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Hall effect

  1. Oct 18, 2012 #1
    Look at the picture... Here current is flowing through a semiconductor... First think about holes... The holes will pile up on the upside... But if you think about electrons then the electrons also pile up on the upside... What's wrong here?

    Is it wrong because it is more appropriate to think of current as positive holes moving rather than negative electrons(I read that)... However,then how to think of flowing of holes???
     

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  3. Oct 18, 2012 #2

    ZapperZ

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    I'm confused.

    Are you not aware that in a semiconductor, you CAN have positive holes as the majority charge carrier?

    In a normal conductor, this doesn't occur. You only have mobile electrons as the charge carrier, even though, by convention, current is the flow of positive charges. This is different than a semiconductor where you DO have an actual flow of positive charges represented by these mobile holes.

    Zz.
     
  4. Oct 18, 2012 #3
    In case what you call "normal conductor" means a metal, they can and do conduct by holes. Half of all metals have positive charge carriers, including the most common metals.
     
  5. Oct 18, 2012 #4
    You are absolutely right. In Hall effect, holes and electrons go in the same direction.

    In fact, Hall effect is THE primary measurement - and nearly the only one - to tell that conduction is made by positive or negative charge carriers. The sign of the Hall voltage changes with the charge sign of the carriers, which means that all carriers deviate to the same direction. This is very uncommon outside the Hall effect.

    Not willing to make things even more obscure, but... Well, it's a complicated subject anyway.

    If someone imagines holes as lacks of normal electrons, he's wrong. Normal electrons would deviate to the usual direction for electrons, and then holes would deviate to the opposite direction, which is NOT experimentally observed. Holes DO deviate as positive particles do. This is because is such materials, electrons have a negative mass hence deviate to the abnormal direction. Then, introducing the holes is really useful, because holes have a positive mass there and behave normally.

    Even more: in half of all metals, conduction occurs through holes rather than electrons, which only means that the mobile electrons (the ones near the Fermi level) have a negative mass. In metals, there are so many states available to the electrons that one couldn't possibly say "nearly full, just a few vacant places called holes".

    In a metal, there are huge amounts of electrons, of holes, even more available states, and we choose between electrons and holes just from the positive or negative mass of electrons, to think with a charge carrier of positive mass hence sound behaviour.
     
  6. Oct 18, 2012 #5
    All metals conduct by free electrons, not holes.
    You need to look into band structure of metals and semiconductors to find out about 'holes' and 'electrons'
    'Holes' play no part in conduction in metals
     
  7. Oct 19, 2012 #6
    Thank you very much for your answers...

    Enthalpy, its nice to hear that there's an explanation even if I don't understand that... Could you make some points elaborate please?

    What is negative mass?

    Could you explain Fermi level?


    And ZapperZ
    What you said is written in my book too... But I fail to explain hall effect for this event by that knowledge...
     
  8. Oct 19, 2012 #7
    Enthalpy left out the vital word effective.

    Free electrons in a solid (and therefore crystal or metal lattice) interact with the lattice.
    Because of this interaction the response of these electrons is not the same to external forces as it would be if they were totally free outside the lattice.

    To allow for this the term 'effective mass' was coined. The effective mass obeys Newton's laws for external forces ie external force x effective mass = acceleration.

    The effective mass can be positive or negative and is negative.
    Holes also possess an effective mass.
    It is usually given the symbol m*.

    The effective mass of an electron in

    Copper is +1.01m
    Aluminium +0.97m
    Nickel +28m
    Platinum +13m

    Where m is the mass of the electron
     
    Last edited: Oct 19, 2012
  9. Oct 19, 2012 #8
    You should distinguish better what you know from what you ignore.
    This is important for your learning, as well as for your readers on the forum.
     
  10. Oct 19, 2012 #9
    I do it on purpose, because mass has no other use than acceleration and gravity which are the same. Since the so-called "effective" mass defines acceleration it's simply mass.
     
  11. Oct 19, 2012 #10
    Well I disagree, as do the figures (provided by Beiser).

    This explanation is not too difficult, if you skip to the negative mass slides.

    www.ece.neu.edu/edsnu/mcgruer/class/.../Effective_Mass_0801.ppt [Broken]
     
    Last edited by a moderator: May 6, 2017
  12. Oct 19, 2012 #11

    ZapperZ

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    This is clearly wrong.

    The effective mass in metals reflects the "renormalized" self-interactions within Landau's Fermi Liquid theory. It has nothing to do with just being an affect of "acceleration and gravity", because such interactions are non-existent in the standard Hamiltonian of materials! When was the last time you see gravity in the Hamiltonian for a metal or a semiconductor?

    I still want to see the band structure of a metal in which holes are the charge carriers here.

    Zz.
     
  13. Oct 20, 2012 #12
    Well its good to know that this thing has an explanation... And electrons act abnormally to magnetic force because of their negative mass or effective mass...

    Isn't the mass supposed to be negative here?
     
  14. Oct 20, 2012 #13
    I mean the m is positive and u are multiplying with a positive number... How will you get a negative mass then?
     
  15. Oct 20, 2012 #14
    It is the holes that have negative effective mass.
     
  16. Oct 21, 2012 #15
    Holes are going to a direction as if it had positive charge... It is the electron which is behaving weirdly... Then how come holes having 'negative effective mass' fit here? And Enthalpy said it's the electron which has the negative mass...
     
  17. Oct 21, 2012 #16
    Electrons can have a negative mass due to the effect of the lattice. This corresponds to the curvature of the band, or the energy-to-wavenumber relationship.

    This happens with about half of all metals as well, not only semiconductors. Aluminium is a well-known example.
    http://courses.washington.edu/phys431/hall_effect/hall_effect.pdf
    p6: "For metals, the exact value of the... sign of the Hall coefficient depend on the energy band structure of the particular metal."
    p10: "In the case of the aluminum sample, you will find in such texts as Kittel's 'Introduction to
    Solid State Physics' that the assumed charge carriers are '1-hole per atom'."

    With just nearly-full valence bands, we could go on thinking with electrons, BUT this would give the wrong sign for the Hall voltage.

    This is why people (not just I... This is the usual practice) introduce holes when the electrons mass is negative, including in metals, because then, holes have a positive mass and they, as opposed to electrons, behave as normal particles would do in vacuum, including giving the Hall voltage with the experimentally observed sign.
     
  18. Oct 21, 2012 #17
    No, the electrons, when people introduce the notion of holes.
     
  19. Oct 21, 2012 #18

    ZapperZ

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    You need to learn how "effective mass" is define. It is the 2nd derivative of the dispersion curve. It means that the curvature of the dispersion matters, and if it changes, then the "sign" on the effective mass changes.

    Zz.
     
  20. Oct 21, 2012 #19
    I dare to claim that mass does have to do with acceleration.

    And please feel free to introduce gravity in a Hamiltonian each and every time you're interested in gravity's effects, that is, when you don't want to neglect it.
     
  21. Oct 21, 2012 #20

    ZapperZ

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    I introduce BOTH "gravity and acceleration" because that is part of what you wrote. It is to emphasize that gravitational effects are irrelevant in practically ALL of condensed matter phenomena. Your "invitation" to introduce such a thing is meaningless. Where, for example, is gravity needed in the Hamiltonian for superconductivity? Does the exclusion of gravity affects the accurate description of this phenomenon? What about the description of the band structure of a semiconductor? Where is gravity needed here?

    Zz.
     
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