Re: RF Conductivity of thin Mo film

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


"Peter Simon" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> 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)