Indium Gallium Oxide Alloys: Electronic Structure, Optical Gap, Surface Space Charge, and Chemical Trends within Common-Cation Semiconductors.

The electronic and optical properties of (InxGa1-x)2O3 alloys are highly tunable, giving rise to a myriad of applications including transparent conductors, transparent electronics, and solar-blind ultraviolet photodetectors. Here, we investigate these properties for a high quality pulsed laser deposited film which possesses a lateral cation composition gradient (0.01 ≤ x ≤ 0.82) and three crystallographic phases (monoclinic, hexagonal, and bixbyite). The optical gaps over this composition range are determined, and only a weak optical gap bowing is found (b = 0.36 eV). The valence band edge evolution along with the change in the fundamental band gap over the composition gradient enables the surface space-charge properties to be probed. This is an important property when considering metal contact formation and heterojunctions for devices. A transition from surface electron accumulation to depletion occurs at x ∼ 0.35 as the film goes from the bixbyite In2O3 phase to the monoclinic β-Ga2O3 phase. The electronic structure of the different phases is investigated by using density functional theory calculations and compared to the valence band X-ray photoemission spectra. Finally, the properties of these alloys, such as the n-type dopability of In2O3 and use of Ga2O3 as a solar-blind UV detector, are understood with respect to other common-cation compound semiconductors in terms of simple chemical trends of the band edge positions and the hydrostatic volume deformation potential.

Indium oxide (In 2 O 3 ) is the material of choice (most often doped with Sn) for applications requiring transparent conductive electrodes, owing to its propensity for n-type dopability providing great electrical performance, and its large energy gap (∼2.9 eV fundamental band gap and ∼3.7 eV for the first dipole-allowed transition 1 ) giving high optical transparency. 2 In contrast, β-gallium oxide (β-Ga 2 O 3 ) is a rapidly emerging semiconductor material and its fundamental properties have been relatively less explored in comparison. With a high breakdown voltage and very large optical gap (∼4.8 eV), β-Ga 2 O 3 is a promising candidate for applications in high-power electronic devices and solar-blind UV detectors. 3 Indium gallium oxide alloys have generated much research interest in the past, often in the amorphous state used for thin film transistors. [4][5][6][7] Favourable energy alignment when forming heterojunctions and alloys is imperative for optimal device performance. Hence, careful engineering of the optical gap and surface elec-  Figure 1. β-Ga 2 O 3 has a monoclinic structure with two inequivalent Ga sites, a distorted tetrahedral site and a distorted octahedral site (Figure 1(a)). In 2 O 3 has a cubic (bixbyite) unit cell also with two inequivalent cation sites, a distorted and a symmetric octahedron ( Figure 1(c)). Further, an intermediate hexagonal InGaO 3 phase has been reported, which has a symmetric In site and a trigonal bipyramidal Ga site (Figure 1(b)). [8][9][10] It is not yet well explored how these different structures affect the surface electronic properties of these materials. This fundamental understanding is of great importance for the development of new electronic devices and heterostructures. Recent developments in deposition methods and combinatorial material science (materials possessing a composition gradient) 8 give us the ability to quickly and rigorously determine the properties of many new material compositions using one film. In this study, we employ the recent advances in high quality combinatorial growth methods with the rapid development in combinatorial measurement, in order to fully investigate the electronic structure and behaviour of (In x Ga 1-x ) 2 O 3 alloys. We use high-resolution scanning X-ray photoemission spectroscopy (XPS), as well as state-of-the-art first-principles calculations to determine the electronic structure of (In x Ga 1-x ) 2 O 3 combinatorial films over nearly the whole composition range (0.01<x<0.82). This combined with optical measurements help us to understand the compositional dependence of the Fermi level with respect to the band edges at the surface of (In x Ga 1-x ) 2 O 3 . We explore the surface space-charge transition from electron accumulation in In 2 O 3 to depletion in β-Ga 2 O 3 , a property that has implications for the incorporation of these materials in devices in the future. We compare density functional theory (DFT) calculated density-of-states (DOS) for the different phases looking at the constituent orbital contributions, and also compare this to the XPS valence band spectra and occupied semi-core d levels. From this we observe indicators of p-d repulsion which affects the position of the VBM, as well as s-d hybridisation in the semi-core levels which is associated with materials with similar energy s and d levels and occupied cation d levels. Looking at these orbital contributions, as well as knowledge of the volume deformation potential (how the material's band gap varies with changing volume), allows us to fully explore the chemical trends of In 2 O 3 and β-Ga 2 O 3 . This explains why In 2 O 3 is extremely n-type dopable, and why β-Ga 2 O 3 has an extremely large band gap, even for an oxide semiconductor.

Experimental Details
A continuous composition spread (CCS) (In x Ga 1-x ) 2 O 3 film was grown on a 51 mm-diameter c-plane sapphire wafer via pulsed laser deposition (PLD) using a two-fold azimuthally segmented target for ablation. SiO 2 (0.1 wt. %) was mixed with the In 2 O 3 and Ga 2 O 3 source powders prior to target fabrication, to achieve sufficient conductivity via Si n-type doping to avoid charging when performing XPS measurements. The growth temperature and oxygen background pressure were 650 • C and 3×10 -4 mbar, respectively. Further information on the deposition process is given by von Wenckstern et al. 8 A 4 mm-wide, 51 mm-long strip of the wafer with the full composition gradient across it was cut and all subsequent measurements were performed on this strip. The films surface roughness is not assessed here, but has been determined previously for this system deposited in the same way. 11 Despite an increase in surface roughness when the cubic bixbyite phase is reached, the films should have sufficiently low surface roughness required for device applications including heterostructure-based devices.
The spatial distribution of In, Ga and Si content throughout the film was determined by energy-dispersive X-ray spectroscopy (EDX) using an FEI NovaLab 200 equipped with an Ametek EDX detector. The spatially resolved X-ray diffraction patterns (XRD) from the film were recorded using a PANalytical X'pert PRO MRD X-ray diffractometer equipped with a PIXcel3d detector operating in one-dimensional scanning mode with a monochromated Cu Kα source. The XPS measurements were performed using a Thermo Scientific K-Alpha instrument with a monochromated microfocused Al Kα X-ray source (1486.6 eV). These measurements were performed under ultrahigh vacuum (UHV) conditions (<10 -9 mbar).
The scans were measured by focusing the beam width to 400 µm spot size on areas of the film with the film being translated by 1 mm between each measurement. An analyser pass energy of 50 eV was used, giving a spectrometer resolution of 0.65 eV, enabling peak positions to be determined to within ±0.1 eV. Sample charging was corrected by a dual beam charge compensation system. Optical transmittance determination was performed using a Shimadzu UV-Vis-IR 3700 spectrophotometer with an integrating sphere detector which employs a photomultiplier detector to reach energies up to 6.5 eV. All measurements were performed at room temperature.

Computational Details
The theoretical calculations were performed using the HSE06 screened hybrid functional 12 and projector augmented wave (PAW) approach 13 as implemented in the VASP code. 14 We include semi-core 3d electrons of Ga and 4d electrons of In as explicit valence states and set the fraction of screened Hartree-Fock exchange to 32% for β-Ga 2 O 3 and InGaO 3 , and 28% for In 2 O 3 (in order to better match the experimental band gaps). All unit cell parameters were optimized using a plane-wave cutoff of 520 eV and integrations over the Brillouin zone were performed using a 6×6×6 Γ-centered grid of Monkhorst-Pack special k-points for Ga 2 O 3 , a 10×10×4 grid for InGaO 3 and a 4×4×4 grid for In 2 O 3 . Densities of states were evaluated using the relaxed geometries and the tetrahedron method with Blöchl corrections 15 and included scalar-relativistic effects for the In-containing compounds.
For β-Ga 2 O 3 , this choice yields a direct band gap of 4.85 eV and optimal lattice constants of 12.21, 3.03, and 5.79Å for the a, b, and c cell parameters, respectively, in excellent agreement with experimental values. [16][17][18] Our optimized lattice constants for the hexagonal  phase is (201) oriented. 8,9,19 This holds true for the majority of the film. Figure 2(d) shows that the In 2 O 3 dominated region of the film grows with (111) orientation, although a small peak just to the left of the 222 peak (∼29 • ) is also visible which originates from the 0004 reflection from the hexagonal InGaO 3 phase, consistent with figure 2(c). [8][9][10]19 In both plots we also see the 006 and 00 12 peaks due to the sapphire substrate, which have been left unlabelled. It is clear the (In x Ga 1-x ) 2 O 3 material is crystalline across the whole film (and so the whole composition range).
We are able to directly quantify the spatial distribution of Ga, In and Si content of the film using EDX, and correlate these data with the XRD results by taking measurements at the same positions in the film, demonstrating the power of the combinatorial approach.   (roughly one to one In to Ga ratio). Beyond z = 10 mm, the rate of change of In/Ga content across the film lessens, whilst the film takes on the monoclinic β-Ga 2 O 3 structure. The false-colour plot of In content seen in Figure 3(b) shows this well with a very gradual growth of In content from right to left, until around a third of the distance along the film, when the In content increases rapidly. We also see the great control of In content over the film from the CCS PLD deposition method. The In content varies horizontally across the film but there is negligible variation vertically in the narrow strip of material investigated using photoemission spectroscopy.

Valence Band X-ray Photoelectron Spectroscopy
XPS is an extremely powerful tool for probing the electronic structure of materials. It is made even more informative when used as a combinatorial characterization method. Figure 4 shows the XPS valence band (VB) spectra of the material, with the leading edge enlarged in the right hand panel. The top-most data set, which is coloured in red, is taken from the Ga-rich end of the film, with subsequent spectra fading to black as more In content is incorporated. This is supported by the XPS peak intensities in SI Figure S1 where the Ga 2p peaks slowly diminish in intensity, while the In 3d intensity grows relatively moving down the plot. A very clear change in shape of the valence band can be seen in Figure 4, going from the broad β-Ga 2 O 3 valence spectra to the narrower In 2 O 3 spectra. This directly reflects the changes in structure seen in Figure 2. There is also a larger valence band maximum (VBM) to Fermi level (E F ) separation for β-Ga 2 O 3 than for In 2 O 3 (Ref. 22) as is clearly seen in Figure 4, as the VBM slowly moves from left to right as the In content increases.
The VBM position from each spectrum could be estimated by a linear extrapolation method to the leading edge of the valence spectra. However, due to the effects of instrumental broadening of the spectra, this is not an accurate method for determining the VBM position, especially for systems with a very high DOS at the VBM such as the flat bands of In 2 O 3 and β-Ga 2 O 3 . Instead it is best practice to fit DFT-calculated valence spectra to the data and determine the energy distance from zero. This particular case is complicated further E F Figure 4: High resolution XPS plots of the valence band of (In x Ga 1-x ) 2 O 3 film. 46 spectra were recorded across the film at 1 mm intervals, matching the EDX measurement in Figure 3. The spectra recorded from the Ga-rich end of the film are at the top, with increasing In content down the plot.
by the fact that we have many phases contributing to our spectra, making true calculated representation of the spectra very difficult (many calculations would be required). Instead, we acknowledge a ∼0.6 eV shift determined here and elsewhere from XPS of single phase

Surface Space-Charge
The surface of In 2 O 3 has previously been shown to display electron accumulation 23,26 while β-Ga 2 O 3 displays electron depletion. 24,27,28 This is vital information for surface and interface sensitive devices such as chemical sensors and heterostructures. Naturally then we ask how the surface space-charge evolves over the alloy composition range, with the vision of tuning the surface electronic properties to specific device needs. To determine this, we find the barrier height Φ B (analogous to the Schottky barrier height of a metal/semiconductor contact) which is given as the separation between the conduction band minimum (CBM) and E F .
Optical transmission measurements and derived absorption spectra (see Figure S4) were used to determine the bulk VBM to E F separation (once the dipole forbidden transition from the topmost valence band in In 2 O 3 -like alloys is accounted for) at different composition points of the material. Figure 6 displays the optical gaps extracted from transmission measurements.
The intervals between measurements across the film were greater than for the XPS results, but the positions were again translated into indium content via the EDX results. Optical gaps for end-point compositions (In(x)=0 and In(x)=1) were also added to the plot from the literature. 1,24,29 An optical gap bowing curve is fitted to the data and shown in Figure 6. The optical gap bowing is described by where b is the bowing parameter.
corresponds to the E F lying below (above) the CBM at the surface. Figure 7: (a) Variation of band gap (E g ) and barrier height (Φ B ) at the (In x Ga 1-x ) 2 O 3 surface with respect to varying indium content (x). Energy gaps were determined in this study by transmission measurements ( ), as well as values being taken from the literature ( Oshima, 32 Regoutz, 33 Wenckstern, 34 Yang, 35 ♦ Zhang, 36   VB to lowest CB transition in In 2 O 3 is known to have minimal dipole intensity, 1 and so, to achieve the real E g value, an energy of 0.8 eV was subtracted from the measured absorp-tion onsets (as this is the energy difference between the first allowed transition and dipole forbidden transitions 1 ). Here, we set an In content of x = 0.6 for the phase transition from bixbyite to hexagonal (mixed) phase, as no data points exist in this region. This estimated value is informed by previous literature 31 as well as the data presented in Figures 2 and   3. The band gap smoothly decreases from ∼4.7 eV at low In content, and abruptly alters when the phase changes to bixbyite before decreasing further to ∼2.9 eV at high In content. Φ B is plotted below E g in Figure 5(a), and displays a very similar trend to the band gap.
For the In-poor compositions, a positive value of Φ B is observed corresponding to upward band bending (schematically shown in Figure 7 Their results are in excellent agreement with our findings, showing that the β-Ga 2 O 3 phase has a higher Schottky barrier height which decreases as In content is increased. They find the barrier height difference between the two end phases to be ∆Φ SB ∼ 0.8 eV, reasonably close to the difference we see here of ∆Φ B ∼ 1.2 eV. They also find that the Ga-rich phase has the best Schottky diode response (ideality factor) whilst the In-rich has the lowest series resistance. The band bending diagrams for the two binary materials are shown in Figure 7(b) and (c). Interestingly, both In x Ga 1-x N (Ref. 39) and In x Ga 1-x As (Refs 40,41) also display an electron accumulation to depletion transition at the surface with increasing Ga content.
Those cases are simpler as no phase transition occurs across the composition range. However, the same trend is observed with Ga compounds displaying a larger band gap and higher, positive Φ B and surface electron depletion, while In compounds have a smaller band gap with a negative Φ B and surface electron accumulation. This will be discussed further below in the section on chemical trends.

Electronic Structure
To further explore the effects of the changing cation composition in (In x Ga 1-x ) 2 O 3 alloys, we focus on the electronic structure of the stoichiometric materials In 2 O 3 , InGaO 3 and Ga 2 O 3 , utilizing DFT calculated DOS for the three materials. The partial and total density-of-states are displayed for Ga 2 O 3 , InGaO 3 , and In 2 O 3 in Figure 8(a-f). These plots show the orbital contributions (without any cross section corrections) and include a small amount of Gaussian broadening (0.1 eV full-width at half-maximum) to assist in visualizing the data. For the calculated spectra, the zero of the binding energy scale is set to the VBM.
The VBs of β-Ga 2 O 3 (Figure 8      the spectra. Figure 9(a) displays the calculated β-Ga 2 O 3 spectra in red, followed by the InGaO 3 phase in the middle in brown, and finally the In 2 O 3 in black at the bottom, with the PDOS contributions labelled. Figure 9(b) shows the experimental data where the phase transition is demonstrated utilizing phase pure single crystalline data for the top and bottom spectra. 23,24 The brown spectrum in the centre belongs to the hexagonal (mixed) phase InGaO 3 , while the spectra either side of this correspond to an In content of approximately 25% and 75%, respectively. All experimental spectra have been shifted to locate their VBM at 0 eV for comparison with the calculated DOS. Comparing the spectra in Figure 9(b), the highest binding energy feature of the β-Ga 2 O 3 (Ga 4s dominated) is prominent around 6.5 eV, but diminishes in size and shifts to lower binding energy as In content is increased.
In the InGaO 3 spectra, this feature is extended in energy but much less intense, matching the calculations in Figure 9(a) extremely well albeit with slightly less features resolved than calculated. This feature shifts and diminishes further, being located at ∼5.5 eV in pure The leading edge at the VBM looks similar in the two end-point spectra, but the InGaO 3 phase has additional intensity due to the contribution from two cation d-levels.
Turning attention now to the calculated semi-core levels in Figure 9 This is a deficiency of the DFT approach used in these calculations, 52 despite the HSE06 functional generally giving very accurate band gaps, quasiparticle effects are neglected which have been shown to redistribute spectral weight at higher binding energies. 46,48,51 We also see that the experimentally measured peaks are much wider than those calculated (which are broadened in the same manner as the VB in Figure 9(a)). This may be attributed to an increase in lifetime broadening for the localized semi-core levels compared with the much less localized valence states, 29 although we cannot rule out final-state relaxation effects working to narrow the valence band spectra, which are not included in the calculation. 53 Despite this, the measured regions share similar features to the calculated ones, such as the asymmetry seen in the low energy peaks. It is clear in Figure 9(d) that the In 4d-derived peak is much wider than the Ga 3d peak. This is due to a higher degree of spin-orbit interaction which splits the In 4d band. Spin-orbit coupling (SOC) has been included in the DOS for In 2 O 3 in Figure 9(c), explaining its irregular shape relative to the Ga 3d level in agreement with previous studies. 54 See SI Figure S6 for a comparison of the In 4d level calculated with and without SOC included.
The higher binding energy peaks seen around ∼ 19 eV in Figure 9(c) and (d), which comprise of mostly O 2s character, are vastly overestimated in intensity in the calculation compared to experiment, where the intensity had to be multiplied by a factor of ×15 before it was visible. This again may be attributed to the issues discussed above. The theory predicts a fairly strong contribution from the metal d-level to this peak, giving further evidence that s-d hybridization occurs in all three materials. It is also worth noting that, for the mixed phase InGaO 3 spectra, there are two distinct peaks around 13 and 15 eV in the theory (15 and 17 eV in the experiment). The peak intensities vary heavily with indium content (x), which is a good indicator of the extent of alloying and the stoichiometry of the system (acknowledging that the photoionisation cross section is roughly twice as large for In 4d compared to Ga 3d, explaining why the In 4d peak is twice as intense as the Ga 3d peak in the stoichiometric InGaO 3 material).
The natural question that follows the determination of the electronic structure of a material is how does this fit with the chemical trends of related materials, such as those with a commoncation (or indeed common-anion). Here we compare the properties of In 2 O 3 , InGaO 3 and β-Ga 2 O 3 with each other, and with other indium-and gallium-containing compounds in the form of the zinc-blende (ZB) and wurtzite III-V semiconductors, that have seen a lot of research in previous years. [55][56][57] The understanding gained from these arguably simpler systems can be used to further our understanding of the metal oxides investigated here. and X (Ref. 61) (In 2 O 3 and β-Ga 2 O 3 may have a smaller indirect transition also but these may be too close to the direct band gaps to definitively prove experimentally 46,51,64 ). Note also that the differences between the VBM position of the common-anion materials (see for example β-Ga 2 O 3 and In 2 O 3 , where the VBM of β-Ga 2 O 3 is lower relative to E CN L ) have been explained for ZB III-V and II-VI semiconductors to be due to the p-d interaction, 42,65,66 a relatively small effect in these materials compared to the orbital positioning, but explaining why the VBM of Ga-V tends to have a lower energy than In-V.
The CBM of these systems all derive from cation-anion s − s hybridization. However, it is clear from Figure 10 Table 1. and a Γ,v V ). The band edge deformation potentials were determined using the branch-point energy (E BP , defined relative to each material's VBM) as a reference level, as described in the text. The α parameter represents the fraction of Hartree-Fock exact exchange incorporated into HSE06 range-separated hybrid functional, which was tuned to reproduce to the experimental band gaps.  Figure S7 and S8, with the results summarized in Figure 10(c) and Table 1.
When considering the absolute deformation potentials of the band edges, as referenced to the E BP in Figure 10(c), we see that a Γ,v V (the deformation potential of the VBM) is positive for oxides and decreases as the coupling from the anion p orbitals increases, becoming negative for phosphides, arsenides and antimonides, which all share similar values. This seems to have only a small effect on the position of the VBM due to lattice compression, which is instead mostly dependent on the anion p orbital position as mentioned. a Γ,c V tends to be a relatively large negative number, contributing much more heavily to | a V | and to the position of the CBM. 55,56,73 In this respect, we also find that the oxides do exhibit significant differences compared to the III-Vs. We find that the a Γ,c V values are again negative for the oxides, but they exhibit a weaker dependence than that in III-Vs. We find that the conduction and valence band deformation potentials are of more comparable magnitudes in the oxides, whereas III-Vs tend to exhibit much larger magnitudes of the a Γ,c V values relative to the a Γ.v V .
When compared to the III-Vs, we find that the oxide to the density functional theory within the local density approximation. 69 Another apparent outlier in Figure 10(a) and (c) is InN, which was discussed previously by Wei et al. 55 to be in no small part due to the relatively small value of a Γ,c V and hence small a Γ V .
Hence, the shifts in the energy gap are heavily affected not only by the positions of the constituent orbital energy levels, but by the changes in the CBM position, the changes in a V , and on the size of the unit cell. We plot the unit cell volumes and the volume per atom (unit cell volume divided by its occupany) in Figure 10(d) to visualise how these sizes vary between materials. Note that In 2 O 3 has an extremely large unit cell, but it contains many atoms, and so its volume per atom is actually rather small in comparison to those in III-Vs. We see in Figure 10(c) that the Ga-anion semiconductors have larger | a V | than the respective In-anion semiconductors. This coupled with the fact that the Ga-based semiconductors have lower unit cell volumes than the respective indium-based compounds means Ga materials tend to have larger band gaps.
To summarise, our results are consistent with previous results on the III-V materials that identify (1) band gap deformation potentials are negative; and (2) this dependence has a far larger contribution from the deformation potential of the conduction band minima (a Γ,c V ) rather than for the valence band maxima (a Γ,v V ). 56,[67][68][69] However, in contrast to the III-Vs, we find (3) larger contributions to the a Γ,v V for the more ionic oxide semiconductors which are of comparable magnitude to the a Γ,c V .

Conclusion
The evolution of the electronic structure of a variable composition (In x Ga 1-

Supporting Information Available
XPS core levels and associated analysis, optical transmission and absorption spectra, XPS semi-core levels, DFT of semi-core levels accounting for SOC, DFT calculated band gap deformation potentials.
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