# Fileset

[Irokawa_2026_ECS_J._Solid_State_Sci._Technol._15_055002.pdf](https://mdr.nims.go.jp/filesets/73b099f7-414e-475f-9f4b-bb7d924f27e2/download)

## Creator

[Yoshihiro Irokawa](https://orcid.org/0000-0002-6531-4356), [Mamoru Usami](https://orcid.org/0009-0002-3188-7380), [Jun Uzuhashi](https://orcid.org/0000-0003-2023-8158), [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), [Toshihide Nabatame](https://orcid.org/0000-0002-5973-0230), [Yasuo Koide](https://orcid.org/0000-0001-8321-9822)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Investigation of Deep States in GaN Metal-Oxide-Semiconductor Interfaces](https://mdr.nims.go.jp/datasets/4a8e7461-ecc1-49c7-b3e7-5b8df642a9e0)

## Fulltext

Investigation of Deep States in GaN Metal-Oxide-Semiconductor InterfacesECS Journal of SolidState Science andTechnology     OPEN ACCESSInvestigation of Deep States in GaN Metal-Oxide-Semiconductor InterfacesTo cite this article: Yoshihiro Irokawa et al 2026 ECS J. Solid State Sci. Technol. 15 055002 View the article online for updates and enhancements.You may also likeGroove Influence on Lapping Quartz Glasswith Fixed Abrasive PadZhankui Wang, Yihang Fan, FengsongDong et al.-Optical and Dielectric Characteristics ofPVC/Mn0.95Mg0.05WO4/PANI TernaryNanocomposites for MultifunctionalApplicationsA. M. El-Naggar and A. M. Kamal-Co-Ni-Mn Sulfide Mixed-Phase CompositeElectrode Recovered from Spent LIB BlackMass for High-PerformanceSupercapacitorsOuzhan Onar, Sezgin Yasa, Ozan Aydinet al.-This content was downloaded from IP address 144.213.253.16 on 12/05/2026 at 21:59https://doi.org/10.1149/2162-8777/ae6689https://iopscience.iop.org/article/10.1149/2162-8777/ae613chttps://iopscience.iop.org/article/10.1149/2162-8777/ae613chttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae668ahttps://iopscience.iop.org/article/10.1149/2162-8777/ae672fhttps://iopscience.iop.org/article/10.1149/2162-8777/ae672fhttps://iopscience.iop.org/article/10.1149/2162-8777/ae672fhttps://iopscience.iop.org/article/10.1149/2162-8777/ae672fhttps://pagead2.googlesyndication.com/pcs/click?xai=AKAOjsv_z9RebzhQajsbdGLVoG9Ok8YrEKh2wJ4GXOE2UQ_UJrkE5iEGSqBglNRWR8ArJi9pJ8ZNd1TpFYgCp2ONfwsiS0H6_7IqJjVpkok3hSsfWokTq-dK2in-PLYHSzrjPZB8--H3S2jm9PIVw8GzA74tZNw1-4tugoMaMDOnq99q4rbzaT3ZcI5srqLDSi1YyghH4nlQnvfuURq-LbC-C1IUV_lbaSkmhH4RIXMrI8sLlbN821ciKYy5Up-azWrGi6UYWjRvrlaZ2fKhfTSsfSdWpVs811ptb0DQU7obOJTnj3b1oX8f1I9oIl7hsZj8hr_UzCFiGjCtsujSJZTd9DMl3AXhdwfkU0KXAtD8mj01P-yIXkxcXZVmEyg&sig=Cg0ArKJSzIE8ArZpz0Kx&fbs_aeid=%5Bgw_fbsaeid%5D&adurl=https://www.el-cell.com/products/test-cells/force-test-cells/pat-cell-solid/%3Fmtm_campaign%3DIOP-banner%26mtm_kwd%3DPAT-Cell-Solid%26mtm_source%3Dbanner%26mtm_cid%3D2026Investigation of Deep States in GaN Metal-Oxide-SemiconductorInterfacesYoshihiro Irokawa,1,z m Mamoru Usami,2,z m Jun Uzuhashi,1 m Tadakatsu Ohkubo,1 mToshihide Nabatame,1,z m and Yasuo Koide1,3 m1National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan2ASMS Co., Ltd, Shinagawa, Tokyo 141-0022, Japan3Meijo University, Nagoya, Aichi 468-8502, JapanWe previously reported a powerful method to improve dielectric/GaN interface properties: the dummy SiO2 process [Y. Irokawaet al., ECS J. Solid State Sci. Technol. 13, 085003 (2024)]. Here, GaN metal-oxide-semiconductor (MOS) interfaces prepared withthis process were investigated using a sub-bandgap photo-assisted capacitance–voltage technique. GaN MOS interfaces werepreviously revealed to have deep states, and the dummy process was expected to reduce the number of deep states through itsinterface modification process. However, the deep state densities in Al2O3/GaN MOS interfaces after the dummy process did notsubstantially change compared with those in devices fabricated without the dummy process. Meanwhile, we recently observedoxygen atoms in positions proximate to nitrogen sites in MOS interface regions, with the GaN crystal maintaining the samestructure [J. Uzuhashi et al. ECS J. Solid State Sci. Technol. 14, 085001 (2025)]. We therefore performed first-principlescalculations and found that, under certain circumstances, a pair of oxygen atoms replacing nitrogen atoms in GaN created deepstates in the bandgap, with slight displacements, similar to DX centers; this substitution could be one of the origins of deep states inGaN MOS interfaces.© 2026 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited. This is an open accessarticle distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2162-8777/ae6689]Manuscript submitted February 12, 2026; revised manuscript received April 22, 2026. Published May 12, 2026.Improving energy efficiency in electric systems such as invertorsand convertors is an important issue from an energy-savingperspective, and transistors based on wide-bandgap semiconductorscontribute to the solution to this problem.1,2 Gallium nitride (GaN)has a relatively wide bandgap of 3.4 eV and has been used inelectronic devices to decrease their energy losses.3–6 Among GaNelectronic devices, normally-on-type devices that utilize an AlGaN/GaN heterostructure were developed as early as the 1990s and havedisplayed excellent performance.7 Some electric systems, however,require normally-off-type devices for safety reasons, and suchdevices incorporating GaN have been developed since the2000s.8,9 Though various normally-off-type devices have beenreported, the metal-oxide-semiconductor (MOS) structure plays akey role in such devices because it offers advantages such as highinput impedance, high switching speed, and a large safe operatingarea.10The interface state density (Dit) is one of the most importantproperties in MOS devices because it reflects the carrier trap densitybetween the oxide and semiconductor.11 GaN MOS interfaces havebeen known to have a low Dit near the conduction band12; however,the Dit suddenly increases as the energy approaches the valenceband.13–17 The high Dit deep in the bandgap should be reduced toimprove the device performance18; however, the reason for this highDit remains unclear. We previously found that thin crystallinegallium oxide layers exist at the interface between the oxide andGaN and that the properties of the layers can be modified using anewly developed method referred to as the dummy process.19 Wethen confirmed that the dummy process restored the disorderedatomic arrangement of oxygen and nitrogen in the crystalline galliumoxide layers at the interface in GaN MOS capacitors to some extentand presumed that the improvement of the interfacial-layer crystal-linity resulted in the reduction of the flat-band voltage (Vfb) shiftsafter positive-bias stressing (PBS).20 Therefore, whether the dummyprocess has a positive effect on the Dit deep in the bandgap is aninteresting topic for investigation.In this report, we used a sub-bandgap photo-assisted capacitance-–voltage (C–V) technique and studied the Dit deep in the bandgap ofGaN MOS capacitors. As a result, we found that the dummy processdid not substantially reduce this Dit, contrary to our expectations.Meanwhile, we recently observed oxygen atoms in positionsproximate to nitrogen sites in MOS interface regions (at depthsgreater than ∼1.0 nm), with the GaN crystal being maintained in thesame structure.20 In addition, an oxygen donor impurity in III–Vnitrides has been reported to create deep levels in the bandgap undercertain conditions.21–30 Therefore, the observed oxygen atoms inpositions proximate to nitrogen sites in GaN MOS interfaces may berelated to the higher Dit deep in the bandgap of GaN MOScapacitors. Given this consideration, we conducted first-principlescalculations and revealed that a pair of oxygen atoms replacingnitrogen atoms in a GaN crystal created deep states in the bandgap,with these oxygen sites slightly shifted from the original nitrogenpositions under certain circumstances, similar to DX centers, whichhave been thoroughly studied, especially in AlxGa1−xAs.31 This pairof oxygen atoms replacing nitrogen atoms in GaN could be one ofthe origins of the experimentally observed deep states in GaN MOSinterfaces.ExperimentalFor sub-bandgap photo-assisted C–V measurements, we investi-gated two types of samples: Pt/Al2O3/n-GaN MOS capacitorsfabricated using a standard process and MOS capacitors with thesame architecture but fabricated using the dummy process. Aschematic of the devices is shown in Fig. 1; the details of the devicefabrication and measurement procedures have been describedelsewhere.16 Note that trimethylaluminum (TMA) pre-pulses werenot used in the atomic layer deposition (ALD) process and that thefollowing recipe was used: H2O pulse, Ar purge, TMA pulse, and Arpurge.The atomic-scale Al2O3/n-GaN MOS interface analyses wereperformed by cross-sectional high-angle annular dark field (HAADF)aberration-corrected scanning transmission electron microscopy(STEM) and energy-dispersive X-ray spectroscopy (EDS) at anincident-electron-beam voltage of 200 kV using a Spectra Ultra S/TEM (Thermo Fisher Scientific). Notably, attention was paid to thepreparation of STEM samples to reduce variations in resolution due tochanges in sample thickness during STEM–EDS observations. Wesystematically investigated methods to control TEM sample thicknesszE-mail: IROKAWA.Yoshihiro@nims.go.jp; usami@asms.co.jp; NABATAME.Toshihide@nims.go.jpECS Journal of Solid State Science and Technology, 2026 15 055002 aaahttps://orcid.org/0000-0002-6531-4356https://orcid.org/0009-0002-3188-7380https://orcid.org/0000-0003-2023-8158https://orcid.org/0000-0003-3548-1951https://orcid.org/0000-0002-5973-0230https://orcid.org/0000-0001-8321-9822https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1149/2162-8777/ae6689https://doi.org/10.1149/2162-8777/ae6689mailto:IROKAWA.Yoshihiro@nims.go.jpmailto:usami@asms.co.jpmailto:NABATAME.Toshihide@nims.go.jpmailto:NABATAME.Toshihide@nims.go.jphttps://crossmark.crossref.org/dialog/?doi=10.1149/2162-8777/ae6689&domain=pdf&date_stamp=2026-05-12uniformity using a focused-ion-beam (FIB)–scanning electron micro-scopy (SEM) dual-beam system, including techniques described in ourprevious reports,32,33 and gained a comprehensive understanding ofFIB damage to GaN. On the basis of these techniques and insights, weprepared TEM samples with a uniform 30 nm-thickness whileminimizing FIB-induced damage.The first-principles methods are based on density functional theory(DFT) within the generalized gradient approximation (GGA) using thePerdew–Burke–Ernzerhof for solids (PBEsol) exchange-correlationenergy functional34; the calculations were conducted using thePHASE/0 package based on the projector augmented wave method.35The wave functions were expanded in the plane waves up to the kineticenergy cutoff of 340 eV, and all structural models were fully relaxeduntil the atomic forces were less than 5.1× 10−3 eV Å−1. Brillouin zoneintegrations were carried out using k-point meshes of 6 × 6 × 4 for apure GaN Bravais lattice containing four atoms (two Ga and two N) and2 × 2 × 2 for supercells. All the calculations were performed with thelattice constants kept at fixed values of a = 3.20140 Å and c =5.21598 Å, which were determined by calculation for pure GaN. Inaddition, all of the calculations in this report were performed withoutconsidering spin polarization. Notably, we confirmed that the calcula-tion with spin polarization yielded an electronic state identical to thatobtained from the calculation without spin polarization. All of thecalculations were performed under a neutral charge condition (withoutinserting any charge). We used the following configurations as thevalence electrons in pseudopotential for gallium, nitrogen, and oxygen:3d104s24p1, 2s22p3, and 2s22p4, respectively.Results and DiscussionFigures 2a and 2b show the sub-bandgap photo-assisted C–Vcharacteristics of Pt/Al2O3/n-GaN MOS capacitors fabricated using astandard process and the dummy process, respectively. The incidentphoton energies are relatively large (2.6, 3.0, and 3.3 eV), andelectrons trapped in interfaces at deeper bandgap energies (lower halfof the bandgap) were studied. As shown in Fig. 2, after the deviceswere exposed to light, all of the C–V curves shifted in the negativevoltage direction while almost maintaining their shapes; in addition,larger incident energies led to greater shifts in the initial curves. Asdiscussed elsewhere,16 these C–V characteristics reflect donor-typeinterface trap behavior, where traps act as positive charges after therelease of trapped electrons. Notably, to avoid data-analysis diffi-culties associated with UV light, we used sub-bandgap light in thepresent study, where the photon energy was less than the bandgapenergy of GaN (3.4 eV). Under this condition, holes are notgenerated. In addition, we speculate that the effects of electronexcitation from the valence band to interface traps and/or stepwiseexcitation of electrons via bulk GaN defect levels (from the valenceband) to interface traps are not so significant in our currentexperiments for the following two reasons: First, if the above-mentioned electron transitions occurred, holes would be generated,possibly resulting in changes in C–V curve shapes. However, theC–V curves simply shifted in the negative voltage direction afterlight irradiation, with their shapes being almost maintained (Fig. 2).Second, the results obtained in our current experiments are consistentwith those in previous reports, where the methods differed fromours13–15; that is, the Dit values near the valence band edge weremuch higher than those near the conduction band edge at theAl2O3/GaN interface. Incidentally, the Vfb values in Fig. 2 saturatedwithin ∼20 min of irradiation for each irradiation energy (2.6, 3.0,and 3.3 eV), suggesting that electron transitions with long timeconstants do not occur in our current experiments. Figures 3a and 3bshow the normalized Vfb as a function of the incident photon energyfor Pt/Al2O3/n-GaN MOS capacitors fabricated using a standardprocess and the dummy process and the Dit distribution calculated onthe basis of the data in Fig. 3a, respectively. In Fig. 3a, Vfb measuredin the dark was set to be zero, and changes with respect to the Vfb inthe dark are plotted along the ordinate. In Fig. 3b, the average Ditvalues between two neighboring incident photon energies are plottedat the middle points of these two incident photon energies along theabscissa. Notably, three horizontal dotted lines between two neigh-boring incident photon energies—0 to 2.6 eV, 2.6 to 3.0 eV, and 3.0to 3.3 eV—represent the energy ranges where each average Dit wascalculated. The details of the calculation are found elsewhere.16 Asshown in Fig. 3b, the Dit values for the samples fabricated using thetwo processes do not substantially differ; that is, the Dit values atbandgap energies deeper than the mid-gap level are on the order oflow-to-mid-1012 cm−2 eV−1 and gradually increase as Ec − Etapproaches the valence band energy of 3.4 eV, irrespective of theFigure 1. Schematic of a Pt/Al2O3/n-GaN MOS capacitor investigated usingsub-bandgap photo-assisted C–V measurements. (ALD = atomic layerdeposition).Figure 2. Sub-bandgap photo-assisted C–V characteristics of Pt/Al2O3/n-GaN MOS capacitors fabricated using (a) standard process and (b) dummy process. Theincident photon energies are 2.6, 3.0, and 3.3 eV.ECS Journal of Solid State Science and Technology, 2026 15 055002fabrication process. We previously confirmed that the dummyprocess recovered the atomic arrangement of oxygen and nitrogenin the crystalline gallium oxide interfacial layers (at depths less than∼1.0 nm) in GaN MOS structures to some extent, which may berelated to the previously reported reduction of the Vfb shifts afterPBS.20 Therefore, the dummy process was expected to reduce the Ditdeep in the bandgap. Contrary to our expectation, however, thedummy process did not substantially reduce the Dit at bandgapenergies deeper than the mid-gap level. Incidentally, the Dit valuesfor samples prepared using the standard and dummy processes werefound to be on the order of 1011 cm−2 eV−1 at bandgap energies lessthan 0.6 eV, and these Dit values were similar, as we previouslyreported.19We recently observed oxygen atoms in positions proximate tonitrogen sites in GaN MOS interface regions (at depths greater than∼1.0 nm), with the GaN crystal being maintained in the samestructure.20 Figure 4 shows a HAADF-STEM image (Fig. 4a), thecorresponding EDS element map of gallium and oxygen (Fig. 4b),and the normalized EDS signal intensity line profile for gallium,nitrogen, and oxygen (Fig. 4c) for the dummy-processed sample. InFig. 4, the first to eighth gallium layers from Al2O3 are indicated.(Here, the outermost gallium atomic plane observed by HAADF-STEM imaging is numbered “1”.) In the EDS element map (Fig. 4b),larger spherical areas colored light-orange represent gallium atoms,whereas blurry smaller spherical regions colored red show oxygenatoms. Note that some oxygen atoms occupy positions proximate tonitrogen sites in the gallium-polar GaN structure, as indicated by thewhite arrows. In addition, according to the normalized EDS signalintensity line profile (Fig. 4c), at depths greater than ∼1.0 nm, theoxygen signals and nitrogen signals have peaks at approximately thesame depths, as indicated by the green-colored arrows; these resultsindicate that some of the oxygen atoms might substitute at thenitrogen sites of the GaN crystal structure, with slight displacements,as we reported previously.20 Note that the EDS data contain an errorof a few atomic percent as a technical limitation; the map and profileshown in Figs. 4b and 4c are based on EDS signal intensity toprevent the loss of positional information for the EDS signal as muchas possible. To ensure that some of the oxygen atoms occupypositions proximate to nitrogen sites, we conducted observations atmultiple locations on several samples.20,36In addition to the above-mentioned atomic-scale interface struc-tural analyses, first-principles calculations have shown that oxygendonor impurities in III–V nitrides create deep levels in the bandgapunder certain conditions,21–25 specifically revealing the followingtwo issues: First, an oxygen donor in GaN did not generally form adeep state. Second, an oxygen donor in AlxGa1−xN and GaN underpressure did form deep states. (DX-like behavior of oxygen in GaNunder pressure was also experimentally observed.26–29) However,Figure 3. (a) Normalized Vfb as a function of incident photon energy for Pt/Al2O3/n-GaN MOS capacitors fabricated using a standard and the dummy processes.Here, Vfb measured in dark is set to be zero, and changes with respect to the Vfb in the dark are plotted along the ordinate. (b) Calculated Dit distribution based onthe data in (a). The average Dit values between two neighboring incident photon energies are plotted at the middle points of these two incident photon energiesalong the abscissa. Three horizontal dotted lines between two neighboring incident photon energies—0 to 2.6 eV, 2.6 to 3.0 eV, and 3.0 to 3.3 eV—represent theenergy ranges where each average Dit was calculated.Figure 4. (a) HAADF-STEM image. (b) Corresponding EDS element map of gallium and oxygen. Larger spherical areas colored light-orange represent galliumatoms, whereas blurry smaller spherical regions colored red show oxygen atoms. The white arrows indicate the positions where oxygen atoms occupy positionsproximate to nitrogen sites in the gallium-polar GaN structure near the Al2O3/GaN interface. (c) Normalized EDS signal intensity line profile for gallium (lightorange), nitrogen (blue), and oxygen (red) for the dummy-processed sample. The first to eighth gallium layers from Al2O3 are indicated. (Here, the outermostgallium atomic plane observed by HAADF-STEM image is numbered “1”.).ECS Journal of Solid State Science and Technology, 2026 15 055002these results were reported more than 20 years ago, and recentadvances in computers and first-principles calculation methods mayenable us to obtain more information regarding oxygen donors inGaN. In addition, the previous research mainly focused on the role oflow-concentration oxygen in GaN; the role of high-concentrationoxygen, which we have observed, remains unclear. Therefore, theoxygen atoms we observed proximate to nitrogen sites in GaN MOSinterface regions (at depths greater than ∼1.0 nm) may be related tothe higher Dit deep in the bandgap of GaN MOS capacitors even ifGaN is not under pressure. On the basis of this consideration, wecarried out first-principles calculations.We first carried out the calculations for pure GaN and GaNsupercells with a single oxygen donor replacing a nitrogen atom inGaN to ensure that our calculations worked well. Figures 5a and 5bshow the density of states (DOS) and the energy band structure ofpure GaN, respectively. In Fig. 5, the Fermi energy (EF) is defined asthe top of the valence band in the presence of a bandgap; the states ingray areas are occupied by electrons. In addition, the conductionband is represented by dotted lines. (The same labeling scheme isused in subsequent DOS figures in this report.) The data shown inFigs. 5a and 5b indicate that GaN has a direct bandgap of ∼1.7 eV,which is smaller than the actual bandgap of GaN (3.4 eV). Notably,DFT within the GGA typically underestimates bandgap values,37 andwe do not discuss the calculated bandgap values in this report. Wealso obtained the optimized lattice constants for GaN (a = 3.20140 Åand c = 5.21598 Å), which are close to the experimentally obtainedvalues (e.g., a = 3.18926 Å and c = 5.18523 Å for bulk GaNfabricated by hydride vapor phase epitaxy).38 Figures 5c and 5dshow the DOS for a 3 × 3 × 2 hexagonal GaN supercell and a2 × 3 × 2 orthorhombic GaN supercell containing 72 and 96 atoms,respectively, with a single oxygen donor replacing a nitrogen atom inGaN. As shown in both figures, the conduction bands have tail statesbelow 0 eV that are filled with electrons, which means that a singleoxygen donor replacing a nitrogen atom in GaN creates shallowstates, consistent with previous reports.39,40We next replaced two nitrogen atoms in a 3 × 3 × 2 hexagonalGaN supercell containing 72 atoms, corresponding to a ∼2.8%oxygen concentration in GaN. The positions of the replaced nitrogenatoms correspond to those of two nitrogen atoms in a four-atomprimitive cell of GaN and are located in two adjacent nitrogen planesperpendicular to the [0001] direction. Note that no previous studieshave considered the substitution of two oxygen atoms into GaN.Figures 6a–6c show the atomic arrangements after the structuraloptimization was performed. Here, Figs. 6b and 6c show magnifiedimages of the upper and lower oxygen atoms in Fig. 6a, respectively,and Fig. 6d shows the DOS for the supercell. As shown in Fig. 6d,deep levels are formed in this particular case. Figures 6a–6c showthat the two oxygen atoms are in different positions from thoseoccupied by the original nitrogen atoms; that is, both of theoxygen atoms move far away from each other, breaking theirgallium–oxygen bonds, which are shown by dotted lines inFigs. 6b and 6c. Notably, a large displacement of a donor atomwas previously reported as one of the characteristics of DX centers21;therefore, the oxygen-atom behavior observed in Figs. 6a–6c issimilar to that of DX centers. Our results show that two oxygendonors create deep states without pressure on GaN, unlike the resultsof previous studies, which considered substitution by only oneoxygen donor.21–24 Figure 7 shows contour plots of the chargeFigure 5. (a) Calculated DOS for pure GaN. Here, EF is defined as the top of the valence band in the presence of a bandgap, and the states are occupied byelectrons in gray-colored areas. The conduction band is indicated by dotted lines. (The same labeling convention applies in the following DOS figures in thisreport.) (b) Calculated energy band structure of pure GaN. (c) Calculated DOS for a 3 × 3 × 2 hexagonal GaN supercell containing 72 atoms, with a singleoxygen donor replacing a nitrogen atom in GaN. (d) Calculated DOS for a 2 × 3 × 2 orthorhombic GaN supercell containing 96 atoms, with a single oxygendonor replacing a nitrogen atom in GaN.ECS Journal of Solid State Science and Technology, 2026 15 055002density in deep states (energy range from −1 to 0 eV in Fig. 6d)around two oxygen atoms (Fig. 6a); isosurface values of 0.025 and0.005 e/Bohr3 are displayed in Figs. 7a and 7b, respectively. Asshown in Fig. 7, the electron density around the two oxygen atomsis high and the trapped charges amount to approximately twoelectrons. Note that this calculation was performed under a neutralcharge condition (i.e., without the insertion of any charge), unlikethe calculations in previous reports21–24; that is, in the previousreports, the deep donor formation process was described by thefollowing reaction21:Figure 6. (a) 3 × 3 × 2 hexagonal GaN supercell after the structural optimization; the supercell contains 72 atoms with two nitrogen atoms replaced withoxygen, corresponding to a ∼2.8% oxygen concentration in GaN. The positions of the replaced nitrogen atoms correspond to those of two nitrogen atoms in afour-atom primitive cell of GaN and are located in two adjacent nitrogen planes perpendicular to the [0001] direction. (b) Magnified image of the upper oxygenatom in (a). The broken gallium–oxygen bond is shown as a dotted line. (c) Magnified image of the lower oxygen atom in (a). The broken gallium–oxygen bond isshown as a dotted line. (d) Calculated DOS for the supercell shown in (a).Figure 7. Contour plots of the charge density in deep states (energy range from −1 to 0 eV in Fig. 6d) around two oxygen atoms, as shown in Fig. 6a; isosurfacevalues of 0.025 e/Bohr3 (a) and 0.005 e/Bohr3 (b) are displayed.ECS Journal of Solid State Science and Technology, 2026 15 055002+ [ ]+d DX d2 , 10where d is a substitutional shallow impurity, DX represents a broken-bond (BB) state, and the superscripts specify the charge states. Asshown in Eq. 1, the DX is assumed to acquire electrons from theother impurity.Meanwhile, we investigated how the arrangement of the twooxygen atoms in the same 3 × 3 × 2 hexagonal GaN supercellcontaining 72 atoms affects the DOS and the stability. First, wereplaced two nitrogen atoms located in the closest position in the samecrystal plane perpendicular to the [0001] direction; Figs. 8a and 8cshow the atomic arrangement after the structural optimization andthe DOS for the supercell, respectively. As shown in Fig. 8a, the twoinserted oxygen atoms occupy similar positions to the originalnitrogen atoms after the structural optimization, unlike those inFig. 6a; in addition, as shown in Fig. 8c, the conduction band has tailstates below 0 eV that are filled with electrons, creating shallowstates, as in the case of single-oxygen-atom insertion (Fig. 5c and5d). Second, we replaced two nitrogen atoms located at the farthestpositions from each other, considering periodic boundary conditions;Figs. 8b and 8d show the atomic arrangement after the structuraloptimization and the DOS for the supercell, respectively. As shownin Figs. 8b and 8d, the two inserted oxygen atoms occupy similarlocations to the original nitrogen atoms and deep states are notformed, as in the case shown in Fig. 8a and 8c. With respect to thetotal energy, the atomic arrangement shown in Fig. 6a exhibits thelowest, whereas those shown in Figs. 8a and 8b are 73.5 and106 meV higher, respectively, than that shown in Fig. 6a. In brief,the results obtained from Figs. 6–8 show that the atomic arrangementin Fig. 6 is the most stable and that two oxygen atoms replacingnitrogen atoms in an arrangement shown in Fig. 6 create deep statesin the bandgap. These deep states trap electrons, where the distortedlattice stemming from the oxygen displacements is likely stabilizedby the trapped charges and appears to result in the formation of thesedeep states. These deep states shown in Fig. 6d could be one of theorigins of the large Dit at bandgap energies deeper than the mid-gaplevel (Fig. 3b). Note that, in the 72-atom system, we confirmed thatno energy barrier exists for the transformation between a shallowstate and a deep state. Incidentally, another example of a stabilizedpair of dopant atoms in close proximity can be seen in diamond.41We subsequently investigated the effects of the oxygen concen-tration in GaN. First, we replaced two nitrogen atoms in a 2 × 3 × 2orthorhombic GaN supercell containing 96 atoms, corresponding to a∼2.1% oxygen concentration in GaN. This oxygen concentration islower than that in the previously discussed model (∼2.8%). Theatomic arrangements in Figs. 9a and 9b correspond to those inFigs. 6a and 8a, respectively, and the DOS corresponding to Figs. 9aand 9b is shown in Figs. 9c and 9d, respectively. As shown inFigs. 9a and 9c, the two inserted oxygen atoms are displaced, similarto those in Fig. 6a, and deep states are formed. However, as shown inFig. 9b and 9d, the two inserted oxygen atoms occupy similar sites tothe original nitrogen atoms, and deep states are not formed, as in thecase in Figs. 8a and 8c. With respect to the total energy, the atomicarrangement in Figs. 9b is 53.2 meV lower than that in Fig. 9a,whereas the atomic arrangement in Fig. 9a is locally stable. Second,we replaced two nitrogen atoms in a 4 × 4 × 3 hexagonal GaNsupercell containing 192 atoms, corresponding to a ∼1.0% oxygenconcentration in GaN. Notably, the oxygen concentration is evenlower. The atomic arrangements in Figs. 10a and 10b correspond toFigure 8. (a) 3 × 3 × 2 hexagonal GaN supercell after the structural optimization, containing 72 atoms with two nitrogen atoms replaced with oxygen,corresponding to a ∼2.8% oxygen concentration in GaN. The replaced nitrogen atoms are located in the closest position in the same crystal plane perpendicular tothe [0001] direction. (b) 3 × 3 × 2 hexagonal GaN supercell after the structural optimization, containing 72 atoms with two nitrogen atoms replaced with oxygenatoms, corresponding to a ∼2.8% oxygen concentration in GaN. The replaced nitrogen atoms are located in the farthest positions from each other, consideringperiodic boundary conditions. (c) Calculated DOS for the supercell shown in (a). (d) Calculated DOS for the supercell shown in (b).ECS Journal of Solid State Science and Technology, 2026 15 055002those in Figs. 6a and 8b, respectively, and the DOS in Figs. 10a and10b is shown in Figs. 10c and 10d, respectively. Figure 10c showsthat deep states are no longer formed, even for the same atomicarrangement as in Figs. 6a and 9a where the deep states are actuallyformed. In addition, the total energy for the atomic arrangement inFig. 10a is 68.6 meV higher than that for the arrangement inFig. 10b. In summary, the results obtained from Figs. 9 and 10 arethat two oxygen atoms replacing nitrogen atoms do not create deepstates (with a stable energy) in any arrangement when the oxygenconcentration is low.At this point, we are uncertain whether the oxygen-induced deepstates studied here are identical to DX centers formerly investigatedin AlxGa1−xAs in the following three aspects: First, an energy barrierfor the transformation between a shallow state and a deep state,which is an important characteristic feature of the DX center,42 doesnot exist in our 72-atom system calculations. (Two inserted oxygenatoms are displaced from the original nitrogen atom positions withno energy barrier, resulting in the atomic arrangement shown inFig. 6a). Second, the displacements of the oxygen atoms appear to berelatively small in our calculations (e.g., the upper oxygen atom doesnot move beyond the plane formed by three gallium atoms bondingto the oxygen (Fig. 6b), unlike an α-broken-bond-type DX centerdescribed in a previous report21). Third, the charge states of the twoinserted donors differ, as previously mentioned. Furthermore, theoxygen concentration in GaN clearly plays a critical role in theformation of oxygen-induced deep states. Notably, the relationshipbetween the oxygen concentration in GaN and the formation of deepstates was suggested in previous reports25,30; however, the details areunclear even now. A similar phenomenon in which the formation ofdonor-induced deep states depends on the donor concentration wasreported in a study of Si-doped GaAs based on experimentalresults.43 Our current understanding of why deep state formationstrongly depends on the oxygen concentration is as follows: To formdeep states, a certain amount of oxygen displacement in anenergetically stabilized state is critical, as previously reported21;some negative charges are required to stabilize such oxygendisplacements. We speculate that the position and concentration ofintroduced oxygen atoms would be strongly related to the above-mentioned issues.Throughout this report, we have investigated deep states in GaNMOS interfaces both experimentally and theoretically and haverevealed that a pair of oxygen atoms replacing nitrogen atoms inGaN creates deep states in the bandgap, with slight displacementsunder certain circumstances. However, the created deep states existonly in the middle of the bandgap (Fig. 6d) and do not explain theexperimentally observed Dit distribution shown in Fig. 3b, where thedensity of electron traps near the valence band is even higher thanthat in the middle of the bandgap. To consider this issue, weinspected our calculation model. On the basis of our previousresearch,20 the Al2O3/GaN interface consists of Al2O3, a highlyoriented crystalline GaOxNy interfacial layer, and pure GaN (here,Si-doped GaN), as shown in Fig. 11. The GaOxNy layer exhibits agraded composition; that is, the oxygen content x decreases towardthe bulk GaN region, whereas the nitrogen content y increasestoward the bulk GaN region. In addition, the gallium atoms occupythe same positions as those in bulk GaN, whereas some oxygen andnitrogen atoms are in irregular positions near the Al2O3 (at depthsshallower than ∼1.0 nm). However, at depths greater than ∼1.0 nm,the GaOxNy interfacial layer has a similar crystal structure to bulkGaN, with oxygen atoms in positions proximate to nitrogen sites.The GaOxNy interface layer is formed in GaN as a result of oxygendiffusion. An EDS signal associated with this diffused oxygen can beFigure 9. (a) 2 × 3 × 2 orthorhombic GaN supercell containing 96 atoms, corresponding to a ∼2.1% oxygen concentration in GaN. The atomic arrangementcorresponds to that in Fig. 6a. (b) 2 × 3 × 2 orthorhombic GaN supercell containing 96 atoms, corresponding to a ∼2.1% oxygen concentration in GaN. Theatomic arrangement corresponds to that in Fig. 8a. (c) Calculated DOS for the supercell shown in (a). (d) Calculated DOS for the supercell shown in (b).ECS Journal of Solid State Science and Technology, 2026 15 055002detected to a depth of ∼2.5 nm.20 Given the detection limit of EDS (afew atomic percent), oxygen could diffuse into the GaN more deeplyat dopant-level concentrations. Since the GaOxNy layer is composi-tionally graded and has a high degree of crystallinity, its compositionand crystal structure continuously change in the depth directiontowards those of bulk crystalline GaN. We therefore speculate thatits interface with GaN has a low defect density. In our calculations,the oxygen concentration is a few atomic percent, with two oxygenatoms replacing two nitrogen atoms in a perfect GaN crystal; thesecircumstances approximately reflect those in less defective deeperregions of the GaOxNy layer (at a depth of ∼2.5 nm in Fig. 11). Inaddition, we speculate that the Al2O3/GaOxNy interface also has alow defect density because gallium atoms in the GaOxNy layeroccupy the same positions as those in bulk GaN. We thereforebelieve that the proposed model, which considers only defects in theGaOxNy layer, is realistic for GaN MOS systems, because both theAl2O3/GaOxNy and GaOxNy/GaN interfaces are considered to have alow defect density. Moreover, in the case of SiO2/GaN MOSinterfaces, we observed oxygen diffusion into GaN,18 which possiblyeven occurred unintentionally by natural oxidation.18,36 We thereforeconsider that diffusion of oxygen is a universal phenomenon for GaNsurfaces and interfaces and that our defect formation mechanism isapplicable to any GaN MOS system. Based on previous studies ondeep states created by oxygen donors in GaN,21–25 we initiallysubstituted two oxygen atoms at nitrogen positions in the presentstudy. In the present study, calculation conditions such as the degreeof crystallinity and the oxygen concentration were chosen torepresent those at a depth of ∼2.5 nm in Fig. 11. However, in theGaOxNy interface layer, the oxygen concentration increases withdecreasing distance from the Al2O3. For example, the oxygenconcentration is ∼40% at a depth of 1.0 nm,20 which is much higherthan that in our current calculations. In addition, we also observedthat oxygen atoms were in irregular positions in shallower parts ofthe GaOxNy layer, even in samples prepared with the dummyprocess.20 As explained earlier, oxygen displacement is closelyrelated to the deep states; irregular positions such as interstitial sitescan be regarded as having much larger displacements of oxygenatoms from nitrogen sites than that obtained in the present study.Therefore, we consider that calculations involving oxygen positionsand concentrations might result in the observation of deeper states inthe bandgap. Such calculations would reflect more defective shal-lower regions of the GaOxNy interfacial layer, unlike our presentstudy considering less defective deeper regions of the interfaciallayer. In addition, nitrogen atoms in irregular sites might also createdeep states, which we did not consider in the present study. Giventhis perspective, the reason for the higher Dit deep in the bandgap ofGaN MOS capacitors (Fig. 3b) can be speculated to be as follows: asmentioned above, we previously confirmed that the dummy processimproved the crystallinity of the GaOxNy interfacial layer to someFigure 10. (a) 4 × 4 × 3 hexagonal GaN supercell containing 192 atoms, corresponding to ∼1.0% oxygen concentration in GaN. The atomic arrangementcorresponds to that in Fig. 6a. (b) 4 × 4 × 3 hexagonal GaN supercell containing 192 atoms, corresponding to a ∼1.0% oxygen concentration in GaN. The atomicarrangement corresponds to that in Fig. 8b. (c) Calculated DOS for the supercell shown in (a). (d) Calculated DOS for the supercell shown in (b).Figure 11. Schematic of the Al2O3/GaN interface.ECS Journal of Solid State Science and Technology, 2026 15 055002extent,20 which may be reflected in the slightly lower Dit values nearthe valence band for the sample produced using the dummy process(Fig. 3b). However, recovery of the crystallinity was incomplete;some oxygen and nitrogen atoms were left in irregular sites, whichmight be related to the large Dit at bandgap energies deeper than themid-gap level. We are also aware that our model is an approximationand does not reflect the Al2O3/GaN interface correctly, which couldalso be the reason why the calculated deep states exist only in themiddle of the bandgap. In summary, to resolve the contradictionbetween the experimentally obtained deep-state distribution and thecalculated deep states, more extensive calculations that take intoaccount different oxygen and nitrogen positions, with more than twooxygen atoms introduced, and/or using hybrid functionals would benecessary in future studies.ConclusionsWe used a sub-bandgap photo-assisted C–V technique and studiedthe Dit deep in the bandgap of GaN MOS capacitors. As a result, wefound that the dummy process did not substantially reduce this Ditvalue, contrary to our expectations. However, we directly observed thatsome oxygen atoms occupy positions proximate to nitrogen sites nearthe Al2O3/GaN interface. In addition, our first-principles calculationsrevealed that, under certain circumstances, a pair of oxygen atomsreplacing nitrogen atoms in GaN created deep states in the bandgap,with these oxygen sites being slightly shifted from the original nitrogenpositions, similar to DX centers. These oxygen-induced deep statesmight be one of the origins of the observed higher Dit at deeperbandgap energies in GaNMOS capacitors. The elucidation of the deep-state formation mechanism is an important subject for future studies,and more detailed calculations will be necessary to explain theexperimentally observed Dit distribution more correctly; that is, thepresent calculations only considered less defective deeper regions ofthe highly crystalline GaOxNy interfacial layer. Therefore, calculationscorresponding to more defective shallower regions of the interfaciallayer could resolve the contradiction between the experimentallyobtained deep state distribution and the calculated deep states.Finally, in this report, we introduce the possibility that GaN itselfcould be the origin of the deep states in GaN MOS interfaces byincorporating oxygen. The incorporated oxygen could change theGaN surface/interface properties; in fact, surface property changeshave been reported for MBE-grown GaN upon exposure to air,where the surface EF drastically shifted toward the conduction bandedge after air exposure.44–46 In this case, we speculate that someoxygen atoms replace nitrogen atoms, acting as shallow donors, atsomewhat deeper regions where the oxygen concentration is low.This could also lead to unintentional realization of buried-channeldevices in GaN MOS field-effect transistors, which could be one ofthe reasons why such devices exhibit relatively high mobility.AcknowledgmentsThis research was supported in part by the Ministry of Education,Culture, Sports, Science and Technology, Japan (NEXT), through its“Creation of Innovative Core Technology for Power Electronics”Program Grant Number JPJ009777, ARIM (JPMXP1223NM5088),and JSPS KAKENHI Grant Numbers 23K03949. A part of this workwas supported by the Electron Microscopy Unit, National Institutefor Materials Science (NIMS). The authors thank Kyoko Suzuki forher technical support with the STEM observations. The authorsthank Dr Keisuke Masuda for fruitful discussions.ORCIDYoshihiro Irokawa m https://orcid.org/0000-0002-6531-4356Mamoru Usami m https://orcid.org/0009-0002-3188-7380Jun Uzuhashi m https://orcid.org/0000-0003-2023-8158Tadakatsu Ohkubo m https://orcid.org/0000-0003-3548-1951Toshihide Nabatame m https://orcid.org/0000-0002-5973-0230Yasuo Koide m https://orcid.org/0000-0001-8321-9822References1. T. Kachi, Appl. Phys. Express, 19, 010103 (2026).2. T. Kimoto and J. A. Cooper, Fundamentals of Silicon Carbide Technology (Wiley,Singapore) 445 (2014).3. S. J. Pearton, F. Ren, A. P. Zhang, and K. P. Lee, Mater. Sci. Eng. R, 30, 55 (2000).4. T. Oka, Jpn. J. Appl. Phys., 58, SB 0805 (2019).5. K. Ito, S. Iwasaki, K. Tomita, E. Kano, N. Ikarashi, K. Kataoka, D. Kikuta, andT. Narita, Appl. Phys. Express, 16, 074002 (2023).6. Y. Ichikawa, K. Ueno, T. Kondo, R. Tanaka, S. Takashima, and J. Suda, Jpn. J.Appl. Phys., 63, 02SP31 (2024).7. R. Quay, Gallium Nitride Electronics (Springer, Berlin) 71 (2008).8. S. Jang et al., J. Electron. Mater., 35, 685 (2006).9. H. Kambayashi, Y. Niiyama, S. Ootomo, T. Nomura, M. Iwami, Y. Satoh, S. Kato,and S. Yoshida, IEEE Electron Device Lett., 28, 1077 (2007).10. B. J. Baliga, Modern power devices (Wiley, New York) 263 (1992).11. T. Kimoto and J. A. Cooper, Fundamentals of Silicon Carbide Technology (Wiley,Singapore) 219 (2014).12. H. C. Casey Jr, G. G. Fountain, R. G. Alley, B. P. Keller, and S. P. DenBaars, Appl.Phys. Lett., 68, 1850 (1996).13. C. M. Jackson, A. R. Arehart, E. Cinkilic, B. McSkimming, J. S. Speck, andS. A. Ringel, J. Appl. Phys., 113, 204505 (2013).14. R. D. Long et al., Appl. Phys. Lett., 103, 201607 (2013).15. X. Liu et al., Appl. Phys. Lett., 119, 015303 (2016).16. Y. Irokawa, T. Nabatame, K. Yuge, A. Uedono, A. Ohi, N. Ikeda, and Y. Koide,AIP Adv., 9, 085319 (2019).17. T. Kobayashi, K. Tominaga, M. Nozaki, T. Shimura, and H. Watanabe, Appl. Phys.Express, 17, 011003 (2024).18. Y. Irokawa, K. Mitsuishi, T. Izumi, J. Nishii, T. Nabatame, and Y. Koide, ECS J.Solid State Sci. Technol., 12, 055007 (2023).19. Y. Irokawa, T. Nabatame, T. Sawada, M. Miyamoto, H. Miura, K. Tsukagoshi, andY. Koide, ECS J. Solid State Sci. Technol., 13, 085003 (2024).20. J. Uzuhashi, Y. Irokawa, T. Nabatame, T. Ohkubo, and Y. Koide, ECS J. Solid StateSci. Technol., 14, 085001 (2025).21. C. H. Park and D. J. Chadi, Phys. Rev. B, 55, 12995 (1997).22. C. G. Van de Walle, Phys. Rev. B, 57, R2033 (1998).23. C. G. Van de Walle, C. Stampfl, and J. Neugebauer, J. Cryst. Growth, 189/190, 505(1998).24. C. G. Van de Walle, J. Neugebauer, C. Stampfl, M. D. McCluskey, andN. M. Johnson, Acta Phys. Pol. A, 96, 613 (1999).25. C. Liu and J. Kang, Opt. Mater., 23, 169 (2003).26. C. Wetzel, T. Suski, J. W. Ager III, E. R. Weber, E. E. Haller, S. Fischer,B. K. Meyer, R. J. Molnar, and P. Perlin, Phys. Rev. Lett., 78, 3923 (1997).27. C. Wetzel, J. W. Ager III, M. Topf, B. K. Meyer, H. Amano, and I. Akasaki,Physica B, 273-274, 109 (1999).28. C. Wetzel, H. Amano, I. Akasaki, J. W. Ager III, I. Grzegory, M. Topf, andB. K. Meyer, Phys. Rev. B, 61, 8202 (2000).29. C. Wetzel, H. Amano, I. Akasaki, J. W. Ager III, I. Grzegory, and B. K. Meyer,Physica B, 302-303, 23 (2001).30. T. W. Kang, C. S. Park, and T. W. Kim, Appl. Surf. Sci., 180, 81 (2001).31. P. M. Mooney, J. Appl. Phys., 67, R1 (1990).32. J. Uzuhashi and T. Ohkubo, Ultramicroscopy, 262, 113980 (2024).33. J. Uzuhashi, Y. Yao, T. Ohkubo, and T. Sekiguchi, Microscopy, 74, 279 (2025).34. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria,L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett., 100, 136406 (2008).35. T. Yamasaki, A. Kuroda, T. Kato, J. Nara, J. Koga, T. Uda, K. Minami, andT. Ohno, Comput. Phys. Commun., 244, 264 (2019).36. J. Uzuhashi, Y. Irokawa, T. Nabatame, Y. Koide, and T. Ohkubo, AIP Adv., 16,045004 (2026).37. D. S. Sholl and J. A. Steckel, Density Functional Theory (Wiley, New Jersey) 179(2009).38. V. Darakchieva, B. Monemar, and A. Usui, Appl. Phys. Lett., 91, 031911 (2007).39. W. M. Chen, I. A. Buyanova, M. Wagner, B. Monemar, J. L. Lindström, H. Amano,and I. Akasaki, MRS Internet J. Nitride Semicond. Res., 4, 514 (1999).40. R. Y. Korotkov and B. W. Wessels, MRS Internet J. Nitride Semicond. Res., 5, 301(2000).41. M. N. R. Ashfold, J. P. Goss, B. L. Green, P. W. May, M. E. Newton, andC. V. Peaker, Chem. Rev., 120, 5745 (2020).42. D. J. Chadi and K. J. Chang, Phys. Rev. B, 39, 10063 (1989).43. T. N. Theis, P. M. Mooney, and S. L. Wright, Phys. Rev. Lett., 60, 361 (1988).44. M. Kočan, A. Rizzi, H. Lüth, S. Keller, and U. K. Mishra, Phys. Stat. Sol. (b), 234,773 (2002).45. Y. Dong, R. M. Feenstra, and J. E. Northrup, J. Vac. Sci. Technol. B, 24, 2080(2006).46. D. Majchrzak, M. Grodzicki, P. Ciechanowicz, J. G. Rousset, E. Piskorska-Hommel, andD. Hommel, Acta Phys. Pol. A., 136, 285 (2019).ECS Journal of Solid State Science and Technology, 2026 15 055002https://orcid.org/0000-0002-6531-4356https://orcid.org/0009-0002-3188-7380https://orcid.org/0000-0003-2023-8158https://orcid.org/0000-0003-3548-1951https://orcid.org/0000-0002-5973-0230https://orcid.org/0000-0001-8321-9822https://doi.org/10.35848/1882-0786/ae393ahttps://doi.org/10.1016/S0927-796X(00)00028-0https://doi.org/10.7567/1347-4065/ab02e7https://doi.org/10.35848/1882-0786/ace33chttps://doi.org/10.35848/1347-4065/ad0c43https://doi.org/10.35848/1347-4065/ad0c43https://doi.org/10.1007/s11664-006-0121-1https://doi.org/10.1109/LED.2007.909978https://doi.org/10.1063/1.116034https://doi.org/10.1063/1.116034https://doi.org/10.1063/1.4808093https://doi.org/10.1063/1.4827102https://doi.org/10.1063/1.5098489https://doi.org/10.35848/1882-0786/ad120ahttps://doi.org/10.35848/1882-0786/ad120ahttps://doi.org/10.1149/2162-8777/acd1b4https://doi.org/10.1149/2162-8777/acd1b4https://doi.org/10.1149/2162-8777/ad6fd2https://doi.org/10.1149/2162-8777/adf3e3https://doi.org/10.1149/2162-8777/adf3e3https://doi.org/10.1103/PhysRevB.55.12995https://doi.org/10.1103/PhysRevB.57.R2033https://doi.org/10.1016/S0022-0248(98)00340-6https://doi.org/10.12693/APhysPolA.96.613https://doi.org/10.1016/S0925-3467(03)00049-1https://doi.org/10.1103/PhysRevLett.78.3923https://doi.org/10.1016/S0921-4526(99)00418-4https://doi.org/10.1103/PhysRevB.61.8202https://doi.org/10.1016/S0921-4526(01)00402-1https://doi.org/10.1016/S0169-4332(01)00320-8https://doi.org/10.1063/1.345628https://doi.org/10.1016/j.ultramic.2024.113980https://doi.org/10.1093/jmicro/dfaf006https://doi.org/10.1103/PhysRevLett.100.136406https://doi.org/10.1016/j.cpc.2019.04.008https://doi.org/10.1063/5.0322514https://doi.org/10.1063/1.2753122https://doi.org/10.1557/S1092578300002970https://doi.org/10.1557/S1092578300004427https://doi.org/10.1021/acs.chemrev.9b00518https://doi.org/10.1103/PhysRevB.39.10063https://doi.org/10.1103/PhysRevLett.60.361https://doi.org/10.1002/1521-3951(200212)234:3<773::AID-PSSB773>3.0.CO;2-0https://doi.org/10.1116/1.2214713https://doi.org/10.12693/APhysPolA.136.585