Characterization of hole traps in MOVPE-grown p-type GaN layers using low-frequency capacitance deep-level transient spectroscopy

Traps in MOVPE-grown Mg-doped GaN samples composed of p+/p−/n+ structures were investigated using low-frequency capacitance deep-level transient spectroscopy (DLTS). A drop-off in capacitance with decreasing temperature was observed. This is caused by the longer RC time constant of the diode with lower temperature, which is due to a decrease in the number of ionized Mg acceptors (which have a high ionization energy). This limits the use of lower temperatures in DLTS measurements. To extend DLTS to a lower temperature (105 K), DLTS using a capacitance measurement frequency of 1 kHz was applied. Thus, we can quantitatively discuss concentrations of traps with shallow energy levels. We obtained a nearly one-to-one relation between Ha (EV +0.29 eV) and Hd (EV +0.88 eV) in the p-type layer, which strongly supports the theoretical calculation that a carbon on a nitrogen site forms donor-like (Ha) and acceptor-like (Hd) states.


Introduction
The growth technology of Mg-doped p-type GaN (p-GaN) has made a large contribution to the improvement of optical and power electric devices. [1][2][3][4][5][6] In the case of power devices especially, a MOS structure on a p-GaN layer allows normally-off operation with an optimal threshold voltage by controlling the effective acceptor concentration. 7) Then, hole traps involved in p-GaN layers can generally modify the threshold voltage due to compensating carriers 4,5) and may cause instability during switching operation similar to bulk traps in high-mobility electron transistors. 8,9) From this point of view, characterization of hole traps in p-GaN layers is crucial. Deeplevel transient spectroscopy (DLTS) is generally used to characterize such hole traps. However, DLTS measurement for a p-GaN layer is more difficult than for n-type GaN (n-GaN). DLTS for n-GaN is usually performed using Schottky diode structures composed of Schottky and ohmic electrodes. [10][11][12] To obtain a p-GaN-based Schottky diode, both electrodes are formed for a p-GaN layer because a p-GaN substrate has not been available until now; this reduces the testable doping range. Moreover, such diodes usually suffer from leakage current and/or series resistance, [13][14][15][16] leading to quantitative inaccuracy. Reference 16 provided an answer to this problem by using a p + /p − /n + structure grown by NH 3 -based molecular beam epitaxy. To achieve a similar device structure by metalorganic vapor phase epitaxy (MOVPE), commonly used in manufacturing, the growth technology of a p − layer doped with 10 16 to 10 18 cm −3 Mg was required. Recently, we successfully demonstrated the control of low-Mg doping into GaN 17) and fabricated a p + /p − /n + structure. 18) However, there is another issue unique to capacitance DLTS measurement for a p-GaN layer. Although Mg is only an acceptor for GaN, the energy level is not shallow. The activation energy of around 0.2 eV leads to carrier freeze-out in the measurement at low temperature, 19) where a p − layer acts as a high-resistivity layer and is fully depleted. As a result, a significant capacitance drop occurs below 200 K in capacitance DLTS at 1 MHz, not allowing detection of traps near the valence band. 18) The key to detect traps with a relatively shallow level is the choice of measurement frequency in the capacitance DLTS, considering the temperature-dependent resistance-capacitance (RC) time constant in a p + /p − /n + structure. Actually, the capacitance DLTS at 1 kHz allows the detection of traps near the valence band. 20) In this study, considering the RC time constant of devices, we quantitatively discuss hole traps with relatively shallow energy levels detected in MOVPE-grown p-GaN layers by low-frequency (or 1 kHz) capacitance DLTS.

Experimental methods
MOVPE was used to grow four samples with p + /p − /n + structure on freestanding n-GaN substrates prepared by hydride VPE. Methylsilane gas and bis(cyclopentadienyl) magnesium were used as the n-type and p-type dopants, respectively, for GaN. The layered structure was composed of a 0.2-μm-thick n + layer, a 0.7-μm-thick p − layer and 0.1μm-thick p + layer, where the doping concentrations estimated by secondary ion mass spectroscopy (SIMS) were (6-8) × 10 18 , (0.3-2) × 10 17 and 8 × 10 19 cm −3 , respectively. The carbon (C) concentrations in the p − layers were varied in the range of (0.1-1.3) × 10 16 cm −3 by controlling the growth temperature and pressure. 15) The diodes were fabricated by the same procedure as in Ref. 16. The admittance measurements at zero bias were performed in parallel mode in the range of 1 kHz to 1 MHz to investigate the quantitative relation between measurement frequency and the capacitance dropoff at low temperature. Capacitance DLTS measurement was performed using a filling pulse of 0 V and a reverse bias of -2 V. 18) In the measurement, a depletion layer was extended almost toward the p − layer owing to a p − /n + junction. Our conventional DLTS system using the Boonton 7200 capacitance meter only allows measurement at a frequency of 1 MHz. To change the measurement frequency, we prepared the capacitance measurement system equipped with a lock-in amplifier and a current preamplifier, which offers f = 0.5 mHz to 105 kHz. A current DLTS measurement 21) was also performed for comparison with capacitance DLTS. where ω = 2πf. A significant capacitance drop-off was seen in the temperature range from 100 to 150 K, corresponding to the peak G/ω at each measurement frequency. The peak G/ω, denoted by H 0 , was shifted to a lower temperature with the reduction of measurement frequency. We think that this shift is related to the temperature dependence of the RC time constants of p + /p − /n + diodes. Figure 2 shows an equivalent circuit for p + /p − /n + diodes to explain the drop-off of the capacitance and the corresponding peak of G/ω. C 1 is the depletion layer capacitance determined by ionized Mg acceptors. In the lower temperatures below the capacitance drop-off, Mg acceptors are unionized in the neutral region, which acts as an insulator layer characterized by the capacitance C 2 . Then, an equivalent circuit is expressed by a series connection of C 1 and C 2 , which is simply given by a plate capacitor with thickness l and area A of the p-GaN layer (C 0 = εA/l). At temperatures sufficiently above the drop-off, the neutral region acts as the resistance (R) since Mg acceptors are ionized. When 1/ωC 1 > > R, an equivalent circuit is expressed by the depletion layer capacitance C 1 , which fulfills the condition for accurate performance of the capacitance DLTS measurement. In the intermediate temperature range, an equivalent circuit in the neutral region is the parallel connection of C 2 and R. When the equivalent circuit in Fig. 2 is transformed into the measured capacitance C m and conductance G in the parallel mode, the magnitude of the capacitance drop-off is given by C 1 -C 0 . Then, the peak of G/ω occurs under the condition where 1/ω = R(C 1 + C 2 ) is met.

Results and discussion
Based on an equivalent circuit for p + /p − /n + diodes, the value of R in the neutral region is obtained from the temperature dependence of the capacitance and G/ω at each frequency. The value of R is determined at each peak temperature of G/ω using the peak value of G/ω, its corresponding value of C m and the peak condition of 1/ω = R(C 1 + C 2 ). Then, the resistivity of the p-GaN layer is calculated assuming that the resistivity of the p + region is a factor of 400 lower than that of the p − region due to the doping ratio of between 8 × 10 19 and 2 × 10 17 cm −3 for the respective p + and p − layers. The temperature dependence of the resistivity determined from 16 measurement frequencies, including four frequencies in Fig. 1, is shown in Fig. 3 and satisfies the Arrhenius relation. This indicates that the change in mobility has little influence on the temperature dependence of the resistivity in this limited temperature range. 20,22) The hole mobilities for samples having a similar Mg concentration were estimated to be around 100 cm 2 V −1 s −1 . 20) Assuming this value, the hole concentrations calculated using the resistivity were found to coincide with those determined by Hall effect measurements (data not shown). This result verifies the equivalent circuit model in Fig. 2. From the Arrhenius plot of the resistivity in Fig. 3 the activation energy is estimated to be 0.21 eV, which corresponds to the previously reported ionization energy of Mg acceptors. 20,22,23) By seeing the dropoff temperatures in C m and the peak temperatures in G/ω in Fig. 1, we can properly select the measurement frequency for capacitance DLTS to avoid carrier freeze-out if the peak temperature of the focused trap is known.
To choose the measurement frequency for capacitance DLTS we need to know the energy levels of traps involved in the p-GaN layer as well as the peak temperatures of DLTS signals. Current DLTS measurement is another way to avoid carrier freeze-out, allowing the detection of relatively shallow  trap levels. However, current measurement essentially makes it difficult to estimate the trap concentrations because it does not give the capacitance of the depletion layer. In other words, the capacitance DLTS at a proper measurement frequency has the advantage for quantitative analyses of traps compared with current DLTS. Accordingly, we employed current DLTS only to investigate the trap levels and then determined the proper measurement frequency for capacitance DLTS. The quantitative discussion on trap concentrations was informed by using capacitance DLTS. Figure 4 shows the current DLTS spectrum for the same sample as used in Fig. 1 and in the previous work. 18) The Arrhenius plot of time constants for a peak observed at the lowest temperature is consistent with that obtained from the H 0 peaks of G/ω at different frequencies as shown in Fig. 1(b), although the estimated temperature ranges are different. That is why that peak in the current DLTS spectrum is labeled H 0 . We observed the H a trap as the shallowest level around 160 K. Considering measurements at different time constants as well as different peak temperatures, we performed capacitance DLTS at 1 kHz, allowing detection above 105 K, based on Fig. 1. Figure 5 shows a comparison of capacitance DLTS spectra at measurement frequencies of 1 kHz and 1 MHz in the temperature range from around 100 K to 380 K. The 1 kHz capacitance DLTS spectrum exhibits clear peaks (labeled H a and H b ) of traps at 131 and 150 K, respectively, because 1/ωC 1 > > R. On the other hand, the spectrum at 1 MHz apparently gives a broad single peak with a smaller intensity because the temperature at the capacitance drop-off and the G/ω peak was approximately 150 K. Accordingly, it is important to determine the measurement frequency by taking into account the cut-off temperature. Thus we can quantitatively discuss traps in p-GaN layers near the valence band. Figure 6 shows Arrhenius plots for hole traps detected for this sample. The trap labeled as H x was obtained from the G/ω spectra, as will be discussed later. All trap parameters are summarized in Table I, where the capture cross-section was calculated by assuming 0.9m 0 for the hole effective mass. 16,18) We previously discussed the traps H c and H d , where the respective energy levels were E V + 0.46 and 0.88 eV. 18) On the other hand, two hole traps detected in n-GaN layers grown on GaN substrates were previously marked as H1 and H3 at E V + 0.88 and 0.25 eV, respectively. 24) By comparing hole traps in both n-and p-GaN samples, we found that the H d and H1 traps were identical; their origin was commonly assigned as a carbon on a nitrogen site (C N ). 18) We also mentioned in the previous report that the H a trap concentrations correlate with carbon ones, which can be explained by the idea that the H a trap also   Fig. 1(b).   Fig. 2(b) and those of the other traps were estimated by using the 1 kHz capacitance DLTS measurements. The energy level for each trap was noted in brackets in units of eV. The obtained trap parameters are summarized in Table I. originates from C N but has a different charge state from the H d (or H1) level. 20) To directly confirm this, we examined in the present work the quantitative relation between the H a and H d traps at the same sample position. Figure 7(a) shows the correlation of concentrations between the H a and H d traps, where samples with different C concentrations were examined. The trap concentration of H a was determined using the saturated value of the isothermal DLTS peak height with a pulse width of 10 s, while a pulse width of 10 ms was long enough to saturate the DLTS peak height for H d . The result exhibited a nearly one-to-one relation for both traps, strongly supporting the picture originating from the same C N with the different +1/0 and 0/-1 charged states. 20,25,26) The detection of the same concentration is not surprising considering the different emission time constants in the different ranges of temperature. When applying filling pulse, a C N − can capture two holes and be charged with the +1 state. At a low temperature around 150 K, one hole is emitted from the C N and becomes neutral (i.e. C N +  C N 0 + h + ). Then, emission of the second hole does not occur in the measurement time window because the emission time of the H d level is too long. At around 350 K, the first hole emission (C N +  C N 0 + h + ) can occur before measurement of the capacitance transient. As a result, the capacitance transient due to only the second hole emission (C N 0  C N − + h + ) was reasonably observed in the time window. Therefore, the nearly one-to-one correlation between H a and the H d traps provides direct evidence for the identification.
Next, we focus on the H b trap located at E V + 0.33 eV. The capture cross-section was estimated to be 6.5 × 10 -15 cm 2 . This trap was commonly observed in four samples with the different C concentrations used in this study. We previously reported that the trap having the nearest energy level in n-GaN is the H2 trap located at E V + 0.25 eV. 24,27) Their Arrhenius plots were not in complete agreement (not shown), although this leaves room for investigation. To our knowledge there are few reports on such shallow hole traps detected by DLTS, although some traps with energy levels above 0.4 eV and shallow traps detected by admittance spectra have been reported. 28) The H b trap concentrations were varied in the range of (0.1-1.3) × 10 16 cm −3 . In the sample with the highest H b concentration, the concentration was comparable to the H a and H d ones. The H b concentration had no correlation to that of C, indicating that the H b trap does not originate from C, as shown in Fig. 7(b). Further investigations using different growth conditions are needed to assign its origin.
Finally, we discuss another capacitance step in the temperature above the capacitance drop-off as shown in Fig. 1(a). This was seen as another peak of G/ω in Fig. 1(b). We mark this peak as H x in Fig. 6. Also, two such capacitance steps or two peaks in G/ω have often been observed in p-GaN Schottky diodes. 14,[29][30][31][32] Since the peaks corresponding to H x are observed irrespective of growth methods, it is possible that H x is related to the presence of Mg in the p-GaN layer. As shown in Fig. 6, the Arrhenius plot of the H x level gave a small energy level of 0.08 eV despite the higher peak temperature than H 0 . Therefore, the capture cross-section of H x is expected to be small. In fact, the hole capture cross-section of H x was estimated to be about 6.6 × 10 -18 cm 2 . H x cannot be detected by capacitance DLTS because the peak temperature in the measurement time window is estimated to be below 70 K. Previous studies pointed out that such a small capture cross-section is due to the repulsive barrier associated with Mg. 33) According to  first-principles calculation, however, a simple Mg on a Ga site only forms a 0/-1 acceptor level within the bandgap, 34) which presumably gives an attraction force to a hole. One possible explanation is an energy level due to the Mg-H complex 30) which has its +1/0 transition level located at 0.13 eV above the valence band, as predicted in Ref. 34 Although the H concentration in this sample was below the detection limit of SIMS, the detection limit around 10 16 cm −3 might hide small numbers of Mg-H complexes. The other Mg-related complexes allow the possibility of H x association and therefore the assignment of the origin requires further investigations.

Conclusions
Trap characterization of epitaxial p-GaN samples grown on freestanding GaN substrates was performed using DLTS measurements. We carefully discussed the relation between measurable temperature and measurement frequency based on the equivalent circuit model. The comparison of capacitance DLTS at 1 kHz and 1 MHz showed that a proper measurement frequency (1 kHz) is significant for the detection of relatively shallow traps. Thus by using the carefully determined measurement condition, a nearly one-to-one correlation between the H a and H d traps was presented, strongly supporting the theoretical calculation that a C on a N site forms donor-like (H a ) and acceptor-like (H d ) states.