## 2 Results and Discussion
A very similar activation energy (E\({}_{\rm a}\) = 0.3 eV) has been found in carbon-based materials by [PERSON] et al., who investigated hopping transport between graphitic islands separated by a lower conducting sp\({}^{3}\) carbon layer [72]. In regime III (Figure 8), the carbon concentration was above the percolation threshold for samples prepared at 1600 \({}^{\circ}\)C. Thus, the electrical transport was considered to be dominated by the continuous, three-dimensional carbon sp\({}^{2}\) network, yielding activation energies in the range of E\({}_{\rm a}\) from 0.035 to 0.02 eV, which is in excellent agreement with the conduction energies found in glassy carbon [73]. The transition from semiconducting to semi-metallic conduction is accompanied by the reduction of the gap between carbon \(\pi\) and \(\pi^{\rm e}\) band states. Carbon essentially controlled the density of states, whereas the SiOC states were of minor importance within regime III (Figure 8). Hence, the same transport mechanism (i.e., as in regime III, Figure 8) was assumed to prevail for all samples above the percolation threshold. The electrical behavior of the SiOC/C samples investigated in the present study could be correlated with their Raman data. Upon assuming that the width of the band gap depends on the concentration of carbon precipitations cf. E\({}_{\rm a}=\frac{2.1}{\rm L_{a}}\) for carbon-based semiconductors [74] and E\({}_{\rm a}=\frac{7.7}{\rm L_{a}}\) for graphitic-like materials [75], the activation energy E\({}_{\rm a}\) may be estimated with the help of the L\({}_{\rm a}\) value. Thus, an activation energy of E\({}_{\rm a}\) = 0.28 eV was calculated for semiconducting samples with an average lateral crystal size of L\({}_{\rm a}\) ca. 7.5 nm, which was in excellent agreement with the E\({}_{\rm a}\) values obtained from the conductivity measurements (see Figure 8, regime II); whereas for materials exhibiting a value of 9 nm for L\({}_{\rm a}\), an activation energy of E\({}_{\rm a}\) = 0.085 eV was obtained, which was though larger than the E\({}_{\rm a}\) determined in regime III (E\({}_{\rm a}\) = 0.035-0.02 eV, Figure 8). Information about the density and mobility of the dominant charge carrier type in the SiOC/C ceramic materials was obtained from measurements of the Hall effect. Figure 9 exhibited the carrier density (N) and mobility (\(\mu\)) as a function of the carbon content for SiOC/C samples prepared at 1600 \({}^{\circ}\)C. Literature values of an SiOC/C synthesized at T = 1550 \({}^{\circ}\)C are displayed for comparison [76]. The charge carrier density/mobility can be furthermore estimated from conductivity measurements if the electrical transport solely depends on one charge carrier type (electrons or holes), as follows: \(\sigma=\) e\(\cdot\)N\(\cdot\mu\). The carrier densities derived from dc measurements on SiOC/C samples are shown in Figure 9 (green circles) as a function of the carbon concentration; the charge carrier densities were  
Figure 1:2 Plot of E\({}_{\rm a}\) as a function of the sp\({}^{2}\) carbon content in SiOC/C, the empty symbols represents data published by [PERSON] et al. [34]. The dotted line is shown only as a guideline, it does not represent any fit of the data. I, II and III represent the three conduction regimes as described in text above. calculated using the experimentally determined mobility of \(\mu\) = 3 cm\({}^{2}\)/Vs, which is similar to that of turbostratic carbon (\(\mu\) = 3.1-6.3 cm\({}^{2}\)/Vs [77; 78]). For SiOC/C samples possessing carbon contents higher than ca. 8 vol.%, the charge carrier densities derived from the dc conductivity data showed an excellent agreement to those obtained from the Hall effect measurements and were furthermore comparable to values determined for glassy carbon [79; 80]. However, SiOC/C samples with carbon contents significantly lower than 8 vol.% showed strong discrepancy between the dc-conductivity-derived data and those obtained from the Hall effect measurements.