Shockley–Read–Hall lifetime in homoepitaxial p-GaN extracted from recombination current in GaN p–n+ junction diodes

The Shockley–Read-Hall (SRH) lifetime in homoepitaxial p-GaN (Na = 1 × 1017 cm−3) is investigated by analyzing forward current–voltage (I–V) characteristics in GaN-on-GaN p–n+ junction diodes with mesa-isolation structure. The ideality factor around 2 due to recombination current was obtained in the 1.8–2.7 V window, which is different from the characteristic of a p+-n− junction involving considerable diffusion current. The recombination current was proportional to the junction area, indicating that the recombination current is a bulk component, not a mesa-surface component. Analyzing the recombination current with consideration of the SRH recombination rate in the depletion layer, we obtained an SRH lifetime of 46 ps at 298 K. The temperature dependence of the I–V characteristics was also investigated and the SRH lifetimes were extracted in the range of 223–573 K. The SRH lifetime in homoepitaxial p-GaN followed the empirical power law of τ SRH = 1.2 × 10−16 × T 2.25 (s).


Introduction
Owing to its high critical electric field (∼3 MV cm −1 ), 1) GaN has attracted great attention as a material for the nextgeneration power devices. There have been many reports on GaN vertical power devices fabricated on GaN bulk substrates, which showed high breakdown voltage and low on-resistance. [2][3][4][5][6][7][8] Owing to the low threading dislocation density (∼10 6 cm −2 ) in homoepitaxial GaN, leakage current, inhomogeneity and other non-ideal characteristics were well suppressed in GaN-on-GaN devices, which enables us to analyze the device characteristics in detail. [9][10][11][12][13] Reference 11 investigated forward current-voltage (I-V ) characteristics of GaN-on-GaN p + -n − junction diodes. The recombination current with an ideality factor of 2 in the voltage range of 2.0-2.5 V and the diffusion current with a near unity ideality factor in the voltage range of 2.5-2.8 V were observed. They extracted the Shockley-Read-Hall (SRH) lifetime, which is the square root of the product of hole and electron carrier lifetimes (t SRH = t t p n ), by analyzing the recombination current with consideration of the SRH recombination rate in the depletion layer. 14,15) In the p + -n − junction, the depletion layer extends to the lightlydoped n-layer side and the SRH recombination occurs in the n-layer. The obtained SRH lifetime is one for the n-GaN. In the same way, the SRH lifetime in p-GaN can be obtained using the p − -n + junction. However, there is no report on the SRH lifetime in p-GaN.
Recently, the growth technique of a lightly Mg-doped p-GaN has been developed, and relatively low Mg concentration can be controllable. 16,17) In this study, we investigate the forward I-V characteristics in GaN-on-GaN p-n + junction diodes, in which the depletion layer mainly extends to the player side. The large recombination current with an ideality factor of 2 was clearly observed in the wide voltage range of 1.8-2.7 V. The SRH lifetime in homoepitaxial p-GaN and its temperature dependence are investigated. Figure 1 shows the schematic cross section of the GaN p-n + junction diodes. The GaN layers were grown by metal organic vapor phase epitaxy on a freestanding GaN substrate prepared by hydride vapor phase epitaxy. The doping concentrations and the thickness of the epilayers were obtained by secondary ion mass spectrometry. The thickness of p-layer was 2.5 μm. The Mg concentration in the pepilayer and the Si concentration in the n + -layer were 1 × 10 17 cm −3 and 6 × 10 18 cm −3 , respectively. After the epitaxial growth, high temperature annealing was performed at 1123 K for 5 min to remove hydrogen bound to Mg in the GaN epilayer. The mesa-isolation structures of the p + /p/n + layers were formed by Cl 2 -based inductively coupled plasmareactive ion etching. The mesa height was about 3 μm. The anode and cathode electrodes were formed by the deposition of Ni/Au on the epitaxial layer and Ti/Al/Ni on the backside of the substrate, respectively. From the capacitance-voltage (C-V ) measurements, the net doping concentration

Experiment
d of ∼1 × 10 17 cm −3 was obtained, which shows good agreement with the Mg concentration in the p-layer. I-V and C-V measurements were measured in dry air using a Keysight B1505A parameter analyzer. The temperature of the sample stage was controlled in the range 223-573 K.

Result and discussion
The forward I-V characteristics of a p-n junction diode can be expressed as The first term represents the diffusion current, and the second term is the SRH (non-radiative) recombination current density in the depletion layer. J dif,0 and J SRH,0 are the bias insensitive terms of diffusion and recombination currents. For GaN, the radiative recombination current is very small and negligible in the entire voltage range. 11,18) The constants of e and k are the electric charge and the Boltzmann constant, respectively. V is the voltage applied over the p-n junction. Figure 2 shows the forward I-V characteristics of GaN p-n + junction diodes at 298 K. The ideality factor extracted as is also shown in Fig. 2 as a function of the voltage. The ideality factor of 2 was observed in the voltage range 1.8-2.7 V, indicating that this current component is the SRH recombination current. The calculated SRH recombination current is shown in Fig. 2 as the red broken line. The size dependence of the forward I-V characteristics was investigated, and it was confirmed that the recombination current is proportional to the junction area. This indicates that the recombination current arises from the overall junction area, not from the surface recombination at the mesa periphery. The extrapolated value to the ( ) J ln -axis (J SRH,0 ) was 1 × 10 −25 A cm −2 , which is five times larger than the value of 2.7 × 10 −26 A cm −2 in the GaN p + -n − junction diode reported by Ref. 11. The on-resistance is about 0.1 Ω cm 2 and the voltage drop outside the junction at 1 A cm −2 current density is about 0.1 V. Since the voltage drop due to the series resistance came to be dominant for higher voltage than 2.7 V, a diffusion current component was not clearly observed, which is different from the GaN p + -n − junction diode. 11) An SRH lifetime can be extracted from the SRH recombination current by considering the SRH recombination in the depletion layer. 11,15) For the forward bias condition, the SRH recombination rate in the depletion layer via a non-radiative recombination center (NRC) with a single energy level that is sufficiently far from the band edges can be written as p, n, t , p t p are the hole concentration, the electron concentration, the hole lifetime, and the electron lifetime, respectively. The electron and hole carrier lifetimes are written as t n = s -( ) N v n n t th, 1 respectively. N t is the NRC concentration. v n th, and v p th, are thermal velocities of carriers, which depend on the effective masses. s n and s p are the electron and hole capture cross sections. n i is the intrinsic carrier concentration, which depends on the bandgap, temperature, and the density-of-state effective masses. In this study, temperature dependence of the bandgap 19) was considered and the electron and hole density-of-state effective masses of 0.2 m 0 and 1.5 m 0 were used, 20) respectively. Figure 3 shows (a) the band diagram of the p-n + junction under applied voltage of 2 V and (b) the distributions of n, p, and    is negligible). Therefore, the distribution of U SRH is very similar to the distribution of + -( ) n p 1 as shown in Fig. 3(b). The distributions of carriers near the plane = x x 0 can be written as where = x 0 is the p-n junction interface. Substituting formulae (4) for formula (2), we can obtain the SRH recombination rate near = x x 0 as The SRH recombination current can be written as The SRH lifetime in homoepitaxial p-GaN was extracted from the extrapolated current density in the -( ) J V ln plot (J SRH,0 ) using formula (6). The SRH lifetime of 46 ps was obtained at 298 K. This is much shorter than the lifetime of 12 ns in n-GaN reported by Ref. 11. This suggests that the NRC concentration in p-GaN is much higher than that in n-GaN, and/or the capture cross section of the NRCs in p-GaN is much larger than that in n-GaN.
References 22-24 have investigated the photoluminescence lifetime (t PL ) of the near-band-edge emission in GaN using time-resolved photoluminescence (TRPL) measurements. For GaN, t PL is limited by the non-radiative recombination process at room temperature under low-excitation conditions, 24) and t PL represents the minority carrier lifetime (t n for p-GaN). In homoepitaxial p-GaN layers, 22) two lifetime components (fast t 1 ∼ 10 −11 s and slow t 2 ∼ 10 −10 s) were observed in the TRPL decay, which are much shorter than the photoluminescence lifetime in homoepitaxial n-GaN (∼10 −9 s). 24) References 25-27 have reported on positron annihilation spectroscopy (PAS) measurements, which is a powerful tool to obtain concentrations and identify types of vacancy-type defects, for GaN. They found that t PL was proportional to the inverse of the vacancy-type-defect concentration (N V ), suggesting that the vacancy-type defects are the main NRCs in GaN. From these relationships (t PL versus N V ), they obtained the capture cross sections of the minority carriers. For p-GaN, s n of the NRCs was estimated to the middle of 10 −13 cm 2 , and the origin of the NRCs in p-GaN was identified as Ga N 3 22) On the other hand, in n-type bulk GaN, the s p and the origin of the NRCs were s p = 7 × 10 −14 cm 2 and V V , Ga N respectively. 23,24) It should be noted that the origins as well as the capture cross sections of the NRCs in p-GaN and n-GaN are different.
We have not measured TRPL and PAS for our p-GaN layer. Here we refer to the reported results 22) for similar Mg concentrations. For p-GaN with Mg concentration of 1 × 10 17 cm −3 , t n = 20 ps, and N t = 1 × 10 16 cm −3 were reported. From the relationships of t SRH = t t p n and our obtained SRH lifetime in p-GaN of 46 ps, we obtain t p = 106 ps. The electron capture cross section was calculated to be 3 × 10 −13 cm 2 . Although our estimation is very rough, the NRC in p-GaN is thought to have large capture cross sections for both electrons and holes, i.e. it acts as a very efficient recombination center. Figure 4 shows the forward I-V characteristics of the GaN p-n + junction diode in the range 223-573 K. The recombination current increased with elevating temperature. Figure 5 shows the temperature dependence of the SRH lifetime in homoepitaxial p-GaN extracted from the recombination currents in the range 223-573 K. It is known that the temperature dependence of the SRH lifetime follows an empirical power-law relation (t µ a T SRH ). 11,28) The empirical power law of t SRH = 1.2 × 10 −16 × T 2.25 s for the temperature dependence of the SRH lifetime in the homoepitaxial p-GaN was obtained in this study. This value is different from the temperature dependence of the SRH lifetime in n-GaN (3.9 × 10 −12 × T 1.41 s) reported by Ref. 11. This result suggests that the temperature dependence of the capture cross section of the NRCs in p-GaN is different from that in n-GaN. This may be related to the results reported by Refs. 22-24; the origins of intrinsic NRCs in

Conclusion
We investigated the SRH lifetime in a homoepitaxial p-GaN (N a = 1 × 10 17 cm −3 ) by analyzing the recombination current in GaN-on-GaN p-n + junction diodes. An SRH lifetime in p-GaN of 46 ps was obtained, which is much shorter than that in n-GaN of 12 ns reported previously. Assuming the previously reported minority carrier (electron) lifetime and NRC concentration in homoepitaxial p-GaN with a similar Mg concentration (t n = 20 ps, N t = 1 × 10 16 cm −3 ), we roughly estimated the hole lifetime and the hole capture cross section to be t p = 106 ps and s n = 3 × 10 −13 cm 2 respectively. The temperature dependence of the SRH lifetime was also investigated, and the empirical power law of t SRH = 1.2 × 10 −16 × T 2.25 s was obtained. Analyzing forward I-V characteristics of p-n + junction diodes is a useful way of investigating the properties of an NRC in a p-GaN layer.