Luminescence Properties of Defects in GaN: Solved and Unsolved Problems

Abstract

Gallium Nitride (GaN) is a wide-bandgap semiconductor that has revolutionized optoelectronic applications, enabling blue/white light-emitting devices and high-power electronics. Point defects in GaN strongly influence its optical and electronic properties, producing both beneficial and detrimental effects. This review provides a comprehensive update on the current understanding of point defects in GaN and their impact on photoluminescence (PL). Since our earlier review (Reshchikov and Morkoç, J. Appl. Phys. 2005, 97, 061301), substantial progress has been made in this field. PL bands associated with major intrinsic and extrinsic defects in GaN are now much better understood, and several defects in undoped GaN (arising from unintentional impurities or specific growth conditions) have been identified. Notably, the long-debated origin of the yellow luminescence band in GaN has been resolved, and the roles of Ga and N vacancies in the optical properties of GaN have been revised. Zero-phonon lines have been discovered for several defects. Key parameters, such as electron- and hole-capture coefficients, phonon energies, electron–phonon coupling strength, thermodynamic charge transition levels, and the presence of excited states, have been determined or refined. Despite these advances, several puzzles associated with PL remain unsolved, highlighting areas for future investigation.

1. Introduction

Gallium nitride (GaN), a wide-bandgap semiconductor with a direct bandgap of 3.43 eV at room temperature, is a cornerstone of modern optoelectronics and power electronics. Applications include bright blue and white light-emitting diodes (LEDs), blue lasers, and high-power and high-frequency electronic devices. Its outstanding material properties, including a high breakdown voltage and the availability of both n- and p-type doping, have established GaN as a key platform for next-generation semiconductor technologies [1,2,3,4]. However, defects significantly degrade optical and electrical performance. While structural defects are well-characterized, point defects—including vacancies, interstitials, antisites, impurities, and their complexes—remain insufficiently understood. Identifying and characterizing these defects is essential for improving the efficiency, reliability, and operational lifetime of GaN-based devices.

Point defects in GaN are probed using a wide range of experimental techniques, including photoluminescence (PL), cathodoluminescence (CL), secondary ion mass spectrometry (SIMS), Hall effect measurements, positron annihilation spectroscopy (PAS), Raman and Fourier-transform infrared (FTIR) spectroscopy, deep-level transient spectroscopy (DLTS), electron paramagnetic resonance (EPR), and optically detected magnetic resonance (ODMR) [5]. Among these, PL stands out as the most versatile and widely used method for probing optically active defects. PL enables the determination of key defect parameters, such as concentration, charge states, charge transition levels (with ~1 meV precision), carrier capture coefficients, electron–phonon coupling strengths, and excited-state characteristics. While excitonic luminescence, or, in general, near-band-edge (NBE) emission in GaN is well-understood [6,7,8,9,10,11,12,13,14,15,16], the origins of broad defect-related PL bands remain controversial. Persistent misattributions in the literature have hindered progress in the field.

The review by Reshchikov and Morkoç (2005) [16] provided a comprehensive analysis of PL in undoped and intentionally doped GaN. Since then, advances in material growth, experimental techniques, and first-principles calculations, particularly density functional theory (DFT), have prompted substantial revisions to earlier models. For example, the carbon impurity on a nitrogen site (C_N) was previously misidentified as a shallow acceptor with a −/0 charge transition level ~0.2 eV above the valence band maximum (VBM) [17,18,19,20,21,22], and was believed to be responsible for the ultraviolet luminescence (UVL) band at 3.28 eV [23]. However, modern DFT calculations and experimental evidence have reclassified C_N as a deep acceptor with a −/0 level at 0.9 eV above the VBM, now linked to the yellow luminescence (YL) band centered at ~2.2 eV [24,25,26,27]. Another illustrative case concerns the role of the gallium vacancy (V_Ga) and its complex with oxygen (V_GaO_N) in PL from GaN. Early DFT calculations [17,22] and the results of PAS experiments [28] led to the incorrect conclusion that transitions from the conduction band (or shallow donors) to these defects cause the YL band in undoped GaN [16]. More accurate calculations have since revised the energy levels of V_Ga and V_GaO_N by 1–2 eV [29,30,31,32], and recent experimental findings conclusively rule out their contribution to YL in undoped GaN (Section 3.1.5).

Although many controversies surrounding defect-related PL in GaN have been resolved since 2005, incorrect attributions, outdated theoretical interpretations, and misinterpretations of experimental data persist in the literature. This review aims to consolidate and disseminate an updated understanding of PL arising from major point defects in wurtzite GaN, with a focus on areas where significant revisions have been made. PL phenomena associated with excitons, structural defects, alloys, low-dimensional structures, transition metals, or rare-earth elements are beyond the scope of this work.

Table 1. Classification and main parameters of defect-related PL bands in GaN.

Dopant	PL Band	ħωmax (eV)	ZPL (eV)	EA (eV)	FWHM (eV)	Cp (cm3s−1)	Cn (cm3s−1)	τ (μs) a)	Attribution	Comments	Ref.
C	RLC	1.62							CN-CGa-CN ?	[C] > 1018 cm−3	[33]
−	RL1	1.75		~1.1	0.42	3 × 10−7	4.3 × 10−14		Cl? (−/0)?	HVPE GaN	[34]
−	RL2	1.74		~1	0.35			1000	AVN? (0/+)?	SI, Ga-rich GaN	[16,35,36,37]
Mg	RLMg	1.67		~0.9	0.41			1.3	MgGaVN (0/+)		[36]
Be	RLBe	1.77		~0.8	0.44			3	BeGaVN (0/+)		[36]
Ca	RLCa	1.82		~1.0	0.43			1900	CaGaVN (0/+)		[36]
−	RL3	1.77		~2.8	0.38	~10−5		0.010	RY3 (−/0)	HVPE GaN	[38]
−	RL4	1.6–1.7		~1.2	~0.44				VGa3ON ? (0/+)?	AT GaN	[39]
F,Cl,Cd,Ca,Hg	RL5	~1.6							?	Implantation damage
F	OL1	1.88			~0.47				VGaFN?
-	OL3	2.09			~0.47				VGaON2Hi? (0/+)?	AT GaN	[39]
− C	YL1, YLC	2.19	2.59	0.916	0.43	3.7 × 10−7	1.1 × 10−13		CN (−/0)	Omnipresent, MOCVD	[25,40,41]
−	YL2	2.3		~0.6	~0.49				VGa3Hi ? (0/+)?	AT GaN	[39,41,42]
−	YL3	2.07	2.38	1.130	0.40	~10−7	2 × 10−13		RY3 (−/0)	HVPE GaN	[38,41,43,44]
Be	YLBe	2.15		0.34	0.57	~1 × 10−6	1 × 10−13		BeGa (−/0)	YLBe1, YLBe2	[45,46]
−	GL1	2.35		~0.5	0.48			1	? (0/+)	HVPE GaN	[34]
−	GL2	2.33		~0.5	0.24			300	VN (+/2+)	SI, Ga-rich GaN	[34,47]
Hg	GLHg	2.44		0.8	0.39	(1–5) × 10−7	3 × 10−13		HgGa (−/0)		[48]
− Ca	GLCa	2.49		0.50	0.43	6 × 10−7	1 × 10−13		CaGa (−/0)	undoped MBE	[49]
− Zn	BL1, BLZn	2.86	3.10	0.400	0.36	5 × 10−7	6.8 × 10−13		ZnGa (−/0)	Dual nature?	[34,50,51,52,53,54]
− C	BL2	3.00	3.33	0.15	0.42	4.5 × 10−8		0.3	CNHi (0/+)	Bleaching	[55]
−	BL3	2.8	3.01	~0.46	0.45	~10−9		0.001	RY3 (0/+)	HVPE GaN	[56]
P	BLP	2.89	3.20	0.29	0.37				PN (0/+)		[57,58]
As	BLAs	2.6	2.95	0.54	~0.4			0.09	AsN (0/+)		[57]
Cd	BLCd	2.70	2.95	0.55	0.35	3 × 10−7	2.6 × 10−13		CdGa (−/0)		[48,59]
C	BLC	2.85	3.15	0.33	~0.43	10−10 ?		0.001	CN (0/+)		[25,60]
Be	BLBe	2.6		0.15	0.57	~10−8		0.8	BeGa (0/+) ?		[61]
Mg	BLMg	~2.8		0.22	~0.3				DD→MgGa	Large shifts	[62,63]
− Mg	UVL, UVLMg	3.28	3.28	0.223	0.01	1 × 10−6	3.2 × 10−12		MgGa (−/0)	Dual nature?	[40,62,63]
Be	UVLBe	3.38	3.38	0.113	0.01	~1 × 10−6	1 × 10−11		BeGaONBeGa (−/0)	Dual nature?	[64]

^a) τ at T ≈ 18 K for internal transitions, independent of n.

summarizes the principal PL bands and their updated parameters. Figure 1 illustrates the corresponding electronic transitions schematically.

Traditionally, PL bands in GaN are labeled according to their perceived emission color, such as red luminescence (RL) or green luminescence (GL). However, multiple defects can produce PL bands with similar spectral positions and overlapping hues, leading to ambiguity. To address this, we adopt a refined nomenclature introduced in Ref. [65], which supplements traditional band names with numerical or index-based identifiers. For instance, the GL band described in Ref. [16] is now designated GL1, while GL2 retains its original classification.

The most important changes and remaining challenges in understanding defect-related PL in GaN (in the author’s opinion) are summarized below.

Solved problems:

• The YL band (2.2 eV) in undoped GaN is now conclusively attributed to the C_N acceptor (Section 3.1.2). Remaining issue: Reliable experimental data are lacking for the charge transition levels and PL signatures of V_Ga and V_GaO_N complexes (Section 3.1.5 and Section 3.6).
• The UVL band (3.28 eV) in undoped GaN originates from the Mg_Ga acceptor, and not from C_N, Si_Ga, V_Ga-related, or structural defects (Section 3.5). Remaining issue: The theoretically predicted dual nature of the Mg_Ga acceptor has not been confirmed experimentally (Section 4.3.2).
• The GL2 and RL2 bands are associated with isolated nitrogen vacancies (V_N) and the AV_N complexes, where A denotes a cation-site acceptor (Section 3.2.2 and Section 3.3.2). Remaining questions: What is A in the RL2 from undoped GaN? Is there PL from the AV_N complexes with A = Zn_Ga, Cd_Ga, or Hg_Ga? Can GL2 and RL2 be linked to different charge transition levels of these multi-charged defects?
• The fundamental properties of the isolated Be_Ga acceptor have been well established (Section 4.2.2). Remaining uncertainties: The identities of the shallow acceptor and deep donor responsible for the UVL_Be (3.38 eV) and BL_Be (2.6 eV) bands, respectively, should be verified (Section 4.2.3 and Section 4.2.5).
• The origin of the aquamarine band in undoped GaN has been clarified (Section 4.6.2).
• Novel mechanisms of PL quenching emerged (Section 2.2.2 and Section 4.4.2).
• Significant redshifts of PL bands with decreasing excitation intensity have been explained (Section 4.3.4 and Section 4.4.5).

Unsolved problems:

• The predicted dual nature of acceptors (excluding Be_Ga) remains unverified experimentally (Section 4.3.2 and Section 4.4.1).
• The origins of the GL1 and RL1 bands are still unknown (Section 3.2.1 and Section 3.3.1).
• The RY3 defect remains unidentified (Section 3.1.4, Section 3.2.3, and Section 3.4.3).
• The influence of mobile defects at growth temperatures on the formation of complexes is not yet fully understood.
• The effect of the surface and structural defects on PL from point defects remains insufficiently explored.
• Significant discrepancies persist between predictions of first-principles calculations and experimental observations (Section 5.6).

The structure of the Review is the following. Section 2 outlines specific methodologies for conducting and analyzing PL experiments. Section 3 and Section 4 review PL bands in undoped and doped GaN, respectively. Section 5 summarizes key developments since the previous review [16] and highlights unresolved issues. Section 6 concludes.

2. Luminescence Methods

2.1. Photoluminescence Setup

Steady-state PL (SSPL) and time-resolved PL (TRPL) measurements, conducted over a wide range of temperatures and excitation intensities, are basic techniques for probing defect-related luminescence in GaN [16]. Figure 2 illustrates a schematic of a typical PL setup, employing a continuous-wave HeCd laser (λ = 325.03 nm) for SSPL and a pulsed nitrogen laser (λ = 337 nm) for TRPL. Detailed descriptions of the experimental configuration are provided elsewhere [25,66].

Since 2018, an improved approach to PL spectral presentation has been proposed to ensure consistency between experimentally measured spectra and theoretically calculated band shapes [25]. As before, as-measured spectra are corrected for the spectral response of the detection system. In addition, the PL intensity is now scaled by a factor of λ³, where λ is the emission wavelength, so that spectra are expressed in units proportional to the number of emitted photons as a function of photon energy ħω. These corrections are applied to PL spectra throughout this review (except for Figure 18a, Figure 26a, Figure 35, Figure 36, Figure 37a and Figure 39a). Note that positions and shapes of broad PL bands associated with the same defect may vary when measured on different setups unless proper corrections are applied, partly explaining discrepancies in the literature [66].

The internal quantum efficiency (IQE) of individual PL bands, η, can be estimated by integrating the corrected band intensity and comparing it with that of calibrated GaN standards, as described in previous works [34,52,53]. Challenges associated with measuring external quantum efficiency (EQE) of PL and accurately deriving η have recently been addressed in detail [67,68,69,70,71].

2.2. Phenomenological Models for Defect-Related PL in GaN

Phenomenological models, based on rate equations inspired by the Shockley-Read-Hall formalism [72,73], enable the extraction of key parameters from SSPL and TRPL data, thereby facilitating the identification of defect-related PL bands in semiconductors [65,74,75]. These models, refined specifically for defects in GaN [52,53,76,77], describe carrier recombination dynamics and defect properties, including electron- and hole-capture coefficients, ionization energies, and defect concentrations.

2.2.1. TRPL and Electron-Capture Coefficient

The radiative electron-capture coefficient C_n for a defect (Table 1) can be determined from the PL lifetime τ₀ when the PL arises from electron transitions from the conduction band to the defect level (e-A transitions). The relationship is given by [65,77]:

$$C_n={\displaystyle \frac{1}{n{\tau }_0}}$$

(1)

where n is the free electron concentration, typically obtained via Hall effect measurements. Once C_n is determined for a specific PL band, it can be used to estimate n in other GaN samples [65]. For not purely exponential PL decay, such as when e-A and donor-acceptor-pair (DAP) transitions overlap, the effective PL lifetime τ₀* can be extracted from the maximum of the t·I^PL(t) dependence [78].

2.2.2. Temperature Dependence of PL and Hole-Capture Coefficient

The nonradiative hole-capture coefficient C_p for a defect (Table 1) can be derived from the temperature dependence of PL intensity, I^PL, or PL lifetime, τ. Above a critical temperature T₀, both the I^PL and τ decrease exponentially with increasing temperature in an Arrhenius plot—a phenomenon known as PL quenching. For defects in n-type GaN, PL quenching arises from the thermal emission of holes from defect levels to the valence band via the Schön–Klasens mechanism [74]. For PL driven by e-A transitions, the I^PL(T) and τ(T) dependences are described with the following expression:

$${\displaystyle \frac{I^{PL}\left(T\right)}{I^{PL}\left(0\right)}}={\displaystyle \frac{\tau \left(T\right)}{{\tau }_0}}={\displaystyle \frac{1}{1+C\exp \left(\frac{-E_A}{kT}\right)}}$$

(2)

where C = (1 − η₀)τ₀ C_p N_v g⁻¹; η₀ = η and τ₀ = τ at T < T₀; N_v = 2(2πm_p*kT)^3/2h⁻³ is the effective density of states in the valence band; m_p* is the hole effective mass, k is Boltzmann’s constant; g is the defect level degeneracy; and E_A is the activation energy (defect ionization energy), equal to the energy difference between the defect level and the VBM plus any potential barrier to hole capture [52,53]. Note that the values of C_p in Table 1 are calculated under the assumption that m_p* = 0.8m₀ and g = 2. If these parameters differ, C_p must be scaled by a factor of 0.36g(m_p*)^−3/2. In DLTS measurements, C_p can be found with a similar approach. However, the common practice in DLTS analysis is to calculate the hole-capture cross-section, σ_p. The two quantities are related via C_p = <v_p>σ_p, where <v_p> = (3kT/m_p*)^1/2 is the mean thermal velocity of holes in the valence band.

In semi-insulating (SI) GaN, PL quenching often occurs via a tunable and abrupt quenching (TAQ) mechanism [52]. Although I^PL(T) can be formally fitted using Equation (2), the parameters C and E_A lack direct physical meaning in this case. The apparent E_A may significantly exceed the true ionization energy (abrupt quenching), and T₀ increases with excitation intensity P_exc (tunable quenching). For such samples, the defect ionization energy is instead obtained from

$$E_A=k{T}_0\ln \left({\displaystyle \frac{B^{\prime }}{P_{exc}}}\right),$$

(3)

where B′ depends on C_p and relative concentrations of defects involved in recombination [52]. The nonlinear rate equations governing carrier dynamics in SI semiconductors can lead to counterintuitive behavior, necessitating numerical simulations for accurate analysis [52,79]. The TAQ mechanism resembles a phase transition: at T < T₀, recombination (including PL) is dominated by defects with high hole-capture efficiency, whereas at T > T₀, defects with faster electron capture dominate in recombination.

2.2.3. Excitation Intensity Dependence

The defect concentration N can be found from the dependence of SSPL intensity on the excitation photon flux, P, modeled as:

$${\displaystyle \frac{I^{PL}(P)}{I_0^{PL}}}={\displaystyle \frac{\eta (P)}{{\eta }_0}}={\displaystyle \frac{P_0}{P}}\ln \left(1+{\displaystyle \frac{P}{P_0}}\right),$$

(4)

where P₀ = N(η₀ατ₀)⁻¹ [80,81]. Here, I₀^PL and η₀ denote the PL intensity and the absolute IQE, respectively, in the limit of low excitation intensity, and α is the absorption coefficient for incident photons (1.2 × 10⁵ cm⁻¹ at 325 nm for GaN [82]). For TRPL, Equation (4) applies with τ₀ replaced by the laser pulse duration t_L [77]. The accuracy of N is limited by uncertainties in η₀ [83]. However, relative defect concentrations for a given sample can be determined with higher precision, as the light-extraction efficiency—a primary source of η₀ uncertainty—is approximately the same for different PL bands in a given sample.

Once relative concentrations of radiative defects in a particular sample are known, the relative hole-capture coefficients for PL bands can be obtained because, according to Equation (2),

$${\displaystyle \frac{C_{pi}}{C_{pj}}}={\displaystyle \frac{I_i^{PL}}{I_j^{PL}}}{\displaystyle \frac{N_j}{N_i}}$$

(5)

where I_i^PL/I_j^PL is the ratio of integrated PL intensities for PL bands i and j at T < T₀, and N_i, N_j are the respective defect concentrations. If C_p is known for a reference defect (e.g., the C_N acceptor responsible for the YL1 band), Equation (5) enables the determination of C_p for other defects.

2.3. Configuration Coordinate Model for Defect-Related PL

Parameters associated with electron–phonon coupling can be extracted from PL band shapes modeled within a one-dimensional configuration coordinate framework. The spectral shapes of broad PL bands can be fitted using the expression [47]:

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

(6)

Here, S_e is the Huang–Rhys factor for the excited state of the defect, d_FC^g = E₀* − ħω_max is the Franck–Condon shift in the ground state, E₀* = E₀ + 0.5ħΩ_e, E₀ is the zero-phonon line (ZPL) energy, ħΩ_e is the effective phonon mode energy in the excited state, ħω is the photon energy, ħω_max is the PL band maximum, and Δ is a sample-dependent energy shift (<20 meV) arising from factors such as in-plane biaxial strain in GaN thin layers on sapphire substrates or local electric fields. Typical values of these parameters for broad PL bands are summarized in

Table 2. Vibrational parameters of broad PL bands (at low temperatures).

PL Band	ħωmax (eV)	E0* (eV)	Se	dFCg (eV)	W0 (eV)	ħΩe (eV)
RL1	1.73	2.3	9.5	0.57	0.42
RL2	1.74	2.3	12.5	0.56	0.35	0.033
RLMg	1.67	2.6	27	0.93	0.41
RLBe	1.78	2.65	20	0.87	0.44	0.042
RLCa	1.82	2.23	15	0.41	0.25	0.027
RL4	1.6–1.7	2.26	9	0.56–0.66	0.44
OL1	1.88	2.6	12	0.72	0.47
OL3	2.09	2.8	13	0.71	0.47
YL1	2.17	2.67	7.8	0.50	0.43	0.056
YL2	2.30	2.86	7.3	0.56	0.49
YL3	2.07	2.45	5.0	0.38	0.40	0.06
YLBe	2.15	3.2	24	1.05	0.52	0.038
GL1	2.35	2.97	10.3	0.62	0.48	0.041
GL2	2.33	2.70	13.5	0.24	0.24	0.023
GLHg	2.44	2.7	5	0.26	0.39	0.053
GLCa	2.49	3.02	8.5	0.53	0.43	0.041
BL1	2.86	3.10	3.2	0.36	0.36	0.043
BL2	3.00	3.38	4.6	0.38	0.42
BL3	2.81	3.08	2.0	0.27	0.45
BLCd	2.70	3.0	4.0	0.3	0.35	0.053
BLC	2.85	3.20	3.7	0.35	0.43
BLP	2.88				0.37	0.050
BLBe	2.6	3.4	12	0.8	0.57
BLMg	2.8	3.1	5.0	0.4	0.31

.

Note that, unless the ZPL is explicitly identified, parameters E₀* (or d_FC^g) and S_e remain ambiguous; namely, similar PL band shapes can be obtained by simultaneous increase (or decrease) of these parameters [34]. Nevertheless, three parameters from Table 2 (e.g., E₀*, ħω_max, and S_e) are sufficient to define bands’ positions and shapes, allowing distinctive defect-related PL bands in GaN to be recognized (provided appropriate corrections are applied to as-measured low-temperature PL spectra), and overlapped PL bands to be deconvoluted.

The effective phonon energy ħΩ_e can be extracted from the temperature dependence of the PL band’s full width at half maximum (FWHM), W(T). For a Gaussian-like PL band shape, the FWHM is modeled by [16,47]:

$$W\left(T\right)=W_0\sqrt{\coth \left({\displaystyle \frac{\hslash {\Omega }_e}{2kT}}\right)}$$

(7)

where W₀ is the FWHM at T = 0. Values of W₀ and ħΩ_e for selected broad PL bands are listed in Table 2.

2.4. Electron Transition Mechanisms

Analysis of PL provides insights into the nature of electronic transitions responsible for defect-related luminescence [66]. In n-type GaN, at low temperatures (T < 50 K), most PL bands originate from DAP recombination, involving shallow donors and various acceptors [84,85]. The high efficiency of the DAP transitions at low temperatures arises from the extended electron wavefunctions for shallow donors, which overlap substantially with acceptor states. These PL bands exhibit a blueshift of up to ~10 meV as excitation intensity P_exc increases from 10⁻⁵ to 0.3 Wcm⁻² [16,40,44,62], since emission from distant DAPs, contributing at lower photon energies due to weaker Coulomb interactions, saturates at lower P_exc. The PL decay following a laser pulse is nonexponential in this regime (often exhibiting the t^−m dependence with m ≈ 1), reflecting the distribution of DAP separations [85]. At elevated temperatures, transitions from the conduction band to the same acceptors (the e-A transitions) dominate, gradually replacing DAP recombination. In this regime, the PL decay becomes exponential, with a characteristic lifetime τ₀, which is inversely proportional to the concentration of free electrons, see Equation (1).

PL from deep donors in GaN is typically caused by internal transitions: from an excited state (located near the conduction band) of a positively charged donor to its ground state [66]. These transitions yield exponential PL decays even at very low temperatures, with τ₀ independent of n (Table 1).

DAP transitions involving deep donors are rarely observed in GaN. A notable exception is the BL_Mg band, which shifts from ~2.8 to 2.94 eV as P_exc increases from 10⁻⁶ to 0.3 Wcm⁻² [62]. This band is attributed to electron transitions from an unidentified deep donor to the shallow Mg_Ga acceptor, as discussed in Section 4.3.3. The strongly localized electron wavefunction for the deep donor requires small DAP separations for efficient recombination, thereby restricting the BL_Mg band to heavily Mg-doped GaN ([Mg] > 10¹⁸ cm⁻³) [62]. Note that large PL band shifts (up to 0.5 eV) with varying P_exc may also arise from potential fluctuations in SI GaN or due to local electric fields induced by structural defects or the surface [54]. For instance, the UVL_Mg band can exhibit a giant redshift and broadening with decreasing P_exc, potentially causing confusion with the BL_Mg band [54,62].

3. Luminescence Associated with Defects in Undoped GaN

Over the past two decades, there has been significant progress in explaining defect-related PL in undoped GaN and resolving longstanding controversies, most notably the origin of the yellow luminescence (YL) band. Several PL bands in nominally undoped GaN arise from unintentional impurities such as Mg_Ga, Zn_Ga, Ca_Ga, and C_N, which are responsible for the UVL, BL1, GL_Ca, and YL1 bands, respectively. Additionally, the GL2 and RL2 bands, observed in SI GaN, have been attributed to V_N and the V_N-acceptor complexes. Conversely, the RL1 and GL1 bands in GaN grown by hydride vapor phase epitaxy (HVPE) technique remain unidentified, though a better understanding has emerged. A novel defect, tentatively assigned to Fe and labeled RY3, has recently been recognized in undoped HVPE GaN. Importantly, V_Ga-related defects have been ruled out as sources of any observed PL bands in undoped GaN. The following sections classify defect-related PL bands in undoped GaN by color and provide concise analyses.

3.1. Yellow Luminescence in Undoped GaN (YL1, YL2, YL3)

3.1.1. Historical Overview

The YL band with a maximum at about 2.2 eV is the dominant defect-related PL feature observed in both undoped and doped GaN across various growth techniques, including HVPE, metal–organic chemical vapor deposition (MOCVD), and molecular beam epitaxy (MBE) [41]. Its microscopic origin, a subject of debate for nearly four decades, has now been conclusively identified. Early studies by Ogino and Aoki [86] provided compelling evidence linking the YL band to carbon impurities. In contrast, Pankove and Hutchby [87] observed the YL band in GaN implanted with 35 different ions, with negligible intensity in unimplanted controls, suggesting that implantation-induced native defects, such as V_Ga, were responsible for it. Supporting this view, early DFT calculations predicted that electron transitions from the conduction band to deep acceptor levels, namely the 3−/2−level of V_Ga and the 2−/− level of the V_GaO_N complex, calculated at ~1.1 eV above the VBM, caused the YL band [22]. PAS experiments further seemed to support this model by suggesting a correlation between YL intensity and V_Ga concentration [28]. During this period, multiple competing hypotheses were proposed regarding both the identity of the defect responsible for YL and the nature of the optical transition involved [16].

Nevertheless, accumulating experimental evidence pointed to carbon as the source of the YL band [88]. Although early DFT calculations misidentified C_N as a shallow acceptor with a predicted −/0 level at ~0.2 eV above the VBM [20,22], more accurate hybrid functional DFT calculations have since corrected this assignment. These modern calculations place the C_N −/0 transition level at 0.9 eV above the VBM, confirming that C_N acts as a deep acceptor and is the primary candidate for the YL band [24].

At one point, a widely accepted view prevailed that several distinct defects could produce YL bands with similar shapes and positions [29,89,90,91,92]. In particular, Armitage et al. [89] suggested that the YL band in undoped GaN originates from V_Ga-related defects, while a nearly indistinguishable YL band in C-doped GaN is caused by C-related defects. However, current experimental evidence definitely attributes the YL band at ~2.2 eV in undoped GaN—referred to as YL1—to the isolated C_N acceptor. The prominence of YL1 is especially notable in GaN grown by MOCVD, where residual carbon contamination is unavoidable. Nonetheless, the YL1 band may also be observed in HVPE- and MBE-grown GaN, even when carbon levels fall below the SIMS detection limit of ~10¹⁶ cm⁻³. The prominence of the YL band stems from the high hole-capture efficiency of C_N acceptors, which outcompete nonradiative or weakly radiative defects introduced by contamination, doping, or ion implantation.

Additional yellow luminescence bands include the YL_Be band, induced by intentional doping or implantation with Be (Section 4.2.2), and the YL2 band, observed in bulk GaN crystals grown by ammonothermal (AT) method (Section 3.1.3). The YL3 band, exclusive to Fe-contaminated HVPE GaN, is discussed in Section 3.1.4. The V_Ga and V_GaO_N defects are not associated with any observed PL bands in GaN (Section 3.1.5).

3.1.2. C_N-Related YL1 Band

The YL1 band, attributed to the C_N acceptor, exhibits distinctive spectral features [41]. At low temperatures (T < 40 K), it has a maximum at 2.17 ± 0.05 eV, with a slightly asymmetric shape, and a FWHM of about 0.43 eV when well resolved (Figure 3a). In high-quality samples with minimal spectral overlap from other PL bands, a sharp ZPL can be resolved at 2.57 eV. At these low temperatures, the YL1 band arises from DAP recombination, specifically electron transitions from shallow donors to the −/0 level of C_N, located at 0.916 ± 0.003 eV above the VBM [40].

At higher temperatures (T > 50 K), electrons are thermally excited from shallow donors to the conduction band, and e-A transitions contribute to the YL1 band. The C_N defect also exhibits a 0/+ transition level at 0.33 eV above the VBM, which is responsible for the BL_C band (Section 4.1.1).

The YL1 band can be excited with photons below the bandgap, down to ~2.7 eV. Early PL excitation (PLE) studies modeled the PLE band of YL1 with a Gaussian shape, estimating a characteristic photoabsorption energy ħω_abs between 3.19 and 3.32 eV [86,93]. However, for transitions from a defect to the conduction band, the excitation band is asymmetric due to the continuum of conduction band states [94], yielding a corrected value of ħω_abs = 3.00 ± 0.05 eV [66].

From combined PL and PLE analyses, Ogino and Aoki predicted the ZPL of the YL1 band at 2.64 ± 0.05 eV [86]. More recent studies have directly observed the ZPL at 2.57 eV (at T < 40 K) [40]. The ZPL blue-shifts with increasing excitation intensity, consistent with the DAP recombination mechanism. At higher temperatures, an e-A-related ZPL emerges at 2.59 eV. In some undoped GaN samples (presumably with a low concentration of shallow donors), the e-A-related ZPL dominates already at T = 18 K [41]. Subtracting a smooth shape of the YL1 band reveals phonon replicas, including the longitudinal optical (LO) phonon mode at 91.5 ± 0.5 meV and a pseudo-local phonon mode at 39.5 ± 0.5 meV (Figure 4).

In TRPL experiments, the YL1 band in nondegenerate n-type GaN samples exhibits nonexponential decay at T < 50 K, consistent with DAP recombination dynamics, gradually transitioning to exponential decay at higher temperatures due to the increasing contribution of e-A recombination [78]. In degenerate n-type GaN samples, e-A transitions dominate at all temperatures. The effective PL lifetime τ₀, is inversely proportional to the free electron concentration n (Figure 5), yielding an electron-capture coefficient C_n = (1.1 ± 0.2) × 10⁻¹³ cm³s⁻¹ for the YL1 band [41,65]. Knowing this parameter, the concentration of free electrons can be found in GaN samples from TRPL measurements [65].

Thermal quenching of the YL1 band occurs well above room temperature. In conductive n-type GaN, its temperature dependence follows Equation (2) with E_A ≈ 0.9 eV. The critical temperature T₀, at which the PL quenching begins, is T₀ = E_A(klnC)⁻¹. From the PL quenching, the temperature-independent hole-capture coefficient C_p is determined as (3.5 ± 1.5) × 10⁻⁷ cm³s⁻¹ (assuming g = 2 and m_p = 0.8 m₀). The YL1 band broadens with increasing temperature in agreement with Equation (7), and analysis of the temperature dependence of the band width W(T) yields an effective phonon energy ħΩ_e = 56 ± 2 meV [41]. In SI GaN samples, the YL1 quenching follows the TAQ mechanism [52]. The T₀ shifts with excitation intensity, and E_A ≈ 0.9 eV can be found from Equation (3) [95].

Similar to PL from other acceptors in GaN, the YL1 band exhibits excitation intensity-dependent shifts. In conductive n-type GaN samples, the YL1 band blueshifts by up to 10 meV with increasing P_exc over several orders of magnitude at low temperatures, consistent with the DAP recombination model. In SI or heavily Si-doped GaN samples, the YL1 band may blue-shift by as much as 0.1 eV with increasing P_exc due to screening of potential fluctuations by photogenerated charge carriers [54]. A redshift in the YL1 band with a time delay after a laser pulse is also observed in TRPL measurements. The YL1 band saturates with increasing P_exc in agreement with Equation (4), enabling estimation of C_N defect concentrations [41,80].

Hybrid functional DFT calculations accurately reproduce key properties of the C_N-related YL1 band [24,96,97,98,99]. Theoretical predictions include a ZPL energy E₀ = 2.48–2.71 eV, a band maximum ħω_max = 2.01–2.18 eV, the −/0 level at E_A = 0.78–1.1 eV, and characteristic resonant excitation energy ħω_abs = 2.91–3.04 eV, in close agreement with experimental values (E₀ = 2.59 eV, ħω_max = 2.19 eV for e-A transitions, E_A = 0.916 eV, and ħω_abs = 3.0 eV [40,41]). Calculations predict a classical barrier for hole capture by C_N (ΔE_b = 0.49–0.73 eV with the calculated −/0 level at 1.02 eV [100,101]), which is expected to cause a pronounced temperature dependence of C_p. However, experimentally, the YL1 intensity (which is proportional to C_p) remains nearly constant from very low temperatures up to T₀, suggesting a negligible capture barrier (Figure 3b). Other parameters of the configuration coordinate model extracted from experimental data are also close to theoretical predictions. In particular, the experimental Huang–Rhys factor S_e = 8 ± 1 [41] agrees with the calculated S_e = 10.3 [102].

Attempts to assign defects by formally matching theoretical predictions and experimental data are common [96,103], and they often lead to errors [104]. A recent example includes the incorrect attribution of the YL1 band to the C_NO_N complex [105]. First-principles calculations in that study predicted PL band maxima for the C_N and C_NO_N defects at 1.88 eV and 2.25 eV, respectively. The YL1 band with a maximum at ~2.2 eV was accordingly attributed to the C_NO_N complex [105]. This attribution gained some theoretical support [106], but was subsequently challenged [98,103,107]. According to current advanced calculations, the concentration of isolated C_N defects should be orders of magnitude higher than that of the C_NSi_Ga and C_NO_N complexes, and PL bands from these complexes are predicted at higher photon energies (at 2.23–2.71 eV) [98,103,106]. Finally, experimental evidence consistently supports C_N as the sole contributor to the YL1 band, with no signatures of C_NO_N or C_NSi_Ga in PL spectra [25,41], likely due to their low concentrations and/or low hole-capture efficiencies (Section 4.1.4).

3.1.3. YL2 Band in Ammonothermal GaN

Unlike GaN layers deposited on sapphire substrates by MOCVD, MBE, or HVPE techniques, bulk GaN crystals grown by the AT method contain high concentrations of V_Ga or V_Ga-related complexes [108,109,110,111]. These samples are typically degenerate n-type (n = 10¹⁸–10¹⁹ cm⁻³), contain high concentrations of O and H (10¹⁸–10¹⁹ cm⁻³), as well as significant levels of Si, C, Mg, and Zn (~10¹⁷ cm⁻³) [111]. Their PL spectra contain Mg-related UVL, Zn-related BL1, and a new yellow band at ~2.3 eV, designated YL2 (Figure 6).

The YL2 band, distinct from the C_N-related YL1 (Figure 6a), shifts from 2.28 to 2.34 eV as the excitation intensity in SSPL increases from 10⁻⁴ to ~100 Wcm⁻², and exhibits a red shift of ∼0.1 eV over time delays in TRPL measurements. These shifts may indicate possible contributions from multiple defects [42]. The position of the YL2 maximum and the defect ionization energy, estimated as ~0.7 eV from the band shape, agree with predictions from first-principles calculations for deep donors such as V_Ga3H_i and V_GaO_N2H_i [39,42]. Acceptor complexes (e.g., V_Ga2H_i and V_GaO_NH_i) are predicted to have −/0 levels at 1.4–1.6 eV above the VBM [29,39] and, thus, are not expected to contribute to visible PL. FTIR absorption measurements on degenerate n-type AT GaN samples revealed high concentrations (more than 10¹⁸ cm⁻³) of complexes containing V_Ga and up to three H atoms, in agreement with the estimates from PAS [108,110].

3.1.4. YL3 Band in HVPE GaN

The YL3 band, peaking at 2.07 eV, with a ZPL at 2.36 eV at T ≈ 18 K, is observed in undoped HVPE GaN. It is associated with the RY3 defect, which also gives rise to the RL3 band (Section 3.2.3) [34,38,44]. The RY3 defect is an acceptor, with two deep states (A₁ at 0.5–1.0 eV below the CBM, and A₂ at 1.13 eV above the VBM) and a shallow state (A₃ at ∼ 0.2 eV above the VBM) [38]. Photogenerated holes are quickly captured by the excited state A₃. The RL3 component of the broad RY3 band arises from radiative transitions of the bound hole from A₃ to A₁ with a characteristic time of about 10 ns. Transitions of the bound hole from A₃ to A₂ are nonradiative, over a 0.06–0.07 eV barrier. The YL3 component of the RY3 band arises from DAP transitions (shallow donors to A₂) at T < 40 K or e-A transitions to A₂ at T > 50 K with τ₀ ≈ 100 μs [38,44]. The very different lifetimes of RL3 and YL3 allow us to resolve the YL3 component (Figure 7). The fine structure of the YL3 band includes the DAP-related ZPL at 2.36 eV and the e-A-related ZPL at 2.38 eV, both followed by phonon replicas from three sets of phonons: the LO mode with ħΩ = 91 meV and two pseudo-local modes (19 and 36 meV) [43,44].

The RY3 defect is tentatively associated with Fe_Ga or Fe_Ga-containing complexes, as the RY3 band correlates with the Fe_Ga-related 1.31 eV PL line. Interestingly, the RY3 band is absent in Fe-doped SI GaN, where the Fermi level is expected to lie near the −/0 level of Fe_Ga, ~0.6 eV below the conduction band minimum (CBM) [112,113,114]. The absence of RY3 in SI GaN is presumed to arise from competition for photogenerated electrons. In such samples, electrons are preferentially captured by nonradiative donors, suppressing radiative recombination. In contrast, in conductive n-type GaN, PL intensity is governed by the capture of photogenerated holes, and the hole capture by the excited state A₃ is very efficient.

3.1.5. Exclusion of V_Ga and V_GaO_N as Sources of the YL Band

The V_Ga and V_GaO_N defects, both deep, multi-charged acceptors, are unlikely contributors to the YL band in n-type GaN, where the Fermi level lies near the CBM. Under such conditions, only the 3−/2− level for V_Ga and the 2−/− level for V_GaO_N are expected to be active. While early DFT calculations placed these levels near 1 eV above the VBM [22,115], more accurate hybrid functional DFT calculations have since revised their positions to significantly higher energies: 1.75–3.13 eV above the VBM for V_Ga [29,30,31,32,116,117] and 1.55–2.17 eV above the VBM for V_GaO_N [29,39]. Electron transitions from the CBM to these levels are most likely nonradiative [30,39], precluding PL contributions above 1.5 eV.

Lyons et al. [29] suggested that hole capture at the V_Ga 3−/2− level is radiative and can cause a PL band similar to the YL band. However, such radiative capture would be much slower than competing nonradiative hole capture by more efficient acceptors, such as C_N. As a result, any emission from this mechanism would be masked by stronger PL bands. Similarly, transitions via the 2−/− level of the V_GaO_N complex are nonradiative or weakly radiative with a PL signal in the infrared region [39]. Alkauskas et al. [118] proposed that hole capture by this level in n-type GaN occurs nonradiatively, via an excited state located at 1.15 eV above the VBM. Note that nonradiative capture coefficients depend strongly (approximately exponentially) on the energy of the transition [119].

Wang et al. [117] proposed that the yellow band originates from electron transitions from the CBM to the 0/+ levels of V_Ga or V_GaO_N. However, this mechanism is not viable in n-type GaN, where these defects reside in their fully negative charge states (3− for V_Ga and 2− for V_GaO_N). To date, no reliable experimental evidence supports predictions of PL from either V_Ga or V_GaO_N. In high-quality HVPE-grown GaN samples, where PL bands are reliably recognized, no PL features could be attributed to V_Ga, while the concentration of V_Ga (from PAS measurements) varied between 10¹⁶ and 10¹⁸ cm⁻³ [66].

Historical observations of the YL band in undoped GaN produced by various growth methods can be attributed to trace contamination with carbon [5,35,41]. In particular, Saarinen et al. [28] reported a correlation between the YL band intensity and the concentration of the V_Ga-related defects in GaN. However, the PL in that work was collected from a region near the GaN/sapphire interface, where the concentration of defects is very high. Subsequent studies [92,120,121] have failed to reproduce this correlation and, in some cases, have reported an anticorrelation between the YL intensity and the V_Ga concentration, further weakening the case for the V_Ga-related YL.

3.2. Red Luminescence Bands in Undoped GaN (RL1, RL2, RL3, RL4)

Red luminescence (RL) bands are frequently observed in undoped GaN, particularly in samples grown by HVPE. Four distinct RL bands—designated RL1 through RL4—have been recognized, each characterized by unique spectral features and recombination dynamics. The RL1 and RL3 bands are prominent in HVPE GaN, distinguished mainly in TRPL experiments due to their contrasting decay behaviors. The RL1 band exhibits nonexponential decay at T < 50 K, and exponential slow decay (with lifetimes in the millisecond range) at higher temperatures. The RL3 decays exponentially with τ₀ ≈ 10 ns. The RL2 appears at low temperatures in SI GaN grown by various techniques. It exhibits an exponential decay with τ₀ > 1 μs at T < 100 K. The RL4 band emerges in AT GaN only after thermal annealing. Below, each RL band is discussed in more detail.

3.2.1. RL1 Band in HVPE GaN

The RL1 band, peaking at ~1.75 eV, is the dominant defect-related PL feature in undoped GaN grown by HVPE, particularly at low P_exc, when contributions from YL1 (Section 3.1.2) and GL1 (Section 3.3.1) are minimal (Figure 8a). Its behavior is consistent with a deep acceptor, with an ionization energy E_A ≈ 1.0–1.2 eV. In conductive n-type GaN, the RL1 band is highly efficient at low P_exc, with SSPL intensity nearly constant up to 500 K. At low temperatures (T < 50 K), non-exponential decay is consistent with DAP recombination involving shallow donors. Above 50 K, e-A transitions dominate, yielding a long effective lifetime (in the millisecond range), inversely proportional to the free electron concentration. Due to its long lifetime, the RL1 band saturates at relatively low P_exc.

Thermal quenching of RL1 begins at T > 500 K (Figure 8b), consistent with E_A = 1.0–1.2 eV. TRPL analysis yields C_n ≈ 4.5 × 10⁻¹⁴ cm³s⁻¹ from Equation (1) [65]. The hole-capture coefficient, C_p ≈ 3 × 10⁻⁷ cm³s⁻¹, is derived from comparisons of PL intensities and defect concentrations using Equations (4) and (5) [75,83]. These coefficients align with those of other acceptors in GaN (Figure 9). ODMR studies of HVPE-grown freestanding GaN templates revealed an isotropic g = 2.019 factor for the RL1-related defect [122]. The RL1 origin remains uncertain, but it is tentatively linked to Cl or Cl-containing defects, as it is exclusive to Cl-contaminated HVPE GaN and absent in MBE- or MOCVD-grown GaN [66].

3.2.2. V_N-Related RL2 Band

The RL2 band, peaking at ~1.74 eV, is observed alongside the GL2 band (Section 3.3.2) in SI GaN samples, particularly those grown under extremely Ga-rich conditions (Figure 10a) or after surface mechanical polishing [37,123]. The RL2 emission is characterized by exponential decay, even at very low temperatures (T < 20 K), suggesting that it originates from an internal transition within a deep donor, from an excited state to the ground state. Figure 10a shows the RL2 band, with a small contribution of GL2 at ~2.33 eV. A substantial body of evidence, accumulated since 2005, supports the assignment of the GL2 band to isolated V_N defects (Section 3.3.2). The RL2 band is attributed to a family of red-emitting centers associated with AV_N complexes, where A is a group-II metal substituting for Ga.

In undoped GaN grown by MBE under Ga-rich conditions [16], the RL2 lifetime decreases from 1050 to 3 μs as the temperature rises from 17 to 100 K (Figure 10b) [37]. While the SSPL intensity remains constant below 100 K, it quenches at higher temperatures with an activation energy of 0.1–0.15 eV (Figure 10b). The quenching was initially explained by the Seitz–Mott mechanism, involving a 0.12 eV barrier in the configuration coordinate diagram [16]. However, more recent interpretations favor the Schön–Klasens mechanism, in which quenching is attributed to the thermal emission of electrons from the excited state to the conduction band. This behavior is typical when competition for electrons limits the PL efficiency [36,37]. Although there is a good understanding of the RL2-type bands caused by the AV_N complexes with A = Be_Ga, Mg_Ga, and Ca_Ga (Section 4.2.4, Section 4.3.5, and Section 4.6.3), the specific acceptors involved in the AV_N complexes responsible for the RL2 band in MBE-grown undoped GaN [124,125] remain unidentified. A distinguishing feature of the RL2 band in these samples is the temperature-dependent lifetime behavior, which reveals an activation energy of ~10 meV between 17 and 100 K (Figure 10b). A phenomenological model has been proposed in which two excited states are located near the CBM, while the ground state lies ∼1 eV above the VBM [37]. The observed τ(T) dependence at T < 100 K is attributed to thermal activation of a radiative excited state that lies about 10 meV above a nonradiative (or weakly radiative) excited state.

3.2.3. RL3 Band in HVPE GaN

The RL3 band, peaking at 1.77 eV, is observed in HVPE-grown GaN and, together with the YL3 band, forms the RY3 band (Figure 11). The RL3 component of RY3 exhibits fast, exponential decay with a characteristic lifetime τ₀ ≈ 10 ns at T = 2–200 K [38,126,127], in stark contrast to the YL3 component, which displays much slower decay (τ₀ ≈ 100 μs). The consistent intensity ratio between RL3 and YL3 across a wide range of HVPE samples strongly supports their origin from the same defect, referred to as RY3. The RL3 is distinguished by a less steep high-energy spectral side. Early reports misassigned the ZPL at 2.36 eV and associated phonon structure to RL3 [43], but this was later corrected: these features belong to the YL3 band [38] (Section 3.1.4).

In early works, the RL3 band was attributed to DAP transitions involving C and O impurities that were abundant in HVPE GaN samples (~10¹⁹ cm⁻³ each) [128,129]. However, the fast and purely exponential decay kinetics of the RL3 emission rule out DAP recombination, indicating an internal transition. Moreover, the RL3 band is strong even in samples with very low concentrations of C and O [38], sometimes below the SIMS detection limit of 5 × 10¹⁵ cm⁻³ [127], further invalidating the above attribution. The RY3 defect is tentatively assigned to Fe-related defects, yet the assignment of the RL3 and YL3 bands specifically to isolated Fe_Ga acceptors seems ambiguous, as will be discussed later.

A detailed model of the RY3 defect [38] proposes three acceptor levels (Figure 12): a ground state A₁ at 0.7 ± 0.3 eV below the CBM, another deep state A₂ at 1.13 eV above the VBM, and a shallow excited state A₃ at ~0.2 eV above the VBM. In this model, holes captured at A₃ can follow two competing paths: radiative recombination with electrons at A₁, producing the RL3 (τ₀ ≈ 10 ns), or nonradiative relaxation to A₂ over a 0.06 eV barrier, followed by DAP or e-A recombination, resulting in the YL3. This model successfully explains the observed temperature- and excitation-dependent interplay between RL3 and YL3 components [38]. Notably, Uehara et al. [127] demonstrated that the RL3 band can be excited below the bandgap by photons with energy of 3.42 eV (but not by 3.06 eV).

The RY3 defect resembles the Cu_Zn acceptor in ZnO, which produces the green luminescence (GL_Cu) band, peaking at 2.45 eV, with a ZPL at 2.859 eV [130,131,132,133]. The GL_Cu band originates from internal transitions of holes between an excited state (0.4 eV above the VBM) and the ground state (~0.2 eV below the CBM). Like RL3, the GL_Cu band exhibits exponential decay at cryogenic temperatures (even at 1.6 K), with a PL lifetime of 440 ns [130]. In conductive n-type ZnO, where the Fermi level lies above the ground −/0 level of the Cu_Zn, the GL_Cu band is observed after photogenerated holes are captured by the excited state. However, resonant excitation of the GL_Cu band below the bandgap is possible only in high-resistivity ZnO, where the Fermi level is below the −/0 level of the Cu_Zn [132,133,134]. In contrast, the RL3 band in GaN can be excited below the bandgap (at 3.42 eV) in moderately conductive (n ≈ 10¹⁶–10¹⁷ cm⁻³) HVPE GaN samples [127].

By analogy, the RY3 center in GaN is likely associated with a transition metal impurity. Indeed, Fe concentration appears to correlate with the RY3 band intensity. In particular, the concentration of Fe in a sample with a strong RY3 band was elevated (2.5 × 10¹⁵ cm⁻³), matching the concentration of the RY3 defect estimated from PL measurements [38]. A rough correlation between the intensities of the RL3 band and the Fe-related 1.31 eV line was also noted in a set of HVPE-grown undoped GaN samples. Furthermore, the ground level of the RY3 center (0.7 ± 0.3 eV below the CBM) is close to the reported position of the ground level of Fe_Ga acceptors (at ~0.63 eV [135]). The RY3 band is not observed in Fe-doped SI GaN samples, and this can be explained by conditions where the PL efficiency is dictated by the fast capture of electrons, not holes. However, in some works, the RY3 was not observed in the low-temperature PL spectra, whereas samples were n-type and contained substantial concentrations of Fe [136,137]. This may indicate that the RY3 is a complex defect, not just an isolated Fe_Ga.

3.2.4. RL4 Band in Ammonothermal GaN

The RL4 band, peaking at 1.6–1.7 eV, emerges in PL spectra from AT GaN after thermal annealing (Figure 13a), and its IQE approaches unity at T_ann ≈ 1000 °C [39]. As-grown AT GaN samples contain high concentrations of V_Ga, O, H, and related complexes, as confirmed by FTIR studies [110,111,138,139]. First-principles calculations suggest that complexes such as V_Ga3H_i and V_GaO_N2H_i contribute to yellow PL, whereas V_Ga2O_NH_i and V_Ga3O_N can produce red PL (Figure 13b) [29,39]. The RL4 band has been tentatively attributed to the V_Ga3O_N complex, which may form via the annealing-induced dissociation of nonradiative V_Ga3O_NH_i complexes [39]. The emission energy of the RL4 band is sample-dependent. It has a maximum at 1.7 eV in n⁺-GaN samples with high V_Ga, O, and H concentrations and at 1.6 eV in n-GaN samples with lower concentrations, suggesting possible compositional variations [39]. Spectral deconvolution also reveals a distinct orange PL band (OL3) with a maximum at 2.09 eV in annealed AT GaN samples (Figure 13a) [39].

All candidate defects proposed to contribute to the V_Ga-related PL in as-grown and annealed AT GaN (shown with arrows in Figure 13b) are deep donors. However, the observed high intensities and nonexponential decays of the YL2, OL3, and RL4 bands distinguish them from typical deep-donor-related PL bands in GaN, which are weak in conductive n-type GaN and exhibit exponential decays due to internal transitions (Table 1). The nonexponential decay may indicate that the related defects are, in fact, acceptors. Alternatively, potential fluctuations due to the nonuniform distribution of charged defects or overlapping PL bands may be the reason for the nonexponential decays. High PL efficiency (close to unity for the RL4 band) is another puzzle. Known deep donors in GaN generally have low hole-capture coefficients and produce inefficient PL in conductive n-type samples. However, to explain the exceptionally high IQE of the RL4 band in degenerate n-type AT GaN, the hole-capture coefficient for the related defect was estimated as ~10⁻⁶ cm³s⁻¹ (if its concentration is close to 10²⁰ cm⁻³) or even larger (if the concentration is lower) [39]. Note that the defect assignments in [39] were based on hybrid functional DFT predictions, which may lack precision, necessitating further experimental validation.

3.3. Green Luminescence Bands (GL1, GL2, GL_Ca)

Several distinct green luminescence (GL) bands are observed in undoped GaN, each characterized by unique spectral and temporal properties. The GL1 band, peaking at 2.35 eV, is prominent in HVPE-grown GaN. A spectrally similar but narrower GL2 band, also near 2.35 eV, appears exclusively in SI GaN grown by various techniques. These bands are readily differentiated by their distinct shapes and behaviors in SSPL and TRPL experiments. Additionally, a Ca-related GL_Ca band appears in MBE-grown GaN contaminated with Ca. Each band is discussed in detail below.

3.3.1. Unidentified GL1 Band in HVPE GaN

The GL1 band, peaking at 2.35 eV, is a prominent defect-related PL feature in undoped HVPE GaN (named GL band in [16]). Its intensity scales super-linearly (nearly quadratically) with excitation intensity, suggesting a secondary PL process requiring sequential capture of two holes by a deep defect [140]. TRPL reveals exponential decay kinetics, consistent with internal transitions. Figure 14 shows PL spectra from an HVPE GaN sample at T = 100 K. At low excitation intensity (P_exc = 2 × 10⁻⁶ Wcm⁻²), the RL1 band dominates, with a weak YL1 band at higher photon energy, while the GL1 band is not resolved. As P_exc increases, RL1 and YL1 saturate due to their long lifetimes, while GL1 intensity rises super-linearly (PL intensities are divided by P_exc in Figure 14a). The NBE luminescence (at 3.47 eV, with LO phonon replicas) also shows super-linear increase, typical of SI GaN. TRPL spectra resolve these PL bands at different time delays (Figure 14b). Analysis of the GL1 band shape and temperature-dependent intensity yields the following parameters: E_A ≈ 0.50 eV, C_p = (3.7 ± 1.3) × 10⁻⁸ cm³s⁻¹, and S_e ≈ 10 [66,83].

A unique feature of the GL1 band is a significant increase in its lifetime (by 20–50 times) with increasing temperature from 100 to 300 K [141,142,143,144]. A model proposed in [144] explains this behavior (Figure 15a): following above-bandgap excitation, the defect captures two holes and becomes positively charged. The capture of a free electron into an excited state near the CBM (level 1) occurs via the nonradiative Lax mechanism [145] (characteristic time τ₁), followed by a radiative internal transition to level 2 (with the characteristic time τ₂ ≈ 1 μs), producing the GL1 band. The PL intensity decays with time t after a laser pulse as [144]:

$$I^{PL}\left(t\right)=I_{\max }^{PL}\left[\exp \left({\displaystyle \frac{-t}{{\tau }_1}}\right)-\exp \left({\displaystyle \frac{-t}{{\tau }_2}}\right)\right]$$

(8)

At low temperatures, the cascade capture of free electrons by the excited state 1 is very fast (τ₁ << τ₂), and Equation (8) reduces to I^PL(t) ≈ I^PL_max exp(−t/τ₂). As temperature rises, τ₁ increases as T³ (typical of “giant traps” [145]), while τ₂ remains nearly constant, leading to τ₁ >> τ₂ and I^PL(t) ≈ I^PL_max exp(−t/τ₁) at high temperatures. Overall, at any temperature, the decay of PL is nearly exponential, where τ is determined by the slower process (Figure 15b).

Identifying the defect responsible for GL1 is critical, as it is prominent in high-quality freestanding GaN grown by HVPE, which has low dislocation and point defect densities. ODMR studies of HVPE-grown GaN freestanding templates revealed g factors g_‖ =1.975 and g_⊥ = 1.969 for the defect responsible for GL1 [122]. Early studies attributed YL and GL1 bands, respectively, to the 2−/− and −/0 levels of the V_GaO_N complex [16,140,141]. However, hybrid functional DFT calculations later ruled out V_GaO_N as a visible PL source and instead proposed the C_N and C_NO_N defects as responsible for the YL bands [24,98,103,105]. The YL band at 2.1 eV (now called YL3) and the GL1 band were tentatively linked to two charge states of the C_N defect, while the YL band at 2.2 eV (now called YL1) was thought to be caused by the C_NO_N [142,143]. These assignments have since been disproven. Current understanding identifies the −/0 and 0/+ levels of the C_N as responsible for the YL1 (Section 3.1.2) and BL_C (Section 4.1.1) bands, respectively, while the C_NO_N donor does not contribute observable PL (Section 4.1.4). Lack of correlation between GL1 and either YL1 or YL3 further supports the conclusion that they originate from distinct centers.

The GL1 and RL1 arise from unidentified point defects with estimated concentrations of 10¹⁵–10¹⁶ cm⁻³ in high-quality HVPE GaN [142,146]. Defects containing V_Ga or V_N are unlikely to be responsible [66] (Section 3.6). While Cl, with typical concentrations of ~10¹⁶ cm⁻³ in HVPE-grown GaN, appears to correlate with RL1 intensity in some samples, this may be coincidental [38,142]. The super-linear excitation behavior of GL1 suggests it is a secondary PL process, becoming prominent only after a primary PL band (denoted X) saturates. The X and GL1 may be caused by transitions via the −/0 and 0/+ levels of a deep defect. In n-type GaN, where PL efficiency is governed by hole capture, the IQE of X at low P_exc should exceed that of GL1 at high P_exc, similar to the behavior observed for the C_N defect [25]. While RL1 is a candidate for the X, no consistent correlation has been observed between RL1 and GL1, leaving the identities of both bands unresolved.

3.3.2. V_N-Related GL2 Band

The GL2 band, peaking at ~2.33 eV, with a FWHM of 0.23–0.25 eV (Figure 16), is attributed to internal transitions from an excited state to the +/2+ level of the isolated V_N [47]. This band is usually observed in high-resistivity or SI GaN, particularly in samples grown under Ga-rich conditions or doped/implanted with acceptor impurities such as Mg or Be [16,47,147,148,149,150,151]. A distinguishing feature of the GL2 band is its exponential decay after pulsed excitation, with a lifetime of ~300 μs at T < 100 K. Its relatively narrow FWHM is consistent with the configuration-coordinate model (Figure 17a), and the spectral shape can be quantitatively described with Equation (6) [35,37,47,152].

The GL2 intensity is temperature-independent below 100 K, decreasing exponentially between 100 and ∼200 K with an activation energy E₁ ≈ 0.15 eV. Unlike the RL2 band (Section 3.2.2), both the I^PL(T) and τ(T) show identical temperature behavior (Figure 17b). This quenching is attributed to thermal electron emission from the excited state to the conduction band, with E₁ representing the depth of the excited state below the CBM.

At temperatures above ~180 K, the quenching accelerates and follows distinct mechanisms depending on the sample conductivity: the TAQ mechanism in SI GaN:Mg and the Schön–Klasens mechanism in conductive p-type GaN:Mg [47]. This high-temperature quenching is attributed to the thermal emission of holes from the +/2+ level to the valence band. The +/2+ level is located at E₂ = 0.40–0.43 eV above the VBM as determined from Equation (3) for SI GaN:Mg or Equation (2) for p-type GaN:Mg [47]. In principle, transitions from an excited state to the 2+/3+ level may also cause a similar PL band in p-type GaN:Mg, since the calculated +/2+ and 2+/3+ levels are very close [47]. However, no clear experimental evidence exists to support the existence of two distinct GL2 bands associated with two charge transition levels in GaN. Thus, the question of whether the experimentally observed GL2 band arises from transitions via the +/2+ or 2+/3+ level remains unresolved.

3.3.3. Aquamarine Band in MBE GaN

A PL band, peaking at ∼2.5 eV, was observed in GaN layers grown by MBE on freestanding HVPE GaN substrates [153]. Initially termed the aquamarine luminescence (AL) band due to its color [153,154], it has been eventually identified as the Ca_Ga-related GL_Ga band [49]. Low-temperature MBE growth of GaN and InGaN often introduces Ca contamination [155,156,157]. A more detailed analysis of the GL_Ca band is provided in Section 4.6.

3.4. Blue Luminescence Bands in Undoped GaN (BL1, BL2, BL3)

Two broad blue luminescence (BL) bands are commonly observed in undoped GaN: the BL1 band, peaking at 2.9 eV, and the BL2 band at 3.0 eV. The third band, BL3, emerges at high excitation intensities in HVPE GaN and is associated with the RY3 defect. All three bands exhibit ZPL and phonon-related fine structure in high-quality GaN samples. These spectral features allow for detailed analysis of their vibrational properties.

3.4.1. Zn_Ga-Related BL1 Band

The BL1 band, peaking at 2.9 eV, is observed in undoped GaN grown by MOCVD, HVPE, or AT techniques due to Zn contamination. The assignment of BL1 to Zn_Ga acceptors is well established and supported by both experimental and theoretical studies [51,52,57]. The BL1 band exhibits a ZPL at 3.10 eV and distinctive phonon-related fine structure (Figure 18a). At low temperatures (T < 50 K), BL1 results from DAP recombination involving shallow donors and the Zn_Ga acceptors. A slight blueshift (up to 7 meV) with increasing excitation intensity (inset to Figure 18a) reflects saturation of distant pairs contributing at lower energies, a hallmark of DAP recombination. This shift is constrained by the shallow donor’s ionization energy [84,158].

The fine structure of the BL1 band, observable at low temperatures, consists of two sets of sharp peaks (Figure 18a). Peaks separated by 36 meV are attributed to a pseudo-local phonon mode, while those at 91.5 meV correspond to the LO phonon mode of the GaN lattice [50]. Vibrational parameters for BL1 and other PL bands in GaN are summarized in

Table 3. Pseudo-local and bulk crystal (LO) phonon modes for PL bands in GaN.

PL Band	Attribution	E0 (eV)	ħωmax (eV)	ħΩLO (meV)	ħΩ1 (meV)	ħΩ2 (meV)	ħΩ3 (meV)	Reference
YL1	CN (−/0)	2.57	2.17	91.5	−	39.5	−	[40]
YL3	Fe? (−/0)	2.38	2.07	91	19	36	−	[43,44]
BL1	ZnGa (−/0)	3.10	2.86	91	−	36	−	[50]
BL2	CNHi (0/+)	3.33	3.0	91.2	−	35.4	61	[55]
BL3	Fe? (0/+)	3.01	2.81	91.3	−	39.6	68.2	[56]
BLC	CN (0/+)	3.15	2.85	91.2	−	34.3	−	[60]
BLCd	CdGa (−/0)	2.95	2.70	91	−	39	74	[48,59]
BLAs	AsN (0/+)	2.95	2.60	91	−	38	75	[57]
BLP	PN (0/+)	3.20	2.89	91	−	37–39	73–77	[57]
UVLMg	MgGa (−/0)	3.28	3.28	91.5	−	−	−	[62]
UVLBe3	BeGa (−/0)	3.26	3.26	91.5	−	−	−	[45,46]
UVLBe	BeGaONBeGa (−/0)	3.38	3.38	91.5	−	37.5	−	[64]

. The Zn_Ga-related BL1 band (also referred to as BL_Zn) is prevalent in MOCVD- and AT-grown GaN, and occasionally in HVPE GaN, due to unintentional Zn incorporation.

3.4.2. C_NH_i-Related BL2 Band

The BL2 band, peaking at 3.0 eV, with a ZPL at 3.33 eV, is distinguished by photo-induced metastability—specifically, PL bleaching under continuous UV laser exposure. In early studies, it was linked to Ga vacancies [159] and was often confused with Zn-related BL1. The concurrent bleaching of BL2 and the rise in the YL1 band upon UV illumination [159,160,161,162,163,164] suggested a relationship, later attributed to the dissociation of the C_NH_i complex [55]. Under UV exposure, C_NH_i complexes dissociate, the BL2 intensity decreases, and the C_N-related YL1 intensity increases. This metastability is analyzed in Section 4.1.2, while other features of the BL2 band are briefly discussed below (Figure 19).

The BL2 band arises from internal transitions within the C_NH_i donor, specifically from an excited state ∼20 meV below the CBM to the ground state 0.15 eV above the VBM [55]. Its exponential decay after a laser pulse at low temperatures (τ ≈ 300 ns at T < 20 K) confirms the internal transition mechanism. At ∼60 K, a high-energy shoulder emerges near the ZPL, indicating contributions from CBM-to-defect transitions (Figure 19a). The ZPL energy remains constant (±0.2 meV) across three orders of magnitude in P_exc, further supporting the internal transition model over DAP-type recombination. The fine structure of the BL2 band exhibits phonon replicas involving the LO mode (91–92 meV) and two pseudo-local modes (35.4 and 61 meV) (Figure 18b and Table 3).

The thermal quenching of BL2 is tunable with P_exc but not abrupt (Figure 19b), driven by thermal hole emission from the 0/+ level of C_NH_i to the valence band. The hole-capture coefficient for this defect is estimated as C_p = (4.4 ± 2.0) × 10⁻⁸ cm³s⁻¹ [55].

3.4.3. RY3-Related BL3 Band

In undoped HVPE GaN samples exhibiting strong RL3 and YL3 bands (Section 3.1.4 and Section 3.2.3), a blue band, BL3, emerges at high P_exc (Figure 20a). It has super-linear dependence on P_exc, a signature of a secondary PL arising from radiative recombination following two-hole capture by a defect [56]. Two ZPLs at 3.0071 and 3.0147 eV are observed, followed by phonon replicas, including LO phonons (ħΩ_LO = 91.3 meV) and two pseudo-local vibrational modes (ħΩ₁ = 39.6 meV, ħΩ₂ = 68.2 meV) (Figure 20b). The BL3 band is attributed to transitions from excited states 20–30 meV below the CBM to the 0/+ level of the RY3 defect, located ∼0.47 eV above the VBM. The two ZPLs likely arise from excited states separated by 7.6 meV [56]. The PL lifetime is short (τ₀ < 10 ns), further supporting a fast internal transition mechanism in a donor-type defect.

3.5. Ultraviolet Luminescence Band (UVL)

The UVL band peaking at ∼3.27 eV, is ubiquitous in undoped GaN grown by various techniques. It results from electron transitions from the conduction band (or shallow donors at low temperatures) to the shallow Mg_Ga acceptor with a −/0 level at 0.223 eV above the VBM [40,62,165]. Also known as the shallow DAP or shallow donor-shallow acceptor (SD-SA) band [9,76,166], it is denoted hereafter UVL (or UVL_Mg to reflect its Mg_Ga origin), as DAP transitions dominate all acceptor-related PL in GaN at low temperatures [66].

Early studies proposed alternative shallow acceptors, including V_Ga, C_N, and Si_N [16,166,167,168]. In particular, Glaser et al. [166] observed a UVL band in MOCVD-grown Si-doped GaN, indistinguishable from UVL_Mg in Mg-doped GaN. In those experiments, Si concentrations were (2–3) × 10¹⁷ cm⁻³, and the UVL intensity increased with increasing Si content [166,167]. Interestingly, ODMR studies revealed the identical behavior of the UVL band in both Mg- and Si-doped samples, suggesting the involvement of shallow effective-mass acceptors in both cases [166,169]. Note that early theoretical calculations also predicted that C_N and Si_N are shallow acceptors in GaN [17,18,19,20,21,22]. However, more recent hybrid functional DFT calculations have demonstrated that these impurities form deep acceptor levels: at 0.9 eV for C_N [24] and 2.1 eV for Si_N [103,170].

Based on analysis of a variety of undoped and doped GaN samples grown by various techniques, we concluded that the Mg_Ga acceptor is the sole source of the UVL band in undoped GaN (see also Section 4.3.2). Its large hole-capture coefficient (C_p = 10⁻⁶ cm³s⁻¹) enables efficient hole capture in conductive n-type GaN, allowing UVL detection at Mg concentrations as low as 10¹³ cm⁻³ [83], well below the SIMS detection limit (~10¹⁵ cm⁻³).

In AT GaN, the UVL_Mg band exhibits an atypical shape, particularly reduced ZPL intensity [39,42]. This distortion of the UVL_Mg band shape can be explained by self-absorption of PL originating from deeper regions of bulk, high-quality GaN templates, where the diffusion length of photogenerated carriers is relatively large.

3.6. Role of V_Ga in GaN Luminescence

Gallium vacancies and related complexes were historically considered the primary origin of the YL band in undoped GaN [16]. However, recent studies have revised this view. Given their high mobility at typical GaN growth temperatures, isolated V_Ga are unlikely to persist in as-grown material; instead, they tend to form stable complexes with donors during the cooling phase [14,171,172]. PAS studies by Chichibu et al. [14] identified V_GaV_N complexes as the dominant vacancy-type defects in n-type GaN grown by HVPE, MOCVD, and MBE, with concentrations ranging from 10¹⁶ to 5 × 10¹⁷ cm⁻³, lowest in freestanding HVPE templates (<1 × 10¹⁶ cm⁻³). Tuomisto et al. [172] also concluded that isolated V_Ga do not persist in as-grown GaN. In samples with a high concentration of O, they form the V_GaO_N complexes that are stable at growth temperatures [171,172,173,174,175]. Interestingly, in Si-doped HVPE GaN ([Si] = 10¹⁷–10¹⁹ cm⁻³), V_Ga concentrations remain below 10¹⁶ cm⁻³ [176]. V_Ga may also associate with H [139,177,178] and form multi-component complexes, which is common for GaN grown by the AT method [139,179,180]. Nevertheless, in high-quality GaN samples grown by HVPE, MOCVD, and MBE, V_Ga-related defects are generally at or below the PAS detection limit (~10¹⁶ cm⁻³) [172].

V_Ga-related defects are often regarded as nonradiative defects [14,179]. No PL bands in HVPE- or MOCVD-grown GaN could be attributed to the V_Ga or the complexes mentioned above [66]. Hybrid functional DFT calculations place the 2−/− level of the V_GaV_N complex at 1.75–1.97 eV above the VBM [30,181,182], which excludes it as a candidate for producing PL bands in n-type GaN between 1.3 and 3.5 eV. However, a broad band at 0.93 eV, observed after electron irradiation [183], may originate from transitions via this defect. The V_GaO_N complexes are likely nonradiative [35,39,118]. The YL2, OL3, and RL4 bands in AT GaN (Section 3.1.3 and Section 3.2.4) are tentatively linked to V_Ga3H_i, V_GaO_N2H_i, V_Ga2O_NH_i, and V_Ga3O_N. Nevertheless, these assignments remain speculative and require further experimental validation.

4. Luminescence from Intentionally Introduced Defects

This section examines the PL characteristics of defects intentionally introduced in GaN, with a focus on C, Be, Mg, and Zn.

4.1. Carbon-Related Defects (YL1, BL_C, BL2, RL_C)

Carbon impurities in GaN form C_N acceptors, responsible for the YL1 band, and C_NH_i complexes, associated with the BL2 band. Another blue luminescence (BL_C) band arises as a secondary PL process from C_N upon capturing two holes. The red RL_C band is attributed to C-containing complexes.

4.1.1. PL from the −/0 and 0/+ States of C_N (YL1 and BL_C)

The YL1 band, peaking at ~2.2 eV, is a dominant defect-related PL feature in undoped, Si-doped, or C-Si co-doped n-type GaN thanks to efficient hole capture by C_N acceptors (Section 3.1.2). Its long PL lifetime (∼100 µs for n ≈ 10¹⁷ cm⁻³) leads to saturation at low excitation intensities. Subsequent capture of a second hole activates the 0/+ level, located 0.33 eV above the VBM, producing the BL_C band at 2.85 eV [25]. Figure 21a shows the BL_C emerging superlinearly with P_exc as YL1 saturates in conductive n-type GaN co-doped with Si and C. Comparing PL efficiencies of YL1 (pre-saturation) and BL_C (after its IQE stops rising) yields a hole-capture coefficient for the 0/+ level of C_p ≈ 10⁻¹⁰ cm³s⁻¹, significantly lower than values from DLTS [184] or first-principles calculations [185]. This unexpectedly low radiative efficiency could be attributed to the trap-assisted Auger-Meitner (TAAM) recombination, which may become dominant at high P_exc [185].

TRPL reveals fast (~1 ns) and exponential BL_C decay, with only YL1 persisting beyond 0.1 μs after a laser pulse (Figure 21b). Across samples with free electron concentrations between 3 × 10¹⁶ cm⁻³ and 3.8 × 10¹⁸ cm⁻³, BL_C lifetimes range from 0.27 to 1.3 ns [25]. This short and almost insensitive to n PL lifetime is modeled by competing internal transitions (from an excited state near the CBM to the 0/+ level) and transitions from the conduction band, with contributions varying with n (Figure 22a). The model yields a high electron-capture coefficient for BL_C (C_n ≈ 10⁻⁹ cm³s⁻¹). A configuration-coordinate diagram in Figure 22b illustrates transitions leading to YL1 and BL_C in C-doped GaN. The experiments supported theoretical predictions of two charge transition levels for C_N [105,107] and confirmed that the YL1 band is caused by the isolated C_N [24,25]. The C_NO_N complexes, erroneously considered as the origin of YL1 [105,106,142], are either weakly radiative or not formed in sufficient concentration, and therefore are absent in PL spectra (Section 4.1.4).

DLTS studies provided independent evidence that the C_N defect in GaN possesses two charge transition levels. Employing low-frequency capacitance DLTS for MOCVD-grown p-type GaN:Mg, Narita et al. [26] found the 0/+ level of the C_N at 0.29 eV above the VBM at T ≈ 135 K by correlating the DLTS signals with C concentration. The most precise determination of the 0/+ level at low temperatures was achieved via PL measurements (Figure 23). From the ZPL at 3.172 eV, the 0/+ transition level of C_N is found at 0.33 ± 0.01 eV above the VBM [60]. Phonon-related fine structure reveals coupling to the LO crystal mode and a pseudo-local mode of 34.3 meV (Figure 23b). The experimentally determined 0/+ level of the C_N agrees with values of 0.23–0.36 eV obtained from first-principles calculations [25,107,182].

4.1.2. PL from the C_N and C_NH_i (YL1 and BL2)

In high-resistivity or SI GaN, particularly in MOCVD-grown samples, the YL1 and BL2 bands are dominant features in the defect-related low-temperature PL spectrum (Section 3.1.2 and Section 3.4.2). These bands originate from carbon-related defects: substitutional carbon (C_N) and its hydrogenated form (C_NH_i). Hydrogen is a ubiquitous impurity in GaN, especially in samples grown by MOCVD. Hydrogen is mobile at growth temperatures only in the form of H⁺ ions [186,187], and it is positively charged when the Fermi level lies more than ~0.5 eV below the CBM [55]. Consequently, C_NH_i complexes are formed, and the BL2 band is observed only in high-resistivity n-type and in p-type GaN. The metastable behavior of PL in such samples—specifically, the interplay between the YL1 and BL2 bands, driven by reversible formation and dissociation of C_NH_i complexes and influenced by UV exposure or thermal annealing—is analyzed below [55,188].

Under continuous above-bandgap excitation at low temperatures (T < 80 K), BL2 band bleaches, while the YL1 intensity increases simultaneously (Figure 24a) [55,159,160,161,162,163,164,188,189,190,191]. This behavior is explained by photo-induced dissociation of C_NH_i, with a dissociation probability per recombination event of γ = 5 × 10⁻⁸ [55], implying one dissociation per 10⁷–10⁸ radiative recombination events involving the complex, in agreement with earlier estimates [164]. This bleaching is permanent at low temperatures but can be reversed at room temperature after a few days, implying a barrier of ~1 eV for the complex formation [188]. Quantitative analysis of these processes yields a hole-capture coefficient ratio of C_p,BL2/C_p,YL1 = 0.12 and also allows for the extraction of defect concentrations [55].

Thermal annealing has a pronounced effect on the stability of C_NH_i complexes in GaN. Annealing in N₂ ambient at T_ann > 700 °C leads to the dissociation of C_NH_i and the subsequent removal of hydrogen from MOCVD-grown GaN samples, resulting in a drastic reduction in the BL2 intensity (Figure 24b). Remarkably, the BL2 band can be fully restored by annealing in an H₂ + N₂ atmosphere at 650–850 °C, confirming the incorporation of H and restoration of C_NH_i complexes [55].

The effect of annealing (in N₂ ambient at T_ann between 300 and 1000 °C) on the YL1 band in MOCVD-grown undoped GaN was studied in detail in [188] (filled blue squares in Figure 25a). The drop in the YL1 intensity at T_ann = 350–400 °C corresponds to a ~2 eV activation energy. This behavior was explained by the release of hydrogen from unidentified nonradiative defects and its subsequent capture by C_N [188]. One of the samples was isochronally annealed in vacuum (for 30 min with 25 °C steps up to T_ann = 400 °C) and exhibited a similar trend (empty squares in Figure 25a). Annealing at T_ann > 900 °C permanently removed H from the samples (as evidenced by the disappearance of BL2) and restored YL1 intensity.

Interestingly, when C_N defects were initially passivated by H (through annealing at 400–800 °C) and subsequently reactivated via photo-induced dissociation of C_NH_i at cryogenic temperatures, additional annealing at significantly lower temperatures (T_ann = 100–150 °C) resulted in a pronounced decrease in YL1 intensity and a concurrent increase in BL2 intensity (Figure 25b and empty triangles in Figure 25a). These observations suggest that after low-temperature photo-induced dissociation of C_NH_i, H remains in close proximity to C_N, separated by an energy barrier of ~1 eV, and readily re-passivates the C_N upon mild annealing or even at room temperature (after a couple of days) [188].

A similar annealing response (except for the photo-induced activation) was observed for the Be_Ga-related YL_Be band [188]. The YL_Be intensity dropped by up to an order of magnitude at T_ann ≈ 400 °C, which was attributed to the release of hydrogen from unknown traps and passivation of Be_Ga acceptors. Interestingly, the YL_Be intensity slowly recovered at room temperature (on a timescale of months) [188].

4.1.3. RL_C Band in C-Doped GaN

In HVPE-grown GaN doped with carbon, the intensities of the YL1 and BL2 bands decrease markedly as the concentration of C increases from ~10¹⁸ to 3 × 10¹⁹ cm⁻³ [33]. This trend has been attributed to the formation of tri-carbon complexes that outnumber isolated C_N centers in heavily doped GaN [33,192]. At these high carbon concentrations, a red luminescence (RL_C) band, peaking at 1.62 eV, emerges [33,193]. The RL_C band is mostly excited under below-bandgap excitation (resonantly), and its PLE spectrum has a Gaussian shape with a maximum at 2.7 eV (Figure 26a). The RL_C is quenched above 80 K, revealing an activation energy of ~0.1 eV. Based on these observations, Zimmermann et al. [33] attributed RL_C to tri-carbon complexes. They proposed that this defect has a ground state at about 1.1 eV above the VBM and an excited state at 0.1 eV below the CBM.

Figure 26b illustrates a configuration coordinate diagram adapted from [33] to explain the PL and PLE characteristics of the RL_C band. In the ground state, the defect is a neutral donor D⁰ (the lowest parabola). Resonant excitation (transition a-b₁) promotes an electron from the donor ground state to an excited state located at Δ = 0.1 eV below the CBM, producing the PLE peak at 2.7 eV. The system then relaxes (b₁-c₁) to a new equilibrium position x₀ via phonon emission. Radiative recombination (c₁-d) produces the RL_C band with a maximum at 1.62 eV, and the defect system returns (d-a) via phonon emission to the initial state. Such internal transitions, not involving the valence or conduction band, are known to produce nearly Gaussian PLE spectra [94], consistent with experimental observations (Figure 26a).

If electrons were excited to the conduction band (transition a-b₂), the PLE spectrum would show a stepwise rise (instead of a Gaussian shape) due to continuous states in the conduction band [94]. According to the results shown in Figure 26a, such contributions are negligible, suggesting that electrons excited to the conduction band predominantly recombine nonradiatively via some other defects.

The transition a-b₃ in Figure 26b corresponds to the above-bandgap excitation of an electron-hole pair when the defect is in the ground state D⁰. It appears that the capture of holes (transition b₃-c₂) is inefficient for these defects (because they are donors, and there may also be a potential barrier for the hole capture). This would explain why the RL_C band is very weak (or not observed) under above-bandgap excitation [33].

A similar behavior was observed for F centers that are deep donors in alkali halides, with excited states near the CBM [194,195,196,197]. The shapes of PL and PLE bands for F centers are Gaussian. PL quenching begins at T ≈ 100 K, and the quenching is attributed to thermal emission of electrons from the excited state to the conduction band. Similar to the RL_C band in GaN, PL from F centers is efficiently excited via resonant excitation, but remains undetectable under above-bandgap excitation [198].

4.1.4. Other Carbon-Related Complexes

Although C_NO_N complexes were initially suggested as potential contributors to the YL band [105,106], more recent hybrid functional DFT calculations indicated insufficient binding energies for C_NO_N and C_NSi_Ga to form at concentrations comparable to isolated C_N [98]. Specifically, for GaN grown at 1300 K and co-doped with C and Si, the predicted concentration of C_NSi_Ga complexes is less than 1% of the isolated C_N concentration when the concentration of shallow Si_Ga donors is ~10¹⁸ cm⁻³. The C_NO_N, with lower binding energy, is expected to be present at even lower levels [98].

Figure 27 presents SSPL and TRPL spectra at T = 17 K from a MOCVD-grown GaN sample co-doped with C (7 × 10¹⁷ cm⁻³) and Si (1.4 × 10¹⁸ cm⁻³). The only emission observed below 3 eV is the YL1 band. Its characteristic features (the band shape, hole- and electron-capture coefficients, the ZPL at 2.59 eV, and BL_C band emerging at high P_exc) confirm its origin from the isolated C_N. The SSPL and TRPL spectra are identical (the simulated lineshape is shown with the orange dashed line), further confirming that no other PL bands contribute to the broad yellow band. The residual background observed between 2.7 and 3.0 eV is attributed to monochromator stray light, as confirmed by the use of interference filters. A hypothetical C_NSi_Ga band, predicted to occur in the 2.3–2.7 eV range [98,103], is not observed. Its estimated intensity, represented with the dotted line in Figure 27, is at least four orders of magnitude lower than YL1. Thus, C_NO_N and C_NSi_Ga complexes are not observable in PL, due to low concentrations [98] and relatively low hole-capture coefficients, as these complexes are donors.

4.2. Beryllium-Related Defects (YL_Be, UVL_Be3, UVL_Be, RL_Be, BL_Be, GL_Be)

Beryllium (Be) doping in GaN introduces a variety of defect-related PL bands, including YL_Be, UVL_Be3, UVL_Be, RL_Be, BL_Be, and GL_Be. This section summarizes their experimental characteristics, theoretical interpretations, and associated defect models.

4.2.1. Historical Overview

For a long time, the Be_Ga acceptor was regarded by experimentalists and theorists as the shallowest acceptor in GaN and was proposed as an alternative to Mg_Ga for achieving p-type doping [199,200,201,202,203,204,205]. However, more recent first-principles calculations have demonstrated that Be_Ga is a deep acceptor with the predicted −/0 level at 0.45–0.65 eV above the VBM [206,207,208,209]. In addition to this deep state, the theory also predicted a shallow state with a delocalized hole [206,210]. Early experimental PL studies revealed two primary Be-related bands (Figure 28a): a broad yellow band with a maximum at 2.15 eV (YL_Be) and a UVL band consisting of a sharp peak at 3.38 eV accompanied by a few LO phonon replicas (UVL_Be). Initially, YL_Be was attributed to various Be-containing complexes, including Be_GaO_N donors [211], Be_GaV_NBe_Ga acceptors [150], and Be_iV_Ga complexes [212]. The UVL_Be band was erroneously attributed to the shallow Be_Ga acceptor [150,199,200,201,202,203,210]. PL bands in Be-doped GaN were the subject of continued debate until the dual nature of the Be_Ga acceptor was experimentally verified [45]. Comprehensive PL studies [45,46,213,214], in fair agreement with early theoretical predictions [206], have led to a consistent model of the Be_Ga acceptor in GaN (Figure 28b).

According to this model, the Be_Ga acceptor forms two deep, polaronic states (Be1 and Be2) in which the hole is localized on adjacent nitrogen atoms, and a shallow state (Be3) with a delocalized hole. The −/0 transition levels for these states are experimentally found at 0.35 ± 0.03 eV (Be1), 0.39 ± 0.02 eV (Be2), and 0.24 ± 0.01 eV (Be3) above the VBM [45,46]. Recent temperature-dependent Hall-effect measurements on MOCVD-grown GaN:Be samples have confirmed the p-type conductivity associated with the Be_Ga acceptor level at 0.40 ± 0.02 eV above the VBM [215]. Electron transitions from the conduction band to Be1 and Be2 levels are responsible for the YL_Be1 and YL_Be2 components of the YL_Be band. Transitions via the shallow Be3 level result in a distinct PL band (labeled UVL_Be3) with a peak at 3.26 eV followed by LO phonon replicas. In bulk GaN:Be grown by the high nitrogen pressure solution (HNPS) method, these PL bands can also be found. However, a significant contribution of the C_N-related YL1 band in those samples and blurred PL bands can complicate the attribution of individual PL features [46].

The UVL_Be band at 3.38 (initially thought to be caused by isolated Be_Ga) has recently been attributed to the Be_GaO_NBe_Ga complex [64]. The BL_Be band with a maximum at 2.6 eV is preliminarily attributed to the 0/+ transition level of Be_Ga [61].

4.2.2. Three States of Isolated Be_Ga (YL_Be1, YL_Be2, UVL_Be3)

At temperatures below T₁ ≈ 80–100 K, photogenerated holes in GaN:Be are efficiently captured by the shallow Be3 level (0.24 eV above the VBM). These holes rapidly relax, via barrier-free transition, into the Be1 level at 0.35 eV. A significant energy barrier (>0.17 eV) between Be1 and Be2 polaronic states prevents hole transfer to the deepest Be_Ga level (Be2) at these temperatures. Consequently, the YL_Be band is observed, caused by electron transitions from the CBM (or from shallow donors at T < 50 K) to the Be1 level (YL_Be1). According to ODMR studies on MBE-grown GaN:Be [216], the Be_Ga polaronic state (apparently Be1 causing the YL_Be at T = 1.6 K) is characterized by isotropic g = 2.004 ± 0.002.

At T ≈ T₁, a thermally activated transition occurs: the hole relocates from an in-plane N atom to the c-axis N atom, corresponding to the lowest energy configuration Be2, and the YL_Be1 component (transitions to Be1) is replaced by YL_Be2 (transitions to Be2). As a result, the YL_Be band redshifts by about 40 meV at T ≈ T₁. Though the radiative lifetimes of the two components are comparable (τ_n1/τ_n2 = 1.2 ± 0.2), a noticeable discontinuity appears in the measured PL lifetime at T ≈ T₁ (Figure 29a). This is due to rapid hole transfer from Be1 to Be2, occurring on a timescale shorter than the YL_Be1 lifetime at T > T₁.

The YL_Be band consistently exhibits two-step quenching at temperatures T₁ and T₂ (Figure 29). In SI GaN:Be samples, both quenching steps are tunable with P_exc, i.e., T₁ and T₂ increase with increasing P_exc (the TAQ mechanism). Notably, the second step is abrupt in SI samples and exhibits an apparent activation energy (up to 1.5 eV) that is unrelated to the ionization energy. In contrast, in conductive n-type GaN:Be samples, the two-step quenching is neither tunable nor abrupt. The second quenching step in such samples is described by the Schön–Klasens quenching mechanism, and the activation energy of approximately 0.30 eV corresponds to the Be2 ionization energy, although thermal emission of holes from Be2 occurs via the Be3 level [45].

Interestingly, the IQE of the YL_Be band remains unchanged when the temperature passes T₁ [213]. The observed PL intensity drops at T ≈ T₁ due to reduced light extraction efficiency from c-axis dipoles (Be2 polarons) [45], the axis of which in GaN:Be layers grown on c-plane sapphire coincides with the direction of PL observation. The magnitude of the PL drop during the first quenching step is sample-dependent and depends on the PL detection geometry (Figure 29b). In agreement with the prediction [45], the YL_Be intensity rises at T > T₁ in bulk GaN:Be crystals when PL is observed in a direction perpendicular to the GaN c-axis [217].

The dual nature of the Be_Ga acceptor, which possesses both deep polaronic and shallow delocalized hole states, was verified with PL experiments, where the UVL_Be3 band emerging at T > 100 K (Figure 30) provided key evidence [45].

The UVL_Be3 band was initially overlooked due to its similarity to the UVL_Mg band, which originates from the shallow Mg_Ga acceptor (ZPL at 3.27–3.29 eV, followed by LO phonon replicas). The UVL_Mg band typically quenches at T > 100 K and disappears by 200 K in undoped GaN due to the low ionization energy of the Mg_Ga acceptor (0.223 eV). However, in Be-doped GaN, a similar PL band emerges at T > 100 K, exponentially increasing with temperature (Figure 30a). In Mg-contaminated GaN:Be samples, both the UVL_Mg and UVL_Be3 can be spectrally resolved, revealing that the UVL_Be3 ZPL is ~15 meV below the UVL_Mg ZPL (Figure 30b).

The UVL_Be3/YL_Be2 intensity ratio increases exponentially with temperature (Figure 31a) and fits well the expression:

$${\displaystyle \frac{I_{Be3}^{UVL}}{I_{Be2}^{YL}}}=\delta \exp \left({\displaystyle \frac{-\Delta E_{23}}{kT}}\right)$$

(9)

where δ = τ_n2/τ_n3, τ_n2 and τ_n3 are intrinsic PL lifetimes of radiative transitions via Be2 and Be3, respectively, and ΔE₂₃ is the energy difference between the respective levels. Fitting yields ΔE₂₃ = 0.15 ± 0.02 eV and δ ≈ 10 across multiple GaN:Be samples grown by MBE and MOCVD. This behavior reflects Boltzmann population redistribution between Be2 and Be3 states [45]. Interestingly, the measured PL lifetimes of the UVL_Be3 and YL_Be2 bands are identical at all temperatures (Figure 29a). It was shown in Ref. [45] that the true PL lifetime of PL via the Be3 level is about 10 times shorter than that of the YL_Be2 band, as is expected for shallow and deep acceptors [34]. However, thanks to dynamic feeding after a laser pulse, the Be3 state is continuously populated by hole transfer from Be2, resulting in synchronized PL decay [45].

Thermal quenching of UVL_Be3 and YL_Be2 begins at T = T₂ ≈ 120–200 K. In SI and high-resistivity p-type GaN:Be samples, the quenching is tunable and abrupt (Figure 31b). In conductive n-type GaN:Be samples, the YL_Be quenching begins at T₂ ≈ 200 K, and the slope of the quenching reveals an activation energy of 0.30 eV. Initially, the activation energy was attributed to the deep level of Be_Ga. However, according to the above model, the quenching is primarily caused by the thermal emission of holes from the shallow Be3 level to the valence band [45]. The effective activation energy for the YL_Be quenching corresponds to the sum of Be3 energy (about 0.20 eV at T = 200 K) and the energy difference between the Be3 and Be2 levels (~0.15 eV). It should be noted that activation energies extracted from PL quenching slopes are typically slightly lower than the true defect ionization energy, due to several factors [66,75].

The results of the hydrostatic pressure experiments [211] have been interpreted using a model in which the broad yellow band in HNPS-grown GaN:Be consists of a C_N-related YL1 band and a yellow band caused by the Be_GaO_N complex. According to first-principles calculations in [211], the polaronic 0/+ level of Be_GaO_N shifts from 0.26 eV to 0.12 eV above the VBM as hydrostatic pressure increases from 0 to 8 GPa. At higher pressures, a UVL band (with a peak at ~0.2 eV below the bandgap) emerges and is attributed to the shallow 0/+ level of Be_GaO_N with a delocalized hole, reflecting its dual nature. The model based on isolated Be_Ga was dismissed in [211], primarily because the calculated PL band maximum of the Be_Ga polaron (1.80 eV) markedly disagreed with the experimentally observed YL_Be maximum. However, these experimental results can be well explained with the above-discussed model of the isolated Be_Ga, in which the deep Be1 level shifts toward the VBM (by ~0.17 eV under 8 GPa pressure [211]) and intersects with the shallow Be3 level, resulting in a sudden intensification of the UVL_Be3 band [46].

4.2.3. Shallowest Acceptor in GaN (UVL_Be)

The UVL_Be band at 3.38 eV, initially misattributed to a shallow level of Be_Ga [210], arises from Be doping and exhibits all characteristic features of the shallowest acceptor in GaN [64]. Figure 32a shows two components of the UVL_Be band (eA and DAP) observed in two GaN:Be samples grown by MOCVD. Both UVL_Mg and UVL_Be bands feature a sharp ZPL followed by a few LO phonon replicas. The Huang–Rhys factor, S, defined as the intensity ratio of the first phonon replica to the ZPL, is 0.15 for the UVL_Be—the lowest among GaN defects—indicating the lowest electron–phonon coupling strength [64].

Analysis of temperature and excitation-intensity dependences of the DAP and eA components yields the −/0 transition levels at 222 meV (Mg_Ga) and 114 meV (Be-related defect) at T = 18 K [64]. Due to these low ionization energies, the UVL_Mg and UVL_Be bands are quenched at relatively low temperatures (above 100 K and 70 K, respectively). Furthermore, it is known that the electron- and hole-capture coefficients generally decrease with increasing ionization energy for acceptors in GaN [34,66]. Consistent with this trend, UVL_Mg and UVL_Be exhibit the highest C_n (3.2 × 10⁻¹² and 1 × 10⁻¹¹ cm³s⁻¹, respectively) and C_p (both about 1 × 10⁻⁶ cm³s⁻¹), see Figure 9.

The differences between the UVL_Mg and UVL_Be bands offer insights into the origin of the latter. The UVL_Mg band is prevalent in undoped n-type GaN due to residual Mg contamination, with its intensity increasing markedly under moderate Mg doping while the material remains n-type [34,62]. In contrast, the UVL_Be band is either very weak or absent in conductive n-type GaN:Be samples, regardless of Be concentration, as well as in SI GaN:Be if [Be] < 10¹⁸ cm⁻³. In MOCVD-grown GaN, Mg is passivated by hydrogen (with [Mg] ≈ [H]), and Mg_Ga activation requires post-growth annealing above 500–600 °C to dissociate Mg-H complexes [218]. In contrast, both UVL_Be and YL_Be bands are present in as-grown MOCVD GaN:Be (annealing is not required), and [H] does not noticeably increase with Be doping.

On the other hand, in MBE-grown GaN:Be, the UVL_Be appears only after annealing at T_ann > 700 °C (Figure 32b). At higher annealing temperatures, the RL_Be band at 1.8 eV appears (Section 4.2.4), and the YL_Be band intensity decreases. The difference between the MOCVD and MBE GaN:Be can be explained as follows. During MOCVD growth in Ga-rich conditions, mobile species such as V_Ga and H are abundant at growth temperatures and promote the formation of Be_Ga and Be_GaO_NBe_Ga acceptors. In GaN grown by MBE under N-rich conditions, mobile nitrogen vacancies, which act as donors, are abundant and tend to passivate the Be_GaO_NBe_Ga acceptors. Post-growth annealing at T = 700–900 °C activates Be_GaO_NBe_Ga, while the released nitrogen vacancies passivate Be_Ga by forming V_NBe_Ga complexes, thereby reducing YL_Be emission and enhancing RL_Be intensities.

First-principles calculations predict that Be_GaO_NBe_Ga complex acts as a dual-nature acceptor with shallow and deep levels at 0.12 and 0.34 eV above the VBM, respectively [64]. However, no PL signal could be found from the deep level. One explanation is that the deep level is actually closer to the VBM than the shallow level. Alternatively, the deep state may not participate in electron-hole recombination if a substantial potential barrier exists between the shallow and deep states. Finally, it remains possible that the UVL_Be band originates from a distinct Be-containing complex that has not yet been identified.

4.2.4. Be_GaV_N-Related RL_Be Band

In GaN:Be samples grown by MBE, annealing at T_ann ≈ 900 °C induces a strong RL_Be band with a maximum at 1.8 eV (Figure 33a). This band is attributed to transitions involving the Be_GaV_N complex donors [36,150]. In PL spectra from these samples, the V_N-related GL2 band (Section 3.3.2) is also observed. First-principles calculations predict a PL band with a maximum at 1.69 eV for transitions from the CBM to the 0/+ level of the Be_GaV_N complex, which is close to the experimentally determined value of 1.77 eV [36].

The SSPL intensity of the RL_Be band remains constant up to ~70 K and decreases at higher temperatures, with an activation energy of about 0.1 eV (Figure 33b). In TRPL experiments, exponential decay of RL_Be is observed at the lowest temperatures, in line with its attribution to internal transition from an excited state of the deep donor. The PL lifetime of the RL_Be decreases from 2 μs at T = 18 K to 1 μs at T ≈ 70 K (Figure 33b). The PL quenching at T > 70 K is explained by thermal emission of electrons from an excited state located at 0.1 eV below the CBM to the conduction band [36]. These I^PL(T) and τ(T) dependences resemble those of the RL2 band in undoped GaN (Section 3.2.2), and the exponential decrease in PL lifetime at T < 70 K can be explained by two excited states with closely spaced levels. However, the slope of the τ(T) dependence is much smaller, and the separation between the levels is smaller for the Be_GaV_N (2.5 meV) than for the RL2-related defect in undoped GaN (10 meV).

4.2.5. Deep Donor PL (BL_Be)

At elevated excitation intensities, the YL_Be band becomes saturated, and a new band (BL_Be) emerges at 2.6 eV (Figure 34). Its shape can be fitted using Equation (6) with parameters from Table 2. The BL_Be band is tentatively attributed to transitions via the 0/+ level of the Be_Ga defect [61]. When the Fermi level is above the −/0 level of Be_Ga, two-hole capture may lead to radiative recombination via the 0/+ level of Be_Ga, making BL_Be prominent only at high P_exc, when the Be_Ga defects are saturated with holes. In p-type GaN:Be, a significant fraction of the neutral Be_Ga defects are expected to be neutral even at low P_exc; however, the BL_Be intensity remains low. This is likely due to a low hole-capture coefficient for the 0/+ level of Be_Ga, similar to what has been observed for the C_N defect (Section 4.1.1).

After a laser pulse, the BL_Be intensity decays exponentially at T = 18 K, with a characteristic lifetime of 0.75 ± 0.15 μs, indicative of an internal transition from an excited state to the ground state [61]. The behavior is typical for deep donors in GaN. The quenching of the BL_Be band at T > 100 K is attributed to thermal emission of bound holes to the valence band. Concurrently, the PL lifetime decreases with the same activation energy. From these dependences, the 0/+ level was estimated to lie 0.15 ± 0.05 eV above the VBM, and this value agrees with the position and shape of the BL_Be band [61]. Note that hybrid functional calculations for Be_Ga in GaN do not find the 0/+ transition level of this defect [61], possibly because of the close location of this level to the VBM.

4.2.6. Other Be-Related Defects

In MOCVD-grown GaN samples, heavily doped with Be, a weak green luminescence (GL_Be) band with a maximum at ~2.4 eV may contribute to the high-energy side of the stronger YL_Be band. However, this GL_Be component remains unresolved in SSPL and TRPL measurements when the excitation intensity and temperature are varied over wide ranges [61]. This band could be caused by a complex defect containing one or more Be atoms.

Be_GaO_N complexes are expected to form readily in GaN samples containing high concentrations of Be and O, such as bulk GaN crystals grown by the HNPS method with [Be] ≈ [O] ≈ 3 × 10¹⁹ cm⁻³ [46,211]. In hydrostatic pressure experiments on such samples, Teisseyre et al. [211] attributed a broad yellow band, which blue-shifted markedly with pressure, to the Be_GaO_N complex. However, as discussed in Section 4.2.2, these results may also be explained by the assumption that the yellow band originated from isolated Be_Ga.

Recent PL studies of bulk HNPS GaN:Be,O revealed the Be_Ga-related YL_Be band and the C_N-related YL1 band, but no distinct emission band could be conclusively assigned to the Be_GaO_N complex [46]. These results were explained by the assumption that the Be_GaO_N complexes, even when they are present with high concentrations (~3 × 10¹⁹ cm⁻³), are either electrically neutral or exhibit poor hole-capture efficiency, such that their emission is overshadowed by stronger YL_Be and YL1 bands. Calculations using Heyd-Scuseria-Ernzerhof (HSE) hybrid functional predict that the Be_GaO_N complex is either a deep donor with the 0/+ level at 0.26 eV above the VBM [211], or it is electrically neutral and does not have transition levels in the band gap [150]. Similarly, the Be_GaH_i complex has been predicted to be electrically neutral [219].

4.3. Magnesium-Related Defects (UVL_Mg, BL_Mg, RL_Mg)

Magnesium is currently the only impurity reliably used to achieve conductive p-type GaN. This section reviews the PL characteristics of Mg-related defects, focusing on the ultraviolet (UVL_Mg), blue (BL_Mg), and red (RL_Mg) luminescence bands. These bands are discussed in terms of spectral features, defect assignments, and theoretical interpretations.

4.3.1. Historical Overview

Maruska et al. [220] were the first to report Mg doping in GaN, for use in m-i-n diodes emitting violet light. PL measurements at 77 K revealed a blue band with a maximum at 2.925 eV, which the authors attributed to an Mg-related defect with a level at ~0.5 eV above the VBM. However, the Mg-doped GaN samples retained their highly resistive nature, and the realization of effective p-type conductivity remained elusive for several years. It was not until 1989 that a breakthrough was achieved by the team at Nagoya University, who demonstrated conductive p-type GaN through post-growth low-energy electron beam irradiation (LEEBI) treatment of Mg-doped layers [221]. This advance resolved a critical obstacle and ultimately paved the way for the development of bright blue LEDs [222]. Low-temperature (4.2 K) PL spectra from early p-type GaN:Mg samples grown by MOCVD showed the UVL_Mg band at 3.27 eV (for [Mg] = 1.6 × 10¹⁹ cm⁻³) and a blue band with a maximum at 2.95 eV ([Mg] = 7.1 × 10¹⁹ cm⁻³), both attributed to the Mg acceptor [223,224].

Since then, the Mg-doped GaN has been extensively studied. In particular, it was found that Mg_Ga acceptors, passivated by H during MOCVD growth, can be activated not only via LEEBI treatment [221] but also by thermal annealing at temperatures above 500 °C [225,226]. Early studies of MOCVD-grown GaN:Mg, using room-temperature PL, revealed two PL bands: blue and red [226]. The red band was observed in as-grown, high-resistivity GaN:Mg samples and attributed to Mg-H complexes. The blue band was initially assigned to Mg levels [226]. Later, compelling evidence supported the deep DAP nature of transitions, involving a deep donor and the shallow Mg_Ga acceptor [63,227,228]. The identity of the deep donor remains uncertain (Section 4.3.3).

Conductive p-type GaN can also be achieved without post-growth annealing by MBE technique [169,229,230]. Such samples exhibit the UVL_Mg band with a maximum at about 3.27 eV (Section 4.3.2). The BL_Mg band at ~2.9 eV is typically observed in GaN grown by MOCVD heavily doped with Mg and less often in HVPE GaN:Mg (Section 4.3.3). Mg-doped GaN often exhibits the V_N-related GL2 band (Section 3.3.2) and the RL_Mg band (Section 4.3.5).

4.3.2. Shallow or Dual-Nature Acceptor?

Lany and Zunger [206] proposed that Mg_Ga is a dual-nature acceptor. A shallow level with a delocalized hole was predicted at 0.18 eV, and a deep level with a localized hole is calculated at 0.21 eV above the VBM. Transitions of electrons via the shallow level produce the UVL_Mg band, whereas the BL_Mg band was hypothesized to arise from the deep level. According to this model, at room temperature and in the dark, holes predominantly populate the deep level, which is therefore responsible for p-type conductivity [206]. Several theoretical studies supported this dual nature [231,232], though others identify only the deep state [233,234]. In particular, Lyons et al. [233] proposed that the Mg_Ga with the calculated deep level at 0.26 eV is responsible for the blue band with a maximum at 2.7 eV, while the UVL_Mg band is caused by the Mg_GaH_i complexes with the 0/+ level at 0.13 eV above the VBM.

PL experiments consistently identify only the shallow Mg_Ga level producing the UVL_Mg band (Figure 35).

The BL_Mg band, observed in heavily Mg-doped MOCVD-grown samples, cannot be attributed to the predicted deep-state of Mg_Ga. Indeed, PL intensities from shallow and deep states of dual-nature acceptors must correlate [45]. In particular, their relative contribution may vary with temperature according to the Boltzmann occupation of levels with holes, but the ratio should remain consistent across samples, as it was observed for Be_Ga (Section 4.2.2). However, in n-type GaN:Mg and in MBE-grown p-type GaN:Mg, only the UVL_Mg band is found (Figure 35). If Mg_Ga is a dual-nature acceptor, the absence of deep-level PL suggests either identical transition energies for both states or a substantial potential barrier separating them [45,235].

Heavily Mg-doped GaN contains a variety of defects that affect PL. The analysis of PL is complicated by the fact that even p-type GaN:Mg becomes semi-insulating at low temperatures due to an insufficiently shallow Mg_Ga level. In such material, potential fluctuations due to nonuniform distribution of charged defects or local electric fields associated with structural defects may lead to unstable PL [236,237,238], significant shifts and broadening of PL bands (Section 4.3.4). PL results from GaN:Mg are often difficult to reproduce, and misinterpretations are common.

Pozina et al. [239] initially proposed that two distinct Mg-related acceptors exist in GaN: A1 is responsible for the UVL_Mg band at 3.27 eV, and A2 is responsible for a broader band at 3.15 eV. However, later these researchers attributed only the 3.27 eV peak to the isolated Mg_Ga acceptor, whereas the 3.15 eV band was explained as PL from Mg_Ga perturbed by a nearby basal plane stacking fault [165].

Callsen et al. [240] proposed that the UVL_Mg band consists of three components related to three acceptor states, with levels E_A = 164, 176, and 195 meV. In their opinion, these results supported the dual nature of the Mg_Ga acceptor proposed earlier [206]. However, these components were not clearly resolved, and variations in the UVL_Mg peak position across samples are more plausibly explained by donor variability, strain or local electric fields. Even if the proposed states are real, they all look like shallow states with delocalized holes, distinct from the broad blue band expected for the deep Mg_Ga state [206,233].

4.3.3. BL_Mg Band in Heavily Doped GaN:Mg

The BL_Mg band, peaking between 2.7 and ~3.0 eV, is commonly observed in MOCVD-grown GaN when Mg concentrations exceed ~10¹⁸ cm⁻³ [16,226,241]. This band exhibits a pronounced blue shift with increasing excitation intensity in SSPL and a red shift with time delay in TRPL (Figure 36). Such behavior is characteristic of deep DAP transitions, specifically involving deep donors and shallow Mg_Ga acceptors [63,227,228].

In contrast, DAP transitions, involving shallow donors (Si_Ga or O_N) and various acceptors in GaN, show only minor spectral shifts (<10 meV) [66]. The large shifts observed for deep DAPs are attributed to the strongly localized nature of the carrier wavefunctions [63,242]. For deep donors with energy levels 0.4–0.6 eV below the CBM, the electron wavefunction is highly confined. In such cases, tunneling to nearby Mg_Ga acceptors is efficient only at high acceptor concentrations (>10¹⁸ cm⁻³). Strong Coulomb interactions between closely spaced DAPs result in a broad distribution of recombination energies, thereby explaining the substantial spectral shifts observed in both SSPL and TRPL.

The BL_Mg band is notably absent in GaN implanted with Mg, even for Mg concentrations above 10¹⁹ cm⁻³ [243,244,245,246,247], and also in samples co-implanted with Mg and H ions [248]. It is rarely observed in HVPE-grown GaN:Mg [62,249] and is absent in MBE-grown p-type GaN:Mg [169,229,230]. The specific conditions in MOCVD, particularly the abundance of hydrogen, likely facilitate the formation of the responsible deep donor. In particular, Kamiura et al. [250] reported an enhanced BL band in MOCVD-grown GaN:Mg ([Mg] ≈ 1 × 10²⁰ cm⁻³) after hydrogen plasma treatment. The V_NH complex has been proposed as the associated deep donor [165,251,252]. Alternatively, Mg interstitial (Mg_i) and Mg-related donors such as Mg_GaMg_i have been suggested by first-principles calculations [47,234,253]. Although earlier reports proposed the V_NMg_Ga complex as the deep donor associated with BL_Mg [227], it is now more reliably attributed to the RL_Mg band [36,254] (Section 4.3.5). It is important to note that distinguishing PL bands in Mg-doped GaN, particularly UVL_Mg and BL_Mg, can be challenging, as their spectral positions and shapes are sensitive to experimental conditions in SI samples (Section 4.3.4).

4.3.4. Giant Shifts in PL Bands in GaN:Mg

Large spectral shifts in PL bands can result not only from deep DAP transitions but also from screening with photogenerated carriers of potential fluctuations or local electric fields [63,242,255]. This is more typical for SI materials with nonuniformly distributed charged impurities. Diagonal tunnel transitions with reduced energies dominate in PL from a sample with potential fluctuations. The transition energy increases with increasing P_exc (as photogenerated carriers partly screen potential fluctuations), and it eventually becomes equal to the energy in an ideal semiconductor. An example is shown in Figure 37. The UVL_Mg band (labeled UVL*) redshifts by up to 0.4 eV with decreasing P_exc. Interestingly, the shifting UVL* band coexists with the stable UVL_Mg at 3.27 eV (Figure 37a). The UVL* band in this case likely originates from a near-surface layer, where band bending may remain significant even at low temperatures (despite being screened by photogenerated charge carriers), whereas stable UVL_Mg arises from bulk regions [62].

Distinguishing between energy shifts caused by deep DAP nature and those due to the electric-field mechanism is not straightforward. In both cases, a PL band blue-shifts with increasing P_exc and redshifts with time delay after a laser pulse. Nevertheless, there are important differences. For DAP transitions, the total shift is typically limited by the ionization energy of the shallower component [84,158,242]. Shallow DAP shifts are small (<10 meV for a variety of acceptors in n-type GaN [16,62,66]), whereas the BL_Mg shifts are large, but still limited by the Mg_Ga ionization energy (0.2 eV). In Figure 37b, the BL_Mg band shift is fitted with a DAP model [158], where the ionization energies of the deep donor and shallow Mg_Ga acceptor are 0.4 and 0.2 eV, respectively. The total shift in the BL_Mg band in a very wide range of P_exc does not exceed 0.2 eV. On the other hand, shifts due to potential fluctuations or local electric fields may reach magnitudes comparable to the bandgap [242]. In Figure 37b, the UVL_Mg band redshifts by ~0.5 eV with decreasing P_exc, and the trend does not show any saturation.

4.3.5. Mg_GaV_N-Related RL_Mg Band

The RL_Mg band, peaking at 1.6–1.7 eV, is occasionally observed in Mg-doped GaN (Figure 38). It has been attributed to the Mg_GaV_N complex [36,254] and often appears alongside the V_N-related GL2 band. ODMR studies of MOCVD-grown Mg-doped GaN revealed a sharp and isotropic signal with a g factor of 2.003 ± 0.003 associated with the RL_Mg band [256].

PL studies indicate that the RL_Mg band, with a maximum at 1.68 eV at T = 18 K, originates from electron transitions between an excited state located near the CBM and the ground state ~0.8 eV above the VBM [36]. The PL decay is exponential at T < 50 K, with a lifetime of about 1 μs (Figure 38b). At T > 70 K, both PL intensity and PL lifetime decrease due to the thermal emission of electrons from the excited state to the conduction band. The extracted activation energy of 35 meV corresponds to the energy separation between the excited state and the CBM.

According to first-principles calculations, the Mg_GaV_N defect has the +/2+ and 0/+ levels ~0.8 eV above the VBM [36,234,254], with the +/2+ level possibly 50 meV higher (negative U behavior) [254]. Optical transitions from the CBM to the +/2+ and 0/+ levels are predicted to produce two red PL bands with maxima at 1.83 and 1.81 eV, respectively [254].

When the Fermi level (F) lies above ~0.8 eV, the Mg_GaV_N defects are predominantly neutral under dark conditions or at low P_exc. In this case, hole capture at the 0/+ level, followed by electron capture into the excited state, leads to an internal transition that produces a red PL band (RL_Mg1). In conductive n-type GaN:Mg samples (overcompensated by shallow donors), the RL_Mg1 intensity is expected to be significantly lower than the UVL_Mg intensity, by a factor N^RLC_p^RL/N^UVLC_p^UVL, where N and C_p are the concentrations and hole-capture coefficients for defects responsible for the RL_Mg1 and UVL_Mg bands.

In conductive p-type GaN:Mg samples (F ≈ 0.2 eV), the Mg_GaV_N defects are in the 2+ charge state in the dark, and transitions via the +/2+ level can produce another red PL band (RL_Mg2). In such samples, an electron must first be captured by the excited state, after which a hole is captured at the +/2+ level; their recombination then produces RL_Mg2. This mechanism is similar to the one suggested for the V_N-related GL2 band (Section 3.3.2).

Although theoretical predictions suggest two distinct red PL bands associated with the 0/+ and +/2+ transition levels in Mg-doped GaN, experimental validation is still lacking. The RL_Mg band with ħω_max = 1.68 eV and τ₀ = 1 μs (Figure 38) is likely caused by transitions via the 0/+ level (RL_Mg1) in SI GaN:Mg because the GL2 band is also observed. According to limited experimental reports, a weak red band is observed in conductive p-type GaN, sometimes together with the GL2 band [47,257]. Note that GaN:Mg samples may be nonuniform, with conductive p-type and SI regions [47]. In such samples, p-type conductivity can be confirmed by the Hall effect, while the PL response may predominantly arise from SI regions.

The red band reported by Nakamura et al. [225,226] in GaN:Mg may differ from RL_Mg1 and RL_Mg2, as it was observed at room temperature in SI GaN:Mg and was absent in conductive p-type samples. Bayer et al. [258,259] observed a weak red band at T = 5 K in MOCVD-grown p-type GaN:Mg, but they did not provide its temperature dependence. In our measurements, a weak red band consistent with RL_Mg1 was detected at T = 18 K in MBE-grown GaN:Mg. At room temperature, it could not be resolved (completely quenched), whereas the UVL_Mg band remained strong [47]. The quenching of that RL_Mg band with an activation energy of ~0.1 eV is attributed to electron thermal escape from the excited state to the conduction band [36].

4.4. Zinc (BL_Zn)

The Zn_Ga acceptor, with the −/0 level at 0.40 eV above the VBM, efficiently captures photogenerated holes, producing the BL1 band in undoped GaN contaminated with Zn (Section 3.4.1). In Zn-doped GaN, this band, referred to as BL_Zn, is the dominant defect-related PL feature.

4.4.1. BL_Zn Band in Zn-Doped GaN

The BL_Zn band exhibits ZPL at 3.10 eV, followed by phonon replicas (Figure 18a and Figure 39a). At T < 50 K, the band arises from DAP transitions involving shallow donors and Zn_Ga acceptors. At higher temperatures, e-A transitions dominate thanks to thermal emission of electrons from shallow donors to the conduction band. In Zn-doped GaN, BL_Zn is the strongest defect-related band (Figure 39a). In the NBE region, excitons bound to neutral Zn_Ga acceptors (ZnX_A) are resolved. Zn-doped GaN samples are typically semi-insulating, although p-type conductivity is occasionally confirmed [260].

4.4.2. Tunable and Abrupt Quenching

The BL_Zn band in SI and p-type GaN:Zn displays remarkable features, such as quenching by the TAQ mechanism, two-step quenching, and strongly superlinear dependence on excitation intensity [52,261,262]. The BL_Zn quenching occurs at a critical temperature T₀, which increases with excitation intensity (Figure 39b). The quenching is abrupt, with a slope much larger than any reasonable activation energy. The TAQ is explained by a transition from an inverse carrier population regime at T < T₀ to an equilibrium population regime (p-type or SI) at T > T₀. At low temperatures, photogenerated electrons and holes rapidly populate donors and acceptors, respectively, saturating nonradiative deep donors with electrons, even at very low excitation intensities. This suppresses nonradiative recombination, enabling efficient radiative recombination. Under SSPL conditions, the concentration of electrons in the conduction band can greatly exceed the concentration of holes in the valence band (photo-induced n-type conductivity). With increasing temperature, holes from acceptors are thermally emitted to the valence band. At T ≈ T₀, the excess of these thermal holes over photogenerated holes unblocks nonradiative recombination channels, causing an abrupt reduction in radiative recombination efficiency, including the BL_Zn and NBE emissions. Since the concentration of photogenerated holes is proportional to the excitation intensity, a higher temperature T₀ is needed at higher P_exc to activate nonradiative recombination channels. Figure 39b shows the I^PL(T) dependences and their fit with numerical solutions of rate equations for a p-type semiconductor with three types of defects: shallow donors D, radiative acceptors A (Zn_Ga), and unknown nonradiative donors S.

4.4.3. Two-Step Quenching

When two acceptor species with comparable concentrations coexist, two-step quenching by the TAQ mechanism is possible [261]. An example is shown in Figure 40a for a Zn-doped GaN sample contaminated with Mg. The first quenching step at T₁ occurs due to hole emission from the Mg_Ga acceptor (E_A = 0.2 eV) to the valence band, partially unblocking the nonradiative channel. An abrupt drop at T₂ (the second step) is caused by thermal emission of holes from the Zn_Ga acceptor (E_A = 0.4 eV) to the valence band and complete activation of the nonradiative channel. Both T₁ and T₂ are tunable with P_exc.

4.4.4. Superlinear Excitation Intensity Dependence

The excitation intensity dependences in samples exhibiting the TAQ mechanism demonstrate strongly superlinear behavior [262]. Figure 40b shows the quantum efficiency of the BL_Zn band at selected temperatures. In contrast to a linear I^PL(P_exc) dependence in conductive n-type GaN samples, PL intensity sharply increases at a critical P_exc, which itself increases with temperature. The TAQ and superlinear rise in PL intensity represent two aspects of the same underlying mechanism: the suppression or reactivation of nonradiative recombination channels as a function of carrier population dynamics.

4.4.5. Other PL Bands in Zn-Doped GaN

Early studies of Zn-doped GaN reported, in addition to BL_Zn at 2.87 eV, three other PL bands (at 2.6, 2.2, and 1.8 eV), attributed to Zn-related defects [263,264]. The 2.6 eV band appeared as a shoulder on the low-energy side of the BL_Zn band and is likely the BL_Zn band red-shifted due to local electric fields (shifts by up to 0.2 eV were observed for other PL bands with increasing P_exc in [263]). Note that the BL_Zn band may red-shift by up to 0.8 eV with decreasing P_exc in SI GaN:Zn and could be confused with other PL bands [54]. The 2.2 eV band is most likely the YL1 band, caused by carbon contamination. The band at 1.8 eV aligns with predictions from first-principles calculations for the Zn_GaV_N complex [36]. A similar PL band with a maximum at 1.8 eV has also been observed in Zn-doped GaN grown by HVPE [36]. However, careful analysis of SSPL and TRPL indicated that it is the RL3 band, likely caused by contamination with Fe (Section 3.2.3). It is also probable that the Zn_GaV_N complex is a nonradiative defect [265]. Thus, BL_Zn with a maximum at ~2.9 eV is the only PL band in GaN that can be reliably attributed to Zn.

4.5. Cadmium (BL_Cd)

The Cd_Ga acceptor, with the −/0 level at 0.55 eV above the VBM [48,59,266], produces the blue (BL_Cd) band with a maximum at 2.7 eV (Figure 41a). Lagerstedt and Monemar [59] observed a ZPL at 2.937 eV at T = 1.6 K, followed by phonon replicas. Assuming that this ZPL originates from DAP transitions involving shallow donors and Cd_Ga acceptors, the Cd_Ga acceptor ionization energy was estimated to be E_A = 0.55 eV [48], consistent with earlier assessments [266]. In conductive n-type GaN:Cd (overcompensated with Si_Ga donors), the BL_Cd band quenches at T > 310 K (Figure 41b). The quenching can be fitted using Equation (2) with E_A = 0.435 eV, a value slightly lower than the low-temperature spectroscopic value of 0.55 eV [48,59,266].

The electron- and hole-capture coefficients for the Cd_Ga acceptor have been estimated from TRPL and SSPL analyses to be C_n = 2.6 × 10⁻¹³ and C_p = 3 × 10⁻⁷ cm³s⁻¹, respectively [48]. The PL properties of Cd_Ga resemble those of Zn_Ga [48,59,266]. The attribution of the BL_Cd band to Cd has also been confirmed via PL experiments involving radioactive isotopes [267,268]. In these experiments, the decay of the ¹¹¹Ag isotope to ¹¹¹Cd (half-life = 7.6 days) correlated with the emergence of the BL_Cd band at the same temporal rate.

First-principles calculations using HSE hybrid functional, parametrized to fulfill the generalized Koopmans’ conditions, predict a ZPL at 3.0 eV and a band maximum at 2.57 eV, in close agreement with experimental observations [235]. Additionally, these calculations predict a yellow band at 2.12 eV, attributed to electron transitions from the CBM (or an excited state close to it) to the 0/+ level of the Cd_GaV_N complex. However, this band has not been observed experimentally [48].

4.6. Calcium (GL_Ca, RL_Ca)

The Ca_Ga is a deep acceptor in GaN, with the −/0 level at 0.50 ± 0.02 eV above the VBM [49]. It causes the green luminescence band (GL_Ca) with a maximum at 2.5 eV [49,87,269]. In the presence of nitrogen vacancies, Ca_GaV_N complexes form, producing a red luminescence (RL_Ca) band with a maximum at 1.82 eV [36]. The properties of both bands are reviewed below.

4.6.1. Ca_Ga-Related GL_Ca Band

The GL_Ca band is typically observed in GaN implanted with Ca [49,87,269], although it may also appear in undoped GaN grown at low temperatures due to unintentional contamination with Ca [49]. The PL band is broad and structureless, and its shape can be modeled using Equation (6) with parameters listed in Table 2 (Figure 42a).

HSE hybrid functional calculations, tuned to satisfy the generalized Koopmans’ condition, accurately reproduce the GL_Ca band features [235]. In particular, they predict ħω_max and ZPL at 2.53 eV and 3.08 eV, closely matching the experimental values of ħω_max = 2.5 eV and E₀ = 3.0 eV. Note that other HSE parametrizations yield poorer agreement, predicting: ħω_max = 2.23 eV and E₀ = 2.80 eV [49], or ħω_max = 2.07 eV and E₀ = 2.49 eV [270,271].

In SI GaN:Ca samples, the quenching of the GL_Ca band by the TAQ mechanism is observed at T > 200 K [49]. In n-type GaN:Ca samples, the GL_Ca quenching occurs by the Schön–Klasens mechanism [74]. The following parameters of the Ca_Ga acceptor have been determined from SSPL and TRPL dependences: E_A = 0.49 ± 0.01 eV, C_p = (6 ± 2) × 10⁻⁷ cm³s⁻¹, and C_n = (9.5 ± 2) × 10⁻¹⁴ cm³s⁻¹ [49].

4.6.2. GL_Ca Band in Undoped GaN

The GL_Ca band was also found in undoped GaN grown by MBE on freestanding GaN substrates (Figure 42b). It was originally referred to as the aquamarine luminescence (AL) band [153]. Young et al. [155] demonstrated that undoped GaN samples grown by the MBE method may contain Ca concentrations as high as 10¹⁸ cm⁻³. From the analysis of excitation intensity dependences, the concentrations of Ca_Ga defects in MBE GaN samples analyzed in [49,153] (Figure 42b) were estimated to be 2 × 10¹⁶ cm⁻³ (MBE-1) and 6 × 10¹⁴ cm⁻³ (MBE-2). The GL_Ca band is strong even for low concentrations of Ca because the Ca_Ga acceptors efficiently capture photogenerated holes.

4.6.3. Ca_GaV_N-Related RL_Ca Band

In SI GaN samples implanted with Ca, the RL_Ca and GL2 bands are observed at 1.82 and 2.33 eV, respectively (Figure 43a). The GL2 band originates from isolated V_N (Section 3.3.2), while the RL_Ca band is attributed to the Ca_GaV_N complex [36,49]. The RL_Ca band arises from electron transitions between an excited state located 0.25 ± 0.05 eV below the CBM and the 0/+ level of the Ca_GaV_N donor, which lies at about 1 eV above the VBM [36]. The PL decay after a laser pulse is exponential, with τ ≈ 2 ms at T = 18–160 K. This PL lifetime is three orders of magnitude longer than for other AV_N complexes (A = Be_Ga and Mg_Ga), suggesting a forbidden transition. At higher temperatures, the RL_Ca intensity and its lifetime decrease with an activation energy of about 0.25 eV (Figure 43b). The PL quenching is explained by thermal emission of electrons from the excited state to the conduction band, followed by capture by nonradiative defects.

In contrast to other AV_N complexes (Section 3.2.2, Section 4.2.4, and Section 4.3.5), but similar to isolated V_N (Section 3.3.2), the RL_Ca band is relatively narrow (W₀ = 0.25 eV). First-principles calculations, using the HSE hybrid functional tuned to fulfill the generalized Koopmans’ condition [36], disagree with the experimental results. Specifically, the Ca_GaV_N-related PL band is predicted to be broad (W₀ ≈ 0.48 eV), and the calculated optical transition level is expected at 1.47 eV below the CBM, whereas the experimental value (after correcting for the excited state location) is 2.07 eV.

4.7. Mercury (GL_Hg)

The Hg_Ga acceptor is responsible for the green luminescence (GL_Hg) band with a maximum at ~2.5 eV [87,267,272] or, more precisely, at 2.44 eV (Figure 44a) [48]. A sharp intensity drop at 2.73 eV (marked by an arrow in Figure 44a) is attributed to the GL_Hg band ZPL [48]. Based on this assignment, the −/0 level of Hg_Ga is estimated at 0.77 eV above the VBM. From the GL_Hg band quenching at T > 500 K (Figure 44b), E_A = 0.62–70 eV and C_p = (1–5) × 10⁻⁷ cm³s⁻¹ have been determined for the Hg_Ga acceptor [48]. From TRPL experiments, the electron-capture coefficient was found as C_n = 3 × 10⁻¹³ cm³s⁻¹ [48].

The assignment of the ~2.5 eV band to Hg was also confirmed in PL experiments involving radioactive isotopes [267]. Specifically, in samples doped with ¹⁹⁷Hg, which decays to ¹⁹⁷Au with a half-life of 64 h, the GL_Hg band diminished at the same rate, affirming its origin from Hg_Ga centers.

HSE hybrid functional calculations tuned to fulfill the generalized Koopman’s condition, reproduce the shape and position of the Hg_Ga-related GL_Hg band relatively well [48,235]. The band maximum and ZPL are calculated at 2.45 eV and 2.83 eV, respectively, in close agreement with experimental observations (2.44 eV and 2.73 eV) [235].

4.8. PL from Other Defects

4.8.1. Isoelectronic Impurities

Isoelectronic defects, As_N and P_N, are responsible for the BL_As and BL_P bands with maxima at 2.6 and 2.9 eV, respectively. In high-quality GaN samples, both bands exhibit sharp ZPLs (at 2.952 eV for BL_As and 3.197 eV for BL_P) followed by phonon replicas [57]. These PL bands are often interpreted as excitons bound to isoelectronic defects [57]. Note that exciton binding energy cannot be directly compared to charge transition levels. For example, the −/0 transition level of Zn_Ga lies 400 meV above the VBM and is responsible for the BL_Zn band with a maximum at 2.9 eV and ZPL at 3.10 eV, whereas an exciton bound to Zn_Ga, with a binding energy of ~24 meV, produces a line at 3.455 eV in GaN [16].

According to early DFT calculations, the As_N defect is neutral in n-type GaN (as expected for isoelectronic impurities), and it acts as a donor with a 0/+ transition level at 0.31 eV [273] or 0.41 eV [274] above the VBM. Similar to other deep donors in GaN, after capturing a photogenerated hole, an electron can be captured at an excited state of As⁺ near the CBM, followed by an internal transition that produces the BL_As band. Gil et al. [275] observed exponential decay of the blue band (at ~2.6 eV) in MBE-grown GaN:As, with τ₀ = 92 ns at T = 8 K. Assuming the excited state lies ~0.02 eV below the CBM [55], and using the ZPL at 2.952 eV (with E_g ≈ 3.512 eV) [57], the 0/+ level of As_N can be estimated to lie 0.54 eV above the VBM. Thermal quenching of the BL_As band with an activation energy of ~50 meV at temperatures between 100 and 300 K was attributed to thermal release of electrons from As_N [276].

Similarly, the 0/+ level of P_N can be calculated at 0.29 eV above the VBM from the experimentally observed ZPL for the BL_P band, closely matching early DFT predictions (0.22 eV) [274]. The related BL_P band is quenched with an activation energy of 0.28 eV at T > 290 K [58], consistent with thermal release of holes bound to P_N.

Interestingly, the intensity of the BL_As band in GaN:As samples varies significantly between reports. In HVPE GaN implanted with As ([As] = 10¹⁷ cm⁻³), the BL_As band was well resolved (yet ~3000 times weaker than the NBE emission at P_exc = 0.26 Wcm⁻²), and no other defect-related PL bands were observed between 2.4 and 3.4 eV [57]. In contrast, As-doped GaN samples grown by MOCVD with [As] = (0.3–5) × 10¹⁷ cm⁻³ (from SIMS) remained conductive n-type with n = (1–5) × 10¹⁷ cm⁻³, and no BL_As band could be found [277,278]. In Ref. [277], the PL spectra were dominated by the C_N-related YL1 and Mg_Ga-related UVL bands (which could be recognized by their positions and shapes). The YL1 intensity decreased by a factor of ~100, while the UVL intensity increased by ~100-fold with increasing As concentration [277]. From these results, one could conclude that As either contributes to the UVL band or acts as a nonradiative defect. In fact, it is likely that the BL_As was too weak in that work because As_N donors in n-type material are expected to capture photogenerated holes very inefficiently compared to negatively charged C_N and Mg_Ga acceptors. The C, Mg, and possibly some nonradiative defects could be introduced due to specific growth or doping conditions. We observed relatively strong YL1 and UVL_Mg bands in GaN samples with concentrations of C and Mg below the SIMS detection limit [83].

4.8.2. PL from Implantation Damage

GaN, implanted with various elements, becomes non-luminescent due to the creation of numerous nonradiative defects. For example, simulations indicate that implantation of Zn ions into GaN with a fluence of 10¹⁶ cm⁻² creates ~10²² cm⁻³ of V_Ga and over 10²³ cm⁻³ of V_N defects [279]. Post-implantation annealing partially repairs this damage, though some defects remain. Pankove and Hutchby [87] implanted 35 elements into GaN and observed yellow and red PL bands in nearly all samples after annealing for one hour at 1000–1050 °C in flowing ammonia. Although the YL band at 2.15 eV was thought to be implantation-damage-related [87], it is highly likely that it was the C_N-related YL1 band due to contamination with C (except for the YL_Be band in Be-implanted GaN). The red band at ~1.75 eV, however, was linked to a defect forming during thermal annealing (appearing even in unimplanted GaN) [87]. Chen and Skromme [57,280] investigated GaN implanted with various elements and attributed a similar red band (at 1.73–1.78 eV) to implantation-induced damage, as the band was absent in annealed unimplanted GaN.

We observed a red band with a maximum at ~1.6 eV (Positions of the broad band maxima reported by various authors must be compared with caution. In particular, the RL5 band maximum redshifts by about 0.1 eV after applying the λ³ correction) (denoted RL5) in GaN implanted with Cd, Ca, Hg, F, or Cl ions (Figure 45a). Due to limitations of the measurement setup, the full RL5 band shape could not be studied at ħω < 1.5 eV. Nevertheless, its consistent appearance in GaN implanted with various ions suggests a common origin—implantation damage.

The RL5 intensity decreases modestly (by a factor of 2–3) with increasing temperature from 18 to 300 K. At least in the cases of implantations with F, Cl, or co-implantation with Be and F, the RL5 band was observed only in conductive n-type GaN samples (HVPE GaN with [Si] ≈ 3 × 10¹⁸ cm⁻³) [214]. TRPL measurements reveal nonexponential decay of RL5 at T = 18–100 K (as t^−m with m = 0.8–1.0 between 0.02 and 1000 μs), while nearly exponential decay was observed for YL1 and BL1 in the same samples, with lifetimes corresponding to n = 10¹⁸ cm⁻³. The RL5 band could not be excited by the 2.805 eV line of the HeCd laser, unlike the RL_C band in C-doped GaN (Section 4.1.3). It is likely that the RL5 band is caused by deep DAP transitions involving implantation-induced defects.

In SI GaN implanted with F, Cl, or co-implanted with Be and F, an orange luminescence (OL1) band with a maximum at ~1.9 eV was observed [214]. The OL1 was particularly strong in PL spectra of SI GaN:Be,F with [Be] < [F] (Figure 45b). The same OL1 band also appears in GaN samples implanted with only F, and possibly the same band contributes to the PL spectrum from SI GaN implanted with Cl (Figure 45b). The defect responsible for OL1 is unlikely to include Be, as the band is absent in GaN:Be,F samples with [Be] > [F] or in Be-implanted GaN [151]). It may involve F (because the OL1 band appears only when [Be] < [F] or in F-implanted GaN). However, the OL1 band could also originate from a defect unrelated to F if the OL1 band in F- and Cl-implanted samples is identical, which is premature to conclude because the OL1 band in Cl-implanted GaN overlaps with the C_N-related YL1 band and is poorly resolved. First-principles calculations suggest that the OL1 band may originate from the V_GaF_N complex, with transitions via its 0/+ level at about 1.0 eV above the VBM (if the Fermi level is lower than ~2 eV above the VBM) [151]. However, in n-type GaN, the F_NV_Ga defect is predicted to be negatively charged and is not expected to contribute to visible PL. The identity of the shoulder at ~2.5 eV in Cl-implanted GaN (the GL_X band in Figure 45b) remains unresolved.

5. Advances in Defect-Related Photoluminescence in GaN Since 2005

This section reviews key developments in understanding defect-related PL in GaN since 2005, focusing on the identification of PL bands, quenching mechanisms, recombination processes, multi-charged defects, and advances in computational modeling. While significant progress has been made, persistent challenges remain in defect identification and establishing a quantitative understanding of their optical activity.

5.1. PL Bands in Undoped GaN

As of 2005, the origins of several major PL bands in undoped GaN were under debate. In particular, the YL band at 2.2 eV was commonly attributed to carbon-related defects (excluding isolated C_N) or to V_Ga-related complexes, such as V_GaO_N. The UVL band at 3.28 eV was linked to a variety of candidates, including Mg_Ga, C_N, Si_Ga, and structural defects. The RL2 and GL2 bands in SI GaN were incorrectly assigned to Ga_N antisite defects, while the GL1 band observed in HVPE Ga_N was interpreted as a secondary emission from YL-related centers. The BL2 band in high-resistivity GaN was often linked to Ga vacancies or confused with the Zn-related BL1 band.

Recent studies have clarified the assignments of most PL bands (Table 1). The YL band (YL1) is now firmly attributed to the C_N acceptor, which forms readily due to residual carbon contamination. Its -/0 and 0/+ charge transition levels give rise to the YL1 and BL_C bands, respectively, in agreement with modern theoretical predictions. The UVL band (UVL_Mg) at ~3.28 eV is unambiguously attributed to Mg_Ga; no evidence supports the presence of other shallow acceptors in undoped GaN (an exception is the shallow Be-related acceptor in Be-doped GaN). The BL2 band originates from the C_NH_i complex, which can dissociate under UV exposure, subsequently giving rise to the YL1 band. The GL2 and RL2 bands are attributed to V_N-related centers, specifically isolated V_N and AV_N complexes, respectively.

In conductive n-type GaN, PL bands, such as RL1, YL1, BL1, and UVL, result from electron transitions involving acceptor levels. Hole capture at these acceptors occurs without an energy barrier. At low temperatures, DAP-type recombination occurs, involving these acceptors and shallow donors. Above 50 K, transitions from the CBM become dominant. These PL bands are strong due to efficient hole capture by negatively charged acceptors. In high-resistivity or SI GaN samples, competition for photogenerated electrons enables PL from deep donors, such as RL2, GL2, BL2, via internal transitions.

5.2. Mechanisms of PL Quenching

Before ~2010, quenching of PL from defects in semiconductors was attributed to two mechanisms, both modeled with Equation (2): (i) conversion of a radiative defect to a nonradiative state (Seitz–Mott mechanism), where the activation energy E_A represents a potential barrier in adiabatic potentials, and (ii) thermal emission of bound carriers to the conduction or valence band, followed by recapture at nonradiative defects (Schön–Klasens mechanism), where E_A in Equation (2) is an ionization energy. In fact, no examples of the first mechanism can be found for defects in GaN. The quenching of the GL2 and RL2 bands, erroneously explained with the Seitz–Mott mechanism [16], is now attributed to thermal emission of electrons from an excited state ~0.1 eV below the CBM to the conduction band (Section 3.2.2 and Section 3.3.2).

A significant development came in 2011 with the discovery of the TAQ mechanism, initially observed in Zn-doped GaN [52]. Although the I^PL(T) dependences could be formally fitted with Equation (2), the extracted parameters C and E_A are anomalously large, lacking physical meaning. Subsequent studies demonstrated that the TAQ mechanism is a general phenomenon, applicable to GaN doped with various acceptors, including Zn, Mg, C, Be, Cd, and Hg, as well as other SI semiconductors [74]. The essence of the TAQ mechanism is a conversion from population inversion at low temperatures to near-equilibrium population above a critical temperature, which increases with excitation intensity—hence the term “tunable”.

Furthermore, it is sometimes challenging to explain PL quenching and interpret associated activation energies. For example, when PL from acceptors in n-type GaN is quenched by the Schön–Klasens mechanism, the E_A found from fits with Equation (2) is often lower than the true ionization energy. This discrepancy can arise from inadequate experimental conditions (e.g., very high P_exc), nonexponential PL decay, or the presence of local electric fields [75].

An additional phenomenon, known as “negative thermal quenching”, where the PL intensity increases with temperature, has been observed and explained by a competition between radiative and nonradiative recombination channels for photogenerated carriers [53,81]. A special case of two-step quenching of the YL_Be band in Be-doped GaN samples is explained by a sudden reduction in light extraction efficiency from Be_Ga centers after temperature-activated reorientation of related defect dipoles (Section 4.2.2).

5.3. Radiative and Nonradiative Recombination

5.3.1. Internal Quantum Efficiency

While quantum efficiency is a key parameter to quantify PL, determining the EQE of PL remains technically challenging, and the IQE η cannot be measured directly. The EQE can be obtained using integrating sphere techniques, which require careful calibration and analysis [67,68,69,70,71]. IQE exceeds EQE by the light extraction efficiency, which depends on various sample-specific parameters, including surface morphology, crystal polarity, and refractive index contrast at interfaces.

Nevertheless, several phenomenological models have been developed to estimate the absolute IQE from temperature- or excitation-dependent PL measurements, particularly in samples exhibiting strong PL [53,81]. One such approach is based on analyzing the competition among radiative channels when an intense PL band (with a close to unity η) undergoes quenching via the Schön–Klasens mechanism. Under these conditions, the intensities of all other PL bands increase by a factor of R (the negative thermal quenching), and the absolute IQE of the quenched band can be expressed as η = 1 − R⁻¹ [53]. The method is particularly efficient in conductive n-type, where PL intensities are proportional to the product of hole-capture coefficients and defect concentrations [39]. Once absolute IQEs are found, the concentrations of defects responsible for specific PL bands can also be estimated [80]. While foundational concepts for quantifying PL in this manner were introduced earlier [16], these methods have been substantially refined and extended in recent studies [38,39,52,53,80,81,83].

5.3.2. Nonradiative Recombination

Nonradiative recombination in GaN originates from both point defects and extended structural defects, including dislocations, domain boundaries, interfaces, and surfaces. Point defects responsible for nonradiative recombination are typically deep-level centers characterized by strong electron–phonon coupling, where the recombination energy of electrons and holes is dissipated through multiphonon emission. Recent studies have also suggested that radiative defects may become nonradiative under high carrier concentrations or intense optical excitation via the TAAM recombination mechanism [185,281,282].

Structural defects, particularly threading dislocations, have long been implicated in nonradiative losses. Spatially resolved micro-CL and micro-PL studies consistently reveal reduced emission at dislocation sites, observed as “dark spots” in PL or CL maps [283,284,285]. The suppression of emission at these locations can be attributed to either nonradiative recombination at dislocation sites or local carrier depletion induced by electric fields from charged dislocations.

Phenomenological models of carrier recombination typically describe the recombination rate as a sum of parallel radiative and nonradiative processes, where each recombination channel is associated with a specific recombination center. Nonradiative recombination through a large number of unresolved pathways is commonly modeled by an effective deep-level defect characterized by empirical electron- and hole-capture coefficients, as well as an effective concentration [52,53].

5.3.3. Surface Effects on PL

The surface of GaN can significantly affect its PL, especially at elevated temperatures and in oxygen- or water-containing ambient. For example, the NBE intensity in undoped n-type GaN has been observed to increase by a factor of 3–14 after photoelectrochemical oxidation [286], and by 4–6 times after sulfide treatment [287]. In contrast, prolonged exposure to HeCd laser irradiation in air can reduce the NBE intensity due to photoinduced surface oxidation [288]. Under high-vacuum conditions at T = 10 K, however, continuous HeCd laser exposure enhances the NBE intensity, which is attributed to photoinduced desorption of surface oxygen [289]. Similarly, the YL1 intensity in SI GaN:C was found to decrease by a factor of ~300 in ambient air or oxygen compared to vacuum [290]. These observations illustrate the strong influence of surface conditions on PL, which are typically attributed to nonradiative recombination at surface states and/or changes in the width of the near-surface depletion region.

In n-type GaN, an upward band bending (~1 eV at room temperature) is observed due to the accumulation of negative charges at the surface [291,292,293]. The associated depletion region in such material extends up to ~0.1 μm (for n ≈ 10¹⁷ cm⁻³). Within this region, photogenerated electrons and holes are rapidly separated by the strong built-in electric field and subsequently recombine nonradiatively—a phenomenon described as the field-effect mechanism [294]. Modifying the surface charge changes the width of the depletion region and, consequently, the PL intensity. Although the minority hole diffusion length in GaN is short (0.2 µm or less [291,295]), accurate modeling of PL intensity variations must account for both carrier drift and diffusion within the depletion layer [296]. Nevertheless, in many GaN samples, the field-effect mechanism plays only a minor role. Instead, significant changes in PL intensity arise primarily from nonradiative recombination at surface states, the concentration of which depends on ambient atmosphere and surface treatment conditions [297]. High density of nonradiative defects near the surface can also significantly suppress PL. For example, mechanical polishing of freestanding GaN templates with diamond slurries, ending with ~1 μm particle size, reduced the PL intensity by four orders of magnitude despite minimal changes in band bending [123].

In p-type GaN, surface band bending is downward and can reach up to 2 eV at elevated temperatures [298,299]. However, the depletion region is narrow (<10 nm) because of the high concentration of uncompensated Mg acceptors. At low temperatures, band bending is expected to be small in conditions of PL (< 10 kT). Nevertheless, surface effects in such samples can still significantly influence the PL intensity and its temperature behavior. Notably, large shifts (up to 0.6 eV) of the UVL_Mg band with varying excitation power have been observed in Mg-doped GaN at low temperatures (Section 4.3.4). These shifts were attributed to diagonal electron transitions occurring within the near-surface depletion region [54,62].

5.4. Electronic Structure

5.4.1. Multi-Charged Defects

Transitions via different charge transition levels of multi-charged defects in GaN are expected to produce distinct PL bands. A well-established example is the C_N defect responsible for the YL1 and BL_C bands, associated with electron transitions via the −/0 and 0/+ levels, respectively [25,60] (Section 4.1.1). Preliminary results also suggest that the −/0 and 0/+ levels of the Be_Ga defect produce the YL_Be and BL_Be bands [61] (Section 4.2.5). In another case, the BL3 band, observed in HVPE GaN at high P_exc, is presumably a secondary emission from the RY3 defect, occurring after the capture of two holes. The GL1 band is a secondary emission from yet unknown defects.

Distinct charge transition levels for other multi-charged defects, such as V_Ga, V_N, and complexes containing these vacancies, have not been clearly identified in PL experiments. Attributions of the GL2 band to transitions via the +/2+ level of V_N and RL_A bands to transitions via the 0/+ level of AV_N complexes (with A representing cation acceptors) are also preliminary, as more than one transition level of a multi-charged defect may contribute to the observed PL bands.

5.4.2. Dual-Nature Defects

The concept of dual-nature defects, where a single charge state exhibits multiple transition levels due to different carrier localization configurations, has been theoretically proposed [206]. This phenomenon is believed to be potentially widespread in wide-bandgap semiconductors. Experimentally, however, dual-nature behavior has been unambiguously confirmed for only one defect in GaN: the Be_Ga acceptor [45]. In its neutral charge state, this defect exhibits two polaronic configurations, with the −/0 transition levels located at 0.35 and 0.39 eV above the VBM. In the higher-energy state (0.39 eV), the hole is localized on a neighboring nitrogen atom along the c-axis, whereas in the lower-energy state (0.35 eV), the hole is localized on one of the three basal-plane nitrogen atoms. Additionally, a third, shallow −/0 level at 0.24 eV above the VBM corresponds to a weakly localized hole. First-principles calculations also predict dual-nature behavior for other acceptors, including Mg_Ga [206,231,232,235], Zn_Ga [206,235], and Be_GaO_NBe_Ga complex [64]. To date, however, these predictions remain experimentally unverified, and PL associated with only shallow levels has been observed for these defects.

5.4.3. Excited States

Excited states associated with deep donors have recently been identified by PL for several centers in GaN, including C_NH_i (BL2), V_N (GL2), and AV_N complexes (RL_A bands with A = Be_Ga, Mg_Ga, and Ca_Ga). Donor-like states of multi-charged defects also exhibit excited states near the CBM, as observed for C_N (BL_C), Be_Ga (BL_Be), and RY3 center (BL3). Among acceptor-like defects, only the RY3 center exhibits an excited state near the VBM (Section 3.2.3). Excited states have also been predicted for multi-charged defects, such as V_GaO_N and V_GaH_i [118], though these states have not yet been directly confirmed experimentally.

An unusual behavior, where PL lifetime significantly increases with temperature, has been observed for the GL1 band. This effect is attributed to nonradiative capture of electrons via a ladder of excited states by the Lax mechanism and subsequent radiative recombination producing the GL1 band (Section 3.3.1). By analogy with the so-called giant traps in Ge and Si, the related defects have been termed optically generated giant traps.

5.5. Identification of Defects

5.5.1. Conventional Approaches

PL spectroscopy is an indispensable tool for identifying defect-related emission bands and probing their properties. However, it often fails to provide direct information about the chemical composition or atomic structure of the underlying defects. Historically, in undoped semiconductors and insulators, PL bands were typically attributed to native point defects (e.g., cation vacancies in crystals grown under anion-rich conditions), whereas in doped materials they were commonly linked to impurity dopants [300,301]. A widely used strategy for defect identification involves correlating PL intensities with impurity concentrations obtained from SIMS measurements. Another approach compares the positions and shapes of PL bands with theoretical databases generated from first-principles calculations to propose defect assignments.

However, extensive studies of GaN have revealed serious limitations of these approaches. In particular, the assumption that PL intensity scales linearly with defect concentration holds only under restricted conditions, such as low concentrations of radiative defects, weak excitation, and in conductive n-type material. As illustrated in Figure 46, the intensities of the UVL_Mg (UVL), BL_Zn (BL1), and YL1 bands are proportional, respectively, to the concentrations of Mg, Zn, and C impurities only up to ~10¹⁶ cm⁻³, where the IQE of these PL bands approaches unity. Note that the SIMS detection limit for these impurities is in the 10¹⁵–10¹⁶ cm⁻³ range. Beyond these limits, the lack of proportionality (and sometimes even anticorrelation) between PL intensity and impurity concentration often leads to erroneous defect assignments.

Modern first-principles calculations can predict the properties of point defects with relatively high accuracy (Section 5.6). When combined with reliable experimental data, they provide a powerful framework for defect identification in GaN. Although PL offers the most direct and accurate information on defects in GaN, complementary experimental techniques supply essential corroborative evidence. In particular, temperature-dependent Hall effect measurements have confirmed the spectroscopically found −/0 levels of the Be_Ga, Zn_Ga, and C_N acceptors in SI (p-type) GaN [215,260,302]. Photo-EPR studies of C-doped GaN have verified the model of the C_N acceptor (Section 3.1.2), for which an isotropic g-value of 1.987 ± 0.001 has been found [302,303,304]. It is worth noting that g factors for acceptors are generally expected to exceed the free-electron value (g_e = 2.0023) [122,216,305]; however, exceptions exist (including the case of C_N), and relying solely on the g-value for defect identification may lead to misassignments.

Capacitance-based techniques, such as DLTS and DLOS, have revealed numerous electrically active defects in GaN, providing key parameters, including thermal ionization energies and carrier-capture cross-sections [5,306,307]. For brevity, only a few examples, closely related to the PL data discussed in this review, are highlighted here. The presence of two charge states of the C_N defect has been conclusively verified by DLTS [26,184]. Horita et al. [308] identified the 0/+ level of V_N at 0.13 eV below the CBM and the −/0 level of N_i at 0.98 eV below the CBM in n-type GaN irradiated with 137 keV electrons. In similarly irradiated p-type GaN, a DLTS peak, corresponding to a hole trap with an ionization energy of 0.52 eV above the VBM, was observed and tentatively attributed to either the +/3+ level of V_N or the +/2+ level of N_i [309]. Zajac et al. [310] investigated Mg-doped p-type GaN grown by the AT method. Using Laplace-transform photoinduced transient spectroscopy, they revealed hole traps at 0.43–0.45 eV above the VBM, with hole-capture coefficients C_p ≈ 3 × 10⁻¹¹–10⁻¹⁰ cm³s⁻¹. These traps were attributed to the 3+/+ and 2+/+ transition levels of V_N. An electron trap at 0.6 eV below the CBM, detected by DLTS in Si-doped n-type GaN grown by MOCVD, was attributed to the Fe_Ga acceptor [311]. A Be-related electron trap with a level at 0.24–0.39 eV below the CBM was found by thermal admittance spectroscopy and DLTS in GaN implanted with radioactive ⁷Be isotopes [312], likely corresponding to the Be_i donor.

Despite these advances, correlating PL with DLTS (or other capacitance techniques) remains challenging [5]. In DLTS, activation energies correspond to carrier emission from a defect to the conduction band (electron traps) or to the valence band (hole traps), and are accompanied by measurements of electron or hole-capture coefficients (or capture cross-sections). This approach is conceptually similar to the extraction of E_A and C_p from PL quenching (Section 2.2.2), with the difference that DLTS detects both radiative and nonradiative defects. As with PL quenching, the uncertainties in extracted E_A and C_p may be significant. Moreover, both E_A and C_p may be temperature-dependent, and the activation energies measured by DLTS may differ from actual ionization energies if a capture barrier exists [101]. Although numerous electron and hole traps in GaN have been reported in DLTS studies [2,5,313], and databases of defect levels have been compiled [314], the large scatter in the reported parameters often makes it difficult to reliably correlate DLTS data with PL results.

5.5.2. Identification from Radioactive Isotopes

One of the most reliable methods for revealing the chemical origin of luminescence centers in GaN involves implantation of radioactive isotopes, where the parent or daughter nucleus is directly responsible for a specific PL band. As discussed in Section 4.5 and Section 4.7, the BL_Cd and GL_Hg bands were conclusively attributed to Cd and Hg, respectively, through the decay of implanted ¹¹¹Ag isotope into ¹¹¹Cd, and ¹⁹⁷Hg isotope into ¹⁹⁷Au [267,268]. In the same experiments, PL bands near 1.5 eV with characteristic fine structures were assigned to Ag and Au impurities.

From decays of radioactive ⁷²Se and ⁷¹As isotopes, undergoing chemical transmutation, the BL_As band, with the ZPL at 2.945 eV and characteristic phonon-related fine structure, was confirmed as originating from As_N. Additional PL bands at 1.49 eV and 3.398 eV were attributed to recombination centers involving Se and Ge, respectively [315]. From the decay of radioactive ¹⁹¹Pt isotopes, sharp lines at 1.461, 1.446, and 1.273 eV, followed by phonon replicas, were attributed to Pt [316].

5.5.3. Confidence Levels

The defect attributions summarized in Table 1 represent the current state of understanding and are subject to change as new experimental and theoretical evidence emerges. Nonetheless, the following confidence levels reflect the author’s assessment.

• High Confidence (90–99%): YL1 and BL_C (C_N), UVL or UVL_Mg (Mg_Ga), BL1 or BL_Zn (Zn_Ga), YL_Be and UVL_Be3 (Be_Ga), BL2 (C_NH_i), BL_Ca or AL (Ca_Ga), BL_Cd (Cd_Ga), GL_Hg (Hg_Ga).
• Moderate Confidence (50–80%): GL2 (+/2+ level of V_N), RL_Mg (+/0 level of Mg_GaV_N), RL_Ca (+/0 level of Ca_GaV_N), RL_Be (+/0 level of Be_GaV_N), BL_Mg (Deep DAP), BL_As (As_N), BL_P (P_N), UVL_Be (Be_GaO_NBe_Ga). The V_Ga, V_GaO_N, V_GaH_i, Be_GaO_N, C_NO_N, and C_NSi_Ga defects do not contribute to PL, at least at ħω > 1.5 eV.
• Low Confidence (20–40%): YL2, OL3, and RL4 (V_GaxO_NyH donors with x, y = 1,2), RL_C (tri-carbon complex), BL_Be (0/+ level of Be_Ga).
• Speculative (<10%): RL3, YL3, and BL3 (Fe_Ga or Fe_Ga-containing complex), RL1 and GL1 (Cl), RL2 (AV_N, with A being an acceptor other than Be, Mg, or Ca), GL_Be (Be-containing complex), RL5 (unknown defect from implantation damage), OL1 (F or implantation damage-related defects).

5.6. Advances in First-Principles Calculations

Early first-principles calculations of defects in semiconductors relied on local or semi-local approximations within DFT, which significantly underestimated the calculated bandgap and required corrections that introduced large uncertainties in defect levels [17,21,22,317]. As a result, inaccurate predictions of defect transition levels, combined with the limited reliability of experimental identification methods, often led to incorrect assignments of PL bands.

In recent years, major progress has been made in improving the accuracy of defect calculations in GaN and other wide-bandgap semiconductors [318]. The adoption of hybrid functionals, particularly the widely used HSE functional [319], has provided a practical compromise between computational cost and accuracy. By incorporating a portion of Hartree–Fock exchange energy, these methods yield more reliable predictions of defect formation energies and transition levels. A common tuning of the HSE functional includes adjusting the fraction of Hartree-Fock exchange to 0.31, along with a range separation parameter of 0.2 Å⁻¹, to reproduce the experimental GaN bandgap of 3.5 eV [24,182,234,320]. An alternative approach is to tune the HSE functional using the Koopmans’ theorem, which ensures that the self-interaction energy in the defect state orbitals is canceled by wavefunction relaxation [232,235,321]. While this improves defect transition energies referenced to the VBM, it also tends to underestimate the bandgap. Since different parametrizations can yield different outcomes, careful and consistent calibration is essential [104]. Most calculations employ periodic boundary conditions in supercells, which require a posteriori corrections to the total energy. The most common correction is the Freysoldt-Neugebauer-Van de Walle (FNV) [322,323] scheme.

Despite these improvements, theoretical predictions of PL band maxima and their ZPLs still exhibit typical uncertainties of 0.1–0.5 eV [235]. Overconfidence in theoretical predictions and the unreliability of some experimental data continue to hinder accurate defect identification. In practice, many reported assignments are based on a superficial agreement between calculated transition energies and experimental PL maxima or DLTS peaks [96,103,324]. Given the large number of unidentified PL bands and traps in GaN and the even greater number of theoretically predicted transitions via all possible defects, the likelihood of accidental matches is high. To improve reliability, PL band identification must go beyond a formal energy comparison. Detailed spectroscopic analysis (which includes revealing ZPL and fine structure), consideration of temperature dependence, recombination dynamics, isotope effects, and corroborating evidence from complementary methods (e.g., DLTS, Hall effect, ODMR, PAS) are essential.

A case study involving the Be_Ga acceptor highlights both the progress and pitfalls of theory-experiment comparison [45,46]. Although first-principles theory correctly predicted the dual nature of this acceptor [206], advanced HSE hybrid functional calculations suggested that its polaronic states should produce a PL band with a maximum at 1.67–1.80 eV [207,208,209,210]. The closest match for this prediction would be the RL_Be band at 1.77 eV, observed in some Be-doped GaN samples (Section 4.2.4). However, comprehensive PL studies conclusively demonstrated that the polaronic states of Be_Ga are instead responsible for the YL_Be band with a maximum at 2.15 eV [45].

6. Conclusions

Substantial progress has been made in recent years toward understanding PL from defects in GaN. Most notably, the origin of the long-debated yellow band (YL1) has now been definitively resolved. In the majority of undoped GaN samples, YL1 arises from unintentional carbon contamination and is associated with electron transitions from the CBM (or from shallow donors at T < 50 K) to the C_N acceptor. The discovery of ZPLs for the YL1 and BL_C bands at 2.59 eV and 3.15 eV, respectively, enabled precise determination of the C_N defect’s −/0 and 0/+ charge transition levels: at 0.916 ± 0.003 and 0.33 ± 0.01 eV above the VBM in the low-temperature limit. Several other PL bands in undoped GaN have also been reliably identified, including the BL2 band at 3.0 eV (attributed to C_NH_i) and the GL2 band at 2.33 eV (associated with V_N).

To facilitate consistent classification and discussion, a new nomenclature has been introduced, in which PL bands are designated and recognized according to their peak position (or color), shape, and other distinctive properties (Table 1, Table 2 and Table 3). The accurate identification of PL bands requires careful experimental characterization, since band positions and shapes may vary substantially with temperature and excitation intensity, particularly in semi-insulating samples.

The temperature dependence of PL has long been used to estimate defect ionization energies, in a manner analogous to the DLTS method. However, this approach is valid only when PL quenching follows the Schön–Klasens (multicenter) mechanism. To date, no clear cases of the Seitz–Mott (one-center) mechanism have been identified in GaN. Instead, a third mechanism—tunable and abrupt quenching—has been found for many defects in semi-insulating GaN. This abrupt quenching occurs at a critical temperature T₀, which increases with excitation intensity. The phenomenon is reminiscent of a phase transition, in which population inversion and photo-induced n-type conductivity at T < T₀ are replaced by near-equilibrium carrier population and p-type conductivity at T > T₀.

Recent PL studies have also elucidated the electronic structures of several important defects in GaN. In particular, the theoretically predicted dual nature of the Be_Ga acceptor has been experimentally confirmed. Three distinct −/0 transition levels, corresponding to different hole localizations, have been identified for the Be_Ga acceptor. The growing body of high-quality experimental data from PL studies now provides a critical foundation for refining first-principles calculations, ultimately aiming at reliable predictions of defect properties in GaN and other wide-bandgap semiconductors.