for measurements of RI multiple interference is required.
and for measurements of extinction coefficient (k) we can use the eqn:
k = (2.303 λ log (1/T)) / 4πd
where λ is wavelength
T is transmittance and
d is thickness of the film
Hi Raghu, I know that for RI calculation multiple interference is needed, but I'm not getting any interference fringes in my spectra.
Refractive index is in general a function of frequency, although in some cases (e.g. dielectrics) it can be almost constant for a wide range of frequencies.
There are two approaches to find the refractive index from R and T data:
Having the thickness of your layers and the refractive index of your substrate, you can write the equations for R and T of your substrate/epilayer system using transfer matrix method and set it equal to the measured values for each frequency (each measured point). In this way you have two equations and two unknowns (real and imaginary part of the refractive index) for each point.
Another approach is to assume a proper frequency dependent complex function for the refractive index of your epilayer (this function is called dielectric function) and calculate R (or T) using the transfer matrix method and then try to fit the calculated R spectra to the measured one and find the parameters of the dielectric function using a curve fitting algorithm. In this way in theory you don't need to have the refractive index of the substrate and the thickness of the layers, because you can fit them simultaneously together with the dielectric function of the epilayer; but having the exact values for all these parameters before the fitting will help you to have a more accurate and easier fitting process.
In both cases you do not need the interference fringes to do the job.
If you have access to an ellipsometer, you can easily use it to find the refractive index of your epilayer. In fact ellipsometer does the same fitting procedure as mentioned above automatically.
We have done the same thing for semiconductor epilayer/substrate systems in one of our recent publications:
M. E. Aryaee Panah, L. Han, K. Norrman, N. Pryds, A. Nadtochiy, A. E. Zhukov, A. V. Lavrinenko, and E. S. Semenova “Mid-IR optical properties of silicon doped InP,” Optical Materials Express 7(7), 2260-2271 (2017).
In this case we did not use an ellipsometer and did all the fitting procedure using the R data and a custom made curve fitting program.
The better way to calculate n and k is ellipsometer with high accuracy...
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