I want to know that how can we calculate the combined (one line graph) refractive index of multilayer thin films of different materials?
If I understand the question correctly, the effective medium approximation (Bruggeman's model )could be applied.
https://en.wikipedia.org/wiki/Effective_medium_approximations
To determine the band gap values of polycrystalline Si and Ge single layers as well as of Si/Ge multilayer structures the valence band (VB) photoemission supported by ultraviolet–visible–near infrared spectroscopy techniques were used.
In this case if your sample is semitransparent you can make a Tauc plot from an absorbance spectrum. This gives you OPTICAL band gap of each layer. If your samples aren't transparent you can use Difuse Reflectance Spectroscopy, then convert your data using Kubelka-Munk ecuation to get absortivity vs wavelength. After that, you can make Tauc plot from your data.
Dear Syed,
your question is very complex and it seems me difficult to answer it generally. I try an answer in three steps. The expression "thin film" (thickness d) is to discuss in relation to the wavelength lambda.
- d > lambda
Here, the Fresnels equations can be applied. For layers and parcels of films, the reflection and transmission coefficients can be calculated. This allows to define an effective refractive index as an average for all layers. Classical electrodynamics determines the behaviour of films.
- d compares with lambda
In this case, interferences must be considered. Amplification and extinctions of light determine the transmission.
- d < lambda
Here, quantum mechanics must be taken into account. If you have a multilayer system, the interaction of the layers behaves like a new material. Lets assume, you have a periodic arrangement of different films. This creates a so called superlattice with new additional energy subbands.
Generally, the effective n or gap can be measured by optical measurements (reflection, transmission and absorption). This gives a first input into the macroscopic properties of the layered system. Calculations require the exact knowledge of wavelength, filmthicknesses and material combination.
With Regard
R. Mitdank
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