Thetametrisis - Technology: White Light Reflectance Spectroscopy

The White Light Reflectance Spectroscopy (WLRS) methodology resembles SWI but involves, instead of a laser (single wavelength), a UV, VIS or NIR light source and a PC-driven miniaturized spectrometer, in the coresponded spectra range, instead of a photodetector (fig. 1). The white light coming out from the light source is guided to a reflectance optical probe through the fiber a1-a6 (fig. 1a) guiding the white light onto the sample under investigation. The typical sample consists of a stack of transparent and semi-transparent films over an appropriate reflective or transmitting substrate (e.g. Si wafer, glass slide). At the same time the reflectance foptical probe collects the reflected beam (through th fiber b, fig. 1a), directing it to the spectrometer. The beam from the light source interacts with the sample (fig. 1b) and produces a reflectance signal, in the incident light spectrum range, which is continuously recorded, from the spectrometer

Figure 1: Typical WLRS set up. (a) detail of the configuration of Reflection Probe, (b) detail of the light optical path through a two layer sample

The total reflection coefficient for a k-layer sample, can be calculated by various models. In our case the Abeles approach was followed where the effective Fresnel coefficient for the k-1 layer is:

where ρ is the amplitude and Δ the phase. From this set of equations the reflectance from any k-th layer can be calculated. In the particular case of the present study i.e. two transparent layers between the substrate and the environment the total energy can be written as:

where ni is the refractive index of the ith layer (i=0 for air, 1 for the first film, 2 for the second film and 3 for the substrate, in the case of suspending films stack the n3 correspond to air), and di of the ith layer and λ the corresponding wavelength. The light propagation at the various interfaces is illustrated in fig. 2. A typical reflectance spectrum for a two transparent layer on the case of Si substrate is illustrated in fig. 3. In the same figure it is also illustrated the incident (reference) white light spectrum in the VIS-NIR range. The number and the shape of interference fringes depends of the thickness and the refractive index of the measurements films stack. The fitting of the experimental spectrum with the above equation is performed by using the Levenberg-Marquardt algorithm. The refractive indexes ni of all layers vs. wavelength are calculated with a spectroscopic ellipsometer and fitted to a three parameter (A, B, C) Cauchy model. By applying eq. 2.2 for all wavelengths in the desirable spectrum range, the film thickness may be calculated for each recorded spectrum. The fitting can be applied to more than one film thickness, or reversely for known thickness can be applied to calculate the refractive index, or a combination of film thickness and refractive index. The increment of the calculated parameters must be done with care, because it is also increased the results inaccuracy.


Figure 2: Light propagation schematic in a stack consisting of two layers (1, 2) on the substrate (3), and a media (0) above the films stack (e.g. air or water).	Figure 3: Reflectance (interference) spectrum of a two layer stack (PHEMA/SiO2) over Si and the incident (reference) white light spectrum

Figure 4 shows a screen shot of the FR-Monitor with the Reference and Reflected spectrum as acquired from a double layer Si3N4/SiO2 films stack over Si substrate. In Figure 5 illustrated the Reflectance (normalized 0-100%) spectrum of the previous films stack after the fitting spectrum (red line) as calculated the thickness of Si3N4 and SiO2 layers (138.4nm and 577.3nm respectively).


Figure 4. Screenshot of FR-Monitor with the acquired spectrum of the Si3N4/SiO2/Si stack and the incident (reference) spectrum.	Figure 5. The normalized (0-100%) reflectance spectrum of the figure 4, after the fitting of the thickness of Si3N4 and SiO2 layers (red line). The normalized value is greater than 100% at 740nm, due to the positive interference.