Coherently strained (001) β-(Al_xGa_1−x)₂O₃ thin films on β-Ga₂O₃: Growth and compositional analysis

As the need increases for efficient power electronics with high-power and high-frequency switching, ultra-wide bandgap semiconductors like β-Ga₂O₃ have gained much interest. Its large bandgap (4.8 eV),¹ high breakdown field (5–8 MV/cm),^2,3 availability of melt-grown bulk substrates,^4,5 and n-type^6–12 and acceptor doping^13–15 make it an ideal candidate for unipolar semiconductor devices. The demonstration of high-quality β-Ga₂O₃ thin film growth via Halide Vapor Phase Epitaxy (HVPE),¹⁶ Metal Organic Chemical Vapor Deposition (MOCVD),¹⁷ and Molecular Beam Epitaxy (MBE)^6,7 has already shown potential for diode^18,19 and transistor applications.^20–23 There is still much to understand in the growth of β-Ga₂O₃ and its alloys on different crystallographic orientations to realize the full potential of the material system.

The β-(Al_xGa_1−x)₂O₃ alloy is of particular interest for β-Ga₂O_3­based devices due to the wider bandgap and large conduction band offsets achievable between β-(Al_xGa_1−x)₂O₃ and β-Ga₂O_3­.^24–26 Modulation-doped heterostructures and field effect transistors (MODFETs) have been demonstrated using β-(Al_xGa_1−x)₂O₃, which utilizes a two-dimensional electron gas (2DEG) channel below the heterostructure interface in β-Ga₂O₃.^{22,23,27–31} By increasing the Al content x in the β-(Al_xGa_1−x)₂O₃, a higher 2DEG charge can be achieved in the channel due to the larger conduction band offset. Additionally, it has been predicted that at very high 2DEG charge, enhanced screening of polar optical phonons could further improve mobility in β-Ga₂O₃.³² 

Still, there are limitations for achieving high Al contents in β-(Al_xGa_1−x)₂O₃. The stable phase of Al₂O₃ is the α-corundum phase, and Hill et al. have demonstrated the phase diagram of the Al₂O₃-Ga₂O₃ system, showing that the maximum Al solubility in β-(Al_xGa_1−x)₂O₃ is ∼25% Al at temperatures <800 °C and 60% Al content at higher temperatures.³³ At higher Al contents, the α-corundum phase was present. In the case of β-(Al_xGa_1−x)₂O₃ film growth, the effects of strain³⁴ and growth environment can limit the maximum Al content, with a maximum Al content of ∼26% achievable in (010) β-(Al_xGa_1−x)₂O₃ grown via MBE and MOCVD techniques despite growth temperatures up to 900 °C. Bhuiyan et al.³⁵ and Johnson et al.³⁶ demonstrated that at higher Al contents, γ-phase inclusions were observed in (010) β-(Al_xGa_1−x)₂O₃ films, limiting this maximum Al content for coherent single phase growth.

The (010) orientation has been the primary growth plane for β-(Al_xGa_1−x)₂O₃ films due to superior material quality on this orientation via MBE^37,38 and MOCVD growth.^29,30,35,36 Recently, the use of an In flux in MBE growth has demonstrated marked improvement in growth rates and material quality in various orientations including (001) β-Ga₂O₃.^{10,12,39–42} This metal oxide catalyzed epitaxy (MOCATAXY),¹⁰ also referred to as metal-exchange catalysis MBE (MEXCAT-MBE) by Mazzolini et al.,⁴² could allow for improved (001) β-Ga₂O₃ devices. In this study, we investigate growth of (001) β-(Al_xGa_1−x)₂O₃ films via MOCATAXY.

Films were grown on commercially available Fe-doped (001) β-Ga₂O₃ bulk substrates from Novel Crystal Technology in a Varian 620 MBE with a Veeco Unibulb oxygen plasma source run at a power of 200 W and a foreline pressure of 60 Torr. The resulting O₂ pressure in the chamber was about 10⁻⁵ Torr measured by beam equivalent pressure (BEP) with about 1%–2% of that being the active O flux. A typical Ga flux of 2–2.5 × 10⁻⁷ Torr at a growth temperature of 800–850 °C (as measured by the thermocouple) was used, allowing for a maximum growth rate of 5.0 nm/min. High-resolution x-ray diffraction (HRXRD) was used to determine growth rates and Al content in films. Surface morphologies were characterized by atomic force microscopy (AFM). Cross-sectional transmission electron microscopy (TEM) was performed to characterize the structural quality of the films, and atom probe tomography (APT) was used to determine group III site fractions of Al and Ga.

First, to determine the relationship between the Al content of β-(Al_xGa_1−x)₂O₃ and out-of-plane lattice parameter, which corresponds to the Bragg angle (θ₀₀₂) measured in HRXRD, the fundamental stiffness tensor and stress–strain relationships for a coherently strained β-(Al_xGa_1−x)₂O₃ film were used. Oshima et al. derived this relationship between the Al content in coherently strained (010) β-(Al_xGa_1−x)₂O₃ and out-of-plane lattice parameter (b) using the stiffness tensor of β-Ga₂O₃ in standard Voigt notation.³⁸ The unit cell was placed in the Cartesian coordinate system where [100] || $x^1$⁠, [010] || $x^2$⁠, and g₀₀₁ (same as c*) || $x^3$⁠. Note that for (001) oriented films, the out-of-plane direction is g₀₀₁ or c* and not the [001] direction. This same coordinate system and stiffness tensor can be used for derivation presented here.³⁸ The Cartesian coordinate systems used for the (001) and (100) stiffness tensors are shown in Fig. 1.

The standard Voigt notation used to express stiffness tensor c_ij, stress tensor σ_i, and strain tensor ɛ_j is used as shown in Eq. (1) (i.e., σ_j = c_ij ɛ_j). For (001) β-(Al_xGa_1−x)₂O₃ coherently strained on (001) β-Ga₂O₃, the β-(Al_xGa_1−x)₂O₃ layer is subject to unbalanced plane stress, corresponding to $(x^1)$ and $(x^2)$ directions (along [100] and [010] directions) and represented by σ₁ and σ₂ in Eq. (1). The out-of-plane direction has a stress component (σ₃) equal to 0. The shear strains ɛ₄ and ɛ₅ are also 0. From the third line in Eq. (1), an expression for ɛ₃ can be determined as shown in Eq. (2),

The components of Eq. (2) can be expressed using Eqs. (3a)–(3d), where a_c, b_c, and β_c are in-plane and, therefore, the lattice parameters of β-Ga₂O₃. The relaxed lattice parameters, denoted by the subscript r, for β-(Al_xGa_1−x)₂O₃ with varying Al contents (x) have been expressed by Kranert et al.⁴³ as shown in Eqs. (4a)–(4d), where k_a = 0.42, k_b = 0.13, k_c = 0.17, and k_β = 0.31,

Substituting Eqs. (4a)–(4d) and (3a)–(3d) into Eq. (2) yields a relationship between Al content x and lattice parameter c_c for the coherently strained (001) β-(Al_xGa_1−x)₂O₃ film as shown in Eq. (5), which can then be simplified to the form shown in Eq. (6),

Substituting in stiffness constants and lattice parameters from Kranert et al.⁴³ and expressed in the supplementary material, yields Eq. (7). Relating this to the out-of-plane lattice parameter and, therefore, d-spacing of the (002) planes for the β-(Al_xGa_1−x)₂O₃ film yields a relationship between Al content x and peak separation Δθ₀₀₂ between the (002) β-Ga₂O₃ and β-(Al_xGa_1−x)₂O₃ peaks assuming Cu K_α x-ray diffraction as shown in Eq. (8),

A full explanation of this derivation is provided in the supplementary material, along with a similar derivation for coherently strained (100) β-(Al_xGa_1−x)₂O₃ films that yield the following relationships:

To investigate (001) β-(Al_xGa_1−x)₂O₃ growth for a range of Al contents, growth conditions similar to optimized (001) Sn-doped β-Ga₂O₃ films grown via MOCATAXY were used. Ga and In fluxes were 2.5 × 10⁻⁷ and 4.0 × 10⁻⁷ Torr, respectively, with a growth temperature of 800 °C and a Sn cell temperature of 800 °C, corresponding to an approximate Sn concentration of 10¹⁸ cm⁻³ measured by secondary ion mass spectrometry.¹⁰ Al fluxes of 1.0–1.8 × 10⁻⁸ Torr were used for (001) β-(Al_xGa_1−x)₂O₃ films grown on β-Ga₂O₃ films on (001) β-Ga₂O₃ substrates. Figure 2(a) shows the HRXRD 2θ-ω scans with (002) β-Ga₂O₃ and (002) β-(Al_xGa_1−x)₂O₃ peaks for ∼90–100 nm films with varying Al contents. Al contents calculated from Eq. (8) are also shown in Fig. 2(a). Under the growth condition described earlier, we were able to obtain single crystalline β-(Al_xGa_1−x)₂O₃ films with a maximum of 15% at Al BEP of 1.8 × 10⁻⁸ Torr. High-intensity (002) β-(Al_xGa_1−x)₂O₃ peaks with clear thickness fringes can be observed, indicative of a high-quality, uniform film. Figure 2(b) shows the smooth surface morphology of the 11% (001) β-(Al_xGa_1−x)₂O₃ film measured by AFM with a root mean squared roughness of 1.2 nm and a surface morphology similar to that of (001) β-Ga₂O₃ films grown via MOCATAXY.

Various attempts to grow unintentionally doped (UID) (001) β-(Al_xGa_1−x)₂O₃ were also performed for a range of MOCATAXY growth fluxes used for films in Fig. 2(a) without introducing a Sn flux during growths. Interestingly, similar growth conditions and growth times resulted in much worse film quality in the absence of a Sn flux. Figure 3(a) shows the HRXRD 2θ-ω scans showing the spread out (002) β-(Al_xGa_1−x)₂O₃ peaks with the absence of clear thickness fringes, indicative of the non-uniformity of Al composition or film thickness. The surface morphology of a UID (001) β-(Al_xGa_1−x)₂O₃ film is shown in Fig. 3(b), with a rougher surface than the Sn-doped (001) β-(Al_xGa_1−x)₂O₃ in Fig. 2(b). Additionally, RHEED patterns after completion of growth are shown in Fig. 3(c) for UID and in Fig. 3(d) for Sn-doped (001) β-(Al_xGa_1−x)₂O₃, demonstrating a spotty RHEED pattern indicative of a rough surface morphology for the UID film and a streaky pattern indicative of a smooth surface for the Sn-doped (001) β-(Al_xGa_1−x)₂O₃ film. The results suggest that the presence of a Sn flux seemed to act as a surfactant for (001) β-(Al_xGa_1−x)₂O₃ growth via MOCATAXY. However, further investigation beyond the scope of this work is necessary to fully understand the role of Sn in (001) growth via MOCATAXY.

To confirm that the (001) β-(Al_xGa_1−x)₂O₃ films from Fig. 2(a) were coherently strained to the underlying (001) β-Ga₂O₃ layers, reciprocal space maps (RSMs) in HRXRD were performed for the off-axis (024) and (404) reflections, measured in an asymmetric geometry, of a 11% (001) β-(Al_xGa_1−x)₂O₃ film as shown in Fig. 4. For both cases, the β-(Al_xGa_1−x)₂O₃ and β-Ga₂O₃ peaks appear to have the same q_// position, suggesting that the β-(Al_xGa_1−x)₂O₃ films are coherently strained (in-plane) to β-Ga₂O₃.

Next, to investigate the structural quality of the films, the a ∼ 100 nm (001) β-(Al_xGa_1−x)₂O₃ layer between two β-Ga₂O₃ 200 nm layers was grown on a (001) β-Ga₂O₃ substrate. A Sn cell temperature of 800 °C and a growth temperature of 800 °C were used for all layers. The Ga and In fluxes were identical to those used for samples in Fig. 2(a). Cross section TEM was performed on these film structures as shown in Fig. 5 with no evidence of extended defects in either β-(Al_xGa_1−x)₂O₃ or β-Ga₂O₃ layers.

Finally, to determine the Al composition on the group III site, APT was performed on the same film stack. The APT tip with the elemental map of the (001) β-(Al_xGa_1−x)₂O₃ layer on the top of the (001) β-Ga₂O₃, showing the higher Al content in the β-(Al_xGa_1−x)₂O₃ layer, is shown in Fig. 6(a). Additionally, Fig. 6(b) shows the Al and Ga fraction on the group III site throughout the depth of β-(Al_xGa_1−x)₂O₃ and β-Ga₂O₃ layers. An average Al content of 15.6% was measured in the film via APT, similar to the calculated Al content of 14% from peak separation in XRD.

The ability to grow (001) β-(Al_xGa_1−x)₂O₃ via MOCATAXY shows great potential for heterostructure-based devices in this orientation. While (001) oriented growth for β-Ga₂O₃ has been limited in PAMBE without a supplied In flux due to significant suboxide desorption, MOCATAXY has allowed for improvement of material quality and growth rates in this orientation. Application to alloys with Al has allowed for high-quality heterostructure growth in (001) orientation via MOCATAXY. Sn acts as a surfactant during (001) β-(Al_xGa_1−x)₂O₃ growth, with high intensity (002) β-(Al_xGa_1−x)₂O₃ peaks observed in HRXRD of films grown with both Sn and In fluxes supplied during growth. Additionally, films grown with Sn doping demonstrated smoother surface morphologies as characterized by RHEED and AFM.

The derived relationship between out-of-plane lattice spacing and Al content can be used to relate peak spacing in HRXRD and Al content. This allows for characterization of Al content via this technique for both (001) and (100) orientations. Al contents up to 15% on the group III site were achieved for (001) β-(Al_xGa_1−x)₂O₃ films. Additionally, reciprocal space maps in HRXRD confirmed that the β-(Al_xGa_1−x)₂O₃ was coherently strained in plane to (001) β-Ga₂O₃ beneath. APT also confirmed the actual Al content on the group III site. Furthermore, TEM demonstrated no evidence of extended defects in the (001) β-Ga₂O₃ or β-(Al_xGa_1−x)₂O₃, confirming the structural quality of the films grown via MOCATAXY in (001) orientation.

Heterostructure β-Ga₂O₃-based devices like MODFETs rely on high-quality β-(Al_xGa_1−x)₂O₃ with maximum Al content to achieve ideal channel charge and maximum electron mobility. Smooth heterostructure interfaces and lack of extended or point defects in the films are necessary for device performance. MOCATAXY growth allows for (001) β-(Al_xGa_1−x)₂O₃ films that meet these requirements. Still, the necessity of the Sn surfactant for (001) β-(Al_xGa_1−x)₂O₃ and the current maximum Al content of 15% provide current challenges for this orientation. Further study into the influence of Sn incorporation on electrical characteristics of β-(Al_xGa_1−x)₂O₃ is needed to understand whether the use of this surfactant inhibits device performance. Additional growth innovations or different growth mechanisms may also be needed to increase maximum Al contents for (001) β-(Al_xGa_1−x)₂O₃ if this orientation is to be competitive for β-(Al_xGa_1−x)₂O₃-based devices.

(010) β-(Al_xGa_1−x)₂O₃ growth has demonstrated higher Al contents (20%–27%)^23,29,35,40 via MBE and MOCVD. Recent results from Bhuiyan et al. have shown promise for (100) β-(Al_xGa_1−x)₂O₃ grown via MOCVD with Al contents of 17% for (100) β-(Al_xGa_1−x)₂O₃ coherently strained films with uniform Al content. Films with a higher average Al content of 52% were also grown but demonstrated local segregation of Al. The highest Al contents achieved for uniform, coherently strained β-(Al_xGa_1−x)₂O₃ films grown across various orientations are shown in Fig. 7. The reason for the difference in maximum Al contents achieved for growth on different orientations is still an open area of investigation. This could be linked to the difference in thermodynamics and kinetics of growth that also leads to different film morphologies, quality, and dopant incorporation across orientations.^6–10,40 This maximum Al content could also be limited by strain, which is predicted to limit critical thickness of β-(Al_xGa_1−x)₂O₃ films before relaxation, particularly for (001) orientation.³⁴ This strain may promote Al segregation, extended defects, or the formation of new phases; however, additional study of (001) β-(Al_xGa_1−x)₂O₃ with higher Al contents is needed to confirm this. Ultimately, higher Al contents are still needed if the β-(Al_xGa_1−x)₂O₃/Ga₂O₃ material system is to achieve the higher electron mobility prediction by Ghosh et al. and maintain high 2DEG charge.³² These material growth achievements along with the demonstration of ultra-scaled device designs that take advantage of the high critical electric field of the materials system would be important advancements for future viability of β-(Al_xGa_1−x)₂O₃/Ga₂O₃-based devices.

See the supplementary material for the full stress–strain analysis for β-(Al_xGa_1−x)₂O₃ coherently strained to β-Ga₂O₃ for the (010), (001), and (100) orientations. This includes the derivation of the relationships between the Al content and the out-of-plane lattice parameter, along with corresponding peak spacing measured via x-ray diffraction for each of these orientations.

We acknowledge funding from AFOSR through program GAME MURI (Award No. FA9550-18-1-0479) under project manager Dr. Ali Sayir. Additional support was provided through a subcontract from Agnitron Technology through ONR Program No. N00014-16-P-2058.

The authors have no conflicts to disclose.

Akhil Mauze: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead); Writing – review & editing (lead). Takeki Itoh: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Writing – review & editing (supporting). Yuewei Zhang: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (supporting). Evelyn Deagueros: Data curation (supporting); Investigation (supporting); Writing – review & editing (supporting). Feng Wu: Data curation (supporting); Writing – review & editing (supporting). James S. Speck: Conceptualization (supporting); Formal analysis (supporting); Funding acquisition (lead); Investigation (supporting); Methodology (supporting); Supervision (lead); Writing – original draft (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available within the article and its supplementary material.