Experimetal Facilities - SOPRA Broadband Spectroscopic Ellipsometer

Instrumentation
The Sopra GES 5 spectroscopic ellipsometer allows for variable-angle broadband spectroscopic ellipsometry. It covers a spectral range from 230 nm to 20 microns using three different detectors: a photomultiplier detector for the UV/Visible spectrum from 230 nm to 880 nm, an InGaAs detector in the Near Infra-Red spectrum from 880 nm to 2050 nm and a MCT-A (HgCdTe) detector in the Infra-Red spectrum from 1.9 microns to 20 microns Photomultiplier detectors are known to require high-voltage power supplies and to exhibit non-linearities and polarization sensitivity. Semiconductor photodiodes have significant advantages in that they are very linear over a broad range of intensity levels and reasonable sensitive over a broad spectral range. A calibration procedure is employed to measure the nonlinearity and polarization sensitivity of the different detectors and to compensate for these effects during measurements. The UV/Visible/NIR source is a Xenon lamp whose maximum of intensity is located at 450 nm. Two attenuators are available corresponding to an attenuation of 17 % and 7 % respectively and the system can be set to automatically remove them during a measurement when the intensity is very low in order to improve the signal to noise ratio. Our configuration in the UV-Visible-NIR spectrum is rotating polarizer - fixed analyzer ellipsometry. When the polarizer rotates, the incident beam is linearly polarized with a direction that rotates in time. After reflection on the sample, the light is elliptically polarized with its axis rotating in time. After the analyzer, the light is again linearly polarized with a fixed direction and a time dependent amplitude. The advantage of this technique is that the measurement is not affected by the polarization sensitivity of the detector (fixed polarization) but it requires a perfectly randomly polarized incident beam. Using a monochromator, the intensity of the signal at each wavelength is measured in time and Fourier transformed to determine the ellipsometric parameters. The beam size is typically between 1 mm² and 10 mm ² depending on the aperture. To achieve small spot sizes, the probing light can be first focused and then recollimated after reflection on the sample, resulting in a spot size around 0.05 mm ². However, the use of focusing lenses can be the source of systematic errors: the beam has no longer a unique angle of incidence but rather hits the sample with a range of angles (this can be taken into account in the regression analysis) and the focusing lenses can induce a change of the beam polarization. This error usually translates in an overestimate of the absorption and then of the k values. The minimal angle that can be achieved is 8 degrees (12 degrees with focusing lenses).

Analysis
The ellipsometric parameters are fitted using the Levenberg-Marquardt regression method. Different models are available to describe the dispersion relation of the refractive index of the measured materials including the Gaussian and Lorentz oscillator models, the Cauchy and Sellmeir laws, the Kramers-Kronig relations, the Forouhi interband model, the model dielectric function, the Drude model... Point to point calculation (i.e. calculation of the n and k values from the data at each wavelength for a single layer of known thickness) is also possible. In addition, whenever the sample is bulk or can be treated as such because of its strong absorption, the dispersion relation is simply obtained by direct calculation of n and k at all wavelengths without any assumption. 

Reference
W. A. M. Harland G. Tompkins, Spectroscopic Ellipsometry and Reflectometry - A user's guide , John Wiley & Sons, Inc., 1999.

Spectroscopic ellispometry tutorial