RF Conductivity of thin Mo film

I am very interested in predicting the RF reflection and transmission (at a frequency of 2.6 GHz) through a thin layer of Molybdenum (Mo)
that may be sputtered onto a 2 mil plastic substrate. The Mo sputtering process will be very slow: over a cumulative time span of several thousand hours the thickness will build up to as much as 500 Angstrom. I'm interested in looking at the RF properties as a function of the thickness of the layer from 0 to 500 Angstrom, and as a function of temperature from 90 to 400 K.
I know how to do the calculation given the value of the conductivity of Mo: for a thin layer of good conductor the metal can be modeled as a sheet resistance R = 1/(sigma*t), where sigma is the conductivity and t is the thickness. For a thicker layer one can use a more rigorous transmission line analogy. However, from browsing the literature, I've seen that the effective conductivity depends on several factors, including temperature, film thickness, and the manner in which the Mo is arranged: single crystal, polycrystalline, or amorphous.
This deposition is going to occur in a vacuum, due to ion bombardment of a molybdenum surface, at temperatures that vary over the range of 90 to 400 K.
I have found a paper (R. C. Hansen and W. T. Pawlewicz, "Effective conductivity and microwave reflectivity of thin metallic films," IEEE Trans. Antennas Propagat., vol 30, no 11, Nov 1982) that shows how to calculate the effective conductivity of a thin metallic layer given the bulk conductivity sigma_0 and the electron mean free path length L (in the bulk metal). The calculation is based on earlier work by Fuchs, Sondheimer, and Campbell. Hansen and Pawlewicz do not provide any comparison with measurements, but state that "this model fits polycrystalline films reasonably well" along with the claim that "most thin films will be polycrystalline." They provide an example calculation for a gold (Au) film, using the values of sigma_0 = 4.1e7 S/m and L = 570 Angstrom, which I assume are both valid at room temperature, approx. 300 K.
My questions:
1. Should I expect the deposited Mo layer to be polycrystalline, so that the Hansen/Pawlewicz formulas are valid? If not, how to proceed?
2. What is the electron mean free path length for Mo? Does this depend on temperature?
3. Is it true that the bulk conductivity of metals is inversely proportional to temperature over my working range (90K to 400K)?
4. Any pointers to other useful books or papers? I have only a minimal undergraduate EE background in solid state theory from 25 years ago!
Thanks very much,
Peter Simon peter underscore simon at ieee dot org (return email address is a spam trap)
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Peter,
I suggest contacting NIST. It sounds like you may need to determine empirically the conductivity of the material. See:
http://www.boulder.nist.gov/div813/emagprop.htm http://www.boulder.nist.gov/div813/rfelec/properties/Pages/publications.html
Grant

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Thanks, Grant, for the useful pointers.
--Peter
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Peter Simon wrote:

Peter,
S parameter measurements? Skin conductance/Impedance? where is your ground plane? What geometry to achieve ? 50 Ohm ? Imoedances.
boerr
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Peter Simon wrote:

> Angstrom.

Are you writing a proposal, or doing design work? I ask because if the former, you have a lot of paper to plow through to find such arcane data. If the latter, you can do some preliminary labwork to narrow things down.

Elsewhere I suggested you provide a cold finger to collect the Mo before it contaminates your radome; why is that unacceptable?

<some possible answers interspersed>

There doesn't seem to be a lot of info about pure Mo films. But
http://msewww.engin.umich.edu/research/groups/yalisove/publications/impurities_in_Mo/sct132124
and similar papers suggest film structure (both mechanical and chemical) is strongly influenced by substrate temperature, trace gas(es) present, and so on, implying the film structure will change as it deposits unless your radome is a very precisely controlled environment.
You may have to build it and collect some data.

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1975PhLA...54..229A
Got a CRC? Plot some graphs.

No, but an aside; Mo goes superconducting at ~.915K, but many of its compounds (what's your ion source?) do so at much higher temperatures. If the radome is exposed to vacuum it may get cold enough that one or more layers of your film is a superconductor; then things get ugly. Why not prevent the deposition in the first place?
Mark L. Fergerson
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Design work. We are planning on measuring the plane wave return loss and insertion loss of some test pieces, but I would like to obtain analytic predictions first.

I apologize. I have never before heard of a "cold finger" and thought that your answer was some kind of jest or sarcastic comment. Could you please enlighten me on this subject?

http://msewww.engin.umich.edu/research/groups/yalisove/publications/impurities_in_Mo/sct132124
Thanks for the reference. I fear that duplicating the space environment, with its hard vacuum, diurnal temperature variations, and very intermittent firing of the plasma thruster for short bursts over several years, may be very difficult to replicate in the lab. But we will do the best we can here.

Great reference! Thanks! How'd you find it?

I only have a very old CRC (1978) here at home, and it doesn't seem to have anything relevant, at least that I can find (it lacks a detailed table of contents <amazing!>)
[snip]

I agree. My job is to help convince the configuration people that the electrical performance of the radome is going to be unacceptably degraded and that they need to do something to remove the source of the contamination. I look forward to your reply with more details about the "cold finger" approach.
--Peter
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Peter Simon wrote:

Right. Is the physical layout absolutely fixed? Can you relocate the radome so it's out of the exhaust plume(s)?

Just a piece of refrigerated metal juxtaposed to catch the hot stuff. But as Unc points out it likely won't help unless the geometry's just right.
This is why I asked for more info on the actual problem; your request was a bit too general.
<snip>

Well, I meant try to duplicate just the conditions of deposition, do a worst-case buildup, and then do your transmissivity tests without worrying about other elements' possible inclusion in the film (due to outgassing etc). All the rest shouldn't have much effect as I can't see vacuum-sintering and annealing altering the film's properties much. But I could be wrong.

I Googled for
Molybdenum +"electron mean free path"
I think it was the third or fourth return.

Hm. Organization was never the CRC's strong suit; I browse mine regularly just for the hell of it otherwise I'd never be able to find anything in it.
Best I can suggest is to look at the Resistivity Table(s) in the Electricity and Magnetism section; mine (the 38th edition, '57-'58) lists only drawn Mo, but gives resistivity at 20C as 5.7 ohm-cm and at 750C as 21.0 ohm-cm. The coefficients at 25C, 100C, and 1000C are in the following table, "Temperature Coefficient Of Resistivity". Convert units as appropriate. How to extrapolate from bulk drawn Mo to films, I have no idea. Unc?

First I'd find out what "unacceptable" means. Is this an Earth-communication antenna? What range, ERP, etc?
Mention to them that _any_ metal on the radome could kill the TWT or whatever the RF source is.
Mark L. Fergerson
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I'm afraid not. The radome covers the feed horn for a very large reflector antenna made of Mo mesh. The thruster plume will hit the reflector and dislodge Mo particles. The feed and radome must be located very precisely wrt the reflector. Various problems arise when considering repositioning the thruster, or deflecting its plume, though the latter may be the best solution so far (but see Uncle Al's suggestion about a sheet of mylar being continously rolled up to remove the contaminants).

My reading (and the post from Joseph D. Warner) lead me to believe that the character of the resulting film is strongly dependent on the temperature and other factors present during the deposition process.

I thought that I had done the same thing, but perhaps without the quotes.

I will check it out.

Range and EIRP are not really relevant here, because the radome is located in close proximity to the feed horn. In this case, "unacceptable" means any of the following: radome return loss less than 20 dB, insertion loss increased by more than 0.1 dB, power dissipated in the contamination layer greater than about 0.5% of incident power density (it's a high-power, transmit feed antenna). My preliminary calculations using the Hansen-Pawlewicz formula show that a thickness of even 10 Angstrom will be unacceptable. However, I have my doubts about their validity when the layer thickness is this small.
Thanks for the inputs, Peter
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Peter Simon wrote:

Ugh. I assume there's an array of thrusters; can they be rearranged such that none of their plumes reach the antenna structure or aren't hot enough to sputter bits off it by the time they do reach it? By rearranged I mean "detaching", rotating, and "reattaching" the entire thruster array so to speak without disturbing the relationship to the craft's C.G. It should "just" be a matter of relocating the thruster attachment points and rewriting some software. Or the thrusters could be boomed out farther if launch volume and weight allow. Are folding booms considered reliable these days?
Failing that Unc's sheet could be fitted over the horn. That way it'd be smaller and lighter than putting it between the thruster and the antenna structure (ISTM that could act as a sail, doing bad things to the thrust vector). The transport mechanism would produce its own spurious reflections though.
OTOH let's back up a step; Mo is fairly refractory. Who determined what the off-sputter rate will be? Was it extrapolated from ground-based industrial stuff, or known from spacecraft experience?

Your "unacceptable" definitions below seem to mean that you could say with some confidence that the merest amount of even pure metal plated onto the radome is an adequate approximation to reality.

Google sees words in quotes as a block and returns documents containing them as a block. Leaving off the quotes gives you everything including any of the words.

I was worrying about power reflected back into the feed guide.

Then you may just have to plate up a few radomes to various thicknesses (corresponding to various aging rates) and see. Your prelim figures (and the lack of available data) ought to justify the time and expense; they would make me sufficiently nervous to want it checked out if I were project management.

You're welcome. Please let us know how it turns out.
Mark L. Fergerson
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Mark Fergerson wrote:

Well, as I recall even in laser ablation of oxides materials in a hard vacuum with a distribution of particles that went as (cos (theata))^10 and with an angle of 45 degrees between the laser beam and the normal of the target I needed to clean the windows every six months. I don't think the thursters have as sharp of distribution of particles as I had; though, I could wrong on that point.
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Joseph.D.Warner wrote:

Ugh again. As project administration I'd definitely want it checked out if for no other reason than CYA (for the next grant cycle).
Now I'm wondering how this has been avoided in previous spacecraft design. Somebody's already done this work.
Mark L. Fergerson
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Mark Fergerson wrote:

Perhaps by not positioning the antenna in the exhaust plume of a rocket motor?
:-)
jk
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Peter Simon wrote: >snip
, or

Look sputtering Mo and the deposit of it on a surface can lead to many different crystalline structures. These structures as you rightly point out depends on temperature, sputtering rates, co-sputtering of the film, the kinetic energy of the clusters and ions hitting the film, the energy and type of ions used to sputter from the target, and the rate of sputtering. The best way I believe to get accurate estimates of the properties you desire is to just make the film in an environment as close as you can to the space environment and then measure the DC resistivity versus temperature and use that in your calculations. Also, remember Mo may oxide over long periods in space do to atomic oxygen. This will change the reflectivity of the film.
Measuring the DC resistivity only requires a closed cycle refrigerator, a temperature controller, dc constant current source, a nanovoltmeter, some connectors, a Si-thermometer. If you want it automated then you need a 486 computer with an IEEE-488 card for controller and limited programming skills.

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