With the MProbe, it is possible to accurately measure almost any translucent film with a thickness between 1 nm and 1 mm, making it an appropriate tool for the majority of thin film applications.
The system’s data can be analyzed through two distinct approaches, namely model/curve fitting, or Fast Fourier Transform (FFT) analysis on the captured spectrum. Model fitting is typically applied for thinner films (between 1 nm and 1 µm in width), while FFT is used for films with a thickness greater than 20 µm.
In the range between these two extremes (thickness of 1 µm to 20 µm), either approach can be applied, with experimental requirements determining the preferred method.
Figure 1. Data analysis method depending on the thickness range.
The FFT approach has minimal calibration requirements, with results unaffected by variations in intensity. The analysis can be carried out rapidly, and with very little existing information required on the sample. For these reasons, the Fast Fourier Transform method is often preferred, but it does have its drawbacks.
To use the FFT method, it is necessary to know the refractive index (R.I) information of the materials, and, until recently, FFT has been unable to match the accuracy offered by the curve fitting method. Thanks to recent additions to Semiconsoft’s TFCompanion software, now with an enhanced decomposition algorithm, FFT has seen great improvements in this area and can now offer accuracy better than 0.01%.
Thickness Range of the Practical FFT Use
FFT makes use of periodicity of interference between the wavelength and intensity, a phenomenon known as interference fringes. The material’s R.I. and the wavelength range of the measurement define the minimum thickness of a film, which can be measured with precision using FFT.
The reason for this is that sampling just one period, or a portion of a period’s function, as would take place with very thin films, provides lowquality FFT data. Table 1 shows the measurement error and the thicknesses of FFT methods for varying wavelength ranges.
Table 1. FFT measurement errors.
Thickness/
Wavelength range 

200
nm 
500
nm 
700
nm 
1,000
nm 
4001,000 nm 
Error(absolute value) 
92 nm 
36 nm 
6 nm 
0.6 nm 
Error (%) 
46% 
7% 
0.9% 
0.06% 
4001,700 nm 
Error (absolute value) 
49 nm 
2 nm 
1.2 nm 
0.4 nm 
Error (%) 
24% 
0.4% 
0.017% 
0.04% 
An FFT method was applied to study simulated reflectance spectra for oxide films with thicknesses of 200 nm, 500 nm, 700 nm and 1,000 nm, and the absolute and relative measurement errors were calculated. Spectra were then calculated for the measurement ranges 400 – 1,700 nm and 400 – 1,000 nm.
Figure 1. Simulated reflectance spectrum (wavelength range: 4001,000 nm) of the SiO_{2}/Si. Oxide thicknesses: 200 nm, 500 nm, 700 nm and 1,000 nm (Oxide thickness corresponding to one period in visible range is ~ 320 nm).
Figure 2. Thickness of the 200 nm oxide determined using FFT (4001,000 nm wavelength measurement range). A large thickness measurement error (92 nm) shows that FFT maybe not practical for this thickness.
Figure 3. Thickness of the 1000 nm oxide determined using FFT (4001,000 nm wavelength measurement range). A very small measurement error (0.6 nm) shows that FFT can be used successfully for this thickness.
Applications of FFT Analysis
Analyzing Multilayer Polymer Films
Multilayer Polymer Films have a broad range of applications, being utilized in a variety of ‘everyday’ products, such as stickers and food packaging.
This example details the analysis of a 4layer polymer film, used as a sticker. The film has a structure of separator/silicon/adhesive/PET (substrate). The silicon layer is a thin film, with a thickness less than 1 µm, which allows protective separator layer to be peeled off smoothly and expose adhesive.
Figure 4. Reflectance spectrum measured with MProbeVisHR (700 nm 1,000 nm wavelength range). Sample 1 is a 4 layer polymer web (sticker).
Figure 5. FFT decomposition data analysis of the data (Fig. 4). Position of the peaks indicate the thickness of the layers.
Carrying out an FFT analysis results in a peak for every interface pair. These also correlate to layers in the multilayer film. The position of the peak indicates the thickness of the layer, while the height of the peak can help to explicate information on the quality of the interface.
As each interface is given a peak, a stack with three layers should result in an FFT spectrum with six peaks, with the final peak linked to the overall thickness of the stack. An example of this can be seen in Figure 5.
In Figure 5, the silicon layer (peak 3*) has too low a thickness (less than 1 µm) to be identified alone, and is instead joined with the separator + adhesive, and the separator layers. The silicon layer’s low thickness means that the overall thickness peak (peak 6) is also wider.
Figure 6. Reflectance spectrum measured with MProbeVisHR (700 nm – 1,000 nm wavelength range). Sample 2 is a 4 layer polymer web (sticker). Sample 2 has the same structure as Sample 1 but, in this case, the thicknesses of the Separator and PET (Substrate) layers are similar.
Figure 7. FFT decomposition data analysis of the data (Fig. 6).
TFCompanion software permits researchers to automatically identify each peak and match them to the layers with which they correspond. Where both the structure of the film being measured and the approximate thicknesses of each layer are known, it is easier for the software to correctly identify each layer.
Where these details have not been made available, it is often possible to extrapolate the information from the FFT data before inputting back into the model.
The FET decomposition spectrum, with all layers other than silicon shown, can be seen in Figure 5. In instances where a film is not thick enough, layers can be obscured by other peaks, or the peak may not be high enough to identify.
Deconvolution of the FFT data from Sample 2 (as illustrated in Figure 7) does not display Layer 3 directly, but the impact of this layer can be detected in the widening of Layer 1’s peak.
While it would be possible to deconvolute the peak of L1 to determine the thickness of L3, a more workable route to obtaining this figure is to use the information provided on the overall thickness and the thickness of L1 and L2.
Figure 8 indicates how the software’s various thickness options can be used to determine the missing thickness of a layer, such as L3, from the total thickness.
Figure 8. Setting differential thickness option to determine thickness of the “hidden” layer/interface from the total thickness. Noise level setting helps separate Layer thickness data from the noise.
Measuring an Alumina (Sapphire) Layer
Thick layers such as alumina, yttrium oxide and parylene each have a refractive index which is greatly reliant on the deposition conditions of the layers. As the R.I. can vary between samples, using data from a library or other optical properties databases together with the FFT method can result in flawed data.
Figure 9. Reflectance of Alumina on glass measured with MProbe UVVisSR system (wavelength range: 200 nm 1,000 nm).
Figure 10. FFT decomposition of the data on Fig. 8. using library Alumina material properties. The peak position indicates the thickness of 1,164 nm.
When an FFT method is used to compare the library data model against measured data, it can be seen that the R.I value provided in the library data is inaccurate.
Figure 11. Direct comparison of the FFT results model (red) and measured data (blue) shows that R.I. is not correct.
Figure 12. Direct fit of the model to measured data to determine the thickness and R.I. of alumina. Thickness 1,202 nm.
Figure 13. Alumina R.I. determine from the measurement (yellow) and library alumina R.I. (red).
Measuring Hard Coatings
Hard coatings are a vital element of countless systems, for example, the polycarbonate surfaces used in automotive lighting covers and eyeglass lenses. When a hard coating is deposited on a surface, it diffuses into polycarbonate substrate, an Inter Penetration Layer (IPL) which is comparatively thin (approx. 1 μm).
When measuring hard coatings for QC, it is key to measure the thickness of both the hard coating layer and the IPL.
Figure 14. Reflectance spectra of polycarbon with hardcoat sample (headlight). Measurement is taken with MProbe Vis system (wavelength range: 4001,000 nm).
Figure 15. FFT decomposition of the measurement data (Fig. 14). A differential thickness option is activated and IPL is determined from total thickness. Hard coat: 5.2 μm, IPL: 1.85 μm.
The IPL layer displays a refractive index which is between the R.I. values of the hard coating and the polycarbonate layer, indicating a weak optical contrast between the two distinct materials.
This means that the IPL peak is very weak. However, it is possible to circumvent this issue by running a differential IPL thickness measurement (from the total thickness) to offer more precise results.
Improving the Accuracy of FFT Analysis
Where an FFT method is applied, the total accuracy of the thickness measurement relies on precisely locating the peak position. The error of this measurement can be given using the equation: (X_{n+1}X_{n})/2, where, as in Figure 1, X_{n }and X_{n+1 }are points either side of the peak.
Figure 16. FFT points resolution. Distance between adjacent FFT points (bins) determines maximum error.
The TFCompanion software offers numerous options to increase the accuracy of the analysis, including:
 Interpolating between data points
 Fit a Gaussian function to the peak to define the position
 Increasing the number of data points
 Filter the data (apodization) – this indirectly improves accuracy by removing aliases and additional peaks, and is particularly useful for noisy data
The alternative methods below are used with TFCompanion for the measurement of a polymer film.
Figure 17. Measured reflectance spectrum of coating (~ 18 µm) on 38 µm PET.
Interpolating Between Points and Applying a Gaussian Fit
TFCompanion allows for three distinct modes of accuracy:
 Maximum accuracy – A full Gaussian curve is fitted to the peak
 High accuracy – Interpolation between the points using a Gaussian model
 Default – No fitting or interpolation
Figure 18. Selecting accuracy level.
Increasing the Number of Data Points
The data points from FFT analysis are spread over the greatest range of the thickness measurement for which data can be collected. Nonetheless, in the majority of cases, only a portion of this range is of importance to the researcher. For example, in this example, the sample thicknesses are just 18 µm and 38 µm, whereas the thickness range of measurement is 280 µm.
A method known as oversampling can be applied to increase the number of data points in the thickness range of interest.
Figure 19. Peaks using default resolution (1).
Figure 20.Resolution improvement by using increased number of FFT points. 1 is default resolution, 5 – maximum resolution .
Figure 21.Peak detail from fig. 20 (default resolution  1) .
Figure 22. Peaks using high resolution (4).
Figure 23. Peak detail from Fig. 20 (high resolution  4).
Resolution 
1 
2 
3 
4 
Maximum possible error (µm) 
0.548 
0.274 
0.137 
0.068 
Filtering the Data (Apodization)
Figure 24. Apodization filter selection.
Figure 25. Peak without data apodization/ Two aliases are visible.
Figure 26. Peak with data apodization (peak is the same as on Fig. 25).
Figure 27. Reflectance spectrum of GaN on sapphire (4001000 nm wavelength range)
Figure 28. Measurement of GaN (fig. 27) without data apodization.
Figure 29. Measurement of GaN (Fig. 27) with data apodization.
This information has been sourced, reviewed and adapted from materials provided by SemiconSoft.
For more information on this source, please visit SemiconSoft.