Temperature coefficient of resistance - size effects vs bulk

[Hyo X]

I am looking for a reference to discuss the effects of resistor size on alpha, the temperature coefficient of resistivity.
If we use the linear R=R0*(1+alpha*(T-T0))
alpha is a material constant, presumably for bulk-type resistors. Will alpha change as size (cross sectional area) of the resistor shrinks to tens of nanometers in one dimension? any reference on this? thanks

 

[Baluncore]

Alpha is a material constant that is independent of the dimensions.

 

[Hyo X]

Alpha is a material constant that is independent of the dimensions.

I concluded something different, based on literature.

http://iopscience.iop.org/1347-4065/9/11/1326there is also the fuchs-sondheimer theory but i don't think it dicusses alpha

 

[Baluncore]

I cannot access that article because it is behind a pay-wall.

The abstract refers to resistivity as being determined by surface roughness in thin films. I would interpret that as a “virtual thickness” parameter, not as a change in the bulk material resistivity.

Although the abstract mentions the temp-co was also studied, it reveals no temp-co effect due to thickness. That might suggest that there was no significant effect on alpha observed.

 

[Hyo X]

I can't attest to the quality of the article but it has the suggestion that alpha may have some dependence on the physical dimensions of the sample.

I think a difference in the effect of surfaces and grains on the scattering of electrons and scattering or localization of phonons could conceivably contribute to changes in alpha as a function of surface:volume ratio or some other size parameter.

for completeness, from the article
Here h is the amplitude of oscilations describing the surface roughness and lambda is the mean-free-path of electrons.

if you are really interested in the article let me know and i can send you a dropbox link or something