18 years ago
(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
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.
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
Thanks very much,
peter underscore simon at ieee dot org
(return email address is a spam trap)