PHYSICAL REVIEW MATERIALS 8, 044601 (2024) Origin and quantification of the ultimate carrier concentration limits in In2O3 and Sn-doped In2O3 Andreas Klein ,* Alexander Frebel , Kim Alexander Creutz , and Binxiang Huang Electronic Structure of Materials, Institute of Materials Science, Technische Universität Darmstadt, Otto-Berndt-Strasse 3, 64287 Darmstadt, Germany (Received 21 November 2023; revised 2 February 2024; accepted 12 March 2024; published 1 April 2024) The ultimate limits of the carrier concentrations in In2O3 and Sn-doped In2O3 are derived from operando photoelectron spectroscopy of a solid oxide electrochemical cell with Y-doped ZrO2 as the oxygen electrolyte. It is demonstrated that the limits are determined by the transition of the oxygen vacancy to the neutral state and to the reduction of Sn4+ donors to Sn2+ electron traps, respectively. Maximum Fermi energies of 3.85 and 3.35 eV above the valence band maximum are identified for ITO and In2O3. The ultimate carrier concentrations achievable by Sn doping and by oxygen vacancies are estimated to be 1.8–1.9 × 1021 cm−3 and 6–7 × 1020 cm−3. DOI: 10.1103/PhysRevMaterials.8.044601 I. INTRODUCTION Transparent conducting oxides, such as Sn-doped In2O3, are widely used as electrodes in solar cell and display technologies [1]. In these materials, the highest electrical conductivity above 104 S/cm and optical transparency are achieved by high carrier concentrations and mobilities. The highest carrier concentrations of n > 1021 cm−3, preferred for high conductivity, and carrier mobilities of μ > 140 cm2/V s, essential for high transparency reaching into the near-infrared regime, do not occur simultaneously [2,3]. In order to over- come this trade-off, understanding the origin of the limitations is crucial. The carrier concentration in donor-doped In2O3 is often described to be limited by self-compensation, that is, by the generation of oxygen interstitial defects [4–8], which are formed as their formation energy decreases with increasing Fermi energy, as sketched in Fig. 1(b). If this is the case, the maximum achievable carrier concentrations should be independent of the donor species. This is in contrast to exper- imental observations, which clearly indicate that the highest carrier concentrations can be achieved only with Sn. This is illustrated in Fig. 1(a), which displays the carrier con- centrations for differently doped In2O3 thin films. All films were prepared by magnetron sputtering with a thickness of 200–400 nm, as determined by optical transmission and pro- filometer measurements. Targets with different dopant species and concentrations, which are indicated in Fig. 1, were used. For lower dopant concentrations the carrier concentrations correspond well to the dopant concentrations or even exceed them. While the highest carrier concentration increases with increasing Sn concentration in the target, it is almost inde- pendent of the dopant concentration for Zr-, Ge-, Mo-, and Ti-doped films. Moreover, apart from the Ge-doped films, the latter do not reach the carrier concentrations of ITO films. It is evident that the maximum carrier concentration depends *andreas.klein@tu-darmstadt.de on the used dopant species. This suggests that the carrier concentrations in donor-doped In2O3 are not generally limited by self-compensation, but by different mechanisms, which are specific for the used dopant. Apart from self-compensation, the carrier concentration in donor-doped materials can be limited by three other mecha- nisms [9], one of them being the reduction of the donor. The energy at which such a reduction occurs corresponds to the defect energy, or the charge transition level of the dopant. The reduction of the dopant is also discussed as a potential limitation of the carrier concentration in oxides [7,10], but a quantification of the effect is still lacking. The scenarios relevant for the analysis of the presented experiments, the reduction of the Sn donor or of oxygen vacancies, are sketched in Figs. 1(c) and 1(d). In the case of ITO, Sn will act as a donor only as long as it is in the 4+ valence state. As the 3+ valence state is unlikely for Sn, a reduction of Sn4+ to Sn2+, which constitutes an electron trap, is assumed. The Sn4+/2+ charge transition would therefore constitute an upper limit of the Fermi energy and carrier concentration. In the case of oxygen vacancies, the diagram in Figs. 1(d) includes doubly, singly, and uncharged states as reported in some density functional theory calculations [11–13]. It is noted that other calcula- tions describe only doubly and uncharged oxygen vacancies [7,14,15]. For the present work it is only relevant at which Fermi energy the oxygen vacancy becomes neutral and not whether that results from the doubly or singly charged state because both of them are donors and contribute electrons to the conduction band. The second mechanism, which can limit the Fermi energy and carrier concentration, is the reduction of In. One may expect a reduction of In3+ either to In1+ or directly to metallic In. An electrochemical reduction corresponds to a thermody- namic instability of the material and will directly result in a limitation of Fermi energy. It has been observed for a se- ries of compounds, mostly containing transition metal species such as Fe2O3, BiVO4, and BiFeO3 [16–18]. In the case of hematite Fe2O3, the reduction of Fe occurs at a Fermi energy about 0.5 eV below the conduction band minimum [16]. The 2475-9953/2024/8(4)/044601(9) 044601-1 ©2024 American Physical Society Urheberrechtlich geschützt / In copyright https://rightsstatements.org/page/InC/1.0/ https://orcid.org/0000-0001-7463-1495 https://orcid.org/0009-0007-7010-0372 https://orcid.org/0009-0004-2850-3897 https://orcid.org/0000-0002-6449-2847 https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevMaterials.8.044601&domain=pdf&date_stamp=2024-04-01 https://doi.org/10.1103/PhysRevMaterials.8.044601 KLEIN, FREBEL, CREUTZ, AND HUANG PHYSICAL REVIEW MATERIALS 8, 044601 (2024) FIG. 1. (a) Room temperature carrier concentrations obtained from Hall effect measurements of undoped and differently doped In2O3 thin films. The gray regions and black horizontal bars indicate the nominal concentration of dopants from the sputter targets. All films have thicknesses between 200 and 400 nm. The mechanisms causing an upper limit of the Fermi energy EF which are relevant for this work are illustrated in (b)–(d). The upper limits, which are indi- cated by the red dashed lines, can be induced by a vanishing defect formation enthalpy �Hd of (b) compensating oxygen interstitials, (c) a valence change in Sn or (d) oxygen vacancies. given limitation of the Fermi energy is expected to prevent efficient charge transfer to adsorbed water molecules and ef- ficient hydrogen evolution. The reduction of Fe or V at Fermi energies below the conduction band minimum is equivalent to polaron formation, which happens when electrons added to the conduction band localize on a specific atom. Electron trapping preferentially occurs in the case of low dispersive energy bands, such as those formed by transition metal d orbitals. Due to the highly dispersive nature of the conduction band of In2O3, which is formed by In 5s orbitals, a localization of electrons on individual In atoms is not expected. An elec- trochemical reduction of In is therefore expected only if the number of electrons added to the conduction band approaches the number of In atoms of 3.09 × 1022 cm−3, which is still an order of magnitude higher than typical doping concentrations of ITO films. The third mechanism, which can constitute a limitation of the Fermi energy in donor-doped In2O3, is the segregation of the dopant on the surface or grain boundaries. Segregation of Sn on the surface of ITO thin films has been directly observed using in situ x-ray photoelectron spectroscopy (XPS) [19,20]. The Sn concentration observed on the surface of films with carrier concentrations �1021 cm−3 by means of XPS is almost a factor of 2 higher than that of films with lower carrier concentrations deposited from the same target [20]. Using near-ambient pressure XPS, it could further be shown that this segregation is reversible for temperatures above 300 ◦C [19]. The reversibility of segregation indicates an equilibrium situation. In such a case, the origin of the segregation can be related to the dependence of the formation enthalpy of the SnIn donor on the Fermi energy [9], the same behavior as that of intrinsic donor species, such as oxygen vacancies. However, in contrast to the formation enthalpy of intrinsic lattice defects, which must be positive to ensure thermody- namic stability, the formation enthalpy of dopants should ideally be negative in order to be soluble. If the formation enthalpy of the dopant becomes positive, the maximum site fraction of dopants, which can be dissolved in the material, is given by exp(−�HD/kBT ), where �HD is the formation enthalpy of the dopant. At typical processing temperatures of ITO films of 400 ◦C, a formation enthalpy of 1 eV would already limit the mole fraction of soluble Sn donors to < 10−7. According to the formation energy of Sn calculated by Lany and Zunger [7], the formation enthalpy of the SnIn donor indeed becomes positive for higher Fermi energies in In2O3, in agreement with the observed segregation. It is further noted that there is evidence from work function mea- surements and analysis of grain boundary potential barriers that Sn segregates as Sn2+ [20,21], which may be expected as it occurs at high carrier concentrations, that is, under reducing conditions. This contribution provides an experimental determination and quantification of the ultimate limit of the Fermi energy in undoped In2O3 and Sn-doped In2O3 (ITO). It is stressed that the ultimate limitation of the carrier concentration will be observed only under very reducing conditions. Otherwise, self-compensation by oxygen interstitials will limit the carrier concentration, but it will be demonstrated that this does not hold until the highest possible concentrations. Moreover, the ultimate limit in ITO can be observed only if the Sn con- centration is higher than the ultimate electron concentration. The experiments described in this contribution will reveal that the carrier concentration in ITO is limited by the reduction of the Sn donors following Sn4+ → Sn2+, which occurs at a distance between the Fermi energy EF and the valence band maximum EVB of EF − EVB = 3.85 ± 0.1 eV. It will further be shown that degenerate electron concentrations can be in- duced in undoped In2O3 by oxygen vacancies, which act as donors as long as EF − EVB � 3.35 ± 0.1 eV. The extracted limits of the Fermi energy correspond well to experimental data on electron concentrations. II. EXPERIMENT In order to access the origin of the doping limits, x-ray photoelectron spectroscopy measurements of ITO and In2O3 thin films used as the cathode in a solid oxide cell setup were carried out. Similar experimental setups have been described in the literature [22–27] but have only recently been used to analyze Fermi energies [28]. In the present experiments, either a thin (20 nm) In2O3 or ITO film was grown on top of a (111)-oriented Y-stabilized zirconia (YSZ) single crystal. The (111) orientation was chosen to avoid faceting of the film’s surface, as the (111) surface exhibits the lowest surface energy [29–31]. As a counter electrode, a thick (300 nm) ITO film was deposited onto the bottom surface of the YSZ crystal. The sample configuration is shown in Fig. 2(h). All films were grown by magnetron sputtering at a substrate 044601-2 ORIGIN AND QUANTIFICATION OF THE ULTIMATE … PHYSICAL REVIEW MATERIALS 8, 044601 (2024) FIG. 2. Color intensity maps of In 3d , O 1s, and Sn 3d x-ray photoelectron spectra from (a)–(d) ITO and (e)–(g) In2O3 thin films recorded with applied voltage at a temperature of 300 ◦C. The voltages applied at the bottom electrode relative to the grounded top electrode are shown in (a) and (e). The last data point is measured after cooling to room temperature. Spectra recorded at room temperature before heating are not included in the maps for clarity but are presented in the Supplemental Material [32]. The sample configuration is schematically depicted in (h). Selected In 3d and Sn 3d core level spectra representative of regions I–IV are presented in (i) and (j) for ITO and in (k) for In2O3. The spectra are deconvoluted in different components using a least squares fitting procedure. Details are provided in the Supplemental Material [32]. temperature of 400 ◦C, ensuring sufficient conductivity of the films [19]. The ITO films were deposited from a target con- taining 10 wt % SnO2, corresponding to 9.21 cation% Sn or 2.846 × 1021 cm−3 Sn atoms. The samples were then mounted on a sample holder, which allowed us to apply a voltage be- tween the top and bottom electrodes inside the electron spec- trometer system (Physical Electronics PHI 5700). Prior to the measurements, the samples were heated at 400 ◦C in 0.5 Pa O2 for 1 h to remove adsorbates originating from exposure of the samples to air [19]. As the annealing chamber is directly connected to the photoelectron spectrometer (see Fig. S1 in the Supplemental Material [32]), the samples do not show any carbon emissions at the beginning of the experiment, as demonstrated in Fig. S2 in the Supplemental Material [32]. The removal of hydrocarbon and hydroxide/water adsorbates by this treatment is furthermore important for establishing flat-band conditions [21], which is a prerequisite for inter- preting the surface sensitive XPS measurements in terms of bulk Fermi levels. While surfaces of In2O3 or ITO can exhibit a surface electron accumulation after exposure to air [33], leading to downward surface band bending [21], the surface Fermi energies of in situ processed samples directly corre- spond to the electrical and optical properties measured on the same samples [21]. X-ray photoelectron spectra were recorded at room tem- perature, after heating to 300 ◦C without applied voltage and subsequently at 300 ◦C with stepwise increasing voltage. A temperature of 300 ◦C was selected as a compromise between fast enough oxygen and slow enough cation diffusion [34]. Experiments performed at 250 ◦C exhibit slower changes and poor saturation of the effects. At higher temperature, cations will diffuse and segregate on surfaces or grain boundaries, thereby affecting the doping level in the films [19,20,35]. XPS binding energies were calibrated with a sputter-cleaned Ag foil on the same day as the measurement. During mea- surements, the top electrode was connected to the ground to eliminate direct binding energy shifts induced by the applied voltage. The conical shaped top electrode allowed us to apply several hundred volts across the sample without disturbing the spectra [28]. 044601-3 KLEIN, FREBEL, CREUTZ, AND HUANG PHYSICAL REVIEW MATERIALS 8, 044601 (2024) III. RESULTS AND DISCUSSION Applied voltages, color intensity maps, and selected In 3d and Sn 3d core level spectra recorded with monochromated Al Kα excitation are shown in Fig. 2 (see Figs. S4 and S6 in the Supplemental Material [32] for a direct representation of all spectra). The line shape analysis of the In 3d and Sn 4d spectra are also included in Fig. 2(i) and 2(j). Before a voltage at 300 ◦C is applied, the In 3d , Sn 3d , and O 1s binding energies of the ITO film all shift to lower binding energies [see region I in Fig. 2(b)–2(d)]. This can be assigned to the oxidation of the top ITO layer caused by migration of oxygen from the thicker ITO film at the bottom. This oxida- tion of the thin top layer concurs with the sign of the current between the two electrodes (see Fig. S3 in the Supplemental Material [32]). As soon as the top electrode is cathodically polarized (a positive voltage is applied to the bottom electrode with respect to the grounded top electrode), the current is inverted, and the binding energies of all three core levels increase significantly [region II in Figs. 2(b)–2(d)], indicating extraction of oxygen from the film. With increasing binding energy, all core levels of the ITO film also develop pronounced asymmetry at higher binding energy. This is caused by an excitation of the electron gas, leading to an increased splitting of the core levels into a sharper screened component at lower binding energy and a broader unscreened component at higher binding energy [see labeled components in Figs. 2(i) and 2(j)] [36]. The asymmetry, therefore, also confirms the reduction (increasing carrier concentration) of the film. In the early stages of region II, large changes in binding energy are not reflected in a reduction of the oxygen content of the film [see Fig. 3(e)]. This is not surprising, as the number of compen- sating oxygen interstitials is not very high. The difference in atomic oxygen content between fully compensated Sn donors (one oxygen interstitial per two donors) of 10 wt % SnO2 doped In2O3 is only 0.7%. Increasing the voltage to �1.4V [region III in Figs. 2(b)– 2(d)] results in only a little further increase of binding energy, but a new component emerges in the Sn 3d at lower binding energy [≈ 485.7eV; see Fig. 2(j)]. This broadening can be attributed to a partial reduction of Sn. As Sn3+ is not a com- mon oxidation state of Sn, we assign this peak to Sn2+. When the voltage is further increased to 1.7 V in region IV, metallic Sn and In species emerge at binding energies of ≈ 444 and ≈ 485eV, respectively. An increase in binding energy is also observed when the undoped In2O3 film is cathodically polarized [see Figs. 2(e)– 2(g) and 2(k)]. The binding energies of the In 3d and O 1s emissions are lower compared to those of ITO, and the asym- metries of the two peaks at higher binding energy are less pronounced. Both observations correspond to a lower carrier concentration in the In2O3 film. Metallic indium is observed when the voltage is increased to 1.4 V. In the case of the In2O3 film, the metallic component of the In 3d emission is not separated from the oxide component as in the case of ITO, as the binding energy of the screened oxide component of In2O3 is lower than that of ITO. The evolution of core level binding energies and the oxy- gen content of the samples are shown in Fig. 3. The oxygen content is determined from the integrated core level intensities FIG. 3. Extracted data from analysis of XP spectra recorded in the course of the electrochemical polarization experiments at 300 ◦C depending on the applied voltage for (a)–(f) ITO and (g)–(l) In2O3. Applied voltages are given in (a) and (g). In 3d and O 1s binding energies are given in (b) and (h) and (c) and (i), respectively. Binding energy differences between screened and unscreened components of the In 3d emission are given in (d) and (j). Atomic oxygen concentra- tions are given in (e) and (k). Relative contributions of Sn oxidation states are given in (f), and that of the metallic In fraction of In2O3 is given in (l). The first and the last data points are recorded at room temperature before sample heating and on the day following the high-temperature measurements after sample cooling. Solid and dashed lines in (b), (c), and (h) correspond to barycenter energies and peak maxima, respectively. Note that binding energies measured at 300 ◦C are typically 0.1–0.2 eV lower than those measured at room temperature. while taking the sensitivity factors of the spectrometer system into account [37]. In the case of ITO, the binding energies clearly saturate at the end of region II, in which the oxygen content starts to decrease. The oxygen content of the ITO film saturates in region III, before it starts to decrease in region IV to a value of 50 %. The final reduction in oxygen content comes with the observation of metallic indium. The same oxygen content of 50% is determined for the In2O3 film when metallic In emerges. Note that the atomic concentration of oxygen, which is determined from the integrated intensities of 044601-4 ORIGIN AND QUANTIFICATION OF THE ULTIMATE … PHYSICAL REVIEW MATERIALS 8, 044601 (2024) the O 1s, In 3d5/2 and Sn 3d5/2 core level emissions divided by their respective sensitivity factors given by the manufacturer [37], should not be taken as absolute values. Nevertheless, they exhibit reproducible relative numbers. The atomic oxy- gen contents of In2O3 films doped with different amounts of Sn are given in Fig. S7 in the Supplemental Material [32]. The values are obtained from x-ray photoelectron spectra recorded directly after deposition without breaking vacuum and reveal an average atomic oxygen content of a little less than 56% of clean In2O3 surfaces, which is assigned to stoi- chiometric In2O3 with a nominal oxygen content of 60%. The higher initial oxygen contents given in Figs. 3(e) and 3(f) are attributed to the different preparations of the films, which in- volves exposure to air after deposition and subsequent heating in oxygen for surface cleaning. The different treatments can affect the surface termination and result in different amounts of adsorbed oxygen species. The metallic In in In2O3 is observed at a lower Fermi energy than in ITO. Therefore, it can be concluded that the for- mation of metallic In at 1.4 V in In2O3 is a chemical reduction caused by the removal of oxygen. An electrochemical reduc- tion of In3+ in In2O3 should occur at a Fermi energy which is at least as high as that observed in ITO. Consequently, an electrochemical reduction of In is not the ultimate limitation for the Fermi energy in In2O3. That metallic In appears only if the oxygen content is reduced to 50% in In2O3 and ITO indicates a chemical reduction is the origin of the observation of metallic In in both materials. A chemical reduction will happen when the oxygen chemical potential, which is related to the oxygen deficiency δ in In2O3−δ , exceeds the formation enthalpy of In2O3. Applications of ITO in electrical devices are mostly at ambient temperatures not exceeding 100 ◦C. At these temper- atures, the diffusivity of oxygen is too low to allow exchange of oxygen during operation [34]. At higher temperatures, when oxygen diffusion is fast enough [35,38], reduction and oxidation processes in electrochemical cells are, in princi- ple, reversible. Li-ion batteries, solid oxide fuel cells, and solid oxide oxygen sensors are examples of this. Therefore, the reduction of Sn4+ → Sn2+ is expected to be completely reversible. In contrast, the formation of metallic In and Sn after reduction of In2O3 or ITO thin films is only partially reversible. Once metallic In and Sn are formed at elevated temperatures, the metals will agglomerate and form three- dimensional islands due to the surface tension of the metals. Such morphological changes are, indeed, observed in our experiments, as the appearance of metallic In and Sn is accom- panied by the observation of Zr and Y signals from the YSZ substrate, indicating the formation of pinholes in the film (see Fig. S2 in the Supplemental Material [32]). While the metallic In and Sn clusters will be completely reoxidized by inverting the voltage, the morphological changes will not be reversible. In the case of ITO, a reoxidation of the metallic particles may also not result in the formation of a mixed In-Sn-O phase but in separate In2O3 and SnO2 phases. The Sn content at the surface of the sample does not change in the presented experiments. It corresponds well to the nominal target composition (10 wt % SnO2) throughout the whole experiment. Segregation of Sn dopants was ob- served previously for sample temperatures >300 ◦C [19,20]. The segregation is reversible and occurs under reducing con- ditions. Therefore, it is likely that the segregation is driven by a reduced solubility of the dopant at higher Fermi energy [9], which is caused by an increased formation enthalpy of the donor defect [7]. This is a bulk phenomenon which does not depend on specific surface orientation. A potentially preferred surface orientation or microstructure of the films grown on YSZ single crystals should therefore not affect the segrega- tion. The absence of dopant segregation, which was observed previously [19,20], might be caused by a too low sample temperature. Alternatively, Sn can segregate at the YSZ/ITO interface, where the reduction of the films starts. In any case, the Fermi energy at the surface and the observed reduction of Sn is not affected by segregation of Sn. As the reduction of In and the segregation of Sn can be ruled out and as the concentration of Sn in the used ITO film is higher than the electron concentration extracted from the Fermi energy and, independently, from the amount of Sn2+ (see below), the only remaining mechanism limiting the carrier concentration in ITO is the reduction of Sn: Sn4+ → Sn2+. This is fully consistent with the recorded Sn 3d spectra, which clearly develop an additional shoulder at lower binding energies in region III (see Figs. 2(d) and 2(j) and the Supple- mental Material [32]). The observation of Sn2+ in XPS studies of ITO thin films is unique to the cathodically polarized films presented in this study. None of the ITO thin films stud- ied in situ right after deposition exhibited a Sn 3d emission comparable to that observed in region III in Fig. 2, even if the carrier concentration exceeded 1021 cm−3. Evidently, the electrochemical polarization is able to produce more oxygen deficient films. The formation of Sn2+ cannot be caused by the removal of oxygen from the film to substoichiometric values. Such a removal would introduce oxygen vacancies, which would be charge neutral at the Fermi energy at which the reduction of Sn is observed. The electrons introduced by the oxygen vacancies are therefore trapped on the vacan- cies themselves and not available to reduce Sn. The situation is different for undoped In2O3, where it seems straightforward to assign the rise of the Fermi energy upon cathodic polarization to an increase in oxygen vacancy concentration. However, the generation of high electron con- centrations by oxygen vacancies has been controversially discussed in the literature. Employing density functional the- ory calculations of oxygen vacancy formation in the bulk and at surfaces together with the thickness-dependent Hall effect and conductivity measurements, Lany et al. concluded that surface oxygen vacancies rather than bulk defects dominate the conductivity of In2O3 thin films [39]. This conclusion has been related to the fact that oxygen vacancies form deep donor states well below the conduction band minimum in the performed calculations. In contrast, density functional theory calculations using hybrid functionals revealed that oxygen vacancies are shallow donors [8,13] or even inside the con- duction band [12]. This is consistent with the observation of carrier concentrations >1020 cm−3 in nominally undoped In2O3 thin films (see Fig. 1) and ≈1019 cm−3 in In2O3 single crystals [40]. Therefore, it is concluded that the rise in the Fermi energy upon cathodic polarization of undoped In2O3 is due to the generation of bulk oxygen vacancies as donor species with a charge transition inside the conduction band. 044601-5 KLEIN, FREBEL, CREUTZ, AND HUANG PHYSICAL REVIEW MATERIALS 8, 044601 (2024) FIG. 4. Energy levels of the Sn4+/2+ and VO 2+/0 transitions in ITO and In2O3 as determined from the presented experiments. The energy levels correspond to the highest possible Fermi energies in ITO and In2O3, respectively. The reduction of the conduction band minimum energy of ITO relative to In2O3 is caused by mixing with Sn 5s states [41]. The energy gap of In2O3 is taken from [33,42]. Consequently, the upper limits of the Fermi energy and of the carrier concentration in “oxygen-vacancy-doped” In2O3 are determined by the charge neutralization of the oxygen vacancies. According to the difference in barycenter energies [see Figs. 3(b), 3(c), 3(h), and 3(i)], which is the average energy of the screened and unscreened components and best represents the shift of the Fermi energy [36], the highest Fermi energy achievable by oxygen vacancies is 0.5–0.6 eV lower in energy than the one given by the Sn4+/2+ transition. The upper limits of the Fermi energy in ITO and In2O3, which correspond to the charge transition levels of Sn and oxygen vacancies, respectively, can now be extracted from the binding energies provided in Figs. 3(b) and 3(g). For this, we take the barycenter energies and subtract the binding energy difference between the In 3d5/2 level and the valence band maximum, which has been determined to be 441.8 ± 0.05 eV [19]. It was argued by King and coworkers [33] that this value has to be decreased by ≈ 0.2 eV due to the sharp increase in the density of states below the valence band maximum and the limited experimental resolution; this idea was later adapted by Klein [21]. Moreover, the barycenter energies have to be taken at room temperature, which adds another 100 meV due to the temperature dependence of the binding energies. Taking this into account, the In 3d barycenter en- ergies of 445.35 ± 0.05 and 444.85 ± 0.05 eV measured for ITO and In2O3 at 300 ◦C before the metallic In species appear correspond to Fermi energies of EF − EVB = 3.85 ± 0.1 eV and EF − EVB = 3.35 ± 0.1 eV, respectively. The result is il- lustrated in Fig. 4. The maximum Fermi energy of In2O3 of 3.35 eV above the valence band maximum extracted from the experiment is within the range of 3.2–3.85 eV determined by DFT calculations with different hybrid functionals [12]. The Fermi energies determined by surface sensitive XPS measurements in the present experiments should agree with the Fermi energies in the bulk within an uncertainty of ±0.1 eV. As already mentioned in Sec. II, the absence of noticeable surface contaminations suppresses the surface elec- tron accumulation layer observed for air-exposed surfaces [33]. Adsorption of water, for example, can particularly in- duce a substantial increase in the surface Fermi energy on semiconducting oxides [17,18]. Moreover, the samples be- come highly conducting upon reduction. Consequently, the extension of the space charge region at the surface will even- tually be reduced to values lower than the inelastic mean free path of the photoelectrons. Therefore, the core level binding energies extracted from XPS will hardly be affected by the space charge region (a detailed discussion of the effect of surface space charge regions of degenerately doped oxide semiconductor is given by Weidner [43]). The limits of the Fermi energy can be used to estimate the limits of carrier concentrations if the band gap shift by oc- cupation of the conduction band states (Burstein-Moss shift) and the band gap lowering (renormalization) can be quan- tified. For this purpose, we refer to the work of Feneberg and coworkers, who studied epitaxial doped and undoped In2O3 thin films and single crystals by means of spectro- scopic ellipsometry [44]. From Fig. 13 of Ref. [44], the carrier concentrations corresponding to Fermi energies of 3.85 ± 0.1 and 3.35 ± 0.1 eV are 1.9 ± 0.25 × 1021 and 6 ± 1.5 × 1020 cm−3, respectively. According to Fig. 3(f), the concen- tration of Sn2+ exhibits a clear saturation at 18% of the total Sn content. As every Sn2+ ion removes two electrons from those donated to the crystal, the maximum electron concen- tration estimated from the Sn2+ content of a total of 2.846 × 1021 cm−3 Sn atoms amounts to 1.82 × 1021 cm−3. Therefore, the maximum electron concentration extracted from the Sn2+ concentration agrees well with the one estimated from the Fermi level position, providing quantitative validation for the conclusion that the ultimate carrier concentration in Sn-doped In2O3 is limited by the reduction of Sn. The absence of Sn2+ in 119Sn Mössbauer spectra [45] is also not in conflict with the conclusion, as no Sn2+ is expected as long as the carrier con- centrations are still limited by oxygen interstitials under not too strongly reducing conditions. Moreover, reported reliable carrier concentrations of ITO are close to this limit but do not exceed the value given above [4,44,46–48]. In particular, films grown by molecular beam epitaxy showed highest carrier con- centrations of 1.5 × 1021 cm−3 and the formation of volatile Sn2+O at high Sn concentration [48]. The ultimate carrier concentration estimated from the Fermi energy for undoped In2O3 of 6 × 1020 cm−3 agrees well with the highest carrier concentrations of Ti-doped In2O3 thin films of 7 × 1020 cm−3, for which it has been suggested that the free carriers are not directly generated by the Ti atoms but by oxygen vacancies introduced by the scavenging of oxygen required for the for- mation of TiO2 precipitates [49]. The upper limits of the Fermi energy, which are related to the charge transition levels of the active dopant species (see Fig. 1), are different from those calculated using density functional theory. We are aware of only a single calculation for the Sn donor, which gives a Sn4+/3+ charge transition just below the bottom of the conduction band [39]. Regard- ing oxygen vacancies, several calculations derive V2+/0 O or V1+/0 O charge transitions very close to the conduction band 044601-6 ORIGIN AND QUANTIFICATION OF THE ULTIMATE … PHYSICAL REVIEW MATERIALS 8, 044601 (2024) minimum or below it but not 0.5 eV above it [7,11,13–15]. An analysis of the lattice relaxation of the different charge states performed by Linderälv et al. [15] particularly sug- gests a deep donor state of the oxygen vacancy, i.e., a charge transition well below the minimum of the conduction band. Apparently, there is a pronounced discrepancy between the experimental charge transition levels and those calculated us- ing density functional theory. The origin of this discrepancy might partially be related to entropy contributions to the defect formation enthalpies, which can be several kB but have been quantified for only the doubly charged state of the oxygen vacancy [50]. The charge transition level will be affected only if entropy contributions are different for the different charge states. A major difference between the reported experiments and the calculations is the concentration of defects. While the calculations are ideally performed for isolated (nonin- teracting) defects, defect-defect interactions are relevant in the present experiments. An association of the derived Fermi energy limits in terms of charge transition levels of isolated defects is therefore not reasonable. However, the limits ex- tracted from our experiments are those which are relevant for the limitation of the carrier concentration, and it remains valid that this limit is caused in ITO by the reduction of the Sn donors and in undoped In2O3 by the neutralization of the oxygen vacancies. While defect calculations can be easily performed for many materials, experimental data for charge transition levels are very scarce. Therefore, the values reported in this work may become a benchmark for revealing the origin of the differences in the present calculations. IV. SUMMARY AND CONCLUSIONS The chemical and electronic modification of In2O3 and 10 wt % (2.846 × 1021 cm−3) Sn-doped In2O3 were studied by photoelectron spectroscopy using an electrochemical cell with an oxygen ion conducting Y-stabilized ZrO2 as the electrolyte. At a substrate temperature of 300 ◦C, cathodic polarization of the films leads to the removal of oxygen, which is accompanied first by an increase in the Fermi energy and, eventually, by the appearance of metallic In (and Sn). The Fermi energy in Sn-doped In2O3 can be raised up to a value of EF − EVB = 3.85 ± 0.1 eV. Further increasing the applied voltage does not raise the Fermi energy anymore but results in the observation of reduced Sn2+ species. This leads to the con- clusion that the ultimate limitation of the carrier concentration in ITO is determined by the reduction of the dopant and not by self-compensating formation of oxygen interstitials. The carrier concentrations related to the upper limit of the Fermi energy are 1.9 ± 0.25 × 1021 cm−3. For nominally undoped In2O3, the Fermi energy can also be increased by cathodic polarization of the film up to EF − EVB = 3.35 ± 0.1 eV. Fur- ther removal of oxygen leads to the observation of metallic In. Only oxygen vacancies can be the origin of such a high Fermi energy in nominally undoped In2O3 films. Therefore, it is con- cluded that the charge transition of oxygen vacancies does not occur inside the energy gap but inside the conduction band and that it determines the limit of the carrier concentration in nom- inally undoped In2O3 at a value of ≈6 ± 0.15 × 1020 cm−3. The described experiments constitute a unique opportu- nity to experimentally determine charge transition levels and Fermi energy limits, particularly for oxide materials. Such data can serve as guidelines for developing suitable deposition processes and also as a benchmark for unraveling the existing differences between experimental values and those predicted by ab initio calculations. ACKNOWLEDGMENTS The presented work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Founda- tion) under Project No. KL1225/9-1 and by the Son- derforschungsbereich (SFB, Collaborative Research Centre) 1548, FLAIR (Fermi Level Engineering Applied to Oxide Electroceramics). The development of the experimental ap- proach was carried out within the LOEWE priority project FLAME (Fermi Level Engineering of Antiferroelectric Ma- terials for Energy Storage and High Voltage Insulation Systems), which was funded by the Hessisches Ministerium für Wissenschaft und Kunst (hmwk), Germany. 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