Systematic study of shockley-read-hall and radiative recombination in GaN on Al2O3, freestanding GaN, and GaN on Si

Here we study and correlate structural, electrical, and optical properties of three GaN samples: GaN grown by metalorganic chemical vapor deposition on sapphire (GaN/Al2O3), freestanding GaN crystals grown by the high nitrogen pressure solution method (HNPS GaN), and GaN grown by hydride vapor phase epitaxy on silicon (GaN/Si). Defect and impurity densities and carrier concentrations are quantified by x-ray diffraction, secondary mass ion spectroscopy, and Hall effect studies, respectively. Power-dependent photoluminescence measurements reveal GaN near-band-edge emissions from all samples having mixtures of free exciton and band-to-band transitions. Only the defect luminescence in the GaN/Si sample remains unsaturated, in contrast to those from the HNPS GaN and GaN/Al2O3 samples. Carrier lifetimes, extracted from time-resolved photoluminescence measurements, and internal quantum efficiencies, extracted from temperature-dependent photoluminescence measurements, are used to extract radiative and nonradiative lifetimes. Shockley–Read–Hall (A) and radiative recombination coefficients (B) are then calculated accordingly. Overall, the A coefficient is observed to be highly sensitive to the point defect density rather than dislocation density, as evidenced by three orders of magnitude reduction in threading dislocation density reducing the A coefficient by one order of magnitude only. The B coefficient, while comparable in the higher quality and lowly doped GaN/Al2O3 and HNPS GaN samples, was severely degraded in the GaN/Si sample due to high threading dislocation density and doping concentration.


Introduction
Gallium nitride (GaN) based devices find use in a wide range of photonics applications: Ultraviolet (UV) photodetectors [1], light emitting and laser diodes [2], and p-i-n betavoltaic cells [3]. The limited availability and high cost of freestanding substrates necessitates that GaN be heteroepitaxially grown on lattice-mismatched non-native substrates (i.e. sapphire, silicon carbide, and silicon). Such lattice mismatch generates high threading dislocation density (TDD ∼10 8 -10 10 cm −2 ) [4], which creates current leakage paths and non-radiative recombination centers in devices [5,6]. Point defects such as vacancies and impurities (whose concentrations are typically dominated by material growth chemistry and conditions), have also been shown to degrade device performance [7]. The quantification of the effect of threading dislocations and point defects in GaN on recombination characteristics is important for the design of efficient GaN-based photonic devices.
In this study, structural, electrical, and optical properties of GaN crystals grown by multiple techniques (i.e. metalorganic chemical vapor deposition (MOCVD), high nitrogen pressure solution (HNPS), and hydride vapor phase epitaxy (HVPE)) and on several common substrates (freestanding GaN, Al 2 O 3 , Si) are experimentally studied. Shockley-Read-Hall and radiative recombination in GaN on Al 2 O 3 , freestanding GaN, and GaN on Si samples are systematically studied and compared. We found the A coefficient to be strongly correlated to point defect density rather than TDD, while the B coefficient was found to be constant except for TDD > 10 10 cm −2 and doping concentration >5 × 10 18 cm −3 .

Experiment
Three GaN samples were studied in this work: a 5 µm thick GaN layer grown by MOCVD on sapphire (GaN/Al 2 O 3 sample), a 325 µm thick freestanding GaN crystal grown by the HNPS method (HNPS GaN sample), and 500 nm thick GaN grown by HVPE on silicon with a 200 nm thick AlN buffer layer (GaN/Si). Growth conditions have been reported in the literature previously [8][9][10]. Structural characterizations (i.e. x-ray diffraction and secondary mass ion spectroscopy measurements) were conducted to quantify the defect and impurity densities. Electrical characterizations (i.e. van der Pauw Hall measurements) were conducted to extract the free carrier type and concentrations. Finally, optical characterizations (i.e. temperature-, time-resolved-, and power-dependent-photoluminescence measurements) were conducted to extract internal quantum efficiencies, carrier lifetimes, and A and B recombination coefficients.

Structural characterization
Symmetric (002) and asymmetric (102) ω scans of GaN were conducted using a PANalytical Philips X'pert MRD System with 0.154056 nm Cu K-alpha 1 source to quantify the threading dislocation density (TDD) of each sample. Densities of screw (TDD screw ) and edge type (TDD edge ) dislocations were calculated by inputting experimentally measured (002) and (102) full-width-at-half-maximum (FWHM), β 002 and β 102 , into the following equations [11,12]: where b edge and b screw are the Burgers vector lengths of 0.3189 and 0.5185 nm for edge-and screw-type dislocations, respectively, and β 002 and β 102 are in radians. Total TDD is found by summing TDD edge and TDD screw , which totals to (2.93 ± 0.02) × 10 8 , (2.8 ± 0.1) × 10 7 , and (5.59 ± 0.1) × 10 10 cm −2 for the GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples studied in this work (table 1). Secondary Ion Mass Spectroscopy (SIMS) measurements were used to determine the concentrations of Si, H, C, and O impurities in each GaN sample. A Physical Electronics TRIFT III Time of Flight SIMS with a 3 kV Cs + ion beam was utilized. The detector was set up to detect the negative secondary atomic ions, Si -, H -, C -, and O -, and the detection limits were 1 × 10 15 , 7 × 10 16 , 5 × 10 15 , and 5 × 10 15 cm −3 for Si, H, C, and O, respectively. For the GaN/Al 2 O 3 sample, H and C were found to be the dominant impurities with concentrations of 2.4 and 1.3 × 10 17 cm −3 , respectively. For the HNPS GaN sample, Si was identified as the dominant impurity with a concentration of 3.0 × 10 17 cm −3 . For the GaN/Si sample, Si, H, and C were found to be in the 10 17 cm −3 range (table 1).

Electrical characterization
Room temperature free electron concentration (n 0 ) and Hall mobility (µ n ) of each sample were determined by Hall effect measurements in Van der Pauw configuration using an Accent HL5500 PC Hall effect measurement system. Square pieces of each sample were diced off and liquid In-Ga melt was deposited on each corner to serve as electrical contacts. Mobilities of 208, 699, and 51 cm 2 V −1 × s were measured for the GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples, respectively. The µ n decreased significantly with increasing TDD in the GaN samples as dislocations scatter carriers and degrade mobility severely when in high concentrations [13]. The n 0 were found to be 1.3 × 10 17 , 2.3 × 10 17 , and 6.5 × 10 18 cm −3 for the GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples, respectively. Table 1 tabulates Hall-effect, XRD, and SIMS data.

Optical characterization
Power-dependent photoluminescence (PDPL) measurements were performed to investigate the nature of the GaN near-band-edge (NBE) emissions at room-temperature. A frequency-quadrupled continuous-wave Nd:YAG (266 nm) laser with a spot size of ∼1800 µm 2 was implemented, and laser power (P Laser ) was varied from 0.1 to 3.5 mW via a crossed polarizer setup. This yielded an incident excitation intensity range of ∼5-195 W cm −2 . Sample luminescence was then collected via an Acton SP-300i spectrometer with 300 grooves mm −1 grating blazed at 500 nm and a CCD camera. The spectrometer resolution was 0.2 nm and, after calibrating the PL spectra to the UV peaks of a HgNe lamp, peak positions were accurate to within ±0.01 eV. The steady-state carrier concentration from the PL excitation was determined by first calculating the generation rate G, which can be found via [14]: where P Laser is from 0.1-3.5 mW, α is the absorption coefficient of GaN at 266 nm and is equal to 2.24 × 10 5 cm −1 [15], R is the reflectivity and was 0.11 for all 3 samples, A spot is the laser spot size, and E photon is 4.66 eV for 266 nm excitation. This yields a maximum G of 4.9 × 10 25 cm −3 s −1 for the highest excitation condition and, when multiplied by the effective carrier lifetimes determined later in the time-resolved experiment, yields a maximum steady-state carrier concentration of <1.7 × 10 16 cm −3 for all samples. Figure 1 plots the room-temperature PDPL spectra for GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples, respectively, as P Laser was increased from 0.1 to 3.5 mW. For the GaN/Al 2 O 3 sample in figure 1(a), a yellow luminescence (YL) band was observed with a peak at ∼2.25 eV, a slight blue luminescence (BL) band was observed around 2.8 eV, an ultraviolet luminescence (UVL) shoulder was observed at ∼3.25 eV, and the NBE emission was observed at 3.42 eV. The YL band in the GaN/Al 2 O 3 sample was attributed to a combination of intrinsic V Ga and extrinsic C N -related defects, as both have been shown to contribute to YL luminescence in GaN [16]. The BL band in the GaN/Al 2 O 3 sample is attributed to carbon-related defects [17]. The UVL band was attributed to a free electron-shallow acceptor transition [18]. A peak at 3.35 eV, also observed as a weak, low-energy shoulder of the NBE for the HNPS GaN and GaN/Si samples, was attributed to a band-to-impurity transition [19]. For the HNPS GaN sample in figure 1(b), a strong YL band was observed with a peak at ∼2.25 eV, and in addition to the NBE emission with a peak energy of 3.40 eV, a UVL peak was observed at ∼3.25 eV. The intensity of the YL band in the HNPS GaN sample is strong, despite a lower C concentration in the HNPS GaN sample than that in the GaN/Al 2 O 3 sample (see table 1: 8 × 10 15 vs 1.3 × 10 17 cm −3 ). It is difficult to separate YL emission from C N and V Ga defects, though earlier literature reports indicate that the HNPS growth method leads to a high density of V Ga defects [20]. Given the stronger YL and lower C concentration, however, we believe the YL in the HNPS GaN sample is attributed primarily to V Ga and its complexes. For the GaN/Si sample, (figure 1(c)), YL (at 2.25 eV), BL (at 2.8 eV), and NBE luminescence (at 3.38 eV) were observed. Similar to the GaN/Al 2 O 3 sample, the YL in the GaN/Si sample was attributed to V Ga and C N complexes, and the BL to carbon-impurities. The silicon concentrations in the HNPS GaN and GaN/Si samples were determined to be nearly two orders of magnitude higher than in the GaN/Al 2 O 3 sample. Moderate silicon concentrations have been shown to enhance YL emission [21], and high silicon concentrations have been shown to enhance the NBE/radiative recombination by contributing additional free carriers [22]. The silicon impurity concentrations of 3-4 × 10 17 cm −3 in the HNPS GaN and GaN/Si samples are too low to significantly enhance the NBE/radiative recombination over the GaN/Al 2 O 3 sample, however. At 10 17 cm −3 levels, though, silicon may act to slightly enhance the YL intensity in the HNPS GaN and GaN/Si samples.
Next, the GaN NBE emissions were studied. The emission energy of the GaN NBE is slightly different for each sample: 3.42, 3.40, and 3.38 eV for the GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples, respectively. The difference in the NBE emission energy is due to the different strain state, with the GaN/Al 2 O 3 and GaN/Si samples being under compressive and tensile residual strain from the heteroepitaxy, respectively. The compressive strain acts to increase the NBE emission energy while tensile strain decreases it, in agreement with our observations [23]. The exciton binding energy in GaN is on the order of ∼25 meV [24], meaning that the GaN NBE at room temperature (kT ∼26 meV) may be a superposition of band-to-band and excitonic transitions. The power-law dependences of defect-related luminescence (DL) and GaN NBE emission, obtained by varying the excitation intensity, are critical in understanding the SRH and NBE recombination characteristics of the GaN samples in this work. Figure 2(a) plots the integrated intensity of the room-temperature GaN NBE emission (I NBE GaN ) vs P Laser for the three GaN samples. The integration was performed over the energy interval 3.2-3.55 eV, and I NBE GaN was fit to the following equation to determine its excitation dependence: where γ is the power law coefficient for I NBE GaN and A 1 is a fitting parameter. In the literature, γ values of 1 and 2 for the GaN NBE emission have been associated with free exciton recombination and band-to-band recombination, respectively, while a γ value in the range 1 to 2 is indicative of an intermediate system involving both recombination mechanisms [25]. The NBE peaks from exciton and band-to-band recombination should be separated by the exciton binding energy, but thermal and impurity broadening at room-temperature prevent the two peaks from being resolvable. The varying n 0 between samples obscures a direct comparison of the relative amount of free exciton/band-to-band recombination in each sample. Under the same n 0 , a lower γ implies a greater contribution from free exciton recombination in the room-temperature NBE makeup [25]. It has been reported in the literature, however, that a high n 0 can lead to a linear dependence of I NBE GaN on P Laser [26], which masks the true amount of free exciton and band-to-band recombination in the GaN/Si sample (which has a high n 0 of 6.5 × 10 18 cm −3 ). The implications of the NBE makeup (free exciton vs band-to-band dominated) on the radiative recombination in GaN will be discussed later.
When defect luminescence centers are unsaturated, the trap recombination will have a linear dependence on carrier density [27,28], and thus the integrated luminescence intensity of defects will increase linearly with P Laser . In this work, a low excitation intensity (5-195 W cm −2 ) was utilized to avoid saturating the SRH-related defect luminescence. If this assumption is incorrect, then the defect luminescence intensity (I NBE GaN ) should be observed to increase with P Laser 1/2 , which is indicative of saturated SRH recombination behavior, rather than linearly [26]. Figure 2(b) plots I NBE GaN at room-temperature vs P Laser . The integration was performed over the energy interval 1.75-3.1 eV to sum contributions from both the YL and BL bands, andI DL GaN was fit to the following equation to determine its excitation dependence: where χ is the power law coefficient forI DL GaN , and A 2 is a fitting parameter. For the GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples in this work, χ values of ∼0.70, 0.68, and 0.96 were derived, respectively. In the case of the GaN/Si sample, the χ value is very close to 1, indicating unsaturated trap center behavior. However, the GaN/Al 2 O 3 and HNPS GaN samples have χ values closer to 0.5, indicating that the defect luminescence centers are getting saturated. This behavior is attributed to a lower concentration of traps in the higher-quality GaN/Al 2 O 3 and HNPS GaN samples, which leads to saturation of the I DL GaN . In contrast, as the lower-quality GaN/Si sample has a higher trap concentration, defect PL in this sample is unsaturated.
Time-resolved photoluminescence (TRPL) measurements were conducted to determine effective carrier lifetimes τ eff . A spectral interval from 3.3-3.6 eV was chosen to measure the luminescence decay of the NBE emission in each sample. The TRPL setup consisted of a 2-kHz repetition rate, frequency-tripled Ti:Al 2 O 3 laser (λ = 266 nm, spot size = 0.17 mm 2 , pulse width = 150 fs, 1 nJ per pulse) and a Hamamatsu streak camera with a temporal resolution of ∼1 ps. The excited carrier concentration ∆n from the TRPL experiment was calculated essentially via equation (3) by substituting in the energy per pulse for P Laser , using the A spot of the TRPL setup, and using R = 0.11 for the GaN samples. ∆n was therefore found to be ∼1.6 × 10 17 cm −3 . Figure 3 shows normalized TRPL decay curves for each sample.
For the GaN/Al 2 O 3 and HNPS GaN samples, a biexponential decay was observed. Biexponential decay behavior has been reported in literature for GaN before, and has been attributed to capture at multiple deep levels [29]. For 266 nm excitation, carriers are mostly generated within ∼100 nm of the surface since the absorption coefficient of GaN is roughly 2.24 × 10 5 cm −1 . Therefore, the biexponential decay was attributed to a fast component representing nonradiative decay at the surface states, and a slower nonradiative decay representative of the bulk nonradiative recombination [30]. The TRPL decay for the GaN/Al 2 O 3 and HNPS GaN samples were thus fit to the following function: where τ 1 and τ 2 represent the fast and slow decay lifetimes, and C 1 (table 2). For the GaN/Si sample, a monoexponential decay was observed, and τ 1 , (equal to τ eff ), was calculated to be 20 (±1)  (table 2). The monoexponential decay for the highly defective GaN/Si sample is due to the overall recombination rate being dominated by nonradiative recombination at the surface. For the GaN/Al 2 O 3 sample, both τ 1 and τ 2 were longer than for the HNPS GaN sample, indicative of a higher quality surface and bulk.
Due to the biexponential decay of the GaN/Al 2 O 3 and HNPS GaN samples, it was necessary to derive a single τ eff for later calculations of the radiative and nonradiative lifetimes. Here, τ eff is calculated via the averaging of the time over the intensity decay curve [31]: For a biexponential decay model, equation (6) can be substituted for I(t) in equation (7), allowing τ eff to be calculated as [31]: which yields τ eff of (342 ± 12) and (221 ± 11) ps for the GaN/Al 2 O 3 and HNPS GaN samples, respectively. C 1 and C 2 , τ 1 and τ 2 , and τ eff for all samples are listed in table 2. Temperature-dependent photoluminescence (TDPL) was conducted with the addition of a liquid He bath cryostat and a PID temperature controller to allow the temperature to be varied from 1.4 to 300 K to determine the internal quantum efficiencies (η IQE ), and finally extract the A and B coefficients for each sample. The traditional ABC model used to study steady-state carrier recombination in semiconductors is expressed via [32]: where G is the generation rate and is equal to the recombination rate in the steady-state, n is the carrier concentration, A is the SRH recombination coefficient, B is the radiative coefficient, and C is the Auger recombination coefficient. In quantum well structures the carrier leakage may contribute to second, third, and higher-order terms as well [33], though these can be ignored for the study of bulk materials. The ratio of radiative recombination to the overall rate of recombination is then used to calculate η IQE via [32]: At sufficiently low temperatures (i.e. 1.4 K), η IQE is assumed to be unity due to the thermal deactivation of SRH recombination centers [34], and η IQE was thus calculated via the low-temperature high temperature (LT-HT) method [35]: where I (300 K) and I (1.4 K) are the spectrally integrated PL intensities of the GaN NBE emission at 300 K and 1.4 K, respectively. The integration was performed over the energy interval of 3.3-3.55 eV for the 1.4 K emissions, and 3.2-3.55 eV for the 300 K emissions. The lower integration limit for the 300 K NBE emissions was shifted downward to account for the decrease in bandgap with increasing temperature. There have been reports that η IQE at low temperatures (∼5 K) is not precisely unity, but rather close to unity (∼0.9) when samples have sufficiently high concentrations of SRH centers, and the average distance between them is on the order of the exciton Bohr diameter [36]. Here our measurements are conducted at even lower temperatures (1.4 K) and the GaN/Al 2 O 3 and HNPS GaN samples exhibited saturated SRH behavior in figure 2(b), which indicates a lower defect concentration, and thus indicates that the assumption of unity  η IQE at 1.4 K for these two samples is acceptable. For the GaN/Si sample with high defectivity, however, SRH saturation behavior was not observed, and η IQE calculated by the LT-HT method may be overestimated. The implications of this η IQE overestimation for the GaN/Si sample will be discussed later. Figure 4 shows the normalized PL spectra of all samples at 1.4 and 300 K. For each sample, the 1.4 and 300 K emissions were normalized to the highest intensity PL peak in the 1.4 K PL spectrums. For better visualization, the 300 K PL spectra for all samples were scaled up by 20 × . The η IQE values of the GaN/Al 2 O 3 , HNPS GaN, and GaN/Si samples were determined as 9.6, 7.9, and 1.9%, respectively. Given the use of the unity η IQE assumption at low temperature, these are upper bound values.

Discussion
Comparing A coefficients between samples, the A value for the HNPS GaN sample is almost 2× as high as the GaN/Al 2 O 3 sample (2.6 vs 4.2 × 10 9 s −1 ) despite an over 10× reduction in TDD and a nearly two orders of magnitude lower carbon content. This suggests that threading dislocations and carbon are not responsible for the high A coefficient in this sample. A possible culprit is V Ga point defects, which based on the high YL intensity observed in the room-temperature photoluminescence spectra, may be present in high concentration [16]. It would appear that TDD in the range 10 7 -10 8 cm −2 does not significantly affect the A coefficient. This agrees with the literature [7,29], which reported that the gross concentrations of V Ga point defects and complexes determined the nonradiative lifetime and A coefficient of GaN [7]. Beyond a TDD of 10 8 cm −2 , however, TDD begins to dominate the A coefficient behavior, as evidenced by the large increase in the A coefficient for the GaN/Si sample with TDD > 10 10 cm −2 [6]. Comparing B coefficients between samples, the B coefficient for the GaN/Si sample is severely reduced by a factor of six compared to the higher quality and less-doped GaN/Al 2 O 3 and HNPS GaN samples, where the B coefficients were the same. High doping levels can significantly reduce the B coefficient via screening of the free exciton state in GaN [39,40]. Threading dislocations have been reported to generate stress and charge fields that separate electron and hole wavefunctions in space and decrease the radiative recombination rate [41]. The high n 0 > 5 × 10 18 cm −3 and high TDD > 10 10 cm −2 in the GaN/Si sample thus heavily impact the radiative recombination rate, and an overall smaller B coefficient is observed.
Earlier it was noted that the unity η IQE assumption for the GaN/Si sample was incorrect due to the higher defect concentration. Due to the overestimation of η IQE , the degradation of the B value for the GaN/Si sample is even worse than the calculated value. Given the low η IQE 's of less than 10% for all samples, the use of the unity η IQE assumption at low temperatures will not significantly change the derived A coefficients, nor the results.

Conclusion
In summary, GaN samples grown by MOCVD, HNPS, and HVPE methods on different substrates were experimentally studied to compare the A and B recombination coefficients. XRD, Hall Effect, and SIMS were used to quantify defect and impurity densities. Power-dependent photoluminescence revealed mixed free-exciton and band-to-band recombination in the GaN NBE emission of all samples and revealed unsaturated luminescence from defects in the GaN/Si sample. Time-resolved and temperature-dependent photoluminescence techniques were then used to extract carrier lifetimes, internal quantum efficiencies, and the A and B recombination coefficients. It is observed that even when the TDD is lowered by three orders of magnitude from 10 10 to 10 7 cm −2 , the A coefficient in GaN remains on the order of 10 9 s −1 due to nonradiative recombination at point defects, indicating that further performance gains for devices must focus on point defect reduction through optimized growth conditions. In addition, the GaN/Si sample was found to have a B coefficient six times lower than the other samples due to high defectivity and doping (TDD > 10 10 cm −2 and free electron concentration >5 × 10 18 cm −3 ). The GaN/Al 2 O 3 and HNPS GaN samples, which had lower TDD in the range 10 7 -10 8 cm −2 and doping ∼10 17 cm −3 , exhibited a similar B coefficient of ∼9.5 × 10 -10 cm 3 s −1 , indicating that the B coefficient is constant in higher-quality and lower-doped GaN.