Adsorption-controlled growth of Ga₂O₃ by suboxide molecular-beam epitaxy

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 (g) species that evaporate from a heated crucible containing Ga (⁠$ℓ$⁠) or the As₄ (g) species that evaporate from a heated crucible containing As (s), where g, $ℓ$⁠, and s denote gaseous, liquid, and solid, respectively. In gas-source MBE, the species in the molecular beams 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 molecular beams are metal–organic molecules such as trimethylgallium or trimethylaluminum.¹ “Suboxide” MBE refers to an MBE growth process utilizing molecular beams of suboxides such as Ga₂O (g) or In₂O (g). We have applied this method to the growth of Ga₂O₃ thin films and find that it can produce epitaxial Ga₂O₃ films with greater crystalline perfection combined with much higher growth rates than currently demonstrated by any other MBE method for the growth of this material.

Gallium-sesquioxide (Ga₂O₃) synthesized in its different polymorphs [i.e., α-Ga₂O₃ (rhombohedral), β-Ga₂O₃ (monoclinic), γ-Ga₂O₃ (cubic spinel), ϵ-Ga₂O₃ (hexagonal), and κ-Ga₂O₃ (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 Ga₂O₃ may be widened by alloying Ga₂O₃ with Al₂O₃ to form $(AlxGa1-x)2O3$⁠.³ The synthesis of $(AlxGa1-x)2O3$/Ga₂O₃ heterostructures with high Al content x is desired for high-power transistors with large band gap offsets.^3,5,6

It is known that the “conventional” MBE of Ga₂O₃—i.e., when supplying elemental Ga and active O species during growth—is strongly limited by the formation and subsequent desorption of its volatile suboxide Ga₂O.^7–11 In the adsorption-controlled regime (i.e., grown with an excess of Ga), the growth rate strongly decreases with increasing Ga flux, ϕ_Ga, because not enough oxygen is available to oxidize the physisorbed Ga₂O to Ga₂O₃ (s) and the Ga₂O desorbs from the hot substrate. At sufficiently high ϕ_Ga, film growth stops and even goes negative (i.e., the Ga₂O₃ film is etched).⁸ This effect is enhanced as the growth temperature, T_G, increases due to the thermally activated desorption of Ga₂O from the growth surface. The enhanced, T_G-induced Ga₂O 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 flux¹²), followed by an even further decreasing growth rate in the adsorption-controlled regime.^9,12,13 These effects, i.e., the O-deficiency induced and thermally activated desorption of suboxides,^9,11–13 are detrimental for the growth of III–VI (e.g., Ga₂O₃) and IV–VI (e.g., SnO₂) materials in the adsorption-controlled regime.

Nevertheless, the MBE of thin films in the adsorption-controlled growth regime is often desired for high crystal perfection,^14–16 smooth surface morphology,¹⁷ avoiding undesired oxidation states,^18,19 or suppressing the formation of electrically compensating defects.^20,21

The growth rate evolution of Ga₂O₃ is microscopically explained by a complex two-step reaction mechanism.^11,12 In the first reaction step, all Ga oxidizes to Ga₂O via the reaction

with adsorbate and gaseous phases denoted as a and g, respectively. The Ga₂O formed may either desorb from the growth surface (in the O-deficient regime or at elevated T_G) or be further oxidized to Ga₂O₃ via a second reaction step through the reaction

with the solid phase denoted as s.

This two-step reaction mechanism and the resulting Ga₂O desorption define the growth-rate-limiting step for the “conventional” MBE of Ga₂O₃ and related materials.^11,12 This results in a rather narrow growth window associated with low growth rates in the adsorption-controlled regime.^7–9,11 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., In₂O₃) and IV–VI (e.g., SnO₂) compounds by “conventional” MBE.^8,11,13 This two-step 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^22–24 and II–VI²⁵ compounds. This difference in reaction kinetics 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 (S-MBE), we avoid the first reaction step (1) by directly supplying a Ga₂O (g) molecular beam to the growth front of the substrate surface. Using this approach, we bypass the growth-rate-limiting step of Ga₂O₃ by removing the O-consuming step to Ga₂O formation that occurs on the substrate in the “conventional” MBE growth of Ga₂O₃.^11,12 A related approach has been used by Ghose et al.^26,27 with Ga₂O provided from Ga₂O₃ source material heated to temperatures well in excess of 1600 °C to produce a molecular beam of Ga₂O for the growth of Ga₂O₃ films by MBE.²⁸ Motivated by known vapor pressure data of oxides²⁹ and their mixtures with the respective metals, e.g., Ga + Ga₂O₃,³⁰ as well as the possibility of decomposing Ga₂O₃ by Ga and SnO₂ by Sn under MBE conditions,⁸ Hoffmann et al.³¹ demonstrated how mixtures of Ga with Ga₂O₃ and Sn with SnO₂ provide MBE-relevant fluxes of Ga₂O 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 $μ$m h⁻¹.^31,32

As we demonstrate, S-MBE enables the synthesis of Ga₂O₃ in the highly adsorption-controlled regime, at growth rates >1 $μ$m h⁻¹ with unparalleled crystalline quality for Ga₂O₃/Al₂O₃ heterostructures as well as homoepitaxial Ga₂O₃ at relatively low T_G. The growth rate of S-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 n-type donor mobilities in Ga₂O₃ thin films doped with Sn, Ge, or Si grown by S-MBE, as well. The relatively low T_G at which it becomes possible to grow high-quality films by S-MBE is a crucial enabler for material integration where temperatures are limited, e.g., back end of line (BEOL) processes.

Figure 1 illustrates a schematic of how the growth rates of III–V and III–VI compounds depend on cation fluxes during their MBE growth. In this figure, all growth rate axes are normalized by the respective anion flux. Figure 1(a) depicts the observed behavior for III–V compounds, e.g., GaN.²⁴ Figure 1(b) shows the observed behavior for III–VI compounds, e.g., Ga₂O₃, 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., Ga₂O₃, when the group III element is supplied by a molecular beam of a III₂VI subcompound containing the group III constituent (e.g., Ga₂O).¹² The units of the horizontal and vertical axes are chosen to make the crossover between the anion-rich [gray areas in panels (a)–(c)] and cation-rich flux regimes [white areas in panels (a)–(c)] to occur at values of unity. For the sake of simplicity, henceforth, we only discuss the reaction behavior of GaN and Ga₂O₃ in detail. We emphasize, however, that this discussion holds true for the MBE growth of AlN,²² InN,²³ In₂O₃ (Refs. 8, 11, and 13), and other III–VI^11,35 and II–VI compounds.²⁵ 

As drawn in Figs. 1(a)–1(c), the growth rate of GaN and Ga₂O₃ increases linearly with increasing ϕ_Ga in the N-rich [Fig. 1(a)] and O-rich regimes [Figs. 1(b) and 1(c)], respectively. Here, the incorporation of Ga is limited by the impinging ϕ_Ga or Ga₂O flux, $ϕGa2O$ (i.e., Ga-transport and Ga₂O-transport limited growth regimes).

For GaN MBE [Fig. 1(a)], once the supplied ϕ_Ga exceeds the flux ϕ_N of active available N, the growth rate saturates, is independent of the ϕ_Ga/ϕ_N ratio, and is limited by ϕ_N and T_G. The measured plateau in the 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 reaction²⁴ 

and excess Ga either adsorbs onto or desorbs from the growth surface depending upon ϕ_N and T_G. Note that Eq. (3) and its discussion given in the text are identical for II–VI compounds (e.g., ZnO).

Figure 1(b) depicts the reaction kinetics of Ga₂O₃ in the Ga-rich regime (O-deficient growth regime) by supplying ϕ_Ga. Here, the growth rate linearly decreases with increasing ϕ_Ga, and the growth eventually stops at ϕ_Ga ≥ 3ϕ_O (in growth rate units). The fact that desorbing Ga₂O removes Ga and O from the growth surface—that cannot contribute to Ga₂O₃ formation—leads to the decreasing growth rate in the O-deficient growth regime.^8,9,11 This behavior is microscopically governed by the two-step reaction process, Eqs. (1) and (2),¹¹ and is fundamentally different from the single-step reaction kinetics, Eq. (3), governing the MBE of GaN [Fig. 1(a)].

In Fig. 1(c), the anticipated growth kinetics of Ga₂O₃ while using a Ga₂O beam is depicted, showing a constant growth rate in the Ga₂O-rich regime (i.e., in an excess of Ga₂O).¹² Excess Ga₂O (that cannot be oxidized to Ga₂O₃) 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 S-MBE, one may effectively achieve single-step reaction kinetics for Ga₂O₃ MBE [reaction (2)], as is the case for the growth of GaN by “conventional” MBE [reaction (3)].

The synthesis of III–V and II–VI materials with cation flux-independent growth rates in adsorption-controlled growth regimes—originating from their simple single-step reaction kinetics [e.g., reaction (3)]—is beneficial for device-relevant growth rate control and the improvement of their crystal properties.^36–38 Through the use of S-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 S-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., Ga₂O₃ and In₂O₃) and IV–VI films (e.g., SnO₂) to be grown much faster with excellent crystalline quality at relatively low T_G.

S-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: Ga₂O,^26,27,32 GdO,^39,40 LuO,⁴⁰ LaO,⁴⁰ NdO,⁴¹ PrO,^42,43 ScO,⁴⁴ SnO,^{18,19,31,45,46} and YO.³⁹ Even before these MBE studies, thin films of the suboxides SiO,^47,48 SnO,^49–53 and GeO⁵⁴ had been deposited by thermal evaporation, exploiting the same underlying vapor pressure characteristics that make S-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.^29,55

What is new about S-MBE is the recognition that the use of suboxide molecular beams reduces the complexity of the reaction kinetics of III–O and IV–O compounds from a complex two-step reaction mechanism^11,12 to a simple single-step reaction process. The growth kinetics during the S-MBE of III–O and IV–O compounds are equal to those of III–V and II–VI materials when they are grown by “conventional” MBE. Using this knowledge, S-MBE is applied in a targeted way to achieve epitaxial growth of desired oxides (e.g., Ga₂O₃) at very high growth rates in an adsorption-controlled regime. This leads to the benefits of the far simpler (from a growth kinetics, growth control, and growth standpoint) growth rate-plateau regime shown in Fig. 1(c) to be harnessed rather than the growth rate-decrease regime shown in Fig. 1(b) that has posed limits to the growth of Ga₂O₃ films and related materials by “conventional” MBE up to now.

The use of a Ga₂O (g) molecular beam to grow Ga₂O₃ (s) thin films by MBE in the O-rich regime (i.e., in an excess of active O) has been demonstrated by placing a stoichiometric solid of the compound Ga₂O₃ into a crucible and using it as an MBE source.^26,27 Possible reactions that produce a Ga₂O molecular beam by the thermal decomposition of Ga₂O₃ are

One disadvantage of using Ga₂O₃ (s) as the MBE source is that Ga₂O₃ does not evaporate congruently. Our thermodynamic calculations indicate that when Ga₂O₃ (s) is heated to a temperature where the Ga₂O (g) has a vapor pressure of 0.1 Pa (a vapor pressure typical for MBE growth), the Ga₂O molecular beam contains only 98.0% Ga₂O molecules. The remaining 2% of the beam consists of Ga, O₂, and O species.

The other disadvantage of using Ga₂O₃ (s) as the MBE source is that quite high effusion cell temperatures are required to evolve appreciable $ϕGa2O$⁠; temperatures in excess of ∼1600 ^○C,²⁸ ∼1700 ^○C,⁵⁶ or ∼1800 ^○C²⁶ have been used. At such high effusion cell temperatures, crucible choices become limited and prior researchers have used iridium crucibles.^26,27,32,56 Ga₂O₃ thin films synthesized utilizing an iridium crucible at an effusion cell temperature of ∼1700 ^○C⁵⁶ were limited to growth rates <0.14 $μ$m h⁻¹ (Ref. 32) with ∼5 × 10¹⁸ cm⁻³ iridium contamination in the grown Ga₂O₃ films.^56,57 These aspects of Ga₂O₃ compound sources hamper the synthesis of semiconducting Ga₂O₃ layers at growth rates exceeding 1 $μ$m h⁻¹ with device-relevant material properties. For comparison, the Ga + Ga₂O₃ mixture that we describe next and have used to grow Ga₂O₃ films at growth rates exceeding 1 $μ$m h⁻¹ provides a Ga₂O molecular beam that is 99.98% pure according to our thermodynamic calculations. This is for the same Ga₂O vapor pressure of 0.1 Pa, which happens at a source temperature about 600 ^○C lower for this Ga + Ga₂O₃ mixture than for pure Ga₂O₃, enabling us to use crucibles that do not result in iridium-contaminated films.

Years ago as well as more recently, Ga + Ga₂O₃-mixed sources producing a Ga₂O molecular beam have been studied^30,31 and suggested as efficient suboxide sources for oxide MBE.^31,55 Using this mixed source, a Ga₂O (g) molecular beam is produced by the chemical reaction

with the liquid phase denoted as $ℓ$⁠. S-MBE uses the thermodynamic³⁰ and kinetic⁸ properties of Ga + Ga₂O₃ mixtures favoring reaction (6) under MBE conditions.

For the S-MBE of Ga₂O₃, we explored Ga-rich and Ga₂O₃-rich mixtures of Ga + Ga₂O₃ with stoichiometries

and

respectively. The latter mixture has an oxygen mole fraction of x(O) = 0.4, and the properties of this Ga₂O₃-rich mixture are described below. The corresponding reaction rate constants κ_Ga-rich and $κGa2O3-rich$ define the production rate of Ga₂O (g) at a given temperature T_mix of the Ga + Ga₂O₃ mixture.

The flux of Ga₂O (g) in the molecular beam emanating from the mixed Ga + Ga₂O₃ sources is significantly larger than that of Ga (g)^30,58 emanating from the same source. This is also true under MBE conditions.^31,55 The resulting high ratio of Ga₂O/Ga ≫ 1 provides a more controllable and cleaner growth environment than accessible by decomposing a stoichiometric Ga₂O₃ source, which produces molecular beam ratios of Ga₂O/Ga, Ga₂O/O₂, and Ga₂O/O. Hence, the growth surface of the substrate during film growth using S-MBE is exposed to controllable and independently supplied molecular beams of Ga₂O and reactive O adsorbates.

We have experienced that a Ga₂O₃-rich mixture enables higher T_mix and higher, stable Ga₂O (g) molecular beams than a Ga-rich mixture. Thus, Ga₂O₃-rich mixtures enable higher growth rates by S-MBE than Ga-rich mixtures. This experimental observation is confirmed by our thermodynamic calculations of the phase diagram of $Ga (ℓ)+Ga2O3(s)$ mixtures, which we describe next.

The calculated Ga–O phase diagram in Fig. 2 shows that at T_mix below the three-phase equilibrium of $gas+Ga (ℓ)+Ga2O3(s)$ around 907 K, a two-phase region of $Ga (ℓ)+Ga2O3(s)$ 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.⁶¹ For T_mix > 907 K, the two-phase regions are $gas+Ga (ℓ)$ when the mole fraction of oxygen is below 1/3, corresponding to what we refer to as Ga-rich mixtures, and gas + Ga₂O₃ (s) when the mole fraction of oxygen is between 1/3 and 0.6, which we refer to as Ga₂O₃-rich mixtures. These two-phase regions become a single gas-phase region at a T_mix of (907–1189) K for Ga-rich mixtures and at (907–1594) K for Ga₂O₃-rich mixtures, respectively. All of these phase transition temperatures decrease with decreasing pressure,⁵⁹ as shown in the pressure vs temperature (P − T) phase diagrams in Fig. 3.

To contrast the difference between Ga-rich vs Ga₂O₃-rich mixtures, we have performed additional thermodynamic calculations at oxygen mole fractions of x(O) = 0.2 and x(O) = 0.4. These two chosen oxygen mole fractions correspond to Ga-rich and Ga₂O₃-rich mixtures, respectively. In Figs. 3(a) and 3(b), the solid (red) lines denote the three-phase equilibrium between $gas+Ga (ℓ)+Ga2O3(s)$⁠; these are identical at x(O) = 0.2 and x(O) = 0.4. The dotted (black) lines denote the equilibrium between the gas and $gas+Ga (ℓ)$ phase regions for x(O) = 0.2 as well as the gas and gas + Ga₂O₃ (s) phase regions for x(O) = 0.4, i.e., their respective boiling temperature/pressure.

Figure 4 shows Gibbs energies of the gas, Ga(⁠$ℓ$⁠), Ga₂O₃(s) phases at temperature T = 1100 K and total pressure P = 0.1 Pa. There are seven distinct atomic and molecular species in the gas phase: Ga, Ga₂, GaO, Ga₂O, O, O₂, and O₃. The kink in the Gibbs energy of the gas phase at x(O) = 0.33 corresponds to the composition of the Ga₂O species because it is the major species in the gas phase. It can be seen that the values of the oxygen activity in the $gas+Ga (ℓ)$ vs in the gas + Ga₂O₃ (s) regions differ by more than seven orders of magnitude, i.e., 6.4 × 10⁻²⁴ Pa vs 1.8 × 10⁻¹⁶ Pa as indicated by the brown and green common tangent lines in Fig. 4.

In Fig. 5(a), the partial pressure of oxygen in the gas phase is plotted as a function of temperature (for a total pressure of 0.1 Pa) for a Ga-rich mixture at x(O) = 0.2 and a Ga₂O₃-rich mixture at x(O) = 0.4. It can be seen that the oxygen partial pressure in the Ga₂O₃-rich mixture at x(O) = 0.4 is orders of magnitude higher than that at x(O) = 0.2 at relevant MBE growth temperatures. For example, the value of the partial pressures of oxygen at T_mix = 1000 K at x(O) = 0.2 is 5.6 × 10⁻²⁵ Pa and at x(O) = 0.4 is 4.5 × 10⁻²¹ Pa. The higher oxygen activity of Ga₂O₃-rich mixtures compared with Ga-rich mixtures makes it easier to form fully oxidized Ga₂O₃ thin films. At lower total pressure, all lines shift to lower temperatures.

Furthermore, our thermodynamic calculations plotted in Fig. 5(b) show the ratio of the partial pressures of Ga₂O to Ga in the gas phase as a function of the temperature of a Ga-rich mixture [x(O) = 0.2] and of a Ga₂O₃-rich mixture [x(O) = 0.4], where the total pressure is fixed at 0.1 Pa. The ratio of the partial pressures of Ga₂O to Ga in a Ga-rich mixture with x(O) = 0.2 is much lower than this ratio in a Ga₂O₃-rich mixture with x(O) = 0.4. For example, the $PGa2O/PGa$ ratio is 158 in a Ga-rich mixture [x(O) = 0.2] and 1496 in a Ga₂O₃-rich mixture [x(O) = 0.4] at T_mix = 1000 K. The higher Ga₂O/Ga ratios at higher T_mix are another reason why Ga₂O₃-rich mixtures are preferred. Higher Ga₂O/Ga ratios and the higher purity of the Ga₂O molecular beam [99.98% Ga₂O according to our calculations at x(O) = 0.4] mean that the Ga₂O₃ films are formed by a single-step reaction [reaction (2)] and that reaction (1) is bypassed.

We used Ga metal (7N purity) and Ga₂O₃ powder (5N purity) for the Ga + Ga₂O₃ mixtures, loaded them into a 40 cm³ Al₂O₃ 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, outgassed the mixture, and set our desired Ga₂O flux for the growth of Ga₂O₃. We measured the flux of the Ga₂O (g) molecular beam reaching the growth surface prior to and after growth using a quartz crystal microbalance. The 10 × 10 mm² substrates were back-side coated with a 10 nm thick Ti adhesion layer followed by 200 nm of Pt, enabling the otherwise transparent substrates to be radiatively heated during MBE growth. For S-MBE growth the substrate was held within a substrate holder made of Haynes® 214® alloy, and loaded into the growth chamber. The growth temperature T_G was measured by an optical pyrometer operating at a wavelength of 1550 nm. To determine the surface crystal phases during growth, in situ high-energy electron diffraction (RHEED) using 13 keV electrons was utilized. After growth x-ray reflectivity (XRR), optical reflectivity in a microscope (ORM),⁶² scanning electron microscopy (SEM), scanning transmission electron microscopy (STEM), and secondary-ion mass spectrometry (SIMS) were used to accurately measure the thicknesses of homoepitaxial (ORM, SEM, SIMS, and SEM) and heteroepitaxial (XRR, ORM, SEM, STEM, and SIMS) grown Ga₂O₃ films to determine the growth rate. X-ray diffraction was performed using a four-circle x-ray diffractometer with Cu Kα₁ radiation.

Figure 6 plots the growth rate of Ga₂O₃ as a function of $ϕGa2O$ at different T_G and constant ϕ_O. The growth rates obtained follow the anticipated growth kinetics depicted in Fig. 1(c). In the adsorption-controlled regime, an increase in $ϕGa2O$ (at otherwise constant growth parameters) does not lead to a decrease in the growth rate as observed for “conventional” Ga₂O₃ 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 Ga₂O (g) suboxide molecular beam while reducing the complexity of the Ga₂O₃ reaction kinetics from a two-step [Eqs. (1) and (2)] to a single-step [Eq. (2)] reaction mechanism.

The reaction kinetics of S-MBE for the growth of Ga₂O₃ (s) 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 Ga₂O₃ (s) by S-MBE (this same model applies to other III–VI and IV–VI compounds, as well),

The Ga₂O₃, Ga₂O, and O adsorbate densities are denoted as $nGa2O3$⁠, $nGa2O$⁠, and n_O, respectively. Their time derivative is described by the operator d/dt. The reaction rate constant $κGa2O$ kinetically describes the growth rate $Γ$ of Ga₂O₃ (s) on the growth surface. The desorption rate constants of Ga₂O and O adsorbates are denoted as $γGa2O$ and γ_O, respectively.

The flux of available O adsorbates, for Ga₂O to Ga₂O₃ oxidation at a given T_G, is determined by its sticking coefficient σ on the Ga₂O₃ growth surface and is described by a sigmoid function

with dimensionless pre-factor σ₀ and energy Δσ. Equation (12) reflects the decreasing probability of O species to adsorb as T_G is increased. This leads to an effectively lower surface density of active O for Ga₂O oxidation and thus to lower growth rates.

We find that σ does not depend on the concentration of active O and only weakly on the partial pressure of active O (values not shown in this work). Thus, the active O may be scaled up or down by either changing the concentration of O₃ in the O₃ beam or by changing the partial pressure of O₃ in the chamber. Note that O₃ supplies O to the surface of the growing film when it decomposes by the reaction: O₃ (g) → O₂ (g) + O (g). A similar behavior of an increasing desorption or recombination rate of active O species with increasing T_G has also been observed during O plasma-assisted MBE using elemental Ga and O molecular beams.^9,12,13

Based on this model, we scaled up ϕ_O in order to achieve Ga₂O₃ (s) growth rates that exceed 1 $μ$m h⁻¹. Figure 7(a) demonstrates our fastest (to date) growth rate of 1.6 $μ$m h⁻¹ of a β-Ga₂O₃ thin film grown on Al₂O₃(0001), at T_G = 500 ^○C. For comparison, the data point plotted as a hollow hexagon (see also Fig. 6) shows the highest possible growth rate at a five times lower active ϕ_O and similar T_G. This result demonstrates, scaling up the active O enables S-MBE to scale up the growth rates of Ga₂O₃ thin film exceeding 1 $μ$m h⁻¹ in the adsorption-controlled regime. In addition, the growth rate values plotted in Fig. 7(b) were obtained by homoepitaxial growth of β-Ga₂O₃(010) on β-Ga₂O₃(010). The growth rate of Ga₂O₃ on Ga₂O₃(010) is 2.1 times larger than the growth rate on Al₂O₃(0001) at similar growth conditions—e.g., as plotted in Fig. 7(a) (hollow diamond) and Fig. 7(b) (solid diamond), respectively. This result suggests that the growth rate of S-MBE grown on Ga₂O₃(010) and other surfaces of Ga₂O₃ may vastly exceed 1 $μ$m h⁻¹ in the adsorption-controlled regime. The higher growth rate of Ga₂O₃(010) compared with Ga₂O₃(⁠$2¯$01) is similar to what has been observed during the “conventional” MBE of Ga₂O₃.^45,64 Fluctuations in T_G and $ϕGa2O$ for different samples and, e.g., during the long duration growth of the “thick” sample (>3 h), are considered by the standard deviations of the measured values of T_G and $ϕGa2O$⁠, as given in Fig. 7.

We investigated the impact of variable growth conditions (i.e., $ϕGa2O$⁠, ϕ_O, and T_G) on the structural perfection of epitaxial Ga₂O₃ (s) films grown on Al₂O₃(0001) and Ga₂O₃(010) substrates. Figure 8 shows θ–2θ x-ray diffraction (XRD) scans of selected Ga₂O₃ films—the same samples depicted in Fig. 7(a) (solid blue hexagon and hollow hexagon). The reflections of the films coincide with the β-Ga₂O₃ phase grown with their (⁠$2¯01$⁠) plane parallel to the (0001) plane of the Al₂O₃ substrate. The inset shows transverse scans (rocking curves) across the symmetric $4¯02$ reflection of the same layers. The full width at half maxima (FWHM) in ω of the profiles is a measure of the out-of-plane mosaic spread of the Ga₂O₃ layer. The obtained Δω = 0.11° ≈ 400′′ (arc sec) does not change with the growth rate and is particularly remarkable since β-Ga₂O₃(⁠$2¯01$⁠) films grown on Al₂O₃(0001), using elemental Ga^7,66 or compound Ga₂O₃ sources,²⁷ usually show much broader line profiles in their out-of-plane crystal distributions (from Δω ≈ 0.23°²⁷ to Δω ∼ 1.00°).⁷ Thus, the profiles in Fig. 8 reveal a well-oriented and high quality epitaxial Ga₂O₃(⁠$2¯$01) thin film. Furthermore, reflection high-energy electron diffraction (RHEED) and XRR measurements reveal a sharp and well-defined interface between Ga₂O₃(⁠$2¯$01) and Al₂O₃ as well as a relatively smooth surface morphology obtained by S-MBE. We note that in the highly adsorption-controlled regime at lower T_G, the accumulation of Ga₂O 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 Ga₂O₃(⁠$2¯$01) films on Al₂O₃(0001) with thicknesses ≫1 $μ$m and have not mapped all growth regimes (e.g., Ga₂O “droplet” formation at very high $ϕGa2O$⁠). Further investigations of the structural perfection and electrical properties of Ga₂O₃ grown by S-MBE need to be performed. This could be particularly interesting for the growth of Ga₂O₃ (s) at even higher Ga₂O (g) fluxes, which push even further into the adsorption-controlled regime.

We used S-MBE to grow homoepitaxial β-Ga₂O₃(010) films on β-Ga₂O₃(010) substrates. Figure 9 shows the θ–2θ XRD scans of two selected Ga₂O₃(010) films grown under the same growth conditions. The θ–2θ XRD profiles of the Ga₂O₃(010) film with thickness d = 0.74 $μ$m (plotted in blue) and the one of the substrate (data not shown) coincide. The Ga₂O₃(010) layer with d = 4.55 $μ$m (depicted in gray) also shows small contributions of the meta stable γ-Ga₂O₃ 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 d = 0.74 $μ$m and d = 4.55 $μ$m is comparable and narrower than the one obtained for the bare Ga₂O₃(010) substrate (depicted as a black line). [Note that the measured XRD spectra were obtained on different 10 × 10 mm² substrates, which were all cut from the same 1 in. diameter Ga₂O₃(010) wafer from Synoptics.] We attribute the different rocking curve widths measured to the non-uniformity in the crystalline perfection across the 1 in. diameter Ga₂O₃ substrate on which these measurements were made.

STEM of the “thick” film with d = 4.55 $μ$m [the same sample as plotted as a gray line in Fig. 9 and solid square in Fig. 7(b)] are shown in Figs. 10(a)–10(e). The epilayer shows a clear, uniform, and single-crystalline β-Ga₂O₃(010) film. Defects such as dislocations or strain fields are not observed throughout this sample, indicating the very high crystal quality of this film. Only a thin γ-Ga₂O₃(110) layer at the top of the surface of the Ga₂O₃(010)/Ga₂O₃(010) homoepitaxial film can be seen, as marked by white circles in Figs. 10(b), 10(d), and 10(e). The 440 γ-Ga₂O₃ peak measured by XRD is attributed to this thin surface phase, which may increase with increasing film thickness and T_G. The formation of a γ-Ga₂O₃ surface phase has also been observed during the growth of β-Ga₂O₃ by “conventional” MBE and might be an intrinsic issue for the homoepitaxy of Ga₂O₃(010).⁶⁷ 

The surface morphology of Ga₂O₃(010) films grown by S-MBE at growth rates >1 $μ$m h⁻¹ was investigated by atomic force microscopy (AFM) and is plotted in Figs. 11(a)–11(c). The root mean square (rms) roughness of the “thin” film with d = 0.74 $μ$m is lower than the one measured for the “thick” film with d = 4.1 $μ$m grown at similar conditions. The thick film with d = 4.55 $μ$m grown at T_G = 575 ^○C shows a smoother surface, indicating that the thickness of the film does not influence the surface morphology detrimentally. This evolution in the rms roughness follows the same trend as observed by XRD scans of the same layers (blue and gray lines in the inset of Fig. 9), i.e., no decrease in crystalline quality with increasing film thickness of the Ga₂O₃(010)/Ga₂O₃(010) structures was observed. We note that the difference in surface morphology seen in Figs. 11(a) and 11(b) may be caused by the slightly different off-cuts and crystal qualities among the bare β-Ga₂O₃(010) substrates used, similar to the observed spread in rocking curves widths, as shown in Fig. 9.

We investigated the incorporation of impurities into the Ga₂O₃(010) thin films grown with growth rates > 1 $μ$m h⁻¹ by SIMS. Figure 12 shows the SIMS profile of the same film as plotted in Fig. 7 (solid square) and Figs. 10 and 11(c). This profile reveals that the Ga₂O₃-rich (Ga + Ga₂O₃) mixtures employed lead to Ga₂O₃(010) thin films with very low impurity incorporation. Only a slight increase of B ∼ 10¹⁶ cm⁻³ is detected. This impurity likely originates from our use of an Al₂O₃ crucible for the Ga₂O₃-rich (Ga + Ga₂O₃) mixture. We note that we have also used pyrolytic boron nitride (pBN) crucibles for the Ga + Ga₂O₃ mixture but find high concentrations of B in the grown films by SIMS (∼10²⁰ B cm⁻³) when the background pressure of a mixture of O₂ + 80%O₃ is P_O = 5 × 10⁻⁶ Torr. We attribute this to the oxidation of the surface of the pBN crucible to B₂O₃ at the high oxidant pressures used. At the T_mix = 1020 °C used for growth, the vapor pressure of B₂O₃ is significant.⁵⁵ The small Si and Al peaks measured at the film–substrate interface originate from unintentional incorporated Si and Al at the substrate surface. Note that we have tried Ga₂O-polishing (for the first time) to remove the Si from the surface prior to growth. Our observation is that Ga₂O-polishing does not provide the same reduction in Si contamination at the sample surface as can be accomplished by Ga-polishing.⁶⁸ All other detected impurities in the epilayer, i.e., Si (SIMS detection limit signal, S_Si = 5 × 10¹⁵ cm⁻³), Fe (S_Fe = 1 × 10¹⁵ cm⁻³), Sn (S_Sn = 5 × 10¹⁴ cm⁻³), Al (S_Al = 2 × 10¹⁶ cm⁻³), In (S_In = 2 × 10¹⁴ cm⁻³) (not shown), and C (S_C = 5 × 10¹⁶ cm⁻³) (not shown) in the film are below the detection limit of the cation standards used.

Our SIMS results show that the low effusion cell temperatures and Ga₂O₃-rich (Ga + Ga₂O₃) mixtures employed for S-MBE—in order to produce the high Ga₂O fluxes used to grow Ga₂O₃ with growth rates exceeding >1 $μ$m h⁻¹—do not lead to significant impurity incorporation into the grown Ga₂O₃(010) films. This is an advantage of S-MBE compared with the growth Ga₂O₃ from a crucible containing pure Ga₂O₃. Using a Ga₂O₃ compound source at extremely high effusion cell temperatures (∼1700 ^○C)⁵⁶ not only produces a flux containing a relatively low Ga₂O molecular beam resulting in low Ga₂O₃ film growth rates but also results in films contaminated with iridium.^32,56,57 Nonetheless, electrical transport properties are extremely sensitive to impurities, and measurements of mobility in doped Ga₂O₃ films grown by S-MBE remain to be performed. It could turn out that a higher purity Ga₂O₃ powder will be needed than the 5N Ga₂O₃ powder we have used in this study.

The growth rates we have achieved by S-MBE are more than one order of magnitude faster than what has been reported for the growth of Ga₂O₃ films from pure Ga₂O₃ sources.³² 

The quality of the homoepitaxial β-Ga₂O₃(010) films (with thicknesses > 4.5 $μ$m) assessed by XRD (Fig. 9), STEM (Fig. 10), AFM (Fig. 11), and SIMS (Fig. 12) reveal that S-MBE with growth rates > 1 $μ$m h⁻¹ is competitive to other industrial relevant synthesis methods [such as (MO)CVD] for the growth of vertical Ga₂O₃-based structures with thicknesses in the $μ$m-range.

Based on our model and experimental results, we anticipate growth rates up to 5 $μ$m h⁻¹ on Ga₂O₃(010) and other growth surfaces to be possible by S-MBE. This estimation is based on the physical MBE limit: the mean free path λ of the species (e.g., Ga₂O and O₃) emanating from their sources to the target. In our estimate, we have used an upper limit for the O partial pressure of P_O ∼ 2 × 10⁻⁴ Torr (resulting in λ ∼ 0.1 m)⁶⁹ and a lower T_G limit of T_G ≥ 725 ^○C [required for the adsorbed species (e.g., Ga₂O and O) to crystallize into a homoepitaxial film of Ga₂O₃ grown at a high growth rate].

We have demonstrated the growth of high quality Ga₂O₃ (s) thin films by S-MBE in the adsorption-controlled regime using $Ga (ℓ)+Ga2O3(s)$ mixtures. The high growth rate ≫ 1 $μ$m h⁻¹ and unparalleled crystalline quality of the homoepitaxial and heteroepitaxial structures obtained (with d ≫ 1 $μ$m) suggest the possibility of unprecedented mobilities of Ga₂O₃ thin films containing n-type donors (Sn, Ge, Si) grown by S-MBE.

We have also developed Sn + SnO₂ and Ge + GeO₂ mixtures in order to produce SnO (g) and GeO (g) beams for use as n-type donors in Ga₂O₃-based heterostructures. Furthermore, we have grown SnO₂ using a Sn + SnO₂ mixture.³¹ Moreover, we have grown Ga₂O₃ doped with SnO using Ga₂O and SnO beams and achieved controllable Sn-doping levels in these Ga₂O₃ films. Nevertheless, the improvement of the n-type mobilities obtained during S-MBE, at growth rates >1 $μ$m h⁻¹, still needs to be demonstrated and shown to exceed the state-of-the-art mobilities in Ga₂O₃ films grown by “conventional” MBE.⁷⁰ 

Our 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 + Ga₂O₃, have led us to recognize additional systems appropriate for growth by S-MBE. This thermodynamic knowledge coupled with our understanding of the S-MBE growth of Ga₂O₃ enabled us to develop In + In₂O₃ and Ta + Ta₂O₅ mixtures from which we have grown high-quality bixbyite In₂O₃ and In₂O₃:SnO₂ (ITO) as well as rutile TaO₂ by S-MBE, respectively.

Growing thin films with very high crystalline qualities at growth rates >1 $μ$m h⁻¹ by using suboxide molecular beams—with up to 5 $μ$m h⁻¹ anticipated growth rates by our model—will make MBE competitive with other established synthesis methods, such as CVD³³ or MOVPE.³⁴ The T_G that we have demonstrated for high quality Ga₂O₃ layers grown by S-MBE is significantly lower than what has been demonstrated for the growth of high quality Ga₂O₃ films by CVD or MOVPE. This makes S-MBE advantageous for BEOL processing. Additionally, Ga₂O₃ grown with a vast excess of Ga₂O (g) and high oxygen activity in Ga₂O₃-rich mixtures may suppress Ga vacancies in the Ga₂O₃ layers formed, which are believed to act a compensating acceptors^20,71—potentially improving the electrical performance of n-type Ga₂O₃-based devices significantly.

The development of Al + Al₂O₃ mixtures for the growth of epitaxial Al₂O₃ and $(AlxGa1-x)2O3$ at comparably high growth rates by S-MBE is foreseeable. In order to fabricate vertical high-power devices, thin film thicknesses in the micrometer range are desired. S-MBE allows the epitaxy of such devices in relatively short growth times [i.e., within a few hours as demonstrated for Ga₂O₃(010) in this work] while maintaining nanometer scale smoothness. In addition, the use of an Al₂O (g) and Ga₂O (g) molecular beams during $(AlxGa1-x)2O3$ S-MBE may also extend its growth domain toward higher adsorption-controlled regimes—being beneficial for the performance of $(AlxGa1-x)2O3$-based heterostructure devices.

Our demonstration (not shown in this work) of high quality films of Ga₂O₃, Ga₂O₃ doped with SnO, In₂O₃, ITO, TaO₂, LaInO₃, and LaAlO₃ suggests that this synthesis-science 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.⁵⁵ We anticipate S-MBE to be applicable to all materials that form via intermediate reaction products (a subcompound). Examples following this reasoning include ZrO₂, Pb(Zr,Ti)O₃, and (Hf,Zr)O₂ all via the supply of a molecular beam of ZrO (predicted by our thermodynamic calculations⁵⁵) Ga₂Se₃ via Ga₂Se,^11,72,73 In₂Se₃ through In₂Se,^11,74,75 In₂Te₃ by In₂Te,^11,76 or Sn₂Se via SnSe.^11,77

We thank J. D. Blevins for the Ga₂O₃(010) substrates from SYNOPTICS used in this study and are grateful for stimulating discussions with R. Droopad, J. P. Maria, and M. Passlack. K.A., C.S.C., J.P.M., D.J., H.G.X., D.A.M., and D.G.S. acknowledge support from the AFOSR/AFRL ACCESS Center of Excellence under Award No. FA9550-18-1-0529. J.P.M. also acknowledges support from the National Science Foundation within a Graduate Research Fellowship under Grant No. DGE-1650441. P.V. acknowledges support from ASCENT, one of six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by DARPA. F.V.E.H. acknowledges support from the Alexander von Humboldt Foundation in the form of a Feodor Lynen fellowship. F.V.E.H. and H.P. acknowledge support from the National Science Foundation (NSF) [Platform for the Accelerated Realization, Analysis and Discovery of Interface Materials (PARADIM)] under Cooperative Agreement No. DMR-1539918. J.P. acknowledges support from the Air Force Office of Scientific Research under Award No. FA9550-20-1-0102. S.-L.S. and Z.-K.L. acknowledge the support of the NSF through Grant No. CMMI-1825538. This work made use of the Cornell Center for Materials Research (CCMR) Shared Facilities, which are supported through the NSF MRSEC Program (Grant No. DMR-1719875). Substrate preparation was performed, in part, at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the NSF (Grant No. NNCI-2025233). Work by G.H. and O.B. was performed in the framework of GraFOx, a Leibniz-ScienceCampus partially funded by the Leibniz association. G.H. acknowledges financial support by the Leibniz-Gemeinschaft under Grant No. K74/2017. B.J.B. was supported by a NASA Space Technology Research Fellowship (grant number 80NSSC18K1168) and he acknowledges support and training provided by the Computational Materials Education and Training (CoMET) NSF Research Traineeship (grant number DGE-1449785)

The authors P.V., D.G.S., F.V.E.H., K.A., Z.-K.L., B.J.B., and S.-L.S., Cornell University (D-9573), and the Pennsylvania State University (2020-5155) have filed a U.S. patent on October 21, 2020, Serial No. 17/076, 011, with the title “Suboxide Molecular-Beam Epitaxy and Related Structures.”

The data supporting the findings of this study are available within the paper. Additional data related to the growth and structural characterization are available at https://doi.org/10.34863/a2jw-kh18. Any additional data connected to the study are available from the corresponding author upon reasonable request.