Re: RF Conductivity of thin Mo film

Peter Simon wrote:
> 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.

  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.

> 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.

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

> 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:

<some possible answers interspersed>

> 1. Should I expect the deposited Mo layer to be polycrystalline, so
> that the Hansen/Pawlewicz formulas are valid?  If not, how to proceed?

  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.

> 2. What is the electron mean free path length for Mo?  Does this
> depend on temperature?

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1975PhLA...54..229A

> 3. Is it true that the bulk conductivity of metals is inversely
> proportional to temperature over my working range (90K to 400K)?

  Got a CRC? Plot some graphs.

> 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!

  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