## 2 Experimental Section  
### PyC Films Fabrication  
PyC films (see Figure 1) were deposited on 0.5 mm thick quartz substrates by chemical vapor deposition (CVD), described in more detail elsewhere [6,8]. Briefly, the CVD chamber was heated to 700 \({}^{\circ}\)C in hydrogen atmosphere \(\sim\)10 mBar. At the temperature of 700 \({}^{\circ}\)C the hydrogen atmosphere was replaced by CH\({}_{4}\):H\({}_{2}\) gas mixture (the CH\({}_{4}\):H\({}_{2}\) ratio and pressure are shown in Table 1). Next, in order to start the spontaneous methane decomposition, the CVD chamber was heated up to 1100 \({}^{\circ}\)C by rate of 10 \({}^{\circ}\)C/min. The temperature of the chamber was kept in 1100 \({}^{\circ}\)C for five minutes and then cooled down to 700 \({}^{\circ}\)C during 80 min. At the temperature of 700 \({}^{\circ}\)C the CH\({}_{4}\):H\({}_{2}\) gas mixture was replaced by hydrogen. The rest of the cooling was done in hydrogen atmosphere (\(\sim\)10 mBar). It is worth noting that there was no gas flow in the CVD chamber during the deposition process. This allowed us to reduce the gas consumption and also gave more time for polyaromatic hydrocarbon formation and cross linking. However, the change of the temperature during the deposition process was accompanied with change of the pressure in the CVD chamber. After the CVD process both sides of the quartz substrate were covered by the PyC film. In order to characterize the film by microwave measurement, one of the substrate surfaces was cleaned out with the harsh oxygen plasma.  
The homogeneity of samples was controlled by SEM (LEO-1455 Vand, Cambridge, UK). PyC films thickness was measured by a stylus profiler (Dektak 150 Veeco Instruments, Plainview, NY, USA) with accuracy of 1.5 nm and was also controlled by atomic force microscope. The average  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Thickness (nm)**} & \multirow{2}{*}{**CH\({}_{4}\) (mL)**} & \multirow{2}{*}{**H\({}_{2}\) (mL)**} & \multicolumn{2}{c}{**Pressure at**} & \multicolumn{2}{c}{**Pressure at**} & \multirow{2}{*}{**Roughness**} \\  & & & **1100 \({}^{\circ}\)C (mBar)** & & **700 \({}^{\circ}\)C (mBar)** & \\ \hline
9 & 50 & 20 & 22 & 18.0 & 1.08 \\
20 & 75 & 20 & 30 & 24.4 & 1.07 \\
30 & 85 & 20 & 34 & 27.1 & 0.92 \\
75 & 160 & 0 & 53 & 39.0 & 1.25 \\
110 & 180 & 0 & 60 & 45.0 & 1.25 \\ \hline \hline \end{tabular}
\end{table}
Table 1: PyC films synthesis parameters.  
roughness of the films was measured with atomic force microscope (AFM Autoprobe M5, Veeco Instruments, Plainview, NY, USA) for films thinner than 30 nm and atomic force microscope (Solver P47 PRO NT-MDT, St Petersburg, Russia) for thicker films. One can observe from Table 1 that the roughness of the fabricated PyC films shows a weak dependence on the thickness. The average and root-mean-square roughness were 1.1 \(\pm\) 0.2 nm and 1.5 \(\pm\) 0.3 nm, respectively. Raman spectroscopy measurements reported elsewhere [8] revealed that PyC films produced at our experimental conditions are composed of randomly oriented and intertwined graphene flakes with typical size less than 5 nm. The films also consist of small amounts of amorphous carbon and sp\({}^{2}\)-sp\({}^{3}\) bonds.