# Stoichiometry-driven tuning of hole conductivity in MOCVD-grown β-Ga2O3 on r-sapphire substrates

Zeyu Chi, Corinne Sartel, Yunlin Zheng, Yves Dumont, Ekaterine Chikoidze

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Zeyu Chi, Corinne Sartel, Yunlin Zheng, Yves Dumont, Ekaterine Chikoidze. Stoichiometry-driven tuning of hole conductivity in MOCVD-grown β-Ga2O3 on r-sapphire substrates. Crystal Growth & Design, 2023, 969. hal-05532287

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# Stoichiometry-driven tuning of hole conductivity in MOCVD-grown β-Ga₂O₃ on r-sapphire substrates

Zeyu Chi ¹,*, Corinne Sartel ¹, Yunlin Zheng ², Yves Dumont ¹, Ekaterine Chikoidze ¹, *

¹ Groupe d'Etude de la Matière Condensée (GEMaC), Université Paris-Saclay, UVSQ- CNRS, 45 Av. des Etats-Unis, 78035, Versailles Cedex, France

² Institut des Nano Sciences de Paris (INSP), CNRS UMR7588, Sorbonne Université, 4 place Jussieu, 75252 Paris, France

## Abstract

β-Ga₂O₃ is a promising ultra-wide bandgap semiconductor for next-generation power and optoelectronic devices, but achieving stable p-type conductivity remains a major challenge with limited understanding of native point defects engineering. In this work, we report a systematic study on the influence of Ga and O flow rate during MOCVD growth on the structural and electrical properties of undoped β-Ga₂O₃ epilayers. Two sets of samples were grown: (i) varying oxygen content to span O/Ga ≈ 180–2700 at fixed Ga content, and (ii) varying gallium content at fixed O/Ga = 1600. Structural characterization using out-of-plane and in-plane high resolution X-ray diffraction, Raman spectroscopy, and scanning electron microscopy revealed a strong correlation between growth conditions and film microstructure. Increasing O/Ga flow ratio improves grain alignment, reduces lattice disorder. Hall effect measurements show the semi-insulating p-type conductivity in all samples, with enhancement of native p-type conductivity in oxygen-rich conditions, increasing the hole concentration from 6.0×10¹³ to 1.7×10¹⁵ cm⁻³ at 800 K. Interestingly, the improvement in hole mobility correlates with the increasing in Ga content (up to 18.5 cm²/V·s) at higher growth rate and improved grain alignment. These results demonstrate that reproducible control of stoichiometry and microstructure of β-Ga₂O₃ thin films grown by MOCVD provides a possibility to tune native-defect concentrations, thus electrical properties of material.

E-mail addresses: zeyu.chi@uvsq.fr (Z. Chi), ekaterine.chikoidze@uvsq.fr (E. Chikoidze)

<footnote>* Corresponding authors.</footnote>
Introduction

β-Ga₂O₃ exhibits an ultra-wide band gap of 4.6 – 4.9 eV and a predicted high critical electric field larger than 8 MV/cm ¹,², together with the commercial availability of 6-inch wafers, controllable *n*-type doping typically in the range of 10¹⁶–10²⁰ cm⁻³, using commonly group IV elements including Si ³,⁴, Sn ⁵,⁶ and Ge ⁷,⁸, together with alternative elements such as Nb ⁹, Hf ¹⁰, and room-temperature electron mobilities exceeding 200 cm²/(V·s) ¹¹, making it a promising candidate for next-generation power electronics and optoelectronics ¹²,¹³. Its potential has been demonstrated in field-effect transistors ¹⁴,¹⁵, Schottky barrier diode ¹⁶, *p*-NiO/*n*-Ga₂O₃ heterojunction diode ¹⁷,¹⁸, and 2D transistor ¹⁹. Beyond power devices, the large bandgap and radiation hardness also make β-Ga₂O₃ attractive for solar-blind UVC photodetectors ²⁰⁻²². The excellent radiation tolerance was also reported for different Ga₂O₃ polytypes ²³⁻²⁵. Despite significant progress in realizing *n*-type doping, achieving reliable *p*-type conductivity remains a critical challenge, this absence limits the development of bipolar devices (e.g., *p*- *n* junction diodes), while native point defects play a key role in the determination of the electrical properties.

In β-Ga₂O₃, among native defects, oxygen vacancies (V>O) and gallium vacancies (V>Ga) are the
most studied native defects because their formation is strongly affected by oxygen-rich vs. gallium-
rich conditions and they critically influence carrier compensation. V>O is predicted to introduce deep
levels (> 1 eV below the conduction band) and has high formation energy under oxygen-rich
conditions ²⁶⁻³¹. Experimentally, V>O has instead been correlated with blue luminescence and is
thought to act more as a compensating center than a donor ³²⁻³⁴. Gallium vacancies (V>Ga), in contrast,
are widely recognized as deep acceptors with lower formation energy under oxygen-rich conditions.
EPR ³⁵, IR ³⁶, DLTS ³⁷, and positron annihilation ³⁸ studies demonstrate their role as compensating
centers in *n*-type samples. In addition, it was suggested to be the origin of the *p*-type conductivity in
semi-insulating samples with the ionization energy of *E*ᵢ ~1.2 eV ³⁷,³⁹,⁴⁰. In addition to vacancies,
oxygen interstitials (Oᵢ) have also been proposed as relevant native defects under oxygen-rich
conditions. First-principles calculations generally predict Oᵢ to introduce deep levels within the
bandgap, with charge states and stability strongly dependent on the Fermi-level position ²⁶,³¹,⁴¹.
Experimentally, Oᵢ-related defects have been associated with deep trapping behavior and green
luminescence, indicating their potential role in compensation rather than in shallow acceptor doping
²⁶. Beyond isolated point defects, intrinsic complex defects such as the V>Ga–V>O divacancy also
contributes to the blue luminescence ³²,³⁴,⁴²⁻⁴⁵ and may have formation energy comparable to or even
lower than isolated vacancies under oxygen-rich conditions, they are charge-active with stability
depending on the Fermi level ²⁹,⁴⁶. Their acceptor levels are estimated to be from a few hundred meV
above the valence band to around the mid-gap. Recent positron annihilation ⁴⁷ experiments also confirm the presence of such complexes in both conductive and insulating β-Ga₂O₃ samples.

Metal-organic chemical vapor deposition (MOCVD) routinely delivers high-quality epitaxial films with a high growth rate, wafer-scale uniformity. Reported room-temperature mobilities up to 194 cm²/(V·s) ⁴⁸ and low temperature mobility peaks up to 23000 cm²/(V·s) ⁴,⁴⁹,⁵⁰, attest to the attainable material quality. This technique is also suitable for controllable *n*- ⁷,¹⁰ and *p*-type doping ⁵¹,⁵². Critically, the formation and concentration of the point defects mentioned above are strongly dependent on growth conditions, such as oxygen partial pressure, and cation to anion precursor ratios (O/Ga ratio) during MOCVD growth. Yet, a systematic demonstration that controlling O/Ga stoichiometry can be used to promote native *p*-type conduction remains limited.

Here, we investigate high-temperature *p*-type conductivity in undoped β-Ga₂O₃ epilayers grown under controlled oxygen/gallium content. By correlating film structural quality X-ray diffraction (XRD) spectra, Raman spectroscopy, scanning electron microscopy (SEM) images with electrical transport as the O/Ga ratio and the gallium content at fixed O/Ga ratio are varied, we establish specific growth windows that correlate stoichiometry, defect landscape, and microstructural features with the realization of stable, native, semi-insulating *p*-type conduction.

## Results and discussion

For all the β-Ga₂O₃ thin films deposited on sapphire substrates, trimethylgallium (TMGa) and O₂ were used as Ga and O sources, respectively. The oxygen-to-gallium molar ratio (O/Ga) was controlled by adjusting the O₂ flow and the TMGa vapor pressure. To map how O/Ga stoichiometry governs growth rate, structural and electrical properties, we prepared two sets of β-Ga₂O₃ samples (S1 – S15). Key growth parameters and electrical transport measurement data are summarized in Table 1.

1/. The first set, fixed TMGa = 36 µmol/min: the O₂ flow was varied from 100 to 1500 sccm, resulting in different O/Ga ratios = 180 – 2700.

For clarity, samples in this set are referred to by their calculated O/Ga ratios throughout the manuscript, the corresponding sample numbers will also be indicated in each analysis section.

2/. The second set, fixed O/Ga ratio = 1600: the O₂ flow was increased from 300 to 1500 sccm in 300 sccm steps, while the gallium supply was proportionally raised from 12 to 60 µmol/min correspondingly, in 12 µmol/min steps.
**Figure 1 (a)** plots growth rate versus O/Ga ratios at fixed gallium content. The rate rises with oxygen addition at low O/Ga flux ratio, indicating that oxygen is initially a limiting factor for film growth; beyond O/Ga ratio ≈ 500, the growth rate invariant, suggesting a transition to gallium-limited growth at this temperature. As shown later, this kinetic crossover coincides with changes in the film morphology and crystalline order. In contrast, **Figure 1 (b)** shows the growth rate versus Ga content at fixed O/Ga ratio = 1600. A nearly linear increase is observed, consistent with previous reports <sup>49,53</sup>, reaching a maximum growth rate of 2.1 µm/h at 60 µmol/min Ga supply.

<figure><img src="image_2.png" /><figcaption>Figure 1. (a) Growth rate vs. O/Ga ratios at fixed gallium content (36 µmol/min). (b) Growth rate vs gallium flow rate at fixed O/Ga ratio = 1600.</figcaption></figure>

**Figure 2 - Figure 4** show detailed XRD analysis of β-Ga₂O₃ films grown at a fixed TMGa content (TMGa = 36 µmol/min), with varying O/Ga ratio = 180 – 2700 (samples S1, S3, S5, S9, and S10). The specific epitaxy of β-Ga₂O₃ on the Al₂O₃ (012) differs from conventional epitaxy in that no lattice plane lies in the film plane: no film Bragg peaks are expected on the X-ray θ/2θ scan. We showed that the main (-201) lattice planes of β-Ga₂O₃ are tilted relative to the film plane by about 30° toward the *a*-axis of Al₂O₃ (**Figure 2 (a)**) <sup>54,55</sup>. This main orientation is called here as orientation *A*. A secondary orientation, orientation *B*, was also identified as a twin of *A* in keeping the β-Ga₂O₃ *c*-axis (**Figure 2 (b)**). Two equivalent orientations *A'* and *B'* are automatically present, due to the symmetry of the substrate *a*-plane mirror. The sample described in <sup>54</sup> serves here as a reference to monitor deviations in film orientations as a function of O₂ flow.
$$ \beta\text{-Ga}_2\text{O}_3 / \text{Al}_2\text{O}_3 \text{(012)} $$

<figure><img src="image_3.png" /></figure>

Figure 2. Orientation projections of expected epitaxies of β-Ga₂O₃ on Al₂O₃ (012) plane: orientation A (a) and orientation B (b) where the magenta dashed horizontal line indicates Al₂O₃ *a*-axis azimuth and the vertical one Al₂O₃ [02-1] direction azimuth. Equivalent orientations A' and B' are obtained by the substrate vertical *a*-plane mirror symmetry. Δϕ used hereafter is defined as the azimuthal angle from the Al₂O₃ [02-1] azimuth. The β-Ga₂O₃ unit-cell axes, namely the invariant *c*-axis ([001]), are indicated by black dots. The red dashed circles outline the sets of HK0 and H0L reflections which are represented by red dots. β-Ga₂O₃ nearly in-plane 110-type reflections, marked by large red dots, are used for grazing incidence in-plane *ϕ*-scans to track structural changes in films.

At high O/Ga ratio (≈ 2700), as expected, only the substrate peaks are present in the X-ray θ/2θ scan in **Figure 3 (a)**, similarly to the references ⁵⁴,⁵⁵. This is inherent to the epitaxy of β-Ga₂O₃ on Al₂O₃ (012), where the main (−201) lattice planes are tilted by ~30° with respect to the substrate normal meaning that no film Bragg peaks are expected in a conventional Bragg-Brentano θ−2θ geometry. Therefore, the surface orientation and epitaxial relationship of the films are determined using azimuthal φ-scans and pole figure measurements as discussed below. Weak additional peaks appear as the O/Ga ratio decreases from 2700 to 370 and 229, and they become less distinct at O/Ga ratio = 180, where the film approaches a polycrystalline state. However, an increase in background noise level is observed between 20 and 40°, indicating an increase in the overall structural disorder of the film. As sketched in **Figure 2**, the 110-type reflections associated with orientations A and B lie nearly in-plane within 1°, or the lattice planes are nearly vertical with respect to the film plane. To further examine the evolution of crystallographic texture, 360-degree azimuthal φ-scans of 110-type reflection are performed (**Figure 3 (b)**). The peaks associated with orientations A and B, and symmetrically with orientations A' and B', are at azimuths of ±18.3°. Importantly, for all samples where these peaks remain visible, their azimuthal positions stay centred at ±18.3° (within experimental uncertainty), indicating that the epitaxial orientation relationship with the substrate is
preserved. The degradation observed at low O/Ga ratios actually arises from peak broadening and the emergence of additional orientations, which progressively lead to a quasi-polycrystalline texture, rather than from any modification of lattice parameters. Indeed, the peak widths broaden from 0.4° (O/Ga ratio = 2700, 2200) to 1.1 (370) and 6.5° (229). Furthermore, broad 110 peaks appear at other unexpected azimuths even with the O/Ga ratio = 2700. The azimuthal modulation of the 110 reflection is clearly visible for O/Ga ratios = 370 and 229, revealing the existence of multiple grain's orientations in these films. For the sample O/Ga ratio = 180, the azimuthal modulation nearly vanishes, approaching the case of a polycrystalline ring. These trends indicate a progressive loss of single-orientation texture with decreasing oxygen content.

<figure><img src="image_4.png" /><figcaption>Figure 3. X-ray diffraction of β-Ga₂O₃ films on Al₂O₃ (012) as a function of O/Ga ratios. (a) θ/2θ scans. (b) Grazing incidence in-plane φ-scans of β-Ga₂O₃ 110-type reflection. The azimuthal angle (-18.3°) of 110 reflections from orientations A and B are indicated by A, B and that (+18.3°) from mirror orientations by A', B'.</figcaption></figure>
To track the multiple film orientations, X-ray pole figures of 001 and -201 reflections were performed in the films with O/Ga ratios = 2700, 370, 229 (Figure 4). At O/Ga ratio = 2700, the 001 and -201 poles are located at the expected tilt and azimuth angles for orientations A and B, and symmetrically for orientations A' and B' (Figure 4 (a,b)). However, the presence of weak peaks reveals a minority orientation (see the arrows in Figure 4 (a,b)). Minority orientations are multiplied at O/Ga ratio = 370, involving at least six orientations labeled A to F (Figure 4 (c,d)). Here, a couple of 001 and -201 poles is identified as belonging to the same orientation by their relative angle of 49.92°. At O/Ga ratio = 229, the poles are widening in angles (Figure 4 (e,f)). Interestingly, a complex structure, like a ring organization, appears to occur around an axis tilted about 18° toward the Al₂O₃ [0-21] azimuth (see the arrows in Figure 4 (e,f)). It should be noted that for a nearly polycrystalline film such as that with O/Ga ratio = 180 sample, peak broadening would lead to constant intensities in the pole figures, similarly to the 360-degree φ-scans (Figure 3 (b)).

Overall, the θ-2θ, φ-scans, and pole-figures clearly demonstrate that films with good structural order are obtained at high O/Ga ratios of 2700 and 2200, with mainly the expected film orientations A and B and the mirror ones. Whereas lower O/Ga ratios (370 and 229) produce multiple orientations and pronounced angular broadening, indicating increasing structural disorder. Further lowering the O/Ga ratio of 180 results in a nearly polycrystalline film.
<figure><img src="image_5.png" /></figure>

Figure 4. X-ray 001 and -201 pole figures of β-Ga₂O₃ films on Al₂O₃ (012), with O/Ga ratios of 2700, 370 and 229. (a), (b) O/Ga ratio = 2700: in plus of spots from orientations A and B and twinned ones, extra weak spots indicated by black arrows. (c), (d) O/Ga ratio = 370: main extra spots labelled by C, D, E and F. (e), (f) O/Ga ratio = 229: extra spots organizing into ring structures around an axis, indicated by red arrows, which is tilted by 18° towards Al₂O₃ [02-1] azimuth.

**Figure 5** shows the Raman spectra recorded in the range of 130 – 1000 cm⁻¹ using 514.5 nm excitation for samples S1, S3, S5, S6, S7, S8, S9, and S10, demonstrating a systematic spectral evolution with O/Ga ratio. As shown in **Figure 5 (a)**, at lower O/Ga ratios (≤ 370), spectra exhibit broad, asymmetric peaks with pronounced tailing and elevated background, indicating significant structural disorder and lattice distortions that can be induced by point defect and non-stoichiometry ⁵⁶⁻⁵⁸. As O/Ga ratio increases, peaks progressively become sharper and more symmetric, reflecting improved crystallinity of the film and reduced phonon scattering. From O/Ga ratio = 550, Raman modes can be well-defined. These modes can be classified into three parts: (a) low frequency modes (100 – 200 cm⁻¹), attributed to liberations and translations of the Ga₁O₄ tetrahedral and Ga₁₁O₆ octahedral chains; (b) mid frequency modes (~310 – 480 cm⁻¹), corresponding to deformation of Ga₁₁O₆ octahedra; (c) high frequency modes (~500 – 770 cm⁻¹), associated with stretching and bending of Ga₁O₄ tetrahedral chains ⁵⁹,⁶⁰. In addition to the Ga₂O₃ phonon modes, a broad band in the ~1300–1500 cm⁻¹ (not shown in the manuscript) region is observed for samples grown under low
O/Ga ratios. This contribution progressively weakens and becomes negligible under O/Ga ratio = 1100. Such a broad band is commonly attributed to disordered or graphitic carbon and is consistent with residual carbon incorporation originating from incomplete oxidation of MO source under oxygen-poor conditions. Although contributions from second-order $Ga_2O_3$ Raman scattering in this spectral range cannot be fully excluded $^{61}$, the systematic suppression of this band with increasing O/Ga ratio supports its association with carbon-related disorder rather than intrinsic lattice vibrations.

The parameters such as full width at half maximum (FWHM) and the position of Raman shifts serve as direct probes of lattice dynamics, thermal expansion effect, anharmonic coupling between lattice points, and anharmonic coupling between phonons $^{62}$. To understand the structural evolution in $\beta$-$Ga_2O_3$ layers more clearly, Ag(3), Ag (5), and Ag(10) modes are analyzed as shown in (Figure 5 (b)-(d)). To note that the modes for sample at O/Ga ratio = 180, and the mode Ag(10) for sample O/Ga ratio = 370 are not available due to insufficient definition. All three modes show clear narrowing of FWHM with different levels from low to intermediate O/Ga ratio, reflecting improved lattice order. At higher O/Ga ratios (> 1100), the variations of both Raman shift and FWHM become plateau, reaching a regime where further changes drop below the spectral resolution limit (~0.2 cm$^{-1}$) in our system, indicating that the crystallinity improvement is less significant with further increase in oxygen flow during the growth. In particular, The Ag(5) mode exhibits the most pronounced narrowing from FWHM of 14.3 to 6.7 cm$^{-1}$ (Figure 5 (c)), highlighting its exceptional sensitivity. Similar observations were reported in ref. $^{62,63}$ for $\beta$-$Ga_2O_3$ single crystals. The Ag(5) Raman mode was identified as the most sensitive to uniaxial stress along (010) direction, exhibiting the largest sharpen under deformation, making it well suited for evaluating internal stress and lattice strain in $\beta$-$Ga_2O_3$. Which further confirms that oxygen-rich growth conditions relieve structural stress and improve crystalline order. Besides, the pronounced intensity of the Ag(3) mode can be attributed to its exceptionally large Raman tensor elements among the Raman-active Ag modes $^{64}$, which induce a strong modulation of the crystal polarizability and thus a markedly enhanced Raman scattering cross-section. There is less discussion on Ag10 mode that originates from high-frequency GaO4 stretching vibrations, it is therefore sensitive to local stoichiometry and tetrahedral-unit strain, making its redshift and narrowing a clear indicator of reduced disorder under oxygen-rich growth.
<figure><img src="image_6.png" /><figcaption>Figure 5. (a) Raman spectra of β-Ga₂O₃ layers with different O/Ga ratios at fixed TMGa = 36 µmol/min. (b) – (d) the Raman shift and FWHM of Ag(3), Ag(5), and Ag(10) modes, respectively.</figcaption></figure>

To probe how microstructure evolves with O/Ga ratio and with Ga content at fixed O/Ga ratio, scanning electron microscope (SEM) analysis was carried out (**Figure 6**). All cross-section SEMs were taken from samples cleaved along the same substrate azimuth and imaged under identical conditions.

At a constant Ga content (TMGa = 36 µmol/min) with varying O/Ga ratios (samples S1, S5, S6, S9, and S10), the SEM cross-sectional and surface images (**Figure 6 (a)**) demonstrate a clear structural evolution as the O₂ flow increases. Under O/Ga ratios < 370, the films exhibit pronounced faceting, coarse surface morphology, randomly oriented and short columns in cross-section. Increasing O/Ga ratio to ~1100 produces a marked transition to dense, better coalesced surfaces and more aligned columnar grains that run through the thickness. Further increase to 2200–2700 does not
significantly alter the microstructure. These observations are consistent with the XRD results, which reveal the transition from polycrystalline to single-orientation films with larger and larger coherence lengths as O₂ flow increases. In addition, the azimuthal broadening of the in-plane XRD reflections decreases in the same trend, highlighting a reduction in structural disorder and misorientation.

At fixed O/Ga ratio = 1600, the influence of increasing TMGa molar flow on film morphology is shown in **Figure 6 (b)** for samples S11, S12, S13, S14, and S15. Top-view SEM images show that the surface evolves from rough and granular at low TMGa (12–24 µmol/min) to smoother and more uniform at higher TMGa values (48 – 60 µmol/min) reflecting improved surface coverage and grain coalescence. Cross-sectional SEM images further reveal longer and more parallel columns along the growth direction with increasing TMGa, indicating enhanced vertical crystallinity and preferred orientation. These changes reflect a transition from sparse, short grains to dense and well-aligned microstructures, which may play a crucial role in enhancing charge carrier transport.
<figure><img src="image_7.png" /><figcaption>Figure 6. SEM cross-sectional and top-view images of β-Ga₂O₃ films grown at (a) TMGa = 36 µmol/min with varying O/Ga ratios = 180 – 2700. (b) O/Ga ratio = 1600 with TMGa = 12 – 60 µmol/min.</figcaption></figure>

The well crystallized samples (O/Ga ratios ≥ 550) were selected for electrical transport measurements, carried out at 800 K as the samples are semi-insulating as room temperature. The Ohmic contacts were prepared by the silver paste at four corners of each square-shaped sample of 1×1 cm and measured in a Van der Pauw configuration.

Here, the *I-V* characteristic and the Hall voltage (*V*<sub>H</sub>) versus applied magnetic field (*B*) at 800 K of the sample S10 (with the fastest growth rate (2.08 µm/h)) in this series are shown as an example (Figure 7). The *I-V* curve shows a linear response, assuring the subsequent electrical transport measurement. The Hall voltage increases linearly with the applied magnetic field from -1.6 – +1.6 T, confirming *p*-type conduction. All the other studied samples exhibit similar behavior and thus exhibit *p*-type nature. Such semi-insulating *p*-type conductivity has been discussed in the context of an
established defect framework, where V<sub>Ga</sub>-related defects have been widely reported to act as dominant acceptors in *p*-type *β*-Ga<sub>2</sub>O<sub>3</sub> or compensating centers in *n*-type *β*-Ga<sub>2</sub>O<sub>3</sub><sup>37–39</sup>.

<figure><img src="image_8.png" /></figure>

Figure 7. (a) *I*-*V* characteristic, (b) Hall voltage as a function of perpendicularly applied magnetic field from –1.6 T to 1.6 T, at 800 K for sample S10.

**Figure 8 (a) (b)** shows the electrical transport behavior when O/Ga ratio at fixed Ga content (TMGa = 36 µmol/min) (samples S6, S7, S8, S9, S10): Resistivity (*ρ*) continuously decreases from 7.3×10<sup>3</sup> to 2.7×10<sup>2</sup> Ω·cm with increasing O/Ga ratios from 550 to 2700. At relatively low O/Ga ratios (*< 1600*), increasing the O/Ga ratio leads to a more pronounced decrease in resistivity. This suggests a progressive modification of film stoichiometry and a reduction of donor-like compensating defects commonly associated with oxygen-deficient growth conditions. Beyond O/Ga ratio ≈ 2200, further oxygen addition during the growth results in less significant resistivity change, indicating that the electrical behavior cannot be explained solely by the suppression or filling of oxygen vacancies. Instead, additional defect-related mechanisms are expected to contribute to the observed transport behavior. In particular, complex defects such as V<sub>Ga</sub>-V<sub>O</sub> divacancies were predicted to have comparable or even lower formation energy than single vacancies in oxygen-rich conditions based on *ab*-initio and DFT calculations <sup>29,46</sup>, indicating their potential stability during oxygen rich condition growth. It is also believed to be responsible for the appearance of shallow acceptor center in oxygen anneal *β*-Ga<sub>2</sub>O<sub>3</sub> sample <sup>65</sup> and layers grown under high O/Ga ratio <sup>54</sup>. Nevertheless, their role in the present study should be regarded as consistent with the observed trends rather than as a definitive attribution. In addition, oxygen interstitials (O<sub>i</sub>), which are thermodynamically favored under oxygen-rich conditions, may also influence the electrical transport behavior <sup>26,31,41</sup>. The enhancement of the *p*-type conductivity can be mainly attributed to the increase of hole concentration as shown in the **Figure 8 (b)**, from 6.0×10<sup>13</sup> to 1.7×10<sup>15</sup> cm<sup>-3</sup> in the O/Ga ratio range of 550 to 2700. While, the Hall mobility was determined to be in the range of 12.3 and 14.3 cm<sup>2</sup>/(V·s) without a clear
dependence to the O₂ flow. This trend corresponds to the observations in SEM and XRD in-plane scan, showing that further increase in O₂ flow does not significantly improve the crystalline quality.

**Figure 8 (c) (d)** shows the electrical transport behavior when Ga content at fixed Beyond O/Ga ratio = 1600 (samples S11, S12, S13, S14, and S15). Resistivity drops at relatively lower Ga supply (12 – 24 µmol/min), from 2.7×10⁴ to 6.3×10² Ω·cm, and becomes relatively stable above **Figure 8 (c)**, which can be mainly attributed to the increase of hole concentration. Notably, hole mobility continuously increases from 9.5 to 18.5 cm²/(V·s) with higher Ga content during film growth. This observation may correlate with the evolution of film morphology observed by SEM, increasing Ga content leads to elongated and more uniformly aligned columnar structures. Such microstructural evolution is expected to improve effective charge transport pathways and reduce carrier scattering, thereby enhancing mobility, although nanoscale defect structures such as intra-grain defects and nanoscale grain boundaries cannot be directly resolved by SEM.

In summary, these results demonstrate that the electrical transport properties of undoped semi-insulating *p*-type β-Ga₂O₃ films can be effectively tuned, O/Ga ratio primarily sets the free carrier density through defect chemistry, whereas gallium content (at fixed O/Ga) influences film texture and microstructural alignment, leading to enhanced free hole mobility.
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Figure 8. Electrical measurement at 800 K for semi-insulating β-Ga₂O₃ films. (a-b) Samples grown at fixed TMGa = 36 µmol/min: resistivity, hole concentration and mobility vs. O/Ga ratio. (c-d) Samples grown at fixed O/Ga ratio = 1600: resistivity, hole concentration and mobility vs. TMGa flow rates. Arrows indicate the general evolution trend of the electrical transport parameters with increasing O/Ga ratio or Ga content.</figcaption></figure>

The vapor pressure of TMGa was determined by the bubbler temperature (set to -14 °C in this work). Under these conditions, the TMGa molar flow was tuned from 12 to 60 µmol/min, while the O₂ flow rate set from 100 to 1500 sccm, resulting in O/Ga molar ratios ranging from ~200 to ~2700, as summarized in Table 1.
<table><caption>Table 1. Summary of selected growth conditions for β-Ga₂O₃ films, including TMGa, O₂ flow rates, and growth duration. The growth rate and O/Ga ratio were calculated for each sample; film thickness, hole concentration and hole mobility were measured for selected samples.</caption><thead><tr><th>Sample ID</th><th>TMGa (µmol/min)</th><th>O₂ (sccm)</th><th>O/Ga ratio</th><th>Duration (min)</th><th>Thickness (nm)</th><th>Growth rate (nm/h)</th><th>Resistivity (Ω·cm)</th><th>Hole concentration (cm⁻³)</th><th>Mobility (cm²/V·s)</th></tr></thead><tbody><tr><td>S1</td><td>36</td><td>100</td><td>180</td><td>90</td><td>860</td><td>570</td><td>-</td><td>-</td><td>-</td></tr><tr><td>S2</td><td>36</td><td>110</td><td>200</td><td>90</td><td>1690</td><td>1130</td><td>-</td><td>-</td><td>-</td></tr><tr><td>S3</td><td>36</td><td>125</td><td>229</td><td>90</td><td>1850</td><td>1230</td><td>-</td><td>-</td><td>-</td></tr><tr><td>S4</td><td>36</td><td>150</td><td>270</td><td>90</td><td>2060</td><td>1370</td><td>-</td><td>-</td><td>-</td></tr><tr><td>S5</td><td>36</td><td>200</td><td>370</td><td>90</td><td>2030</td><td>1350</td><td>-</td><td>-</td><td>-</td></tr><tr><td>S6</td><td>36</td><td>300</td><td>550</td><td>90</td><td>1890</td><td>1260</td><td>7.3×10³</td><td>6.0×10¹³</td><td>14.1</td></tr><tr><td>S7</td><td>36</td><td>600</td><td>1100</td><td>90</td><td>1805</td><td>1200</td><td>3.3×10³</td><td>1.2×10¹⁴</td><td>14.3</td></tr><tr><td>S8</td><td>36</td><td>900</td><td>1600</td><td>90</td><td>1850</td><td>1230</td><td>9.7×10²</td><td>5.1×10¹⁴</td><td>12.5</td></tr><tr><td>S9</td><td>36</td><td>1200</td><td>2200</td><td>90</td><td>1950</td><td>1300</td><td>3.7×10²</td><td>1.4×10¹⁵</td><td>12.3</td></tr><tr><td>S10</td><td>36</td><td>1500</td><td>2700</td><td>90</td><td>1810</td><td>1210</td><td>2.7×10²</td><td>1.7×10¹⁵</td><td>13.6</td></tr><tr><td>S11</td><td>12</td><td>300</td><td>1600</td><td>120</td><td>830</td><td>415</td><td>2.7×10⁴</td><td>2.4×10¹³</td><td>9.5</td></tr><tr><td>S12</td><td>24</td><td>600</td><td>1600</td><td>105</td><td>1450</td><td>830</td><td>6.3×10²</td><td>9.1×10¹⁴</td><td>10.9</td></tr><tr><td>S13</td><td>36</td><td>900</td><td>1600</td><td>90</td><td>1850</td><td>1230</td><td>9.7×10²</td><td>5.1×10¹⁴</td><td>12.5</td></tr><tr><td>S14</td><td>48</td><td>1200</td><td>1600</td><td>75</td><td>2050</td><td>1640</td><td>2.1×10³</td><td>2.2×10¹⁴</td><td>13.8</td></tr><tr><td>S15</td><td>60</td><td>1500</td><td>1600</td><td>60</td><td>2080</td><td>2080</td><td>5.6×10²</td><td>6.0×10¹⁴</td><td>18.5</td></tr></tbody></table>
Conclusion

This work demonstrates that the structural and electrical properties of undoped β-Ga₂O₃
epilayers can be effectively tuned by controlling the O/Ga stoichiometry during MOCVD growth. By
systematically varying the O/Ga ratio and TMGa molar flow, we identify key growth parameters
when the films exhibit enhanced crystallinity and semi-insulating (high temperature) p-type
conductivity: By varying the O/Ga ratio (≈ 180 – 2700) at fixed Ga content (TMGa = 36 µmol/min),
we identify an oxygen-rich condition range where texture alignment improves, lattice disorder
decreases, and well-oriented columnar grains emerge. XRD and Raman spectra evidence a transition
from polycrystalline to aligned textures with increasing oxygen flow, while electrical resistivity
reduction is primarily driven by an increase in free hole concentration. In contrast, varying the gallium
content (TMGa = 12 – 60 µmol/min) at fixed O/Ga ratio = 1600 refines the microstructure, promoting
vertical grain elongation, and a corresponding enhancement hole mobility from 9.5 to 18.5 cm²/V·s
with comparable carrier densities. Overall, our results show that adjusting the oxygen/gallium flow
during the deposition, i.e., varying stoichiometry, systematically can tune electrical transport
properties of semi-insulating p-type β-Ga₂O₃ thin films. We believe that the present work establishes
a growth technology capable of manipulating native point defects, thereby enabling both a
fundamental understanding and the practical realization of hole conductivity in β-Ga₂O₃.
Experimental details

**Thin film growth:** All Ga₂O₃ samples were grown in a RF-heated horizontal MOCVD reactor on Al₂O₃ (012) (r-oriented sapphire) substrates. A standard substrate cleaning procedure was applied prior to growth. The substrates were sequentially cleaned in acetone, isopropanol, and deionized water in an ultrasonic bath, 15 minutes each, followed by drying under N₂ flow. Trimethylgallium (TMGa) and O₂ were used as precursors for Ga and O, respectively, with separated inlets between TMGa and O₂ to avoid premature reactions in the manifold. The growth is carried out under quasi hot-wall conditions: in addition to the heated substrate holder, the surrounding chamber walls in quartz are also heated to keep the temperature. The temperature and pressure in the growth chamber were kept at 825 °C and 33 torr, respectively. The TMGa bubbler temperatures were fixed at -14 °C. Key growth parameters and measurement result for both sets are summarized in **Table 1**.

**Raman spectra:** Raman spectra were recorded using a Renishaw Invia Reflex micro-Raman spectrometer at room temperature. The samples were excited using a cw Modu-Laser Stellar-REN laser emitting at 514.5 nm with a power of 2 – 4 mW. The reflecting microscope objective was 50 with a NA 0.75; the excitation spot diameter was 1 mm. The back-scattered light was dispersed by a monochromator with a spectral resolution of 1.4 cm⁻¹. The light was detected by a charge coupled device. The typical accumulation time was 30 s. Raman shifts were calibrated using an optical phonon frequency (520.5 cm⁻¹) of a silicon nanocrystal.

**Scanning electron microscopy:** Surface morphologies of films was obtained by FEG SEM 7001-F JEOL. Electron source was produced by field effect cannon. Electrons secondary detection Everhart-Thornley had resolution of 1,2nm at 30 KV and 1nm at 1KV. Acceleration voltage and beam current were varied between 1KV to 30KV and 1pA to 200nA, respectively. Magnification's image goes up to 1000000.

**X-ray diffraction:** The structure of the samples was studied using X-ray diffraction (XRD). Data were collected on a 5-circle diffractometer (Rigaku SmartLab) with Cu Kα radiation from a rotating anode (40 kV, 9 kW). For out-of-plane (OP) measurements, Cu Kα1 radiation was selected by a channel-cut Ge(220) 2-reflection monochromator. The film in-plane (IP) orientation and strain were probed by grazing incidence XRD (GIXRD) at the constant incidence of 0.5°, without monochromator. The film global orientation texture was explored by x-ray pole figures (PFs), using the IP PF configuration.

**Hall effect measurements:** Ohmic contacts were prepared by silver paint at the four corners of the sample. Hall Effect measurements were performed by home-built high impedance high
temperature setup in a Van der Pauw configuration at 800 K applying the magnetic fields
perpendicularly to the film plane varying from -1.6 to 1.6 T, under N₂ environment.

Acknowledgement

This work has been funded by “GALLIA” International Research Project (CNRS, France),
French National Agency of Research (ANR), project "GOPOWER", CE-50 N0015-01 and MRSEI
PHC-Maimonide N50047TD.
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Stoichiometry-driven tuning of hole conductivity in MOCVD-grown β-Ga₂O₃ on r-sapphire substrates

Zeyu Chi ¹, *, Corinne Sartel ¹, Yunlin Zheng ², Yves Dumont ¹, Ekaterine Chikoidze ¹, *

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