Substrate-orientation dependence of -Ga 2 O 3 (100), (010), (001), and ( ) homoepitaxy by indium-mediated metal-exchange catalyzed molecular beam epitaxy (MEXCAT-MBE)

We experimentally demonstrate how In-mediated metal-exchange catalysis (MEXCAT) allows us to widen the deposition window for β Ga 2 O 3 homoepitaxy to conditions otherwise prohibitive for its growth via molecular beam epitaxy (e.g., substrate temperatures ≥ 800 ○ C) on the major substrate orientations, i.e., (010), (001), ( ¯201 ) , and (100) 6 ○ -offcut. The obtained crystalline qualities, surface roughnesses, growth rates, and In-incorporation profiles are shown and compared with different experimental techniques. The growth rates, Γ , for fixed growth conditions are monotonously increasing with the surface free energy of the different orientations with the following order: Γ (010) > Γ (001) > Γ ( ¯201 ) > Γ (100). Ga 2 O 3 surfaces with higher surface free energy provide stronger bonds to the surface ad-atoms or ad-molecules, resulting in decreasing desorption, i.e., a higher incorporation/growth rate. The structural quality in the case of ( ¯201 ) , however, is compromised by twin domains due to the crystallography of this orientation. Notably, our study highlights β -Ga 2 O 3 layers with high structural quality grown by MEXCAT-MBE not only in the most investigated (010) orientation but also in the (100) and (001) ones. In particular, MEXCAT on the (001) orientation results in both growth rate and structural quality comparable to the ones achievable with (010), and the limited incorporation of In associated with the MEXCAT deposition process does not change the insulating characteristics of unintentionally doped layers. The (001) surface is therefore suggested as a valuable alternative orientation for devices. the same regardless of the different investigated surfaces, with T g = 720 ○ C, an O-flux of 1 sccm, Al cell temperature = 1008 ○ C (BEP Al ≈ 4 × 10 − 8 mbar), and deposition time = 80 s (targeted Al compo-sition ≈ 5 cat. %, thickness ≈ 1–5 nm). The surface morphology was characterized by atomic force microscopy (AFM, Bruker Dimension Edge) in PeakForce tapping mode. The homoepitaxial layers were monitored by XRD symmetric, out-of-plane 2 θ - ω scans (PANalyt-ical X’Pert Pro MRD using Cu K α radiation), and their composi-tion was investigated by means of time-of-flight secondary ion mass spectrometry (SIMS) using ToF-SIMS IV from IONTOF GmbH. The quantitative ToF-SIMS calibration of the In-concentration was obtained from pulsed laser deposited (In x Ga 1 − x ) 2 O 3 reference films on c-plane sapphire substrates analyzed by EDX in a scanning electron microscope (5 samples with In content 1–40 c at. %—Oxford Instruments GmbH/JEOL GmbH). Depth profiling of SIMS craters was performed by interference microscopy (Veeco Instruments, Inc.). Selected samples were investigated by transmission electron microscopy (TEM—aberration corrected FEI Titan 80–300 operat-ing at 300 kV). Scanning TEM (STEM) images were recorded with a high-angle annular dark-field (HAADF) detector with an inner acceptance angle of 35 mrad and a camera length of 196 mm. TEM samples were prepared and studied in the cross section view perpen-dicular to the [010] direction for the (100), (001), and ( ¯201 ) growth orientations.Weinitially applied on all the substrate orientations the nomi-nal deposition parameters that we previously reported to be effective for the In-mediated MEXCAT-MBE of (010)-oriented layers, i.e.,

Driven by its application potential for high power electronics, gallium oxide in its most thermodynamically stable monoclinic structure, β-Ga 2 O 3 , has recently shown signs of rising interest from the scientific community. 1 Its successful implementation in devices requires high purity, low structural defectivity, 2 and the controlled incorporation of dopants at the nanoscale, all of which can be achieved by molecular beam epitaxy (MBE). A definitive advantage of β-Ga 2 O 3 over its direct competitors in power electronics (e.g., SiC and GaN) is the possibility of growing the material from the melt. 3,4 This results in the availability of native gallium oxide substrates with currently four different crystal orientations-i.e. (100), (001), (201), and (010)-that enable the highest structural quality of Ga 2 O 3 films by homoepitaxial growth. Despite the perfect crystalline match between substrate and film, the homoepitaxy of β-Ga 2 O 3 still presents two major challenges. The first one is related to the peculiar structure of the respective growth surfaces 5 that can result in the formation of twin lamellae due to double positioning, i.e., the formation of 2D nuclei in twinned or true epitaxial relation as shown in (100)-homoepitaxy by metal organic vapor phase epitaxy (MOVPE) 6 and MBE. 7 These defects strongly deteriorate the electrical properties of the deposited layers 8 but can be prevented by an appropriate offcut of the substrate as recently demonstrated by MOVPE (100)-homoepitaxy. 9 On (010)-oriented substrates, the symmetry of the growth surface prevents double positioning and thus twin formation. For the other available Ga 2 O 3 orientationsi.e., (001) and (201)-systematic experimental work on the structural quality of the deposited layers is lacking so far. The second challenge is the limited growth rate during MBE of Ga 2 O 3 , 10,11 which is related to the peculiar two-step growth kinetics via the intermediate formation of the suboxide Ga 2 O in the first step and its further oxidation to Ga 2 O 3 in the second step. 12 As Ga 2 O has a significantly higher vapor pressure than Ga, 13 its desorption limits the growth rate due to the following three factors: (1) metal-rich conditions, providing insufficient O-flux Φ O to oxidize all formed suboxide, 14 (2) high substrate temperatures (Tg) at which the thermally activated desorption of Ga 2 O outperforms its oxidation even under O-rich growth conditions, 15 and (3) β-Ga 2 O 3 substrate orientations that provide only weak bonds to the adsorbed Ga 2 O, resulting in a low activation energy for its desorption. In fact, surfaces with higher stability (i.e., cleavage planes) such as (100) and (001) have been found to suffer from very limited growth rates with respect to noncleavage planes such as (010) during MBE, 10,16 while MOVPE evidences almost identical growth rates for β-Ga 2 O 3 homoepitaxy on different substrate orientations. 17 For these reasons, the homoepitaxy of β-Ga 2 O 3 by MBE has so far been mostly restricted to the (010) orientation and growth conditions that are not limiting its growth rate (e.g., O-rich, Tg < 800 ○ C). 10,16 In contrast, metal-rich deposition conditions are predicted to avoid the formation of gallium vacancies (acting as compensating deep acceptors) 18,19 and higher Tg generally result in higher crystalline quality and allows us to increase the stability range of β-(AlxGa 1−x ) 2 O 3 alloys. 20 Moreover, substrate orientations other than (010) are desirable to mitigate the following drawbacks: (i) the (010) surface has been shown to be unstable under metal-rich growth conditions, i.e., resulting in the formation of (110)-facets, 21 and (ii) it is not a cleavage plane and therefore currently more challenging to be prepared 22 with respect to the (001), (201), and (100) surfaces, at least without considering the possible need of defined substrate offcuts. 9 Consequently, there is a need to increase the growth rate for crystal orientations other than (010) and interest in exploring growth conditions that so far have prevented layer growth by MBE, i.e., high Tg and metal-rich conditions. MBE growth using metal-exchange catalysis 23,24 (MEXCAT) is a promising avenue to overcome these limitations. This process is based on the collaborative effect of kinetically favored formation of intermediate In 2 O 3 (which can grow at lower O-flux and higher Tg than Ga 2 O 3 ) 13,14 and the subsequent thermodynamically driven exchange of its In-atoms by Ga (due to stronger Ga-O than In-O bonds). 25 In-mediated MEXCAT-MBE has been shown to enable a high Ga 2 O 3 growth rate with limited In-incorporation under conditions (Ga-rich, high Tg) prohibitive for growth of Ga 2 O 3 due to severe Ga 2 O desorption. 23 Likewise, Sn-flux mediated Ga 2 O 3 heteroepitaxy by MEXCAT-MBE 24 lead to the same qualitative results, demonstrating the generality of the MEXCAT approach for MBE. Both Sn-and In-mediated MEXCAT-MBE performed on top of a buffer layer of (201)-oriented β-Ga 2 O 3 on c-plane sapphire substrates resulted in the formation of the metastable ε/k-phase of Ga 2 O 3 . 23,24,26 Recently, In-mediated MEXCAT on β-Ga 2 O 3 (010) substrates has been demonstrated to triple the Ga 2 O 3 growth rate under Ga-rich conditions at Tg = 900 ○ C, preserve the monoclinic structure, and maintain a low surface roughness (rms <0.5 nm) while limiting the In-incorporation (not detectable X-ray diffraction XRD peak shift and no In-signal from energy dispersive xray spectroscopy EDX). 21 Furthermore, the concept of In-mediated MEXCAT has been extended to the deposition of β-(AlxGa 1−x ) 2 O 3 alloys on (010) substrates, allowing for stabilization of up to x = 0.2 incorporation at high Tg. 20 In this experimental work, we investigate the In-mediated MEXCAT on all the available orientations of β-Ga 2 O 3 substrates, aiming at insights in the crystal quality and future perspective of Ga 2 O 3 homoepitaxy by MBE on different surfaces. In particular, we show that MEXCAT allows for homoepitaxial growth under deposition conditions otherwise prohibitive on all the major β-Ga 2 O 3 orientations. The synthesis parameters that allow for layer growth (i.e., Tg, O/Ga-flux ratio) as well as the growth rates are found to depend on the surface orientation, which we explain by the relation between surface free energy from ab initio calculations (Ref. 9) and ad-atom binding energy extracted from our data using the growth model for MEXCAT-MBE presented in Ref. 23. Furthermore, we show that the (201)-orientation is challenging for β-Ga 2 O 3 homoepitaxy due to the formation of twins. MEXCAT, however, allows for the homoepitaxy of high quality β-Ga 2 O 3 layers on both (100) 6 ○ -offcut and (001) substrates (no structural defects identified, rms < 0.5 nm), with low In incorporation (In < 0.1 cation cat. %). In particular, the (001)orientation also allowed for growth rates comparable to the ones obtainable in (010) homoepitaxy (i.e., 2.3 nm/min).
The (201) and (010) β-Ga 2 O 3 orientated substrates for this study were unintentionally doped and Fe-doped, respectively, and were both purchased from the Tamura company, while the (100) and (001) oriented wafers were Mg-doped and prepared from bulk crystals obtained from the Czochralski method 4 at the Leibniz-Institut für Kristallzüchtung. To prevent the formation of twin domains, the (100)-substrates were offcut by 6 ○ toward the -c direction. 9 Before being loaded into the MBE chamber, the substrates were chemically etched in phosphoric acid (85 wt. % H 3 PO 4 , T = 130 ○ C, t = 15 min) to remove potential polishing damage in the first 100 nm from the substrate surface; 27 the process was then followed by an O 2 -annealing treatment (p = 1 bar, T = 950 ○ C, t = 60 min) in a tube furnace. The experiments were performed in a MBE chamber equipped with an O-plasma source run at a plasma power P = 300 W. Before the deposition, all the substrates were in situ oxygen-plasma treated at an O-flux of 1 standard cubic centimeter per minute (sccm) at a substrate temperature Tg = 875 ○ C for t = 30 min. All growth runs were performed for a fixed deposition time of 30 min. The beam equivalent pressure of Ga was fixed to BEP Ga = 1.27 × 10 −7 mbar, equivalent to a particle flux of Φ Ga = 2.2 nm −2 s −1 (determined from the measured growth rate under O-rich deposition conditions on c-plane sapphire substrates 14 )i.e., full Ga incorporation ≈100 nm (i.e., growth rate 3.3 nm/min). The particle flux of In for the catalyzed growths was fixed to Φ In = 1/3 Φ Ga (BEP In = 5.2 × 10 −8 mbar). The Tg was measured by an optical pyrometer. For some of the depositions, an additional thin (AlxGa 1−x ) 2 O 3 marker layer was deposited at the substrate-layer interface. The growth parameters for the interlayer were maintained the same regardless of the different investigated surfaces, with Tg = 720 ○ C, an O-flux of 1 sccm, Al cell temperature = 1008 ○ C (BEP Al ≈ 4 × 10 −8 mbar), and deposition time = 80 s (targeted Al composition ≈ 5 cat. %, thickness ≈ 1-5 nm). The surface morphology was characterized by atomic force microscopy (AFM, Bruker Dimension Edge) in PeakForce tapping mode. The homoepitaxial layers were monitored by XRD symmetric, out-of-plane 2θ-ω scans (PANalytical X'Pert Pro MRD using Cu Kα radiation), and their composition was investigated by means of time-of-flight secondary ion mass spectrometry (SIMS) using ToF-SIMS IV from IONTOF GmbH. The quantitative ToF-SIMS calibration of the In-concentration was obtained from pulsed laser deposited (InxGa 1−x ) 2 O 3 reference films on c-plane sapphire substrates analyzed by EDX in a scanning electron microscope (5 samples with In content 1-40 c at. %-Oxford Instruments GmbH/JEOL GmbH). Depth profiling of SIMS craters was performed by interference microscopy (Veeco Instruments, Inc.). Selected samples were investigated by transmission electron microscopy (TEM-aberration corrected FEI Titan 80-300 operating at 300 kV). Scanning TEM (STEM) images were recorded with a high-angle annular dark-field (HAADF) detector with an inner acceptance angle of 35 mrad and a camera length of 196 mm. TEM samples were prepared and studied in the cross section view perpendicular to the [010] direction for the (100), (001), and (201) growth orientations.
We initially applied on all the substrate orientations the nominal deposition parameters that we previously reported to be effective for the In-mediated MEXCAT-MBE of (010)-oriented layers, i.e., Tg = 900 ○ C, Φ In = 1/3 Φ Ga , and O-flux = 0.33 sccm. 21 With the formation of (110)-facets, the resulting (010)-homoepitaxial layer shows the typical morphology previously highlighted for metal-rich deposition conditions (see Ref. 21). Its thickness of 50 nm (detected by XRD thickness fringes, not shown) signifies an effective incorporation of ≈50% of the incoming Ga flux; the thickness reduction with respect to what we have previously reported 21 can be attributed to a slightly different efficiency of our O-plasma source. More importantly, no layer growth was detected on all the other substrate orientations (not shown), indicating a substrate-orientation dependence of In-mediated MEXCAT for β-Ga 2 O 3 homoepitaxy. The mean surface roughness of the substrates after these growth experiments are reported in Tables I-III for (201), (100), and (001), respectively. We point out that when no growth takes place, the rms values might be altered by localized Ga-etching effects that cause a roughening of the surfaces with respect to an untreated substrate.
In the following, we report the results of growth on the different substrate orientations under various growth conditions (Tg, O-flux).
MEXCAT on (201). Growth of homoepitaxial layers on this substrate orientation was found to require much lower Tg and/or higher O-fluxes with respect to the (010) Fig. 1(b)] is visible. Figure 1(c) shows an atomically resolved STEM HAADF image of a part of an island, which reveals three kinds of defects, i.e., twin lamellae on the (201) plane, twins on the (100) plane, and a defect induced by a lateral shift of a part of the layer with respect to the other on the (201) growth surface. All of these defects can be explained by the 2D-island growth on the respective growth surfaces. Evidence for these defects comes from the analy- . Within this twinned island, additional twins on the (100) planes appear as dark lines. These dark lines correspond to half unit cell high twin lamellae. 28 The image pattern in the region marked IV [green arrow Fig. 1(c)] has already been observed in homoepitaxial layers grown on the (100) plane of β-Ga 2 O 3 . 29 It is explained by the overlap of two different grains, whose lattices have been shifted in the (201) plane with respect to each other. The ToF-SIMS measurement performed on a twin sample deposited under the same conditions independently confirms the presence of a layer consisting of islands with broad height distribution, as visible from the double-peak in the In-intensity profile [red dots in Fig. 2(a)]. From the calibration, the In-concentration in this sample is found to be around C In ≈ 2 × 10 19 cm −3 [i.e., ≈0.05 cat. %] at a depth of x ≈ 5 nm. Si impurities are usually found as a contaminant in Ga 2 O 3 homoepitaxy at the substrate-layer interface 30 and can therefore be used as an interface marker [blue dots in Fig. 2(a)]. The absence of a second Si-peak at ≈20 nm is related to its lower intensity with respect to the In one (near the detection limit). The layer thickness can be estimated around 10-25 nm from the SIMS profile, in line with TEM results [ Fig. 1 during this growth run, the presence of a certain amount of In in the first nanometers of the substrate (C In ≈ 2 × 10 19 cm −3 ) has to be considered as a surface impurity most likely coming from the sample holder, which has been the same for all the deposition runs.
Further deposition conditions were screened aiming at improving the quality of the homoepitaxial (201) layers. In-catalyzed growth with an increased O-flux of 0.5 sccm resulted in a nonhomogeneous rough surface (rms = 9.81 nm) with high incorporation of the incoming Ga-flux (≈85 nm thick layer, not shown) and C In ≈ 5 × 10 20 cm −3 (i.e., ≈1.3 cat. %, not shown). Increasing incorporation of In with increasing O-flux and/or decreasing Tg has already been reported for the heteroepitaxy of (InxGa 1−x ) 2 O 3 . 25 A higher Tg of 800 ○ C required to increase the O-flux up to 0.75 sccm to detect layer growth with In-catalysis (i.e., no growth detected for 0.33 and 0.5 sccm). With these growth conditions, a 60-70 nm layer was deposited: the C In as a function of probed depth [ Fig. 3(a)] shows that after an intial broad peak detected at the substrate-layer interface (max C In ≈ 7.2 × 10 19 cm −3 , i.e., ≈0.19 cat. %), the C In stabilizes to a value of ≈9.8 × 10 18 cm −3 , i.e., ≈0.03 cat. %. The presence of an In-peak at the substrate-layer interface has been generally identified in all the samples and is probably related to the first stages of the catalytic growth. An AFM image of this sample [inset of Fig. 3(a)] shows a rough surface (rms = 6.99 nm) dominated by islands oriented along the [010] direction, similarly to the ones shown in Fig. 1(a). A reference sample deposited without Incatalysis under the very same growth conditions resulted in no layer growth (not shown). A further increase of the O-flux to 1 sccm at Tg = 800 ○ C with In-catalysis resulted in almost full Ga-flux incorporation and a surface characterized by several micrometers large islands with an irregular shape and a typical height of ≈50-80 nm [similar morphology to Fig. 4(d)]. Also in this case, the increased O-flux resulted in significant In-incorporation into the layer (C In up to 1.5 × 10 21 cm −3 , i.e., ≈3.92 cat. %). In Fig. 3(b), we report the (603) XRD peaks of catalyzed samples deposited at different O-fluxes at the same Tg of 800 ○ C; in line with the SIMS results, a larger O-flux induces a gradually higher incorporation of In in the form of the β-(InxGa 1−x ) 2 O 3 alloy (i.e., left-side shift of the β-Ga 2 O 3 diffraction peak). In contrast to what has been previously reported in Ga 2 O 3 heteroepitaxy on c-plane sapphire substrates with a (201)-oriented β-Ga 2 O 3 seed layer, 23 In-mediated MEXCAT in (201)-homoepitaxy never resulted in the formation of the metastable ε/k-phase 26 in our layers.
As summarized in Table I, we show that In-mediated MEX-CAT allows us to widen the growth window in (201) homoepitaxy to regimes otherwise prohibitive for β-Ga 2 O 3 growth, enabling large Ga-flux incorporation (up to ≈65%) with limited In-incorporation (<0.1 cat. %). Nonetheless, our results suggest that obtaining (201) layers with high structural quality would require a proper choice of the substrate offcut to prevent the formation of twin lamellae due to the possibility of double positioning during growth. Twin lamellae can limit the electrical transport properties and results in considerable surface roughness in our deposited layers.
MEXCAT on (100) 6 ○ -offcut. The In-assisted synthesis conditions that allowed for growth at the lowest Tg for the (201)   Fig. 4(e)]. Thus, we tested conditions that previously resulted in higher growth rates for (201) homoepitaxy, i.e., Tg = 800 ○ C and O-fluxes ≥ 0.75 sccm. For these samples, an additional (AlxGa 1−x ) 2 O 3 interlayer was deposited at the substrate-film interface. The highest tested O-flux (2 sccm) resulted in a rough surface containing irregularly shaped islands with a typical height of about 150 nm [ Fig. 4(d)], similar to the one previously discussed for the (201)-oriented layer deposited at 1 sccm. ToF-SIMS of this sample (not shown) suggests an almost full incorporation of the Ga-flux, with additional In-incorporation of about 21.4 cat. % (i.e., 65% of the total provided In-flux, C In ≈ 8.2 × 10 21 cm −3 ). Just for this sample, we detected an additional XRD reflection that we attribute to bixbyite In 2 O 3 (not shown). The coexistence of both monoclinic and bixbyite phase in the (InxGa 1−x ) 2 O 3 alloy system is expected for such a large amount of In. 31,32 A lower O-flux of 1 sccm resulted in a smoother surface (rms = 1.07 nm), with a morphology compatible with step bunching along the substrate offcut direction [ Fig. 4(c)]. ToF-SIMS shows that the layer is ≈30 nm thick [green dots in Fig. 4(e)] with an estimated ≈2 nm thick (AlxGa 1−x ) 2 O 3 interlayer at the substrate interface. C In as a function of depth is showing a similar trend as the one of thick layers, with a peak at the interlayer-layer interface (C In ≈ 2.2 × 10 21 cm −3 , i.e. 5.7 cat. %) followed by a plateau region with limited In incorporation (C In ≈ 2.2 × 10 18 cm −3 , i.e., 0.006 cat. %).
A further decrease in the O-flux to 0.75 sccm resulted in a smoother layer [rms = 0.32 nm, Fig. 4(b)] with a morphology resembling the one of the offcut substrate [ Fig. 4(a)], and a thickness of 8-10 nm determined by ToF-SIMS [red dots in Fig. 4(e)]. Due to the limited thickness of the layer though, it is not possible to identify a clear plateau of C In in the deposited layer; nonetheless, the C In peak at the interlayer-layer interface is ≈9.5 × 10 19 cm −3 (i.e., 0.25 cat. %), while the lowest detected C In in the layer is ≈3.5 × 10 18 Fig. 4(e)]. The step edges due to the 6 ○ -offcut in the -c direction are resulting in (201)-planes 9 [purple dotted lines in Fig. 5(d)]. While the substrate surface presents only half-unit cell steps (≈0.62 nm), the layer surface presents steps of different heights as illustrated in the highmagnification STEM images in Fig. 5(d). All step heights correspond to multiples of half a unit cell in the a-direction, with the largest steps of 2.5 unit cells (≈3.1 nm). This points towards step bunching in some parts of the layer during growth, although this is not influencing the crystalline quality of the film.
As summarized in Table II, In-mediated MEXCAT is a fundamental ingredient to grow β-Ga 2 O 3 layers on (100)-oriented substrates in the presence of an offcut along the c-direction. We have shown that the growth of high quality (100)-homoepitaxial layers is not just limited to MOVPE 9 but can be also extended to MBE.
MEXCAT on (001). We tested two deposition conditions that were previously investigated for the other two discussed orientations, i.e., Tg = 735 ○ C-O-flux = 0.33 sccm and Tg = 800 ○ C-O-flux = 0.75 sccm. The In-mediated growth run at the lowest Tg resulted in a ≈32 nm thick layer with a C In peak at the substrate-layer interface of ≈7.5 × 10 19 cm −3 (i.e., 0.19 cat. %) and a constant intralayer C In of ≈1.1 × 10 19 cm −3 (i.e., 0.03 cat. %) [ Fig. 6(a)], highlighting a ARTICLE scitation.org/journal/apm  Fig. 4(e)] 0.28 [ Fig. 4(a)] . . .  Tables I and II). The AFM micrograph of this layer [inset of Fig. 6(a)] shows (i) the presence of ≈100 nm large and ≈10 nm high dots on the surface whose origin is not currently understood, and (ii) elongated features along the [010] direction as already reported in other homoepitaxial growths on this orientation. 16,33 The resulting rms surface roughness is 3.11 nm.
For the growth at Tg = 800 ○ C and O-flux = 0.75 sccm, an approximately 2 nm thick (AlxGa 1−x ) 2 O 3 marker layer was intentionally deposited at the substrate-layer interface. The thickness of the β-Ga 2 O 3 layer is estimated from ToF-SIMS as ≈65 nm, with a C In peak at the substrate-layer interface of ≈1.1 × 10 20 cm −3 (i.e., 0.29 cat. %) and a constant intralayer C In of ≈3 × 10 19 cm −3 (i.e., 0.08 cat. %) [ Fig. 6(b)]. Under these deposition conditions, the layer is smooth (rms = 0.41 nm), still presenting elongated features oriented along the [010] direction [AFM in the inset of Fig. 6(b)]. The presence of well-defined XRD fringes in the vicinity of the (002) diffraction peak [facilitated by the (AlxGa 1−x ) 2 O 3 marker layer] allows us to precisely determine the thickness of the layer = 70 nm, i.e., 70% incorporation of the Ga total flux-growth rate = 2.3 nm/min [ Fig. 6(c) red line], in line with the thickness range previously extracted from the SIMS profile [ Fig. 6(b)]. Even though we are not maximizing the Ga-flux for our deposition runs, we highlight that the growth rate obtained here is exceeding what has been so far reported in the literature for this orientation with MBE (≈0.9 nm/min). 16 Fig. 6(b)]. The presence of elongated features along the [010] direction seems to be related to a partial faceting of the surface.
As summarized in Table III, we show that In-mediated MEX-CAT allows us to obtain smooth (001) layers with a large incorporation of the provided Ga-flux with similar efficiency as previously reported for (010) 21 although at a lower substrate temperature. Our experiments suggest that (001) is a promising surface for β-Ga 2 O 3 homoepitaxy because of the high quality of the deposited layers. It is important to highlight that the In-concentrations in the In-mediated MEXCAT deposited layers should not affect their electrical properties: In is energetically favorably replacing Ga in the octahedral site of the monoclinic cell, 31 and their isovalent nature excludes electrically active doping and ionized impurity scattering. We electrically characterized two unintentionally doped 50 nm thick Ga 2 O 3 layers deposited with optimized In-mediated MEXCAT conditions on (001)-and (010)-oriented insulating substrates. Hgcontact capacitance-voltage measurements did not show any free carriers on both layers (even under forward bias the measured capacitance corresponded to the parasitic capacitance measured on an insulating glass slide). Additional 2-terminal current-voltage measurements between annealed Ti/Au contacts confirmed the presence of insulating layers (resistance >1 GΩ). These results confirm that, similar to Ga 2 O 3 layers grown by MBE, 34 undoped Ga 2 O 3 layers grown by MEXCAT-MBE are insulating. A separate dedicated study is needed to understand the interplay of the catalytic growth with n-type extrinsic doping, particularly with respect to the conflicting role of Sn as catalyst (i.e., not incorporated in the film) 24 and donor 10 during In-mediated MEXCAT.
From our results, it is clear that In-mediated MEXCAT allows us to widen the growth window on all the major substrate orientations (see Tables I-III). Nonetheless, there are visible differences in the growth rates Γ on the different β-Ga 2 O 3 surfaces. Figure 8(a) allows for a direct comparison of Γ obtained with MEXCAT on different substrate orientations under three selected growth conditions as a function of their respective surface free energies from first principle calculations of Ref. 9.
Comparing the three sets of data collected in this work [blue, red, and green points Fig. 8(a)], we notice a monotonically increasing growth rate with increasing surface free energy of the different orientations, following the order Γ(010) > Γ(001) > Γ(201) > Γ(100). We relate these experimental findings to the mechanism of the In-catalytic growth, which relies on the presence of In adatoms on the growth surface (i.e., Ga 2 O 3 ) that can either form the catalyzing In 2 O 3 (kinetically driven steps of the catalysis) or desorb off the surface. Once In 2 O 3 is formed on the surface, its In atoms can be exchanged by Ga (thermodynamically driven step of the catalysis) forming Ga 2 O 3 layer material and surface In ad-atoms that can re-enter the catalytic cycle or desorb. In the simple, quantitative, rate-equation based model for the In-mediated MEXCAT-MBE put forward in Ref. 23, the growth-rate limiting step is the thermally activated desorption of the In ad-atoms. Hence, the growth rate can be described as a function of all growth parameters [Eq. (6)  − Φ Ga −1 )]/J 0 } with pre-exponential factor J 0 arbitrarily fixed at 10 14 nm −2 s −1 . 23 The resulting values are shown in Fig. 8(b) as a function of surface free energy of the investigated Ga 2 O 3 surface orientations. Larger Δ correspond to a larger barrier for the desorption of the In ad-atoms. Figure 8(b) shows that for given growth conditions, Δ increases with increasing surface free energy of the Ga 2 O 3 , suggesting that the stronger bonds/higher bond densities reflected by higher surface free energies also correspond to stronger bonds of this surface to the In ad-atoms. For example, the presence of low  In (a), we also report the growth rate obtained in our previous study 21 on (010) homoepitaxy under similar conditions (star symbol). The black arrows in (b) mean that the data points (obtained by an assumed growth rate of 0.1 nm/min) are upper limits for the energy as these data points arise from samples without growth (i.e., a growth rate below 0.1 nm/min).
density/weak dangling bonds on a very stable surface such as the (100) results in an easier desorption of the In ad-atoms therefore not allowing their oxidation to form the In 2 O 3 and thus no Ga 2 O 3 formation by MEXCAT. While the absolute energies of Δ may be influenced by J 0 , we note that their differences can provide experimental input for ab initio theory of the binding energy of In to the different Ga 2 O 3 surfaces.
In conclusion, MBE homoepitaxial growth on all the major β-Ga 2 O 3 substrate orientations is shown in this work. In-mediated MEXCAT is proven to fundamentally widen the deposition window of β-Ga 2 O 3 on all of its native substrate orientations, neither forming ε/k-Ga 2 O 3 nor incorporating large amounts of In (C In < 0.1 c at. %). Notably, we highlight that the growth rate of the In-catalyzed layers deposited under the same synthesis conditions monotonically increases with the surface free energy of the used β-Ga 2 O 3 substrate orientations according to Γ(010) > Γ(001) > Γ(201) > Γ(100). We relate this behavior to an increasing binding energy of the In ad-atoms with increasing surface free energy. Moreover, we address fundamental differences on the obtainable structural quality of the layers deposited on different substrate orientations related to the growth mode and the crystal symmetry. Similar to the (100) orientation, the (201) one is a twinning plane in the monoclinic lattice; 2D nucleation and double positioning in this case leads to the formation of twin lamellae, low structural quality, and high surface roughness of the layers which might be mitigated by using substrates with proper offcut. Nonetheless, we demonstrate the possibility to obtain high quality thin films with In-mediated MEXCAT-MBE on the (001) and offcut (100) orientations, i.e., no structural defects and rms < 0.5 nm. Notably, in the case of (001) homoepitaxy, we demonstrate that In-mediated MEXCAT-MBE allows for similar growth rates to the ones obtainable on the widely investigated (010) surface (2.3 nm/min, i.e., 70% incorporation of the impinging Ga-flux). In this regard, we would like to remark that the present work is not aiming at maximizing the absolute value of the growth rate, which could be scaled up with the provided metal and oxygen fluxes. Moreover, we demonstrate that the limited incorporation of In associated with MEXCAT-MBE depositions (10 18 -10 19 cm −3 ) is not changing the insulating characteristics of unintentionally doped layers. Our experimental findings therefore suggest that (001) is a strong candidate for the homoepitaxial deposition of high quality layers on large area substrates. For practical purposes, future MEXCAT-MBE studies should aim at maximizing the growth rates, particularly on the (100) orientation, while maintaining a high crystalline quality.