High mobility approaching the intrinsic limit in Ta-doped SnO2 films epitaxially grown on TiO2 (001) substrates.

Achieving high mobility in SnO2, which is a typical wide gap oxide semiconductor, has been pursued extensively for device applications such as field effect transistors, gas sensors, and transparent electrodes. In this study, we investigated the transport properties of lightly Ta-doped SnO2 (Sn1-xTaxO2, TTO) thin films epitaxially grown on TiO2 (001) substrates by pulsed laser deposition. The carrier density (ne) of the TTO films was systematically controlled by x. Optimized TTO (x = 3 × 10-3) films with ne ~ 1 × 1020 cm-3 exhibited a very high Hall mobility (μH) of 130 cm2V-1s-1 at room temperature, which is the highest among SnO2 films thus far reported. The μH value coincided well with the intrinsic limit of μH calculated on the assumption that only phonon and ionized impurities contribute to the carrier scattering. The suppressed grain-boundary scattering might be explained by the reduced density of the {101} crystallographic shear planes.


Results and Discussion
We first optimized the substrate temperature (T s ) 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 T s . Only 002 diffraction peaks from SnO 2 and TiO 2 were observed in all the films, which indicated epitaxial growth of (001)-oriented SnO 2 films on TiO 2 (001) without any impurity phases. Epitaxial growth of the SnO 2 films were further confirmed by off-specular Φ-scan of 101 diffraction peaks from SnO 2 and TiO 2 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 T s = 600 °C. The film was almost fully relaxed, as reported 16 for undoped SnO 2 films on TiO 2 (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 (FWHM 002ω ) as a function of T s . Notably, FWHM 002ω monotonically decreased with an increase of T s and reached 0.07° at the highest T s = 700 °C. This FWHM 002ω value is much smaller than that reported for the SnO 2 film on a thick self-buffer layer 12 , that is, 0.31°, which indicated very high crystallinity of the present TTO film. A similar trend, that is, improved crystallinity at high T s , was reported in the previous research on SnO 2 epitaxial films 23,25,26 . The TTO films grown at higher T s tended to exhibit higher μ H , as shown in Fig. 1(c). However, a slight decrease in μ H was observed for the film grown at T s = 700 °C in spite of the good crystallinity. We speculate that at such high T s , interdiffusion of Sn and Ti atoms occurred at the film/substrate interface 27 , which might have caused impurity scattering and thus suppressed μ H . Hereafter we fixed T s 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 n e = 4 × 10 17 cm −3 and μ H = 36 cm 2 V −1 s −1 , which are close to those 16 reported for undoped SnO 2 films on TiO 2 (001). Furthermore, n e was proportional to x and lay on the line representing a 100% doping efficiency, which indicated that each Ta 5+ ion generated one carrier electron. This implied that the lightly-doped TTO films were free from unfavourable defects such as clustered dopants 28 and accepter-like defects 29 . Remarkably, μ H dramatically increased with increasing x at x ≤ 3 × 10 −3 . This behavior was rationalized by assuming an enhanced screening of dislocations 13 and/or grain boundaries 18,23 owing to the increased n e . The TTO films with x = 3 × 10 −3 (n e ~ 1 × 10 20 cm −3 ) exhibited the highest μ H of 126-131 cm 2 V −1 s −1 , which is the highest among the μ H values reported for undoped and doped SnO 2 films so far. Further increase in x yielded a slight decrease in μ H , 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 μ H against n e for thin films 12,13,16,23 , including ours, and bulk single crystals 9,11 of SnO 2 . The previously reported μ H values for thin films were generally lower than those of bulk single crystals with similar n e values. However, our TTO films with n e ~ 1 × 10 20 cm −3 exhibited a record-high μ H (130 cm 2 V −1 s −1 ) for thin films, which is comparable to that for a bulk single crystal with a similar n e value. Such an extremely high μ H 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 μ H .
To test the above-mentioned hypothesis, we calculated the Hall mobility (μ cal ) taking only phonon and ionized impurity scattering into account, as where μ lat is the lattice mobility associated with phonon scattering and μ iis is the Hall mobility limited by ionized impurity scattering. For μ lat , we used a fixed value (260 cm 2 V −1 s −1 ) observed for undoped single crystals in the a-direction 9 . The μ iis value was calculated by using the Brooks-Herring-Dingle (BHD) formula 30 , which has www.nature.com/scientificreports www.nature.com/scientificreports/ been successfully used to analyze μ iis for Sn-doped In 2 O 3 31 , Al-doped ZnO 28,29 , and Nb-doped TiO 2 32 . The BHD formula is written as where ε 0 is the permittivity of free space, ε r 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 n I are the charge and the density of the ionized impurity, respectively. The screening function F ii is given by Considering the high doping efficiency, all the doped Ta was supposed to behave as singly charged ions (Ta 5+ substituting for Sn 4+ ). Although it was difficult to determine the valence state of Ta in TTO experimentally 33 (see Supplementary Fig. S3 online), theoretical calculations 34,35 reported that Ta exists in the pentavalent state (Ta 5+ ) in TTO. Thus, we assumed Z = 1 and n I = n e . Because the films in this study were (001)-oriented, we used ε ra = 13.5 for ε r 36 . For m*, we used experimentally determined * m a values as a function of n e and their linear interpolation 37 . As shown in Fig. 3, μ cal was higher than most of the experimental data, which indicated that the suppression of μ H arose from carrier scattering by extrinsic sources. Notably, however, the μ H values at n e ≥ 9 × 10 19 cm −3 (x = 3 × 10 −3 and 1 × 10 −2 ) in the present study agreed well with μ cal . This proved that in these high μ H 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 μ H at n e = 2.4 × 10 20 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 n e and μ H for in the TTO films with x = 3 × 10 −4 -1 × 10 −2 . As shown in Fig. 4(a), the n e 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 μ H (Fig. 4(b)) around room temperature, being the specific characteristic of phonon scattering. This implies that, at room temperature, the μ H 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 suppressed 9 , and ionized impurities are supposed to be the intrinsic sources of carrier scattering. Remarkably, as shown in Fig. 4(c), μ H at 10 K for the TTO film with x = 1 × 10 −2 (n e = 2.4 × 10 20 cm −3 ) agrees well with μ iis , which is known to be temperature-independent in degenerately-doped regime. This result supports the conclusion that μ H of the film is dominated by ionized impurity scattering and phonon scattering at room temperature (Fig. 3). As x and thus n e decreased, μ H at 10 K started deviating downward from μ iis . This behaviour indicates that the TTO films with x < 1 × 10 −2 contain extrinsic www.nature.com/scientificreports www.nature.com/scientificreports/ sources of carrier scattering, pronounced especially at low temperature. Thermal-activation-type behaviour of μ H was observed for the TTO film with x = 3 × 10 −4 (Fig. 4(d)), demonstrating that μ H is governed by grain boundary scattering 38 in the film, although grain-boundary scattering in SnO 2 epitaxial films has scarcely been studied so far. Dominguez et al. proposed that {101} crystallographic shear planes (CSPs) in SnO 2 films, which are induced by misfit dislocations 39 , may act like grain boundaries 18 . Similarly, we speculated that the carrier scattering at {101} CSPs was responsible for the lower μ H than μ cal at n e < 9 × 10 19 cm −3 .
Judging from the complete screening by free carriers at n e ≥ 9 × 10 19 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 SnO 2 , the TiO 2 (001) substrate would induce lower densities of misfit dislocations and thus CSPs in the films than other substrates 18,39 . Furthermore, the angle between {101} CSPs and the basal plane of the SnO 2 (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} CSPs 39 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 TiO 2 substrate had lower densities of CSPs than those on other substrates 18,39 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 TiO 2 (001). However, SnO 2 epitaxial films on other substrates than TiO 2 (001) have reportedly shown highly populated {101} CSPs inclined steeply to the basal planes 18,39 , as schematically illustrated in Fig. 5(a). The CSPs in SnO 2 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 TiO 2 crystals 40 . Therefore, the density of CSPs decreased as the film thickness increases 18 . Nevertheless, some of the CSPs in those films survived even near the surface of the films 18 . These results suggest that the CSP-based grain-boundary scattering is more significant in the SnO 2 epitaxial films on other substrates than TiO 2 (001), which can account for the lower μ H than those for the TTO films on TiO 2 (001), as depicted in Fig. 3.
To verify the proposed model, we investigated film thickness and growth orientation dependence of μ H for TTO films with x = 3 × 10 −3 grown on various substrates [12][13][14][15][16][17][18][19][20][21][23][24][25][26][27]39,41,42 , (001)-, (101)-, and (110)-planes of TiO 2 , and m-, r-, and c-planes of Al 2 O 3 substrates (see Supplementary Fig. S4 online). Figure 6 plots room temperature n e and μ H for the TTO films with various film orientations as a function of the film thickness. With increasing film thickness, the μ H values increased probably owing to the synergistic effect of enlarged crystalline grains 43,44 and reduced density of threading dislocations 24   www.nature.com/scientificreports www.nature.com/scientificreports/ (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 μ H values even though different kinds of substrates were used. The orientation dependence of μ H cannot be explained by the anisotropy in electron effective mass of SnO 2 (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 Sn 1−x Ta x O 2 (TTO) films with x = 3 × 10 −5 -1 × 10 −2 epitaxially grown on TiO 2 (001) substrates. The n e values for the TTO films were almost equal to the concentrations of Ta dopants, which demonstrated the very high doping efficiency of Ta. The μ H values of the TTO films with n e ≥ 9 × 10 19 cm −3 (x ≥ 3 × 10 −3 ) agreed well with the intrinsic limit of μ H assuming that only phonon and ionized impurities contributed to carrier scatterings. Negligible contribution of the grain-boundary scattering to μ H might arise from a reduced density of CSPs. The TTO films with n e ~ 1 × 10 20 cm −3 (x = 3 × 10 −3 ) exhibited a very high μ H of 130 cm 2 V −1 s −1 , which is the highest among SnO 2 films thus far reported. The μ H 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 n e .

Methods
TTO films with a thickness of 100-120 nm, with x = 3 × 10 −5 -1 × 10 −2 , were grown on TiO 2 (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 TiO 2 , and m-, r-, and c-planes of Al 2 O 3 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 ablation 23 of a commercial undoped SnO 2 (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 condition 23 . The base pressure of the PLD chamber was maintained at 3 × 10 −9 Torr. Oxygen partial pressure and T s 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)).

Data availability
The datasets during the current study are available from the corresponding author on reasonable request.