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Anomalous skin effect in metallic conductors

Discussion in 'General Electronics' started by pervect, Aug 21, 2003.

  1. pervect

    pervect Guest

    I'm looking for some basic information on this effect. Specifically, I'm
    wondering whether it increases or decreases the penetration of appropriately
    high frequency EM radiation in thin conducting metal films?

    I'm fairly sure it does one or the other from what little information I do
  2. pervect

    pervect Guest

    Thinness of the conductor isn't the issue in the effect I'm interested in.

    See for example

    where they work out an example for copper, where they conclude that the
    classical skin depth formula is good up to about 400ghz.

    However, it isn't clear to me at all what happens above this critical
    frequency. You obviously have to at a minumum modify the classical skin
    effect formula, but it's not clear what happens physically.
  3. The link says it: the frequency a getting close to the relaxation rate,
    which means that the AC conductivity becomes frequency dependent.

    Read about the Drude model of conductivity:
  4. The 1/tau at the website is porportional to the plasma frequency.
    You should ask them to derive their formula. They are using the mass of
    the atom in their calculations. I strongly believe it is the effective
    mass of the electron in these metals that should be used. Otherwise
    copper would be transparent for visible light. They are only off by few
    thousand in their estimate of tau.

    Think of what their tau means. It should mean, it is how fast can the
    electron respond a change in the electric field, ie. how fast can it
    move. If the electron can't respond to a changing electric field then it
    cannot absorb the energy from the electric field. It just sits there and
    becomes transparent to the radiation. All material eventually becomes
    nearly transparent to high frequency radiation like x-ray, and gamma rays.
    Above that frequency the material will begin to be transparent. It is a
    slow roll off in the absorptivity of the material with increasing
    frequency. But as I said I think their Fmax is wrong by several a factor
    of several thousands.
  5. pervect

    pervect Guest

    Another website provided by another poster works out the same number for
    tau - so if it's an error, it's in more than one place. OTOH your argument
    does make some sense to me. So overall I'm still not sure what to believe.

    pointed me to

    (which was extremely helpful to me in understanding what was going on here).
    Working out tau as d, the mean free path, divided by the fermi velocity vf,
    gives the same answer the first website gave, tau = 2.5e-14 sec, which
    corresponds to f=1/tau = 40 Thz or 7500nm, about a tenth the frequency of
    visible light.

    But you may be right - I seem to recall that the rate of change of momentum
    with velocity is not equal to the bare electron mass in a crystal latice
    (but this was from some old semiconductor courses, I don't know if metals
    have a regular enough crystal structure for this analysis to be applied
  6. Well, the reference given by Pieter Kuiper is right. The first site you
    sited has something wrong and it is not the problem of the mass. I just
    lighted on the mass because that gave the order of magnitude they were
    off by. One of their problem is converting from Hz to GHz. If you are in
    contact with the people who put up the site then you might point out the
    site given by Peter and their problem with going from Hz to GHz.

    1 GHz = 10E9 Hz

    BTW. I think it is a coincidence their value is close to that given in
    the Web page that Peter gave you.
  7. pervect

    pervect Guest

    I looked more closely at the first web site, and apparently what they did is
    sneakily divide by 100. The factor of 100 is there in the formula, but the
    rationale for including it is not explicitly mentioned in the text.

    I noticed this when I noticed that 400Ghz was not 1/tau, but .01 of 1/tau.

    I would presume that their motivation is to say that the classical skin
    effect formula applies with good accuracy when the frequency is less than
    ..01 of the cutoff, but they were not very clear. This lack of clarity is
    ultimately what prompted my question to the newsgroup, because I'd never
    heard of this particular effect before, and the website's explanation and
    what I could dig up with Google wasn't particularly helpful to me in
    understanding it.
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