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Shigefusa F. Chichibu, Kohei Shima, Akira Uedono, Shoji Ishibashi, Hiroko Iguchi, Tetsuo Narita, Keita Kataoka, Ryo Tanaka, Shinya Takashima, Katsunori Ueno, Masaharu Edo, Hirotaka Watanabe, Atsushi Tanaka, Yoshio Honda, Jun Suda, Hiroshi Amano, Tetsu Kachi, [Toshihide Nabatame](https://orcid.org/0000-0002-5973-0230), [Yoshihiro Irokawa](https://orcid.org/0000-0002-6531-4356), [Yasuo Koide](https://orcid.org/0000-0001-8321-9822)

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[Impacts of vacancy complexes on the room-temperature photoluminescence lifetime of state-of-the-art GaN substrates, epitaxial layers, and Mg-implanted  layers](https://mdr.nims.go.jp/datasets/4190371a-58b3-4f9f-b344-f9757d096515)

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Impacts of vacancy complexes on the room-temperature photoluminescence lifetimes of state-of-the-art GaN substrates, epitaxial layers, and Mg-implanted layersViewOnlineExportCitationRESEARCH ARTICLE |  MAY 08 2024Impacts of vacancy complexes on the room-temperaturephotoluminescence lifetimes of state-of-the-art GaNsubstrates, epitaxial layers, and Mg-implanted layers Shigefusa F. Chichibu   ; Kohei Shima  ; Akira Uedono  ; Shoji Ishibashi  ; Hiroko Iguchi  ;Tetsuo Narita  ; Keita Kataoka  ; Ryo Tanaka  ; Shinya Takashima  ; Katsunori Ueno; Masaharu Edo;Hirotaka Watanabe; Atsushi Tanaka; Yoshio Honda  ; Jun Suda  ; Hiroshi Amano  ; Tetsu Kachi  ;Toshihide Nabatame  ; Yoshihiro Irokawa  ; Yasuo Koide J. Appl. Phys. 135, 185701 (2024)https://doi.org/10.1063/5.0201931 08 May 2024 10:00:43https://pubs.aip.org/aip/jap/article/135/18/185701/3290595/Impacts-of-vacancy-complexes-on-the-roomhttps://pubs.aip.org/aip/jap/article/135/18/185701/3290595/Impacts-of-vacancy-complexes-on-the-room?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0001-9558-1642javascript:;https://orcid.org/0000-0003-0967-141Xjavascript:;https://orcid.org/0000-0001-6224-4869javascript:;https://orcid.org/0000-0002-4896-3530javascript:;https://orcid.org/0000-0003-2714-4111javascript:;https://orcid.org/0000-0002-0849-360Xjavascript:;https://orcid.org/0000-0003-4855-4339javascript:;https://orcid.org/0000-0002-4058-7649javascript:;https://orcid.org/0000-0002-3212-4521javascript:;javascript:;javascript:;javascript:;javascript:;https://orcid.org/0009-0003-6591-847Xjavascript:;https://orcid.org/0000-0002-5453-4943javascript:;https://orcid.org/0000-0002-7598-2593javascript:;https://orcid.org/0000-0002-4300-5720javascript:;https://orcid.org/0000-0002-5973-0230javascript:;https://orcid.org/0000-0002-6531-4356javascript:;https://orcid.org/0000-0001-8321-9822https://crossmark.crossref.org/dialog/?doi=10.1063/5.0201931&domain=pdf&date_stamp=2024-05-08https://doi.org/10.1063/5.0201931https://servedbyadbutler.com/redirect.spark?MID=176720&plid=2372057&setID=592934&channelID=0&CID=872259&banID=521836438&PID=0&textadID=0&tc=1&scheduleID=2290742&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&matches=%5B%22inurl%3A%5C%2Fjap%22%5D&mt=1715162443681463&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0201931%2F19934522%2F185701_1_5.0201931.pdf&hc=44beda2156701e60ae66aa3cfb2042b0b600a521&location=Impacts of vacancy complexes on theroom-temperature photoluminescence lifetimesof state-of-the-art GaN substrates, epitaxial layers,and Mg-implanted layersCite as: J. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931View Online Export Citation CrossMarkSubmitted: 1 February 2024 · Accepted: 19 April 2024 ·Published Online: 8 May 2024Shigefusa F. Chichibu,1,a) Kohei Shima,1 Akira Uedono,2 Shoji Ishibashi,3 Hiroko Iguchi,4Tetsuo Narita,4 Keita Kataoka,4 Ryo Tanaka,5 Shinya Takashima,5 Katsunori Ueno,5 Masaharu Edo,5Hirotaka Watanabe,6 Atsushi Tanaka,6 Yoshio Honda,6 Jun Suda,6 Hiroshi Amano,6 Tetsu Kachi,6Toshihide Nabatame,7 Yoshihiro Irokawa,7 and Yasuo Koide7AFFILIATIONS1Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan2Division of Applied Physics, Faculty of Pure and Applied Science, University of Tsukuba, Tsukuba 305-8573, Japan3Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Scienceand Technology, Tsukuba 305-8568, Japan4Toyota Central R&D Labs., Inc., Nagakute, Aichi 490-1192, Japan5Advanced Technology Laboratory, Fuji Electric Co., Ltd., Hino, Tokyo 191-8502, Japan6Institute of Materials and Systems for Sustainability, Nagoya University, Nagoya 464-8601, Japan7National Institute for Materials Science, Tsukuba 305-0047, JapanNote: This paper is part of the special topic, Native Defects, Impurities and the Electronic Structure of CompoundSemiconductors: A Tribute to Dr. Wladyslaw Walukiewicz.a)Author to whom correspondence should be addressed: chichibulab@yahoo.co.jpABSTRACTFor rooting the development of GaN-based optoelectronic devices, understanding the roles of midgap recombination centers (MGRCs),namely, nonradiative recombination centers and deep-state radiative recombination centers, on the carrier recombination dynamics is anessential task. By using the combination of time-resolved photoluminescence and positron annihilation spectroscopy (PAS) measurements,the origins of major MGRCs in the state-of-the-art GaN epilayers, bulk crystals, and Mg-implanted layers were identified, and their concen-trations were quantified for deriving the capture coefficients of minority carriers. In this article, potential standardization of the room-tem-perature photoluminescence lifetime for the near-band-edge emission (τRTPL ) as the concentration of major MGRCs well below the detectionlimit of PAS is proposed. For n-GaN substrates and epilayers grown from the vapor phase, τRTPL was limited by the concentration of carbonon N sites or divacancies comprising a Ga vacancy (VGa) and a N vacancy (VN), [VGaVN], when carbon concentration was higher or lower,respectively, than approximately 1016 cm−3. Here, carbon and VGaVN act as major deep-state radiative and nonradiative recombinationcenters, respectively, while major MGRCs in bulk GaN crystals were identified as VGa(VN)3 vacancy clusters in Na-flux GaN and VGa orVGaVN buried by a hydrogen and/or VGa decorated with oxygen on N sites, VGa(ON)3–4, in ammonothermal GaN. The values of τRTPL in n-GaN samples are compared with those of p-GaN, in which τRTPL was limited by the concentration of VGa(VN)2 in Mg-doped epilayers and bythe concentrations of VGaVN and (VGaVN)3 in Mg-implanted GaN right after the implantation and after appropriate activation annealing,respectively.© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0201931Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-1© Author(s) 2024 08 May 2024 10:00:43https://doi.org/10.1063/5.0201931https://doi.org/10.1063/5.0201931https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0201931http://crossmark.crossref.org/dialog/?doi=10.1063/5.0201931&domain=pdf&date_stamp=2024-05-08https://orcid.org/0000-0001-9558-1642https://orcid.org/0000-0003-0967-141Xhttps://orcid.org/0000-0001-6224-4869https://orcid.org/0000-0002-4896-3530https://orcid.org/0000-0003-2714-4111https://orcid.org/0000-0002-0849-360Xhttps://orcid.org/0000-0003-4855-4339https://orcid.org/0000-0002-4058-7649https://orcid.org/0000-0002-3212-4521https://orcid.org/0009-0003-6591-847Xhttps://orcid.org/0000-0002-5453-4943https://orcid.org/0000-0002-7598-2593https://orcid.org/0000-0002-4300-5720https://orcid.org/0000-0002-5973-0230https://orcid.org/0000-0002-6531-4356https://orcid.org/0000-0001-8321-9822mailto:chichibulab@yahoo.co.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0201931https://pubs.aip.org/aip/japI. INTRODUCTIONFor bridging the sustainable development goals, the exploita-tion of energy-saving, high-power electronic devices1 and advancedsolid-state lighting2 based on high-efficiency light-emitting diodes(LEDs)3 is one of the significant ways. Gallium nitride (GaN) andrelated (Al,Ga,In)N alloys are a suitable candidate for such apurpose: InGaN alloys are used in near ultraviolet (UV) to visibleLEDs and laser diodes (LDs) as well as in white LEDs comprisingan InGaN quantum well (QW) blue LED and yellow phosphors.3 Itis quite important to note that such consumer LEDs are grown onheteroepitaxial GaN or AlN films on a c-plane Al2O3 substrate,generally labeled “GaN template” or “AlN template,” respectively.Because both GaN and AlN have large lattice mismatch(Δa/a . 16%) against Al2O3, the entire LED structure containshigh-density threading dislocations (TDs) in the order of 108–1010 cm−2. Nevertheless, such high threading dislocation density(TDD) InGaN QWs exhibit sufficiently high-intensitynear-band-edge (NBE) emissions with the aid of defect- and polari-zation field-tolerant2,4–6 radiation probability of localized excitons.4GaN also has a potential to achieve high-power transistors work-able at high frequencies,1 relying on its outstanding characteristicsincluding the large bandgap energy (Eg) of 3.4 eV, high break-downfield strength of 3.3 MV/cm,7 and high saturation electron velocityof 2:5� 107 cm s�1 (Ref. 8). A normally-off vertical GaN-basedtransistor on a GaN substrate exhibiting a low specific on-stateresistance (RON) of 1 mΩ cm2 and a high off-state breakdownvoltage (VBD) of 1.7 kV has been demonstrated by fabricating ap-type GaN (p-GaN)/unintentionally doped (UID) AlGaN/GaNheterostructure.9 Moreover, vertically current flowing GaN metal–oxide–semiconductor field-effect-transistors capable of largecurrent switching have been explored progressively.10–12 However,further improvements in the device performances, for example,better stability and reliability, are preferred to integrate GaN powerdevices in consumer systems.For rooting the realization of such high-performanceGaN-based devices, the use of large-area, single-domain, mosaic-and bowing-free GaN wafers of low TDD is preferred. As for GaNpower devices,1,9 highly pure designated electron concentrationn−-type drift layer, p-GaN layer or p-GaN segments fabricated byselective area Mg ion implantation (I/I) for inversion channels, andhigh carrier concentration n+ and p+ contacting layers are indis-pensable. While, low optical absorption waveguiding and claddinglayers as well as quantum-structured active regions hardly affectedby midgap recombination (MGR) channels that shorten carrier life-times are required. There are a variety of MGR channels such asstructural defects like cracks; voids; grain boundaries; stackingfaults (SFs); TDs with edge, screw, and mixed components; surfacedefects causing surface recombinations; and bulk deep levels (DLs)originating from impurities and/or point defects. With respect to(Al,In,Ga)N, TDs higher than 108 cm−2 had been invoked to as thedominant nonradiative recombination (NR) channels that limit theinternal quantum efficiency (ηint) of the NBE emission (ηNBEint ).13With the aid of the appearance of freestanding (FS) GaN or AlNsubstrates, typical TDDs in (Al,Ga,In)N films have been decreasedto below 107 cm−2 and the corresponding TD spacings (>3 μm)have become much longer than the diffusion length (LD) ofminority carriers (Lminority): in most cases, holes (Lp) in (Al,Ga,In)N. However, ηNBEint has not reached unity.14 Therefore, ηNBEint ofstate-of-the-art (Al,Ga,In)N LEDs is no longer limited by TDs butlimited by other MGR channels, most likely intrinsic pointFIG. 1. Schematic representation of (a) the relationship among the excitation ofe–h pairs or excitons with the rate G, radiative recombination emitting the NBE lumi-nescence with the rate RR (lifetime τR), nonradiative recombination at NRCs withthe rate RNR (lifetime τNR), and deep radiative recombination emitting the DL lumi-nescence band with the photon energy hυDL at DRCs with rate RDR (lifetime τDR).The model is drawn for the case of weak-excitation conditions to underline themidgap recombination (MGR) processes with negligible classical17,18 andtrap-assisted19 Auger–Meitner nonradiative recombination (NR) processes. BothNRCs and DRCs obey the Shockley–Read–Hall (SRH) statistics20,21 emitting onlyphonons and photons with the energy hυDL in addition to phonons, respectively, asshown using the configuration coordinate model in panel (b), and accordingly, theyare categorized as MGRCs. (c) The roles of the three types of recombinations onthe luminescence spectrum. Radiative recombination generates the NBE emission,nonradiative recombination decreases overall luminescence intensity, and deep radi-ative recombination emits a DL luminescence band and decreases the NBE emis-sion intensity. (d) Schematic model of MGRCs in an n-type semiconductor thatcapture minority carriers (holes) with the capture coefficient Cp, which is a productof capture cross section σp and thermal velocity vth (vp). According to the SRH sta-tistics,20,21 MGR lifetime (τMGR) is expressed by Eqs. (2) and (3), namely,τMGR ¼ 1Cminority�NMGRCffi 1σp�vp�NMGRC, where Cminority ¼ Cp ¼ σp � vp is a holecapture coefficient [Modified with permission from Chichibu et al., J. Appl. Phys.123, 161413 (2018). Copyright 2018 AIP Publishing LLC].25Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-2© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japdefects,15 impurities, or their complexes. Consequently, origins andproperties of MGR channels in GaN are worth investigating. Suchrecombination centers are expressed “midgap recombinationcenters (MGRCs)” in this article.The essence of the roles of MGRCs on the carrier recombina-tion phenomena is summarized16 in Fig. 1: MGRCs cause carrierrecombination emitting only phonons or phonons plus photonswith energy (hυ) defined as hυDL, which is lower than Eg. TheMGRCs with and without hυDL emission are classified into “deep-state radiative recombination centers (DRCs)” and “nonradiativerecombination centers (NRCs),” respectively. In Fig. 1(b), the con-figuration coordinate model is used to show Stokes’ shifts for a DLluminescence by DRCs. After the excitation of electron–hole (e–h)pairs or excitons with the rate G, the exited quanta recombinethrough (i) a direct radiative recombination emitting the NBEluminescence such as free exciton (FX) emission, bound exciton(BX) emission, and band-to-band emission with a representativerate RR (lifetime τR), (ii) NR recombination at NRCs with a rateRNR (lifetime τNR), and (iii) sequential NR and radiative recombi-nations emitting hυDL at DRCs with the rate RDR (lifetime τDR).We should mention that Fig. 1 is drawn for the case of weak-excitation conditions to underline the MGR processes. Here, thedefinition of “weak-excitation conditions” throughout this paper isthat the excited carrier or exciton concentration (nexcited) is far lessthan the majority carrier concentration giving rise to nexcited asminority carrier concentration and also far below the threshold formaintaining negligible classical17,18 and trap-assisted19 Auger–Meitner nonradiative recombination processes. According to theShockley–Read–Hall (SRH) statistics20,21 represented in Fig. 1(d),overall MGR lifetime (τMGR), which is an inverse of the rate RMGRand is a function of τNR and τDR,1τMGR¼ 1τNRþ 1τDR, (1)is expressed byτMGR ¼ σpvp � σnvnσpvp þ σnvn� 1NMGRC, (2)where NMGRC is the concentration of MGRCs; σp and σn are thecapture cross sections and vp and vn are thermal velocities for ahole and an electron, respectively. In n-GaN, Eq. (2) is approxi-mated byτMGR ffi 1Cminority � NMGRC¼ 1σp � vp � NMGRC, (3)where Cp ¼ Cminority, σp ¼ σminority, and vp ¼ vminority are thecapture coefficient, capture cross section, and thermal velocity (vth),respectively, for a minority carrier (hole). Here, vp ¼ vth ¼ffiffiffiffiffiffiffiffi3kBTmpq,where kB is the Boltzmann constant, T is the temperature, and mpis the hole effective mass.Generally, MGRCs play an important role in limiting ηNBEint ,which is expressed byηNBEint ¼ RR(RR þ RNR þ RDR)¼1τR1τRþ 1τNRþ 1τDR� � ¼ 11þ τRτMGR: (4)Because τR in the bulk semiconductor is unique to a materialunder fixed carrier concentration at a given temperature (T), τMGRlimits ηNBEint . With increasing T, τMGR is supposed to first decreasedue to the increase in vth and reach a constant value22,23 when LDof a minority carrier Lminority ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDminority � τminorityp� �reachesapproximately half of the average MGRC spacing, whereDminority ¼ kBTq � μminority� �and τminority are the diffusivity and life-time of a minority carrier, respectively, where μminority is a minoritycarrier mobility. Accordingly, NMGRC limits τminority of low- tomedium- (or even high-) grade GaN at room temperature. Here,τminority can be quantified as a photoluminescence (PL) lifetime(τPL) in (Al,Ga,In)N under weak-excitation conditions defined inthe preceding paragraph,22,24–281τPL¼ 1τminority¼ 1τRþ 1τMGR: (5)Here, we note again that other important NR recombinationprocesses are classical17,18 and trap-assisted19 Auger–Meitnerrecombinations, which arise from different mechanisms andbecome significant under medium- to high-excitation conditions.According to Eq. (5), room-temperature PL lifetime for the NBEemission (τRTPL ) of GaN under the weak-excitation conditions22,24–28can be predicted as a function of NMGRC and Cminority using theroom-temperature τR value (τRTR ) of approximately 40 ns for GaN(Refs. 22 and 23), as shown in Fig. 9 of Ref. 25, in which corre-sponding ηNBEint has been calibrated on the right vertical axis. Wenote that typical Cminority of MGRCs reported for n-GaN, p-GaN,and Mg ion-implanted (I/I) GaN are in the range between 10�8and 10�5 cm3 s�1, as described later.25–32 For high NMGRC regime,τRTPL linearly decreases with increasing NMGRC.For decreasing NMGRC, in-depth probing of τminority andknowing true origins of MGRCs are essential tasks. For thismission, a combinatorial use24–28 of positron annihilation spectro-scopy (PAS)33–38 and time-resolved photoluminescence (TRPL)measurements is advantageous because PAS identifies thespecies37–41 and quantifies the concentration25–28,42–44 of vacancy-type defects while TRPL quantifies22–30 τPL, which representsτminority under weak-excitation conditions.22,24–28 By using thiscombinatorial approach, some of the authors have long been sug-gesting since 2005 (Ref. 24) that vacancy complexes22,24 comprisinga Ga vacancy (VGa), more precisely divacancies comprising a VGaand a nitrogen vacancy (VN), namely, VGaVN, are the origin of pre-dominant intrinsic NRCs in a variety of UID and n-type GaN;25the details will be explained in Sec. II. We should note that in1990s, several theorists have predicted the presence of VGa and VNin GaN, and the importance of VGa on the “yellow luminescence(YL)” band45–47 at around 2.2 eV and the NR recombination48,49Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-3© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japhas been proposed. However, experimental evidence showing thepresence of VGa has not been reported48,49 until 1997 when Saarinenet al.35 have probed VGa in GaN by using PAS technique. Uedonoet al.36 have supported the existence of VGa in GaN epilayers usingPAS later in 2001. Nevertheless, our assignment24,25 is basically con-sistent with the results of the calculations46,50,51 that the formationenergy (EForm) of negatively charged defects such as V�Ga in GaN canbecome lower due to the Fermi level (EF) term (+qEF).46,50,51In this article, the origins and Cminority(σminority) of majorMGRCs in the state-of-the-art GaN epilayers, bulk crystals, andMg-I/I layers obtained by using the combinatorial PAS and TRPLmeasurements are summarized to propose a potential standardiza-tion of the weak excitation22,24–28 τRTPL as the concentration of majorMGRCs well below the detection limit of PAS measurement. As forUID and n-type GaN substrates and epilayers grown by halidevapor phase epitaxy (HVPE) and metalorganic vapor phase epitaxy(MOVPE), τRTPL was limited by the concentration of carbon impuri-ties substituted on N sites ([CN]) when [CN] was higher thanapproximately 1016 cm−3: C0/�N is the origin of the YL band.47 τRTPLwas limited by the concentration of VGaVN ([VGaVN]) that act asmajor NRCs when [CN] was lower than approximately 1016 cm−3.The GaN crystals grown by the Na-flux method contained larger-size VGa(VN)3 vacancy clusters while those grown by the ammono-thermal (AT) method contained vacancy complexes such as VGa orVGaVN buried by a hydrogen (HGa and HVGaVN , respectively) and/or VGa decorated with oxygen (O) impurities on N sites,VGa(ON)3–4, and all these vacancy complexes appear to act asMGRCs. For Mg-doped p-type GaN epilayers, τRTPL was limited bythe concentration of VGa(VN)2, [VGa(VN)2]. For Mg-I/I GaN,VGaVN and (VGaVN)3 are the major NRCs right after the implanta-tion and after appropriate post-implantation annealings (PIAs),respectively. Because of larger σn of VGa(VN)2 and (VGaVN)3 andfaster vn, τRTPL of p-GaN becomes approximately an order of magni-tude shorter than that of n-GaN with the same NMGRC.II. EXPERIMENTAL AND ANALYTICAL DETAILSFor elucidating the species, concentration, and Cminority ofvacancy-type defects in GaN, various crystals and epilayers grownby a variety of methods and thin layers prepared by Mg-I/I tech-nique were analyzed. At first, PAS measurement33–38 and theoreti-cal calculations38–44 were carried out to identify the species andquantify the concentrations of major vacancy-type defects. Thesamples were also inspected by impurity analyses usingsecondary-ion mass spectrometry (SIMS) measurement. Then,TRPL measurement was carried out to quantify τRTPL (¼τMGR).When τMGR was inversely proportional to the concentration of aunique defect (NMGRC), the defect could be assigned as the majorMGRCs. Then, Cminority ¼ σminority � vminority of the MGRCs can bederived using Eq. (3).A. SamplesSpecifications of UID or doped n-GaN samples are summa-rized in Table I. The data in column “General information” aremerely typical ones and N.A. indicates “not available.” Supplieridentifications (IDs) are represented by bold italic capital letters.Suppliers A, B, C, and D grew “thick” GaN layers by HVPE underthe growth conditions listed on the table. These samples includedboth c-plane and m-plane epilayers and FS-GaN substrates; thelatter were fabricated by slicing thick GaN boule detached fromforeign substrates. These samples were bowed mosaic crystals buthad flat surface by appropriate polishing treatments. They con-tained low concentration of carbon ([C]), as the Ga precursor(GaCl) nor NH3 contain C in the molecule. Suppliers E, F, and Ggrew a few-μm-thick GaN layers by MOVPE under the growth con-ditions listed on the table. These samples also included c-plane andm-plane epilayers. For MOVPE samples, it was difficult to decrease[C] less than 3 × 1015 cm−3 due to the incorporation of C from themetalorganic Ga precursors such as trimethylgallium (TMGa). The[C] values were close to those reported previously by several otherresearchers:52–55 [C] and some other impurity concentrations werequantified by the SIMS measurement. In HVPE and MOVPE GaNsamples (A–G), [C] was varied from low (1 × 1015 cm−3) to high(∼1017 cm−3) concentrations, and typical TDD were less than a fewtimes 106 cm−2.Bulk crystals of GaN were grown from the liquid phase or inthe supercritical state. Suppliers H and J grew GaN crystals by theNa-flux method56 using Na–Ga melt57 or Na vapor,58,59 respec-tively. Details of the growths other than the growth temperature(Tg) or growth pressure (Pg) have been given in Refs. 57–59.Supplier K grew Ge-doped (3 × 1018 cm−3) GaN by using theliquid-phase epitaxy (LPE) method, of which [C] was quantified tobe 3 × 1017 cm−3 by SIMS measurement. The growth details areundisclosed, although TDD was less than 5 × 106 cm−2. Suppliers Land M grew GaN crystals by the AT methods using basic mineral-izers within the supercritical ammonia, namely, basic ammonother-mal (BAT) methods, at high-pressure conditions (>200MPa). Onanother front, suppliers N and P grew GaN crystals by the ATmethods using acidic mineralizers within the supercriticalammonia, namely, acidic ammonothermal (AAT) methods. Thegrowths were carried out at Pg up to 300MPa (Ref. 60) for supplierN and approximately 100MPa (Ref. 61) for supplier P. Because Pgfor P is much lower than that for N, the method of supplier P hasbeen named the low-pressure acidic ammonothermal (LPAAT)method,61 which is forecasted to provide large-size bulk GaN crys-tals with the aid of the thinner wall thickness of the autoclave ofthe same outer diameter. In the case of AAT methods, a corrosion-resistant lining was carried out using noble metals on the innerwall of the autoclave made of Ni-based superalloys. Conversely,such noble metal lining cannot be applied in BAT autoclavesbecause the ammonobasic fluids corrode such noble metals.Accordingly, the incorporation of metals from a corroded autoclaveis inescapable in BAT growths of GaN.Specifications of Mg-doped p-type GaN samples are summa-rized in Table II. The data in the column “General information”are again merely typical ones. Suppliers Q and R, which are suppli-ers A and B in Ref. 26, respectively, grew a few-μm-thickMg-doped p-GaN layer by MOVPE on GaN substrates prepared byHVPE. The Mg concentration, [Mg], was varied from 3 × 1016 to7 × 1019 cm−3 (Refs. 26 and 42). Suppliers S, T, and U preparedMg-I/I layers using GaN substrates or MOVPE GaN films on GaNsubstrates, in order to minimize potential influences of TDs on theluminescent properties. All Mg-I/I layers essentially had a box-shaped Mg profile fabricated using multistage I/I with differentJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-4© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japTABLEI.Specificationsofunintentionallydoped(UID)ordopedn-typeGaNsamples.Thedatainthecolumn“Generalinformation”aremerelytypicalonesandN.A.indicates“notavailable.”SupplierIDGrowthmethodTypicalconditionsGeneralinformationTemperature(Tg)Pressure(Pg)PointdefectspeciesFastcomponentoftheroom-temperaturePLlifetime(τRTPL)(ns)StatesMethod(°C)(MPa)AVaporHalidevaporphaseepitaxy(HVPE)1000–11500.001–0.1VGaVNa0.4toafewB0.2–0.7C0.2toafewD0.02–0.1EMetalorganicvaporphaseepitaxy(MOVPE)1000–11000.01–0.10.31–0.34F0.2–0.6G0.1–0.6HLiquidNaflux(melt)800–9004–10VGa(VN) 3bN.A.JNaflux(vapor)c,dN.A.0.05–0.23dKLiquidphaseepitaxy(LPE)UndisclosedbutGedoped(3×1018cm−3 )N.A.0.035LSupercriticalBasicammonothermal(BAT)500–600200–450VGa(ON) 4<0.004M<0.001NAcidicammonothermal(AAT)500–600∼200eHVGaVNorVGa(ON) 4e0.003gP500–630∼100f0.040ga IdentifiedinRef.25.bIdentifiedinRef.57.c Ref.58.dMeasuredinRef.59.e Ref.60.f Ref.61.g Ref.94.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-5© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japacceleration energies from 20 to 420 keV with different doses atroom temperature.27,28,42–44,62–64 The samples provided by supplierS were sequentially Mg- and H-implanted N-polar GaN substrates(I/I-GaN:Mg +H).27,43 For comparison, the same I/Is were carriedout on a Ga-polar MOVPE epilayer.27 The samples provided by thesupplier T were sequentially Mg- and N-implanted Ga-polarMOVPE epilayers.62,63 For these samples, very shallow implanta-tion of Mg was followed by the box-shaped deep implantation ofN, in order to give rise to the “vacancy-guided redistribution(VGR)”62,63 of Mg and to decrease the concentration of VN, [VN],by burying VN with the “excess” implanted N. Indeed, gross I/Idamage for the VGR technique was lower than the conventionalmultistage I/I of Mg. Supplier U carried out so-called “ultrahigh-pressure annealing (UHPA)”64,65 of Mg-I/I GaN on GaN up to1480 °C at 1 GPa in N2. The most remarkable advantage of usingUHPA64,65 is that high-pressure N2 suppresses surface decomposi-tion of GaN during high-temperature annealing up to 1480 °C,without any capping layers on the implanted surface. Accordingly,surface damages due to the thermal stress are prevented andp-GaN layers of excellent electrical properties are routinelyobtained.64B. Positron annihilation spectroscopyPositron annihilation spectroscopy (PAS)33–38 is an estab-lished, nondestructive, and exclusive tool for detecting neutral andnegatively charged vacancy-type defects in a semiconductor. A pos-itron (e+) is an antimatter of an electron (e−) having a positivecharge with a mass (m) identical to that of e−. Implanted e+ annihi-lates with a surrounding e− and emits two γ rays. According to therelationship Eγ =mc2, Eγ is approximately 511 keV, where Eγ is theenergy of the γ ray and c is the speed of the light. The annihilatingγ-ray spectra are broadened in energy due to the momentum distri-bution of the annihilating electron–positron (e− − e+) pair pL,which is parallel to the direction of the γ rays. The energy of the γrays is expressed as Eγ =mc2 ± ΔEγ. The Doppler shift ΔEγ is givenby the relationship ΔEγ = pLc/2.A freely diffusing e+ likely localizes in a vacancy-type defectbecause of Coulomb repulsion from ion cores. Because the momen-tum distribution of e− surrounding vacancy-type defects is smallerthan that in defect-free (DF) delocalized regions due to larger con-tribution of valence electrons, the defects can be detected by mea-suring the Doppler broadening spectra of the γ rays. The resultingchange in the γ-ray spectra is characterized by the line shapeparameter S and the wing parameter W, where the former mainlyreflects the fraction of annihilating e− − e+ pairs of small momen-tum distribution (mostly valence electrons) and the latter repre-sents the fraction of the pairs of large momentum distribution(mostly core electrons). Since VGa and vacancy complexes compris-ing VGa may form acceptor-type defects in GaN, they are the mostprobable candidates of e+ trapping centers.35–38 Accordingly,(S, W) coordinates can be used as a measure of species and con-centration of VGa and vacancy complexes comprising VGa.In order to identify the species and quantify the concentrationof defects, Doppler broadening spectra of the annihilating γ rayswere theoretically calculated using the QMAS (Quantum MAterialsSimulator) code,39–41 which uses valence-electron wavefunctionsTABLEII.SpecificationsofMg-dopedp-typeGaNsamples.Thedatainthecolumn“Generalinformation”aremerelytypicalones.N.A.indicates“notavailable.”SupplierIDPreparationmethodTypicalconditionsGeneralinformationGrowthorannealingGrowthorannealingPointdefectspeciesRoom-temperaturePLlifetime(τRTPL)(ns)CategoryMethodtemperature(°C)pressure(MPa)QEpitaxyMetalorganicvaporphaseepitaxy(MOVPE)Tg∼1000Pg=0.001–0.1VGa(VN) 2a<0.001–0.025bR0.002–0.080bSIonimplantation(I/I)MgandHsequentialI/IonN-polarGaNc,dTa=800–1260P a=0.1(VGaVN) 3d0.003–0.018cTMgandNsequentialI/IonGa-polarGaN(vacancy-guided)e,fTa=1000–1300P a=0.1(VGaVN) 3e0.0014fUMgI/IwithoutcappinggTa=1000–1480P a=1000h(VGaVN) 3i<0.001ja Ref.42.bRef.26.c Ref.27.dRef.43.e Ref.62.f Ref.63.g Ref.64.hRef.65.i Ref.44.j Ref.99.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-6© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japdetermined using the projector augmented-wave (PAW)method.66,67 To describe the electronic exchange and correlationenergies of electrons, the generalized gradient approximation68 wasused. The calculations were carried out on orthorhombic supercellsthat are equivalent to 4� 4� 2 wurtzite cells containing 128 atomswhen there is no vacancy. The supercell dimensions were2ffiffiffi3pa0 � 4a0 � 2c0, where a0 = 0.3189 nm and c0 = 1.03725 nmwere the lattice parameters. For the supercell that contains a defect,atomic positions in the fixed cell (with the experimental latticeparameters) were optimized computationally. The formalism of thelocal density approximation69,70 was used to describe the correla-tion of e− − e+.Localized e+ at vacancy-type defects may affect the defect con-figuration and accordingly the corresponding e+ annihilation.41Such effects due to the trapped e+ can be treated appropriately bythe two component density functional theory (TC-DFT)scheme.69,70 However, different from the case of a Zn vacancy(VZn) and divacancies comprising a VZn and an O vacancy inZnO,71 the positron annihilation parameters (S, W parameters andpositron lifetime) of GaN are only marginally affected.72Accordingly, calculations were carried out neglecting the aforemen-tioned effects.The Doppler broadening spectra for the annihilation of e+in DF and various trapped states were calculated, and the direction-ally averaged (S, W) coordinates for e+ annihilation at the DFregion [(SDF, WDF)], VGa [(SVGa , WVGa )], VGaVN divacancies[(SVGaVN , WVGaVN )], VGa(VN)2 trivacancies [(SVGa(VN)2 , WVGa(VN)2 )],(VGaVN)2 tetravacancies [(S(VGaVN)2 , W(VGaVN)2 )], vacancy-impuritycomplexes like VGaON, and so on are shown by open and half-opensymbols in Fig. 2 (after Refs. 41, 60, and 73). Here, for directly com-paring each calculated (S, W) coordinate and experimentallyobtained (S, W), the S parameter was defined as the intensity of thesimulated γ-ray spectrum for the energy range of 511 keV ± ΔEγ,where ΔEγ = 0.76 keV, around the center of the peak, over the totalintensity. The W parameter was calculated for the intensity of the γray in the tail of the spectrum (3.4 keV≤ |ΔEγ|≤ 6.8 keV) over thetotal intensity.The assignment and quantification of the vacancy-type defectswere carried out as follows. When the samples contain mono-defects of vacancy-type (including vacancy-impurity complexes), e+annihilate either from the DF state or from the trapped (defect)state. In such a case, (S, W) becomes a weighted average of(SDF, WDF) and (Sdefect, Wdefect), where Sdefect and Wdefect are char-acteristic S and W, respectively, of the defect under consideration.Accordingly, experimental (S, W) should lie on a line segment(SDF, WDF)� (Sdefect, Wdefect). Here, we emphasize that the slope ofthe line is also important for identifying the defect species, asexperimental data plots commonly suffer from “lower right”shifts.42–44,57,60,73 Nevertheless, by comparing experimental (S, W)and calculated (S, W) in Fig. 2, the defect species can be identified.Then, the defect concentration can be estimated from thevalues of lower and upper dynamic range of PAS measurement,37as follows. When the concentration of the defects is less than thelower dynamic range, namely, the detection limit, e+, implanted inthe sample are delocalized in the DF regions, and (S, W) coordi-nate represents (SDF, WDF). Conversely, when the defect concentra-tion exceeds the upper dynamic range, almost all e+ are trapped bythe defects and (S, W) represents (Sdefect, Wdefect).37 The concentra-tion of the defects can eventually be estimated by placing a loga-rithmic gauge between (SDF, WDF) and (Sdefect, Wdefect), whichcorrespond to the lower and upper limits of the dynamic range,respectively. The dynamic range of PAS measurement for VGa isapproximately between 1015 and 1018 cm−3 in n-GaN and approxi-mately between 1016 and 1019 cm−3 in semi-insulating and p-GaN,as the trapping coefficient of e+ at negative vacancies (typically�1015 � 1016 s�1) is an order of magnitude higher than that atneutral vacancies (typically �1014 � 1015 s�1) at 300 K (Ref. 37).Accordingly, the concentration of VGa ([VGa]) can be estimatedfrom the values of (SDF, WDF) and (SVGa , WVGa ) coordinates. In thisarticle, 1015 and 1018 cm−3, respectively, in n-GaN and 1016 and1019 cm−3, respectively, in semi-insulating and p-GaN (Ref. 37)were used.For counterchecking the defect concentration, characteristic Sand positron diffusion length (Lþ) in each layer of epitaxial struc-tures were determined by using a monoenergetic e+-beam,34–38 bywhich the mean implantation depth of e+ can be controlled. Theanalysis74 is based on solving the diffusion equation of e+ as a func-tion of acceleration energy E using the initial implantation profile.Here, Lþ can be used as a measure of gross concentration of e+trapping and scattering centers because both of them shorten Lþ.In a three-dimensional (3D) space, Lþ is likely close to an inversethird root of the defect concentration. The scattering centers arepositively charged and neutral point defects such as VN, interstitials(Gai and Ni), and certain complexes. The relationship between Sand E was analyzed by a computer program named VEPFIT devel-oped by van Veen et al.74 The one-dimensional (1D) diffusionFIG. 2. Calculated (S, W ) values41,60,73 using the QMAS code for positronannihilation in GaN at the defect-free (DF) region (delocalized state) (circle),VGa (upward triangle), VGaVN (downward triangle), VGa(VN)2 (diamond), and soon. [Calculated data plots are reproduced with permission from Ishibashi andUedono, J. Phys. Conf. Ser. 505, 012010 (2014). Copyright 2014 IOPPublishing LLC;41 Uedono et al., J. Cryst. Growth 448, 117 (2016). Copyright2016 Elsevier B.V.;60 and Uedono et al., Phys. Status Solidi B 255, 1700521(2018). Copyright 2017 WILEY-VCH Verlag GmbH & Co.73].Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-7© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japmodel of e+ is expressed by33Dþd2dz2n(z)� κeff (z)n(z)þ P(z, E) ¼ 0, (6)where Dþ is the diffusion coefficient of e+, n(z) is the probabilitydensity of e+ at a distance z from the surface, κeff (z) is the effectiveescape rate of e+ from the diffusion process, and P(z, E) is theimplantation profile of e+. Then, Lþ(z) is given byLþ(z) ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDþ/κeff (z)p: (7)In the fitting procedure, a homogeneous distribution ofdefects was assumed. The S–E curve was fitted to the followingequation:S(E) ¼ SeFe(E)þ SSFS(E)þXSiFi(E), (8)where Fe(E), Fs(E), and Fi(E) are the fractions of epithermal (non-thermalized) positrons annihilated at the surface, that of positronsannihilated at the surface, and that of positrons annihilated in theith block, respectively [Fe(E) + Fs(E) + ΣFi(E) = 1]. The values of Se,Ss, and Si are characteristic S parameters for the respective annihila-tion events. The analytical procedures used in this study are similarto those described in Ref. 36.The monoenergetic e+-beam line used to measure the Dopplerbroadening spectra of the annihilating γ ray as a function of E witha Ge detector was the same as in Refs. 36, 38, 42–44, 57, 60, 62, 63,and 73. A spectrum with 3 × 106 counts was measured at each E.The low-momentum portion for determining the S parameter wasdefined for the energy range of 511 keV ± ΔEγ, whereΔEγ = 0.76 keV, around the center of the peak, over the totalcounts. The W parameter was calculated for the annihilation eventsin the tail of the spectra (3.4 keV≤ |ΔEγ|≤ 6.8 keV) over the totalcounts. For semi-insulating and p-type GaN, the samples were illu-minated with the 325.0 nm line of a He–Cd laser during the mea-surement, in order to supply electrons to neutral or positivelycharged levels73 for increasing the positron trapping probability.To examine the annihilation characteristics of positrons indetail, the coincidence detection system36 was also used. Thespectra with about 5 × 106 counts were obtained and then charac-terized using the S and W parameters.C. Steady-state and time-resolved photoluminescencemeasurementsSteady-state and time-resolved PL measurements were carriedout under the weak-excitation conditions22,24–28 defined in Sec. I,in order to underline the MGR processes.5 Steady-state PL wasexcited using the 325.0 nm line of a cw He–Cd laser with thepower density of 38Wcm�2. TRPL measurement was carried outusing approximately 110 fs pulses of a frequency-tripled mode-locked Al2O3:Ti laser (λ ¼ 267 nm) with the energy density of120 nJ cm�2 per pulse, of which repetition rate was decreased by apulse picker to 8MHz. The spot diameter and estimated nexcitedwere 100 μm and a few times 1016 cm−3, respectively, when τPL was1 ns. We note that this nexcited was the highest because τRTPLdistributed from 1 ns (A) down to 2 ps (R), which will be shownlater. Under these excitation conditions, nexcited was far less thanthe majority carrier concentration and also far below the thresholdfor maintaining negligible classical17,18 and trap-assisted19 Auger–Meitner nonradiative recombination processes at 300 K. It is alsoimportant to note that the measured τRTPL increased with increasingexcitation power density, for example, from 220 to 510 ps byincreasing the energy density from 0.2 to 120 nJ cm�2 for one ofthe samples (A), indicating that the weak-excitationconditions22,24–28 were maintained and the increase in τRTPL reflecteda progressive saturation of MGRCs. One of the other examples canbe found in a literature,75 in which τRTPL increased from 42 to 170 pswith increasing the laser energy density from 4 to 600 nJ cm�2.The TRPL signals were collected using a streak camera. Theacquisition was carried out using either a synchro-scan mode withthe highest temporal resolution of 1 ps or a conventional slow-scanmode. The temporal decay signals for the NBE emission of GaNshowed a single- or precisely multiple-exponential line shape. Theappearance of multiple decay components most likely arose fromspatial inhomogeneity in τRTPL , i.e., NMGRC and/or the presence ofany quantum confined transition such as discrete transitions takingplace in strain or structural singularities76–80 within the excitationvolume. Because spectrally (energy) resolved decay signals acrossthe photon energy range for the NBE emission did not showenergy dependences in all samples at 300 K, spatial inhomogeneityin NMGRC within the excitation volume79 appears to be the mostprobable cause. Nevertheless, most of the PL decay signals werewell fitted using a single- or bi-exponential line shape function,I(t) ¼ A1exp(�t/τ1)þ A2exp(�t/τ2), (9)where I(t) is the PL intensity at time t. A1(A2) and τ1(τ2) are thepre-exponential constant and lifetime, respectively, for the fast(slow) decay component. The value of τ1 is used as a principal τRTPLrepresentative because cw ηNBEint and thereby PL intensity are usuallylimited by τ1. Contribution of slow decay components such as τ2will be discussed later. Because τRTPL in bulk 3D GaN is approxi-mately 40 ns,22,23 τMGR at room temperature can be derived fromEq. (5) using the measured τRTPL . Practically, τRTPL nearly agrees withroom-temperature τMGR in bulk semiconductors without quantumconfinement structures or localization mechanisms.III. RESULTS AND DISCUSSIONA. n-type GaN1. Species and capture coefficients of vacancy-typedefectsMeasured (S, W) for n-GaN supplied by A, H, and N areshown by black, dark gray, and carmine closed symbols, respec-tively, in Fig. 3. Error bars are not given on all S–W plots hereafterbecause the experimental errors to determine S and W were bothless than 0.1%. Each supplier ID is shown by an italic outline char-acter on a colored square background in the figures. Some of thecalculated41,60,73 (S, W) shown in Fig. 2 are plotted by opensymbols for identifying the vacancy-type defect species. For com-parison, previously measured24,25 (S, W) values for the GaNJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-8© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japsamples of various origins, which have been grown by HVPE,MOVPE, and molecular-beam epitaxy (MBE), are displayed byclosed light gray symbols. The (S, W) values of HVPE GaN (sup-plier A, defined “defect-free-control: DF-CTRL”), of which qualityis equivalent to the highest quality sample “C0” in Ref. 22, mea-sured in the present study (closed black circle) and in 2012 (closedlight gray circle) are mismatched, especially in W parameter, andboth plots exhibited larger S than calculated SDF (open blackcircle).The difference in W likely originates from improved sensitivityof the Ge detector used in the present study, which improved thedetection limit and, thus, gave rise to the decrease in the baseline,resulting in the decrease in the signal of the spectral tails (wingportions). The distinct “lower right” shifts of the measured (S, W)of DF-CTRL with respect to calculated (SDF, WDF) in the presentstudy could be due to several reasons such as the limitations offirst-principle calculations applied to Doppler broadening spectra,temperature-dependent differences between the modeling andexperimental conditions, the experimental background, and/or theenergy resolutions of our Ge detectors. Nevertheless, the measured(S, W) coordinates of DF-CTRL most likely represent “experimen-tal” (SDF, WDF) in the present study (black) and in 2012 (lightgray) based on the following reasons: (i) DF-CTRL showed thesmallest S and largest W; (ii) DF-CTRL exhibited long τRTPL (for theNBE emission) of 1.1 ns;22 and (iii) Lþ of DF-CTRL was 116 nm(Ref. 22) that supported gross concentration of e+ trapping andscattering centers (Ngrossdefect) less than 1015 cm−3 since 3D average dis-tance between adjacent defects for Ngrossdefect ¼ 1015 cm�3 is 100 nm.The value of Ngrossdefect � 1015 cm�3 almost agrees with the detectionlimit of PAS for n-GaN,37 as described in Sec. II B.Because experimental data plots commonly suffer from lowerright shifts, the slope of the approximated line for the (S, W) coor-dinates is important to determine the defect species. As the slopeof an approximated line for the light gray (S, W) plots nearlyagreed25 with the slope of a line connecting the calculated(SDF, WDF) and (SVGaVN , WVGaVN), major vacancy-type defects in avariety of n-GaN grown from the vapor phase by HVPE, MOVPE,and MBE were identified to be VGaVN (Ref. 25). Consistently,(S, W) coordinates for the GaN samples from suppliers B, C, E, F,and G were close to (S, W) of DF-CTRL (supplier A) and alignedon a virtual line with the slope of a line connecting the calculated(SDF, WDF) and (SVGaVN , WVGaVN). Because of the large number ofsamples supplied, the data plots for B, C, E, F, and G are notshown for avoiding congestion.Different from GaN films and layers grown from vapor phase,major vacancy-type defects in Na-flux GaN (H) have been revealedto be larger vacancy clusters like VGa(VN)3 because the approxi-mated line for the experimental (S, W) coordinates of H (thickdark gray line) has been parallel to a virtual line connecting the cal-culated (SDF, WDF) and (SVGa(VN)3 , WVGa(VN)3 ).57 It is interesting tonote that the size of the major intrinsic point defects in the bulkGaN crystals grown from the melt at high Pg of the order of 4–10MPa (Ref. 57) is much larger than that for the epitaxial films(VGaVN) grown from the vapor phase at Pg lower than 0.1 or0.01MPa.Major vacancy-type defects in AAT GaN (N) has been identi-fied to be HGa and/or VGa(ON)3–4 because the approximated linefor (S, W) coordinates of N and experimental (SDF, WDF) ofDF-CTRL was parallel to the virtual line connecting the calculated(SDF, WDF) and (SHGa , WHGa ) or (SVGa(ON)3�4, WVGa(ON)3�4).60 Theassignment is consistent with the previous report81 on the defectcharacterization of BAT GaN. The reason why VGa buried by mul-tiple H atoms such as (H2–3)Ga was excluded was that e+ was notfully trapped in the case of AAT crystals (N) that exhibited Lþ of60–90 nm: if the major defects were (H2)Ga, Lþ should be muchshorter22,24,25 because (H2)Ga concentration would be close to theupper dynamic range being 1019 cm−3, as shown in Fig. 3, and e+would be fully trapped.In Fig. 4, relationships between τRTPL and NMGRC (τRTPL � NMGRCrelationships) of common MGRCs in n-GaN, namely, Fe on Gasite (Fe3þ/2þGa ) (Ref. 30), C0/�N (Ref. 29), and VGaVN (Ref. 25), aredrawn by green, red, and black curves, respectively, using Eqs. (3)and (5), where τR ¼ 40 ns (Refs. 22 and 23) and Cp values of5 × 10−8 (Ref. 30), 2 × 10−7 (Ref. 29), and 6 × 10−7(Ref. 25) cm3 s−1, respectively, are used. We note that Reshchikov32has reported similar large Cp of 3.7 × 10−7 cm3 s−1 for theFIG. 3. Measured (S, W ) for n-GaN supplied by A, H, and N (closed black,dark gray,57 and carmine60 symbols, respectively). Error bars are not given onall S–E plots hereafter because the experimental errors for the determination ofboth S and W were less than 0.1%. Each supplier ID is shown by an italicoutline character on a colored square background in the figure. The calcu-lated41,60,73 (S, W ) coordinates already shown in Fig. 2 are plotted by opensymbols for determining the vacancy defect species. For comparison, previouslymeasured24,25 (S, W ) for the GaN samples of various origins, which have beengrown by HVPE, MOVPE, and molecular beam epitaxy (MBE), are displayed byclosed light gray symbols. [Calculated data plots are reproduced with permissionfrom Ishibashi and Uedono, J. Phys. Conf. Ser. 505, 012010 (2014). Copyright2014 IOP Publishing LLC;41 Uedono et al., J. Cryst. Growth 448, 117 (2016).Copyright 2016 Elsevier B.V.;60 and Uedono et al., Phys. Status Solidi B 255,1700521 (2018). Copyright 2017 WILEY-VCH Verlag GmbH & Co.73Experimental data plots are reproduced with permission from Chichibu et al.,J. Appl. Phys. 123, 161413 (2018). Copyright 2018 AIP Publishing LLC;25Uedono et al., J. Cryst. Growth 475, 261 (2017). Copyright 2017 Elsevier B.V.;57and Uedono et al., J. Cryst. Growth 448, 117 (2016). Copyright 2016 ElsevierB.V60].Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-9© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japC0/�N center. By using vth ¼ vp ¼ 9:1� 106 cm s�1 that is obtainedfrom hole effective mass (mp) of 1:66m0, corresponding σp are6� 10�15, 2� 10�14, and 7� 10�14 cm2, respectively. Here,Fe3þ/2þGa and C0/�N are known as E3 (Ref. 82) and H1 (Ref. 54) traps,respectively. In the figure, corresponding ηNBEint (¼ τRTPL /τR) at 300 Kis shown on the right y-axis. Herein, we propose the use ofτRTPL � NMGRC curves in Fig. 4 as calibrating measures for quantify-ing (or semi-quantifying) the concentrations of respective MGRCsbelow the detection limits of PAS (or SIMS for [C]). For substitu-tional impurities in Si, a standardization of B, P, and low-level Cconcentrations well below the detection limits of SIMS measure-ments has been realized by using a low-temperature PL measure-ment.83,84 In the present case, the concentrations of native defectscould be quantified, although the definition of the weak-excitationconditions22,24–28 may become more important.Blue and orange curves in Fig. 4 are τRTPL � NMGRC relation-ships for p-GaN, and the details will be given in Sec. III B. InFig. 4, measured τRTPL (fast component τ1) of n-GaN samples (sup-pliers A, B, D, E, F, G, and K) and p-GaN samples (suppliers Rand S) are plotted by italic outline characters on colored-squarebackground. In the following, several experimental data areexplained more precisely.2. MOVPE and HVPE GaNFor the GaN samples grown from the vapor phase (HVPEand MOVPE) except for D, τRTPL was principally limited by [C0/�N ]when [C] was higher than about 1016 cm−3 and by [VGaVN] forlow [C] samples, as follows. Steady-state PL spectra of MOVPEGaN (F) of different [C], namely, 2 × 1015 and 2 × 1016 cm−3, areshown in Figs. 5(a) and 5(b), respectively. In each panel, upper(black) and lower (red) curves show the spectra at 12 and 300 K,respectively. The PL intensity (y-) axis has a unit of count persecond (cps), and the spectra can be directly compared with thoseat different temperatures or other samples throughout this article,except for those shown using arbitrary units. As shown, both epi-layers exhibited distinct NBE PL peaks and shoulders originatingfrom the recombination of free A-excitons (FXA) at 3.478 eV,recombination of excitons bound to a neutral donor (DBEs) at3.472 eV, and their LO phonon replicas at the energies higher than3.2 eV at 12 K. In addition, weak luminescence bands called “blueluminescence (BL)” due to the transition of an electron from theconduction band to a Cþ/0N center32 or from a deep-donor state ofcarbon on a Ga site (CGa)79 at around 2.9 eV (carbon-blue), “YL”at around 2.2 eV (Refs. 45–47, 51, and 86), and “red luminescence(RL)” at around 1.8 eV (Ref. 87) were detected. By using the first-principles calculations, Reshchikov et al.87 have suggested that VNare the origin of the RL band. In this context, the appearance of RLimplies noticeable [VN] in these epilayers. There could be two inde-pendent origins for the YL band: one is the transition of an elec-tron in the conduction band (or bound to a shallow donor) to anacceptor-like C0/�N deep center47,54 and the other is the emissiondue to the complex of a VGa and a donor impurity such as an O ona N site (ON), VGaON.47,51 It is noted that room-temperature YLintensity increased and NBE emission intensity decreased with theincrease in [C] from 2 × 1015 to 2 × 1016 cm−3. The results indicatethat most of C substitute N sites to form CN and act as DRCs,being consistent with the C0/�N transition model for the YL band.47Consistent with the steady-state PL results, τRTPL of the NBEemission decreased from 0.6 to 0.2 ns with increasing [C], as indi-cated beside the integrated spectral TRPL decay signals for the NBEemissions of the MOVPE layer (supplier F) with [C] of 2 × 1015 and2 × 1016 cm−3 in Figs. 5(c) and 5(d), respectively. The τRTPL value(0.2 ns) of F with [C] = 2 × 1016 cm−3 is plotted by red F nearthe center in Fig. 4. The τRTPL value almost agreed with the value onthe calculated red curve for [CN] = 2 × 1016 cm−3, while τRTPL of Fwith [C] = 2 × 1015 cm−3 (0.6 ns) was shorter than the calculatedvalue for [CN] = 2 × 1015 cm−3 being approximately 2.5 ns (crossingbetween the red line and NMGRC = 2 × 1015 cm−3). In such low [C]samples, τRTPL was no longer limited by [CN] and, therefore, mostlikely limited by [VGaVN] because the major vacancy defects inn-GaN grown from the vapor phase is [VGaVN],25 as revealed fromFig. 3. Then, [VGaVN] can be estimated from the crossing betweenthe black curve and τRTPL ¼ 0:6 ns to be approximately 2 × 1015 cm−3(black F located on the black curve in Fig. 4). Because[VGaVN] = 2 × 1015 cm−3 nearly agrees with the detection limit(lower dynamic range) of PAS in n-GaN,37 the (S, W) coordinateFIG. 4. τRTPL � NMGRC relationships for common MGRCs in n-GaN: Fe3þ/2þGa(Ref. 30), CN (Ref. 29), and VGaVN (Ref. 25). They are drawn by green, red,and black curves, respectively, using Eqs. (3) and (5), where τR ¼ 40 ns(Refs. 22 and 23) and Cp values of 5 × 10−8 (Ref. 30), 2 × 10−7 (Ref. 29),and 6 × 10−7 (Ref. 25) cm3 s−-1, respectively, are used. By usingvth ¼ vp ¼ 9:1� 106 cm � s�1 that is obtained from hole effective mass(mp) of 1:66m0, σp are 6� 10�15, 2� 10�14, and 7� 10�14 cm2, respec-tively. Here, Fe3þ/2þGa and C0/�N are known as E3 (Ref. 82) and H1 (Ref. 54)traps, respectively. Blue and orange curves are τRTPL � NMGRC relationships forcommon MGRCs in p-type GaN: VGa(VN)2 (Ref. 26) and (VGaVN)3 (Ref. 27),respectively. For both vacancy clusters, nearly equal Cn value of 5 × 10−6 cm3 s−1(Refs. 26 and 27) is used. By using vth ¼ vn ¼ 2:6� 107 cm � s�1 that isobtained from electron effective mass (mn) of 0:20m0, σn is 2� 10�13 cm2. Inthe figure, corresponding ηNBEint (¼ τRTPL /τR) at 300 K is shown on right y-axis.Measured τRTPL of n- and p-type GaN (suppliers A, B, D, E, F, G, K, R, and S) areplotted by italic outline characters on colored-square background. [Presentationstyle partially reproduced with permission from Chichibu et al., J. Appl. Phys. 123,161413 (2018). Copyright 2018 AIP Publishing LLC].25Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-10© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japalmost overlaps with the experimental (SDF, WDF). For avoidingcongestion of data plots, the (S, W) data are not plotted in Fig. 3.As described in the preceding paragraph, either [C] or[VGaVN] limited τRTPL of MOVPE epilayers depending on the recip-rocal numbers of Cp � NMGRC. The dominance of [VGaVN] in limit-ing τRTPL was observed in thick HVPE layers or sliced substrates,which principally contain low [C]. In Figs. 6(a) and 6(b), integratedspectral TRPL decay signals at 300 K for the NBE emission of theHVPE GaN from suppliers A and B, respectively, are shown. Inboth samples, [C] was less than the detection limit of the particularSIMS measurement (∼3 × 1015 cm−3), which predicts τRTPL longerthan 2 ns (see the red curve in Fig. 4). However, the samplesexhibited relatively short and different τRTPL of 0.43 and 0.11 ns,respectively, although [C] and TDD are nearly the same. The resultindicates the dominance of [VGaVN] in limiting τRTPL . Accordingly,symbols A (0.43 ns) and B (0.11 ns) are plotted on the black curvein Fig. 4 at the crossings with respective τRTPL values. Then, each[VGaVN] is obtained from the intersection between a perpendicularline from the symbol and horizontal axis. The obtained [VGaVN]values are lower than approximately 1.3 × 1016 cm−3 for bothsamples, and therefore, (S, W) coordinates almost overlap with theexperimental (SDF, WDF) again.In addition to C0/�N and VGaVN, Cp of Mg0/�Ga was obtainedfrom MOVPE GaN, as supplier G accidentally gave us an n-GaNepilayer containing Mg impurity of approximately 2 × 1016 cm−3, inaddition to a high-purity epilayer with τRTPL ¼ 0:8 ns (black symbolFIG. 5. Steady-state PL spectra of MOVPE GaN (F) with [C] of (a) 2 × 1015 and (b) 2 × 1016 cm−3. In each panel, upper (black) and lower (red) curves show the spectraat 12 and 300 K, respectively. The PL intensity (y-) axis has a unit of count per second (cps), and the spectra can be compared with those at different temperatures orother samples. The NBE emission includes free and bound excitons and their phonon replicas. BL, YL, and RL indicate the blue luminescence,32,85 yellowluminescence,45–47,51,86 and red luminescence87 bands, respectively. Integrated spectral TRPL decay signals for the NBE emissions measured at 300 K of the MOVPEGaN (F) with [C] of (c) 2 × 1015 and (d) 2 × 1016 cm−3. The signal denoted by “System” shows the overall system response. The decay curves were fitted using abi-exponential line shape function [Eq. (9)]. For plotting the data on Fig. 4, τ1 values are used as principal τRTPL representative.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-11© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japG in Fig. 4). Because the Mg-containing sample showed n-typeconductivity, τRTPL value of 50 ps (plotted by magenta symbol inFig. 4) gave Cp value of approximately 1 × 10−6 cm3 s−1(σp ¼ 1:1� 10�13 cm2). This large Cp exactly agrees with the datareported by Reshchikov.323. GaN crystals grown from the liquid and supercriticalstatesDifferent from the GaN samples grown from the vapor phase,the results shown in Fig. 3 indicated that GaN crystals grown bythe Na-flux method contained larger-size vacancy clusters such asVGa(VN)3 (Ref. 57) and those grown using the supercritical NH3(BAT and AAT) contained vacancy-impurity complexes such asHGa or VGa(ON)3−4 (Ref. 60). Such vacancy complexes also influ-ence τRTPL . PL spectra of the Na-flux56 GaN crystals (supplier J,grown using Na–Ga melt58 and Na vapor58,59) and LPE GaN wafer(supplier K) are shown in Figs. 7(a) and 7(b), respectively. Asshown by top two traces in Fig. 7(a),59 the PL spectrum at 9 K(293 K) of the crystal grown using the Na–Ga melt58 exhibited abroad NBE emission band with the peak at 3.470 eV (3.425 eV), ofwhich full-width at half-maximum (FWHM) was about 67 meV(150 meV). According to the fact that the FWHM value of theNBE emission often reflects the bandgap broadening caused by theresidual impurities,88,89 the residual electron concentration is esti-mated to be in the range of high 1019 cm−3. The PL spectra alsoexhibited broad emission bands at around 3.3 and 2.9 eV. Becausesimilar emission bands have been reported in C, Mg, or Zn-dopedGaN,86,90,91 the origins of the 3.3 and 2.9 eV bands are tentativelyassigned as a conduction band to acceptor (FA) transition and adonor-to-acceptor pair (DAP) transition, respectively. The originswill be discussed later because both bands appear to suffer fromspectral broadenings caused by high concentration impurities.Conversely to the GaN crystal grown using the Na–Ga melt,the emission bands due to DLs were absent and the FWHM valuefor the NBE peak was as small as 1.3meV at 9 K for the crystalgrown using Na vapor,58 as shown by bottom black trace inFig. 7(a).59 More precisely, PL peaks originating from radiativerecombinations of free A- and B-excitons (FXA and FXB, respec-tively) and those bound to a neutral donor (DBE peaks I2,A and I2,B,respectively) were observed. From the peak energy (3.414 eV) andFWHM (45meV) of the NBE emission at 293 K, the electron con-centration is estimated to be mid-1017 cm−3. Since O concentrationquantified by the SIMS measurement was in the order of 1017 cm−3,O appears to be the major donor impurity. The concentrations ofother impurities such as Si and C were lower than the detectionlimits. All data indicate superior properties of GaN crystals grownusing Na vapor58,59 compared with those using the Na–Ga melt.57The PL spectrum at 12 K of the Ge-doped (3 × 1018 cm−3)LPE GaN (K) exhibited the NBE (a DBE) peak at 3.472 eV and itsLO phonon replicas at the energies higher than 3.2 eV, as shown inFig. 7(b). The FWHM value for the DBE peak (∼14 meV) wasintermediate among the Na-flux GaN crystals (J) grown using theNa–Ga melt and Na vapor,58,59 reflecting the intermediate donorimpurity concentration. In addition to the NBE peak, distinct ultra-violet luminescence (UVL) band at around 3.26 eV was observed,which most probably originate from a free electron or a shallowdonor to a MgGa acceptor transition.86,91 Moreover, low-energy tailof the UVL band (BL band) and distinct “green luminescence(GL)” band were observed. Because [C] of the GaN crystal (K)quantified using SIMS measurement was 3 × 1017 cm−3, which wasthe highest among the samples measured in this study, the BLFIG. 6. Integrated spectral TRPL decay signals at 300 K for the NBE emissions of the HVPE GaN from suppliers (a) A and (b) B. The signal denoted by “System” showsthe overall system response. In both samples, [C] was less than the detection limit of the particular SIMS measurement (∼3 × 1015 cm−3), which predicts τRTPL longer than2 ns when C0/�Nh ilimits the lifetime (see Fig. 4). The decay curves were fitted using a bi-exponential line shape function [Eq. (9)], and τ1 values are used as representa-tive τRTPL . In these low [C] GaN, τRTPL is most likely limited by [VGaVN].Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-12© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japlikely originates from Cþ/0N (Ref. 32) or CGa (Ref. 85) and GL mayinclude a high-energy shifted YL band that mainly originates fromC0/�N (Refs. 47 and 54). Another well-known origin for the GL bandis VN (Ref. 87), which does not contradict the present finding that-GaN crystals grown from liquid phase contained VN-rich vacancyclusters like VGa(VN)3 (Ref. 57) instead of VGaVN.Integrated spectral TRPL decay signals at room temperaturefor the NBE emissions of Na-flux GaN (J) grown using the Na–Gamelt and Na vapor59 are shown in Fig. 7(c). Consistent with thewell-resolved NBE emissions displayed in Fig. 7(a), τRTPL of the GaNcrystal grown using Na vapor (50 ps) was more than three timesthe crystal grown using the Na–Ga melt (16 ps).59 Because [C] waslower than the detection limit of the SIMS measurement and YLband originating from C0/�N (Refs. 47 and 54) was not observed inthe lower trace of Fig. 7(a), τRTPL is most likely limited by the con-centration of intrinsic point defects. Unfortunately, typical dimen-sions of the GaN crystals (J) were 1- to 5-mm-long along the c-axisand 300-μm-diameter surrounded by naturally formed sixm-planes,58,59 which were too small for PAS measurements.Therefore, the τRTPL values of J are not displayed in Fig. 4. It is notedfrom Fig. 7(c) that the appearance of three decay components indi-cates the presence of at least three major domains of differentdefect concentrations or species. Integrated spectral TRPL decaysignal at 300 K for the NBE emission of the LPE GaN (K) is shownin Fig. 7(d). The obtained τRTPL was 35 ps, which is consistentlyintermediate between the two Na-flux GaN crystals (J). The τRTPLFIG. 7. PL spectra of (a) Na-flux GaN crystals from supplier J grown using Na–Ga melt and Na vapor58,59 and (b) LPE GaN wafer from supplier K. Room-temperatureintegrated spectral TRPL decay signals measured for the NBE emissions of (c) the Na-flux GaN (J) grown using Na–Ga melt and Na vapor59 and (d) LPE GaN (K) con-taining high concentration carbon ([C] = 3 × 1017 cm−3). The signal denoted by “System” shows the overall system response. The decay curves were fitted using abi-exponential (or tri-exponential) line shape function [Eq. (9)], and τ1 values are used as representative τRTPL . [The data in (a) and (c) are reproduced with permission fromOnuma et al., Appl. Phys. Express 2, 091004 (2009). Copyright 2009 IOP Publishing LLC].59Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-13© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japvalue of 35 ps is plotted by the italic outline character K on a redsquare background at NMGRC ¼ [C] ¼ 3� 1017 cm�3 in Fig. 4,which is close to the red curve drawn for CN.29Steady-state PL spectra of the LPAAT GaN crystal (P) takenfrom the (000�1) growth plane are shown in Fig. 8(a).61 At 12 K, theNBE peak intensity was more than three orders of magnitudehigher than those of BL, YL, and RL bands. The BL band was alsofound in AAT and BAT crystals, which may originate from thecomplexes comprising hydrogenated VGa and ON (HGa–ON)92 and/or VGaON (VGa–ON),93 according to the fact that BAT and AATcrystals grown using supercritical NH3 tend to contain high con-centration H and O due to the difficulty in evacuating the autoclaveand to the use of hygroscopic mineralizers.61,94 The BL band seenin Fig. 8(a) is named “supercritical blue.”94 At 295 K, the GL bandappears to be superimposed in the high energy side of the YLband. However, the NBE emission remained dominant andincluded at least two low-energy shoulders originating from LOphonon replicas. Integrated spectral TRPL decay signals measuredat 300 K for the NBE emissions of the LPAAT GaN (P) and AATGaN (N) are shown in Fig. 8(b).94 Obviously, τRTPL of LPAAT GaN(P) (40 ps) was an order of magnitude longer than that of AATGaN (N) (4 ps). The results shown in Figs. 8(a) and 8(b) indicatefar lower NMGRC in the LPAAT GaN (P)61,94 than that in the AATGaN (N),60 although the latter has been grown at higher pressure(Pg > 200MPa) because an order of magnitude longer τRTPL (Ref. 94)is a fingerprint of lower concentration of NMGRCs (NMGRC).Evidence to support this assignment is that the room-temperaturePL spectrum of the AAT GaN crystal was dominated by the YLband60 although much higher excitation power density of51W cm−2 was used:60 The result indicates higher concentration ofDRCs (NDRC). We note that τRTPL of 40 ps for the LPAAT GaN (P)(Ref. 94) is the longest among AT GaN crystals: the BAT GaNcrystal (L) exhibited short τRTPL of approximately 4 ps (data not dis-played). Because Cp of HGa, VGa(ON)3–4,60 and VGa(VN)n buried byH and/or O (Ref. 94) are approximately 3–8 × 10−7 cm3s−1 but thevalues are under confirmation,94 τRTPL for LPAAT (P) and AAT (N)GaN are not plotted in Fig. 4. Nevertheless, LPAAT method hasadvantages in fabricating plenty of large-size mosaic-free GaNwafers of better qualities than conventional AAT in a single run.61B. p-type GaNFor obtaining a complete view of the recombination dynamicsgoverned by MGRCs in GaN, those in p-type material must beunderstood. To comply with such demand, our state-of-the-artunderstandings on the origins and roles of MGRCs in Mg-dopedp-GaN (GaN:Mg) epilayers and Mg-I/I p-GaN films are describedin the following. Measured (S, W) for GaN:Mg epilayers grown byMOVPE (supplier Q)42 are shown by closed blue triangles in Fig. 9,for which annealing temperatures (Ta) are labeled. The calcu-lated41,60,73 (S, W) shown in Fig. 2 are plotted by open symbols forthe determination of the defect species. The experimental(SDF, WDF) is plotted by closed black circle labeled DF-CTRL.Because the slope of an approximated line for the blue (S, W)plots nearly agreed42 with the slope of a line connecting the calcu-lated (SDF, WDF) and (SVGa(VN)2 , WVGa(VN)2 ), major vacancy-typedefects were identified as VGa(VN)2 (Ref. 42). Different from theseeded-grown epilayers,26,42 defect species of Mg-I/I GaN variedFIG. 8. (a) Steady-state PL spectra of the LPAAT GaN crystal (P).61 Upper (black) and lower (red) curves show the spectra at 12 and 295 K, respectively. The PL intensity(y-) axis has a unit of cps and the spectra can be compared with those at different temperatures or other samples. The NBE emission includes free and bound excitonsand their phonon replicas. (b) Integrated spectral TRPL decay signals measured at 300 K for the NBE emissions of the LPAAT GaN (P) (upper) and AAT GaN (N) (lower).The signal denoted by “System” shows the overall system response. The decay curves were fitted using a bi-exponential line shape function [Eq. (9)], and τ1 values aredenoted as representative τRTPL . [The data in (a) are reproduced with permission from Kurimoto et al., Appl. Phys. Express 15, 055504 (2022). Copyright 2022 IOPPublishing LLC;61 the data in (b) are reproduced with permission from Shima et al., Appl. Phys. Lett. 124, 181103 (2024). Copyright 2024 AIP Publishing LLC].94Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-14© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japwith annealing conditions.43,44,62 Common to three suppliers S, T,and U, (S, W) plots almost overlapped with (SVGaVN , WVGaVN ) coor-dinate right after I/I, as shown in Fig. 9, indicating the formation ofhigh concentration VGaVN by Mg-I/I.43,44,62 We note that closedorange plots were measured with the 325.0 nm laser illumination andclosed carmine plots were measured without illumination. Here, thelaser illumination was carried out to supply electrons in the vacancy-type defects to increase the sensitivity of the PAS measurement.43,44,62With increasing Ta, (S, W) of the Mg-I/I GaN (S) shifted once to theright and then to the upper left, indicating an agglomeration ofVGaVN into large-size vacancy clusters. Because the slope of theapproximated line for the downward triangle plots agreed with thatof the line connecting the calculated (SDF, WDF) and(S(VGaVN)3 , W(VGaVN)3 ), major vacancy-type defects after PIAs wereassigned as (VGaVN)3 “hexavacancies.”43,44,62 We note that suchmovement of (S, W) was also found in T and U (Refs. 62 and 44,respectively). In case of supplier T, (S, W) further shifted to theleft,62 approaching to a virtual line connecting calculated (SDF, WDF)and (S(VGaVN)2 , W(VGaVN)2 ), because sequentially implanted excess Natoms may have buried some VN to reduce the vacancy cluster size.62In Fig. 9, (S, W) plots for suppliers T and U are not displayed toavoid congestion of data plots and approximated lines.τRTPL � NMGRC relationships for the MGRCs in p-GaN areshown in Fig. 4: blue and orange curves show τRTPL as a function ofVGa(VN)2 and (VGaVN)3 concentrations, [VGa(VN)2] and[(VGaVN)3], respectively. They are drawn using Eqs. (3) and (5),where common τR ¼ 40 ns (Refs. 22 and 23) andCn ¼ 5� 10�6 cm3 s�1 (Refs. 26 and 27) are used. This Cn value isapproximately an order of magnitude larger than Cp of VGaVN(6� 10�7 cm3 s�1).25 By using vth ¼ vn ¼ 2:6� 107 cm s�1 that isestimated from electron effective mass (mn) of 0:20m0, correspond-ing σn is 2� 10�13 cm2, which is more than twice the σp of VGaVNin n-GaN (7� 10�14 cm2). These values are summarized inTable III. In Fig. 4, measured τRTPL of the p-GaN epilayer (supplierR) and Mg-I/I p-GaN (supplier S) are plotted by italic outline char-acters on blue- and orange-square backgrounds, respectively. Asclearly seen, τRTPL of p-GaN is generally an order of magnitudeshorter than the n-GaN for the same NMGRC because of approxi-mately three times larger σn and three times faster vn.Representative PL spectra of MOVPE GaN:Mg epitaxial filmannealed at 850 °C (reference control sample), Ga- and N-polar710-nm-deep I/I-GaN:Mg +H annealed at 1230 °C, and Ga- andN-polar 100-nm-deep I/I-GaN:Mg +H annealed at 1230 °C areshown in Figs. 10(a)–10(e), respectively.27 All samples were pro-vided by supplier S, where [Mg] was commonly 1 × 1019 cm−3. InFigs. 10(f)–10( j), PL spectra of as-implanted and annealedN-polar 100-nm-deep I/I-GaN:Mg + H of Ta = 800, 1000, 1100, and1260 °C are shown, respectively. In each panel, PL spectra measuredat 10 and 300 K are shown at the top and bottom, respectively. Asshown in Fig. 10(a), the PL spectrum at 10 K of the Ga-polar GaN:Mg epilayer after annealing was dominated by the UVLband.86,87,92,95,96 Also, a distinct peak due to the recombination ofexcitons bound to a neutral acceptor (acceptor-bound excitons:ABEs)96 was observed. Both results indicate a progressive formationof MgGa acceptors. In addition, the emergence of a BL band (mag-nesium blue)91,95 at around 2.8 eV at 300 K [lower solid curve inFig. 10(a)] is a fingerprint of p-type conductivity of GaN:Mg. Theemissions from DRCs such as GL or RL were almost absent.The Ga- and N-polar 710-nm-deep I/I-GaN:Mg +H also exhib-ited the UVL band at 10 K, as shown in Figs. 10(b) and 10(c), respec-tively, implying the formation of MgGa acceptors.86,91,93,96 However,their intensities were three orders of magnitude lower than the epi-layer [Fig. 10(a)]. Moreover, distinct GL band87 peculiar to I/I-GaN:Mg +H (Ref. 97) was dominant, and the RL band with almost equalintensity as UVL was found in both Figs. 10(b) and 10(c). Theseresults indicate higher NMGRC in I/I-GaN:Mg +H than the epilayer.Conversely, the Ga- and N-polar 100-nm-deep I/I-GaN:Mg +Hexhibited a predominant UVL band at 10 K, of which intensities wereapproximately one and two orders of magnitude higher than the710-nm-deep ones, as shown in Figs. 10(d) and 10(e), respectively.Moreover, a distinct ABE peak was found only in the 100-nm-deepsamples, indicating lower NMGRC. Indeed, both GL and RL were sig-nificantly suppressed. Therefore, the depth of I/I, i.e., total doses andenergies used, seriously affected PL intensities:97 to form constant[Mg] and [H] profiles, higher total doses and a greater number oftimes of I/I with higher energies are required for deeper profilesamples, meaning that the samples suffer from severer I/I damage.97FIG. 9. Measured (S, W ) for p-GaN supplied by Q (closed blue triangles)42and S (closed orange and carmine downward triangles).43 For the plot Q,annealing temperatures (Ta) are labeled. For S, closed orange plots were mea-sured with the 325.0 nm laser illumination and closed carmine plots were mea-sured without illumination. Error bars are not given on all S–E plots because theexperimental errors for the determination of both S and W were less than 0.1%.The calculated41,60,73 (S, W ) coordinates shown in Fig. 2 are plotted by opensymbols to determine the vacancy defect species. The “experimental”(SDF, WDF) is plotted by closed black circle (DF-CTRL). [Calculated data plotsare reproduced with permission from Ishibashi and Uedono, J. Phys. Conf. Ser.505, 012010 (2014). Copyright 2014 IOP Publishing LLC;41 Uedono et al.,J. Cryst. Growth 448, 117 (2016). Copyright 2016 Elsevier B.V.;60 and Uedonoet al., Phys. Status Solidi B 255, 1700521 (2018). Copyright 2017 WILEY-VCHVerlag GmbH & Co.;73 Experimental data plots are reproduced with permissionfrom Uedono et al., Phys. Status Solidi B 252, 2794 (2015). Copyright 2015WILEY-VCH Verlag GmbH & Co.42 and Uedono et al., Phys. Status Solidi B256, 1900104 (2019).43].Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-15© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japTABLEIII.OriginsandcapturingperformancesofmajorMGRCsinGaNat300K(vth:vp=9.1×106cms−1andv n=2.6×107cms−1 ).ConductivitytypeOriginCapturingperformanceforminoritycarriersGeneralinformationandcommentsCapturecoefficient(cm3 ⋅s−1 )Capturecrosssection(cm2 )nFe3þ/2þGaCp=5×10−8aσp=6×10−15aResidualimpurity:transitionmetal:(E3)bMg0/� GaCp=1×10−6σp=1×10−13ResidualimpurityC0/�NCp=2×10−7cσp=2×10−14cDRC:indelibleimpurityforMOVPE(H1)dVGaVNeCp=6×10−7eσp=7×10−14eMajorNRCsinn-GaNgrownbyHVPE,MOVPE,andMBEVGa(VN) 3f……NRCpresentinNa-fluxcrystalsfHVGaVNorVGa(ON) 4gCp=3–8×10−7gσp=3–9×10−14gDRC/NRCpresentinAATandLPAATcrystalsgpVGa(VN) 2hCn=5×10−6iσn=2×10−13iNRCsinMOVPEGaN:Mgepilayersh,i(VGaVN) 3jCn=5×10−6kσn=2×10−13kNRCsinMgionimplanted(I/I)GaNafterPIAi,kDRCsMg Ga(notsodeep)ProbablysameasMg0/� GacenterUVL(ultravioletluminescence)lMg Ga−VN……BL(magnesiumblue)mCþ/0N(orCGa)……BL(carbonblue)nVGa(VN) nburiedbyHand/orOoCp=3–8×10−7Oσp=3–9×10−14OBL(supercriticalblue)pVN-related……GL(greenluminescence)qC0/�NCp=4×10−7rσp=4×10−14rYL(yellowluminescence)sVGaON……YL(yellowluminescence)VN-related……RL(redluminescence)pa Ref.30.bRef.82.c Ref.29.dRef.54.e Ref.25.f Ref.57.g Refs.60and94.hRef.42.i Ref.26.j Refs.43,44,and62.kRefs.27and28.l Refs.86,87,91,95,and96.mRefs.91and95.nRefs.32and85.oRef.94.pRefs.92and93qRef.87.r Ref.32.s Refs.45–47,51,and86.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-16© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japAt 300 K, the dominant PL peak of the control GaN:Mg epi-layer was the BL band91,96 often called Mg-blue, as shown inFig. 10(a). The Ga- and N-polar 710-nm-deep I/I-GaN:Mg +H didnot exhibit NBE emissions at 300 K, as shown in Figs. 10(b) and 10(c).The 100-nm-deep I/I samples, conversely, exhibited the NBE emis-sions at 300 K, as shown in Figs. 10(d) and 10(e). These results alsosupport lower NMGRC, more precisely NNRC, in the 100-nm-deepsamples. In addition to the NBE emission, the N-polar100-nm-deep I/I-GaN:Mg +H exhibited distinct BL band (mostlikely Mg-blue)91,93 as the low energy tail of UVL at 300 K, asshown in Fig. 10(e). Because the NBE emission intensity at 300 Kof the N-polar 100-nm-deep I/I-GaN:Mg + H [Fig. 10(e)] was anorder of magnitude higher than that of the Ga-polar edition[Fig. 10(d)], NNRC in the N-polar sample is likely lower than theGa-polar one, provided that the major NRCs in both samples havea common origin. Indeed, Mg-I/I GaN contained the samevacancy-type defects right after room-temperature I/I, namely,VGaVN,43,44,62 in the samples provided by supplier S, T, and U irre-spective of polar directions.43 Here, we mention that major NRCsand their concentrations in the Ga- and N-polar samples before I/Iwere also commonly VGaVN (Refs. 24 and 25) but lower than thedynamic range of the PAS measurement (∼1015 cm−3).37 After thePIA, VGaVN commonly agglomerated into (VGaVN)3 (suppliers Sand U) except for the case of using sequential I/I of N (supplier T),in which smaller vacancy clusters such as (VGaVN)2 weredominant.62 Nevertheless, in addition to the depth of I/I, the crys-tallographic plane used for I/I and PIA is shown to be the otherconsiderable factor affecting the PL intensities. As mentioned byNarita et al.,98 the (000�1) plane offers better thermal stability than(0001) plane does, and therefore, the formation of vacancy clustersacting as NRCs at the surface during PIA is less likely. These con-siderations are consistent with the fact that the N-polar100-nm-deep I/I-GaN:Mg +H showed a p-type conductivity.97,98Sakurai et al.64 showed that sequential I/I of Mg and N(I/I-GaN:Mg + N) into (0001) Ga-polar GaN followed by uncappedPIA in 1 GPa N2 atmosphere at 1480 °C (supplier U) gave rise tothe observation of an intense UVL band originating from MgGaacceptors86,87,91,95,96 and suppressed GL band in the low-temperature cathodoluminescence (CL) spectra. Their resultsimplied reduced [VN] by sequential I/I of N followed by the high-temperature UHPA. Recently, Uedono et al.44 identified (VGaVN)3as the major vacancy-type defects in the I/I-GaN:Mg + N after theUHPA at 1480 °C (supplier U) and found progressive decrease in[(VGaVN)3] by increasing Ta.44 However, τRTPL was shorter than thetemporal resolution of our TRPL system99 due to the presence ofcertain damaged zones at and near the surface44,99 likely created bythermal stress.Recently, Hu et al.100 and Maeda et al.101 independentlyreported the SRH lifetime (τSRH), which is expressed byτSRH ¼ ffiffiffiffiffiffiffiffiffiτnτpp, where τn and τp are the lifetimes of an electron andFIG. 10. Steady-state PL spectra at 10 K (top traces) and 300 K (bottom traces) of (a) Ga-polar GaN:Mg epilayer after annealing at 850 °C for 5 min in a N2 ambient, (b)Ga-polar 710-nm-deep and (c) N-polar 710-nm-deep, (d) Ga-polar 100-nm-deep and (e) N-polar 100-nm-deep I/I-GaN:Mg + H annealed at Ta = 1230 °C. (f )–( j) PLspectra of N-polar I/I-GaN:Mg + H. The Ta values were (g) 800, (h) 1000, (i) 1100, and ( j) 1260 °C. The [Mg] values were (a) 1.5 × 1019 and (b)–( j) 1.0 × 1019 cm−3. Allsamples were fabricated on FS-GaN substrates by supplier S. The PL intensity (y-) axis has a unit of cps, and all spectra can be quantitatively compared. [Reproducedwith permission from Shima et al., Appl. Phys. Lett. 113, 191901 (2018). Copyright 2018 AIP Publishing LLC.]27Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-17© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japa hole at the recombination plane in the depletion layer, respec-tively, in p+n− and n+p− junctions of GaN as 12 ns (Ref. 100) and46 ps (Ref. 101), respectively. This difference most likely reflects thedifferences in vminority and σminority of the dominating NRCs. Theresults by Hu et al.100 and Maeda et al.101 are consistent with theauthors’ results.25–28IV. SUMMARYIn this article, current knowledges on the origins and capturecoefficients for minority carriers, Cminority, of major MGRCs in thestate-of-the-art GaN substrates, epilayers, and Mg-implanted layersobtained using temporally resolved photoluminescence and PASmeasurements are summarized. For unintentionally doped andn-type GaN grown by HVPE and MOVPE, τRTPL for thenear-band-edge emission was limited by the concentration of C0/�N ,which exhibit the YL band,45–47,51,86 or VGaVN that acts as majornonradiative recombination centers (NRCs)24,25 when [C] washigher or lower, respectively, than approximately 1016 cm−3. Themajor vacancy-type defects in Na-flux GaN was identified asVGa(VN)3 that is larger in size than VGaVN of n-GaN grown fromthe vapor phase. The major defects in ammonothermal GaN werevacancy complexes such as VGa buried by a hydrogen (HGa) and/orvacancy clusters buried by impurities such as HVGaVN andVGa(ON)3–4. All these vacancy complexes appear to act as MGRCs.For Mg-doped p-GaN epilayers, τRTPL was limited by the concentra-tion of VGa(VN)2. For Mg-implanted GaN, VGaVN and (VGaVN)3are the major NRCs right after the implantation and after appropri-ate activation annealing, respectively. The origins and Cminorityvalues of major MGRCs in GaN at 300 K are summarized inTable III. Because of larger electron capture cross sections ofVGa(VN)2 and (VGaVN)3 defects in addition to faster thermal veloc-ity of electrons, τRTPL of p-GaN is generally an order of magnitudeshorter than that of n-GaN with the same NMGRC. For the case ofsubstitutional impurities in Si, a standardization of B, P, and low-level C concentrations well below the detection limits of analyticalmethods like SIMS measurements has been realized by using a low-temperature PL measurement.83,84 As one of the perspectives, wepropose a standardization of τRTPL � NMGRC curves in Fig. 4 as cali-brating measures for quantifying (or semi-quantifying) the concen-trations of respective MGRCs well below the detection limits of PASand SIMS, as described in Sec. III A 1. We should again mentionthat the restriction for this proposal is the use of the weak-excitationconditions22,24–28 that give rise to the excited minority carrier con-centration constant and far below the concentrations of majority car-riers and threshold for maintaining negligible classical17,18 andtrap-assisted19 Auger–Meitner nonradiative recombination processes.ACKNOWLEDGMENTSThis work was supported in part by MEXT-Program forResearch and Development of Next-Generation Semiconductor toRealize Energy-Saving Society (No. JPJ005357), MEXT-Programfor Creation of Innovative Core Technology for Power Electronics(No. JPJ009777), MEXT-Program of Dynamic Alliance for OpenInnovation Bridging Human, Environment and Materials, and JSPSKAKENHI (Nos. JP16H06427 and JP21H01826) by MEXT and theCouncil for Science, Technology, and Innovation (CSTI),Cross-ministerial Strategic Innovation Promotion Program (SIP),“Next-generation power electronics-Research and Development ofFundamental Technologies for GaN Vertical Power Devices”(funding agency: NEDO).AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsShigefusa F. Chichibu: Conceptualization (lead); Data curation(equal); Formal analysis (equal); Funding acquisition (equal);Investigation (lead); Methodology (lead); Project administration(equal); Resources (equal); Software (equal); Supervision (lead);Validation (lead); Visualization (lead); Writing – original draft(lead); Writing – review & editing (lead). Kohei Shima: Data cura-tion (equal); Formal analysis (equal); Investigation (equal);Resources (equal); Software (equal); Validation (equal). AkiraUedono: Data curation (equal); Formal analysis (equal);Investigation (equal); Resources (equal); Validation (equal);Visualization (equal). Shoji Ishibashi: Data curation (equal);Formal analysis (equal); Investigation (equal); Methodology(equal); Software (equal); Supervision (equal). Hiroko Iguchi: Datacuration (equal); Resources (equal). Tetsuo Narita: Data curation(equal); Investigation (equal); Resources (equal). Keita Kataoka:Data curation (equal); Formal analysis (equal); Investigation(equal). Ryo Tanaka: Data curation (equal); Formal analysis(equal); Resources (equal). Shinya Takashima: Data curation(equal); Formal analysis (equal); Funding acquisition (supporting);Investigation (equal). Katsunori Ueno: Data curation (equal);Formal analysis (equal); Funding acquisition (supporting);Investigation (equal). Masaharu Edo: Data curation (equal);Funding acquisition (supporting); Investigation (equal); Resources(equal). Hirotaka Watanabe: Data curation (equal); Investigation(equal); Resources (equal). Atsushi Tanaka: Data curation (equal);Investigation (equal); Resources (equal). Yoshio Honda: Data cura-tion (equal); Formal analysis (supporting); Funding acquisition(supporting); Investigation (supporting); Project administration(supporting); Resources (equal); Supervision (supporting). JunSuda: Funding acquisition (equal); Investigation (equal); Projectadministration (equal); Resources (equal). Hiroshi Amano:Funding acquisition (lead); Project administration (equal);Resources (equal); Software (equal). Tetsu Kachi: Data curation(equal); Investigation (equal); Resources (equal); Supervision(equal). Toshihide Nabatame: Data curation (equal); Fundingacquisition (equal); Project administration (lead); Resources(equal); Validation (equal). Yoshihiro Irokawa: Data curation(equal); Investigation (equal); Resources (equal). Yasuo Koide:Data curation (equal); Formal analysis (equal); Funding acquisition(lead); Investigation (lead); Project administration (equal);Resources (equal); Visualization (equal).DATA AVAILABILITYThe data that support the findings of this study are availablein Refs. 44, 62, 63, and 73 in addition to this article.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-18© Author(s) 2024 08 May 2024 10:00:43https://pubs.aip.org/aip/japREFERENCES1S. J. Pearton, J. C. Zolper, R. J. Shul, and F. Ren, J. Appl. Phys. 86, 1 (1999).2In the statement of Scientific Background on the Nobel Prize in Physics 2014,Efficient blue light-emitting diodes leading to bright and energy-saving whitelight sources. Compiled by the Class for Physics of the Royal Swedish Academyof Sciences, October 7, 2014; I. Akasaki, Rev. Mod. Phys. 87, 1119 (2015);H. Amano, ibid 87, 1133 (2015); S. Nakamura, ibid 87, 1139 (2015);Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes,edited by S. Nakamura and S. F. Chichibu (Taylor & Francis, London, 2000).3S. Nakamura, M. Senoh, N. Iwasa, and S. Nagahama, Jpn. J. Appl. Phys. 34,L797 (1995).4S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys. Lett. 69, 4188(1996).5Y. Narukawa, Y. Kawakami, S. Fujita, S. Fujita, and S. Nakamura, Phys. Rev. B55, R1938 (1997).6S. F. Chichibu, A. Uedono, T. Onuma, B. A. Haskell, A. Chakraborty,T. Koyama, P. T. Fini, S. Keller, S. P. DenBaars, J. S. Speck, U. K. Mishra,S. Nakamura, S. Yamaguchi, S. Kamiyama, H. Amano, I. Akasaki, J. Han, andT. Sota, Nat. Mater. 5, 810 (2006); Philos. Mag. 87, 2019 (2007); preciselyreviewed in S. F. Chichibu, ECS J. Solid State Sci. Technol. 9, 015016 (2020).7Y. Saitoh, K. Sumiyoshi, M. Okada, T. Horii, T. Miyazaki, H. Shiomi, M. Ueno,K. Katayama, M. Kiyama, and T. Nakamura, Appl. Phys. Express 3, 081001(2010).8J. Kolník, İ. H. Oğuzman, K. F. Brennan, R. Wang, P. P. Ruden, and Y. Wang,J. Appl. Phys. 78, 1033 (1995).9D. Shibata, R. Kajitani, M. Ogawa, K. Tanaka, S. Tamura, T. Hatsuda,M. Ishida, and T. Ueda, IEDM Technical Digest (IEEE, 2016), p. 248.10M. Kodama, M. Sugimoto, E. Hayashi, N. Soejima, O. Ishiguro, M. Kanechika,K. Itoh, H. Ueda, T. Uesugi, and T. Kachi, Appl. Phys. Express 1, 021104 (2008).11T. Oka, T. Ina, Y. Ueno, and J. Nishii, Appl. Phys. Express 8, 054101 (2015).12Reviewed in H. Amano, Y. Baines, E. Beam, M. Borga, T. Bouchet,P. R. Chalker, M. Charles, K. J. Chen, N. Chowdhury, R. Chu et al., J. Phys. D:Appl. Phys. 51, 163001 (2018).13T. Sugahara, H. Sato, M. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita,K. Nishino, L. T. Romano, and S. Sakai, Jpn. J. Appl. Phys. 37, L398 (1998).14M. Auf der Maur, A. Pecchia, G. Penazzi, W. Rodrigues, and A. Di Carlo,Phys. Rev. Lett. 116, 027401 (2016).15S. F. Chichibu, H. Marchand, M. S. Minski, S. Keller, P. T. Fini, J. P. Ibbetson,S. B. Fleischer, J. S. Speck, J. E. Bowers, E. Hu, U. K. Mishra, S. P. DenBaars,T. Deguchi, T. Sota, and S. Nakamura, Appl. Phys. Lett. 74, 1460 (1999); laterprecisely reviewed in S. F. Chichibu, ECS J. Solid State Sci. Technol. 9, 015016(2020).16S. F. Chichibu, H. Miyake, and A. Uedono, Jpn. J. Appl. Phys. 61, 050501(2022).17L. Meitner, Z. Phys. 9, 131 (1922).18P. Auger, C.R. Acad. Sci.(F) 177, 169 (1923), see http://gallica.bnf.fr/ark:/12148/bpt6k3130n.image.f187.langFR19F. Zhao, M. E. Turiansky, A. Alkauskas, and C. G. Van de Walle, Phys. Rev.Lett. 131, 056402 (2023).20W. Shockley and W. T. Read, Jr., Phys. Rev. 87, 835 (1952).21R. N. Hall, Phys. Rev. 87, 387 (1952).22S. F. Chichibu, K. Hazu, Y. Ishikawa, M. Tashiro, H. Namita, S. Nagao,K. Fujito, and A. Uedono, J. Appl. Phys. 111, 103518 (2012).23K. Kawakami, T. Nakano, and A. A. Yamaguchi, Proc. SPIE 9748, 97480S (2016).24S. F. Chichibu, A. Uedono, T. Onuma, T. Sota, B. A. Haskell, S. P. DenBaars,J. S. Speck, and S. Nakamura, Appl. Phys. Lett. 86, 021914 (2005).25S. F. Chichibu, A. Uedono, K. Kojima, H. Ikeda, K. Fujito, S. Takashima,M. Edo, K. Ueno, and S. Ishibashi, J. Appl. Phys. 123, 161413 (2018).26S. F. Chichibu, K. Shima, K. Kojima, S. Takashima, M. Edo, K. Ueno,S. Ishibashi, and A. Uedono, Appl. Phys. Lett. 112, 211901 (2018).27K. Shima, H. Iguchi, T. Narita, K. Kataoka, K. Kojima, A. Uedono, andS. F. Chichibu, App. Phys. Lett. 113, 191901 (2018).28S. F. Chichibu, K. Shima, K. Kojima, S. Takashima, K. Ueno, M. Edo,H. Iguchi, T. Narita, K. Kataoka, S. Ishibashi, and A. Uedono, Jpn. J. Appl. Phys.58, SC0802 (2019).29K. Kojima, F. Horikiri, Y. Narita, T. Yoshida, H. Fujikura, and S. F. Chichibu,Appl. Phys. Express 13, 012004 (2020).30T. Aggerstam, A. Pinos, S. Marcinkevicius, M. Linnarsson, andS. Lourdudodd, J. Electron. Mater. 36, 1621 (2007).31T. Narita, Y. Tokuda, T. Kogiso, K. Tomita, and T. Kachi, J. Appl. Phys. 123,161405 (2018).32Reviewed in M. A. Reshchikov, J. Appl. Phys. 129, 121101 (2021).33R. Krause-Rehberg and H. S. Leipner, Positron Annihilation inSemiconductors, Solid-State Sciences (Springer, Berlin, 1999), p. 127.34P. G. Coleman, Positron Beams and Their Application (World Scientific,Singapore, 2000).35K. Saarinen, T. Laine, S. Kuisma, J. Nissilä, P. Hautojärvi, L. Dobrzynski,J. M. Baranowski, K. Pakula, R. Stepniewski, M. Wojdak, A. Wysmolek, T. Suski,M. Leszczynski, I. Grzegory, and S. Porowski, Phys. Rev. Lett. 79, 3030 (1997).36A. Uedono, S. F. Chichibu, Z. Q. Chen, M. Sumiya, R. Suzuki, T. Ohdaira,T. Mikado, T. Mukai, and S. Nakamura, J. Appl. Phys. 90, 181 (2001).37F. Tuomisto and I. Makkonen, Rev. Mod. Phys. 85, 1583 (2013).38A. Uedono, S. Ishibashi, T. Ohdaira, and R. Suzuki, J. Cryst. Growth 311, 3075(2009).39S. Ishibashi, Mater. Sci. Forum 445–446, 401 (2004).40S. Ishibashi, T. Tamura, S. Tanaka, M. Kohyama, and K. Terakura, Phys. Rev.B 76, 153310 (2007).41S. Ishibashi and A. Uedono, J. Phys.: Conf. Ser. 505, 012010 (2014).42A. Uedono, S. Takashima, M. Edo, K. Ueno, H. Matsuyama, H. Kudo,H. Naramoto, and S. Ishibashi, Phys. Status Solidi B 252, 2794 (2015).43A. Uedono, H. Iguchi, T. Narita, K. Kataoka, W. Egger, T. Koschine,C. Hugenschmidt, M. Dickmann, K. Shima, K. Kojima, S. F. Chichibu, andS. Ishibashi, Phys. Status Solidi B 256, 1900104 (2019).44A. Uedono, H. Sakurai, T. Narita, K. Sierakowski, M. Bockowski, J. Suda,S. Ishibashi, S. F. Chichibu, and T. Kachi, Sci. Rep. 10, 17349 (2020).45T. Ogino and M. Aoki, Jpn. J. Appl. Phys. 19, 2395 (1980).46J. Neugebauer and C. G. Van de Walle, Phys. Rev. B 50, 8067 (1994);Appl.Phys. Lett. 69, 503 (1996).47J. L. Lyons, A. Janotti, and C. G. Van de Walle, Appl. Phys. Lett. 97, 152108 (2010).48A. Y. Polyakov, N. B. Smirnov, A. S. Usikov, A. V. Govorkov, andB. V. Pushniy, Solid-State Electron. 42, 1959 (1998).49V. A. Joshkin, C. A. Parker, S. M. Bedair, J. F. Muth, I. K. Shmagin,R. M. Kolbas, E. L. Piner, and R. J. Molnar, J. Appl. Phys. 86, 281 (1999).50A. F. Wright, J. Appl. Phys. 90, 1164 (2001).51C. G. Van de Walle and J. Neugebauer, J. Appl. Phys. 95, 3851 (2004).52G. Piao, K. Ikenaga, Y. Yano, H. Tokunaga, A. Mishima, Y. Ban, T. Tabuchi,and K. Matsumoto, J. Cryst. Growth 456, 137 (2016).53F. Horikiri, Y. Narita, T. Yoshida, T. Kitamura, H. Ohta, T. Nakamura, andT. Mishima, Jpn. J. Appl. Phys. 56, 061001 (2017).54T. Narita, K. Tomita, Y. Tokuda, T. Kogiso, M. Horita, and T. Kachi, J. Appl.Phys. 124, 215701 (2018).55A. Tanaka, Y. Ando, K. Nagamatsu, M. Deki, H. Cheong, B. Ousmane,M. Kushimoto, S. Nitta, Y. Honda, and H. Amano, Phys. Status Solidi A 215,1700645 (2018).56H. Yamane, M. Shimada, S. J. Clarke, and F. J. DiSalvo, Chem. Mater. 9, 413(1997).57A. Uedono, M. Imanishi, M. Imade, M. Yoshimura, S. Ishibashi, M. Sumiya,and Y. Mori, J. Cryst. Growth 475, 261 (2017).58T. Yamada, H. Yamane, H. Iwata, and S. Sarayama, J. Cryst. Growth 281, 242(2005).59T. Onuma, T. Yamada, H. Yamane, and S. F. Chichibu, Appl. Phys. Express 2,091004 (2009).60A. Uedono, Y. Tsukada, Y. Mikawa, T. Mochizuki, H. Fujisawa, H. Ikeda,K. Kurihara, K. Fujito, S. Terada, S. Ishibashi, and S. F. Chichibu, J. Cryst.Growth 448, 117 (2016).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-19© Author(s) 2024 08 May 2024 10:00:43https://doi.org/10.1063/1.371145https://doi.org/10.1103/RevModPhys.87.1119https://doi.org/10.1103/RevModPhys.87.1133https://doi.org/10.1103/RevModPhys.87.1139https://doi.org/10.1201/9781482268065https://doi.org/10.1143/JJAP.34.L797https://doi.org/10.1063/1.116981https://doi.org/10.1103/PhysRevB.55.R1938https://doi.org/10.1038/nmat1726https://doi.org/10.1080/14786430701241689https://doi.org/10.1149/2.0382001JSShttps://doi.org/10.1143/APEX.3.081001https://doi.org/10.1063/1.360405https://doi.org/10.1143/APEX.1.021104https://doi.org/10.7567/APEX.8.054101https://doi.org/10.1088/1361-6463/aaaf9dhttps://doi.org/10.1088/1361-6463/aaaf9dhttps://doi.org/10.1143/JJAP.37.L398https://doi.org/10.1103/PhysRevLett.116.027401https://doi.org/10.1063/1.123581https://doi.org/10.1149/2.0382001JSShttps://doi.org/10.35848/1347-4065/ac46b1https://doi.org/10.1007/BF01326962https://gallica.bnf.fr/ark:/12148/bpt6k3130n.image.f187.langFRhttps://gallica.bnf.fr/ark:/12148/bpt6k3130n.image.f187.langFRhttps://gallica.bnf.fr/ark:/12148/bpt6k3130n.image.f187.langFRhttps://doi.org/10.1103/PhysRevLett.131.056402https://doi.org/10.1103/PhysRevLett.131.056402https://doi.org/10.1103/PhysRev.87.835https://doi.org/10.1103/PhysRev.87.387https://doi.org/10.1063/1.4717955https://doi.org/10.1117/12.2211914https://doi.org/10.1063/1.1851619https://doi.org/10.1063/1.5012994https://doi.org/10.1063/1.5030645https://doi.org/10.1063/1.5050967https://doi.org/10.7567/1347-4065/ab0d06https://doi.org/10.7567/1882-0786/ab5adchttps://doi.org/10.1007/s11664-007-0202-9https://doi.org/10.1063/1.5010849https://doi.org/10.1063/5.0041608https://doi.org/10.1103/PhysRevLett.79.3030https://doi.org/10.1063/1.1372163https://doi.org/10.1103/RevModPhys.85.1583https://doi.org/10.1016/j.jcrysgro.2009.01.051https://doi.org/10.4028/www.scientific.net/MSF.445-446.401https://doi.org/10.1103/PhysRevB.76.153310https://doi.org/10.1103/PhysRevB.76.153310https://doi.org/10.1088/1742-6596/505/1/012010https://doi.org/10.1002/pssb.201552345https://doi.org/10.1002/pssb.201900104https://doi.org/10.1038/s41598-020-74362-9https://doi.org/10.1143/JJAP.19.2395https://doi.org/10.1103/PhysRevB.50.8067https://doi.org/10.1103/PhysRevB.50.8067https://doi.org/10.1063/1.3492841https://doi.org/10.1016/S0038-1101(98)00137-3https://doi.org/10.1016/S0038-1101(98)00137-3https://doi.org/10.1063/1.370727https://doi.org/10.1063/1.1383980https://doi.org/10.1063/1.1682673https://doi.org/10.1016/j.jcrysgro.2016.08.030https://doi.org/10.7567/JJAP.56.061001https://doi.org/10.1063/1.5057373https://doi.org/10.1063/1.5057373https://doi.org/10.1002/pssa.201700645https://doi.org/10.1021/cm960494shttps://doi.org/10.1016/j.jcrysgro.2017.06.027https://doi.org/10.1016/j.jcrysgro.2005.04.022https://doi.org/10.1143/APEX.2.091004https://doi.org/10.1016/j.jcrysgro.2016.05.015https://doi.org/10.1016/j.jcrysgro.2016.05.015https://pubs.aip.org/aip/jap61D. Tomida, Q. Bao, M. Saito, R. Osanai, K. Shima, K. Kojima, T. Ishiguro, andS. F. Chichibu, Appl. Phys. Express 13, 055505 (2020); K. Kurimoto, Q. Bao,Y. Mikawa, K. Shima, T. Ishiguro, and S. F. Chichibu, Appl. Phys. Express 15,055504 (2022).62A. Uedono, R. Tanaka, S. Takashima, K. Ueno, M. Edo, K. Shima, K. Kojima,S. F. Chichibu, and S. Ishibashi, Sci. Rep. 11, 20660 (2021).63K. Shima, R. Tanaka, S. Takashima, K. Ueno, M. Edo, K. Kojima, A. Uedono,S. Ishibashi, and S. F. Chichibu, Appl. Phys. Lett. 119, 182106 (2021).64H. Sakurai, M. Omori, S. Yamada, Y. Furukawa, H. Suzuki, T. Narita,K. Kataoka, M. Horita, M. Bockowski, J. Suda, and T. Kachi, Appl. Phys. Lett.115, 142104 (2019).65K. Sierakowski, R. Jakiela, B. Lucznik, P. Kwiatkowski, M. Iwinska, M. Turek,H. Sakurai, T. Kachi, and M. Bockowski, Electronics 9, 1380 (2020).66P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).67G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).68J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).69E. Boronski and R. M. Nieminen, Phys. Rev. B 34, 3820 (1986).70M. J. Puska, A. P. Seitsonen, and R. M. Nieminen, Phys. Rev. B 52, 10947(1995).71S. F. Chichibu, A. Uedono, K. Kojima, K. Koike, M. Yano, S. Gonda, andS. Ishibashi, J. Appl. Phys. 127, 215704 (2020).72S. Ishibashi and A. Uedono, J. Phys.: Conf. Ser. 674, 012020 (2016).73A. Uedono, S. Takashima, M. Edo, K. Ueno, H. Matsuyama, W. Egger,T. Koschine, C. Hugenschmidt, M. Dickmann, K. Kojima, S. F. Chichibu, andS. Ishibashi, Phys. Status Solidi B 255, 1700521 (2018).74A. Van Veen, H. Schut, M. Clement, J. M. M. de Nijs, A. Kruseman, andM. R. Ijpma, Appl. Surf. Sci. 85, 216 (1995).75T. Onuma, Y. Kagamitani, K. Hazu, T. Ishiguro, T. Fukuda, andS. F. Chichibu, Rev. Sci. Instrum. 83, 043905 (2012).76P. Corfdir, P. Lefebvre, J. Levrat, A. Dussaigne, J.-D. Ganiere, D. Martin,J. Ristic, T. Zhu, N. Grandjean, and B. Deveaud-Pledran, J. Appl. Phys. 105,043102 (2009).77P. Corfdir, J. Ristic, P. Lefebvre, T. Zhu, A. Dussaigne, J. D. Ganiere,N. Grandjean, and B. Deveaud-Pledran, Appl. Phys. Lett. 94, 201115 (2009).78M. Kagaya, P. Corfdir, J.-D. Ganiere, B. Deveaud-Pledran, N. Grandjean, andS. F. Chichibu, Jpn. J. Appl. Phys. 50, 111002 (2011).79Y. Ishikawa, M. Tashiro, K. Hazu, K. Furusawa, H. Namita, S. Nagao,K. Fujito, and S. F. Chichibu, Appl. Phys. Lett. 101, 212106 (2012).80K. Furusawa, Y. Ishikawa, M. Tashiro, K. Hazu, S. Nagao, H. Ikeda, K. Fujito,and S. F. Chichibu, Appl. Phys. Lett. 103, 052108 (2013).81F. Tuomisto, T. Kuittinen, M. Zając, R. Doradziński, and D. Wasik, J. Cryst.Growth 403, 114 (2014).82M. Horita, T. Narita, T. Kachi, and J. Suda, Appl. Phys. Express 13, 071007(2020).83M. Tajima, Appl. Phys. Lett. 32, 719 (1978).84M. Tajima, S. Samata, S. Nakagawa, Y. Shinozuka, J. Oriyama, and N. Ishihara,Jpn. J. Appl. Phys. 60, 026501 (2021).85R. Armitage, Q. Yang, and E. R. Weber, J. Appl. Phys. 97, 073524 (2005).86M. A. Reshchikov and H. Morkoç, J. Appl. Phys. 97, 061301 (2005).87M. A. Reshchikov, D. O. Demchenko, J. D. McNamara, S. F. Garrido, andR. Calarco, Phys. Rev. B 90, 035207 (2014).88E. F. Schubert, I. D. Goepfert, W. Grieshaber, and J. M. Redwing, Appl. Phys.Lett. 71, 921 (1997).89M. Yoshikawa, M. Kunzer, J. Wagner, H. Obloh, P. Schlotter, R. Schmidt,N. Herres, and U. Kaufmann, J. Appl. Phys. 86, 4400 (1999).90B. J. Skromme, K. Palle, C. D. Poweleit, H. Yamane, M. Aoki, andF. J. DiSalvo, J. Cryst. Growth 246, 299 (2002).91G. Pozina, P. P. Paskov, J. P. Bergman, C. Hemmingsson, L. Hultman,B. Monemar, H. Amano, I. Akasaki, and A. Usui, Appl. Phys. Lett. 91, 221901(2007).92M. Toth, K. Fleischer, and M. R. Phillips, Phys. Rev. B 59, 1575 (1999).93H. C. Yang, T. Y. Lin, and Y. F. Chen, Phys. Rev. B 62, 12593 (2000).94K. Shima, K. Kurimoto, Q. Bao, Y. Mikawa, M. Saito, D. Tomida, A. Uedono,S. Ishibashi, T. Ishiguro, and S. F. Chichibu, Appl. Phys. Lett. 124, 181103 (2024).95H. Alves, M. Bohm, A. Hofstaetter, H. Amano, S. Einfeldt, D. Hommel,D. M. Hofmann, and B. K. Meyer, Physica B 308–310, 38 (2001).96B. Monemar, P. P. Paskov, G. Pozina, C. Hemmingsson, J. P. Bergman,T. Kawashima, H. Amano, I. Akasaki, T. Paskova, S. Figge, D. Hommel, andA. Usui, Phys. Rev. Lett. 102, 235501 (2009).97K. Kataoka, T. Narita, H. Iguchi, T. Uesugi, and T. Kachi, Phys. Status Solidi B255, 1700379 (2018).98T. Narita, T. Kachi, K. Kataoka, and T. Uesugi, Appl. Phys. Express 10, 016501(2017).99K. Shima, H. Sakurai, S. Ishibashi, A. Uedono, M. Bockowski, J. Suda,T. Kachi, and S. F. Chichibu, presented at the 83rd Fall Meeting of Japan Societyof Applied Physics (2022), No. 22p-B204-7.100Z. Hu, K. Nomoto, B. Song, M. Zhu, M. Qi, M. Pan, X. Gao, V. Protasenko,D. Jena, and H. G. Xing, Appl. Phys. Lett. 107, 243501 (2015).101T. Maeda, T. Narita, H. Ueda, M. Kanechika, T. Uesugi, T. Kachi, T. Kimoto,M. Horita, and J. Suda, Jpn. J. Appl. Phys. 58, SCCB14 (2019).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 135, 185701 (2024); doi: 10.1063/5.0201931 135, 185701-20© Author(s) 2024 08 May 2024 10:00:43https://doi.org/10.35848/1882-0786/ab8722https://doi.org/10.35848/1882-0786/ac67fchttps://doi.org/10.1038/s41598-021-00102-2https://doi.org/10.1063/5.0066347https://doi.org/10.1063/1.5116866https://doi.org/10.3390/electronics9091380https://doi.org/10.1103/PhysRevB.50.17953https://doi.org/10.1103/PhysRevB.59.1758https://doi.org/10.1103/PhysRevLett.77.3865https://doi.org/10.1103/PhysRevB.34.3820https://doi.org/10.1103/PhysRevB.52.10947https://doi.org/10.1063/5.0011309https://doi.org/10.1088/1742-6596/674/1/012020https://doi.org/10.1002/pssb.201700521https://doi.org/10.1016/0169-4332(94)00334-3https://doi.org/10.1063/1.3701368https://doi.org/10.1063/1.3075596https://doi.org/10.1063/1.3142396https://doi.org/10.1143/JJAP.50.111002https://doi.org/10.1063/1.4767357https://doi.org/10.1063/1.4817297https://doi.org/10.1016/j.jcrysgro.2014.06.005https://doi.org/10.1016/j.jcrysgro.2014.06.005https://doi.org/10.35848/1882-0786/ab9e7chttps://doi.org/10.1063/1.89897https://doi.org/10.35848/1347-4065/abd282https://doi.org/10.1063/1.1856224https://doi.org/10.1063/1.1868059https://doi.org/10.1103/PhysRevB.90.035207https://doi.org/10.1063/1.119689https://doi.org/10.1063/1.119689https://doi.org/10.1063/1.371377https://doi.org/10.1016/S0022-0248(02)01754-2https://doi.org/10.1063/1.2809407https://doi.org/10.1103/PhysRevB.59.1575https://doi.org/10.1103/PhysRevB.62.12593https://doi.org/10.1063/5.0208853https://doi.org/10.1016/S0921-4526(01)00663-9https://doi.org/10.1103/PhysRevLett.102.235501https://doi.org/10.1002/pssb.201700379https://doi.org/10.7567/APEX.10.016501https://doi.org/10.1063/1.4937436https://doi.org/10.7567/1347-4065/ab07adhttps://pubs.aip.org/aip/jap