There is no relation whatsoever as long as the material properties do not change with the thickness.

See following references:

http://www.perkinelmer.com/lab-solutions/resources/docs/APP_Thin-films.pdf

 https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-14-24-11885&id=119191

 https://www.degruyter.com/downloadpdf/j/phys.2008.6.issue-2/s11534-008-0035-z/s11534-008-0035-z.pdf

 I agree with Thomas: in principle, thickness and refractive index are 2 independent parameters.

However, if the structure of the layer is not homogeneous, you may end up with a variation of the refractive index with thickness.  Also, some films have a different growth regime when they are very thin, inducing a variation of the refractive index with thickness (it happens with many metals for example).

I agree with both answers, generally, there is no relation between thickness and refractive index, but usually for thin films a dependence of refractive index on thickness is observed. From my experience with thin films I can summarize that refractive index increases with thickness reaching seady state values around 40-50 nm.

Many thanks to all of you.

Hmm! II think t’s not that simple and straightforward.

Of course, if the film density is PERFECTLY homogenous throughout it thickness (which is NEVER the case, experimentally I mean), then, the two parameters are indeed not correlated. However, films thickness (dependent of the deposition methods) generally impacts the material density (variation of the mechanical properties as a function of the thickness), which in turns impacts the material density and hence the refractive index. We have already observed a clear variation of a TCO' RI as a function of its thickness.

Brahim Aïssa Ok, then let's come back to the original question: what is the relation of thin film thickness and refractive index?

I think as the question was formulated, it aimed at a fundamental relation assuming a perfectly homogeneous layer.

Thank you Thomas Mayerhöfer , yes this obvious clarification was already included in my answer.

I am quite agree with Daniel Poitras

I agree with poitars: in principle, thickness and refractive index are 2 independent parameters.

However, if the structure of the layer is not homogeneous, you may end up with a variation of the refractive index with thickness. Also, some films have a different growth regime when they are very thin, inducing a variation of the refractive index with thickness (it happens with many metals for example).

if you learn the structure zone diagram, you will find the how the microstructure change with the temperature of the substrate and the working pressure and the porosity of the thin film will change also with the thickness and the microstructure and if you apply the effective medium theory you find that the refractive index change with the porosity of the film and the porosity of the film change with the thickness