Towards smooth (010) beta-Ga2O3 films homoepitaxially grown by plasma assisted molecular beam epitaxy: The impact of substrate offcut and metal-to-oxygen flux ratio

Smooth interfaces and surfaces are beneficial for most (opto)electronic devices based on thin films and their heterostructures. For example, smoother interfaces in (010) beta-Ga2O3/(AlxGa1-x)2O3 heterostructures, whose roughness is ruled by that of the Ga2O3 layer, can enable higher mobility 2DEGs by reducing interface roughness scattering. To this end we experimentally prove that a substrate offcut along the [001] direction allows to obtain smooth beta-Ga2O3 layers in (010)-homoepitaxy under metal-rich conditions. Applying In-mediated metal-exchange catalysis (MEXCAT) in molecular beam epitaxy at high substrate temperatures (Tg = 900 {\deg}C) we compare the morphology of layers grown on (010)-oriented substrates with different unintentional offcuts. The layer roughness is generally ruled by (i) (110) and (-110)-facets visible as elongated features along the [001] direction (rms<0.5 nm), and (ii) trenches (5-10 nm deep) orthogonal to [001]. We show that an unintentional substrate offcut of only 0.1{\deg} almost oriented along the [001] direction suppresses these trenches resulting in a smooth morphology with a roughness exclusively determined by the facets, i.e., rms 0.2 nm. Since we found the facet-and-trench morphology in layers grown by MBE with and without MEXCAT, we propose that the general growth mechanism for (010)-homoepitaxy is ruled by island growth whose coalescence results in the formation of the trenches. The presence of a substrate offcut in the [001] direction can allow for step-flow growth or island nucleation at the step edges, which prevents the formation of trenches. Moreover, we give experimental evidence for a decreasing surface diffusion length or increasing nucleation density with decreasing metal-to-oxygen flux ratio. Based on our results we can rule-out step bunching as cause of the trench formation as well as a surfactant-effect of indium during MEXCAT.


Introduction
Gallium oxide in its most thermodynamically stable monoclinic structure β-Ga2O3 has recently been proposed as a promising material for power electronics. 1 The possibility to deposit it on native substrates grown from the melt 2 can allow for the synthesis of high quality thin films. Nonetheless, the growth of β-Ga2O3 is orientation-dependent, and this can affect both the structural quality 3,4 and the growth rate 4,5 of the deposited layers [e.g. structural defects and low deposition rate in (100)oriented layers]. For these reasons, the most widely employed substrate orientation for β-Ga2O3 homoepitaxy has been so far the (010) one as it prevents formation of twin defects and provides a comparably high growth rate in molecular beam epitaxy 2 (MBE). MBE and metal-organic vapor phase epitaxy (MOVPE) have been so far the deposition techniques that provided high quality homoepitaxial β-Ga2O3 layers, also enabling for a fine control of their electrical properties throughout n-type extrinsic doping, [6][7][8] as well as the growth of modulation-doped heterostructures. [9][10][11] Nonetheless, different synthesis conditions can affect the electrical properties of the deposited layers through the formation of deep level acceptors that could work as electron traps in β-Ga2O3 (e.g., Ga-vacancies), potentially limiting both charge carrier density and mobility. 12,13 Therefore, Ga-rich deposition conditions 12 and high growth temperatures Tg 14 have been theoretically predicted to be favorable for the synthesis of β-Ga2O3 layers. Unfortunately, due to the strong desorption of the intermediately formed volatile suboxide Ga2O from the growth surface, 15 the deposition of Ga2O3 under these conditions is challenging even in the case of (010) homoepitaxy. 16 The employment of an additional In-flux as a catalyst during Ga2O3 deposition in MBE, i.e., metal-exchange catalysis (MEXCAT), 17 has been shown to result in large incorporation of the impinging Ga-flux even under synthesis conditions that would not otherwise allow for layer growth (e.g., metal-rich, high Tg) with very limited In-incorporation in the deposited layer. 4,16,17 A similar effect has been also demonstrated using Sn as catalyzing element. 18 In particular, for β-Ga2O3 (010)homoepitaxy we have shown 16 that In-mediated MEXCAT-MBE provides high quality β-Ga2O3 layers with almost full Gaflux incorporation under metal-rich deposition conditions at Tg = 900 °C. Moreover, we identified that the surface roughness of the (010)-oriented layers is usually dominated by two distinct morphologies, 16 Figure 1). The presence of (i) facets is ruled by thermodynamics [i.e., (110) more stable surface with respect to (010) under reducing/metal-rich conditions], but has nonetheless found to have a limited impact on the overall surface roughness of the deposited layers, since for high Tg it is possible to obtain peak-to-valley height of less than 0.5 nm with lateral spacing of ≈ 5-10 nm. 16 Differently, the (ii) trenches/grooves are found to be usually 5-10 nm deep with a typical trench-to-trench distance in the order of 300-500 nm 16 and could therefore be problematic for the realization of heterostructures, e.g., by reducing the mobility of 2-dimensional electron gases (2DEGs) at the interface of modulation-doped single [9][10][11] or double 19 β-(AlxGa1-x)2O3/Ga2O3 structures. The formation of trenches/grooves on the surface of (010)-oriented β-Ga2O3 and β-(AlxGa1-x)2O3 layers has been widely reported (but little commented) in literature for both MBE 6,7,9,16,20 and MOVPE. 8,21,22 Figure 3 (c)). The presence of two facets is exemplarily highlighted in red, while some trenches are exemplarily marked as blue dotted lines.
To date, different explanations have been given for the formation of these trenches. Based on homoepitaxial growths by ozone MBE, Sasaki et al. 7 suggested that the groove formation should be related to step-bunching along the [001] direction, given the possibility to reduce the rms of the deposited layers by lowering Tg. In contrast, smooth (010)-layers have been obtained by Okumura et al. 6 using plasma-assisted MBE at high substrate temperatures on substrates with a large (2°) unintentional offcut along the [001] in-plane direction, suggesting the absence of step-bunching in favor of step-flow growth. We have recently reported a trench-free (010) β-Ga2O3 homoepitaxial layer deposited at Tg = 900 °C grown by In-mediated MEXCAT via plasma-assisted MBE whereas a layer deposited under the very same conditions (i.e. Tg and O-to-Ga flux ratio), but without In-mediated MEXCAT resulted in the formation of trenches, speculating on either an impact of different unintentional offcuts or an increase of the surface diffusion length due to In-mediated MEXCAT. 16 Additionally, it has been shown that In-mediated MEXCAT via plasma-assisted MBE also realized trench-free β-(AlxGa1-x)2O3 layers on (010) β-Ga2O3 substrates, 23 suggesting both a catalytic and a surfactant effect of In. A possible role of In as a surfactant has been also suggested in (100) homoepitaxy of β-(InxGa1-x)2O3 via MOVPE. 24 In this work we experimentally investigate the cause of trench formation in (010) β-Ga2O3 homoepitaxy by plasma-assisted MBE with respect to the substrate offcut and the metal-to-oxygen flux ratio during plasmaassisted MBE.

4
We use In-mediated MEXCAT to deposit β-Ga2O3 homoepitaxial layers on top of substrates with different unintentional offcuts previously measured by a combination of X-ray reflectivity (XRR) and X-ray diffraction (XRD -PANalytical X'Pert Pro MRD). An O-plasma treatment at Tg = 900 °C has been always performed prior to the deposition process and resulted in a featureless surface. 16 For the details regarding the experimental process and the substrate characterization please consult ref. 16 .
The offcut measurements were collected on 10x15 mm 2 substrates which were afterwards cut in 5x5 mm 2 pieces. For their inplane orientation the skew-symmetric reflection of the (111) crystal plane was measured. We performed four different offcut measurements by rotating the in-plane direction (Φ angle) of the sample in steps of 90°, each time aligning ω for the (020) crystal planes and afterwards measuring the shift of the surface reflection with respect to this alignment [2-Theta = 0.5°, 1/16° beam width, 0.18 mm detector slit, see Figure 2  We found that with our experimental setup the measurement of the substrate offcut on (010) substrates can be reliably done just before the full crystal cut in 5x5 mm 2 pieces; we believe this could be related to the round edges on the sides of the (010) crystals which could induce a broadening of the surface reflection component in such a small sample size. A sum up of the 5 measured unintentional offcuts α on the 4 different employed substrates is reported in Table 1. The expected associated terrace length has been evaluated considering monolayer steps equal to the b unit cell parameter, i.e. 0.303 nm; 25 nonetheless, consistently to what we have previously reported, 16 we never identified monolayer steps before the deposition process. The film thickness was determined from XRD "Pendellösung" fringes in the vicinity of the (020) β-Ga2O3 reflection in 2Θ-ω scans. 6,16 The surface morphology of the deposited layers was characterized by AFM (Bruker Dimension Edge) in the PeakForce tapping mode on two different image sizes (1x1 -5x5 μm 2 ).  Figure 2.

Substrate
We deposited a series of samples with MEXCAT at Tg = 900 °C under identical, nominally metal-rich conditions 16 (Table 1). In line with our previous report, 16 under these growth conditions we were able to obtain for all the deposited layers a comparable thickness (range of 80-100 nm) without XRDdetectable In incorporation [i.e., without shift of the layer peak with respect to the (020) reflection of the substratee.g., red curve in Figure 6 crystal (see Table 1). Figure 3 summarizes the AFM micrographs of all the layers deposited under these conditions. They all show homogeneous morphologies as visible comparing 1x1 and 5x5 μm 2 images.  In order to confirm our results, we performed a twin deposition (same growth conditions) on top of a second 5x5 mm 2 unintentionally doped substrate coming from the same 15x10 mm 2 crystal (reference deposition Figure 3(d) and blue line in Figure 4). The AFM pictures of the deposited layer [ Figure 5(a)] confirm the presence of a layer without the presence of trenches, whose rms is slightly lower than its twin deposited sample (rms ≈ 0.15 nm) and is just ruled by the (110)-faceting. Remarkably, it is possible to identify in this case the presence of monolayer steps whose direction and spacing [ Figure 5 respectively] is in line with the measured substrate offcut (Table 1 and Figure 2). This evidence points towards a potential stepflow growth of the deposited (010) homoepitaxial layer. Finally, we investigated the effect of different Ga-to-O fluxes. We deposited on top of two 5x5 mm 2 Sn:Ga2O3 substrates from the same investigated 15x10 mm 2 crystal (Table 1)

Discussion
We interpret the collected experimental results by an anisotropic diffusion lengths and associated nucleation densities of the adsorbed species on the (010) Ga2O3 surface. This becomes obvious already by considering the morphologies of films, shown in Fig. 4 of Ref. 16 that were grown without MEXCAT but at otherwise identical conditions to those discussed here. In particular, we can consider the case of (i) the (110)-facets and (ii) the trenches for the layers deposited at slightly metal-rich conditions, what has been proposed elsewhere, 23,24 these experimental data suggests that In does not act as a surfactant for the Ga2O3 layer growth. Instead, our present work indicates that a sufficiently large absolute offcut mostly oriented along the [001] direction (unintentionally doped Ga2O3 substrate, see Table 1 and Figure 2) is the key for the formation of a trench-free (010) homoepitaxial layer [ Figure 3(d) and Figure 5]. The related monolayer steps (highlighted in Figure 5) with spacing below or equal the diffusion length along the [001] direction of the surface-diffusing species can act as a regular array of nucleation sites. As shown by the presence of off-cut-related monolayer steps on the deposited layer shown in Figure 5, this approach can eventually allow for step-flow growth in (010) homoepitaxy. Therefore, the resulting layers are homogeneously smooth with a low surface roughness (rms ≈ 0.2 nm) just ruled by the formation of the (110)-facets. The obtainment of such a low surface roughness despite the faceting is allowed by the low angle of the (110)-facets with respect to the (010) surface (≈ 14°) and their limited lateral size (≈ 5-10 nm). 16 We propose that the employment of proper offcuts could be fundamental for the growth of the highest surface quality β-Ga2O3 homoepitaxial layers on all the available orientations since a well-defined substrate offcut has already allowed to achieve step flow growth in (100) β-Ga2O3 homoepitaxy by MOVPE. 26 Moreover, our data suggest that a too-low offcut and related long distance of monolayer steps (above the surface diffusion length) in the [001]-direction results in the random nucleation of islands whose coalescence forms the trenches during (010) homoepitaxy by plasma-assisted MBE with or without MEXCAT. An exception to this tentative explanation is the film grown on the substrate Fe:Ga2O3-2 which exhibits trenches (shown in Figure 3 (c)) despite an offcut component along the [001] ( Table   1) that is comparable to that of the trench-free film grown on the unintentionally doped Ga2O3 substrate. Notwithstanding, this discrepancy suggests the actual absolute offcut direction along [001] to play a key role for obtaining trench-free layers.
In addition, the comparison among layers deposited on the same crystal with different O-to-Ga flux ratios allows us to identify the O-flow as an important parameter to change the diffusion length of the adsorbed species on the layer surface. In particular, while maintaining the same metal flux, a larger O-flow decreases the diffusion length (and increases the nucleation density) along the [001] direction resulting in the formation of closer spaced trenches [ Figure 6(b,c)]. We conclude that step bunching is not responsible for the formation of trenches that roughen the (010) layers in plasma assisted MBE since this mechanismcontrary to our observationsshould be (i) promoted by the presence of a shorter distance of monolayer steps along the (high diffusion length) [001] direction rather than a longer one and (ii) suppressed/reduced by a shorter diffusion length due to higher O-fluxes (0.5 sccm instead of 0.33 sccm). 27

Conclusion
In conclusion, we found (010) β-Ga2O3 films homoepitaxially grown under slightly metal-rich conditions by plasma-assisted MBE with and without In-mediated MEXCAT to be significantly roughened due to the formation of trenches whereas the faceting into shallow (110)-(1 ̅ 10) facets elongated along the [001] direction plays a minor role for the total film roughness.
The trench formation is likely related to coalescence boundaries due to an island growth regime with significantly higher diffusion length, and thus lower nucleation density, along the [001] direction than perpendicular to it. In agreement with this the metal-to-oxygen flux ratio was identified as an important synthesis parameter that controls the diffusion length of the adsorbed species during layer growth and thus the trench density: A higher oxygen flux results in lower diffusion length and thus a higher density of trenches.
Using In-mediated MEXCAT, we demonstrate, that a sufficiently large substrate offcut oriented along the [001] direction can enable the growth of smooth, trench-free layers, i.e., about 100 nm thick layers with rms roughness as low as 0.2 nm, in (010) β-Ga2O3 homoepitaxy by plasma-assisted MBE. The absence of the trenches is tentatively attributed to the formation of proper monolayer steps whose width is comparable to or lower than the diffusion length of the surface diffusing species in that particular in-plane direction, indicating the possibility of step flow growth. The observed dependency of trench formation on offcut and oxygen flux excludes both (i) step bunching as their creation mechanism, as well as (ii) the possible role of In as a surfactant in (010) β-Ga2O3 homoepitaxy.
We believe that this work can be fundamental for the realization of high quality interfaces and surfaces in multilayer heterostructures like β-(AlxGa1-x)2O3/Ga2O3 on (010) β-Ga2O3 substrates with increased electron mobility due to reduced surface or interface roughness scattering.