Calculation of thin film thickness from complex refractive index

[Paritosh1985]

Hello,

I want to ask how can one calculate the thickness of a thin film (or each of the thin films in a stack of 3-4 thin films on one another) when

- complex refractive index of each thin film is known (n and k). This refractive index is obtained from a single wavelength ellipsometer and not a spectroscopic ellipsometer
- approximate spectral reflectance/transmission of each layer is known (measured with some spectrometers available in the market)

In short, I want to predit the physical thickness of a thin film based on n, k and spectral tendency

The spectral tendency is a general one and I know approximately where in the spectrum is the absorption band for each of these thin layers.

thank you very much for reply.

Regards,

Paritosh

 

[eljose79]

Hello Paritosh,

Thank you for your question. Calculating the thickness of a thin film can be done using a few different methods, depending on the information you have available. In your case, it seems that you have the complex refractive index (n and k) and the approximate spectral reflectance/transmission of each layer. With this information, you can use the following equations to estimate the thickness of each thin film in your stack:

1. Using the Fabry-Perot equation: This equation relates the thickness of a thin film to its refractive index, the wavelength of light, and the spectral reflectance/transmission. It assumes that the film is transparent and has a uniform thickness. The equation is as follows:

t = (m*λ)/(4*n), where t is the thickness of the film, m is the number of interference fringes observed in the reflectance/transmission spectrum, λ is the wavelength of light, and n is the refractive index of the film.

2. Using the Cauchy equation: This equation is based on the Cauchy dispersion formula and relates the refractive index of a material to its wavelength-dependent refractive index. The equation is as follows:

n(λ) = A + (B/λ^2) + (C/λ^4), where n is the refractive index, λ is the wavelength of light, and A, B, and C are constants that depend on the material. By fitting this equation to your measured refractive index values, you can determine the constants and use them to estimate the thickness of the film.

3. Using ellipsometry: Since you have obtained the refractive index values from an ellipsometer, you can also use this instrument to measure the thickness of the thin film. Ellipsometry measures the change in polarization of light reflected from a sample, which is affected by the thickness and optical properties of the film. By analyzing the ellipsometric data, you can extract the thickness of the film.

I hope this helps. Please note that these methods provide estimates of the thickness and may not be accurate for all types of thin films. It is always best to validate the results with other techniques such as microscopy or profilometry. Additionally, the spectral tendency you mentioned can also be used to refine the thickness calculation, but it may require more advanced modeling techniques. I recommend consulting with a thin film expert or using specialized software for this purpose.


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