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Quantum tunneling

  1. May 8, 2003 #1
    What is quantum tunneling?
     
  2. jcsd
  3. May 8, 2003 #2

    drag

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    Greetings !
    The square of the Wave Function of a particle
    discribes the probability of finding a
    particle in certain points in space.
    This probability(theoreticly) is never
    0 anywhere.

    According to Heisenberg's Uncertainty Principle
    the mommentum/location, time/energy of a
    particle are never known exactly. This also
    means that for a sufficiently short time period
    a particle can gain a lot of energy provided
    it is "returned" afterwards.

    Now, if you consider a certain particle
    somewhere it is theoreticly possible according
    to the HUP that for a short enough time
    period it will gain a sufficient amount of
    energy to overcome the potential energy barrier
    between different points in space and end
    up at that other point.

    Qunatum tunneling is limmited by the speed
    of light above the Plack scale that is the
    limmit of possible certainty/uncertainty.
    It is usefull in electronics when electrons
    can tunnel "over" a potential difference.

    Live long and prosper.
     
  4. May 8, 2003 #3
    Also, all chemical and nuclear reactions (including life as a consequence of chemical reactions) are results of tunneling.

    As well as most properties of solids are the result of tunneling (of electrons away from their hosting atoms).
     
    Last edited by a moderator: May 8, 2003
  5. May 9, 2003 #4
    So it's not just something that can happen, it actually does happen. . How common is it?
     
  6. May 9, 2003 #5
    Twist two wires together and hook up a voltage potential across them. The electron has to tunnel through the barrier of the air that exists between the twisted together wires.
     
  7. May 9, 2003 #6

    chroot

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    Mmm.. no.. sorry. This is not quantum tunneling!

    Quantum tunneling happens all the time -- it is the reason the Sun is able to produce energy. Without the tunneling mechanism, much higher temperatures would be required in the Sun's core -- but the Sun would not be massive enough to generate those temperatures.

    Normal electrical circuits do not involve tunneling, but there are a variety of specialized devices that do -- for example, the aptly named 'tunnel diode.'

    In addition, we use quantum tunneling in electron microscopy. :)

    - Warren
     
  8. May 9, 2003 #7
    All semiconductors and most poor conducting metals conduct current due to tunneling (atom-to-atom jump of electron from time to time).
     
  9. May 9, 2003 #8

    chroot

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    I'm sorry, that's incorrect. The electrons have enough thermal energy to cross the energy barrier. There is no tunneling in normal semiconductors or poor conductors.

    - Warren
     
  10. May 9, 2003 #9

    marcus

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    chroot I'm impressed
    you understand all these cases: electrons in semiconductors, or crossing a gap between wires, protons overcoming resistance to fusion at lower than expected temperature, and so forth.

    Could you give me a rule that I can apply so as to be able to distinguish cases of true tunneling?
     
  11. May 9, 2003 #10

    chroot

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    Find the height of the energy barrier. Determine whether or not the interaction is classically possible. If it's not classically possible, but yet still occurs, it's quantum tunneling. :)

    - Warren
     
  12. May 10, 2003 #11
    Copper oxide can easily have an energy barrier of >10 eV. An electron with less than this will not cross the barrier classically.
     
  13. May 10, 2003 #12

    drag

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    Fascinating !
    Could you, please, put an approxiamte number
    on the scale of the difference made by q.t.
    in this case ?
    Thanks !

    Live long and prosper.
     
  14. May 10, 2003 #13

    chroot

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    Perhaps you should do a little more research. I'd love to see some references.

    (Psst: there's no quantum tunneling going on here.)

    - Warren
     
  15. May 10, 2003 #14

    marcus

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    Warren I am guessing you hold the high cards here.
    In QTM, quantum tunneling microscopy, there is a gap between
    the probe and the surface being probed.

    Current flows across this gap. I forget easily----what is the size of this gap (1) as distance and (2) as energy barrier?

    Then the question is, what size voltage is applied to the probe relative to the sample so that current flows. This voltage will---according to the criterion you gave---be lower than the barrier voltage. Because actual tunneling happens.

    I'm sure you know the figures here because I believe microscopy is one area where you are working or at least know a lot. So please fill out the details for me rather than my having to slog thru a websearch. Interesting thread and not too hard.
     
  16. May 10, 2003 #15

    Incorrect. Explain, how 0.025 eV electron (room temperature) can jump even 0.1 eV gap between atoms without tunneling (and usually gaps in poor conductors are even higher, say 0.8 eV in Si).
     
  17. May 10, 2003 #16

    chroot

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    Since when did ALL the electrons have only 0.025 eV of energy? I thought we were talking about THERMAL energy, which is a DISTRIBUTION.

    Futhermore, the gaps you speak of in semiconductors are between the valence and conduction bands -- and guess what? The electrons are generally considered to be free-moving once they have been promoted to the conduction band.

    The electrons are able to get into the conduction band solely due to their thermal energy. The distribution of occupation of quantum states is given by the Fermi-Dirac integral, and approximated by the Boltzmann distribution. There is no "quantum tunneling" between the valence and conduction bands, I'm sorry.

    The "Fermi energy" is the level of the highest state occupied by any electron when the semiconductor is at absolute zero. At any temperature above absolute zero, some electrons are naturally in states higher than the Fermi energy -- all due to our good ol' friend translational kinetic energy -- or heat.

    I am using as a reference the book "Semiconductor Physics & Devices" by Neamen. Perhaps you should give me your references?

    - Warren
     
  18. May 11, 2003 #17
    Alexander doesn't need a reference, guaranteed.

    The time independent schroedinger equation is
    d2phi /dx2= ((2m(U-E))/hbar2) phi (x)

    Since d2/dx2e(+-alpha x)= alpha2 e(+- alpha x)
    ,

    alpha = (2m(U-E))1/2/hbar
    where m = mass of particle, U = energy barrier, E= particle energy
    penetration depth = 1/ alpha

    So when U > E, tunneling must happen. the Transmission coefficient that can quantify the energy of the particles that tunneled is dependant upon the distance between the materials as well.
     
    Last edited: May 11, 2003
  19. May 11, 2003 #18

    chroot

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    Uh.. yeah, thanks -- I understand tunneling... however, it doesn't happen in the situations listed here. :)

    - Warren
     
  20. May 11, 2003 #19

    marcus

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    I mentioned the Quantum Tunneling Microscope (QTM) in my last post. Does it happen in that situation?

    One would assume it does due to the name.

    And if so how does your criterion apply to prove it does.
    Presumably there is a small gap between the probe and the sample and the energy barrier represented by this gap can be
    estimated back-of-envelope style in a couple of minutes or less
    by someone familiar with today's microscopes. I apologize if
    I am mistaken---ignore this request if it is any real difficulty.

    Also I liked your example of the core of the sun. I happen to know the temp is 15 million kelvin which is 1300 eV. So protons are bumping each other with energy of several thousand eevee and you are telling me the barrier to their sticking to each other is much higher than that. What is the number that the proton-proton fusion chain has to tunnel thru---since you say that their thermal 1300 eV is not enough?

    Would very much like some more concrete examples.
     
  21. May 11, 2003 #20
    You do? then you understand that U > E, tunneling happens. Feynman used the twisted wire situation as an example of tunneling.
     
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