to me...
"What does the photoeffect (photo-electric effect) tell about electrons bound in metals"
...
I was also working on phonons in the same assignment, but if there is a relation to the photoeffect besides energy transfer, I can't see it.

Your response:

Maybe the answer is that (angle-resolved) photoemission gives information about the dispersion relations of electrons in a crystal (the dependence of the electron energy on its wave vector).

You further responded to my objection by saying:

The OP mentioned phonons, and probably read about dispersion relations of phonons, maybe also about inelastic neutron scattering. In connection with dispersion relations, also ARPES may come in.

I continued to clearly indicate that one cannot get any phonon info from the dispersion in my responses to your posts. I said this way in the beginning of my replies to you. If this wasn't your point in the first place, you would have said so much earlier than this.

Zz.

 

[Pieter Kuiper]

The connection that I saw in the OP's question was that in a lecture about phonons, their dispersion relations, and techniques of measuring them, also a question about ARPES may come up, as a technique for measuring dispersion relations of electrons.

ZapperZ seems to be still in the mental mode of a referee of a paper about electron-phonom interactions. Snap out out of that mode, and read my postings again. Or just let it be. I am not going to waste more time on this.

 

[ZapperZ]

The connection that I saw in the OP's question was that in a lecture about phonons, their dispersion relations, and techniques of measuring them, also a question about ARPES may come up, as a technique for measuring dispersion relations of electrons.

So you got all this simply by reading the OP's question? Honestly? And I'm the one misinterpreting things?

ZapperZ seems to be still in the mental mode of a referee of a paper about electron-phonom interactions. Snap out out of that mode, and read my postings again. Or just let it be. I am not going to waste more time on this.

If I am in that "mental mode", I would have demanded that you supply your points with proper references. Trust me, you do NOT want me in that mode.

All I did was tried to correct something that I know to be wrong based on what I believe you said, even AFTER rereading your posts. If you do not wish to be corrected or if you do not have the time to clarify what you posts, then say so and I'll keep that in mind.

Zz.