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

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-μm-thick 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 properties⁴¹⁾ may be minimized, as the TD density was in the range of 10⁶ cm⁻².⁴⁰⁾ The [Mg] values were controlled from 3 × 10¹⁶ to 7 × 10¹⁹ 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 × 10¹⁷, 5 × 10¹⁸, and 4 × 10¹⁹ cm⁻³ (sample set B). All epilayer samples were thermally annealed at T_a = 700 °C for 30 min in a N₂ gas ambient for activating⁴²⁾ the Mg_Ga acceptor.

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The I/I GaN:Mg samples were supplied from suppliers A and C. At supplier A, the samples were formed on a 4-μm-thick 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 × 10¹⁷, 1 × 10¹⁸, and 1 × 10¹⁹ 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 N₂ gas at atmospheric pressure. The AlN film was chemically removed after annealing. By supplier C, approximately 100-nm-deep N-polar I/I GaN:Mg of a box-type profile was prepared by implanting Mg and H ions sequentially to the (000$\bar{1}$) 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 × 10⁶ 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 concentrations of Mg and H in the constant profile region were [Mg] = 1.4 × 10¹⁹ cm⁻³ and [H] = 2.1 × 10²⁰ cm⁻³. The PIA was carried out without any protective overlayer at T_a between 800 and 1260 °C for 30 s in a N₂ 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 × 10¹⁹ 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 box-type profile, which was fabricated on a (0001) FS-GaN (Furukawa). The other two were deep-implantation editions, namely, 710-nm-deep Mg- and H-implanted (0001) and (000$\bar{1}$) 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 (000$\bar{1}$) surface did not exhibit serious degradation.¹⁵⁾

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^{32,34,36–39)} of TRPL and PAS measurements is suited, as PAS is sensitive to vacancy-type defects^29–31) and TRPL quantifies ${\tau }_{{\rm{PL}}}$ of the NBE emission that represents the minority carrier lifetime (${\tau }_{{\rm{minority}}}$). The TRPL measurement was carried out at 300 K using approximately 100 fs pulses of a frequency-tripled (3ω) mode-locked Al₂O₃: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 10¹⁵ cm⁻³ when ${\tau }_{{\rm{PL}}}$ is 100 ps. We note that both steady-state PL and TRPL measurements were carried out under weak-excitation 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 ${\tau }_{{\rm{PL}}}$ is the PL decay rate, which is a sum of the radiative and nonradiative recombination rates (${R}_{{\rm{R}}}$ and ${R}_{{\rm{NR}}},$ respectively), expressed by ${\tau }_{PL}^{-1}={\tau }_{R}^{-1}+{\tau }_{NR}^{-1},$ where ${\tau }_{{\rm{R}}}$ and ${\tau }_{{\rm{NR}}}$ are the respective lifetimes. Because ${\tau }_{{\rm{R}}}$ 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) ${\tau }_{{\rm{NR}}}$ can be derived from measured ${\tau }_{{\rm{PL}}}.$ Here, ${\tau }_{{\rm{NR}}}$ is governed by the capture coefficient for minority carriers (${C}_{{\rm{minority}}}$) and N_NRC under the relationship ${\tau }_{{\rm{NR}}}={({C}_{{\rm{minority}}}\cdot {N}_{{\rm{NRC}}})}^{-1}.$ Here, ${C}_{{\rm{minority}}}$ is assumed to be a product of the minority carrier capture-cross section (σ_minority) and thermal velocity (${v}_{{\rm{minority}}}=\,\sqrt{3{k}_{{\rm{B}}}T\cdot {m}_{{\rm{minority}}}^{-1}}$), where k_B is the Boltzmann constant and ${m}_{{\rm{minority}}}$ 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 ${\sigma }_{{\rm{minority}}}$ is the minimum limit.

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For identifying the origin and quantifying the concentration of the major vacancy-type defects, PAS measuremnt^27–39) was carried out. A monoenergetic e⁺ beam line at University of Tsukuba^{27,28,31–34,36,37,39)} 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,^29–31,35) 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^29–33,35) 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^29–33,35) and the magnitude of S parameter,^29–33,35) 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 10¹⁶ and 10¹⁹ cm⁻³, at which implanted e⁺ are nearly fully delocalized in the defect-free (DF) regions and fully trapped by V_Gas, respectively. The range may shift toward the lower values when the vacancy is negatively charged.

When ${\tau }_{{\rm{NR}}}$ 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 (${\sigma }_{{\rm{minority}}}$) of the NRCs can be derived^36–39) 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_GaV_N,^33,36) have been identified as the origin of the major SRH-type NRCs in n-GaN, because ${\tau }_{NR}$ decreased with increasing the concentration of V_Ga-complexes,^32,34) more precisely V_GaV_N concentration ([V_GaV_N]).³⁶⁾ Accordingly, its hole capture coefficient (${C}_{{\rm{p}}}$) was determined from the relationship between ${\tau }_{{\rm{NR}}}$ and N_NRC, ${\tau }_{{\rm{NR}}}={\left({C}_{{\rm{p}}}\cdot {N}_{{\rm{NRC}}}\right)}^{-1},$ and σ_p was deduced from ${C}_{{\rm{p}}}={\sigma }_{{\rm{p}}}\cdot {v}_{{\rm{p}}},$ where ${v}_{{\rm{p}}}=\,\sqrt{3{k}_{{\rm{B}}}T\cdot {m}_{{\rm{p}}}^{-1}}$ is the hole thermal velocity. These parameters are important, as η_int of the NBE emission is given by ${\eta }_{{\rm{int}}}=\tfrac{{R}_{{\rm{R}}}}{{R}_{{\rm{R}}}+{R}_{{\rm{NR}}}}=\tfrac{1}{1+{\tau }_{{\rm{R}}}/{\tau }_{{\rm{NR}}}}.$ Eventually, ${\tau }_{{\rm{PL}}}$ of the NBE emission is expressed by ${\tau }_{{\rm{PL}}}^{-1}={\tau }_{{\rm{R}}}^{-1}+{\sigma }_{{\rm{p}}}\cdot {v}_{{\rm{p}}}\cdot {N}_{{\rm{NRC}}}.$ In the case of n-GaN, ${\sigma }_{{\rm{p}}}$ of V_GaV_N approximately 7 × 10⁻¹⁴ cm² was determined in this way,^36,38) where intrinsic ${\tau }_{{\rm{R}}}$ was taken as 40 ns.^34,43)

Both the spectra and decay signals of the NBE PL in sample sets A and B showed principally similar trends with respect to the change in [Mg], as follows. PL spectra at 10 K of UID, GaN:Mg set A, and GaN:Mg set B are shown in Figs. 3(a), 3(b)–3(e), and 3(f)–3(h), respectively, by the upper solid 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) band²⁵⁾ at around 1.8 eV were detected. By using the first-principles calculations, Ref. 25 have suggested that V_Ns 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.^22,45–49) 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_GaO_N.^46–48)

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The dominant NBE emission at 10 K switched from DBEs in UID to ABEs in GaN:Mg films with [Mg] lower than 5 × 10¹⁸ cm⁻³, as shown in Figs. 3(b)–3(d), 3(f), and 3(g). Simultaneously, UVL band²⁵⁾ appeared in the PL spectra of GaN:Mg films [Figs. 3(b)–3(h)]. Such an observation of the ABEs and UVL indicates the formation of Mg_Ga acceptors. We note that [Mg] of 3 to 4 × 10¹⁹ cm⁻³ is routinely used to obtain a p-GaN hole-injecting layer (p = 1 × 10¹⁸ cm⁻³) in light-emitting 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_Ns 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).^25,45–47)

Even at 10 K, the integrated spectral NBE emission intensity (I_NBE) decreased with increasing [Mg] when [Mg] exceeded 1–5 × 10¹⁸ cm⁻³, as shown in Figs. 3(d), 3(e), 3(g), and 3(h). A drastic decrease in I_NBE was found in the samples with [Mg] > 10¹⁹ cm⁻³, indicating higher ${R}_{{\rm{NR}}}$ compared with UID or less Mg-doped samples. For example, I_NBE (ABE and UVL) of GaN:Mg with [Mg] of 1 × 10¹⁹, 4 × 10¹⁹, and 7 × 10¹⁹ cm⁻³ were more than one, two, and three orders of magnitude lower than I_NBE of UID or less Mg-doped 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 ($2{a}_{{\rm{B}}}$) and excitons do not move at zero carrier temperature, ${\eta }_{{\rm{int}}}$ at 0 K is in principle approximately unity. However, when N_NRC exceeds a critical value, ${\eta }_{{\rm{int}}}$ 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 ${\eta }_{{\rm{int}}}$ (${\eta }_{{\rm{int}}}^{{\rm{\max }}}$) of the emission, which is defined^36,38) by ${\eta }_{{\rm{int}}}^{{\rm{\max }}}=1-\tfrac{4}{3}\pi {a}_{{\rm{B}}}^{3}{N}_{{\rm{NRC}}}.$ Here, ${\eta }_{{\rm{int}}}^{{\rm{\max }}}$ is modeled under the assumption that every NRC within the exciton volume causes the nonradiative recombination. From this simple consideration, the assumption that ${\eta }_{{\rm{int}}}$ is close to unity at 2–4.2 K is not absolutely incorrect when N_NRC is lower than approximately the middle of 10¹⁶ 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 10¹⁶ and 6 × 10¹⁸ 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^{22,25,46–49)} lies higher than E_F of p-GaN:Mg.

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At 300 K, the PL spectrum of UID GaN exhibited a room-temperature FX peak,⁵²⁾ the BL band,⁴⁴⁾ and the YL band,^22,45–49) as shown in Fig. 3(a). A similar spectral feature was observed for the lightly Mg-doped epilayers, as shown in Figs. 3(b), 3(c), and 3(f), in which the UVL band partially overlaps the NBE emission. The GL and RL bands were quenched and almost invisible, and only the weak YL band was observed. The predominant PL peak of GaN:Mg gradually switched from UVL (NBE emission) to BL band and their overall intensity decreased with the increase in [Mg], as shown by the lower solid lines in Figs. 3(b)–3(h).

To correlate I_NBE and ${\tau }_{{\rm{NR}}},$ 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 observed³⁶⁾ in the macroarea TRPL measurement. In the present case, however, the signals were sufficiently fitted using a bi-exponential function: I(t) = A₁exp(−t/τ₁) + A₂exp(−t/τ₂), where I(t) is the PL intensity at time t, and A₁ (A₂) and ${\tau }_{1}$ (${\tau }_{2}$) are the pre-exponential 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, $1/\sqrt[3]{{N}_{{\rm{NRC}}}},$ which is approximately 30 nm in GaN:Mg with N_NRC approximately a few times 10¹⁶ cm⁻³, as discussed in the following paragraphs.

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The values of ${\tau }_{1}$ obtained through the fitting, which mainly limits the cw PL intensity under low excitation conditions,³⁶⁾ is used as the representative ${\tau }_{{\rm{PL}}}.$ The ${\tau }_{1}$ values are plotted as a function of [Mg] in Fig. 5(b). As is clearly seen, ${\tau }_{1}$ for set B were approximately an order of magnitude longer than those of set A at the same [Mg], and [Mg] at which ${\tau }_{1}$ started to decrease rapidly for set B (approximately 10¹⁹ cm⁻³) was higher than that of A (approximately 10¹⁸ cm⁻³). This result indicates higher ${R}_{{\rm{NR}}}$ 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-of-the-art UID GaN on GaN structures. Therefore, the sample set A appears to contain higher concentration NRCs or different species of NRCs having larger ${\sigma }_{{\rm{n}}}.$ As discussed above, the sample set A likely contains higher concentration V_Ns. These results are consistent, because V_N is one of the constituent elements of NRCs in both n-GaN (Refs. 32,34,36) and p-GaN (Refs. 37 and 39). Nevertheless, the decrease in I_NBE at 10 K and ${\tau }_{1}$ at 300 K simultaneously occurred for high [Mg] samples.

The S parameters of the GaN:Mg films with [Mg] less than 5 × 10¹⁸ cm⁻³ were almost equal to the characteristic S for the annihilation of e⁺ and e⁻ in DF states (S_free) being 0.440. However, S increased to approximately 0.442–0.443 for [Mg] higher than 5 × 10¹⁸ cm⁻³, indicating the increased defect concentration. By using the PAS technique, Ref. 27 have studied the vacancy-type defects in GaN:Mg homoepitaxial films grown using MOVPE by supplier A. They have concluded that the GaN:Mg film with [Mg] = 4 × 10¹⁹ cm⁻³ contained multiple vacancies such as V_Ga(V_N)₂ [or V_Ga(V_N)₃] before and after thermal annealing. From S parameters, the concentrations of V_Ga(V_N)₂ [or V_Ga(V_N)₃] in the present GaN:Mg films of [Mg] = 5 × 10¹⁸, 1 × 10¹⁹, and 4 × 10¹⁹ are estimated at approximately 7.0 × 10¹⁵, 7.0 × 10¹⁵, and 2.3 × 10¹⁶ cm⁻³, respectively. Because the decrease in ${\tau }_{{\rm{NR}}}$ synchronized with the increase in [V_Ga(V_N)₂], we attribute V_Ga(V_N)₂ to the origin of major NRCs in the homoepitaxial p-GaN:Mg films.

The relationship between ${\tau }_{{\rm{PL}}}$ 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 ${\eta }_{{\rm{int}}}$ using ${\tau }_{{\rm{R}}}$ = 40 ns.^34,43) In Fig. 6, four ideal curves are drawn for the cases with ${\sigma }_{{\rm{n}}}$ ranging from 1 × 10⁻¹² to 1 × 10⁻¹⁵ cm² using the relationship ${\tau }_{{\rm{PL}}}^{-1}={\tau }_{{\rm{R}}}^{-1}+{\sigma }_{{\rm{n}}}\cdot {v}_{{\rm{n}}}\cdot {N}_{{\rm{NRC}}},$ where ${v}_{{\rm{n}}}=2.6\times {10}^{7}$ cm s⁻¹ and the electron effective mass m_n = 0.20m₀ (m₀ is a free electron mass). This relationship predicts that ${\tau }_{{\rm{PL}}}$-N_NRC shows a straight line under low excitation and high N_NRC conditions, where ${\tau }_{{\rm{NR}}}$ dominates ${\tau }_{{\rm{PL}}}.$ As shown, the data points are scattered around the lines for ${\sigma }_{{\rm{n}}}$ = 10⁻¹³ and 10⁻¹² cm². 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 10¹⁵ cm⁻³, where the change in S with the change in corresponding N_NRC ($\tfrac{\partial S}{\partial {N}_{{\rm{NRC}}}}$) 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, ${\sigma }_{{\rm{n}}}$ of V_Ga(V_N)₂ is determined at the middle of 10⁻¹³ cm², which is approximately four times larger than ${\sigma }_{{\rm{p}}}$ of V_GaV_N in n-GaN being 7 × 10⁻¹⁴ cm² (Refs. 36 and 38). Combined with the large ${v}_{{\rm{n}}},$ ${\tau }_{{\rm{minority}}}$ in p-GaN:Mg becomes much shorter than that in n-GaN.

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The Mg implantation drastically modified the electronic properties of GaN, which is characterized by the appearance of undiminishable GL band, as follows. Changes in the PL spectra of I/I GaN:Mg are summarized as functions of T_a (column) and [Mg] (row) using a matrix in Fig. 7. In each panel, PL spectra measured at 10 and 300 K are shown at the top and bottom, respectively. The top traces in the right edge column of Fig. 7, namely Figs. 7(d), 7(h), and 7(l), show the low-temperature PL spectra of I/I GaN:Mg for [Mg] = 1 × 10¹⁷, 1 × 10¹⁸, and 1 × 10¹⁹ cm⁻³, respectively, after PIA at 1300 °C. All samples exhibited the UVL band, implying the formation of Mg_Ga acceptors.^22–24,50) However, even at 10 K, the absolute intensities of ABEs and UVL were approximately two orders of magnitude lower than those of GaN:Mg epilayers of comparable [Mg] shown in Figs. 3(b)–3(d). At the same time, the GL band, which has not been found in UID or Mg-doped GaN epilayers, appeared in all I/I GaN:Mg [Figs. 7(a)–7(l)] and eventually GL became the dominant emission in the spectra of the samples with [Mg] of 1 × 10¹⁹ cm⁻³, as shown in the topmost row of Fig. 7, namely Fig. 7(i)–7(l). These results indicate that I/I of Mg generates NRCs and simultaneously increases the concentration of the point defects relevant to GL. Because these two major change occurred simultaneously by I/I, the NRCs and GL most likely have a common²⁶⁾ constituent element, namely V_N, of which concentration [V_N] is sufficiently low in most of epitaxial GaN:Mg.

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Reference 28 examined these samples using PAS measurement and found that I/I of Mg at room temperature generated a very high concentration (V_GaV_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 × 10¹⁹ 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 positron-insensitive V_Ns.²⁶⁾ Because (V_Ga)₃(V_N)₃ defects were quite recently³⁹⁾ assigned to the major SRH-type NRCs in the (000$\bar{1}$) 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_Ns 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 × 10¹⁷ 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.

PL spectra of the control GaN:Mg epilayer annealed at 850 °C, 710-nm-deep Ga- and N-polar I/I-GaN:Mg annealed at 1230 °C, and 100-nm-deep Ga- and N-polar I/I-GaN:Mg annealed at 1230 °C are shown in Figs. 8(a)–8(e), respectively. The [Mg] values were commonly 1 × 10¹⁹ 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.^22–24,50) 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.^22–24,50) 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-nm-deep 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⁾

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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 100-nm-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). 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_GaV_N (Refs. 32,34, and 36) and lower than the dynamic range of the PAS measurement (<10¹⁶ cm⁻³),³⁴⁾ respectively, because the sequential I/I was carried out on (0001) and (000$\bar{1}$) 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 (000$\bar{1}$) 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 100-nm-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 N₂ 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-nm-deep N-polar I/I-GaN:Mg after PIA commonly exhibited the YL band.^22,45–49) Different from the case of MOVPE films that contain carbon impurities higher than the middle of 10¹⁵ cm⁻³ (Ref. 54), the present I/I-GaN:Mg samples formed at the (000$\bar{1}$) surface of the HVPE FS-GaN are likely nearly carbon-free. Therefore, these samples likely contain V_Gas. Such V_Gas and V_Ns likely form the vacancy clusters that act as NRCs, as are the cases with V_GaV_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-nm-deep 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 ${\tau }_{{\rm{NR}}}$ 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 signal-to-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 ${\tau }_{1}$ and ${\tau }_{2}$ 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 ${\tau }_{1}$ and ${\tau }_{2}$ 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 ${\tau }_{1}$ and ${\tau }_{2}.$ As the fast component (${\tau }_{1}$) essentially limits the cw PL intensity under low excitation conditions, ${\tau }_{1}$ is generally used as the representative of ${\tau }_{{\rm{PL}}}.$ By increasing T_a, ${\tau }_{1}$ at 300 K was increased to 18 ps at T_a = 1230 °C, which nearly agrees with typical ${\tau }_{{\rm{PL}}}$ being 20 ps of p-GaN:Mg epilayers of the same [Mg] (1 × 10¹⁹ 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 ${\tau }_{2}$ 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), ${\tau }_{2}{{\rm{A}}}_{2}/\left({\tau }_{1}{{\rm{A}}}_{1}+{\tau }_{2}{{\rm{A}}}_{2}\right)$ values are plotted as a function of T_a, where ${\tau }_{2}{{\rm{A}}}_{2}/\left({\tau }_{1}{{\rm{A}}}_{1}+{\tau }_{2}{{\rm{A}}}_{2}\right)$ represents the ratio of carriers recombining in the low N_NRC zone to the total carriers.

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For quantifying N_NRC, identification of the origin of NRCs in I/I-GaN:Mg is mandatory. Reference 39 carried out PAS 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 10¹⁶ cm⁻³ and decreased with increasing T_a. Because ${\tau }_{{\rm{PL}}}$ 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 ${\tau }_{{\rm{PL}}}$ 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, ${\sigma }_{{\rm{n}}}$ of (V_Ga)₃(V_N)₃ is estimated at a few times 10⁻¹³ cm², the value being comparable to that obtained³⁷⁾ for V_Ga(V_N)₂ in the p-GaN:Mg epilayers,²⁷⁾ as plotted by closed squares. Because ${\sigma }_{{\rm{n}}}$ is a parameter representing the trapping probability of minority carriers, it is reasonable that vacancy clusters of different open volumes have similar ${\sigma }_{{\rm{n}}}.$ Nevertheless, this value is approximately four times larger than ${\sigma }_{{\rm{p}}}$ (=7 × 10⁻¹⁴ cm²) of V_GaV_N in n-GaN, and therefore, ${\tau }_{{\rm{minority}}}$ in p-GaN:Mg samples are much shorter than that in n-GaN, combined with the large ${v}_{{\rm{minority}}}.$ Very recently (Refs. 55 and 56) independently reported the SRH lifetime (${\tau }_{{\rm{SRH}}}$), which is expressed by ${\tau }_{{\rm{SRH}}}=\sqrt{{\tau }_{{\rm{n}}}{\tau }_{{\rm{p}}}},$ where ${\tau }_{{\rm{n}}}$ and ${\tau }_{{\rm{p}}}$ 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 ${v}_{{\rm{minority}}}$ and ${\sigma }_{{\rm{minority}}}$ of the major NRCs. These results^{36–39,55,56)} are consistent with each other.