Two n-type GaN layers with Si concentration of 3 × 10¹⁶ cm⁻³ were grown on LT-GaN (sample A) and AlN buffer layer (Sample B), respectively, by metal organic chemical vapor deposition (MOCVD) method. The detailed structure of the samples is shown in Figure 1. The n-GaN (1.7 μm) layer was grown at 1050˚C after the sequence of LT-GaN (30 nm) or AlN (1.0 μm) buffer and i-GaN (3.0 mm) layer on c-plane (0001) sapphire substrate. All the layers except the buffer layer are same for both samples.

The experimental setup for characterizing the n-GaN layers by TWEPL is shown in Figure 2. The sample was mounted in a temperature-controlled cryostat and

irradiated by diode-pumped solid-state (DPSS) laser of 4.66 eV (266 nm) as the AGE. The conventional PL spectra of both samples were measured at a temperature of 12 K. The output power of the AGE laser was kept constant at 16 mW and the neutral density filters were used for changing the excitation density. A temporally switched BGE light by an optical shutter with the internal 500 seconds ON/OFF was superposed on the AGE light to excite the sample at the same point. The BGE light of energy 1.27 eV (980 nm), 1.17 eV (1064 nm), and 0.93 eV (1340 nm) were used for the TWEPL measurement. The modulated PL signal from the sample was fed to a monochromator through a set of objective lenses, converted to photocurrent by a photomultiplier and recorded by a computer after the lock-in amplification. Here, an optical chopper was used with the digital lock-in-amplifier for improving the S/N ratio of the PL signal. By measuring PL intensity with and without the BGE, I_AGE+BGE and I_AGE, respectively, the normalized PL intensity I_N = I_AGE+BGE/I_AGE was determined.

The PL spectra of n-GaN samples measured at 12 K under the irradiation with the AGE light only are shown in Figure 3. Both spectra consist of near band-edge (NBE) luminescence (3.47 eV), shallow donor (oxygen) to valence band transition (I_ox at 3.41 eV), donor acceptor pair (DAP) transition (3.27 eV), and yellow luminescence (YL) (2.3 eV) peaks. Same type of emission spectra has

been also reported for GaN in earlier studies [2] . The NBE luminescence peak intensity of sample B is 8 times higher than that of sample A while the YL intensity of sample B is lower. The PL intensity is used to measure the quality of samples, and here it elucidates that quality of sample B is better than that of the sample A.

In this study, we focus on the NBE luminescence as the principal component for comparative analysis of two samples. The normalized PL intensity (I_N) of the NBE peak has been measured at a fixed temperature of 12 K and the AGE density of 1.10 mW/mm² is shown in Figure 4 as a function of the BGE power density for both samples.

With the addition of the BGE light, the value of I_N quenches from unity for all BGE energies of 0.93, 1.17 and 1.27 eV. The quenching of the I_N can be explained by two levels model schematically shown in Figure 5 indicating the presence of a pair of NRR centers in the sample whose energy difference correspond to that of the BGE energies [22] [23] [24] [25] . Determination of the NRR parameters becomes possible quantitatively by fitting experimental results based on Shockley-Read-Hall (SRH) statistics [22] [26] .

From Figure 4, it is observed that the amount of PL quenching becomes pronounced with increasing the BGE energy and density. It also exhibits that the value of I_N for sample A is always lower than that of sample B throughout the

experimental BGE density range. The minimum values of I_N, 0.60 and 0.74 are obtained for samples A and B, respectively at highest BGE density (1.37 W/mm²) of 1.17 eV BGE. The degree of change of the I_N values from unity represents the density of NRR centers in the samples. Thus, this result implies that the density of NRR centers is higher in sample A compared to that in sample B. It is consistent with the relative intensity of conventional PL for these samples.

When the BGE energy matches the energy difference between two coexisting below-gap NRR levels, electrons in NRR level 1 are excited to NRR level 2 from which they recombine nonradiatively with holes in the valence band of GaN. Hence, the hole density in the valence band decreases. Similarly, the electron vacancies in the NRR level 1 allow an increase of NRR process from conduction band. Thus, the electron density in the conduction band decreases. The combination of both effects reduces the number of electron-hole pairs available for radiative recombination and resulting in the PL intensity quenching. In the region of low BGE densities, the electron occupation function of NRR level 2 remains much lower than 1 and the PL quenching proceeds with the increase in the BGE density. In the region of higher BGE densities, on the other hand, the electron occupation function of NRR level 2 approaches unity and the PL quenching shows saturation tendency with further increase in the BGE density.

The AGE density dependence of I_N has been measured at a fixed BGE density and temperature by utilizing BGE energies of 0.93 and 1.17 eV shown in Figure 6. With increasing the AGE density from 1.10 mW/mm² to 4.60 mW/mm², the value of I_N approaches to unity for both samples. At lower AGE density, the excitation of electrons via below gap states relative to band-to-band excitation

increases which results in higher BGE effect due to the enhancement of the non-radiative recombination. Similar AGE density dependence of the I_N was observed in our previous studies of TWEPL [22] [25] [26] [27] .

The temperature dependence of I_N for samples A and B has been also examined at a fixed AGE (1.10 mW/mm²) and BGE (1.37 W/mm² and 0.95 W/mm²) densities shown in Figure 7. It has been observed that the I_N value increases for both 1.17 and 0.93 eV BGE, with increasing temperature from 12 K to 70 K. The I_N value of sample A enhances from 0.60 to 0.90, and that of sample B from 0.74 to 0.91, for 1.17 eV BGE. Further increase in temperature brings little change in the I_N values, showing a saturating tendency up to 130 K. This type of temperature dependency was observed in previous studies and attributed to the thermal emission of electrons e_n from NRR level 2 to the conduction band in Figure 5 in the two levels model [28] [29] . This type of thermal emission reduces the electronic population in the NRR level 2 even under the below-gap excitation and decreases the BGE effect.

In order to corroborate our qualitative interpretation by the two levels model, a semi-quantitative simulation for the TWEPL results of 1.17 eV BGE energy has been carried out. The rate equations of the two levels model as shown in Figure 5 can be written below with charge neutrality condition (CNC) [22] [30] [31] .

d n d t = G 1 − B n p − C n 1 n N t 1 ( 1 − f t 1 ) = 0 , d p d t = G 1 − B n p − C p 1 p N t 1 f t 1 − C p 2 p N t 2 f t 2 = 0 , d f t 1 d t = C n 1 n N t 1 ( 1 − f t 1 ) − C p 1 p f t 1 − G 2 f t 1 N t 2 ( 1 − f t 2 ) = 0 , d f t 2 d t = G 2 f t 1 N t 2 ( 1 − f t 2 ) − C p 2 p N t 2 f t 2 = 0 , n + N t 1 f t 1 + N t 2 f t 2 = n 0 + p ,

where G₁ [cm⁻³・s⁻¹] and G₂ [cm³・s⁻¹] are generation rate for the AGE and the BGE, respectively, B [cm³・s⁻¹] is the radiative recombination coefficient, N_t is the density of NRR levels, n₀ is the density of free electrons, f_t1 andf_t1 are the electron occupation function of NRR level 1 and NRR level 2, respectively.

For simplicity, we assumed that the electron capture coefficient C_n1 is equal to radiative recombination coefficient B, as 1.2 × 10⁻¹¹ cm³・s⁻¹ for GaN [32] . Such consideration has been taken by other researchers [26] [33] . Reshchikov et al. [1] [34] have reported that the hole capture coefficient of C_p1 is in the order of 10⁻⁶ cm³・s⁻¹ for GaN. The hole capture coefficient of C_p2 has been also reported in the order of 10⁻⁹ cm³・s⁻¹ [35] . The procedure of estimating generation rate of the AGE (G₁) and BGE (G₂) have been explained in our earlier study [30] .

The density of free electrons is assumed as n₀ ≈ 1 × 10¹⁶ cm⁻³ for both samples considering the Si doping concentration. The system of rate equations can be solved numerically and the dependencies of n, p, f_t1, and f_t2 on G₂ was found for the constant parameters of G₁, B, n₀, N_t, C_n, and C_p. By systematically solving and fitting the simulated results with experimental data, the defect parameters have been chosen as G₁= 4.0 × 10²⁰ cm⁻³・s⁻¹, C_p1 = 1 × 10⁻⁶ cm³・s⁻¹, C_n1 = 8.5 × 10⁻¹¹ cm³・s⁻¹ and C_p2 = 6.5 × 10⁻⁹ cm³・s⁻¹ for both samples A and B, respectively. The densities of two NRR levels are obtained as N_t1 = 8.0 × 10¹⁵ cm⁻³, N_t2 = 3.0 × 10¹⁷ cm⁻³ for the sample A, and N_t1' = 6.1 × 10¹⁵ cm⁻³, N_t2' = 6.0 × 10¹⁶ cm⁻³ for the sample B. The value of I_N is calculated as a function of generation rate of BGE (G₂) under fixed AGE generation rate of 4.0 × 10²⁰ cm⁻³・s⁻¹ and shown in Figure 8. The broken and solid lines represent the simulated result together with experimental points for both samples. The simulated I_N value shows a reasonable agreement with the measured points.

The dependence of the I_N as a function of the electron-hole generation rate of the AGE (G₁) at 12 K has been calculated by setting G₂ = 1.0 × 10⁻¹⁴ cm³・s⁻¹ and keeping all the other parameters as constant as previous. Figure 9 shows the I_N value of the NBE peak for both samples as a function of the electron-hole generation rate of the AGE (G₁).

Here, a set of parameters give the insight of below-gap states acting as NRR centers in samples A and B, and a reasonable fitting with experimental data. The estimated result shows that the densities of NRR centers are lower in sample B than that in sample A. From both fitting results, it is concluded that the interpretation based on the two-levels model is valid and the use of the AlN buffer layer is more effective for reducing the density of NRR centers in n-GaN layer than the LT-GaN buffer layer. The TWEPL study of NRR centers guides us to optimize growth conditions further.