2.3.2. Spectroscopic Ellipsometry Experiments

A phase modulated spectroscopic ellipsometer (UVISEL 2, Horiba JobinYvon, Longjumeau Cedex, France) was used to characterize the change over time in the refractive index, *n*, the extinction coefficient, *k*, and the thickness, *d*, of the TEOS and TEOS-LTL films as a function of the incident wavelength. The phase modulated ellipsometer, which contains a Xenon light source, shows higher acquisition speed compared to, for example, null ellipsometer and rotating parts ellipsometer, because of the presence of the photoelastic modulator (PEM) with modulation frequency of 50 kHz. The modulator induces temporal change in polarization state of the light thus eliminating the need of rotating polarizer, analyser and compensator.

A specially designed cell was used in the study to enable measurements in liquid environment. In the first measurement step, the sample was placed in the cell and a measurement was taken in air. Then, without disturbing the sample, the solution of Cu2<sup>+</sup> with particular concentration (0, 2 or 4 mM) was added and the measurements were taken after 90, 500 and 1000 s.

The temporal resolution of a specific scientific instrument is provided by the manufacturer and it is given for a single wavelength. However, the specific measurement time is determined by other parameters. For these measurements, scans were performed over the wavelength range 320–800 nm using a 5 nm increment. The increment was chosen based on the estimated thickness of the sample. The time integration interval was set to 200 ms, so that an optimum signal to noise ratio was achieved, taking into account the reflectivity of the sample. Thus, the time required for a single scan at these measurement conditions was larger than 19.2 s, since some time is required to record the data at a particular wavelength and to carry out the next measurement.

For the determination of the optical constants, a four media model was implemented: silicon substrate, the studied film, a thin (1–3 nm) surface layer that contains 50% voids and water. The top layer was used for modelling the surface roughness of the studied film and its thickness is one of the parameters that was calculated. In spectroscopic ellipsometry for the determination of optical constants (*n* and *k*), the so-called dispersion models were used. They relate *n* and *k* with wavelength through different dispersion parameters that usually have physical meaning. In our case, we used the one-oscillator Lorentz model where the complex dielectric constant, ε, is described as:

$$\varepsilon = \varepsilon\_{\text{ov}} + \frac{(\varepsilon\_{\text{s}} - \varepsilon\_{\text{ov}})\omega\_{\text{t}}^{2}}{\omega\_{\text{t}}^{2} - \omega^{2} + i\Gamma\_{o}\omega} \tag{4}$$

where ε<sup>∞</sup> is the high frequency dielectric constant, ε*<sup>s</sup>* gives the value of the static dielectric constant at a zero frequency of light, ω is the frequency of light (in eV), ω*<sup>t</sup>* (in eV) is the resonant frequency of the oscillator, whose energy corresponds to the absorption peak and Γ<sup>o</sup> (in eV) is the broadening of the oscillator also known as damping factor. The relation between *n*, *k* and ε is:

$$
\varepsilon\_I = n^2 - k^2 \tag{5}
$$

$$
\varepsilon\_i = 2nk\tag{6}
$$

where ε*<sup>r</sup>* and ε*<sup>i</sup>* are the real and imaginary parts of ε, respectively.
