3.1.3. TOF-ERDA

TOF-ERDA was employed for the elemental depth profiling of the S-590 and B-590 samples. Due to the overlapping of Sn and scattered I lines in TOF-E spectra (Figure 3a,b), only the first 10<sup>18</sup> at./cm<sup>2</sup> of sample depth was analysed. Energy spectra belonging to each element were analysed using simulation code Potku [23] (slab analysis) and the Monte Carlo (MC) code CORTEO [24]. Calculated depth profiles (Potku analysis, version 1.1) are presented at Figure 4a,b for S-590 and B-590 respectively. Since the slab analysis does not take into account detector energy resolution and all other contributions to the total energy spread (energy straggling and multiple scattering of incoming and recoiled ions), derived atomic concentrations were used only as input data for the MC simulation. Average atomic concentrations, calculated by MC simulations, are listed in Table 3.

**Table 3.** Summary of TOF-ERDA elemental analysis (MC simulation). Total atomic content is normalized to 100%.


**Figure 3.** TOF-E map for SnO2 samples: (**a**) S-590 and (**b**) B-590. Traces of all detected elements are labelled.

**Figure 4.** TOF-ERDA elemental depth profile calculated by Potku (slab analysis) for SnO2 samples: (**a**) S-590 and (**b**) B-590.

The results in Table 3 confirm that the sample deposited in the one-step process (S-590 and S-610) does not contain fluor, as is expected.

For both types of sample, the ratio of Sn and O atoms are stoichiometric (1:2), within the measured error, considering that part of O atoms are bonded to Si in substrate or C atoms at the sample surface. For samples deposited in the two-step process, the concentration of F atoms (dopant) is almost 1%, while for samples deposited in the one-step process, the amount of F atoms is below the detection limit (<0.1 at.%).

Small amounts of Si, K, Mg and Na, visible in TOF-E spectra (Figure 4a,b), could originate from the glass substrate, since the sample area is not fully covered by SnO2 film. Higher numbers of holes/cracks are expected for thinner samples (single-layer), which could explain the higher contribution of Si, K, Mg and Na in the sample S-590 (Table 3).

#### *3.2. Transport Properties*

#### 3.2.1. Impedance Spectroscopy

Impedance spectroscopy results (Figure 5) show that all samples have a very high electrical conductivity, independent of frequency in a wide frequency range indicating fast electronic transport. As expected, samples deposited in the two-step process (B-590 and B-610) have higher conductivity compared to samples deposited in the one-step process at the same temperature because of doping. Only sample S-590 shows a very small dispersion at the highest frequency range. For samples with higher conductivity, a dispersion phenomena is also expected at higher frequencies that are above the limits of the experimental setup. In addition, electrode polarisation effects are not observed for any of the samples, indicating the absence of ion transport contribution to the electrical conductivity.

**Figure 5.** Electrical conductivity for SnO2 samples as a function of frequency at 20 ◦C.

#### 3.2.2. Magnetotransport Probe

Figure 6 shows the DC resistivity of the four SnO2 thin films as a function of temperature. Interestingly, for all samples, the DC resistivity has a negligible temperature dependence from room temperature down to −269 ◦C, indicating a metallic type of charge transport. The high temperature measurements confirmed that the DC resistivity stays almost independent of temperature up to 150 ◦C. Hall effect measurements showed that the Hall resistivity is linear in a magnetic field up to 5 T and that the carrier density extracted from the Hall coefficient *R*H is in the range 1–3 × 10<sup>20</sup> cm<sup>−</sup>3, which is a typical value for SnO2 films. As expected, *R*H is negative, indicating *n*-type free carriers and doped samples (B-590 and B-610) have a higher electron density (2–3 × 10<sup>20</sup> cm<sup>−</sup>3) than the undoped ones (S-590 and S-610) (1 × 10<sup>20</sup> cm<sup>−</sup>3). As can be seen in Figure 7, RH for all samples also shows a negligible temperature dependence, indicating that all samples behave as heavily doped semiconductors and that for both, doped and undoped samples, the Fermi level lies either in the conduction band or in the region where the conduction band is mixed with impurity levels.

**Figure 6.** Resistivity of SnO2 samples as a function of temperature.

**Figure 7.** Hall coefficient RH of SnO2 samples as a function of temperature.

Having determined the DC resistivity ρ and the Hall coefficient *R*H, we are able to calculate the carrier mobility μ = RH/ρ, which is shown in Figure 8 for all four samples. Remarkably, charge carrier mobility is independent on temperature from room temperature down to −269 ◦C, in sharp contrast to behaviour found in conventional semiconductors, indicating the dominance of a non-trivial scattering mechanism.

**Figure 8.** Charge carrier mobility of SnO2 samples as a function of temperature.

There are several scattering mechanisms influencing the charge carrier mobility in doped semiconductors: electron–phonon scattering, scattering of electrons on ionized impurities, electron– electron scattering, scattering of electrons on neutral impurities, and inter-valley scattering [25]. The last three mechanisms are usually much less pronounced and can generally be ignored for a first approximation. Electron–phonon scattering is a standard scattering mechanism present in all materials and is especially pronounced at high temperatures. Scattering of charge carriers on ionized impurities is usually a second dominant scattering mechanism in doped semiconductors. This is due to the excitation of an electron from the impurity level to the conduction band (n-type) or excitation of an electron from the valence band to the impurity level (p-type) that leaves an uncompensated charge on

the impurity. As mentioned earlier, our SnO2 samples are a heavily doped n-type material, intrinsically doped by the oxygen vacancies and extrinsically by the fluorine atoms, so that both electron–phonon and scattering on ionized impurities are expected to play a role in the charge transport. However, both scattering mechanisms show a pronounced temperature dependence [25], in sharp contrast to our negligible temperature dependence of charge carrier mobility (Figure 8), pointing towards the presence of an additional scattering mechanism with basically no temperature dependence.

The charge carrier mobility in polycrystalline samples is known to be determined by grain boundary scattering resulting from the electrostatic charge trapped at the intergrain boundaries, which sets up potential barriers to current flow, although such scattering usually also shows a pronounced temperature dependence. A theoretical model by Prins et al. [26] shows, however, that for certain parameter values the grain–boundary scattering can indeed produce a temperature-independent mobility. The model depends on bulk parameters—the carrier e ffective mass and the mean free path—and the grain boundary parameters—barrier height, barrier width, and a coe fficient of sample inhomogeneity. (The barrier height is defined as the energy di fference between the Fermi level and the top of the barrier and the transport in the interior of the grains is separated from the transport across the intergrain boundaries.) The model is tested on five Sb-doped SnO2 thin films with a di fferent doping level. The films with a charge carrier density >10<sup>18</sup> cm<sup>−</sup><sup>3</sup> showed temperature-independent carrier density (the interior of the grains is degenerately doped) and the sample with the highest dopant concentration showed a negligible temperature dependence of both the carrier density and the carrier mobility over a temperature range of nearly 300 ◦C, very similar to the behaviour found in our thin films. Moreover, the carrier mobility for the sample with the highest dopant concentration in Ref. [26] was found to be around 18 cm<sup>2</sup>/Vs which is very close to the values found in our samples (see Figure 8). Such behaviour is interpreted as originating from the fact that the Fermi level is situated well above the conduction band minimum at the grain boundaries and the negligible electrostatic barriers at the grain boundaries caused by the high dopant concentration (barrier height is negative).

Having established that grain–boundary scattering is responsible for temperature-independent transport in our SnO2 thin films, let us now try to address the small di fference in mobility found between the doped and undoped samples prepared at a di fferent deposition temperature. By comparing the grain structure determined by SEM shown in Figure 1 with the charge carrier mobility determined by magnetotransport in Figure 8, no obvious correlation can be found. For example, in contrast to the expectations, the sample with the biggest grains B-590 turns out to have the smallest carrier mobility, while the biggest carrier mobility was found in the sample with the medium grains B-610.

A relatively recent study by Wang et al. [27] indicated the importance of the preferred orientation of crystallites (texture coe fficient) in limiting the charge carrier mobility in fluorine-doped thin SnO2 films prepared by APCVD. The main conclusion of this study is that the growth in texture coe fficient (110) decreases, while the growth in the texture coe fficient (200) increases the carrier mobility in SnO2 films. Looking at Table 2, we can see that the sample B-610, which has the biggest mobility, indeed has the biggest value of the texture coe fficient (200), while the sample B-590 with the smallest mobility has the smallest value of the texture coe fficient (200), in agreemen<sup>t</sup> with the results in Ref. [27]. We can say that the dominant scattering mechanisms in our SnO2 thin films are grain–boundary scattering, responsible for temperature independent carrier mobility, and crystallite scattering, possibly responsible for small di fferences in carrier mobility among the SnO2 samples prepared under slightly di fferent conditions. More systematic study would be necessary in order to disentangle the contributions coming from the grain–boundary and crystallite–boundary scattering in our SnO2 samples and to establish a direct relationship to the carrier mobility.

Magnetoresistance (Figure 9) of all samples is small (<2%), negative and its value slowly increases with cooling. Negative magnetoresistance is rare in non-magnetic materials and usually has an exotic origin, indicating again that SnO2 samples do not follow simple metallic behaviour. However, negative magnetoresistance is found in impurity conduction of many semiconductors [28–30] and is often attributed to impurity band conduction [31,32], which is in accordance with the conclusions extracted

from the temperature dependence of DC resistivity and the Hall coefficient. There are several theoretical models that try to resolve this behaviour; for example, weak localization [31], two band model with sharp mobility edge in the overlap region [32] and spin disorder [33]. The true nature of negative magnetoresistance in our samples is beyond the scope of this paper, but a more comprehensive study of this feature is likely to be part of future publications.

**Figure 9.** Magnetoresistance of SnO2 samples as function of temperature. Error bars are omitted in plot because they are order of experimental point symbol size.
