Electrical mechanisms for carrier compensation in homoepitaxial nonpolar m-ZnO doped with nitrogen

As a first step, the PL spectra of the sample series was analyzed at 8 K (figure 1), where two well distinct energy regions can be observed. The region at 3.36–3.37 eV shows sharp excitonic peaks in all films except for the highly doped one due to its lower crystalline quality. In this film, and as a result of its low PL intensity, a group of sharp peaks separated at a constant energy of 72 meV becomes evident. These peaks also affect the spectra of the mid N sample and appear at an integer number of the LO phonon energy (72 meV) below the laser pump energy (3.815 eV) as a result of resonant elastic Raman scattering. Indeed, the laser pump energy happens to be almost exactly 6xLO above the free exciton energy (3.377 eV). The dominant excitonic peaks that appear in the 3.36–3.37 eV region thus arise from donor-bound excitons (DX) [20]. These excitonic emissions may arise both from the epilayer and from the ZnO substrate, especially in the undoped sample where the carrier diffusion length is expected to be much larger and the electron-hole pairs may reach the substrate and recombine there. In the N-doped samples, the fact that the DX emission decreases with increasing N concentration may be indicative that it does originate in the epilayer.

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The major change in the PL spectra that results from N incorporation is the appearance of a prominent and broad donor-acceptor-pair (DAP) emission at 3.234 eV, with well-defined LO phonon replicas (figure 1) every 72 meV, in agreement with previous reports [3, 11, 20]. This DAP emission has a small blue shift as the N content is increased from the low to the mid N films and that is explained as a reduction in the donor-acceptor average separation [11]. In the high N sample the DAP is not clearly observed, but the broad weak PL signal is still centered at the DAP energy around 3.24 eV.

Table 1 summarizes the results obtained from the IV profiles (figure 2). The reference sample showed a Schottky barrier height around 1 eV, rising slightly to 1.1–1.2 eV for the N-doped samples. The ideality factor increased from 1.2–1.3 to 2.8 with N concentration, implying a reduced quality of the Schottky diode. The series resistance (R_S) is limited, among other things, by the resistivity of the material, and rises linearly with the N incorporation (table 1), which indicates an increased electrical compensation. The undoped (reference) sample has an R_S = 0.4 Ω · cm², whereas with a low N incorporation, it rises to 61 Ω · cm². The mid N sample shows a further increase in resistance up to 1.6 · 10² Ω · cm², reaching a maximum value for the high N of 1.1 · 10³ Ω · cm². The contact resistance (R_C) rises from ∼10⁸ Ω · cm² in the undoped sample to a stable value between 2–4 · 10⁹ Ω · cm², indicating a reduced effect of N in the ohmic contact quality.

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The CV profiles both at 1 MHz and 10 kHz for all films are shown in figure 3(a), in addition to the resulting carrier concentration vs depth profiles (figure 3(b)). These profiles show that the undoped sample has a net carrier concentration around ∼1 · 10¹⁶ cm⁻³ and a depletion region that lays completely inside the grown layer. The low N sample shows a similar concentration to the reference sample at 1 MHz, although it decreases to ∼2 · 10¹⁵ cm⁻³ when reducing the probing frequency to 10 kHz. This effect suggests a low efficiency of the compensating acceptors, as will be explained in a later section of this paper.

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The mid N sample could not be effectively measured in the dark, due to the high compensation that totally depletes the grown layer at 10 KHz, as can be observed in figure 3(b). However, under illumination above the mid-gap (concurrent with the start of the DLOS spectra), the depletion width shrinks sufficiently and the CV can be effectively measured (not shown), giving a concentration of ∼1 · 10¹⁶ cm⁻³. This value will be used on the trap concentration calculations for this sample, since it is more accurate than the one measured in the dark, because the capacitance values used in equation (1) are obtained with DLOS, i.e., under illumination. Indeed, and in order to clarify the region being probed by DLOS, a CV spectra under 3.2 eV illumination is shown in figure 3(a), where it can be observed that the depletion layer is confined entirely in the epilayer, yielding a value of 1.3 μm. Moreover, by calculating the Debye screening length (around 25 nm), the obtained value can be considered an accurate estimation of the real depletion depth [21]. The high N sample was so heavily compensated, as indicated by the large series resistance (table 1), that its capacitance remained unchanged under any bias or illumination conditions. Thus, this sample was fully depleted and could not be analyzed by DLOS.

Figure 4 shows the SSPC spectra for the three samples that were electrically measurable (undoped, low N and mid N). It can be observed how both the undoped and low N samples show a significant decrease of photocapacitance above the exciton energy (∼3.31 eV). Indeed, a large increase in photogenerated carriers raises the conductivity of the diode, thus degrading the quality factor for the capacitance measurement, affecting the measured capacitance value. Nevertheless, and regardless of the presence or absence of N, all three samples show a level at E_V + 0.25 eV, which for the reference and low N samples is the only trap that can be uniquely resolved.

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In the case of the undoped sample, several levels show up deeper in the bandgap (figure 4(a)). However, they cannot be resolved due to the high sensitivity to illumination of the recorded SSPC spectra, which mixes the signatures from the levels with the lamp intensity variations arising from the Xe discharge lines. These levels account for nearly half of the total capacitance change of the sample, i.e., for the total trap concentrations. Using the carrier concentrations from the CV analysis, and by applying equation (1), a lower bound trap concentration for the E_V + 0.25 eV level of ∼1.4 · 10¹⁶ cm⁻³ is obtained, being the rise in photocapacitance affected by the degradation in the quality factor because of the excitonic absorption.

As for the low N sample, the aforementioned levels deep in the bandgap can hardly be observed, suggesting a reduction in their concentration with N incorporation. In this sample, only the level at E_V + 0.25 eV is clearly observed (figure 4(b)), as in the reference sample. Similarly, a degradation in the quality factor for the capacitance measurement appears above the excitonic absorption energy. Therefore, the concentration for the trap is only a lower bound, giving a very similar value of ∼1.2 · 10¹⁶ cm⁻³.

In the mid N sample, the E_V + 0.25 eV level is still observed but its trap concentration cannot be easily calculated due to the close proximity of a new level (figure 4(c)), which masks the associated rise. Considering the small increase this level generates in the spectra, an approximate concentration of ∼4 · 10¹⁴ cm⁻³ is obtained. However, it is important to note that because of the high electrical compensation already mentioned for the sample, the depletion region remains unchanged until a trap with a concentration high enough is photoexcited, causing an increase in the carrier concentration and a reduction of the depletion region width. Under these conditions the diode capacitance starts to be measurable, as it can be clearly observed in figure 4(c), in which ΔC/C₀ has risen already to a value of 0.02 at the start of the first distinguishable level (E_V + 0.48 eV). This is a direct indication that the steady state value of the photocapacitance (${{{C}}_{{\rm{ss}}}}^{{\rm{photo}}})$ has changed respect to the dark value (C₀), which indicates that the depletion region width is being modulated, and thus the epilayer is no longer frozen out as it was under dark conditions. Therefore, the notion that more levels are present deeper in the bandgap cannot be discarded. This may be the reason why the energy level associated with the N_O substitutional, which should be present at ∼E_V + 1.2 eV [8–10], is not observed. It is also important to note that in DLOS all traps found within the depletion region and below the Fermi level contribute to the photocapacitance, independent to their distance from the depletion region edge. In our samples, the Fermi level is above the midgap, and the Schottky built-in voltage (∼1 V) plus the applied bias (0.5 V) is lower than half the bandgap. Thus, the contribution of the photoexcited traps (all found close to the valence band) to the photocapacitance is present from the depletion edge up to the surface, being the space charge region located entirely in the epilayer.

The most interesting result related to the N incorporation is the presence of three new traps that show up in the spectra under illumination energies of E_photon = 2.89 eV (E_V + 0.48 eV), 3.20 eV (E_V + 0.17 eV) and 3.25 eV (E_V + 0.12 eV). The level at E_V + 0.48 eV is clearly not present in the reference sample without N. By using equation (1), its concentration can be calculated to be ∼1 · 10¹⁴ cm⁻³, which is very small compared to the incorporated N concentration, albeit related to it. However, this concentration must be taken as a lower bound, since, as we mentioned earlier, the sample is depleted in the dark and for lower illumination energies, and the total change in capacitance can be easily underestimated. As will be explained in the discussion, this level has already been observed using DLOS in N-doped MOCVD-grown ZnMgO [13].

The next N-induced trap appears in the SSPC spectra as a decrease in capacitance change at E_photon = 3.20 eV (figure 4(c)), only when a voltage fill pulse of 0 V is applied as detailed in the experimental section. When the DLOS spectrum is recorded without a voltage fill pulse, i.e. under a constant −0.5 V reverse bias, this negative step disappears (figure 4(c), inset). Thus, we conclude that the voltage fill pulse is responsible for the negative step. This can be understood as a result of the competition between the majority (electron) carrier photoemission to the CB and minority (hole) carrier thermal emission to the VB [19]. Indeed, its shallow position with respect to the VB (E_V + 0.17 eV) is consistent with thermal hole emission to this band at RT. Since the sample is fully depleted in the dark, a significant amount of holes may exist to compensate the material, which can be trapped during the electrical fill pulse. Thus, we can conclude that this negative onset can be related to a hole trap found at E_V + 0.17 eV.

The shallowest trap, linked to the last onset observed in the SSPC spectrum, is located at E_V + 0.12 eV and accounts for most of the capacitance change shown by this sample. Using equation (1), a trap concentration of ∼1.2 · 10¹⁵ cm⁻³ is obtained, which is still over three orders of magnitude lower than the N concentration in the sample. Since this trap is also the shallowest among all the traps with respect to the VB, it is key to understanding the effect that the growth under N has on these homoepitaxial films. Its potential physical origin will be discussed in the following section.

In all samples, including the N-free reference sample, a trap at E_V + 0.25 eV is observed, indicating that it is not related to N, which suggests an intrinsic defect that is responsible for the whole capacitance change close to the VB. As has already been described, for the undoped and low N samples, determining the concentration for this trap is largely affected by the excitonic absortion that degrades the capacitance measurement by increasing the conductivity. Nevertheless, a lower bound concentration of ∼1.4 · 10¹⁶ cm⁻³ is obtained. This trap matches the hole trap reported by Muret et al [12] at E_V + 0.28 eV (labeled HT4 in his paper) in N-doped ZnO samples, using optical minority carrier transient spectroscopy (O-MCTS). In their work they suggest that this hole trap is not related to N, since its Arrhenius plot matches well with that from a similar level observed in undoped samples by other groups. Their measured concentration, ∼2 · 10¹⁶ cm⁻³, agrees quite well with our measured concentration (∼1.4 · 10¹⁶ cm⁻³), clearly showing that this level is the dominant intrinsic trap close to the VB in m-ZnO. The difference in energy between HT4 (E_V + 0.28 eV) and our result (E_V + 0.25 eV) could arise from the experimental error bar as well as the fact that DLOS yields the actual trap energy in the bandgap, whereas O-MCTS yields the activation energy that assumes, among other things, that the trap capture cross section is temperature independent [19].

Zinc vacancies have been proposed as an intrinsic defect creating a level with a very similar energy. Janotti et al [22] calculated this level to have a transition energy ranging 0.08–0.45 eV from the VB, depending on the calculation method. More recently, Bang et al [2] calculated this transition to be E_V + 0.17 eV. In their review, the intrinsic V_Zn defect is more likely to be found in O-rich samples, with a much shallower energy (closer to VB [22, 23]) and lower formation energy. However, since these energies come from different calculation methods and conditions, their value must be taken with caution. Moreover, Hierro et al [14] also reported a level at E_V + 0.28 eV in undoped ZnMgO grown by MOCVD in sapphire substrates that is responsible for the compensation measured in the samples, showing a large concentration. Gür et al [24] also found a level at E_V + 0.3 eV in both ZnO and ZnMgO films grown by MBE on sapphire. This level was, as in our case, the dominant onset in the DLOS spectra, driving the majority of the capacitance change, further confirming the common intrinsic origin for the trap. In addition, unpublished work from our group also shows that this level is present in undoped homoepitaxial ZnO grown in a- and r- planes, which combined with the former reports, indicates that a level at E_V + 0.25 eV is indeed an intrinsic level independent of the growth method and substrate orientation.

This trap starts to be observable in the mid N sample suggesting a relationship with N incorporation. Moreover, its concentration is quite low, ∼1 · 10¹⁴ cm⁻³, indicative of a reduced impact in the electrical compensation shown by this sample. Several levels have been previously reported by Muret et al [12] by O-MCTS with similar trap energies. Their HT5 level yields an equal energy of E_V + 0.48 eV, although with a much higher concentration. However, and because of the error bar, our level could also correspond to their HT6 or HT7 traps, with energies of E_V + 0.466 eV and E_V + 0.503 eV, respectively. Also, a previous report from our group [13] shows a similar trap at E_V + 0.47 eV in MOCVD-grown Zn_0.9Mg_0.1O:N films measured by DLOS, whose concentration increases with increasing N exposure during  growth.

The level at E_V + 0.17 eV is only observable as a reduction in the overall capacitance in the DLOS spectra. As already explained in the previous sections, the thermal emission of trapped holes to VB dominates over the trapped electron photoemission to the conduction band, producing a decrease of the total measured capacitance. Unfortunately, this competition of emission mechanisms does not allow the quantification of its trap concentration [19], but it does imply that the defect behaves as a minority carrier trap, in this case, a hole trap.

The energy measured by DLOS is consistent with the acceptor involved in the N-related DAP emission we observe in the LT-PL (figure 1) spectra, for which there is a consensus that it is found at 165 meV above the valence band [3, 6, 11, 25, 26]. In addition, Muret et al [12] reported a level at E_V + 0.19 ± 0.04 eV, labeled HT2, with a large capture cross section, related to N incorporation. Thus, this trap at E_V + 0.17 eV can be linked to the N-induced DAP. We should note that this level can only be observed by DLOS in the mid N sample, although it is also likely to be present in the low N sample. However, because of the large rise in capacitance from the dominant intrinsic E_V + 0.25 eV level, it may not be possible to detect the trap, even though the DAP emission to which it contributes is clearly present in the LT-PL spectra (figure 1). In previous work from our group [13], a level at E_V + 0.16 eV was reported in ZnMgO films, with a concentration increasing with N exposure during growth, and related to the electrical compensation observed in the samples.

There is an open question about what is the physical origin for the acceptor that appears with the introduction of N. In the literature, many possible N configurations in ZnO have been described, although great discrepancy can be found in the calculated energy position of the acceptors they generate, which depend on the calculation method. Recently, Bang et al [2] presented a revision of the most plausible levels related to N incorporation, which provides a new canvas for the analysis of the acceptor-like levels found in N-doped ZnO samples. The simple substitutional N_O level has a large activation energy, it is present deep in the bandgap [8, 10] and is also unlikely to appear in such O-rich samples as the ones presented in this paper, since formation energy increases with O-richness. Thus, it can be discarded.

In a previous section, the V_Zn-related level defect is proposed to be present in the N-doped samples and although it is the only level not related with the presence of N during growth it is needed for the formation of many of the other levels proposed as acceptors. Indeed, the N_O-V_Zn complex defect proposed by Liu et al [27] with an energy level of 160 meV above the VB, may be related to the E_V + 0.17 eV trap. For this complex defect a thermal activation is needed, which in our case could be provided by exposure to the growth temperature [11] during the growth time needed to reach 1.5 μm-thick layers (more than 5 h). However, recently Bang et al [2] suggested that the N_O-V_Zn complex has a paramagnetic nature that, when taken into account in the calculation, yields a much deeper trap energy in the bandgap (E_V + 0.87 eV) [2].

Three defects involving a molecular form of N have also been proposed in the literature. The simplest one, (N₂)_Zn, with an activation energy of E_V + 0.22 eV is also the one with the largest formation energy [2]. It is thus unlikely to be the defect responsible for any of the N-related levels found in the present study. Another one, involving oxygen, (NO)_Zn, shows a much lower formation energy with a similar activation energy (E_V + 0.23 eV). Lastly, the level with the lowest formation energy, (NH₄)_Zn, has an energy of E_V + 0.18 eV, but needs the presence of large quantities of H, which is not the case for the samples presented in this paper, grown by MBE using N₂ as the dopant source.

The new level at E_V + 0.12 eV is not directly observed in the PL spectra, albeit being dominant in the photocapacitance measurement for the mid N sample. However, to understand its origin one has to account for the spatial effects that arise from the fact that this sample is depleted in the dark, and only under illumination can the depletion region be slightly modulated with the AC probe signal. Thus, the region being measured during DLOS is close to the substrate/epilayer interface, and the DLOS spectra can be influenced by the presence of structural defects originating at this interface. In order to fully distinguish the type of defect involved, minority carrier DLTS using a variable fill pulse may be needed, as reported by Hierro et al [28], where different kinetics for point defects, extended defects, and point defects decorating the extended defects can aid in this identification. Also, depth sensitive measurements could help clarify the structural origin of this defect. Unfortunately, both types of measurements cannot be performed in a film so strongly depleted like ours.

Accounting exclusively for its energy position in the bandgap, the E_V + 0.12 eV trap may be related to staking faults. Indeed, Lautenschlaeger et al [29] showed that a PL band at 3.31 eV appeared when N is introduced in ZnO, and in parallel to the formation of the DAP. Their emission is likely to be the same as that shown by Schirra et al [30] to arise from a band-to-acceptor recombination (e, A). The acceptor level involved in this emission was proposed to be generated by staking faults and placed at E_V + 0.13 eV, very close to the level observed in our films. More recently, Lin et al [31] clearly demonstrated that in m-plane ZnO films staking faults are responsible for the presence of a CL band at 3.32 eV. However, we do not observe this stacking fault-related emission in our films, and thus, it is unlikely that they are related. Even though the E_V + 0.12 eV trap concentration is quite low, ∼1.2 · 10¹⁵ cm⁻³, this trap shows a sharp optical onset dominating the DLOS spectra, and it is clear that unveiling its physical origin will likely open the path to understanding how N is incorporated in the crystal.