Adsorption-Controlled Growth of Ga2O3 by Suboxide Molecular-Beam Epitaxy

This paper introduces a growth method---suboxide molecular-beam epitaxy (S-MBE)---which enables the growth of Ga2O3 and related materials at growth rates exceeding 1 micrometer per hours with excellent crystallinity in an adsorptioncontrolled regime. Using a Ga + Ga2O3 mixture with an oxygen mole fraction of x(O) = 0.4 as an MBE source, we overcome kinetic limits that had previously hampered the adsorption-controlled growth of Ga2O3 by MBE. We present growth rates up to 1.6 micrometer per hour for Ga2O3--Al2O3 heterostructures with unprecedented crystalline quality and also at unparalleled low growth temperature for this level of perfection. We combine thermodynamic knowledge of how to create molecular-beams of targeted suboxides with a kinetic model developed for the S-MBE of III-VI compounds to identify appropriate growth conditions. Using S-MBE we demonstrate the growth of phase-pure, smooth, and high-purity homoepitaxial Ga2O3 films that are thicker than 4 micrometer. With the high growth rate of S-MBE we anticipate a significant improvement to vertical Ga2O3-based devices. We describe and demonstrate how this growth method can be applied to a wide-range of oxides. S-MBE rivals leading synthesis methods currently used for the production of Ga2O3-based devices.


I. INTRODUCTION
Molecular-beam epitaxy (MBE) involves the growth of epitaxial thin films from molecular-beams.In 'conventional' MBE the molecular-beams consist of elements.An example is the Ga ( ) species that evaporate from a heated crucible containing Ga ( ) or the As 4 ( ) species that evaporate from a heated crucible containing As ( ), where , , and denote gaseous, liquid, and solid, respeca) Electronic mail: pv269@cornell.edub) Electronic mail: schlom@cornell.edutively.In gas-source MBE the species in the molecularbeams originate from gases that are plumbed into the MBE from individual gas cylinders, for example, arsine or phosphine.In metal-organic MBE the species in the molecularbeams are metal-organic molecules like trimethylgallium or trimethylaluminum. 1 'Suboxide MBE' refers to an MBE growth process utilizing molecular-beams of suboxides like Ga 2 O ( ) or In 2 O ( ).We have applied this method to the growth of Ga 2 O 3 thin films and find that it can produce epitaxial Ga 2 O 3 films with far greater perfection and at much higher growth rates than currently demonstrated by other MBE methods for the growth of this material.
A. 'Conventional' MBE of Ga 2 O 3 and related materials Gallium-sesquioxide (Ga 2 O 3 ) synthesized in its different polymorphs [i.e., α-Ga 2 O 3 (rhomboheral), β-Ga 2 O 3 (monoclinic), γ-Ga 2 O 3 (cubic spinel), ϵ-Ga 2 O 3 (hexagonal), and κ-Ga 2 O 3 (orthorhombic)], is an emerging semiconductor possessing promising features for unprecedented high-power electronics.This is due to its large band gap (∼ 5 eV) 2,3 and very high breakdown field (up to 8 MV cm −1 ). 4 The band gap of Ga 2 O 3 may be widened by alloying Ga 2 O 3 with Al 2 O 3 to form (Al Ga 1− ) 2 O 3 . 3The synthesis of (Al Ga 1− ) 2 O 3 /Ga 2 O 3 heterostructures with high Al content is desired for high-power transistors with large band gap offsets. 3,5,6 is known that the 'conventional' MBE of Ga 2 O 3i.e., when supplying monoatomic Ga and active O species during growth-is strongly limited by the formation and subsequent desorption of its volatile suboxide Ga 2 O. [7][8][9][10][11] In the adsorption-controlled regime (i.e., grown with an excess of Ga), its growth rate strongly decreases with increasing Ga flux, Ga , because not enough oxygen is available to oxidize the physisorbed Ga 2 O to Ga 2 O 3 ( ) and the Ga 2 O desorbs from the hot substrate.At sufficiently high Ga , film growth stops, and even goes negative (i.e., the Ga 2 O 3 film is etched). 8This effect is enhanced as the growth temperature, , increases due to the thermally activated desorption of Ga 2 O from the growth surface.The enhanced,induced Ga 2 O desorption leads to a decreasing growth rate even in the O-rich regime, resulting in a short growth rate plateau (the value of which is far below the available active O flux 12 ), followed by an even further decreasing growth rate in the adsorption-controlled regime. 9,12,13These effects, i.e., the O-deficiency induced and thermally activated desorption of suboxides, 9,[11][12][13] are detrimental for the growth of III-VI (e.g., Ga 2 O 3 ) and IV-VI materials in the adsorptioncontrolled regime.
Nevertheless, the MBE of thin films in the adsorptioncontrolled growth regime is often desired for high crystal perfection, [14][15][16] smooth surface morphology, 17 avoiding undesired oxidation states, 18,19 or suppressing the formation of electrically compensating defects. 20,21e decreasing growth rate of Ga 2 O 3 is microscopically explained by a complex two-step reaction mechanism. 11,12In the first reaction step, all Ga oxidizes to Ga 2 O via the reaction 2Ga ( ) + O ( ) − −−− → Ga 2 O ( , ) , with adsorbate and gaseous phases denoted as and , respectively.The Ga 2 O formed may either desorb from the growth surface (in the O-deficient regime or at elevated ) or be further oxidized to Ga 2 O 3 via a second reaction step through the reaction with the solid phase denoted as .This two-step reaction mechanism and the resulting Ga 2 O desorption defines the growth rate-limiting step for the 'conventional' MBE of Ga 2 O 3 and related materials. 11,129]11 A similar growth rate-limiting behavior, based on this two-step reaction mechanism, has also been reported for the growth of other III-VI (e.g., In 2 O 3 ) and IV-VI (e.g., SnO 2 ) compounds by 'conventional' MBE. 8,11,13This twostep growth process for the growth of III-VI and IV-VI oxides by 'conventional' MBE is fundamentally different from the single-step reaction mechanism of, for example, III-V [22][23][24] and II-VI 25 compounds.It can be attributed to the different electronic configurations of the compound constituents, resulting in different compound stoichiometries between III-VI and IV-VI compared with III-V and II-VI materials, respectively.
In the growth method introduced in this work, which we call suboxide MBE ( -MBE), we avoid the first reaction step (1) by directly supplying a Ga 2 O ( ) molecular-beam to the growth front on the substrate surface.Using this approach, we bypass the growth rate-limiting step for 'conventional' Ga 2 O 3 MBE by removing the O-consuming step to Ga 2 O formation that occurs on the substrate in the 'conventional' MBE growth of Ga 2 O 3 . 11,12A related approach has been used by Ghose et al. 26,27 with Ga 2 O provided from Ga 2 O 3 source material heated to temperatures well in excess of 1600 • C to produce a molecular beam of Ga 2 O for the growth of Ga 2 O 3 films by MBE. 28Motivated by known vapor pressure data of oxides 29 and their mixtures with the respective metals, e.g., Ga + Ga 2 O 3 , 30 as well as the possibility of decomposing Ga 2 O 3 by Ga and SnO 2 by Sn under MBE conditions, 8 Hoffmann et al. 31 have demonstrated how mixtures of Ga with Ga 2 O 3 and Sn with SnO 2 provide MBErelevant fluxes of Ga 2 O and SnO, respectively, at source temperatures below 1000 • C.This prior work has grown films using suboxide molecular beams by MBE at growth rates < 0.2 μm hr −1 . 31,32 we demonstrate, -MBE enables the synthesis of Ga 2 O 3 in the highly adsorption-controlled regime, at growth rates > 1 μm hr −1 with unparalleled crystalline quality for Ga 2 O 3 /Al 2 O 3 heterostructures as well as homoepitaxial Ga 2 O 3 at relatively low .The growth rate of -MBE is competitive with other established growth methods used in semiconductor industry-such as chemical vapor deposition (CVD) 33 or metal-organic CVD (MOCVD) 34 -and moreover, leads to better structural perfection of the obtained thin films.With this improved perfection we expect an improvement of -type donor mobilities in Ga 2 O 3 thin films doped with Sn, Ge, or Si grown by -MBE, as well.The relatively low at which it becomes possible to grow high-quality films by -MBE is a crucial enabler for materials integration where temperatures are limited, e.g., back end of line (BEOL) processes.
Figure 1 illustrates a schematic of how growth rate depends on cation flux during the MBE growth of different types of compounds, where both axes are normalized by the anion flux.Figure 1(a) depicts the observed behavior for III-V compounds, e.g., GaN. 24Figure 1(b) shows the observed behavior for III-VI compounds, e.g., Ga 2 O 3 , when the group III cation is supplied by a molecular-beam of the group III element (e.g., Ga). 8 In Fig. 1(c), the anticipated behavior for III-VI compounds is plotted, e.g., Ga 2 O 3 , when the group III element is supplied by a molecular-beam of a III 2 VI subcompound containing the group III constituent (e.g., Ga 2 O). 12 The units of the horizontal and vertical axes are chosen to make the crossover occur at values of unity.For the sake of simplicity, henceforth, we only discuss the reaction behavior of GaN and Ga 2 O 3 in detail.We emphasize, however, this discussion holds true for the MBE growth of AlN, 22 InN, 23 In 2 O 3 (Refs.8,11,13) and other III-VI, 11,35 and II-VI compounds. 25 drawn in Figs.1(a For GaN MBE [Fig.1(a)], once the supplied Ga exceeds the flux N of active available N, the growth rate saturates, is independent of the Ga / N ratio, and is limited by  24 and III-VI compounds (e.g., Ga 2 O 3 ) 11 as a function of the III/V (e.g., Ga / N ) and III/VI flux ratios (e.g., Ga / O ), respectively.(c) Anticipated growth rate behavior of III-VI compounds (e.g., Ga 2 O 3 ) 12 as a function of the III 2 VI/VI flux ratio (e.g., Ga 2 O / O ).All schematic growth rate evolutions are normalized by the respective fluxes of active available group V ( V ) and group VI elements ( VI ).Each plot is at a constant .Anion-rich and cation-rich regimes are indicated in gray and white, respectively.N and .The measured plateau in growth rate for GaN MBE in the Ga-rich regime results from its single-step reaction kinetics.Here, Ga reacts directly with activated N via the reaction 24 Ga ( ) and excess Ga either adsorbs onto or desorbs from the growth surface depending upon N and .
Figure 1(b) depicts the reaction kinetics of Ga 2 O 3 in the Ga-rich regime (O-deficient growth regime) by supplying Ga .Here, the growth rate linearly decreases with increasing Ga , and the growth eventually stops at Ga ≥ 3 O (in growth rate units).The fact that desorbing Ga 2 O removes Ga and O from the growth surface-that cannot contribute to Ga 2 O 3 formation-leads to the decreasing growth rate in the O-deficient growth regime. 8,9,11This behavior is microscopically governed by the two-step reaction process, Eqs. ( 1) and (2), 11 and is fundamentally different from the singlestep reaction kinetics, Eq. ( 3), governing the MBE of GaN [Fig.1(a)].
In Fig. 1(c), the anticipated growth kinetics of Ga 2 O 3 while using a Ga 2 O beam is depicted, showing a constant growth rate in the Ga 2 O-rich regime (i.e., in an excess of Ga 2 O). 12 Excess Ga 2 O (that cannot be oxidized to Ga 2 O 3 ) either accumulates or desorbs off the growth surface without consuming or removing active O from its adsorbate reservoir-similar to the case presented for GaN in Fig. 1(a).Thus, with -MBE, one may effectively achieve single-step reaction kinetics for Ga 2 O 3 MBE [reaction (2)], as is the case for the growth of GaN by MBE [reaction (3)].
7][38] Through the use of -MBE, we convert the complex two-step reaction kinetics of III-VI [e.g., reactions (1) and ( 2)] and IV-VI compounds into simple single-step kinetics [e.g., (2)], the same as observed for III-V and II-VI materials.We therefore expect a similar growth behavior during -MBE, i.e., constant growth rates in the adsorption-controlled regime, which are highly scalable by the provided active O flux.Such a regime should allow III-VI thin films (e.g., Ga 2 O 3 ) and IV-VI films (e.g., SnO 2 ) to be grown much faster with excellent crystal quality at relatively low .
-MBE utilizes molecular-beams of suboxides and builds upon prior thermodynamic work and thin film growth studies.For example, molecular-beams of the following suboxides have all been used in MBE: Ga 2 O, 26,27,32 GdO, 39,40 LuO, 40 , LaO, 40 NdO, 41 PrO, 42,43 ScO, 44 SnO, 18,19,31,45,46 YO. 39 Even before these MBE studies, thin films of the suboxides SiO, 47,48 , SnO, [49][50][51][52][53] , and GeO 54 had been deposited by thermal evaporation, exploiting the same underlying vapor pressure characteristics that make -MBE possible.In some of these cases the dominant species in the gas phase were not identified, but subsequent vapor pressure studies and thermodynamic calculations establish that they were suboxides. 29,55hat is new about -MBE is the use of suboxide molecular-beams in a targeted way to achieve epitaxial growth of desired oxides (e.g., Ga 2 O 3 ) at high growth rates in an adsorption-controlled regime.This enables the benefits of the far simpler (from a growth kinetics, growth control, and growth standpoint) plateau growth regime shown in Fig. 1(c) to be harnessed rather than the growth regime shown in Fig. 1(b) that has posed limits to the growth of Ga 2 O 3 films by 'conventional' MBE up to now.

II. DETAILED DESCRIPTION OF -MBE
The use of a Ga 2 O ( ) molecular-beam to grow Ga 2 O 3 ( ) thin films by MBE in the O-rich regime (i.e., in an excess of active O) has been demonstrated by placing the stoichiometric solid of the compound Ga 2 O 3 into a crucible and using it as an MBE source. 26,27Possible reactions that produce a Ga 2 O molecular-beam by the thermal decomposition of Ga 2 O 3 are: One disadvantage of using Ga 2 O 3 ( ) as the MBE source is that Ga 2 O 3 does not evaporate congruently.Our thermodynamic calculations indicate that when Ga 2 O 3 ( ) is heated to a temperature where the Ga 2 O ( ) that it evolves has a vapor pressure of 0.1 Pa (a vapor pressure typical for MBE growth), that the Ga 2 O molecular-beam is only 98.0% Ga 2 O molecules.The other 2% of the beam is Ga, O 2 , and O species.
The other disadvantage of using Ga 2 O 3 ( ) as the MBE source is that quite high effusion cell temperatures are required to evolve appreciable Ga 2 O ; temperatures in excess of ∼ 1600 • C, 28 ∼ 1700 • C, 56 , or ∼ 1800 • C 26 have been used.At such high effusion cell temperatures, crucible choices become limited and prior researchers have used iridium crucibles. 26,27,32,56Ga 2 O 3 thin films synthesized utilizing an iridium crucible at an effusion cell temperature of ∼ 1700 • C 56 were limited to growth rates < 0.14 μm hr −1 (Ref.32) with ∼ 5 × 10 18 cm −3 iridium contamination in the grown Ga 2 O 3 films. 56,57These aspects of Ga 2 O 3 compound sources hamper the synthesis of semiconducting Ga 2 O 3 layers at growth rates exceeding 1 μm hr −1 with device-relevant material properties.For comparison, the Ga + Ga 2 O 3 mixture that we describe next and have used to grow Ga 2 O 3 films at growth rates exceeding 1 μm hr −1 provides a Ga 2 O molecular-beam that is 99.98% pure according to our thermodynamic calculations.This is for the same Ga 2 O vapor pressure of 0.1 Pa, which happens at a source temperature about 600 • C lower for this Ga + Ga 2 O 3 mixture than for pure Ga 2 O 3 , enabling us to use crucibles that do not result in iridium-contaminated films.
Years ago as well as more recently, Ga + Ga 2 O 3mixed sources producing a Ga 2 O molecular-beam have been studied 30,31 and suggested as efficient suboxide sources for oxide MBE. 31,55Using this mixed source, a Ga 2 O ( ) molecular-beam is produced by the chemical reaction 4Ga ( ) with the liquid phase denoted as .
-MBE uses the thermodynamic 30 and kinetic 8 properties of Ga+Ga 2 O 3 mixtures favoring reaction (6) under MBE conditions.
For the -MBE of Ga 2 O 3 , we explored Ga-rich and Ga 2 O 3 -rich mixtures of Ga + Ga 2 O 3 with stoichiometries 5Ga ( ) respectively.The latter mixture has an oxygen mole fraction of (O) = 0.4 and the properties of this Ga 2 O 3 -rich mixture are described below.The corresponding reaction rate constants Ga-rich and Ga 2 O 3 -rich define the production rate of Ga 2 O ( ) at a given temperature mix of the Ga + Ga 2 O 3 mixture.
The flux of Ga 2 O ( ) in the molecular-beam emanating from the mixed Ga + Ga 2 O 3 sources is significantly larger than that of Ga ( ) 30,58 emanating from the same source.This is also true under MBE conditions. 31,55The resulting high ratio of Ga 2 O/Ga ≫ 1 provides a more controllable and cleaner growth environment than accessible by decomposing a stoichiometric Ga 2 O 3 source, which produces molecularbeam ratios of Ga 2 O/Ga, Ga 2 O/O 2 , and Ga 2 O/O.Hence, the growth surface of the substrate during film growth using -MBE is exposed to controllable and independently supplied molecular-beams of Ga 2 O and reactive O adsorbates.
We have experienced that a Ga 2 O 3 -rich mixture enables higher mix and higher, stable Ga 2 O ( ) molecularbeams than a Ga-rich mixture.This enables -MBE to achieve higher growth rates.This experimental observation is confirmed by our thermodynamic calculations of the phase diagram of Ga ( ) + Ga 2 O 3 ( ) mixtures, which we describe next.
The calculated Ga-O phase diagram in Fig. 2 shows that at mix below the three-phase equilibrium of gas + Ga ( ) + Ga 2 O 3 ( ) around 907 K, a two-phase region of Ga ( ) + Ga 2 O 3 ( ) forms, which does not change with respect to temperature or oxygen mole fraction between 0 and 0.6.Note that all thermodynamic calculations in the present work were performed using the Scientific Group Thermodata Europe (SGTE) substance database (SSUB5) 60 within the Thermo-Calc software. 61For mix > 907 K, the two-phase regions are gas + Ga ( ) when the mole fraction of oxygen is below 1/3, corresponding to what we refer to as Ga-rich mixtures, and gas + Ga 2 O 3 ( ) when the mole fraction of oxygen is between 1/3 and 0.6, which we refer to as Ga 2 O 3 -rich mixtures.These two-phase regions become a single gas-phase region at mix of (907 − 1189) K for Ga-rich mixtures and at (907 − 1594) K for Ga 2 O 3 -rich mixtures, respectively.All of these phase transition temperatures decrease with decreasing pressure 59 as shown on the pressure versus temperature ( − ) phase diagrams in Fig. 3. FIG. 4. Gibbs energies of the gas, Ga( ), Ga 2 O 3 ( ) phases at temperature = 1100 K and total pressure = 0.1 Pa.The brown dotted line shows the activity (or partial pressure) of oxygen when 0 < (O) < 0.33.In this range the gas phase is in equilibrium with Ga( ) and the activity of oxygen is 6.4 × 10 −24 Pa.The green dashed line corresponds to the case where 0.33 < (O) < 0.6.In this range the gas phase is in equilibrium with Ga 2 O 3 ( ) and the activity of oxygen is O 2 = 1.8 × 10 −16 Pa.This difference in the partial pressure of O 2 between the two regimes is huge and shows the advantage of growing Ga 2 O 3 films from Ga 2 O 3 -rich (Ga + Ga 2 O 3 ) mixtures.
To contrast the difference between Ga-rich versus Ga 2 O 3 -rich mixtures we have performed additional thermodynamic calculations at oxygen mole fractions of (O) = 0.2 and (O) = 0.4.These two chosen oxygen mole fractions correspond to Ga-rich and Ga 2 O 3 -rich mixtures, respectively.In Figs.3(a) and 3(b) the solid (red) lines denote the three-phase equilibrium between gas + Ga ( ) + Ga 2 O 3 ( ); these are identical at (O) = 0.2 and (O) = 0.4.The dotted (black) lines denote the equilibrium between the gas and gas + Ga ( ) phase regions for (O) = 0.2 and the gas and gas + Ga 2 O 3 ( ) phase regions for (O) = 0.4, i.e., their respective boiling temperature/pressure. Figure 4 shows Gibbs energies of the gas, Ga( ), Ga 2 O 3 ( ) phases at temperature = 1100 K and total pressure = 0.1 Pa.There are seven distinct atomic and molecular species in the gas phase: Ga, Ga 2 , GaO, Ga 2 O, O, O 2 , and O 3 .The kink in the Gibbs energy of the gas phase at (O) = 0.33 corresponds to the composition of the Ga 2 O species because it is the major species in the gas phase.It can be seen that the values of the oxygen activity in the gas+Ga ( ) We used Ga metal (7N purity) and Ga 2 O 3 powder (5N purity) for the Ga + Ga 2 O 3 mixtures, loaded them into a 40 cm 3 Al 2 O 3 crucible and inserted it into a commercial dual-filament, medium temperature MBE effusion cell.After mounting the effusion cell to our Veeco GEN10 MBE system and evacuating the source, we heated it up, outgased the mixture, and set our desired Ga 2 O flux for the growth of Ga 2 O 3 .We measured the flux of the Ga 2 O ( ) molecularbeam reaching the growth surface prior to and after growth using a quartz crystal microbalance.The film surface was monitored during growth by reflection high-energy electron diffraction (RHEED) using 13 keV electrons.After growth x-ray reflectivity (XRR), optical reflectivity in a microscope (ORM), 62 scanning electron microscopy (SEM), scanning transmission electron microscopy (STEM), and secondaryion mass spectrometry (SIMS) were used to accurately measure the thicknesses of homoepitaxial (ORM, SEM, SIMS, SEM) and heteroepitaxial (XRR, ORM, SEM, STEM, SIMS) grown Ga 2 O 3 films to determine the growth rate.X-ray diffraction was performed using a four-circle x-ray diffractometer with Cu K 1 radiation.The growth rates obtained follow the anticipated growth kinetics depicted in Fig. 1(c).In the adsorption-controlled regime, an increase in Ga 2 O (at otherwise constant growth parameters) does not lead to a decrease in the growth rate as observed for 'conventional' Ga 2 O 3 MBE [Fig.1(b)], 7,9 but instead results in a constant growth rate: a growth rate-plateau.The data clearly show that we have overcome the growth rate-limiting step by using a Ga 2 O ( ) suboxide molecular-beam while reducing the complexity of the Ga 2 O 3 reaction kinetics from a two-step [Eqs.( 1) and ( 2)] to a single-step [Eq.( 2)] reaction mechanism.
The reaction kinetics of -MBE for the growth of Ga 2 O 3 ( ) can be described in a similar way as 'conventional' III-V [e.g., reaction (3)] and II-VI MBE.We therefore set up a simple reaction-rate model describing the growth of Ga 2 O 3 ( ) by -MBE (this same model applies to other III-VI and IV-VI compounds, as well): The Ga 2 O 3 , Ga 2 O, and O adsorbate densities are denoted as The flux of available O adsorbates, for Ga 2 O to Ga 2 O 3 oxidation at a given , is determined by its sticking coefficient on the Ga 2 O 3 growth surface and is described by a sigmoid function with dimensionless pre-factor 0 , energy ∆ , and temperature off-set d .Equation ( 12) reflects the decreasing probability of O species to adsorb as is increased.This leads to an effectively lower surface density of active O for Ga 2 O oxidation and thus to lower growth rates.For a supplied flux of O corresponding to a background pressure of 1 × 10 −6 Torr (involving mixtures of O 2 and approximately 10 % O 3 as well as 80 % O 3 ) 63 , the values of the variables given in Eq. ( 12) are: 0 = 40, ∆ = 29 meV, and d = 675 • C. In this work, we introduce this model for -MBE to demonstrate its practical value.A physical description of this model including all model parameters is given in Ref. 64.The given values are extracted by fitting the maximum growth rate (defined as the plateau-regime) as a function of , e.g., as plotted in Fig. 6.We find that does not depend on the concentration of active O; it only depends on the partial pressure of active O.Thus, the active O may be be scaled up or down by either changing the concentration of O 3 in the O 3 beam or by changing the partial pressure of O 3 in the chamber.Note that O 3 supplies O to the surface of the growing film when it decomposes by the reaction: O 3 ( ) → O 2 ( ) + O ( ).A similar behavior of an increasing desorption or recombination rate of active O species with increasing has also been observed during O plasma-assisted MBE using elemental Ga and O molecular-beams. 9,12,13sed on this model, we scaled up O in order to achieve Ga 2 O 3 ( ) growth rates that exceed 1 μm hr −1 .Lines are estimations from our model, Eqs. ( 9)-( 11), including all kinetic parameters 64 .The dashed line shows the estimated intersection between the O-rich to the Ga 2 O-rich growth regime 64 .The blue shaded area indicates the adsorption-controlled growth rateregime only accessible by -MBE with growth rates ≥ 1 μm hr −1 .at = 500 • C. For comparison, the data point plotted as an open-dotted hexagon (see also Fig. 6) shows the highest possible growth rate at a five times lower active O and the same .This result shows quite clearly the accuracy of our model and demonstrates the -MBE of Ga 2 O 3 thin films at growth rates exceeding 1 μm hr −1 .In addition, the growth rate values plotted in Fig. 7(b) were obtained by homoepitaxial growth of β-Ga 2 O 3 (010) on β-Ga 2 O 3 (010).The growth rate of Ga 2 O 3 on Ga 2 O 3 (010) is 2.1 times larger than the growth rate on Al 2 O 3 (0001) at similar growth conditions-e.g., as plotted in Figs.7(a) [open hexagon] and 7(b) [solid diamond], respectively.This result suggests that the growth rate of -MBE grown Ga 2 O 3 (010) and other surfaces of Ga 2 O 3 may vastly exceed 1 μm hr −1 in the adsorption-controlled regime.The higher growth rate is likely due to the surface-dependent adhesion energies between of Ga 2 O adsorbates and substrate 11,12,65 , similar to what has been observed for Ga adsorbates during the 'conventional' MBE of Ga 2 O 3 45 .Fluctuations in and Ga 2 O for different samples and during the long duration growth of the 'thick' sample (> 3 hours) are considered by the standard deviations of the measured values of and Ga 2 O as given in Fig. 7.

B. Structural properties
We investigated the impact of variable growth conditions (i.e., Ga 2 O , O , and ) on the structural perfection of epitaxial Ga 2 O 3 ( ) films grown on Al 2 O 3 (0001) and Ga 2 O 3 (010) substrates.Figure 8 shows -2 x-ray diffraction (XRD) scans of selected Ga 2 O 3 films-the same samples depicted in Fig. 7 adsorbates (crystallites) on the growth surface may occur, similar to the formation of Ga droplets during GaN growth 36 .This effect is indicated by the slightly spotty RHEED image (outlined by the blue square) in Fig. 8.We have not yet optimized the growth for Ga 2 O 3 ( 201) films on Al 2 O 3 (0001) with thicknesses ≫ 1 μm and mapped all growth regimes (e.g., Ga 2 O 'droplet' formation at very high Ga 2 O ) .Further investigations of the structural perfection and electrical properties of Ga 2 O 3 grown by -MBE need to be performed.This could be particularly interesting for the the growth of Ga 2 O 3 ( ) at even higher Ga 2 O ( ) fluxes, which push even further into the adsorption-controlled regime.
We performed -MBE for homoepitaxial β-Ga 2 O 3 (010) films grown on β-Ga 2 O 3 (010) substrates.Figure 9 shows the -2 XRD scans of two selected Ga 2 O 3 (010) films grown under the same growth conditions.The -2 XRD profiles of the Ga 2 O 3 (010) film with thickness = 0.74 μm (plotted in dark blue) and the one of the substrate (data not shown) coincide.The Ga 2 O 3 (010) layer with = 4.1 μm (depicted as pale blue) also shows small contributions of the meta stable γ-Ga 2 O 3 phase.The inset of Fig. 9 shows the respective rocking curves across the symmetric 020 reflections of the same films as plotted in the main graph of Fig. 9.The obtained FWHM of the rocking curve of the film with = 0.74 μm is comparable to the one obtained for the bare Ga 2 O 3 (010) substrate (depicted as a black line).
[Note that the measured XRD spectra were obtained on different 10 × 10 mm 2 substrates which were all cut from the same 1" diameter Ga 2 O 3 (010) wafer from Synoptics.]The rocking curve of the 'thick' film with = 4.1 μm is considerably broader than the rocking curve detected for the 'thin' Ga 2 O 3 (010) film with = 0.74 μm.We attribute the different rocking curve widths measured to the non-uniformity in the crystalline perfection across the 1" diameter Ga 2 O 3 substrate on which these measurements were made.STEM of a 'thin' Ga 2 O 3 (010) film with = 0.28 μm (grown under similar conditions as the samples shown in Fig. 9) and the 'thick' film with = 4.1 μm (same sample as plotted as pale blue line in Fig. 9) are shown in Figs.10(a The surface morphology of Ga 2 O 3 (010) films grown by -MBE at growth rates > 1 μm hr −1 were investigated by atomic force microscopy (AFM) and are plotted in Figs.11(a)-11(c).The root mean square (rms) roughness of the 'thin' film with = 0.74 μm is lower than the one measured for the 'thick' film with = 4.1 μm.This evolution in rms roughness follows the same trend as observed by XRD scans of the same layers (dark blue and pale blue lines in the inset of Fig. 9), i.e., a slight decrease in crystal quality with increasing film thickness of the Ga 2 O 3 (010)/Ga 2 O 3 (010) structures.

C. Impurities
We investigated the incorporation of impurities into the Ga 2 O 3 (010) thin films grown with growth rates > 1 μm hr −1 by SIMS. Figure 12 shows the SIMS profile of the same film as plotted in Figs.7 (solid square), Fig. 10, and Fig. 11(c).This profile reveals that the Ga 2 O 3 -rich (Ga + Ga 2 O 3 ) mixtures employed lead to Ga 2 O 3 (010) thin films with low impurity incorporation.Only a slight increase of Al impurities with increasing film thickness and a slight incorporation of B are detected.These impurities likely originate from our use of an Al 2 O 3 crucible for the Ga 2 O 3 -rich (Ga + Ga 2 O 3 ) mixture.We note that we have also used pyrolytic boron nitride (pBN) crucibles for the Ga + Ga 2 O 3 mixture, but find high concentrations of B in the grown films by SIMS (∼ 10 20 B cm −3 ) when the background pressure of a mixture of O 2 + 80%O 3 is O = 5 × 10 −6 Torr.We attribute this to the oxidation of the surface of the pBN crucible to B 2 O 3 at the high oxidant pressures used.At the mix = 1020 • C used for growth, the vapor pressure of B 2 O 3 is significant. 55The small Si peak measured at the film-substrate interface originates from unintentional incorporated Si at the substrate surface.Note, we have tried Ga 2 Opolishing (for the first time) to remove the Si from the surface prior to growth.Our observation is that Ga 2 O-polishing does not provide the same reduction in Si contamination at the sample surface as can be accomplished by Ga-polishing. 68.
Our SIMS results show that the low effusion cell temperatures and Ga 2 O 3 -rich (Ga + Ga grow Ga 2 O 3 with growth rates exceeding > 1 μm hr −1 -do not lead to significant impurity incorporation into the grown Ga 2 O 3 (010) films.This is an advantage of -MBE compared to the growth Ga 2 O 3 from a crucible containing pure Ga 2 O 3 .Using a Ga 2 O 3 compound source at extremely high effusion cell temperatures (∼ 1700 • C) 56 , not only produces a flux containing a relatively low Ga 2 O molecular-beam resulting in low Ga 2 O 3 film growth rates, but also results in films contaminated with iridium. 32,56,57Nonetheless, electrical transport properties are extremely sensitive to impurities and measurements of mobility in doped Ga 2 O 3 films grown by -MBE remain to be performed.It could turn out that a higher purity Ga 2 O 3 powder will be needed than the 5N Ga 2 O 3 powder we have used in this study.

D. Summary
The growth rates we have achieved by -MBE are more than one order of magnitude faster than what has been reported for the growth of Ga 2 O 3 films from pure Ga 2 O 3 sources. 32e quality of the homoepitaxial β-Ga 2 O 3 (010) films (with thickness > 4 μm) assessed by XRD (Fig. 9), STEM (Fig. 10), AFM (Fig. 11) and SIMS (Fig. 12), reveal that -MBE with growth rates > 1 μm hr −1 is competitive to other industrial relevant synthesis methods [such as (MO)CVD] for the growth of vertical Ga 2 O 3 -based structures with thicknesses in the μm-range.
Based on our model and experimental results, we anticipate growth rates up to 5 μm hr −1 on Ga 2 O 3 (010) and other growth surfaces to be possible by -MBE.This estima-tion is based on the physical MBE limit: the mean free path of the species (e.g., Ga 2 O and O 3 ) emanating from their sources to the target.In our estimate we have used an upper limit for the O partial pressure of O ∼ 2 × 10 −4 Torr [resulting in ∼ 0.1 m] 69 and a lower limit of ≥ 725 • C [required for the adsorbed species (e.g., Ga 2 O and O) to crystallize into a homoepitaxial film of Ga 2 O 3 ].

IV. OUTLOOK AND ALTERNATIVES OF -MBE
We have demonstrated the growth of high quality Ga 2 O 3 ( ) thin films by -MBE in the adsorptioncontrolled regime using Ga ( ) + Ga 2 O 3 ( ) mixtures.The high growth rate ≫ 1 μm hr −1 , and unparalleled crystal quality of the homoepitaxial and heteroepitaxial structures obtained (with ≫ 1 μm) suggest the possibility of unprecedented mobilities of Ga 2 O 3 thin films containing -type donors (Sn, Ge, Si) grown by -MBE.
We have also developed Sn + SnO 2 and Ge + GeO 2 mixtures in order to produce SnO ( ) and GeO ( ) beams for use as -type donors in Ga 2 O 3 -based heterostructures.Furthermore, we have grown SnO 2 using a Sn + SnO 2 mixture. 31oreover, we have grown Ga 2 O 3 doped with SnO using Ga 2 O and SnO beams and achieved controllable Sn-doping levels in these Ga 2 O 3 films. 70Nevertheless, the improvement of the -type mobilities obtained during -MBE, at growth rates > 1 μm hr −1 , still needs to be demonstrated and shown to exceed the state-of-the-art mobilities in Ga 2 O 3 films grown by 'conventional' MBE. 71ur comprehensive thermodynamic analysis of the volatility of 128 binary oxides plus additional two-phase mixtures of metals with their binary oxides, 55 e.g., Ga + Ga 2 O 3 , have led us to recognize additional systems appropriate for growth by -MBE.This thermodynamic knowledge coupled with our understanding of the -MBE growth of Ga 2 O 3 enabled us to develop In + In 2 O 3 and Ta + Ta 2 O 5 mixtures from which we have grown high-quality bixbyite In 2 O 3 64,72 and In 2 O 3 :SnO 2 (ITO, with up to 30% Sn) 64,72 as well as rutile TaO 2 73 by -MBE, respectively.
Growing thin films with very high crystalline qualities at growth rates > 1 μm hr −1 by using suboxide molecularbeams-with up to 5 μm hr −1 anticipated growth rates by our model-will make MBE competitive to other established synthesis methods, such as CVD 33 or MOVPE. 34The that we have demonstrated for high quality Ga 2 O 3 layers grown by -MBE is significantly lower than what has been demon-strated for the growth of high quality Ga 2 O 3 films by CVD or MOVPE.This makes -MBE advantageous for BEOL processing.Additionally, Ga 2 O 3 grown with a vast excess of Ga 2 O ( ) and high oxygen activity in Ga 2 O 3 -rich mixtures may suppress Ga vacancies in the Ga 2 O 3 layers formed, which are believed to act a compensating acceptors 20,74 potentially improving the electrical performance of -type Ga 2 O 3 -based devices significantly.
The development of Al + Al 2 O 3 mixtures for the growth of epitaxial Al 2 O 3 and (Al Ga 1− ) 2 O 3 at comparably high growth rates by -MBE is foreseeable.In order to fabricate vertical high-power devices, thin film thicknesses in the micrometer range are desired.-MBE allows the epitaxy of such devices in relatively short growth times (i.e., within a few hours as demonstrated for Ga 2 O 3 (010) in this work) while maintaining nanometer scale smoothness.In addition, the use of a Al 2 O ( ) and Ga 2 O ( ) molecular-beams during (Al Ga 1− ) 2 O 3 -MBE may also extend its growth domain towards higher adsorption-controlled regimes-being beneficial for the performance of (Al Ga 1− ) 2 O 3 -based heterostructure devices.
Our demonstration of high quality films of Ga 2 O 3 , Ga 2 O 3 doped with SnO, 70 In 2 O 3 , 64,72 ITO, 64,72 TaO 2 , 73 LaInO 3 , 75 and LaAlO 3 , 76 suggests that this synthesisscience approach-utilizing a combination of thermodynamics to identify which suboxides can be produced in molecular-beams in combination with a kinetic model of the growth process-can be applied to a wide-range of oxide compounds. 55We anticipate -MBE to be applicable to all materials that form via intermediate reaction products (a subcompound).Examples following this reasoning include ZrO 2 , Pb(Zr,Ti)O 3 , and (Hf,Zr)O 2 all via the supply of a molecular-beam of ZrO (predicted by our thermodynamic calculations, 55 ) Ga 2 Se 3 via Ga 2 Se, 11,77,78 In 2 Se 3 through In 2 Se, 11,79,80 In 2 Te 3 by In 2 Te, 11,81 or Sn 2 Se via SnSe. 11,82 )-1(c), the growth rate of GaN and Ga 2 O 3 increases linearly with increasing Ga in the Nrich [Fig.1(a)] and O-rich regimes [Fig.1(b) and 1(c)], respectively.Here, the incorporation of Ga is limited by the impinging Ga or Ga 2 O flux, Ga 2 O (i.e., Ga-transport and Ga 2 O-transport limited growth regimes).

FIG. 2 .
FIG. 2. Ga-O temperature-composition phase diagram under constant pressure = 0.1 Pa.This phase diagram has been calculated at higher pressures by Ref. 59.

FIG. 5 .
FIG. 5. (a) Partial pressure of oxygen and (b) ratio of the partial pressure of Ga 2 O to that of Ga plotted as a function of temperature with the total pressure being 0.1 Pa for the mole fractions of oxygen at (O) = 0.2 (dotted lines) and (O) = 0.4 (solid lines), respectively.These oxygen mole fractions are chosen to illustrate the difference between Ga-rich mixtures [ (O) = 0.2] and Ga 2 O 3 -rich mixtures [ (O) = 0.4].

III. RESULTS FOR GA 2 O 3 Figure 6
Figure6plots the growth rate of Ga 2 O 3 as a function of Ga 2 O at different and constant O .The growth rates obtained follow the anticipated growth kinetics depicted in Fig.1(c).In the adsorption-controlled regime, an increase in Ga 2 O (at otherwise constant growth parameters) does not lead to a decrease in the growth rate as observed for 'conventional' Ga 2 O 3 MBE [Fig.1(b)],7,9 but instead results in a constant growth rate: a growth rate-plateau.The data clearly show that we have overcome the growth rate-limiting step by using a Ga 2 O ( ) suboxide molecular-beam while reducing the complexity of the Ga 2 O 3 reaction kinetics from a two-step [Eqs.(1) and (2)] to a single-step [Eq.(2)] reaction mechanism.The reaction kinetics of -MBE for the growth of Ga 2 O 3 ( ) can be described in a similar way as 'conventional' III-V [e.g., reaction (3)] and II-VI MBE.We therefore set up a simple reaction-rate model describing the growth of Ga 2 O 3 ( ) by -MBE (this same model applies to other III-VI and IV-VI compounds, as well):

1 )FIG. 6 .
FIG. 6. Measured growth rate of Ga 2 O 3 ( 201)/Al 2 O 3 (0001) as a function of Ga 2 O at different (as indicated in the figure).Solid lines are fits of our model, Eqs.(9)-(11), to the data.A flux of O was provided by an oxidant-a mixture of O 2 and approximately 80 % O 3 63 -supplied continuously during growth at a background pressure of 1 × 10 −6 Torr.The dashed line reveals the transition between O-rich and Ga 2 O-rich growth regimes and indicates the maximum available O flux (which equals the growth rate value of the plateau) for Ga 2 O to Ga 2 O 3 conversion at a given .
FIG. 8. Longitudinal XRD scans recorded for Ga 2 O 3 films grown on Al 2 O 3 (0001) single-crystal substrates in the adsorptioncontrolled regime.The blue line corresponds to a film with thickness of = 0.15 μm grown at Ga 2 O = 11.4 × 10 14 Ga 2 O molecules cm −2 s −1 where O was provided by an oxidant (O 2 + 80 % O 3 ) background pressure of 5 × 10 −6 Torr [see also solid blue hexagon in Fig. (7)(a)].The gray line corresponds to a Ga 2 O 3 film with thickness = 0.05 μm grown at Ga 2 O = 3.0 × 10 14 Ga 2 O molecules cm −2 s −1 where O was provided by an oxidant (O 2 + 80 % O 3 ) background pressure of 1 × 10 −6 Torr [see also gray open-dotted hexagon in Fig. (7)(a)].For both samples was 500 • C. The reflections from the Ga 2 O 3 film are identified to originate from the monoclinic β-phase, 66 as indicated in the figure.(Inset) Transverse XRD scans across the 402 peak with their FWHM indicated in the figure (same value for both films).The 0006 peaks of the Al 2 O 3 substrates are marked by an asterisk.RHEED images taken at the end of the growth along the [010] azimuth of the Ga 2 O 3 films grown at growth rates of 1.6 μm hr −1 and 0.2 μm hr −1 are outlined by the blue and gray boxes, respectively.

FIG. 9 .
FIG. 9. Longitudinal XRD scans recorded for Ga 2 O 3 films grown on Ga 2 O 3 (010) single-crystal substrates in the adsorptioncontrolled regime.The pale blue and dark blue lines correspond to Ga 2 O 3 films with thicknesses of = 4.1 μm and = 0.74 μm, respectively.The reflections of the films coincide with the β-Ga 2 O 3 (010) phase grown with their (010) plane parallel to the plane of the substrate.(Inset) Transverse scans across the 020 peak of the same samples with their FWHM indicated in the figure.For comparison, a transverse scan of a single-crystalline Ga 2 O 3 (010) substrate is also shown.The Ga 2 O 3 (010) films (pale blue and dark blue) were grown at Ga 2 O = 9.1 × 10 14 Ga 2 O molecules cm −2 s −1 and = 550 • C where O was provided by an oxidant (O 2 + 80 % O 3 ) background pressure of 5 × 10 −6 Torr.The surface morphologies of the 'thin' ( = 0.74 μm) and 'thick' ( = 4.1 μm) Ga 2 O 3 (010) films are depicted in Figs.11(a) and 11(b).The growth rates of the 'thin' and 'thick' films are depicted by the solid and open diamonds, respectively, in Fig. 7(b).

FIG. 10
FIG. 10. (a)-(c) STEM images along the [001] zone axis of a Ga 2 O 3 (010) 'thin' film grown at a growth rate of 1.05 μm hr −1 with thickness = 0.28 μm [this is the same sample depicted by the solid square in Fig. 7(b)].The surface morphology of this same sample is shown in Fig. 11(c).(d)-(e) STEM images of a Ga 2 O 3 (010) 'thick' film at growth rate of 1.17 μm hr −1 with thickness 4.1 μm [this is the same sample depicted by the open diamond in Fig. 7(b) and pale blue line in Fig. 9].The surface morphology of this film is depicted in Fig. 11(b).No large-scale defects or dislocations are observed within either layers [panels (a) and (d)].The Ga 2 O 3 films consist only of the β-Ga 2 O 3 (010) phase [panel (c) and (e)], except for a thin γ-Ga 2 O 3 phase at the top surface [highlighted by a white circle in (b) and (e)].
)-10(c) and Figs.10(d)-10(e), respectively.Both samples show a clear, uniform, and single-crystalline β-Ga 2 O 3 (010) film.The vertical banding in Figs.10(a) and 10(d) are moire fringes between the in-focus portion of the crystal lattice and the finite pixel sampling of the STEM image.Defects such as dislocations or strain fields would have distorted the fringes away from straight lines, indicating an absence of such fea-tures.Only a thin ∼ 1 nm thick γ-Ga 2 O 3 (110) phase at the top of the surfaces of their Ga 2 O 3 (010)/Ga 2 O 3 (010) structures can be seen, as marked by white circles in Figs.10(b) and 10(e).

FIG. 11 .
FIG. 11. (a)-(c) Surface morphologies obtained by AFM for Ga 2 O 3 (010) surfaces grown by -MBE.The rms roughness of the surfaces are indicated on the figures.The XRD patterns of the same layers as shown in (a) and (b) are plotted in Fig. 9 as dark blue and pale blue lines, respectively.The growth rates of the films shown in (a), (b) and (c), are depicted in Fig. 7 as solid diamond, open diamond, and solid square, respectively.The thicknesses of the films in (a) and (c) are = 0.74 μm and the thickness of the film with the morphology shown in (b) is = 4.1 μm. was set to 550 • C for the films shown in (a) and (b) and to = 575 • C for the film plotted in (c).RHEED images of the corresponding Ga 2 O 3 film taken at the end of growth along the [001] azimuth are displayed below the respective AFM images.

FIG. 12 .
FIG. 12. SIMS of a Ga 2 O 3 (010) thin film grown at 1.05 μm hr −1 [this is the same sample depicted by the solid square in Fig. 7(b)].The atomic structure of this film and its surface morphology are shown in Figs.10(a)-10(c) and 11(c), respectively.No significant impurity incorporation could be detected.Gray and white areas show the SIMS profile of the Ga 2 O 3 (010) thin film and the Fedoped Ga 2 O 3 (010) substrate, respectively.
Ga 2 O 3 , Ga 2 O , and O , respectively.Their time derivative is described by the operator d/d .The reaction rate constant Ga 2 O kinetically describes the growth rate Γ of Ga 2 O 3 ( ) on the growth surface.The desorption rate constants of Ga 2 O and O adsorbates are denoted as Ga 2 O and O , respectively.