Atomic scale observation of threading dislocations in α-Ga₂O₃

Gallium oxide (Ga₂O₃) has recently emerged as the leading candidate for future power electronic and deep ultraviolet optoelectronic applications.^1,2 This compound is highly polymorphic, with five known phases labeled α, β, κ, δ, and γ.^3–5 Research to date has been driven by the monoclinic β-phase of Ga₂O₃ as the thermodynamic stability of this phase implies that it can be produced in bulk.⁶ On the other hand, the rhombohedral corundum-like α-phase of Ga₂O₃ is rapidly gaining interest⁷ due to its bandgap energy of ∼5.1–5.6 eV (the widest bandgap among all Ga₂O₃ phases)^8–10 and its isomorphism with a range of semiconductor sesquioxides.¹¹ Despite its metastability, α-Ga₂O₃ can now be deposited on the isomorphic, inexpensive, and widely available α-Al₂O₃ (sapphire) substrate using most common deposition techniques.¹² A drawback of heteroepitaxy is that the deposition of the film on a lattice-mismatched substrate will almost unavoidably generate dislocations to accommodate that strain. This has been widely reported in previous generations of semiconductors,^13,14 and early reports on α-Ga₂O₃ show that this compound is no exception. In the absence of dislocation mitigation strategies, epitaxial α-Ga₂O₃ films typically exhibit threading dislocation densities of the order of 10¹⁰ cm⁻².^15–18 Densities down to 10⁸ cm⁻² were achieved using (Al_xGa_1−x)₂O₃ graded buffer layers,¹⁹ epitaxial lateral overgrowth,¹⁶ or rapid low temperature growth of thick films,²⁰ and the combination of the two latter methods results in a further decrease in density down to ∼10⁷ cm⁻².²⁰ Notwithstanding these advances, the reported dislocation densities for α-Ga₂O₃ on α-Al₂O₃ are too high to be ignored.

The impact of dislocations on the properties of α-Ga₂O₃ materials and devices has been poorly understood to date. In the III–V semiconductor systems, dislocations have been associated with reduced light emission,²¹ reduced device reliability,²² or increased leakage current.²³ In β-Ga₂O₃, where these defects are less studied, dislocations have been related to reverse leakage current,²⁴ curbed breakdown voltage,²⁵ and reduced luminescence.²⁶ In α-Ga₂O₃, Takane et al. linked dislocation density to reduced electron mobility and calculated that dislocation density $≤107$–10⁸ cm⁻² was required to nullify their impact.²⁷ 

However, while the general expectation is that they have a negative influence on material properties, not all dislocations are identical nor have deleterious effects. Reports on GaN indicate that only pure screw dislocations affect leakage current, unlike edge and mixed dislocations.^28–30 Moreover, dislocations can enable material engineering breakthroughs, for example acting as porosification channels for novel optical devices.³¹ Similarly to III-nitrides, a better understanding of dislocations in α-Ga₂O₃ will underpin targeted material and device fabrication strategies. This will result in efficient and reliable devices performing to the theoretical promises of the materials. The journey to build this understanding commences by observing and identifying the dislocations present in the material.

Earlier reports used transmission electron microscopy (TEM) and g.b analysis³² to observe dislocations in α-Ga₂O₃ and identify their character (edge, screw, and mixed).^15,17,19,20 As threading dislocations have a line direction along [0001] for epitaxially grown materials, g conditions such as $11̄00$ or $112̄0$ would highlight the dislocation’s edge component, while g conditions parallel to 0001 are used to visualize the screw component. The literature so far concluded that threading dislocations in α-Ga₂O₃ films are dominantly edge-type,^15,17,20 with few reports of dislocations with screw-component.^19,33 Ma et al. and Takane et al. used x-ray diffraction to calculate the density of dislocations from the broadening of the reflection, with similar conclusions as the TEM approach.^18,34 This led to the, perhaps hasty, conclusion that dislocations are perfect with Burgers vector $b=13⟨112̄0⟩$⁠. These conclusions were, however, not informed by dislocation energy theory. Since dislocation energy is proportional to b² and α-Ga₂O₃ has a particularly large unit cell (a = 4.9825 Å; c = 13.433 ų⁵), we can expect that perfect dislocations are likely to be unstable. Instead, we could reasonably expect dislocations to dissociate into partials to reduce their overall energy. Dislocation dissociation has been routinely observed in nitrides,^36–41 as well as in the isomorphic α-Al₂O₃.^42–44 While a result of this nature in α-Ga₂O₃ would not trigger a fundamental reconsideration of previous observations, a more accurate understanding of the type of dislocations present in the material is imperative to grasp their properties and to develop more effective mitigation routes. In the present study, we employ aberration-corrected high-resolution scanning transmission electron microscopy (STEM) to elucidate the nature of threading dislocations in α-Ga₂O₃ and provide the first atomic scale observation of their core structure.

An α-Ga₂O₃ film with a thickness of ∼250 nm was grown on a c-plane sapphire substrate by plasma enhanced atomic layer deposition using an Oxford Instruments OpAL reactor at a temperature of 250 °C. A full description of the growth process can be found in Ref. 45. From previous investigations,^45,46 it is known that under these growth conditions, the resulting α-Ga₂O₃ film is grown epitaxially on the α-Al₂O₃ substrate with $[0001]Ga2O3‖[0001]Al2O3$ and $[112̄0]Ga2O3‖[112̄0]Al2O3$⁠, and with the film consisting dominantly of α-Ga₂O₃ columns, with amorphous and κ-Ga₂O₃ inclusions located between the columns.⁴⁶ 

The sample was prepared for plan-view STEM imaging using the standard mechanical polishing method followed by Ar⁺ ion milling at 5 kV and cleaning from 1 kV down to 0.1 kV.³² The sample was observed in plan-view using an FEI Titan3 aberration-corrected STEM operated at 300 kV in high-angle annular dark-field STEM (HAADF-STEM) mode. The dislocations were viewed end on—i.e., along the [0001] zone-axis—thereby allowing the identification of the core structure. Strain mapping was obtained using geometrical phase analysis.⁴⁷ 

Figure 1 presents an overview of the sample observed by HAADF-STEM in plan-view geometry. The contrast in HAADF-STEM images is dominated by Rutherford scattering, i.e., proportional to Z², with residual contrast provided by strain and misorientation effects. As a result, the atomic scale images shown here along [0001] will be dominated by the projection of Ga (Z = 31) atomic columns rather than O (Z = 8) atomic columns. A crystal structure overlay in the inset clearly highlights the correspondence of the atoms in HAADF-STEM with Ga atomic columns.

This image can be seen to contain two threading dislocations. The presence of threading dislocations observed end on is hinted at by the local blurry contrast in HAADF-STEM [Fig. 1(a)] and by the tensile–compressive strain dipole in the strain map [Fig. 1(c)] resulting from the local distortion of the crystal lattice in the vicinity of the dislocation—more detailed analysis of the Burgers vector and core structure is presented in the following paragraphs. Using the images with widest field of view, we calculate that the film contains a threading dislocation density of ∼5 × 10¹⁰ cm⁻², which is slightly higher compared to other reported values,^15–18 but not overly so, given that here we investigate a comparatively thinner film.

The raw, unfiltered HAADF-STEM image [Fig. 1(a)] also reveals the presence of a high density of white lines throughout the material—these are highlighted in Fig. 1(b) for better clarity. These white lines are observed running along the $⟨11̄00⟩$ directions, and assuming these are the projection of a planar feature parallel to [0001], then these are contained in the ${112̄0}$ planes. These lines are visible in the raw HAADF-STEM images but not in the average background subtraction filter (ABSF) filtered images and exhibit a very faint contrast in the strain maps [Fig. 1(c)]. Similar lines were previously observed in mist chemical vapor deposited α-Ga₂O₃ by Lee et al., who ascribed them to anti-phase domain boundaries,^48,49 and in halide vapor phase epitaxy α-Ga₂O₃ by Myasoedov et al., who assigned them to prismatic stacking faults with displacement vector $R=13⟨11̄00⟩$⁠.³³ In agreement with Myasoedov et al., we observe that the threading dislocations in Fig. 1(a) are located on, or terminating in white lines.

Looking further into the structural properties of dislocations, Burgers circuits were drawn around 86 threading dislocations. All the Burgers circuits were open along $be=13⟨11̄00⟩$⁠, as illustrated in Fig. 2. Given that we here see a projection of the Burgers vector along the [0001] direction, this result implies that all the dislocations we observed are either partial edge dislocations (therefore with $b=13⟨11̄00⟩$⁠) or perfect mixed dislocations (with $b=13⟨11̄01⟩$⁠). The observation of partial edge dislocations implies that perfect edge dislocations have dissociated.

Looking into the sapphire (α-Al₂O₃) literature, $b=13⟨11̄01⟩$ mixed dislocations, as well as dissociation of $b=13⟨112̄0⟩$ and $b=⟨11̄00⟩$ edge dislocations into $b=13⟨11̄00⟩$ partials, have been reported at low-angle grain boundaries.⁴² Given the high mosaicity of epitaxial α-Ga₂O₃ films,^45,50 the film contains a high density and wide variety of low-angle grain boundary configurations, implying that these three types of dislocations and partials could be possible here. In fact, while most reports on α-Ga₂O₃ concluded that edge dislocations formed the dominant category of dislocations, those works also observed dislocation contrast when g = 0006, which implies that dislocations with screw component are expected.^15,34 In addition, Myasoedov et al. and Jinno et al. concluded that a significant proportion of the threading dislocation population exhibited a screw component.^19,33

Figure 2 reveals that all three categories of dislocations coexist in the sample. While in several instances, the local density of dislocations is so high that it is not possible to identify with certainty if a dislocation fits in a given category, we could find examples shown in Fig. 2 where such categorization was clear.

Dislocation dissociation can be rationalized energetically, as mentioned in introduction. The elastic energy of a dislocation scales with b². Taking reaction (2) as an example, the perfect dislocation $(bperf=⟨11̄00⟩)$ dissociates into three partial dislocations with Burgers vectors a third the length $(bpart=13⟨11̄00⟩)$⁠. Dissociation leads to the combined elastic energy of the three partials being a third that of the perfect dislocation $(3×bpart2=3×(bperf3)2=13bperf2)$⁠. As long as the energy of the stacking fault connecting the partial dislocations is not excessive—and calculations in α-Al₂O₃ have shown that prismatic stacking faults are low energy in that material^52,53—the dissociation reaction will be energetically favorable. We can use our observation of partial dislocation separation in Fig. 2 and crystal elastic parameters⁵⁴ to obtain an estimate of the stacking fault energy and gauge if dissociation should be expected. Assuming that the repulsive force between the partials is balanced by the stacking fault attractive force, the stacking fault energy can be approximated by $γSF=Gb24πr$⁵⁵ (G: shear modulus; b: Burgers vector of partials; and r: separation of partials), which yields a stacking fault energy of the order of ∼0.16–0.24 J.m⁻², which is low and well within the predicted prismatic faults energies in α-Al₂O₃^52,53 (we note that since the elastic parameters are not well established in α-Ga₂O₃, a refined formulation of the stacking fault energy would not be meaningful).

Finally, Fig. 2(c) shows a perfect $b=13⟨11̄01⟩$ mixed dislocation. This dislocation is $>$10 nm away from any other dislocation or free surface, which suggests that it cannot be issued from a dissociation mechanism as this would be energetically improbable.

Drawing statistics about the distance of each dislocation (or partial dislocation) to its nearest neighbor, we identify two distinct populations. A first category corresponds to dislocations spaced by $<$10 nm. These exhibit an average dislocation separation of 4.4 ± 0.3 nm and account for ∼50% of the total dislocations. On the basis of dissociation energy balance, we therefore assign these to the partial dislocations. The second category corresponds to dislocations that can be considered as isolated, i.e., spaced by $>$10 nm, and accounts for the other 50% of the total population. We therefore associated that population to the perfect mixed dislocations. This result suggests that our sample exhibits an equivalent proportion of edge and mixed dislocations, in line with previous reports on α-Ga₂O₃ grown using other techniques.^19,33

Finally, we turn our attention to the atomic arrangement of the core of the dislocations. Identifying the core structure of a dislocation is important as this underpins the electronic properties of the defect, and dislocations with identical Burgers vectors can, in fact, exhibit different core arrangements.^36,37 In our sample, 47 dislocations were sufficiently clear to allow unambiguous identification of their core structure—for a study of this nature, this is a statistically significant number of cores. Our analysis reveals that every dislocation exhibits the same 5-atom ring core structure, as illustrated in Fig. 3, irrespectively of whether the dislocation is edge partial or perfect mixed. We need to bear in mind that our micrographs only show the Ga cation columns in the crystal and that there may therefore be further differentiation of core configurations were the O columns visible. This result will, however, be extremely valuable to computational material scientists, allowing them to narrow their possible core exploration to uncover the accurate core structure and resulting density of states associated with the dislocations.

In conclusion, we presented a statistically meaningful investigation of threading dislocations in α-Ga₂O₃ using high-resolution HAADF-STEM. Seen end on, all 86 threading dislocations exhibit a projected Burgers vector $be=13⟨11̄00⟩$⁠. We find that the dislocations can be classified into perfect mixed dislocations (⁠$b=13⟨11̄01⟩$⁠) and edge dislocations (⁠$b=⟨11̄00⟩$ and $b=13⟨112̄0⟩$⁠), which dissociate into combinations of $b=13⟨11̄00⟩$ partials. High-resolution analysis of the core region of 47 dislocations identifies that all the dislocations exhibit a similar 5-atom core, when looking at the cation sites. We believe that this is the first investigation of its kind and magnitude in this material system, which will feed into important future simulation work to understand the electronic properties of dislocations in α-Ga₂O₃ as well as other epitaxial corundum-structured materials.

The authors acknowledge the support from the Engineering and Physical Sciences Research Council (EPSRC Grant Nos. EP/M010589/1 and EP/K014471/1). The authors would like to thank Dr Giorgio Divitini (now at Istituto Italiano di Tecnologia, Genova, Italy) for his technical support on the TEM.