“Hole Redistribution” Model Explaining the Thermally Activated RON Stress/Recovery Transients in Carbon-Doped AlGaN/GaN Power MIS-HEMTs

RON degradation due to stress in GaN-based power devices is a critical issue that limits, among other effects, long-term stable operation. Here, by means of 2-D device simulations, we show that the RON increase and decrease during stress and recovery experiments in carbon-doped AlGaN/GaN power metal–insulator–semiconductor high electron mobility transistors (MIS-HEMTs) can be explained with a model based on the emission, redistribution, and retrapping of holes within the carbon-doped buffer (“hole redistribution” in short). By comparing simulation results with front- and back-gating OFF-state stress experiments, we provide an explanation for the puzzling observation of both stress and recovery transients being thermally activated with the same activation energy of about 0.9 eV. This finds a straightforward justification in a model in which both RON degradation and recovery processes are limited by hole emission by dominant carbon-related acceptors that are energetically located at about 0.9 eV from the GaN valence band.

system exhibit enhanced switching speed and breakdown field capability, enabling operation at higher operating voltage/frequency/temperature [1], [2]. However, the introduction of AlGaN/GaN HEMTs into the mass market not only depends on the demonstration of outstanding performance but also on the stable and reliable operation of these devices.
Mitigation of the failure mechanisms to ensure long-term reliable operation is, therefore, crucial to the success of GaN power electronics. In this regard, several physical aspects related to the so-called current-collapse effect (dynamic drain current drop or ON-resistance increase) and threshold voltage drift (influencing current-collapse as well) occurring when performing OFF-ON (or ON-OFF) switching still need to be fully understood. Experimentally, "stress" tests are carried out by applying bias conditions that are known to accelerate the so-called dynamic R ON degradation, i.e., the increase in the device ON-state resistance (R ON ) during the typical pulse-mode operation of power transistors in power switching converters.
In this work, we propose an explanation for the ON-resistance (R ON ) behavior during both front-and back-gating OFF-state stress and recovery experiments reported for AlGaN/GaN metal-insulator-semiconductor HEMTs (MIS-HEMTs) featuring a carbon-doped buffer, which is based on a hole emission/redistribution/retrapping model ("hole redistribution" in short). This article is based on a recent conference paper of ours [3] where only back-gating stress/recovery was considered and extends our analysis to more customary front-gating stress/recovery experiments.
Carbon (C) doping is a widespread technology solution to reduce buffer conductivity and increase breakdown voltage for power applications [4], [5]. The introduction of acceptor traps associated with C-doping, however, leads to an enhancement of current collapse and dynamic R ON degradation during OFF-state stress [6]. It is widely accepted that this is due to negative charge build-up in the C-related traps within the buffer [7]- [11]. This phenomenon is conventionally attributed to electron capture into buffer traps [8]- [11]. The work by Meneghesso et al. [7] reports on the R ON stress and recovery behavior measured in power MIS-HEMTs during front-and back-gating experiments, finding that both transients under either test conditions are thermally activated with the same activation energy (E A ) of about 0.9 eV. In [7], a possible explanation for this was proposed, based on the observed correlation of the thermally activated stress with the buffer leakage increase due to temperature [8]. Moreover, the discharging of C-related buffer traps during recovery transients was also attributed to thermally activated vertical/lateral leakage paths in other works [6], [12], [13].
Here, we propose that the activation energy of both stress and recovery processes can be directly attributed to the dominant acceptor trap energy level associated with carbon in the buffer, as a result of hole emission, redistribution, and retrapping in the C-doped buffer. Stress is performed either: 1) by applying a negative bias to the gate contact (V G ) and a large positive bias to the drain contact (V D ) (with source and substrate contacts grounded) or 2) by applying a negative bias to the substrate contact (V B ) (with all other contacts grounded). We will refer to the above stress conditions as to front-and back-gating OFF-state stresses, respectively (front gating offstate stress (FGOS)/back gating off-state stress (BGOS) in short).
The proposed model: 1) is seamlessly related to the commonly accepted model for C doping in GaN, i.e., a dominant acceptor trap level at about 0.9 eV from the valence band edge (E V ) [14] that turns the GaN buffer into a weakly p-type region; 2) does not require, though does not exclude, possible charging/discharging mechanism through leakage paths; and 3) self-consistently captures the dynamics of stress/recovery processes up to drain bias for which C doping is able to effectively suppress electron leakage current through the GaN buffer, i.e., before significant electron injection into the buffer from the source and/or from the substrate takes place.
The article is organized as follows. In Section II, the modeling framework is illustrated along with the analyzed device structure and the relevant physical models employed. Results are presented and discussed in Section III. Finally, conclusions are drawn in Section IV.

II. MODELING FRAMEWORK
The structure employed in the simulations in this work is sketched in Fig. 1, resembling a typical power AlGaN/GaN MIS-HEMT. The 2-D numerical device simulations were carried out with SDevice (Synopsys Inc.) Technology CAD (TCAD) simulator [15]. We first calibrated our TCAD simulation deck against experimental I D -V GS data reported in [16]. The outcome is shown in Fig. 2. As reported in [16], the calibrated device features a highly conductive p-type Si  (15 nm) that is added to the structure after partially recessing the barrier and leaving 3.7 nm of residual AlGaN under the gate [16]. The gate-drain access region is 5 µm [16] (while it is 10 µm in [7] from which stress and recovery experimental data are taken).
Charge transport was modeled by means of the driftdiffusion model. The piezoelectric polarization at the heterointerfaces was included by using the default strain model of the simulator [15]. A fully dynamic trap modeling approach was adopted, with one Shockley-Read-Hall (SRH) trap-balance equation for each distinct trap level included, describing the dynamics of trap occupation without any quasi-static approximation. A detailed description of the modeling approach to describe device physics in AlGaN/GaN-based HEMTs can be found in [18]. The gate insulator (Al 2 O 3 ) is assumed ideal, i.e., gate leakage current is neglected.
C doping in the GaN buffer was modeled by considering a dominant deep acceptor trap at 0.9 eV above E V partially compensated for by a shallow donor trap at 0.11 eV below E C [17]. To reproduce the experimental results, the adopted trap concentrations were 2 × 10 18 and 1 × 10 18 cm −3 for Crelated acceptors and donors, respectively. This corresponds to an effective acceptor density of 1 × 10 18 cm −3 with a compensation ratio of 50%. No additional traps were considered, while, in all nitride layers, an n-type doping density of 1 × 10 15 cm −3 was assumed, as conventionally done when simulating GaN devices to account for the unintentional n-type conductivity due to the introduction during growth of shallowdonor impurities (such as oxygen and silicon) [5], [19].
The C doping model employed in this work was developed over the years by our group and allowed explaining measured current-collapse, threshold voltage shifts, and breakdown effects in different GaN power HEMTs [3], [20]- [25]. The dependability of the acceptor-donor model for C doping is further confirmed by its capability of reproducing sourcedrain leakage currents and OFF-state breakdown, as reported in [19]. The key assumption in the adopted C doping model is that the dominant deep acceptor traps for holes are partially compensated by shallow donor traps for electrons. The actual energy position of donor traps, however, if sufficiently shallow, has little influence on simulation results. Indeed, C-related donors could actually be closer to E C or even be modeled as completely ionized doping, in agreement with recent hybrid-functional density functional theory (DFT) calculations [14], [26].
Furthermore, an experimental indication that C doping introduces donors besides acceptors is found in [27]. According to previous reports, for moderate C doping concentration (i.e., ≤10 18 cm −3 ), it is appropriate to model dopants as discrete point defects, whereas, for concentrations of about (or higher than) 10 19 cm −3 , it is more appropriate to use a defect-band model [28].

III. RESULTS AND DISCUSSION
We will first compare simulation results with the experimental data obtained from stress and recovery tests carried out on the MIS-HEMT, as reported in [7]. The sketch of the cross section is shown in Fig. 1. Both stress conditions (i.e., FGOS and BGOS) bias the device in the subthreshold region. However, the BGOS setup is useful to rule out surface trapping effects-which can be present during FGOS instead-thus allowing to attribute the observed phenomena to buffer traps only [29], [30]. Under BGOS tests in fact, the formed two-dimensional electron gas (2DEG) channel screens the superficial layers from the field effect induced by back-gating, so the surface effects should be negligible [29]. The fact that similar kinetics was found for FGOS and BGOS is an indication that buffer traps are mainly involved [8]. The chosen experimental FGOS and BGOS conditions represent "intermediate" OFF-state bias conditions, i.e., with drain voltages that are large enough to have appreciable dynamic R ON effects but, at the same time, low enough not to promote significant electron injection through the C-doped buffer due to lateral source-drain punchthrough or vertical leakage current. During stress simulations, R ON values were obtained by fast sweeping the device bias to measurement conditions (V G , V D ) = (0, 0.5) V in 10 ms to mimic on-the-fly (OTF) measurements [7]. During recovery, instead, R ON was monitored throughout the simulation as recovery and measurement conditions were the same. R ON results in Figs. 3 and 4 are normalized with respect to the fresh value at each temperature to purify results from the R ON degradation induced by mobility reduction. Recovery tests were performed immediately after the stress phase was completed. Since R ON measurement takes about 50 ms [7], no measurement data points were acquired for recovery time less than 100 ms. For both FGOS and BGOS, simulation results can reproduce reasonably well the essential features shown by the experimental results taken at different temperatures. That is, simulations capture the thermally activated processes at the basis of both R ON degradation and recovery, as well as the time constant ranges.
As shown in [7], stress and recovery transients are found to be thermally activated with similar activation energies in the range of 0.84-0.95 eV, irrespective of the stress condition. We report on the experimental Arrhenius plots shown in [7] (for stress only) in Fig. 5 for both FGOS and BGOS conditions and compare them with simulation results (in this case showing both stress and recovery). The time constants at each temperature for both experiments and simulations were extracted by fitting the curves with the stretched exponential method [31]. The data at 60 • C were not suitable for the extraction of a time constant and were, therefore, excluded from the Arrhenius plot, the latter still having four reliable points for the extrapolation of E A . As it can be noted, the Arrhenius signature of the stress process is well reproduced by our simulations, and more importantly, simulations predict the same activation energy of about 0.9 eV for both stress and recovery in either FGOS/BGOS conditions. Before providing the detailed explanation for this, it is important to observe that the R ON increase shown in Fig. 3(a) and (c) [as well as in Fig. 4(a) and (c)] can in principle be induced by either electron trapping into or hole detrapping from the buffer traps. Consequently, the corresponding R ON recovery illustrated in Fig. 3(b) and (d) [as well as in Fig. 4(b) and (d)] can be ascribed to either electron detrapping or hole trapping, respectively. However, regardless of the actual charge carriers involved, the fact that both emission and capture processes are thermally activated, and more importantly, exhibit the same activation energy is not trivial. In fact, while carrier emission is always a thermally activated process, carrier capture can only be thermally activated in traps that feature a capture barrier although the associated activation energy is generally different (and smaller) than the emission one [8], [11]. In the case of the devices considered here, the extracted E A (for both stress and recovery) correlates very well with the transition energy of the dominant acceptor level (C N ) related to carbon in GaN [13].  We will now show that this behavior can be explained with a hole emission, redistribution, and retrapping model. The model applies to both FGOS and BGOS. Thus, we focus only on the latter case for simplicity of data presentation, as, under back-gating conditions, the buffer is uniformly exposed to the backside bias, and all internal quantities are characterized by an almost 1-D distribution (along the device depth direction). In the following, we will explain the processes occurring during stress and recovery with the aid of the plots of the net ionized acceptor trap density (N − A − N + D ) and of the free hole density, p, as shown in Figs. 6 and 7. These plots are taken along a cutline parallel to the device depth drawn in the middle of the gate-drain access region and zoomed in at the top and bottom regions of the buffer, i.e., at the channel/buffer and nucleation/buffer interface, respectively. Note that the ionized donor trap density in the buffer remains constant (not shown) because the energy level of these traps is shallow (i.e., 0.11 eV from E C ) [19]. The C-doped buffer behaves as a weakly p-type region, and the C-related donors simply have the role of partially compensating the dominant acceptor levels, without causing dynamic effects themselves. This picture can change at higher voltages than those considered here, as approaching lateral or vertical breakdown conditions significant electron injection into the C-doped buffer can take place either from the source or the substrate, respectively. Under such conditions, transport processes may impact the stress/recovery kinetics, as suggested in [32]. During stress, (N − A − N + D ) (net negative charge) in the top region of the buffer close to the channel increases because holes are being emitted from the 0.9 eV C-related acceptor traps to the valence band. This correlates with the observed R ON increase during stress. The variation in (N − A −N + D ) close to the channel is evident by comparing the cases before and after stress in Fig. 6(a) and (b). The hole emission process is thermally activated with 0.9-eV activation energy [see Fig. 5 Fig. 6(c), thus explaining the R ON decrease during recovery. The hole retrapping process during recovery is also thermally activated with 0.9-eV energy since the retrapped holes in the upper part of the buffer need to be emitted from the C-related acceptor traps in the bottom region of the buffer [see Fig. 6(f)]. After 1000 s of recovery, the state prior to stress is fully restored (as testified by the results in Fig. 4), and consequently, the p peak at the bottom of the buffer disappears [see Fig. 7(f)]. The recovery phase fully restores the prestress value of R ON because the holes emitted during stress do not leak out from the device contacts or recombine with electrons. This is further confirmed by the fact that, while (N − A − N + D ) varies locally in the buffer, as shown in Fig. 6, its integral value in the buffer stays constant. For instance, ∫(N − A − N + D )dxdy ≈ 1.6 × 10 17 cm −3 µm 2 (at T = 100 • C) prior to and after the stress phase and after the recovery one.

IV. CONCLUSION
We presented a "hole redistribution" model explaining the R ON stress/recovery experiments in C-doped AlGaN/GaN power MIS-HEMTs. Stress is ascribed to hole emission from C-related acceptor traps close to the channel/buffer interface that redistribute and get trapped in the same type of traps in the bottom region of the buffer close to the buffer/nucleation interface. During recovery, the opposite process takes place: the previously trapped holes in the bottom part of the buffer are emitted and get retrapped by the same traps at the top of the buffer that emitted them during stress. The proposed model: 1) solves the puzzle of the activation energy being the same in both stress/recovery phases and 2) explains the full recovery of the R ON after the complete stress-and-recovery cycle in the analyzed devices.