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Methods of synthesis of multilayers and study of thin film materials

One of the main research interest of the RCMO team is the development of robust and performant methods for the determination of the opto-geometrical parameters of optical thin films from spectrophotometric measurements. This study is critical as this is a mandatory preliminary step before the design of any multilayer structure.

Refractive index determination

Knowing how to accurately determine the optical indices - real part n and imaginary part k - is an indispensable step in our process to realize high performance optical filters. In particular, a stack formula is only valid if the optical indices are known - and repeatable - with an accuracy much better than one percent.

It is also important to recall that the indices of the deposited thin film materials depend on the deposition parameters and technology, and must be regularly re-determined, for example after cleaning the deposition chamber.

The method we used consists in modeling the index according to a theoretical formula, with a validity depending on the nature of the material and the recorded spectral range, we can then optimize an error function between the expected spectral response of a monolayer - or of a Fabry Perot cavity - and the response measured with a PE1050+ spectrophotometer. The parameters to be optimized are those from the model considered for the calculation of the theoretical response.

Among the models developped, we use the Cauchy’s laws, Sellmeier, the Drude models, Tauc Lorenz, Urbach, Forouhi Boomer.

Example of determination in the UV/Vis/NIR range:
 dielectric materials: SiO2, Ta2O5, Nb2O5, TiO2
 semiconductor materials: Si, Sb2S3, SiC
 metals: gold, silver, chromium, aluminium, nickel, copper, titanium

Thin film multilayer synthesis

Thin films stack synthesis consists in determining a theoretical formula that meets a precise specification of spectral or angular (reflection, transmission) template. It is therefore necessary to first determine a template, with tolerances allowed by the user. Then, one needs to find the right sequence, alternation of materials, with the nominal thicknesses allowing our final component in accordance with the template.

Some formulas can be analytical, for example bandpass mirrors, bandpass filters, or monochromatic antireflection.

For more complex problems, a numerical synthesis step is to be added, using local or global mathematical optimization algorithms. In this case, we try to minimize a cost function, the difference between desired and calculated performances.

It is also important to take into account the technological aspect into the problem, since the formulas generated must have characteristics that make them doable with our deposition processes. For this, the optimization can be constrained, for example with minimum and maximum layer thicknesses to be deposited.

Finally, by simulating error distributions on the thicknesses of each layers (specific to the chosen control methods), or even small indices variations, it becomes possible to predict the feasibility of a filter even before its fabrication.

Example of specifications for a bandpass filter (Left) and synthesis of a 150-layer filter whose spectral profile reproduces the profile of the Notre-Dame-de-la-Garde basilica in Marseille (Right)