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)

Peter Simon wrote:
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Are you interested in the amount of Mo deposited and then RF properties, or something else? Why not have a naked quartz oscillator crystal in there and track the change of resonant frequency with increasing mass? It's a commercial system. Do your RF measurements concurrently, already knowing the film thickness to excellent accuracy
Google quartz "deposition monitor" 172 hits "deposition monitor" 416 hits
The only no-no is that quartz undergoes a solid state twinning transition at 573 C. Don't go above 500 C at the crystal.
-- Uncle Al http://www.mazepath.com/uncleal/qz.pdf http://www.mazepath.com/uncleal/eotvos.htm (Do something naughty to physics)

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I don't wish to measure the amount of Mo deposited. I am attempting to predict the amount of RF performance degradation to expect over the life of a spacecraft mission due to undesired Mo sputtering. My calculations will help to determine the maximum tolerable Mo layer thickness, and will be used as inputs into the decision as to what, if anything, needs to be done about the undesired sputtering.
Thanks, Peter

Peter Simon wrote:
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The plastic substrate is an RF window and you're concerned with attenuation? Provide a cold finger between the source and the window.
What's the actual exercise? What restrictions do you have?
Mark L. Fergerson

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Yes, I want to predict the transmission through a radome coated with the Mo, for the purpose of determining the severity of the potential problem. I'm quite comfortable with the electromagnetic (EM) calculations involved. What I don't have ready access to are the physical properties of the Mo, such as the electron mean free path length, and its dependence on temperature. I thought that I might get some answers or at least pointers to sources while I'm off work over this long weekend. Please see my original post for the specific questions whose answers I seek.
Thanks,
Peter

Peter Simon wrote:
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0) Looks to Uncle Al like you want to measure the amount of Mo deposited/time, either way. 1) If it is low earth orbit, will you get erosion as volatile MoO3 or (non-volatile) Mo suboxides from local energetic oxygen atoms? 2) An Mo surface rubbed with diamond dust rapidly forms an Mo carbide layer (distinct color change). Is that protective? 3) Will an Mo surface rubbed with silicon dust form a protective Mo silicide layer? That oxidizes to an adherent layer of amorphous silica. 4) If you implant both C and Si...
An engineer's first goal is to determine the real problem. After that, one pursues real solutions. Given NASA's proven inablilty to properly unfurl an antenna (Ulyssess and Hubble), a little window fouling would demand a low tech solution. NASA is institutionally incapable of handling high tech.

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

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

Peter Simon wrote:
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> Angstrom.
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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.
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Elsewhere I suggested you provide a cold finger to collect the Mo before it contaminates your radome; why is that unacceptable?
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<some possible answers interspersed>
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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.
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http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1975PhLA...54..229A
Got a CRC? Plot some graphs.
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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.
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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?
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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.
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Great reference! Thanks! How'd you find it?
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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!>)
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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

Peter Simon wrote: [snip]
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A cold finger or other cryopanel trap is irrelevant. If the mean free path of the Mo atoms in hard vacuum is larger than the physical separation of components, the foulng simply flies in straight lines and connects. A gas curtain won't work for the associated thrust.
The simple (riiight) solution is to have a film periodically pulled across betwen the source and the deposition target. The crud deposits on the film and is moved away; the aperture stays clean. Mylar is fragile in a bunch of ways, but poly(ethylene naphthalate) is much better and Kapton much better still. Now you can sweat the MTBF of the film and its transport mechanism.
Will a strongly divergent magnetic field sufficiently steer the errant atoms? Pointed or grooved Fe-Nd-B magnets are reasonably cheap. [snip]

Uncle Al wrote:
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Right. Now that we know the setup, that's obvious.
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Sounds like a Real Estate problem now (Location^3). Move the damn radome.
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Somebody else gets to handle the crud, eh?
Mark L. Fergerson

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Yes, I discussed this with some of our people who are working the problem and they said the cold finger isn't practical for this situlation for your stated reason and for several other reasons.
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That's a very interesting suggestion, which I will transmit to my coworkers.
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I am told that they expect the Mo particles to be neutral, so the idea of using static electric or magnetic fields had to be abandoned.
Thanks for the constructive thoughts, Peter

Peter Simon wrote:
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When you need research in the worst way possible - Uncle Al's way.
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http://www.dupont.com/kapton / Kapton HN ought to do it. http://www.dupont.com/kapton/products/H-38497-1.html
http://www.scpscience.com/products/XRF/thinfilm.asp http://www.cshyde.com/Films.htm Long rolls of thin films are off the shelf.
<http://www.grc.nasa.gov/WWW/RT2000/5000/5480dever.html <http://techreports.larc.nasa.gov/ltrs/refer/1996/LDEF/TrayF9.html <http://techreports.larc.nasa.gov/ltrs/PDF/2003/cr/NASA-2003-cr212422.pdf Kapton survives a lot of grief in orbit, but it isn't immortal.
Think about 6-8 micron (0.3 mil) Kapton HN. It should survive to 300+ C, though it will be eroded by atomic oxygen. Just about everything else is eaten by 100 C. Kapton doesn't like alkali. U2 cameras were beautiful examples of long roll (more than a mile) precision thin film handling.

Uncle Al wrote:
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Al, this is the same technique several people used in laser ablation of superconductors to keep the windows clean of deposits from the plume from the target material. So commercial vacuum manufacturers have made this already and seems like it only needs to be scaled up to meet his needs.

Peter Simon wrote:
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Right. Is the physical layout absolutely fixed? Can you relocate the radome so it's out of the exhaust plume(s)?
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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.
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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.
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I Googled for
Molybdenum +"electron mean free path"
I think it was the third or fourth return.
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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?
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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).
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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.
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I thought that I had done the same thing, but perhaps without the quotes.
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I will check it out.
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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

Peter Simon wrote:
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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?
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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.
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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.
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I was worrying about power reflected back into the feed guide.
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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.
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You're welcome. Please let us know how it turns out.
Mark L. Fergerson

Mark Fergerson wrote:
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Bad idea. Never drive a bung into the broad end of a funnel. Placed before the horn the protective moved sheet intercepts all sorts of grief that is irrlevant to the radome - and it must be of large area. What about badness that comes in through the sides of the mesh horn? Placed before the radome the film only intercepts that which is objectionable, and its area is much smaller. The mesh horn itself protects the film from energetic nastiness. What little Mo sputters of after all that sturm und drang is intecepted by the film.
When impedence or reflectance grows too large, the film is transported one frame to afford a clean aperture again. Nobody is going to assign an extra five kilos to keep the radome clean. The answer will be of small mass, small size, and high reliablility. Mylar is cheap, Kapton is survivable. KISS, as we say on the production floor.