## 3 Results and Discussion  
X-ray diffraction studies show no detectable influence of proton irradiation (Figure 1). The diffractograms are identical before and after irradiation. The assignment of peaks was carried out based on the ICDD card #00-001-0929 for ITO and #00-005-0664 for AZO. ITO has the structure of the In\({}_{2}\)O\({}_{3}\) cubic Ia3 space group no. 206, and AZO has the structure of the ZnO hexagonal system group P63 mc no. 186. Microscopic observations presented in Figure 2 showed that the films were homogeneous. On the surface of the AZO, there were some precipitates with an increased amount of Zn, as measured using energy dispersive spectroscopy (Figure 2a). The sample after irradiation also exhibited these elements, as well as other impurities (Figure 2b). ITO before and after irradiation had some impurities on the surface whose nature and amount did not change after irradiation. It was possible to observe these samples with higher magnification,  
Figure 1: X-ray diffractograms of ITO and AZO thin films before and after proton irradiation. which is presented in the insets of Figure 2c,d. ITO films have grains that are hundreds of nanometres in size. The transmittance of transparent conductive oxides is a crucial property for these materials. For all samples, the transmittance is above 80% for all measured wavelengths. AZO transmittance decreased after irradiation in the 400 to 630 nm range (Figure 3a). ITO transmittance was slightly reduced throughout the measured range (Figure 3b). The fitting of ellipsometric data to a dielectric function model was performed with CompleteEASE 6.71 software from [PERSON]. To create a model for ITO, two Tauc  
Figure 3: Transmittance measured with a UV-VIS spectrophotometer of (**a**) AZO and (**b**) ITO before and after proton irradiation. Figure 2: Scanning electron microscopy images of samples (**a**) AZO, (**b**) AZO:H+, (**c**) ITO, and (**d**) ITO:H+. Lorentz oscillators, one Gaussian oscillator, and the Drude function were used. For AZO, the same functions were used, but with only one Tauc-Lorentz oscillator. Equations (1)-(8) define these functions. * Tauc-Lorentz oscillator [22]: \[\epsilon_{T-L}(E)=\epsilon_{1}-i\epsilon_{2},\] (1) \[\epsilon_{2}=\left[\frac{Amp\ E_{0}\ Br\left(E-E_{g}\right)^{2}}{\left(E^{2}- E_{0}^{2}\right)^{2}+Br^{2}E^{2}}\cdot\frac{1}{E}\right],\ E>E_{g},\] (2) \[\epsilon_{2}=0,\ E\leq E_{g},\] (3) \[\epsilon_{1}=\frac{2}{\pi}P\int_{E_{g}}^{\infty}\frac{\zeta^{\prime}\epsilon_ {2}(\zeta)}{\zeta^{2}-E^{2}}d\zeta,\] (4) where \(\epsilon_{1}\)--real part of dielectric function, \(\epsilon_{2}\)--imaginary part of dielectric function, \(E_{g}\)--energy band gap, \(E\)--photon energy, \(E_{0}\)--peak central energy, \(Amp\)--amplitude, \(Br\)--broadening, and \(P\)--Cauchy principal value. * Gaussian oscillator [22]: \[\epsilon_{Gaussian}(E)=Amp\Big{(}\Gamma\big{(}Z^{-}\big{)}+\Gamma\big{(}Z^{+} \big{)}+i\Big{[}\exp\Big{(}-\big{(}Z^{-}\big{)}^{2}\Big{)}-\exp\Big{(}-\big{(} Z^{+}\big{)}^{2}\Big{)}\Big{]}\Big{)},\] (5) where \(\Gamma\) is a convergence series that produces a Kramers-Kronig relation consistent shape of the dielectric function, and \(Z^{+}\) and \(Z^{-}\) are equivalent to Gaussian \"Z-values\": \[Z^{+}=\frac{E+E_{0}}{\sigma_{n}}\ \ \ Z^{-}=\frac{E-E_{0}}{\sigma_{n}},\] (6) \(\sigma_{n}\) is equivalent to the Gaussian standard deviation. \[\sigma_{n}=\frac{Br}{2\sqrt{ln2}},\] (7)
* Drude oscillator [22]: Figure 3:0 (8) where \(\rho\) is resistivity and \(\tau\) is scattering time. Figure 4 shows maps of the total thickness calculated for the samples from the ellipsometry measurements. The models are multilayered, with three layers used in the case of both materials. The number of layers was decided on based on knowledge of the samples and by optimizing this number during the data fitting process.