The Origin of the Yellow Luminescence Band in Be-Doped Bulk GaN

Abstract

Photoluminescence (PL) from Be-doped bulk GaN crystals grown by the High Nitrogen Pressure Solution method was studied and compared with PL from GaN:Be layers on sapphire grown by molecular beam epitaxy and metalorganic chemical vapor deposition techniques. The yellow luminescence band in the latter is caused by the isolated Be_Ga acceptor (the YL_Be band), while the broad yellow band in bulk GaN:Be crystals is a superposition of the YL_Be band and another band, most likely the C_N-related YL1 band. The attribution of the yellow band in bulk GaN:Be crystals to the Be_GaO_N complex (a deep donor) is questioned.

1. Introduction

GaN with a bandgap of 3.50 eV attracts significant attention from researchers due to its applications in light-emitting and high-power devices [1,2,3,4]. Point defects that may detrimentally affect the devices’ efficiency and longevity are still poorly understood. Photoluminescence (PL) is a powerful research tool that reveals the properties of point defects, such as charge state, transition levels, and carrier capture coefficients [5,6,7].

The most-studied defect-related PL band in GaN is the yellow luminescence (YL) band [8,9,10]. In undoped GaN grown by metalorganic chemical vapor deposition (MOCVD), the YL band with a maximum at 2.17 eV and zero-phonon line (ZPL) at 2.59 eV (labeled the YL1 band) is commonly observed due to contamination with carbon and attributed to the C_N acceptor [10,11,12,13,14]. The YL1 band can also be recognized in PL spectra from undoped GaN grown by other techniques such as the High Nitrogen Pressure Solution (HNPS) method [15] and the hydride vapor phase epitaxy (HVPE) method [12]. Very low concentrations of carbon (10¹⁵–10¹⁶ cm⁻³) in HVPE-grown undoped GaN lead to the quantum efficiency of the YL1 band close to unity thanks to a relatively high hole-capture cross-section of the C_N defect [16,17]. This explains why the C_N-related YL1 band is omnipresent in undoped GaN and GaN doped with various impurities.

A different (as will be shown below) yellow band is observed in GaN doped or implanted with beryllium (Be) [9,17,18,19]. A renewed interest in doping III-nitrides with Be is fueled by recent findings that shallow Be-related acceptors can potentially be used for conductive p-type GaN and AlN [20,21,22]. We recently studied PL from more than 100 Be-doped GaN samples grown by MOCVD and molecular beam epitaxy (MBE), as well as GaN samples grown by HVPE and implanted with Be or co-implanted with Be and F [23,24]. In almost all these samples, the YL band is the dominant defect-related PL band with absolute internal quantum efficiency approaching unity in some samples. This YL band, with a maximum at 2.15 eV and specific properties (labeled the YL_Be band), is now reliably attributed to the isolated Be_Ga acceptor [25].

In fair agreement with the theoretical predictions of Lany and Zunger [26], deep and shallow states of the Be_Ga acceptor are found in PL experiments [25]. Two deep polaronic configurations with a hole localized at a neighboring N atom in the c direction and one of three other directions have −/0 transition levels at 0.38 ± 0.03 eV (configuration Be2) and 0.33 ± 0.05 eV (Be1), respectively, above the valence band maximum (VBM) in the limit of low temperatures. Electron transitions from the conduction band to these levels are responsible for the YL_Be2 and YL_Be1 components of the YL_Be band, respectively [25]. The shallow state with a delocalized hole (Be3) is at 0.24 ± 0.02 eV above the VBM. Electron transitions from the conduction band to the shallow level cause the ultraviolet luminescence (UVL) band, with the main peak at 3.26 eV (labeled the UVL_Be3). Although the UVL_Be3 band resembles the Mg-related UVL band (the UVL_Mg band with the main peak at 3.28 eV), these two bands can be reliably distinguished thanks to their specific temperature dependences [25]. In particular, the ratio of intensities of the UVL_Be3 and YL_Be2 bands, I^UVL_Be3/I^YL_Be2, is the same for all GaN:Be samples, and it can be fitted with the following expression:

$$\frac{I_{Be3}^{UVL}}{I_{Be2}^{YL}}=\delta \exp \left(-\frac{\mathsf{\Delta }E}{kT}\right),$$

(1)

where δ is approximately equal to the ratio of the electron-capture coefficients for the Be3 and Be2 states of the Be_Ga acceptor (18 ± 8) and ΔE is the energy difference between these states (140 ± 10 meV). This property allows us to reliably recognize PL from the Be_Ga acceptor in GaN:Be samples, even when other PL bands contribute to the PL spectrum.

Another unique feature of the YL_Be band (observed in all studied GaN:Be layers on sapphire) is two-step quenching and complete disappearance at temperatures close to room temperature. The first step at about 100 K is attributed to a replacement of the YL_Be1 component by the YL_Be2 component after a captured hole transits from Be1 to Be2 over a potential barrier. The second quenching begins at about 200 K. The activation energy of this quenching is 0.30 eV in n-type samples, which led us to erroneously assume that the quenching is caused by the thermal emission of holes from the deep polaronic state to the valence band [23]. However, a more detailed analysis indicated that the quenching is caused by the thermal emission of holes from the shallow Be_Ga state (Be3, at ~0.20 eV at these temperatures) to the valence band. The larger nominal activation energy and relatively high temperatures at which the quenching of PL from such a shallow level occurs are explained by the feeding mechanism [25]. Namely, holes from the deep polaronic state are excited to the shallow state before they escape to the valence band, so that the measured activation energy of the quenching is the sum of the shallow state energy (E₃) and the energy difference between the shallow and deep states (ΔE).

A similar and very bright YL band with a maximum at 2.1–2.2 eV is observed in bulk GaN:Be crystals produced by the HNPS growth method [27,28,29]. However, the properties of the YL band in these crystals (labeled YL_bulk, hereafter) appear to be different from those of the YL_Be band in GaN:Be layers grown by MBE or MOCVD. In particular, the YL_bulk band is strong at room temperature, and its quenching begins only at T > 500 K [28]. It can be excited resonantly, with photon energies down to ~2.7 eV [28,29]. These features of the YL_bulk band indicate that the related transition level is at least 0.8 eV above the VBM, much deeper than the levels of the YL_Be band. Teisseyre et al. [27] attributed the YL_bulk band to the Be_GaO_N complex (the YL_BeO, hereafter). The assignment is based on theoretical predictions [27] and seems reasonable because these samples contain very high concentrations of Be and O (about 10¹⁹ cm⁻³). However, the 0/+ transition level of the Be_GaO_N complex is calculated at 0.26 eV [27]. Moreover, first-principles calculations by another research group predict that the Be_GaO_N complex is electrically neutral and does not have transition levels in the band gap [23]. The controversy can be resolved if we assume that more than one PL band contributes to the broad YL_bulk band. Lamprecht et al. [28] proposed that the YL_bulk band consists of three components, with maxima at 1.88 eV (red band), 2.08, and 2.12 eV (yellow). The 2.08 eV component was attributed to the Be_GaO_N complex, while the 2.12 eV component was thought to be caused by the C_N acceptor. Time-resolved PL experiments using a shutter indicated that all three components decay very slowly, so the YL_bulk signal could be observed for several seconds [28].

In this work, we propose a solution to the problem of the yellow band in Be-doped GaN. The Be_Ga-related YL_Be band with its specific properties is found in bulk GaN crystals grown by the HNPS technique. It is buried under a stronger yellow band in bulk GaN:Be crystals (temporarily labeled YL_X). The YL_X band is caused by electron transitions from the conduction band (or from the shallow donors) to a deep level at 0.8–0.9 eV above the VBM and is likely the C_N-related YL1 band.

2. Materials and Methods

Be-doped GaN crystals were grown by the HNPS method at a growth temperature of 1450 °C and at 1 GPa of nitrogen pressure [30,31]. Beryllium doping was at a level of 10¹⁹ cm⁻³. The typical lateral size of spontaneously crystallized GaN:Be hexagonal platelets did not exceed 5 mm and the thickness was 150 μm. According to secondary ion mass spectrometry (SIMS) measurements performed at the Institute of Physics of the Polish Academy of Sciences with CAMECA IMS6F microanalyzer (Gennevilliers, France), GaN:Be crystals grown under similar conditions contain 3 × 10¹⁹ cm⁻³ of Be atoms, 2 × 10¹⁹ cm⁻³ of O, and 5 × 10¹⁷ cm⁻³ of C. The samples are semi-insulating. Point defects in similar crystals were previously studied by PL [27,28,29,31], positron annihilation [32], optically detected magnetic resonance (ODMR) [33], infrared absorption [34], and photo-induced electron paramagnetic resonance (photo-EPR) [35,36].

Steady-state PL was excited with a HeCd laser, dispersed by 1200 rules/mm grating in a 0.3 m monochromator, and detected by a cooled photomultiplier tube. Other details of PL experiments can be found elsewhere [7,13]. The as-measured PL spectra were corrected for the measurement system’s spectral response, and PL intensity was additionally multiplied by λ³, where λ is the light wavelength, to present the PL spectra in units proportional to the number of emitted photons as a function of photon energy [13].

3. Results

3.1. PL Bands in Be-Doped GaN Grown by MOCVD and MBE Techniques

The shape and position of the YL_Be band are well reproduced in many GaN layers grown by MOCVD and MBE. Figure 1 shows representative PL spectra at T = 18 K. The shape of the YL_Be band can be fitted (the dashed line) with the following expression obtained in the one-dimensional configuration coordinate model [37]:

$$I^{PL}(\hslash \omega )=I^{PL}(\hslash {\omega }_{\max })\exp \left[-2S_e{\left(\sqrt{\frac{E_0^{*}-\hslash \omega +\mathsf{\Delta }}{d_{FC}^g}}-1\right)}^2\right].$$

(2)

Here, S_e is the Huang–Rhys factor in the excited state of the defect; d_FC^g = $E_0^{*}$ − ħω_max is the Frank–Condon shift in the ground state; $E_0^{*}$ = E₀ + 0.5ħΩ_e, where E₀ is the ZPL energy and ħΩ_e is the energy of the effective phonon mode in the excited state; and ħω and ħω_max are the photon energy and position of the PL band maximum, respectively. The Δ is a minor shift of the PL band maximum due to sample-dependent reasons such as in-plane biaxial strain in thin GaN layers grown on sapphire substrates (blue shift) or local electric fields (red shift).

In addition to the YL_Be band, PL spectra from Be-doped GaN grown by MOCVD and MBE contain two UVL bands: the Mg_Ga-related UVL_Mg band, with the first peak at 3.27 eV, and the Be-related UVL_Be band, with the first peak at 3.38 eV. Both peaks are followed by a few LO phonon replicas. The UVL_Mg band is caused by mild contamination with Mg during growth (especially significant in our MOCVD GaN:Be samples). The UVL_Be band was found in the majority of GaN:Be samples. In MBE-grown samples, it required activation by annealing at T > 750 °C (Figure 1). Our earlier attribution of this band to the shallow state of the Be_Ga acceptor [20] was later rejected, and the band is preliminary attributed to a complex defect involving Be [25].

The best way to recognize the Be_Ga-related YL_Be band is to investigate the temperature evolution of the PL spectrum, the characteristic features of which were reproduced in all studied GaN:Be samples grown by MBE and MOCVD [25]. The YL_Be band is quenched in two steps. At T ≈ 100 K, the YL_Be band intensity drops (usually by a factor of about 2) and the band abruptly redshifts by up to 50 meV. This behavior is explained by the relaxation of the bound hole from the polaronic state Be1 at 0.33 eV to the polaronic state Be2 at 0.38 eV. At T > 180 K, the second quenching is observed (Figure 2). In conductive n-type GaN:Be samples, the second quenching reveals an activation energy of 0.30 eV, while in semi-insulating samples, the quenching occurs by the abrupt and tunable quenching (ATQ) mechanism [38].

The most important feature of the temperature evolution of PL is the emergence of a UVL band (UVL_Be3) at T > 140 K (Figure 2). The shift of the UVL maximum with temperature is shown in Figure 3. At T < 25 K, the UVL band is caused by donor-acceptor-pair (DAP)-type transitions of electrons from shallow O_N donors to shallow Mg_Ga acceptors. At T > 50 K, the DAP peaks are replaced with similar peaks caused by electron transitions from the conduction band to the Mg_Ga acceptors (eA transitions). At T > 130 K, the UVL_Mg band is quenched by the ATQ mechanism. A similar in shape but slightly red-shifted UVL_Be3 band emerges at higher temperatures. It can be seen from Figure 3 that the ZPL of the UVL_Be3 is red-shifted by 13 ± 3 meV from the ZPL of the UVL_Mg band. Since the transition level of the shallow Mg_Ga acceptor is located at 223 ± 3 meV above the VBM at T = 18 K [12], we conclude that the shallow −/0 transition level of the Be_Ga acceptor (the Be3 state) is located at 236 ± 5 meV above the VBM. With increasing temperature, the Be3 level moves towards the valence band (0.20 eV at T ≈ 200 K) [25].

In agreement with the model proposed in Ref. [25], the ratio UVL_Be3/YL_Be of PL intensities is the same in all GaN:Be samples. This ratio is described in a wide range of temperatures with Equation (1), where ΔE is the energy distance between the Be2 and Be3 states (ΔE = 140–145 meV). Figure 4 shows the dependence for two samples. In the MOCVD GaN:Be sample, the UVL_Mg band is quenched and replaced by the UVL_Be3 band at T > 140 K (compare Figure 3 and Figure 4 for this sample).

A remarkable feature of this model is that the second step of the YL_Be quenching is caused by the thermal emission of holes, not from a deep but from the shallow Be3 level, to the valence band. In particular, the activation energy of 0.30 eV obtained from this quenching in conductive n-type GaN:Be samples is the sum of the Be3 ionization energy and ΔE [25]. From this, the deepest polaronic state of the Be_Ga acceptor is found at 0.38 ± 0.03 eV above the VBM in the limit of low temperatures (≈0.30 eV at T = 200 K). The unique interplay of the UVL_Be3 and YL_Be bands will be used below to recognize the YL_Be band in bulk GaN crystals.

3.2. The Yellow Band in Bulk GaN:Be Grown by High-Pressure Technique

Figure 5 shows PL spectra from bulk GaN:Be excited above-bandgap (with the 325 nm line of the HeCd laser at 3.81 eV) and below-bandgap (with the 442 nm line of the HeCd laser at 2.80 eV). The spectra are compared with the PL spectrum from MBE-grown GaN:Be. In the case of the usual above-bandgap excitation, a very weak near-band-edge (NBE) emission is detected at 3.47 eV. The UVL_Mg band appears as a structureless shoulder at about 3.2 eV. We assume that its ZPL and LO phonon replicas are unresolved because of strong local electric fields caused by short-range potential fluctuations in heavily doped and compensated GaN:Be [39].

The yellow band (YL_bulk) at ~2.1 eV is broad and very strong, in agreement with earlier reports [28,29]. With increasing excitation intensity, P_exc, from 10⁻⁵ to ~100 W/cm², it blueshifts by about 0.1 eV. After a laser pulse at T = 18 K, the PL intensity decays nonexponentially, approximately as t^−1.2 at time delays t between 1 and 1000 s, and the band redshifts by almost 0.1 eV. Such behavior agrees with the presence of potential fluctuations.

The yellow band in bulk GaN:Be crystals can also be excited below the bandgap. The spectrum obtained after excitation with the 442 nm line of the HeCd laser (2.8 eV) is shown in Figure 5 with filled circles. This band (temporarily labeled YL_X) is also broad and its maximum is at 2.07 eV. Interestingly, the sum of the YL_Be band in MBE GaN:Be and the YL_X band matches the shape of the YL_bulk band observed after the above-bandgap excitation (Figure 5). This is the first indication that the YL_bulk band may consist of two unresolved broad bands, one of which is the well-studied Be_Ga-related YL_Be band. A stronger argument follows from the analysis of the evolution of the PL spectrum with temperature, as discussed below.

Figure 6 shows the PL spectrum from bulk GaN:Be at selected temperatures. The intensity of the YL_bulk band changes insignificantly with increasing temperature from 18 to 320 K. The intensity of the UVL band decreases between 18 and 140 K and then increases (between 140 and 200 K). While the fine structure of the UVL band cannot be resolved, the increase in the UVL intensity is very similar to that observed in the GaN:Be samples grown by MBE and MOCVD [25].

Figure 7 compares PL spectra at T = 200 K for bulk GaN:Be (at two crystal locations) and GaN:Be layers grown by MBE and MOCVD (arbitrarily shifted vertically to match the UVL intensity). The ratio of intensities UVL_Be3/YL_Be at the selected temperature must be the same in all Be-doped GaN samples. Assuming that the UVL_Be3 band emerges with the temperature [25], we conclude that the YL_Be band in bulk GaN is hidden under a stronger yellow band of different origin (YL_X).

Figure 8 shows an Arrhenius plot for the studied PL bands in bulk GaN:Be. The expected temperature dependence of the Mg_Ga-related UVL_Mg intensity is shown with a dotted line. The temperature dependences for the Be_Ga-related YL_Be band (shown with dashed lines) are simulated to fit the UVL_Be3 dependences by fixing the UVL_Be3/YL_Be ratio according to Equation (1) with earlier-found parameters.

The first step of the YL_Be quenching is expected at T ≈ 100 K but cannot be resolved. The YL_Be band hides under a stronger yellow band at T < 200 K and completely disappears at temperatures approaching room temperature, as expected [25]. We estimate that the YL_X band is stronger than the YL_Be band by a factor of 2–5 at T < 200 K.

We also studied the temperature dependence of the YL_bulk full width at half maximum (FWHM or W) and compared it with that for the YL_Be band in the GaN:Be samples grown by MOCVD (Figure 9). For PL bands that are broad due to strong electron–phonon coupling, the W(T) dependence can be fitted with the following expression [6]:

$$W(T)=W(0)\sqrt{\coth \left(\frac{\hslash {\mathsf{\Omega }}_e}{2kT}\right)},$$

(3)

where ħΩ_e is the energy of the effective phonon mode. For MOCVD-grown GaN:Be samples, the fit with ħΩ_e = 38 meV is relatively good, and the value of the single fitting parameter is typical for defects in GaN (between 23 and 56 meV) [37,40,41]. However, the W(T) dependence for the YL_bulk band in bulk GaN:Mg shows abnormal narrowing with increasing temperature from ~170 to 250 K. This temperature region roughly corresponds to the region where the YL_Be band is quenched. We conclude that at T > 250 K, the contribution of the YL_Be band to the YL_bulk band can be ignored and only the YL_X band remains. The FWHM of the YL_X band is smaller than that of the YL_Be band, while the parameter ħΩ_e is larger (Figure 9).

Figure 10 shows the temperature dependence of the YL_bulk band maximum (shifted up by 23 meV for P_exc = 0.005 W/cm²) in comparison with the dependence for the YL_Be band in the MOCVD and MBE GaN:Be samples. The sudden shift at about 100 K is similar in all the samples, and it can be explained by replacing the YL_Be1 with the YL_Be2, PL bands associated with two deep polaronic states of the Be_Ga acceptor [25]. At T > 230 K, the band maximum corresponds to the YL_X band because the YL_Be band is quenched. Note that the YL_bulk band shifts significantly with excitation intensity (up to 0.1 eV with a variation of P_exc from 10⁻⁵ to ~100 W/cm²), whereas the shift of the YL_Be band in the MOCVD and MBE GaN:Be samples is insignificant.

To further explore the properties of the YL_X band, we conducted PL experiments by using a high-temperature cryostat (Figure 11). The YL_X band is quenched by the ATQ mechanism, which is typical for defects in semi-insulating GaN [38]. Formally, it can be described with the commonly used expression:

$$I^{PL}(T)=\frac{I^{PL}(0)}{1+C\exp \left(\frac{-E_A}{kT}\right)}$$

(4)

However, unlike the PL quenching in conductive n-type GaN, the parameter E_A does not have a physical meaning [17]. The quenching is very abrupt, yet the slope of the quenching could be smoothened by potential fluctuations [42], or other reasons [38]. The quenching is tunable by excitation intensity.

4. Discussion

The results of this study indicate that at least two PL bands contribute to the YL_bulk band, with a maximum at about 2.1 eV in bulk GaN:Be grown by the HNPS method. These are the YL_Be band (with a maximum at 2.15 eV) associated with the isolated Be_Ga acceptor and the YL_X band (at ~2.06 eV) caused by a different defect. Since the YL_Be band is well studied [25], we will focus below on the analysis of the YL_X band, which is the strongest PL band at all studied temperatures.

4.1. Type of Transition

The YL_X band at T = 18 K can be excited below-bandgap, with photon energies of 2.8 eV (Figure 5). Earlier, the onset of the PL excitation (PLE) spectrum of the yellow band was found at 2.8 eV at 7 K, and the YL_bulk band could be excited with a 2.78 eV laser [28]. At room temperature (when we expect only the YL_X band), the PLE spectrum also shows an onset at about 2.7–2.8 eV [29]. We assume that the YL_X band is caused by electron transitions from the conduction band (or from shallow donors) to a deep defect level, as it occurs for almost all defects in GaN [7,17]. Then, the results of the current work and those of previous studies indicate that the related defect level is located no closer than 0.8 eV to the VBM. Nonexponential and slow PL decay after a laser pulse agrees with the assumed type of transition. This PL cannot be caused by transitions from an excited state to the ground state of some defect because such transitions are characterized by exponential PL decay, even at very low temperatures, and positions of such PL bands are not affected by local electric fields [7,17]. At this point, transitions from a deep donor to an acceptor (or a deeper donor) cannot be excluded since such transitions are possible in heavily doped GaN and are characterized by slow, nonexponential decay. If this was the case, the defect level responsible for the YL_X band would be much closer to the VBM than 0.8 eV. However, the quenching of the YL_X band at T > 450 K (Figure 11 and the data in Ref. [28]) favors the assumption that the related defect level is at 0.8–0.9 eV above the VBM. It was shown in Ref. [17] that for defects with relatively strong PL in GaN, the quenching begins at T = 400–500 K (at P_exc ≈ 0.1 W/cm² when the quenching occurs by the ATQ mechanism) if the defect level is located at 0.6–1.0 eV above the VBM. Transitions from the conduction band (or from shallow donors) to a defect level at ~0.8 eV above the VBM may be characterized by a nonexponential, slow decay of PL and by relatively large PL band shifts with a variation of P_exc if local electric fields (e.g., due to potential fluctuations) are present. ODMR and photo-EPR studies of the yellow band in similar bulk GaN:Be crystals support this type of transition [33,35]. We exclude the possibility of electron transitions from a defect level located in the upper part of the gap to the valence band as the origin of the YL_X band. Such transitions cannot be observed because photogenerated holes are captured by various acceptors with the multiphonon nonradiative mechanism many orders of magnitude faster than via radiative transitions [7].

4.2. On Identification of the YL_X Band in Bulk GaN

The observed broad YL_bulk band in bulk GaN:Be consists of at least two unresolved bands, one of which is a well-studied YL_Be band associated with the isolated Be_Ga acceptor. Another PL band (temporarily labeled YL_X) is caused by electron transitions from the conduction band (or shallow donors) to a deep defect (donor or acceptor), with a transition level at 0.8–0.9 eV above the VBM. Since the main difference between GaN:Be layers grown by MBE or MOCVD methods and bulk GaN:Be crystals grown by the HNPS method is a high concentration of oxygen in the latter, it is tempting to attribute it to the Be_GaO_N complex, which is expected to be a deep donor [27]. However, the first-principles calculations using the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional [43] predict that the 0/+ level of the Be_GaO_N defect is located at 0.26 eV above the VBM [27], or that this defect has no transition levels in the bandgap [23]. Whereas fair agreement of theoretical predictions with experimental findings is observed for the Be_Ga acceptor, the disagreement for the 0/+ level of the Be_GaO_N defect is significant (

Table 1. Calculated and experimentally found values (all in eV) of the charge transition levels relative to the VBM and PL band maxima (for E_g = 3.50 eV) for defects that may contribute to the YL_bulk band in Be-doped GaN, assuming that the YL_X band is caused by the Be_GaO_N complex.

Source	BeGa (−/0)				BeGaON (0/+)		CN (−/0)		References
	Deep		Shallow		Deep		Deep
	EA	ħωmax	EA	ħωmax	EA	ħωmax	EA	ħωmax
VDW 1	0.55	1.80			0.26	2.08	0.90	2.14	[11,27,44]
DD 2	0.58	1.72	0.24	3.20	–	–	0.93	2.08	[13,20,23]
SHW 3	0.65	1.67							[45]
LZ 4	0.45	2.02	0.15	~3.3					[26]
Experiment	0.33 0.38	2.15	0.236	3.26	0.8–0.9	2.06	0.916	2.17	[12,25] and this work

¹ Van de Walle’s group. ² D. Demchenko. ³ Su-Huai Wei. ⁴ Lany and Zunger.

).

Another possibility is that the YL_X band is the C_N-related YL1 band slightly broadened and redshifted because of potential fluctuations (Figure 12). Both PL bands are quenched at T > 500 K in semi-insulating GaN (at P_exc ≈ 0.1 W/cm²). The concentration of carbon impurities in the studied bulk GaN:Be samples is about 5 × 10¹⁷ cm⁻³, which is enough to cause a strong yellow band.

Below, we will discuss two candidates for the YL_X band (C_N acceptor and Be_GaO_N donor). Parameters of defects that may contribute to the YL_bulk band are given in

Table 2. Possible parameters of main defects in bulk GaN:Be.

Scenario	Concentration of Defects (cm−3)				Hole-Capture Coefficient (cm3/s)
	BeGa	BeGaON	ON	CN	BeGa	BeGaON	CN
1 (X = CN)	1017	3 × 1019	1017	1018	10−6	10−9	4 × 10−7
2 (X = BeGaON)	1018	3 × 1019	1018	1018	10−6	10−7	4 × 10−7

. The hole-capture coefficient, C_p, for the C_N acceptor is (3.7 ± 1.6) × 10⁻⁷ cm³/s. The C_p for the Be_Ga acceptor was estimated from the YL_Be quenching as 4 × 10⁻⁷ cm³/s. However, careful analysis of PL quenching in numerous MOCVD GaN:Be samples (which contain C and Be, with concentrations of about 10¹⁷ cm⁻³ and (1–30) × 10¹⁷ cm⁻³, respectively) shows that the C_p for the Be_Ga acceptor is larger, which is consistent with the capture of holes by a shallow acceptor level located at 0.2 eV above the VBM. It was shown in Ref. [25] that C_p = 10⁻⁶ cm³/s agrees with the experimental data. Note that for another shallow acceptor (Mg_Ga), C_p is also 10⁻⁶ cm³/s. We will consider this value hereafter for the Be_Ga acceptor that captures holes at its shallow level at 0.2 eV above the VBM [25]. The C_p for the Be_GaO_N complex is expected to be significantly smaller because of the donor nature of this defect. The C_p for donors in GaN varies from 10⁻¹⁰ to 4 × 10⁻⁸ cm³/s [17]. At low enough temperatures (before the PL quenching begins), the PL intensity from defects in GaN (both conductive n-type and semi-insulating) is proportional to the concentration of defects and their hole-capture coefficient, i.e., I_i^PL = AC_piN_i for defect i, where A is a constant. From the experiment, I_X^PL/I_Be^PL = 2–5.

4.2.1. Can the YL_X Band Be the C_N-Related YL1 Band?

In the first scenario, the intensity of the YL1 band at T ≈ 100 K is about 2–5 times higher than that of the YL_Be band, and the contribution of PL from the Be_GaO_N complex is negligible. For this, the concentration of isolated Be_Ga defects should be about 10¹⁷ cm⁻³. Then, I_C^PL/I_Be^PL = C_p,CN_C/C_p,BeN_Be = 4 if we use the corresponding parameters in Table 2. Such a low concentration of isolated Be_Ga defects (by a factor of 30 lower than the total concentration of Be atoms) implies that the concentration of Be_GaO_N complexes may reach 3 × 10¹⁹ cm⁻³, i.e., the majority of Be atoms form complexes with oxygen. The concentration of O_N donors may not exceed the total concentration of acceptors (C_N and Be_Ga) because the samples are semi-insulating and the Be_GaO_N donors are neutral. Such a high concentration of Be_GaO_N would not contribute to PL if the hole-capture coefficient for this donor is low (I_BeO^PL/I_Be^PL = C_p,BeON_BeO/C_p,BeN_Be = 0.3 if C_p for the Be_GaO_N complex is 10⁻⁹ cm³/s) or if the Be_GaO_N is not participating in electron–hole recombination as it was predicted in Ref. [23].

4.2.2. Can the YL_X Band Be Caused by the Be_GaO_N Complex?

In the second scenario, the intensity of the assumed YL_BeO band from the Be_GaO_N complex at T ≈ 100 K is about 2–5 times higher than that of the YL_Be band, and the YL1 band from the C_N acceptors is negligibly weak. For this, the concentration of isolated Be_Ga defects should be at least 10¹⁸ cm⁻³ (so that I_C^PL/I_Be^PL = C_p,CN_C/C_p,BeN_Be < 0.4), and the C_p for the Be_GaO_N donor should be relatively high (so that I_BeO^PL/I_Be^PL = C_p,BeON_BeO/C_p,BeN_Be = 2–5). This scenario would work if N_BeO = 3 × 10¹⁹ cm⁻³ and C_p,BeO = 10⁻⁷ cm³/s (Table 2). The main argument against this scenario is a conflict between the predicted ionization energy of the Be_GaO_N (0.26 eV or no level) [23,27] and the experimentally found transition level at 0.8–0.9 eV. However, a strong argument favoring this scenario was a good agreement between theoretical predictions and experiments in PL under hydrostatic pressure [27]. Below, we will suggest an alternative interpretation of these experiments.

4.3. Interpretation of Other Experiments

Exciting results were obtained in Ref. [27], where PL from bulk GaN:Be was studied at T = 10 K under hydrostatic pressure, p, up to 12.5 GPa. With increasing p, the YL band splits into two components: component A blue-shifts with a moderate rate (20 meV/GPa, similar to the typical shift of the C_N-related YL1 band), while component B blue-shifts much faster (about 90 meV/GPa). Component A was attributed to the C_N acceptor, while components B and C were related to the deep (polaronic) and shallow (delocalized) states of the Be_GaO_N complex. A remarkable result is that at p > 8 GPa, component C emerges at about 3.6 eV and becomes the strongest PL band at p > 9 GPa. This unusual phenomenon was explained by the dual nature of the Be_GaO_N defect: namely, the deeper state with a highly localized hole (calculated 0/+ level at 0.26 eV above the VBM at p = 0) moves towards the VBM with hydrostatic pressure. At p = 8 GPa, a shallow state of this defect (the 0/+ level at 0.12 eV above the VBM) with a delocalized hole becomes the most stable configuration. At pressures between 9 and 12.5 GPa, both PL signals are observed: a relatively narrow PL band close to the bandgap, which is caused by electron transitions from the conduction band to the shallow level, and a broad band at about 3 eV, which is caused by electron transitions from the conduction band to the deep state of the Be_GaO_N defect. The calculated barrier between the shallow and deep states is 0.24 eV [27]. The same calculations predict that the polaronic state of the isolated Be_Ga defect is deeper (0.55 eV above the VBM), and the deep states of the Be_Ga and Be_GaO_N defects shift similarly with hydrostatic pressure [27].

We agree that component A of the yellow band can be the YL1 band caused by the C_N acceptor but suggest that component B is caused by the isolated Be_Ga defect (the −/0 transition level at 0.38 eV above the VBM and the PL band maximum at 2.15 eV). With increasing p, this level shifts towards the valence band and, at p ≈ 8 GPa, intersects the shallow level of the Be_Ga (at 0.24 eV above the VBM at p = 0). At higher pressures, the UVL_Be3 band of the Be_Ga acceptor emerges even at T = 10 K because this configuration becomes the most stable. It may be interesting to test the above explanation by investigating MOCVD GaN:Be samples under hydrostatic pressure. As for the Be_GaO_N complexes, we expect that they are either nonradiative, weakly radiative, or “inert” defects, so that their contribution to PL can be ignored even if their concentration is about 3 × 10¹⁹ cm⁻³.

Our interpretation of the PL results is consistent with the results of photo-EPR studies on similar bulk Be-doped GaN crystals [35,36]. Willoughby et al. [35] initially attributed the photo-EPR signal from Be-doped GaN crystals to a Be-related acceptor, with the −/0 transition level at 0.7 eV above the VBM. However, these authors later revised their attribution and explained this photo-EPR signal by recombination of electrons with holes bound to the C_N acceptor [36]. Note that slow transients of the photo-EPR signal, explained by trapping electrons by a Be-related defect level close to the conduction band [36], could be caused by potential fluctuations and local electric fields. This is also consistent with the very slow PL decays for the YL_bulk band [28]. The attribution of the YL_bulk band to a superposition of the YL_Be and YL1 bands may also explain the results obtained by Glaser et al. [33]. They observed ODMR signals from bulk GaN:Be crystals grown by the HNPS method (with a carbon concentration of 10¹⁷ cm⁻³) and noted that the g-values for the yellow band in these samples were very close to those for the YL band in undoped GaN (i.e., for the C_N-related YL1 band).

5. Conclusions

The broad yellow luminescence band in bulk GaN crystals grown by high-pressure technique and doped with Be consists of two unresolved bands: the Be_Ga-related YL_Be band and the YL_X band, which is most likely the C_N-related YL1 band. At T > 200 K, the YL_Be band is quenched, while the quenching of the YL_X band begins only at 400–500 K. We conclude that the yellow band, previously attributed to the Be_GaO_N complex based on first-principles calculations and PL experiments with hydrostatic pressure [27], is in fact the Be_Ga-related YL_Be band, whereas the Be_GaO_N defect is either optically inactive or its contribution to PL is negligible. At the same time, the concentration of the Be_GaO_N complexes in these bulk GaN crystals significantly exceeds the concentration of the isolated Be_Ga defects.