# Anomalous skin effect in metallic conductors

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

1. ### pervectGuest

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
have.

2. ### pervectGuest

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

See for example

http://unitmath.com/um/p/Examples/PulsedPower/SkinDepth.html

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. ### Pieter KuiperGuest

The link says it: the frequency a getting close to the relaxation rate,
which means that the AC conductivity becomes frequency dependent.

<http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html>.

4. ### Joseph.D.WarnerGuest

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. ### pervectGuest

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

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html

(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
correctly).

6. ### Joseph.D.WarnerGuest

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. ### pervectGuest

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.