Unusual Formation of Point Defect Complexes in the Ultra-wide Band Gap Semiconductor beta-Ga2O3

Understanding the unique properties of ultra-wide band gap semiconductors requires detailed information about the exact nature of point defects and their role in determining the properties. Here, we report the first direct microscopic observation of an unusual formation of point defect complexes within the atomic scale structure of beta-Ga2O3 using high resolution scanning transmission electron microscopy (STEM). Each complex involves one cation interstitial atom paired with two cation vacancies. These divacancy - interstitial complexes correlate directly with structures obtained by density functional theory, which predicts them to be compensating acceptors in beta-Ga2O3. This prediction is confirmed by a comparison between STEM data and deep level optical spectroscopy results, which reveals that these complexes correspond to a deep trap within the band gap, and that the development of the complexes is facilitated by Sn doping through the increase in vacancy concentration. These findings provide new insight on this emerging material's unique response to the incorporation of impurities that can critically influence their properties.

Controlling point defects in crystalline materials can critically influence their properties, and it is therefore imperative to have well-controlled point defects to advance the materials for successful application. Point defects can be very diverse, both in terms of their structure and function. In particular, understanding the formation of point defect complexes, which may occur in response to impurity incorporation within the structure, is of great importance because of their versatile formations and influence on the materials' properties. This is particularly the case in wideband gap semiconductors, where the intrinsic advantages of a large band gap and the possibility of high optical transparency (e.g., in transparent conductive oxides or TCOs) are severely impaired by the presence of defects. For example, the large critical field strengths that can theoretically be supported in wide-band-gap semiconductors for applications in next-generation power electronics can be ruined by the presence of defects [1], and the existence of significant deeplevel defect concentrations can severely degrade the optical properties of TCOs [2]. Additionally, the presence of impurities and the formation of various types of complexes in TCOs have been suggested to contribute to the observed intrinsic n-type behavior, difficulty in p-type doping, and low doping efficiency [3][4][5]. What has been missing in the field is direct experimental information on the detailed atomic-scale structure of such complexes. Gaining this information is essential to exactly crosslinking theoretical predictions of complexes to measured properties of wide band gap semiconductors, which will then provide important guidance to the synthesis and doping of the material with precisely controlled properties. However, such information has been nearly unattainable because of the small (atomicscale) nature of the defect complexes, especially when they are buried within the three-dimensional material. These challenges have led to the lack of experimental information on how the complexes incorporate within the atomicscale structure and the inability to discover any unknown complexes that may critically affect the properties of the material.
Here, we present the first direct scanning transmission electron microscopy (STEM) observation of the unusual formation of point defect complexes within the atomicscale structure of β-Ga 2 O 3 . Note that β-Ga 2 O 3 is an excellent candidate for high-performance electronic, optical, power device, and sensor applications [6][7][8][9][10][11][12][13][14][15] due to its unique properties, including an ultra-wide band gap of about 4.8 eV [16], optical transparency into the ultraviolet region [17], and high breakdown voltage [18]. However, advancing the material has been hampered by the lack of a detailed understanding of the formation of point defect complexes [4,[19][20][21][22][23][24] and their impact on electrical and optical properties [25][26][27][28][29]. Using STEM, we discovered a new type of point defect complex that involves one cation interstitial atom, which can be positioned at two of the five possible interstitial sites, paired by two cation vacancies. The structure of this unusual cation interstitial-divacancy complex is consistent with the predictions made by density functional theory (DFT). DFT also shows that this defect acts as a deep level and is the dominant compensating acceptor in β-Ga 2 O 3 ; since β-Ga 2 O 3 is n doped for most applications, this defect therefore has a crucial impact on device performance. Comparing the STEM data to deeplevel optical spectroscopy (DLOS) shows that formation of the defects is enhanced by increased Sn doping, confirming the compensating-acceptor character, with a defect level at E C − 2.0 eV. The present atomic-scale investigation identifies this unusual defect as the origin of a number of previously unexplained phenomena in β-Ga 2 O 3 and also sheds light on this material's unique response to the incorporation of impurities that can critically influence its properties.
First, we explain the observation of interstitial defects and defect complexes in Sn-doped β-Ga 2 O 3 bulk crystals (doping concentration of 8.5 × 10 18 cm −3 yielding a carrier concentration of 8.2 × 10 18 cm −3 [30,31]). The unit cell of monoclinic β-Ga 2 O 3 contains two crystallographically different Ga (Ga 1 , Ga 2 ) and three oxygen atom positions Fig. 1(a). The structure is oriented along ½010 m , which is the orientation used throughout this study. Note that Ga 1 and Ga 2 have tetrahedral and octahedral coordination, respectively. Here, O 1 and O 2 have threefold coordination, while O 3 has fourfold coordination. Figure 1(a) also shows five potential cation interstitial sites (i a−e ). As will be explained in detail, these interstitial sites have been derived from both our experimental observation and DFT calculations [19,21]. A high-angle annular dark field (HAADF) STEM image (see the Appendix for details) from the ½010 m Sn-doped sample of a defect-free region is shown in Fig. 1(b). As HAADF intensity depends on the atomic number, high intensity in this image mostly arises from the scattering of the Ga 1 and Ga 2 columns, while only very weak intensity is observed from O positions. Figure 2 shows the direct detection of interstitial defects and defect complexes in the same Sn-doped β-Ga 2 O 3 bulk crystal. In the sample areas shown in Fig. 2 We also note that these interstitial intensities were found to be clustered and concentrated in10 nm 2 areas [ Fig. 2 Clustering likely happens along the direction parallel to the electron beam as well, which can be evidenced by the high interstitial column intensity [e.g., Fig. 2(f)] indicating that there are likely multiple cation interstitial atoms along the column [32,33]. Previous works have identified extended defects (e.g., twin boundaries and screw dislocations) [34][35][36] and some atomic-scale defects [2,37] in β-Ga 2 O 3 , but our present data from aberration corrected STEM provide the first direct identification of the exact positions of interstitial defects.
Next, we identify the unique formation of point defect complexes from the HAADF-STEM intensities by directly correlating them with DFT calculations (see the Appendix for details). DFT calculations [19,20,24] have shown that cation vacancies have low formation energies under O-rich growth conditions, with tetrahedral V 1 Ga being the most favorable. However, the vacancy on the tetrahedral Ga 1 site was identified as metastable; the presence of the vacancy causes a neighboring Ga atom to leave its tetrahedral site (creating a second vacancy) and move towards an interstitial site midway between the two vacancies, effectively resulting in a 2V 1 Ga − Ga i complex (Fig. 3). This complex is lower in energy than the isolated vacancy and acts as a deep acceptor. Figure 3(a) shows how the adjacent Ga 1 atom relaxes to the i c site, becoming octahedrally coordinated and creating an additional V 1 Ga , which can be formed easily due to the relatively small energy barrier [19,21]. These DFT results have also been utilized in recent β-Ga 2 O 3 defect studies using electron spin resonance [38,39] and infrared spectroscopy [40,41] to attribute the presence of proton irradiation-induced defects and implanted O-H bonds to the same point defect complexes. However, the direct confirmation of 2V 1 Ga − Ga c i complexes by STEM in β-Ga 2 O 3 requires the detection of not only the cation interstitial atoms (explained above) but also the vacancies in the neighboring Ga columns. Identifying a single vacancy within an atomic column may not be trivial [42]; however, the presence of several vacancies within a Ga column will decrease the overall HAADF STEM signal due to the loss of scattering from the absent Ga atoms [43]. Image simulations performed using the multislice method [44] (see the Appendix for details) confirmed that the signal increases at interstitial sites from cation interstitials and decreases at Ga 1 sites from vacancies  Fig. 3(b)]. The reduced intensity of Ga 1 columns adjacent to interstitials was substantially more significant than the overall intensity decrease in the area (including the Ga 2 columns that are not expected to be involved in the relaxation process) that may be caused by the strain [45] due to the interstitials (see Supplemental Material [46], Table S1). Image simulations indicate that the effect of electron channeling from interstitials is minimal due to the considerable gap (∼0.18 nm) between the interstitials and the adjacent Ga columns. Therefore, the substantial intensity decrease, apart from the overall decrease due to strain in the Ga 1 columns adjacent to interstitials, suggests that vacancies are most likely present in those columns. Similarly, vacancy-interstitial complexes . Quantitative comparison of atomic column intensity to the image simulation can provide information on the number of defects located within each column (e.g., Ref. [32]). Based on the experimental and simulation data (see Supplemental Material [46], Fig. S1), the estimated number of complexes within these columns is about 10 (see Supplemental Material [46] for details).
Considering the near-equilibrium growth condition of the edge-defined, film-fed growth (EFG) process used to grow these bulk crystals, the formation energy (i c < i b < i a ), predicted by DFT [19], may directly correspond to the number density of each of those point defects within the material. Despite small sampling in STEM images [such as in Fig. 2(g)], the number densities of interstitials observed in the sampled region (i c ¼ 1.6 × 10 20 cm −3 > i b ¼ 3.9 × 10 19 cm −3 > i a ¼ 0) appear to be consistent with the energetic favorability found in the DFT calculation. In fact, we have not observed any interstitial i a intensity above the threshold value in the sampled areas, which suggests the formation of i a interstitials may be much less likely than i b or i c . Based on the analysis of images with visible interstitials [e.g., Fig. 2(g)], the estimated concentration of defect complexes is about 2 × 10 20 cm −3 (see Supplemental Material [46] for details).
Although lesser in signal and fewer in total number, the interstitials observed in sites i d and i e found in Sn-doped β-Ga 2 O 3 display unexplored interstitial complexes that may be important in understanding the material's properties. Interestingly, interstitial intensities in i d and i e sites are always observed to be accompanied by interstitial intensities in nearby i b and i c sites [Figs. 2(d) and 2(e)]. This may imply that 2V 1 Ga − Ga b;c i complexes may facilitate the formation of other complexes that occupy the i d and i e sites. The exact formation mechanism of i d and i e defects and their implication to the properties remain to be further explored in the near future.
The next question is then how Sn doping affects the formation of the interstitial point defect complexes shown above. In general, Sn impurities have been shown to contribute to the n-type behavior of β-Ga 2 O 3 , producing controllable carrier concentrations from 10 16 up to 10 19 cm −3 [30,47]. Formation energy calculations have indicated that Sn can easily be incorporated into β-Ga 2 O 3 acting as a shallow donor and preferring to substitute in the octahedrally coordinated Ga 2 site [20,31]. In fact, our STEM investigation has revealed several of these Sn substitutional atoms based on the high atomic column intensity in the HAADF mode [e.g., Fig. 4(a)]. In addition to incorporating it as a substitutional dopant, Sn, when in high concentration, may promote the formation of the vacancy-interstitial complexes shown above. To verify this hypothesis, we first investigate unintentionally doped (UID) β-Ga 2 O 3 (carrier concentration of 2.4 × 10 17 cm −3 [30]) using HAADF STEM. UID β-Ga 2 O 3 images revealed cation interstitials in the i c site [ Fig. 4(b)], which implies that the interstitials may also be created via the same V 1 Ga migration mechanism explained above. A larger sampling resulted in the conclusion that these complexes are lesser in quantity and smaller in intensity in comparison to Sn-doped β-Ga 2 O 3 . This result is consistent with the expectations that the incorporation of Sn donors that drive the material more n-type simultaneously stimulates the formation of the compensating acceptor species like the 2V 1 Ga − Ga i complexes through the subsequent increase in vacancy concentration [19,24]. Presuming a reduction in vacancy formation energy for increased Fermi level energy [19], Sn doping facilitates this increase in vacancy concentration through the increase in Fermi level energy. Additionally, Sn may also be incorporated as the cation interstitial, forming 2V 1 Ga − Sn i complexes. Its exact role will be discussed among the succeeding results.
DLOS can reveal the rich spectrum of defect states throughout the large band gap [29], by using monochromatic incident light as a function of energy to photo-emit trapped carriers to a band edge, which enables the determination of energy levels, concentrations, and optical cross sections of deep states (see the Appendix for details [29,48,49]). Accompanying our STEM results and DFT calculations, the DLOS results are consistent with the role of Sn dopant concentration and the number of vacancyinterstitial complexes present. Most importantly, the concentration of the trap detected at E C − 2.0 eV shows a positive correlation with Sn concentration [Fig. 4(c)], and the trap has been shown to act as a deep acceptor [50]. This defect behavior is consistent with the electronic state of the 2V 1 Ga − Ga i complexes predicted by DFT, where levels associated with the expected εð−2=À3Þ charge-state transition levels have been predicted to fall between E C − 1.9 and E C − 2.5 eV [19,24]. The analogous εð−=−2Þ levels calculated for the 2V 1 Ga − Sn i complexes are found to be in a similar energy range, at E C − 2.34 and E C − 2.89 eV for the i b and i c sites, respectively. The apparent defect concentrations obtained from DLOS represent the average over large areas (as opposed to the relatively smaller area observations of STEM) and are limited by the finite time response of the defects [50]. Nonetheless, the positive correlation between the DLOS detected trap and doping concentration, along with the detection of this trap in UID β-Ga 2 O 3 , directly coincides with the observation of interstitials by STEM imaging, which affirms the physical source of the E C − 2.0 eV defect state to be the divacancy-interstitial complex.
It would be highly valuable to be able to distinguish whether the observed entities are 2V 1 Ga − Ga i (spatially separated from donor impurities) or actual 2V 1 Ga − Sn i complexes since it could help identify strategies for controlling the compensating acceptor. The proposed 2V 1 Ga − Sn i acceptor complexes have also been suggested to contribute to compensation in Sn-doped β-Ga 2 O 3 [51]. Our calculations show that these complexes can readily form when V Ga are nearby (calculated barriers less than 0.3 eV for an Sn 1 Ga to be displaced to octahedrally coordinated interstitials adjacent to V Ga1 ) and are quite stable, with calculated binding energies of at least 1.4 eV relative to isolated V Ga and Sn Ga species (see Supplemental Material [46], Fig. S2). However, we expect that these complexes would need to form during growth, as Sn is not expected to be appreciably incorporated on the tetrahedral sites, which is a prerequisite for their formation postgrowth [20]. As mentioned above, determining the species of cation interstitials in Sn-doped β-Ga 2 O 3 via HAADF-STEM is difficult because variations in number and location make Ga and Sn interstitials indistinguishable (see Supplemental Material [46], Fig. S1). However, because DLOS results reveal the same trap (E C − 2.0 eV) in both UID and Sn-doped β-Ga 2 O 3 while DFT calculations predict different electronic states for 2V 1 Ga − Ga i and 2V 1 Ga − Sn i complexes, the observed compensating acceptors correlate with native 2V 1 Ga − Ga i complexes. In summary, the STEM results provide the first observation of unusual divacancy-cation interstitial complexes, and the structure of the identified complexes matches with DFT predictions that classify them as compensating acceptors. DLOS results further validate the formation of these complexes, as the detected E C − 2.0 eV defect state shows a positive correlation with Sn doping. Sn was determined to facilitate the divacancy-interstitial complex development by increasing the Fermi level energy and subsequently increasing the vacancy concentration. These STEM results provide new important insight on the material's unique response to the impurity incorporation that can significantly affect their properties, which can ultimately offer important guidance to the development of growth and doping of TCOs for novel applications. The observed complex is, in essence, a low-symmetry configuration of a cation vacancy. It will be highly interesting to explore, using computational theory and/or microscopy, whether vacancies in other materials can also spontaneously undergo such symmetrybreaking distortions.

APPENDIX: METHODS
The (201) Sn-doped and unintentionally doped (UID) β-Ga 2 O 3 bulk crystals used in this investigation were fabricated by the edge-defined, film-fed growth (EFG) process by the Tamura Corporation. The Sn-doped and UID samples have carrier concentrations of 8.2 × 10 18 cm −3 and 2.4 × 10 17 cm −3 , respectively. Crystal orientations such as the ½010 m and ½001 m yield advantageous viewing directions for point defect imaging due to the large atomic spacings. Cross-sectional ½010 m TEM samples were prepared using a focused ion beam (FIB). As atomic resolution imaging of ½010 m β-Ga 2 O 3 requires thin, clean samples, we further milled TEM samples using a low-energy (500-eV) ion mill (Fischione Nanomill). The final thickness of the TEM foils was determined by position-averaged convergent beam electron diffraction to be about 25 nm [32,52], meaning each gallium column contains about 80 atoms along the depth direction. STEM was then performed using aberration-corrected Thermo Fisher Scientific Titan Themis STEM instruments, all operated at 300 kV.
All STEM HAADF image simulations were performed using the multislice algorithm [44]. For each image simulation of randomly distributed defect complexes, ten random arrangements were simulated and then averaged to increase statistical reliability. Thermal vibrations were ignored as their contribution to column intensity is minimal. The image simulations used aberration parameters of our probe-corrected FEI Titan STEM (Cs 3 ¼ 0.002 mm, Cs 5 ¼ 1.0 mm) with a 20.0-mrad convergence half-angle at an acceleration voltage of 300 kV.
The DFT atomistic simulations of the vacancy complex energetics were based on hybrid functional calculations performed using the same methodology as described in Ref. [24]. Specifically, the vacancy and vacancy complexes were modeled within a 160-atom supercell representation of bulk β-Ga 2 O 3 , where corrections to the formation energies of charged defects owing to image-charge interactions were included as detailed in Ref. [24]. Migration barriers were computed between linearly interpolated structures and thus offer upper bounds to the real barriers.