## Introduction

Tin dioxide (SnO2) has been extensively studied as a practical transparent oxide semiconductor in various applications such as field-effect transistors1,2, gas sensors3,4,5, and transparent electrodes6,7,8. Hall mobility (μH) is a key parameter in determining the performance of such devices, and the μH values of bulk SnO2 single crystals are in the range of 70 to 260 cm2V−1s−1 at room temperature9,10,11. However, SnO2 thin films show a rather low μH of less than 100 cm2V−1s−1 even in well-optimized epitaxial films12,13, which limits the practical use of SnO2.

The lower μH in SnO2 epitaxial thin films is primarily attributable to the lack of lattice-matched substrates. Thus far, corundum Al2O3 and rutile TiO2 have been widely used as the substrates for the epitaxial growth14,15 of SnO2. Particularly, Al2O3, with a high thermal and chemical stability, is suitable for the growth of SnO2 thin films at high temperatures, but the SnO2 thin films deposited on Al2O3 suffer from lowered crystallinity owing to the difference between the crystal structures of the film and substrate. For example, very low μH values are frequently observed for epitaxial SnO2 films on Al2O3. TiO2 shares the same rutile structure as SnO2, but it has a relatively large lattice-mismatch with SnO2, which is 3.1% and 7.7% for the a-axis and c-axis, respectively. Indeed, it was reported that μH of the undoped SnO2 film with (001) orientation on TiO2 (001) was limited to a rather small value16, that is, ~40 cm2V−1s−1. To overcome the above-mentioned difficulty, very thick self-buffer layers12,13 have been employed to grow high-μH epitaxial SnO2 films on Al2O3.

Another important factor for achieving high μH is to control the carrier density (ne) because carriers play two competing roles in μH; an increase in ne enhances the screening of the Coulomb scattering potential and thus increases μH, whereas an increased amount of dopants suppresses μH owing to impurity scattering. To date, much effort has been made to grow undoped13,14,15,16,17,18 or heavily doped19,20,21,22 SnO2 films on a wide variety of substrates. Heavily doped SnO2 films, albeit practically important, show a low μH that is dominated by impurity scattering. Attempts to pursue high μH in undoped SnO2 thin films have been unsuccessful owing to the significant carrier scattering by the grain boundary18,23 and dislocation13,24 induced by lattice-mismatched substrates. There is a possibility to realize a high mobility in the intermediate ne region between undoped and heavily doped SnO2, but little attention has been paid to lightly doped12,23 SnO2 films.

In this study, we focus on lightly doped SnO2 thin films to achieve a high μH. We investigated the electrical transport properties of lightly Ta-doped SnO2 (Sn1−xTaxO2, TTO) films grown on TiO2 (001) substrates, which are isostructural to SnO2, with the smallest lattice mismatch. We found that the increase in ne by Ta-doping dramatically enhanced μH, probably owing to a screening of the carrier scattering by the grain boundaries and dislocations. The TTO films with ne ~ 1 × 1020 cm−3 exhibited μH of 130 cm2V−1s−1, which is the highest among SnO2 films thus far reported. Moreover, this value is close to the intrinsic limit of μH calculated by assuming that only phonon and ionized impurities contribute to the carrier scattering.

## Results and Discussion

We first optimized the substrate temperature (Ts) for growth of the TTO film, where the Ta content x was fixed at 3 × 10−3. Figure 1(a) shows ω-2θ X-ray diffraction (XRD) patterns for the TTO films prepared at various Ts. Only 002 diffraction peaks from SnO2 and TiO2 were observed in all the films, which indicated epitaxial growth of (001)-oriented SnO2 films on TiO2 (001) without any impurity phases. Epitaxial growth of the SnO2 films were further confirmed by off-specular Φ-scan of 101 diffraction peaks from SnO2 and TiO2 substrates (see Supplementary Fig. S1 online). Figure 1(b) shows the reciprocal space map observed around the asymmetric 112 diffraction peak for the TTO film grown at Ts = 600 °C. The film was almost fully relaxed, as reported16 for undoped SnO2 films on TiO2 (001). Figure 1(c) plots the full width at half maximum of the rocking curve (ω scan, see Supplementary Fig. S2 online) of the 002 diffraction (FWHM002ω) as a function of Ts. Notably, FWHM002ω monotonically decreased with an increase of Ts and reached 0.07° at the highest Ts = 700 °C. This FWHM002ω value is much smaller than that reported for the SnO2 film on a thick self-buffer layer12, that is, 0.31°, which indicated very high crystallinity of the present TTO film. A similar trend, that is, improved crystallinity at high Ts, was reported in the previous research on SnO2 epitaxial films23,25,26. The TTO films grown at higher Ts tended to exhibit higher μH, as shown in Fig. 1(c). However, a slight decrease in μH was observed for the film grown at Ts = 700 °C in spite of the good crystallinity. We speculate that at such high Ts, interdiffusion of Sn and Ti atoms occurred at the film/substrate interface27, which might have caused impurity scattering and thus suppressed μH. Hereafter we fixed Ts at 600 °C.

Next, we investigated the dependence of the transport properties of the TTO films on x. As shown in Fig. 2, the TTO film with the lowest x = 3 × 10−5 showed ne = 4 × 1017 cm−3 and μH = 36 cm2V−1s−1, which are close to those16 reported for undoped SnO2 films on TiO2 (001). Furthermore, ne was proportional to x and lay on the line representing a 100% doping efficiency, which indicated that each Ta5+ ion generated one carrier electron. This implied that the lightly-doped TTO films were free from unfavourable defects such as clustered dopants28 and accepter-like defects29. Remarkably, μH dramatically increased with increasing x at x ≤ 3 × 10−3. This behavior was rationalized by assuming an enhanced screening of dislocations13 and/or grain boundaries18,23 owing to the increased ne. The TTO films with x = 3 × 10−3 (ne ~ 1 × 1020 cm−3) exhibited the highest μH of 126–131 cm2V−1s−1, which is the highest among the μH values reported for undoped and doped SnO2 films so far. Further increase in x yielded a slight decrease in μH, possibly owing to the manifestation of ionized impurity scattering, as will be discussed later. The lowest resistivity, 2.5 × 10−4 Ωcm, and sheet resistance, 20.2 Ωsq.−1, were obtained for the TTO film with x = 1 × 10−2, as shown in Fig. 2(a).

We now discuss the transport properties of the TTO films in comparison with the literature data. Figure 3 plots μH against ne for thin films12,13,16,23, including ours, and bulk single crystals9,11 of SnO2. The previously reported μH values for thin films were generally lower than those of bulk single crystals with similar ne values. However, our TTO films with ne ~ 1 × 1020 cm−3 exhibited a record-high μH (130 cm2V−1s−1) for thin films, which is comparable to that for a bulk single crystal with a similar ne value. Such an extremely high μH value suggests that the film contained a negligibly small amount of extrinsic sources of carrier scattering, such as neutral impurities, grain boundaries, and dislocations. In other words, intrinsic sources of carrier scattering, such as phonons and ionized impurities, supposedly dominated μH.

To test the above-mentioned hypothesis, we calculated the Hall mobility (μcal) taking only phonon and ionized impurity scattering into account, as

$${{\mu }_{{\rm{c}}{\rm{a}}{\rm{l}}}}^{-1}={{\mu }_{{\rm{l}}{\rm{a}}{\rm{t}}}}^{-1}+{{\mu }_{{\rm{i}}{\rm{i}}{\rm{s}}}}^{-1},$$

where μlat is the lattice mobility associated with phonon scattering and μiis is the Hall mobility limited by ionized impurity scattering. For μlat, we used a fixed value (260 cm2V−1s−1) observed for undoped single crystals in the a-direction9. The μiis value was calculated by using the Brooks–Herring–Dingle (BHD) formula30, which has been successfully used to analyze μiis for Sn-doped In2O331, Al-doped ZnO28,29, and Nb-doped TiO232. The BHD formula is written as

$${\mu }_{{\rm{iis}}}=\frac{24{\pi }^{3}{({{\epsilon }}_{0}{{\epsilon }}_{r})}^{2}{\hslash }^{3}{n}_{{\rm{e}}}}{{e}^{3}{m}^{\ast 2}{F}_{{\rm{ii}}}{Z}^{2}{n}_{{\rm{I}}}},$$

where ε0 is the permittivity of free space, εr is the relative static dielectric constant, ħ is the reduced Planck’s constant, e is the elementary charge, and m* is the electron effective mass. Z and nI are the charge and the density of the ionized impurity, respectively. The screening function Fii is given by

$${F}_{ii}={\rm{l}}{\rm{n}}(1+4/x)-{(1+x/4)}^{-1}$$

with

$${\rm{\xi }}=\frac{{e}^{2}{m}^{\ast }}{\pi {{\epsilon }}_{0}{{\epsilon }}_{r}{\hslash }^{2}{(3{\pi }^{5})}^{1/3}{{n}_{{\rm{e}}}}^{1/3}}.$$

Considering the high doping efficiency, all the doped Ta was supposed to behave as singly charged ions (Ta5+ substituting for Sn4+). Although it was difficult to determine the valence state of Ta in TTO experimentally33 (see Supplementary Fig. S3 online), theoretical calculations34,35 reported that Ta exists in the pentavalent state (Ta5+) in TTO. Thus, we assumed Z = 1 and nI = ne. Because the films in this study were (001)-oriented, we used εra = 13.5 for εr36. For m*, we used experimentally determined $${m}_{a}^{\ast }$$ values as a function of ne and their linear interpolation37. As shown in Fig. 3, μcal was higher than most of the experimental data, which indicated that the suppression of μH arose from carrier scattering by extrinsic sources. Notably, however, the μH values at ne ≥ 9 × 1019 cm−3 (x = 3 × 10−3 and 1 × 10−2) in the present study agreed well with μcal. This proved that in these high μH films, carrier scattering by neutral impurities, dislocations, and grain-boundaries was negligibly small compared with that by ionized impurities and phonons, and that the reduced μH at ne = 2.4 × 1020 cm−3 (x = 1 × 10−2) was attributed to the increased ionized impurity scattering.

To discuss the carrier scattering mechanisms in more detail, we measured temperature dependences of ne and μH for in the TTO films with x = 3 × 10−4 – 1 × 10−2. As shown in Fig. 4(a), the ne values were independent of temperature, indicating that the TTO films in this study were in the degenerately-doped regime. Notably, the TTO films with x ≥ 1 × 10−3 showed negative temperature coefficients of μH (Fig. 4(b)) around room temperature, being the specific characteristic of phonon scattering. This implies that, at room temperature, the μH values are dominated by phonon scattering, in consistence with the arguments based on the room temperature data (Fig. 3). At low temperature, phonon scattering is suppressed9, and ionized impurities are supposed to be the intrinsic sources of carrier scattering. Remarkably, as shown in Fig. 4(c), μH at 10 K for the TTO film with x = 1 × 10−2 (ne = 2.4 × 1020 cm−3) agrees well with μiis, which is known to be temperature-independent in degenerately-doped regime. This result supports the conclusion that μH of the film is dominated by ionized impurity scattering and phonon scattering at room temperature (Fig. 3). As x and thus ne decreased, μH at 10 K started deviating downward from μiis. This behaviour indicates that the TTO films with x < 1 × 10−2 contain extrinsic sources of carrier scattering, pronounced especially at low temperature. Thermal-activation-type behaviour of μH was observed for the TTO film with x = 3 × 10−4 (Fig. 4(d)), demonstrating that μH is governed by grain boundary scattering38 in the film, although grain-boundary scattering in SnO2 epitaxial films has scarcely been studied so far. Dominguez et al. proposed that {101} crystallographic shear planes (CSPs) in SnO2 films, which are induced by misfit dislocations39, may act like grain boundaries18. Similarly, we speculated that the carrier scattering at {101} CSPs was responsible for the lower μH than μcal at ne < 9 × 1019 cm−3.

Judging from the complete screening by free carriers at ne ≥ 9 × 1019 cm−3, the CSP-based grain-boundary scattering in the TTO films was supposed to be weak. We considered that lattice matching and growth orientation play an essential role in the CSP-based grain-boundary scattering as follows. Owing to the good lattice-matching to SnO2, the TiO2 (001) substrate would induce lower densities of misfit dislocations and thus CSPs in the films than other substrates18,39. Furthermore, the angle between {101} CSPs and the basal plane of the SnO2 (001) film was approximately 34°, as shown in Fig. 5(a). The shallow angle would cause termination of the {101} CSPs at the crossing point with complementary {101} CSPs39 at the early stage of the film growth. Indeed, as shown in Fig. 5(b), cross-sectional transmission electron microscopy (TEM) observations revealed that the TTO films on the TiO2 substrate had lower densities of CSPs than those on other substrates18,39 and that the CSPs did not reach the film surface, which supported the above-mentioned scenario. These structural characteristics can account for the lower contribution of carrier scattering at the CSP-based grain boundaries to the carrier transport in the TTO films on TiO2 (001). However, SnO2 epitaxial films on other substrates than TiO2 (001) have reportedly shown highly populated {101} CSPs inclined steeply to the basal planes18,39, as schematically illustrated in Fig. 5(a). The CSPs in SnO2 epitaxial films are induced by misfit dislocations, and they are not energetically favorable in bulk crystal, unlike the CSPs induced by off-stoichiometry, as seen in oxygen-deficient rutile TiO2 crystals40. Therefore, the density of CSPs decreased as the film thickness increases18. Nevertheless, some of the CSPs in those films survived even near the surface of the films18. These results suggest that the CSP-based grain-boundary scattering is more significant in the SnO2 epitaxial films on other substrates than TiO2 (001), which can account for the lower μH than those for the TTO films on TiO2 (001), as depicted in Fig. 3.

To verify the proposed model, we investigated film thickness and growth orientation dependence of μH for TTO films with x = 3 × 10−3 grown on various substrates12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,39,41,42, (001)-, (101)-, and (110)-planes of TiO2, and m-, r-, and c-planes of Al2O3 substrates (see Supplementary Fig. S4 online). Figure 6 plots room temperature ne and μH for the TTO films with various film orientations as a function of the film thickness. With increasing film thickness, the μH values increased probably owing to the synergistic effect of enlarged crystalline grains43,44 and reduced density of threading dislocations24 and {101} CSPs18,39. The highest μH was achieved for the (001)-oriented TTO films, followed in order by the (101)-, the (110)-, and the (100)-oriented ones. This behaviour can be explained by the CSP-based grain-boundary scattering because the angle between the CSP and the basal planes of the films becomes small in the same order (Fig. 5(a)). Notably, the TTO films with the same orientation showed similar μH values even though different kinds of substrates were used. The orientation dependence of μH cannot be explained by the anisotropy in electron effective mass of SnO2 (see Supplementary Fig. S5 online). It was suggested that {101} CSPs play a significant role in the carrier transport in the TTO epitaxial thin films.

## Summary

We investigated the transport properties of Sn1−xTaxO2 (TTO) films with x = 3 × 10−5–1 × 10−2 epitaxially grown on TiO2 (001) substrates. The ne values for the TTO films were almost equal to the concentrations of Ta dopants, which demonstrated the very high doping efficiency of Ta. The μH values of the TTO films with ne ≥ 9 × 1019 cm−3 (x ≥ 3 × 10−3) agreed well with the intrinsic limit of μH assuming that only phonon and ionized impurities contributed to carrier scatterings. Negligible contribution of the grain-boundary scattering to μH might arise from a reduced density of CSPs. The TTO films with ne ~ 1 × 1020 cm−3 (x = 3 × 10−3) exhibited a very high μH of 130 cm2V−1s−1, which is the highest among SnO2 films thus far reported. The μH values for the TTO (x < 3 × 10−3) films rapidly decreased with a decrease of x, which suggested a weakened screening of dislocation and/or grain-boundary scatterings owing to the decreased ne.

## Methods

TTO films with a thickness of 100–120 nm, with x = 3 × 10−5–1 × 10−2, were grown on TiO2 (001) substrates by pulsed laser deposition (PLD) with a KrF excimer laser. TTO films with x = 3 × 10−3 were grown (001)-, (101)-, and (110)-planes of TiO2, and m-, r-, and c-planes of Al2O3 substrates. The repetition rate and the fluence of the laser were set at 2 Hz and 1–2 J ∙ cm−2, respectively. The typical growth rate was 0.14–0.17 Å per shot. Sintered pellets of TTO with x = 3 × 10−4–1 × 10−2 were used as PLD targets. TTO films with x = 3 × 10−5 were fabricated by alternating ablation23 of a commercial undoped SnO2 (4 N purity, Toshima MFG) target and a TTO pellet with x = 3 × 10−4. In this study, nominal x values were used to represent the chemical compositions of the films because stoichiometric transfer of Ta from the targets to the films has been reported for TTO films grown under a similar condition23. The base pressure of the PLD chamber was maintained at 3 × 10−9 Torr. Oxygen partial pressure and Ts during film growth were 1 × 10−2 Torr and 400–700 °C, respectively. Crystal structure and crystallinity were evaluated by XRD measurements using a four-circle diffractometer (Bruker AXS, D8 DISCOVER). The cross-sectional microstructure of the films was observed by using a transmission electron micrscope (FEI, Titan Cubed G2 60-300) operated at 300 kV. Hall effect and resistivity were measured by using a standard six-terminal method. The Hall-bar width and the distance between voltage terminals for four-probe measurements were 1 mm and 2.4 mm, respectively. Ag or In electrodes were used for ohmic contacts. A laboratory constructed system equipped with a 2 T electromagnet was used for room temperature measurements. Current–voltage characteristics and Hall voltage-magnetic field characteristics were measured repeatedly (at least twice) to confirm the reliability and reproducibility of the measurements. Temperature dependence of the transport properties was measured with a commercially available system (Quantum design, physical properties measurement system (PPMS Model 6000)).