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Band gaps between metals and insulators

  1. May 19, 2009 #1
    This seems like almost too much of an elementary question, but what properties of metals / insulators cause their bandgaps to differ?
  2. jcsd
  3. May 19, 2009 #2
    Hi there,

    I am not an expert in solid state physics, and have little souvenirs of my classes, but I see two answer to your question: 1. very simply the type of atom will make the difference.

    2. I guess that was to simple of an answer. Let's try something more detailed (please bare with me and correct me if I am wrong), electrons orbit next to a nucleus. From the Coulomb interactions, electrons are electrically attracted by the protons of the nucleus. But (and this is where it gets interesting), electrons repulse each other from the atoms. Therefore, the electrons on the valence band have a "screening" effect created by the electrons on inner shell, which binds them more weakly to the atom. Depending on this screening effect, an electron will get closer (energy wise) to the conduction band.

    Hope this was right. Cheers
  4. May 19, 2009 #3
    Thanks for the reply. I am familiar with the screening effect of inner electrons and effective nuclear charge experienced by the outer electrons as a result. So the difference between a metal and an insulator would be that a metal atoms outer electrons are bound more weakly than those of an insulator due to screening effects. This makes sense but i can't seem to move this explanation into a proper quantum mechanical argument of why the gap between the two bands of allowed states is present in insulators and not in metals.
  5. May 19, 2009 #4
    Hi there,

    I don't think I understand your problem quite well. What is:
  6. May 19, 2009 #5
    The periodic coulombic potential from the regular array of atoms in a crystal lattice causes the electron wavefunctions to split into two 'bands' of allowed energy states. The bands are just a range of energies where the density of states is large and the bandgap is the energy difference between these two bands of allowed energies.
    I dont know how much quantum mechanics knowledge to assume in explaining it and i am far from an expert (im an undergrad) so i appologise if i cant communicate it very well.
    Thanks for the continued interst :)
  7. May 19, 2009 #6
    Hi there,

    For me, it has been a long time that I have reviewed solid state physics, but I believe you are talking about two different things.

    The gap between the valence band and the conduction band has (to my knowledge) nothing to do with the wavefunctions of electrons. The energy gap simply explains the energy necessary to extract an electron from the valence band. The electron wavefunction explains behaviour of electrons as a wave-like particle.

  8. May 19, 2009 #7


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    Actually, the wavefunction does affect the band structure. In band structure calculation, such overlap of wavefuction will produce these band-structure calculations.

    One can also see this in, say, the Bloch wavefuction with periodic boundary conditions. That alone is sufficient to show the formation of "gaps" in the bands.

  9. May 19, 2009 #8
    I have a new q,perhaps it may solve the problem,
    suppose the electronic sturcture of a solid that represents a two dimensional square lattice of divalent atoms can be discribed using nearly free electronmodel withaweak potentialsuchthat U<<h^2/4M(Pi^2)*(Pi/a)^2
    where a=lattice parameter
    is this solid a metal, an insulator or a semi conductor? why?
  10. May 19, 2009 #9
    Im not sure what hafsa is saying exactly, but in response to ZzapperZs reply the bloch theorem just shows us that a periodic potential causes the separation of energy levels into bands. But a metal is a crystal structure with a periodic potential so why does band theory say that there is not energy gap in a metal?
  11. May 19, 2009 #10


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    Remember, I was trying to illustrate that these bands, and the formation of gaps, can be derived using the wavefunction.

    Whether it is a metal or not depends on the available charge density within each band, i.e. is the band fully occupied, or if it isn't. This too depends on how the valence band wavefunction overlaps. In solid state physics, we often use the tight-binding band structure to calculate such overlaps.

    So yes, it DOES depend intrinsically on the wavefunction. It doesn't mean that we always use it all the time or that it is solvable, but it is always the underlying description.

  12. May 20, 2009 #11
    according to the periodic chart atoms with larger nuclei or with fewer valence electrons tend to be metals. also metals tend to be much denser.
  13. May 20, 2009 #12
    hi granpa,
    what about my question?if elements valence shell contains 2electrons then?
  14. May 20, 2009 #13
    I believe i have got to the bottom of this. It is about how many electrons there are in the primitive cell of the lattice. If there is an even number (due to the two spins an electron can have) then there are no empty states to allow electron movement and we have an insulator. If there is an odd number then there is an empty state that facilitates electron movement and we have a metal. This excludes the more complicated case of semimetals. I believe this is what ZzapperZ was refering to when he discussed band occupancy.
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