Electric Field and Self-Heating Effects on the Emission Time of Iron Traps in GaN HEMTs

In this article, we separately investigate the role of electric field and device self-heating (SHE) in enhancing the charge emission process from Fe-related buffer traps (0.52 eV from <inline-formula> <tex-math notation="LaTeX">${E}_{c}$ </tex-math></inline-formula>) in AlGaN/GaN high electron mobility transistors (HEMTs). The experimental analysis was performed by means of drain current transient (DCT) measurements for either: 1) different dissipated power (<inline-formula> <tex-math notation="LaTeX">${P}_{D,\mathrm {steady}}$ </tex-math></inline-formula>) at constant drain-to-source bias (<inline-formula> <tex-math notation="LaTeX">${V}_{\mathrm {DS,steady}}$ </tex-math></inline-formula>) or 2) constant <inline-formula> <tex-math notation="LaTeX">${P}_{D,\mathrm {steady}}$ </tex-math></inline-formula> at different <inline-formula> <tex-math notation="LaTeX">${V}_{\mathrm {DS,steady}}$ </tex-math></inline-formula>’s. We found that: 1) an increase in <inline-formula> <tex-math notation="LaTeX">${P}_{D,\mathrm {steady}}$ </tex-math></inline-formula> yields an acceleration in the thermally activated emission process, consistently with the temperature rise induced by SHE and 2) on the other hand, the field-effect turned out to be negligible within the investigated voltage range, indicating the absence of the Poole–Frenkel effect (PFE). A qualitative analysis based on the electric field values obtained by numerical simulations is then presented to support the interpretation and conclusions.

deep levels related to intentional or undesired impurities incorporated during material growth or device fabrication induce trapping effects that severely affect the large-signal operation. Iron (Fe) dopants, for instance, are generally adopted in RF transistors [4], [5] to obtain semiinsulating buffer layers to increase the blocking voltage [6]. At the same time, however, the deep-acceptor related to Fe dopants at 0.5-0.6 eV from the conduction band minimum (E C ) [7]- [12] represents a major cause for the current collapse (CC) in these devices [13], leading to a decreased output power and consequent reduction of power added efficiency (PAE) [14]. These detrimental effects have led many authors to study the nature of Fe-trap in GaN (see [15] and references therein), but a precise definition of the physics behind this deep level is still an open issue [12]. Further studies are, thus, required to accurately model the Fe-trap response and, consequently, the device behavior. To this end, the study of the charge emission dynamics from traps represents effective means to gain insights into their physics. More precisely, the emission time constants of deep levels are strongly affected by the operating conditions in terms of bias, temperature, and electric field distribution, and these dependencies are indicative of the traps nature. The aim of this article is, thus, to further extend the knowledge on iron-related traps by investigating their emission rate dependence from temperature and electric field.
Concerning the role of temperature, it is well known that the emission of an electron from an impurity level to the conduction band is a thermally activated process with activation energy E a = E c − E t and emission time constant τ , mutually related by the Arrhenius equation [16]. Accordingly, the net rate of carrier emission from traps is strongly temperaturedependent, and this correlation is typically employed to extract E a from measurements at different ambient temperatures. However, the estimation of E a could be seriously affected by the self-heating effect (SHE) [17], which is known to raise the DUT temperature, thus accelerating the emission process [17].
The electric field plays a similar role in enhancing the emission rate, yielding a substantial reduction of the apparent activation energy [18]. Particularly, the Poole-Frenkel effect (PFE) is expected to dominate the field-enhanced emission for low-medium voltage levels (i.e., conventional RF operations), while secondary effects, such as phonon-assisted tunneling (PAT) and direct tunneling (DT), come into play only for high field values (i.e., high voltages) [19]. However, PFE affects only charged Coulombic traps [20]- [22], making it difficult to predict its contribution without an in-depth knowledge of the trap state involved in the emission process.
To assess the dependence of the Fe-traps emission rate on SHE and electric field, we perform drain current transient (DCT) measurements [23], [24] starting from properly chosen bias conditions to evaluate these two concurrent effects separately. DCTs are, thus, monitored for either: 1) different dissipated power (P D,steady ) with constant drain-to-source bias (V DS,steady ) or 2) different V DS,steady 's with constant P D,steady . The first condition allows investigating SHE while keeping constant the electric field; the second one, instead, allows determining the role of PFE without increasing SHE in the device. To the best of our knowledge, this is the first time in which PFE is studied for Fe-related buffer traps.
From the above analysis, we find that increasing P D,steady accelerates the thermally activated emission process from Fetraps, consistently with the temperature rise induced by SHE. Conversely, we find negligible dependence of the observed DCTs on the varying electric field, suggesting the absence of PFE.
The rest of this article is organized as follows. Section II provides a description of the devices under test (DUTs) and their typical I G − V GS , I D − V GS , I D − V DS , and power sweep characteristics. Afterward, a description of the measurement setup for DCTs used for trap characterization will follow. After proving the presence of dispersion effects connected to Fe-related traps within the tested devices, the emission rate dependence from SHE and the electric field is investigated in Section III. In Section IV, we report 2-D numerical simulations to estimate the electric field experienced by Fe-traps, while Section V reports a qualitative analysis on PFE, showing that, if present, PFE should have affected the emission rate within the investigated range. Finally, Section VI draws the conclusions of this work.

II. DEVICE DESCRIPTION AND PRELIMINARY CHARACTERIZATION
Devices tested in this work were single-AlGaN/GaN heterojunction HEMTs grown on SiC substrate (see Fig. 1). AlGaN  barrier layer was 20-nm thick with a 22% Aluminum concentration, while the 2-μm-thick GaN buffer was iron-doped to obtain a semiinsulating layer [6]. Iron concentration in the GaN buffer starting from the SiC substrate interface is constant at 1 × 10 18 cm −3 until at a distance of 0.6 μm from the AlGaN/GaN interface where the iron concentration starts to decay with a slope of one decade every 0.4 μm. Device fabrication started with Ti/Al/Ni/Au ohmic contact formation followed by device isolation by means of ion implantation. A Si 3 N 4 passivation layer was then deposited followed by a CF 4 -based dry etching for the opening of the device gate foot. Ni/Pt/Au gate metallization was then evaporated selfaligned, yielding an I-shape gate contact without field plates. The device's gate length was 0.5 μm, while gate-source and gate-drain spacings were 1 and 2.5 μm, respectively. Three different gate peripheries were characterized, labeled as types A, B, and C, presenting total gate widths of 10 × 100, 8 × 75, and 4 × 75 μm, respectively.
The device's threshold voltage at 1-mA/mm drain current level at V DS = 7 V was approximately −2.8 V, as shown in Fig. 2. For V DS < 60 V, the drain leakage current at V GS = −6 V was below ∼20 μA/mm (not shown), whereas the breakdown voltage evaluated at I D = 1 mA/mm [25] was about 120 V [see Fig. 3(a)].
In Fig. 3(b), we reported the results of CW load-pull measurements performed on tested devices at a 2.5-GHz frequency and a quiescent drain voltage of 30 V. The output power (P OUT ) reached a maximum of 4.1W/mm with a 40.1% peak PAE.   The presence of the Fe-doped buffer suggests that the observed current dispersion might be related to the response of iron-related traps located within the buffer. The kinetics of said traps was, thus, investigated by means of DCT measurements carried out at different temperatures.
DCTs induced by trapping phenomena have been measured with the double-pulse method sketched in Fig. 5, which allows minimizing the drain-source voltage (V DS ) variation during the transient [26]. The DUT is initially biased for few minutes in ON-state conditions (V DS,steady , V GS,steady ), allowing it to reach a stable I D,steady drain current level. A 1-μs trap-filling pulse is then applied with V GS,pulse = −3.8 V and V DS,pulse = 8 V, ensuring the occupation of the traps [13]. Then, the device is set back to the initial (V DS,steady , V GS,steady ) bias, and the DCT is monitored over several time decades to allow for a full recovery of the initial I D,steady drain current value.
DCTs were, thus, measured at V DS,steady = 4 V, while V GS,steady was settled in order to obtain a 50-mA/mm I D,steady current level. The apparently low values for both V DS,steady and I D,steady have been selected in order to reduce the influence of device self-heating, which is known to affect the estimation of E a [17].
Typical DCTs obtained on a type A device in the 30 • C to 70 • C temperature range are depicted in Fig. 6(a). In order to evaluate the charge emission dynamics, DCTs have been fitted by a stretched multiexponential function [27]. The corresponding d I D /dlog 10 t signals are reported in Fig. 6(b), where a single and well-defined peak can be observed. The associated emission time constant (τ ) has been then extracted in correspondence to the peak obtained in the d I D /dlog 10 t signal, yielding the Arrhenius plot reported in the inset of Fig. 6(b). The linear fit of the points on the Arrhenius plot yielded a 0.52-eV activation energy and 5 × 10 −16 cm 2 cross section, which is consistent with values reported in the literature for Fe-related buffer traps [7]- [12]. To better identify the trap type, we compared the Arrhenius plot obtained in this work, with those obtained in previous reports and associated with Fe-traps [8], [11], [12], [28]- [30] (see Fig. 7). As we can see from Fig. 7, the activation energy, trap cross section, and emission times are consistent with those largely reported for iron traps in GaN. According to this observation and the presence of a highly Fe-doped buffer layer, we can speculate that the monitored DCTs are due to the emission of electrons from traps related to iron dopants [8]. The devices tested in this article can, thus, be used as test vehicles for the characterization of the iron trap under different measurements conditions, i.e., evaluate the effect of device self-heating and electric field on the emission time constant of said trap.

III. FE-TRAP EMISSION TIME DEPENDENCE FROM DEVICE BIAS CONDITIONS
In order to investigate the role of both SHE and electric field on the Fe-trap emission process, the measurement method Fig. 7. Comparison between the Arrhenius plot measured in this work and those associated with Fe-related traps by other authors. Points measured in this work well agree to those in the literature, confirming that the observed DCTs are due to electron emission from Fe-traps.
described in Section II was adopted. A thermal chuck was used for setting the DUT's base-plate temperature at 30 • C during the measurement, fixing the boundary conditions for the experiments. The induced DCTs have been measured starting from several steady-state biasing conditions, with the aim to span a sufficiently broad range of power levels and voltages. To a first approximation, the applied V DS,steady is directly linked to the electric field intensity, whereas I D,steady × V DS,steady product defines the power dissipation within the device. Steady-state bias conditions were, thus, chosen with V DS,steady ranging from 15 to 40 V with a 5-V step and dissipated power (P D,steady ) ranging from 0.4 to 2.0 W/mm with a 0.4-W/mm step for a total of 30 different steady-state bias conditions.
The remainder of this section is organized as follows. First, the choice of the DCT measurement conditions adopted for the analysis is explained in detail. Then, results showing the role of SHE and electric field for a typical type A device are discussed. Finally, we present results of a systematic analysis on devices of the three types that are considered.

A. Choice of the Bias Conditions
Prior to the actual DCT characterization, each steadystate condition was held for a sufficiently long time (more than 2 min) to guarantee thermal equilibrium. Furthermore, the trap-filling pulse parameters were chosen to deliberately induce a relatively small current variation (∼4 mA/mm) to avoid excessive perturbation of the steady-state operating point. This choice was mainly motivated by the following considerations: 1) a large current variation would change significantly the dissipated power during the monitored transient [17], whereas a small perturbation does not affect the power set in a steady-state condition, thus yielding negligible temperature variations and 2) a small current variation is representative of a low amount of trapped charge variation [30]- [32], whose dynamics is expected to not significantly alter the electric field profile during the DCT.
Equivalently to Section II, during the short filling pulse (1 μs), the devices are biased at V GS,pulse = −3.8 V, i.e., 1 V below DUT's V TH , so that the subthreshold current flowing through the channel/buffer provides the electrons to be trapped [30] and just the Fe-traps response is induced. The V DS,pulse level is instead adjusted for each DCT in order to induce a constant amplitude in the d I D /dlog 10 t peak for all the acquired DCTs. This choice was adopted to ensure the same variation of trapped charge into buffer states. In fact, since the amplitude of the peak is related to the amount of current dispersion caused by the trap with the considered time constant [30], i.e., to the amount of trapped electrons [31], [32], maintaining a constant peak amplitude ensures a constant variation of trapped charge during the filling pulse, regardless of the steady-state bias.

B. Role of SHE on emission time constant
In the experiments reported in Fig. 8 As we can see in Fig. 8(b), the peak in the d I D /dlog 10 t plot moves toward shorter times when increasing P D,steady according to the temperature rise in the device active region. The dependence of the emission rate on the SHE is consistent with expectations; in fact, the CC related to Fe-related buffer traps is due to electron capture, and the resulting DCT is due to the emission of trapped carriers to the conduction band. Since charge emission is a thermally activated process, the increase in the temperature caused by SHE is responsible for the speed-up observed while passing from 0.4 to 2.0 W/mm.

C. Role of Electric Field on Emission Time Constant
The electric field effect is shown in Fig. 9. By varying V DS,steady in the device's saturation region between 15 and 40 V while maintaining a constant power dissipation P D,steady = 0.4 W/mm, we investigated operating points where the SHE is the same among all the DCTs considered. As a consequence, if the electric field plays any role in the emission  time constant, we would expect a dependence on V DS,steady . Fig. 9(a) shows that the measured DCTs at different V DS,steady 's are essentially overlapped, and the corresponding peaks in the d I D /dlog 10 t plot are perfectly aligned [see Fig. 9(b)]. Accordingly, we conclude that the emission rate of the Fe-related acceptor is insensitive to the applied V DS up to 40 V.

D. Time Constants From All the Steady State Conditions
In order to highlight the generality of the previously discussed SHE and electric field dependencies, the Comparison between experimental and simulated pulsed I D − V GS characteristics obtained at room temperature for tested devices at V DS = 2 V and V DS = 7 V. characterization was performed on all the 30 steady-state bias points previously defined. The emission time constant from typical devices of types A, B, and C geometries has been extracted [see Fig. 10(a)-(c)], respectively. The emission speed-up produced by SHE is always present, even if this effect is less pronounced for smaller devices, since a reduced periphery yields a lower temperature increase for the same power density. Nevertheless, for all tested devices, we can see the same underlying trends. In the explored bias range, the field effect turned out to be negligible at all dissipated power values, while SHE produces a clear enhancement of the emission process, resulting in parallel lines moving toward shorter times at the increase of dissipated power.

IV. NUMERICAL SIMULATIONS
Experimental data clearly show that the emission rate is not affected by electric field variations at least within the investigated voltage range. This evidence suggests that electric field plays a minor role in enhancing charge emission from Fe-traps at medium-low V DS . To better define the electric field experienced by Fe-traps in our measurements, we carried out 2-D numerical simulations using the commercial Sentaurus (Synopsis Inc.) simulator. Fe-related traps in the GaN buffer were modeled with deep acceptor-like traps at 0.52 eV below the conduction band edge, as experimentally observed by DCTs measurements. The simulation deck was calibrated by comparison with measurements on the devices under examination (see Fig. 11). Fig. 12 shows the simulated concentration of trapped electrons in the device (e.g., at V DS,steady = 40 V and Similar profiles were observed for all the bias conditions investigated in this work, indicating that the largest concentration of ionized Fe-traps is typically located in this region, in accordance with previously published results [5]. Particularly, the depth from which the carriers are emitted does not change significantly for the bias conditions that are explored.
Thus, we consider the electric field in correspondence to the peak in the ionized trap concentration as the one experienced by Fe-traps for the analysis related to the expected PFE contribution that will be presented in Section V.
According to the experimental analysis presented in Section III, we extracted the electric field (F) in the region of maximum trapping for V DS,steady between 15 and 40 V and P D,steady from 0.4 to 2.0 W/mm. The corresponding values of F are reported in Fig. 13, in which F ranges between 0.226 and 0.408 MV/cm while passing from 15 to 40 V. Particularly, the electric field experienced by Fe-traps increases almost linearly with the applied V DS,steady , with a negligible dependence on P D,steady .
According to this observation, we can more thoroughly interpret the results obtained in Section III as follows. Even though the electric field (F) changes considerably while changing V DS,steady between 15 and 40 V, this variation does not produce any appreciable effect on the emission time constant of Fe-traps in this range.

V. ELECTRIC FIELD DEPENDENCE
The electric field values obtained with numerical simulations can, thus, be used to better identify the field-related mechanisms that could affect the trap's behavior in the explored bias range. As previously stated, several electricfield-related effects, such as PFE, PAT, and/or DT, can modify the emission rate. PAT and DT typically occur at a very high electric field, and they are unlikely to occur in the investigated bias points. On the other hand, PFE is expected to affect the emission rate for low-medium voltage levels [19]. The fact that we do not see any field dependence in our experimental data suggests that the traps involved, i.e., the iron-related ones, are not experiencing PFE. In order to gain more insights into this behavior, we perform a simple first-order analysis to prove that, if PFE would occur, completely different experimental trends would have been observed.
The PFE role in enhancing trap emission rate (e = 1/τ ) is given by [18] where k is Boltzmann's constant, E a is the activation energy, T is the absolute temperature, and A is a constant referring to the trap emission cross section. The E PF term in (1) refers to the PFE and is defined as [18] where q is the elementary charge, ε 0 is the vacuum dielectric constant, ε r is the GaN dielectric constant, and F is the electric field [22]. Looking at (1) and (2) it is clear that, in the increase in F, the emission rate should increase. The electric field in (2) can be defined according to the values reported in Fig. 13 since we are interested in the electric field experienced by Fe-traps in the explored bias conditions. By taking the natural logarithm of the ratio between the emission rate (e) at a generic V DS,steady value (for which F is known, according to numerical simulations) and a reference e ref at V DS,ref = 15 V (i.e., F ref ∼ 0.226 MV/cm), it is now possible to predict the relative e enhancement due to PFE. Furthermore, if we compare data obtained at the same P D,steady , as it has been done experimentally, the temperature variations are negligible, thus allowing to simplifying the AT 2 exp(−E a /kT) term in (1), highlighting, in (3), the square root dependence on F Despite this simplification, a realistic value for T (i.e., temperature in the device active region) is still needed to calculate (3). To this end, T was evaluated for device A at several dissipation levels with the McAlister's method [33], yielding a thermal resistance (R TH ) of 22 K/W (not shown). The extracted R TH was then used to infer T for the considered bias range (i.e., P D,steady between 0.4 and 2.0 W/mm) according to (4) Since device A presented a total gate width of 10 × 100 μm, we obtained two limit cases for T : T = 311.8 K for P D,steady = 0.4 W/mm and T = 347 K for P D,steady = 2.0 W/mm. In order to cover the whole temperature range explored in this study, we considered both values of T in our analysis.
A comparison between the emission rate obtained from experimental data in Fig. 10(a) and analytical values computed with (3) is shown in Fig. 14. Interestingly, the comparison shows that the predicted behavior with (3) is completely different from actual data, indicating that PFE is not taking place. Rather than a rigorous comparison, Fig. 14 should be intended as an integrity check for the validity of the speculation that PFE does not take place for iron traps in these devices. In fact, if PFE was actually affecting emission rate, experimental data points would not lie on a horizontal line but would rather be placed nearby the curves calculated with (3). For this reason, we can conclude that the PFE can be ruled out as a mechanism inducing emission acceleration for Fe-traps since, in the explored voltage range, it would have produced a significant V DS (i.e., field) dependence, which is on the contrary absent. This evidence highlights the nature of iron traps. In fact, for a trap state to experience PFE, it must be charged when empty and neutral when it captures a carrier (i.e., donor-like) [20]- [22]. Conversely, iron dopants introduce a deep acceptor-like trap, which is normally neutral and becomes negatively charged by capturing an electron from the conduction band [34]. The trap potential can be approximated at first-order by a Dirac well [21], for which the barrier lowering responsible for PFE would be negligible in agreement with the presented experimental results.

VI. CONCLUSION
In this article, we investigated the role of self-heating and electric field on the emission process from iron-related traps in AlGaN/GaN HEMTs for RF applications. The adopted experimental approach, based on the monitoring of DCTs with either constant dissipated power or constant drain-to-source bias, allowed us to effectively evaluate separately self-heating and electric field roles. We found that self-heating produces a consistent acceleration in the thermally activated emission process, as a result of the temperature rise in the device active region. On the other hand, the experimental results revealed for the first time no evidence of the PFE, consistently with the non-Coulombic nature of Fe-related buffer traps. Consequently, PFE can be excluded for Fe-traps in GaN, corroborating the conclusion that thermal effects dominate the emission dynamics from these traps under conventional operative conditions. This result clarifies the behavior of iron traps in GaN HEMTs for which the absence of PFE can reduce the complexity of the simulation models used to interpret the experiments without loss of accuracy.