Room temperature photoluminescence lifetime for the near-band-edge emission of epitaxial and ion-implanted GaN on GaN structures

For accelerating the development of GaN power-switching devices, current knowledge on the origins and dynamic properties of the major intrinsic nonradiative recombination centers (NRCs) in Mg-doped GaN (GaN:Mg) are reviewed, as lightly to heavily doped p-type planar GaN segments are required but certain compensating defects including NRCs hinder their formation. The results of complementary time-resolved photoluminescence and positron annihilation spectroscopy measurements on the epitaxial and ion-implanted GaN:Mg formed on low dislocation density GaN substrates indicate the following: major intrinsic NRCs are the clusters of Ga vacancies (VGas) and N vacancies (VNs), namely VGa(VN)2 in the epitaxial GaN:Mg and (VGa)3(VN)3 in the ion-implanted GaN:Mg after appropriate thermal annealings. The minimum electron capture-cross-sections of VGa(VN)2 and (VGa)3(VN)3 are commonly the middle of 10−13 cm2 at 300 K, which is approximately four times larger than the hole capture-cross-section of the major intrinsic NRCs in n-type GaN, namely VGaVN divacancies, being 7 × 10−14 cm2.


Introduction
In order to solve the energy crisis problem, the exploitation of high-power electronic devices switchable at high-frequencies is one of the delightful ways of decreasing the total energy consumption. For such devices, GaN is suited 1) according to its outstanding characteristics such as the large bandgap energy (3.4 eV), high breakdown field (3.3 MV cm −1 ), 2) and high saturation electron velocity (2.5 × 10 7 cm · s −1 ). 3) A normallyoff GaN-based transistor on a freestanding (FS)-GaN substrate with low specific on-state resistance (1.0 mΩ cm 2 ) and a high off-state breakdown voltage (1.7 kV) has been demonstrated using p-type GaN (p-GaN)/AlGaN/GaN layers overgrown on the V-shaped groove formed over the drift layer. 4) Moreover, GaN vertical metal-oxide-semiconductor field-effect-transistors (MOSFETs) capable of large current switching have been explored. [5][6][7] Although most of the previous GaN devices have been examined using Mg-doped p-GaN (p-GaN:Mg) epitaxial layers, 4) selective-area impurity doping is an indispensable technique from the viewpoint of versatile designing and processing of devices at a low cost. In particular, ion implantation (I/I) with appropriate activation annealing is preferred for fabricating both vertically and laterally currentflowing transistors. In this connection, both heavily and lightly doped p-type layers are crucial, because the former realizes low resistance for contacting and hole-injecting layers while the latter is applicable for forming inversion channels and for electric field spreading as a guard ring. 8) However, p-type doping by I/I of Mg has long been difficult, [9][10][11][12][13][14] partially because donor-type defects introduced by I/I and/or donor impurities such as O or Si that might be diffused from the protective overlayer during the post-implantation annealing 13) (PIA) likely compensate holes. Another issue is that only Mg serves as an acceptor in GaN.
Several approaches to avoid the compensation have been examined recently. [15][16][17][18][19] Reference 16 fabricated p-GaN:Mg by using a shallow, sequential implantation of Mg and H ions to (0001) N-polar plane of FS-GaN, and demonstrated pn junction diodes with a distinct rectification property. Their explanation was that the use of the (0001) plane allowed a capping-less PIA because of its high thermal stability, which suppressed unwanted hole compensation. Also, the addition of H was assigned to decrease the formation energy of Mg Ga acceptors. 20) Reference 21 have measured the cathodoluminescence (CL) spectra of those N-polar I/I GaN:Mg samples 16) at 10 K, and showed the peak originating from the recombination of excitons bound to a Mg Ga acceptor (ABEs) at 3.465 eV (Refs. [22][23][24] and the ultraviolet luminescence (UVL) band at around 3.26 eV that originates from a free electron or a shallow donor to a Mg Ga acceptor transition. 22,23) However, they simultaneously observed considerable green luminescence (GL) band at around 2.4 eV, which is routinely observed 25,26) in I/I GaN:Mg and has been assigned to a transition involving N vacancies (V N s). 25) Similar to their reports, 16,20) definitive evidence of p-type conductivity with a reliable hole concentration (p) measurement has not been shown, and the device characteristics containing p-GaN:Mg fabricated using I/I have been reported only recently. 15,16,18) For the reliable fabrication of p-GaN:Mg by I/I, an accurate understanding of I/I induced defects is essential, as such defects likely form trapping levels and/or nonradiative recombination centers (NRCs), both of which decrease p. With respect to point defects in GaN:Mg, Refs. 27, 28 have detected vacancy-type defects in p-GaN:Mg homoepitaxial films 27) grown by metalorganic vapor phase epitaxy (MOVPE) and I/I GaN:Mg (Refs. 27 and 28) formed on unintentionally doped (UID) homoepitaxial films on Ga-polar (0001) plane of a FS-GaN substrate by means of positron (e + ) annihilation spectroscopy (PAS) [27][28][29][30][31][32][33][34][35][36] measurement. They have shown that major vacancy-type defects in the epilayers 27) were multiple vacancies consisting of a Ga vacancy (V Ga ) and two or three V N s, namely V Ga (V N ) 2 or V Ga (V N ) 3 , 27) while those in the as-implanted GaN:Mg were V Ga V N divacancies but they agglomerated into larger vacancy clusters such as (V Ga ) 3 (V N ) 3 after a PIA at 1300°C. 28) Combined with the results of time-resolved photoluminescence (TRPL) measurement, Ref. 37 3 ] to the major NRCs in the GaN:Mg epilayer and quantified their electron capture-cross-section (σ n ) approximately the middle of 10 −13 cm 2 at 300 K, which was larger than the hole capture cross-section (σ p ) of the major NRCs in n-type GaN (n-GaN), namely V Ga V N , 32,34,36) being 7 × 10 −14 cm 2 . 37,38) However, because the near-band-edge (NBE) emission has scarcely been observed at 300 K from I/I GaN:Mg for a long time, 24,26) neither t PL nor s n of (V Ga ) 3 (V N ) 3 has been quantified until recently. 39) In this progress review, the origins and σ n of the major intrinsic NRCs in epitaxial and I/I p-GaN:Mg formed on low threading dislocation (TD) density FS-GaN substrates are described, and compared with the major intrinsic NRCs in n-GaN. 32,34,36,38) The epitaxial p-GaN:Mg commonly exhibited the NBE and/or UVL emissions at low temperatures and the NBE emission at 300 K irrespective of Mg doping concentration, [Mg]. Accordingly, photoluminescence (PL) lifetimes (t s PL ) at 300 K were measurable. 37) By contrast, both (0001) Ga-polar 26) and (0001) N-polar 16,21) I/I GaN:Mg with the average implantation depths larger than 500 nm have never exhibited the NBE emission at 300 K, 26) and the results have hampered quantifying t PL or judging the conductivity type. Quite recently, sequential shallow implantation of Mg and H into the (0001) plane with subsequent capping-less PIA has enabled the formation 16) of p-type I/I GaN:Mg. Accordingly, t PL and σ n of (V Ga ) 3 (V N ) 3 defects were quantified very recently. 39) The σ n values of V Ga (V N ) 2 and (V Ga ) 3 (V N ) 3 are commonly approximately the middle of 10 −13 cm 2 at 300 K, which is approximately four times larger than σ p of the major intrinsic NRCs (V Ga V N ) in n-GaN.

Samples
The GaN:Mg epilayers were grown by MOVPE by two suppliers, as shown in Fig. 1(a). From supplier A, approximately 1 to 4-μm-thick GaN:Mg epilayers grown on a 2-μmthick UID GaN epilayer on a Ga-polar c-plane FS-GaN substrate grown by the hydride vapor phase epitaxy (HVPE) method [Mitsubishi Chemical Corp.(MCC)] 40) were provided (sample set A). Potential influences of TDs on the PL properties 41) may be minimized, as the TD density was in the range of 10 6 cm −2 . 40) The [Mg] values were controlled from 3 × 10 16 to 7 × 10 19 cm −3 , which were quantified by using the secondary-ion mass spectrometry (SIMS). As a control sample, a UID GaN film was prepared. From supplier B, approximately 2-μm-thick GaN:Mg epilayers grown on a 2-μm-thick UID GaN epilayer on the same c-plane FS-GaN (MCC) 40) were provided. The [Mg] values were 5 × 10 17 , 5 × 10 18 , and 4 × 10 19 cm −3 (sample set B). All epilayer samples were thermally annealed at T a = 700°C for 30 min in a N 2 gas ambient for activating 42) the Mg Ga acceptor.
The I/I GaN:Mg samples were supplied from suppliers A and C. At supplier A, the samples were formed on a 4-μmthick UID GaN film grown on the same Ga-polar FS-GaN (MCC), 40) as shown in Fig. 1(b). Mg + ions were implanted into the UID GaN film with several energies ranging from 20 to 430 keV, in order to form a 500-nm-deep box-type profile with [Mg] of 1 × 10 17 , 1 × 10 18 , and 1 × 10 19 cm −3 . The I/I was carried out at room temperature and followed by the deposition of a 300-nm-thick AlN decomposition shield by a sputtering method. All samples were annealed under various temperatures (T a ) between 1000 and 1300°C for 5 min with N 2 gas at atmospheric pressure. The AlN film was chemically removed after annealing. By supplier C, approximately 100nm-deep N-polar I/I GaN:Mg of a box-type profile was prepared by implanting Mg and H ions sequentially to the (0001) plane of an n-type FS-GaN substrate grown by HVPE [Furukawa Denshi Co. Ltd. (Furukawa)] through the 30-nm-thick SiN x film, as shown in Fig. 1(c). The total TD density of the edge and screw components was typically 2 × 10 6 cm −2 , which is low enough to maintain the internal quantum efficiency (η int ) of the NBE emission, 41) and almost no structural defects were observed. The concentra- The PIA was carried out without any protective overlayer at T a between 800 and 1260°C for 30 s in a N 2 ambient. The details of the sample fabrication process can be found elsewhere. 16) For comparison, the following four samples were prepared. One was a control Ga-polar GaN:Mg epilayer ([Mg] = 1.5 × 10 19 cm −3 ) grown by MOVPE on a FS-GaN substrate (manufacturer undisclosed). Another was a Ga-polar edition of the principal sample, namely, an approximately 100-nm-deep Mg-and H-implanted GaN of a boxtype profile, which was fabricated on a (0001) FS-GaN (Furukawa). The other two were deep-implantation editions,  26,28) and (c) sequentially Mg-and H-implanted N-polar or Ga-polar GaN. 16,21,39) The FS-GaN substrates were grown by HVPE by MCC and Furukawa, as described in the main text.
namely, 710-nm-deep Mg-and H-implanted (0001) and (0001) FS-GaN (Furukawa). 21) These comparative I/I samples were annealed at 1230°C without any capping layers. After the annealing, the (0001) surface became porous, while the (0001) surface did not exhibit serious degradation. 15) 2.2. Steady-state and time-resolved photoluminescence measurements Steady-state PL was excited by using the 325.0 nm line of a cw He-Cd laser with the power density of 38 W · cm −2 . For understanding the origin and dynamic properties of the major intrinsic NRCs in a direct bandgap semiconductor, the complementary use 32,34,[36][37][38][39] of TRPL and PAS measurements is suited, as PAS is sensitive to vacancy-type defects [29][30][31] and TRPL quantifies t PL of the NBE emission that represents the minority carrier lifetime (t minority ). The TRPL measurement was carried out at 300 K using approximately 100 fs pulses of a frequency-tripled (3ω) mode-locked Al 2 O 3 :Ti laser (λ = 267 nm), of which the repetition rate was decreased to 8 MHz. The power density was approximately 120 nJ cm −2 (per pulse), where the excited carrier concentration is estimated at a few times 10 15 cm −3 when t PL is 100 ps. We note that both steadystate PL and TRPL measurements were carried out under weakexcitation conditions to underline the nonradiative recombination processes. 36) The spot diameter was 1 mm, and the obtained PL and TRPL signals are most likely composed of various signals from corresponding areas with different concentrations of Shockley-Read-Hall (SRH)-type NRCs (N NRC ). The TRPL signal was collected using a synchro-scan streak camera with the temporal resolution better than 1 ps. As shown in Fig. 2, an inverse of t PL is the PL decay rate, which is a sum of the radiative and nonradiative recombination rates (R R and R , NR respectively), expressed by where t R and t NR are the respective lifetimes. Because t R of the NBE emission in a good quality bulk material is a unique value; e.g. approximately 40-50 ns at 300 K for the case of GaN under weak excitation conditions, 34,43) t NR can be derived from measured t . PL Here, t NR is governed by the capture coefficient for minority carriers (C minority ) and N NRC under the relationship Here, C minority is assumed to be a product of the minority carrier capture-cross section (σ minority ) and thermal velocity ( , where k B is the Boltzmann constant and m minority is the minority carrier effective mass. In this traditional model, the mean free path is assumed to be limited by N NRC , and the estimated s minority is the minimum limit.

Monoenergetic positron annihilation spectroscopy measurement
For identifying the origin and quantifying the concentration of the major vacancy-type defects, PAS measuremnt [27][28][29][30][31][32][33][34][35][36][37][38][39] was carried out. A monoenergetic e + beam line at University of Tsukuba 27,28,[31][32][33][34]36,37,39) was used to measure the Doppler broadening spectra of the the annihilating γ-rays of e + and electrons (e − ). The low-and high-momentum portions of the spectra were characterized by the S and W parameters, [29][30][31]35) respectively, where S reflects the size or concentration of the vacancy-type defects. During the PAS measurement, the samples were illuminated with the same He-Cd laser to supply electrons to neutral or positively charged levels. 28) Details of the PAS measurements [29][30][31][32][33]35) and the analytical procedures 27,28) can be found elsewhere. The species and the concentration of major vacancy-type defects were identified and quantified from the S-W relationship [29][30][31][32][33]35) and the magnitude of S parameter, [29][30][31][32][33]35) respectively. Reference 35 have evaluated the dynamic range of PAS for a neutral defect like a V Ga in n-GaN from the sensitivity of e + annihilation lifetime to approximately between 10 16 and 10 19 cm −3 , at which implanted e + are nearly fully delocalized in the defect-free (DF) regions and fully trapped by V Ga s, respectively. The range may shift toward the lower values when the vacancy is negatively charged.
When t NR of the NBE emission is inversely proportional to the concentration of a unique defect, the defect can be assigned to the major NRC. 32,34,36,37,39) As a consequence, the capture-cross-section for the minority carriers (s minority ) of the NRCs can be derived [36][37][38][39] from the relationship given in Sect. 2.2. By using this complementary approach described in Sect. 2.2 and 2.3, 32,34,36) point-defect complexes containing a V Ga , 32,34) more precisely V Ga V N , 33,36) have been identified as the origin of the major SRH-type NRCs in n-GaN, because t NR decreased with increasing the concentration of V Ga -complexes, 32,34) 36) Accordingly, its hole capture coefficient (C p ) was determined from the relationship between t NR and N NRC , 1 is the hole thermal velocity. These parameters are important, as η int of the NBE emission is given by h = In the case of n-GaN, s p of V Ga V N approximately 7 × 10 −14 cm 2 was determined in this way, 36,38) where intrinsic t R was taken as 40 ns. 34,43) 3. Results and discussion  lines. The PL intensity (y-) axis has a unit of count per second (cps), and the spectra can be compared with those at different temperatures or other samples. As shown in Fig. 3(a), the UID GaN film exhibited distinct NBE PL peaks and shoulders originating from the recombination of free excitons (FXs) at 3.478 eV, recombination of excitons bound to a neutral donor (DBEs) at 3.472 eV, and their LO phonon replicas at the energies higher than 3.2 eV. In addition, weak luminescence bands called the blue luminescence (BL) band due to the transition of an electron from a carbon deep donor (C Ga ) to the valence band (carbon-blue) 44) at around 2.9 eV and red luminescence (RL) band 25) at around 1.8 eV were detected. By using the first-principles calculations, Ref. 25 have suggested that V N s are the origin of RL band. In this context, the appearance of RL implies higher V N concentration, [V N ], in the present UID GaN, because state-of-the-art UID GaN films grown by MOVPE do not exhibit RL but exhibit so-called yellow luminescence (YL) band. 22,[45][46][47][48][49] We note that there are two independent origins of the YL band: one is the transition of an electron in the conduction band (or bound to a shallow donor) to a carbon deep acceptor on a N site (C N ) 49) and the other is the emission due to the complex of a V Ga and a donor impurity such as an oxygen on a N site (O N ), V Ga O N . [46][47][48] The dominant NBE emission at 10 K switched from DBEs in UID to ABEs in GaN:Mg films with [Mg] lower than 5 × 10 18 cm −3 , as shown in Figs. 3(b)-3(d), 3(f), and 3(g). Simultaneously, UVL band 25) appeared in the PL spectra of . Such an observation of the ABEs and UVL indicates the formation of Mg Ga acceptors. We note that [Mg] of 3 to 4 × 10 19 cm −3 is routinely used to obtain a p-GaN hole-injecting layer (p = 1 × 10 18 cm −3 ) in lightemitting devices, and the emergence of a BL band (magnesium-blue) 23,50) at around 2.8 eV at 300 K (lower solid lines in Fig. 3) is a fingerprint of p-type conductivity of GaN: Mg epilayers. As can be seen in Fig. 3, most of the PL spectra exhibited a weak RL band. 25) The enhanced incorporation of V N s in GaN:Mg films compared to n-GaN is reasonable, as the formation energies (E Form ) of V N and V N -Mg Ga decrease with the lowering Fermi level (E F ). 25,[45][46][47] Even at 10 K, the integrated spectral NBE emission intensity (I NBE ) 19 , and 7 × 10 19 cm −3 were more than one, two, and three orders of magnitude lower than I NBE of UID or less Mgdoped samples, as shown in Figs. 3(d), 3(h), and 3(e), respectively. By using a simplified model described in Refs. 36 and 38, the upper bound of N NRC in them can be estimated, as follows. When the average distance of NRCs is far longer than the exciton Bohr diameter ( a 2 B ) and excitons do not move at zero carrier temperature, h int at 0 K is in principle approximately unity. However, when N NRC exceeds a critical value, h int at 0 K becomes no longer unity, because an electron-hole pair or an exciton recombines at the NRCs without diffusion or drift, as depicted in Fig. 4. The probability that a diffusion-or drift-free exciton at 0 K is not captured by NRCs and decays with the radiative recombination gives the maximum h int (h int max ) of the emission, which is defined 36,38) is modeled under the assumption that every NRC within the exciton volume causes the nonradiative recombination. From this simple consideration, the assumption that h int is close to unity at 2-4.2 K is not absolutely incorrect when N NRC is lower than approximately the middle of 10 16 cm −3 for GaN. 36,38) Judging from Fig. 4, N NRC of the present GaN: Mg of low I NBE is predicted to be between 10 16 and 6 × 10 18 cm −3 . This concentration range is within the dynamic range of PAS for V Ga , 35) and agrees with the concentration of unknown donors (or donor-type defects) suggested by Ref. 51 using Hall effect measurements on the epitaxial GaN:Mg films, which were grown on FS-GaN substrates manufactured by the same supplier. Such defects may act as NRCs, as the energy level 22,25,[46][47][48][49] lies higher than E F of p-GaN:Mg. At 300 K, the PL spectrum of UID GaN exhibited a roomtemperature FX peak, 52) the BL band, 44) and the YL band, 22,[45][46][47][48][49] as shown in Fig. 3(a). A similar spectral feature was observed for the lightly Mg-doped epilayers, as shown in Figs To correlate I NBE and t , NR PL decay signals for the NBE emissions of GaN:Mg films at 300 K are shown in Fig. 5(a). The spectral integration was carried out at the photon energies (hν) between 3.2 and 3.6 eV, in order to cover all NBE emissions such as excitonic and free to acceptor transitions. The TRPL signals appear to be fitted using a multiple-exponential line shape function. In general, the appearance of multiple decay components at 300 K most likely reflects the fact that several portions of different N NRC , which are away beyond the diffusion length of minority carriers (L minority ), are simultaneously observed 36) in the macroarea TRPL measurement. In the present case, however, the signals were sufficiently fitted using a bi-exponential function: I(t) = A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 ), where I(t) is the PL intensity at time t, and A 1 (A 2 ) and t 1 (t 2 ) are the preexponential constant and the lifetime, respectively, of the fast (slow) decay component. The results are shown by the gray lines superimposed on the experimental data. We note that in these analyses, only the bulk recombination was considered and the surface recombination was not taken into account, as excited carriers may not diffuse out to the surface because L minority is limited by the average distance between the NRCs, N 1 , NRC 3 which is approximately 30 nm in GaN:Mg with N NRC approximately a few times 10 16 cm −3 , as discussed in the following paragraphs.
The values of t 1 obtained through the fitting, which mainly limits the cw PL intensity under low excitation conditions, 36) is used as the representative t . PL The t 1 values are plotted as a function of [Mg] in Fig. 5(b). As is clearly seen, t 1 for set B were approximately an order of magnitude longer than those of set A at the same [Mg], and [Mg] at which t 1 started to decrease rapidly for set B (approximately 10 19 cm −3 ) was higher than that of A (approximately 10 18 cm −3 ). This result indicates higher R NR at the same [Mg] for set A. As shown in Fig. 3(a), the NBE emission intensity of UID GaN at 300 K was more than three orders of magnitude lower than that at 10 K, and this thermal quenching is severer than the state-ofthe-art UID GaN on GaN structures. Therefore, the sample set A appears to contain higher concentration NRCs or different species of NRCs having larger s . n As discussed  The relationship between t PL at 300 K and N NRC of GaN: Mg epilayers is shown by closed squares in Fig. 6, where the right y-axis shows corresponding h int using t R = 40 ns. 34,43) In Fig. 6, four ideal curves are drawn for the cases with s n ranging from 1 × 10 −12 to 1 × 10 −15 cm 2 using the relation- cm s −1 and the electron effective mass m n = 0.20m 0 (m 0 is a free electron mass). This relationship predicts that t PL -N NRC shows a straight line under low excitation and high N NRC conditions, where t NR dominates t . PL As shown, the data points are scattered around the lines for s n = 10 −13 and 10 −12 cm 2 . This large error likely originates from two reasons. One is the fact that [V Ga (V N ) 2 ] are close to the detection limit of PAS being 10 15 cm −3 , where the change in S with the change in corresponding N NRC ( ¶ ¶

S N NRC
) is much smller than that at the middle of the dynamic range. 29,31,35) Another is that set A contains another type of defect. Taking the data for sample set B, s n of V Ga (V N ) 2 is determined at the middle of 10 −13 cm 2 , which is approximately four times larger than s p of V Ga V N in n-GaN being 7 × 10 −14 cm 2 (Refs. 36 and 38). Combined with the large v , n t minority in p-GaN:Mg becomes much shorter than that in n-GaN. Reference 28 examined these samples using PAS measurement and found that I/I of Mg at room temperature generated a very high concentration (V Ga V N )s and that they agglomerated into (V Ga ) 3 (V N ) 3 clusters during PIA, although their concentration, [(V Ga ) 3 (V N ) 3 ], could be decreased by increasing the PIA temperature up to T a = 1300°C. 28) The S parameters of I/I GaN: Mg after PIA (0.46-0.49) 28) were commonly larger than that of epitaxial GaN:Mg of [Mg] = 4 × 10 19 cm −3 (0.449) 27) or S free (0.440). Accordingly, the present I/I GaN:Mg samples contain high concentrations of (V Ga ) 3 (V N ) 3 clusters and positroninsensitive V N s. 26) Because (V Ga ) 3 (V N ) 3 defects were quite recently 39) assigned to the major SRH-type NRCs in the (0001) N-polar GaN:Mg (Refs. 16 and 21) formed by the sequential shallow I/I of Mg and H, (V Ga ) 3 (V N ) 3 likely act as NRCs in these (0001) Ga-polar editions 26,28) in Fig. 7.
The room-temperature PL spectra of epitaxial and I/I GaN: Mg also showed clear differences, as shown by the bottom lines in Figs. 3 and 7. In principle, I/I GaN:Mg did not exhibit the NBE or UVL peak, as shown in Fig. 7, except for the detectable NBE peaks in Figs. 7(b) and 7(c) for the lowest [Mg] sample. Such low quantum efficiencies of the NBE emission, UVL, and BL are caused by high N NRC . The dominance of the GL band at 300 K in Fig. 7(l) is, therefore, the result of the introduction of V N s by Mg I/I. For the same Mg dose, the NBE and UVL intensities at 10 K were increased by increasing T a , implying that high T a annealing is effective in decreasing N NRC . Then, the increase in GL intensity with increasing T a in Figs. 7(i)-7(l) is not due to the increase in [V N ] but to the increased capture of carriers by (V Ga ) 3 (V N ) 3 owing to the reduced N NRC . Nonetheless, the NBE emission intensity at 300 K of the sample with [Mg] = 1 × 10 17 cm −3 was decreased by the increase in T a to 1300°C, presumably because of the increase in [V N ] by N out-diffusion from the surface and/or the downshift of E F by the activation of Mg. Consequently, the overall I/I process, including PIA, must be optimized to decrease [V N ] and [V Ga ] for the reproducible production of p-type conductivity. values were commonly 1 × 10 19 cm −3 . In Figs. 8(f)-8(j), the PL spectra of as-implanted and annealed 100-nm-deep N-polar I/I-GaN:Mg of T a = 800, 1000, 1100, and 1260°C are shown, respectively. In each panel, PL spectra measured at 10 and 300 K are shown at the top and bottom, respectively. As shown in Fig. 8(a), the Ga-polar GaN:Mg epilayer after annealing exhibited the UVL band and ABE peak at 10 K, both of which are associated with Mg Ga acceptors. [22][23][24]50) The emissions from deep energy states such as GL or RL were absent. These spectral features agree with those shown in Fig. 3(d). The 710-nm-deep Ga-and N-polar I/I-GaN:Mg also exhibited the UVL band at 10 K, as shown in Figs. 8(b) and 8(c), respectively, implying the formation of Mg Ga acceptors. [22][23][24]50) However, their intensities were three orders of magnitude lower than the epilayer [Figs. 3(d) and 8(a)]. Moreover, the distinct GL band peculiar to I/I GaN:Mg (Refs. 21 and 26) was dominant and the RL band with almost equal intensity as UVL was found in both spectra. In contrast, the 100-nm-deep Ga-and N-polar I/I-GaN:Mg exhibited a distinct UVL band at 10 K, of which intensities were approximately one and two orders of magnitude higher than the 710-nm-deep ones, as shown in Figs. 8(d) and 8(e), respectively. In addition, a distinct ABE peak was found only in the 100-nmdeep samples, where both GL and RL were significantly suppressed. Therefore, the depth of I/I, i e., total doses and energies used, seriously affected PL intensities. 21) To form constant [Mg] and [H] profiles, higher total doses and a greater number of times of I/I with higher energies are required for deeper profile samples, meaning that the samples suffer from severer I/I damage. 21) At 300 K, the dominant PL peak of the control GaN:Mg epilayer was the BL band, 23,50) as shown in Fig. 8(a). Although the 710-nm-deep Ga-and N-polar I/I-GaN:Mg did not exhibit any NBE emissions at 300 K, as shown in Figs. 8(b) and 8(c), respectively, the 100-nm-deep samples did, as shown in Figs. 8(d) and 8(e). These results again indicate lower N NRC in the 100-nm-deep samples. Because the NBE emission intensity at 300 K of the 100-nm-deep N-polar I/I-GaN:Mg [ Fig. 8(e)] was an order of magnitude higher than the Ga-polar edition [ Fig. 8(d)], N NRC in the N-polar one is likely lower than the Ga-polar one, provided that the major NRCs in both samples have a common origin. Reference 39 carried out PAS analyses of the present samples and concluded from the S-W relationship that major defect species in the N-polar I/I-GaN:Mg after PIA at T a = 1000°C was the same as that in the Ga-polar one, 28) namely, (V Ga ) 3 (V N ) 3 . Accordingly, if (V Ga ) 3 (V N ) 3 are the common major NRCs in Ga-and N-polar I/I-GaN:Mg, above hypothesis is correct. In addition to the NBE emission, the 100nm-deep N-polar I/I-GaN:Mg exhibited the distinct BL band as the low energy tail of UVL at 300 K, as shown in Fig. 8(e).

Sequentially Mg and H implanted N-polar GaN
Here we mention that the major NRCs and their concentrations in these Ga-and N-polar GaN:Mg samples before I/I were commonly V Ga V N (Refs. 32, 34, and 36) and lower than the dynamic range of the PAS measurement (<10 16 cm −3 ), 34) respectively, because the sequential I/I was carried out on (0001) and (0001) planes of an n-type FS-GaN substrate. 21) Therefore, in addition to the depth of I/I, the crystallographic plane used for I/I is the other considerable factor affecting the PL intensities. As already mentioned, the (0001) plane offers better thermal stability than (0001) plane does, 16) and therefore, the formation of NRCs at the surface during PIA is less likely. These considerations are consistent with the fact that the 100nm-deep N-polar I/I-GaN:Mg showed a p-type conductivity. 16) However, because the integrated spectral intensity of the NBE emission and BL band at 300 K of the 100-nm-deep N-polar I/I-GaN:Mg was still lower by two orders of magnitude than that of the epilayer, a further decrease in N NRC and the concentration of the defects responsible for GL (V N ) is mandatory. We note that Ref. 53 very recently showed that the sequential I/I of Mg and N into the (0001) Ga-polar GaN followed by uncapped PIA in 1 GPa N 2 atmosphere at 1480°C gave rise to the observation of an intense UVL band due to Mg Ga and suppressed GL band in the low temperature CL spectra. Their results may indicate that I/I of additional N followed by the high pressure and high temperature PIA partially suppress the formation of V N . As shown in Figs. 8(e)-8(j), PL spectra of the 100-nmdeep N-polar I/I-GaN:Mg after PIA commonly exhibited the YL band. 22,[45][46][47][48][49] Different from the case of MOVPE films that contain carbon impurities higher than the middle of 10 15 cm −3 (Ref. 54), the present I/I-GaN:Mg samples formed at the (0001) surface of the HVPE FS-GaN are likely nearly carbon-free. Therefore, these samples likely contain V Ga s. Such V Ga s and V N s likely form the vacancy clusters that act as NRCs, as are the cases with V Ga V N in n-GaN 32,36) and V Ga (V N ) 2 in the p-GaN:Mg epilayer. 37) It is noted from Figs. 8(e)-8(j) that the overall PL intensity, which is a sum of NBE, UVL, BL, GL, YL, and RL intensities, of the 100-nmdeep N-polar I/I-GaN:Mg appears to increase with increasing T a at both 10 and 300 K. This result implies a progressive decrease in N NRC with increasing T a .
In order to correlate t NR of the NBE emission and N NRC in the 100-nm-deep N-polar I/I-GaN:Mg, the NBE PL decay signals at 300 K are shown in Fig. 9(a) as a function of T a . As shown, PL decay signals were obtained with a sufficient signalto-noise ratio and sufficient temporal resolution. As is the case with GaN:Mg epilayer shown in Fig. 5, the TRPL signals were sufficiently fitted using a bi-exponential function. The fitting results are shown by gray lines superimposed on the experimental data in Fig. 9(a), and the values of t 1 and t 2 are shown as a function of T a in Fig. 9(b). As shown, the N-polar I/I-GaN: Mg annealed at T a = 1230°C exhibited longer t 1 and t 2 compared with the Ga-polar sample (open legends). This result is consistent with the relationship between the NBE emission intensities, as shown in Figs. 8(d) and 8(e). The TRPL results also indicate that higher T a has an advantage in obtaining longer t 1 and t . 2 As the fast component (t 1 ) essentially limits the cw PL intensity under low excitation conditions, t 1 is generally used as the representative of t .
PL By increasing T a , t 1 at 300 K was increased to 18 ps at T a = 1230°C, which nearly agrees with typical t PL being 20 ps of p-GaN:Mg epilayers of the same [Mg] (1 × 10 19 cm −3 ). 37) This result is also consistent with the comparable NBE emission intensities for the GaN:Mg epilayer [ Fig. 8(a)] and 100-nm-deep N-polar I/I-GaN:Mg [ Fig. 8(e)] at 300 K. Because t 2 showed stronger dependence on T a , as shown in Fig. 9(b), the increase in T a appears to increase the area of low N NRC zones. In Fig. 9(c),  analyses of the present samples and concluded that the major defect species is (V Ga ) 3 (V N ) 3 . By comparing the measured and theoretically calculated 27,28) S parameters, [(V Ga ) 3 (V N ) 3 ] in the 100-nm-deep N-polar I/I-GaN:Mg annealed at 800, 1000, 1100, and 1230°C were estimated at a few times 10 16 cm −3 and decreased with increasing T a . Because t PL increased with decreasing [(V Ga ) 3 (V N ) 3 ], (V Ga ) 3 (V N ) 3 clusters are eventually assigned to the major NRCs in the present N-polar I/I-GaN:Mg.
The relationship between t PL of the NBE emission at 300 K and N NRC = [(V Ga ) 3 (V N ) 3 ] of the 100-nm-deep N-polar I/I-GaN:Mg is shown by closed circles in Fig. 6. As shown, s n of (V Ga ) 3 (V N ) 3 is estimated at a few times 10 −13 cm 2 , the value being comparable to that obtained 37) for V Ga (V N ) 2 in the p-GaN:Mg epilayers, 27) as plotted by closed squares. Because s n is a parameter representing the trapping probability of minority carriers, it is reasonable that vacancy clusters of different open volumes have similar s . n Nevertheless, this value is approximately four times larger than s p (=7 × 10 −14 cm 2 ) of V Ga V N in n-GaN, and therefore, t minority in p-GaN:Mg samples are much shorter than that in n-GaN, combined with the large v . minority Very recently (Refs. 55 and 56) independently reported the SRH lifetime (t SRH ), which is expressed by t tt = , SRH n p where t n and t p are the lifetimes of an electron and a hole at the recombination plane in the depletion layer, respectively, in p + n − and n + p − junctions of GaN as 12 ns (Ref. 55) and 46 ps (Ref. 56), respectively. This difference may reflect the differences in v minority and s minority of the major NRCs. These results [36][37][38][39]55,56) are consistent with each other.

Conclusion
Current knowledge on the origins and dynamic properties of the major intrinsic NRCs in the epitaxial and ion-implanted p-type GaN:Mg fabricated on FS-GaN substrates are summarized. The results of complementary TRPL and PAS measurements indicate that the major intrinsic NRCs are the clusters of V Ga s and V N s, namely V Ga (V N ) 2 in the epitaxial p-GaN:Mg and (V Ga ) 3 (V N ) 3 in the I/I p-GaN:Mg after appropriate PIA. Different from the case of 4H-SiC, atomic structures of the major intrinsic NRCs in the p-type GaN:Mg epilayer and n-type GaN are different: V Ga (V N ) 2 in the former and V Ga V N in the latter. The minimum s n values of V Ga (V N ) 2 and (V Ga ) 3 (V N ) 3 are estimated commonly at the middle of 10 −13 cm 2 at 300 K, which is approximately four times larger than s p of V Ga V N in n-GaN being 7 × 10 −14 cm 2 . Although GaN:Mg layers formed by I/I deeper than 500 nm never exhibited the NBE, UVL, or BL emission at 300 K, those fabricated by the shallow (∼100 nm) and sequential Mg and H implantation followed by the capping-less high temperature PIA gave rise to the observation of the NBE and BL emissions at 300 K and p-type conductivity. As t PL of the best (0001) I/I-GaN:Mg ([Mg] = 1 × 10 19 cm −3 ) that was annealed at T a = 1230°C increased to 18 ps, which nearly agrees with typical t PL being 20 ps in (0001) Ga-polar p-GaN:Mg epilayers of the same [Mg], good performance vertically current-flowing GaN transistors using I/I p-GaN:Mg will appear in the market shortly.