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Fig. 1 Filmstack diagram with reflectance and transmittance

 

Fig. 2 Interference diagram

Our MProbe system measures light reflected and/or transmitted from layer structure in a specified wavelength range. Light reflected from the different interfaces can be in or out of phase, resulting in constructive(adding intensities) or destructive (subtracting intensities) interference i.e. causing intensity oscillation that are characteristic of the thin film structure.

Spectroscopic reflectance measurement, like other optical methods, is indirect: the measurement data need to be analyzed in order to determine the filmstack parameters (thickness, optical constants, surface roughness, etc.) There are two basic approaches that are being used to analyze the data:

  • Curve fitting. Software calculates theoretical reflectance of the stack and parameters are adjusted to achieve best fit to the measured data. The filmstack parameters are inferred from the best fit. This method is, typically, used for thin layers or in cases when information about optical constants and/or surface roughness need to be determined.
  • Fourier transform based. This method is used to determine thickness of the thick layers (> 2um)

Interpretation of the reflection data is fairly intuitive and easy to understand, especially in the case of relatively thick films. Thickness information is, primarily, contained in the frequency of reflectance spectrum oscillations, while optical constants (more accurately – optical contrast i.e. difference between optical constants at the interface) information is contained  in the amplitude of the oscillations.

Fig.3  shows a fit using only thickness – incorrect refractive index (optical contrast) shows in the mismatch of the amplitude of intensity oscillation. The period of the oscillations is having a good match, but in order to determine thickness more accurately, both reflective index and thickness need to be fit together.

 

Fig. 4 shows the results of the fit using both thickness and refractive index. Refractive index, in this case, is represented using Cauchy approximation that works well for polymer materials in the visible and NIR range. Other approximations, like Tauc-Lorentz, Drude, Exciton, effective -media, etc. are used depending on the type of the material.

The corollary is refractive index can be measured very accurately if refractive index of the substrate is known 

Curve Fitting is a very powerful method of data analysis that allows to determine many physical properties of the layers but there are situation where it is not suitable. In many cases, films are not perfect, they have some artifacts like coloring, non-uniformity, residual absorption that are of no interest i.e. does not need to be determined. However, in order to use curve fitting all these artifacts need to be taken into account. This is especially true in cases of the thick films (films >2um). As we discussed earlier, information about film thickness is contained in the period of intensity oscillation.

FFT based method is based on determining only film thickness using intensity oscillation frequency and ignoring all the other properties. Of course, optical constants still need to be supplied in order to get correct results.

FFT based method has several other advantages: 

  • High measurement speed.
  • Low sensitivity to the distance change between the probe and the sample
  • Minimal need for calibration

These advantages makes it a preferred  method for inline measurement in manufacturing environment.

 

Fig.3 Curve fit to measured data using  thickness only ( refractive index is not used in the fit)

 

Fig. 4 Curve fit to measured data using thickness and R.I. (refractive index)

Fig. 5 Measured optical dispersion

Fig. 6 Reflectance spectrum of the coated polymer film.

Results of the FFT analysis of reflectance spectra (Fig. 6) are shown above. Since we have a 2 layers, we see three peaks: total thickness (layer1 +layer 2) – this is strong peak since polymer/air optical contrast is good, layer 1 peak and layer 2 peak. Layer 1 (substrate) peak is weak because of the scattering/non-uniformity in the material but using total thickness and thickness of the top layer (layer 2) we can easily confirm its thickness.

Reflectance spectra of the polymer film on a thick polymer substrate is shown on the Fig. 6. Two oscillation frequencies corresponding to 2 layers are clearly visible in the spectrum. We can also see that polymer substrate has some absorption in the visible range (high frequency disappears there) and the shape of the curve indicates that  yellow/red dye is present in the material.

Results of the FFT analysis of reflectance spectra (Fig. 6) are presented on Fig.7 Since we have a 2 layers, we see three peaks: total thickness (layer1 +layer 2) – this is strong peak since polymer/air optical contrast is good, layer 1 peak and layer 2 peak. Layer 1 (substrate) peak is weak because of the scattering/non-uniformity in the material but using total thickness and thickness of the top layer (layer 2) we can easily confirm its thickness.

It must be noted that intensity oscillation/fringes are present only in reflectance spectra of relatively thick films (at least >100nm thick). Reflectance spectra of very thin films has no any fringes but, using curve fitting, one can still determine the thickness.

One monolayer (1.3nm) polymer film thickness is determined using curve fitting of the model to measured data. Measurement sensitivity of better than 1nm using spectroscopic reflectance is readily demonstrated.

Download a more detailed  explanation of the thick film measurement below. 

MProbe Thick Film Measurement
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