If the film is porous, you can do in a standard volumetric adsorption equipment; just be sure that you are loading around a few square meters of sample for this. For example, you can analyze a microporous sample which is only 100 m2/g using only 15 mg, that is, only loading 1.5 m2 in the equipment and still get some meaningful data for analysis.

If sample is non porous, of course it is much more difficult to measure, but still possible by other means, try a quartz crystal microbalance, for example.

You may want to refer to a similar question about using krypton as an adsorbing gas for surface area measurements:

https://www.researchgate.net/post/Why_does_Krypton_work_better_than_N2_or_Ar_for_BET_surface_area_measurement_of_porous_thin_films

I agree with Fernando. That depends on whether the sample is porous or not.

Does the result of the measure change with the size of the measuring stick? For atomic-scale rough surfaces the result is yes. What I mean is that if you measure the surface area with nitrogen and you measure the surface area with krypton, you will get different results. This is so because the smaller the probe species is, the more able it will be to creep into small crevices of the surface, providing a more uniform coverage. 

This refers to Mandelbrot's celebrated question 'How long is the coast of Britain?', and leads us to the realm of fractals. David Avnir and collaborators addressed this question in the 80's, applied to BET measurings, and came up with the fractal dimensions of many solids, from almost flat ones (df ~ 2, like Aerosil spherules), to the most intricate (df ~ 3, like carbon black and silica gel). You might want to check their seminal work.

Regards.

https://www.researchgate.net/profile/David_Avnir?_sg=EcW3M7vBkoXeaRFGGq5t9%2BYCzYz%2B7TCQ3oe74hi%2FbyRPnboOHmgDiV1kI6rpmOzQKAG6J9FY3BwJieoxsxD2EQ%3D%3D

Not impossible, but quite difficult. If the film is non-porous, its surface will be very low, so you'll need to fill as much as possible the measurement cell, for being able to measure several m2 (i.e. more than the uncertainty of the apparatus itself !). In this condition, it is indeed better to use Kr than N2 (see the thread provided above by David Jensen, and especially the anwser of Vanessa Fierro there). Otherwise, if micro/mesoporosity is present, N2 should work, but again, accurate results will be obtained with as much material as possible.

Alain

Tthe BET surface areas of porous thin films could be Determined using surface acoustic wave devices.

You may refer to patent # US4,947,677 (SAW DETERMINATION OF URFACE AREA OF THIN FILMS)

But, as discussed above, in this case porosity is very important parameter. Therefore it would be very helpful to figure out whether your sample is porous or not. For measuring film’s density the XRR method can be used. Note, the maximum measurable thickness for XRR is 300nm.

Maybe some ironed surface studies for AFM could help you. But I'm afraid that all this techniques could bring you some rough analysis. Best regards