Solid State - Band gap?

  1. Might be an easy question (or not).

    What determines the band gap of an element? As far as I know, silicon is the most efficient single-element semiconductor because of it's small (but nonzero) bandgap. Next (as far as I know) is Selenium. I'm aware there are more efficient compounds, but that's outside the scope of the question anyway.

    So what about the element is responsible for band gap size? What could you change (theoretically) if creating a new element (I said theoretically!) that would reduce band gap size? More electrons per first valence band? Or per conduction band? Is this restricted by other forces?
     
  2. jcsd
  3. DrDu

    DrDu 4,095
    Science Advisor

    What do you mean with "efficient"?
     
  4. Sorry, I'm not the most well versed in physics. I was under the impression that the smaller band gap of silicon made it a "better" semiconductor (ie better suited for computing) at room temperature at earth's atmospheric pressure, be that through bonding properties or otherwise. Maybe you can fill in a few gaps?
     
    Last edited: Dec 2, 2011
  5. To clarify..

    Consider a semiconductor with a relatively "small" band gap. Electrons require less energy to "move", correct? So if you had an element with a band gap significantly smaller than that of silicon, it would require less voltage to move the same electrons, and thus less energy is needed for the same computing power? Am I correct so far?

    This is what I had meant by efficient.
     
  6. DrDu

    DrDu 4,095
    Science Advisor

    The energy electrons require to move in a homogeneous does not depend directly on the band gap. In integrated circuits what is more important is the resistivity of pn junctions in field effect transistors. I don't understand this very well, but probably other factors like the dielectric constant etc are as important as the band gap.

    Btw. Germanium has a lower band gap than Si and is therefore used often in transistors or diodes which shall work at low voltage.
     
  7. The band gap of an element is determined mainly by the fermi energy level of the element, which is a purely quantum mechanical consideration... this parameter is the one who have to vary to get better electric conductivity in semiconductors. There is an equation for determining the band gap (I'll put the one in wikipedia since I don't have a book with me right now where I can check it but I guess it's correct):

    http://es.wikipedia.org/wiki/Banda_prohibida#La_ecuaci.C3.B3n_de_la_banda_prohibida

    where kB is the Boltzmann constant, εk is the kinetic energy over the fermi energy level and V is the interaction potential between the cooper pair of electrons
     
  8. DrDu

    DrDu 4,095
    Science Advisor

    From the wikipedia page you were citing:
    "La banda prohibida superconductora Δ, a veces conocida como gap superconductor, a pesar de su nombre, no está relacionada con la banda prohibida de semiconductores"

    Obviously, also the band gap in semiconductors can be calculated. However there is no simple formula but you have to do quite demanding quantum mechanical calculations on a computer.
     
  9. First of all, the bandgap of a certain material is not constant. It depends on temperature. The Varshni empirical model does a pretty good job of modeling the temperature dependence. The bandgap also depends on alloy concentration; by adding a small amount of another material, e.g. Aluminum to Gallium Arsenide, you can tailor the bandgap to a desired size.

    Secondly, the bandgap changes from material to material and is a function of the atomic structure of the constituent atoms as well as the nature of the crystal bonding. For instance, graphite and diamond are both made of pure carbon crystals, but they have vastly different bandgaps. The band gap is the difference in energy between the bottom of the conduction band and the top of the valance band. The prediction of band structures of solids using quantum theory is very complex and is its own field of study.
     
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