Dynamic Behavior of Threshold Voltage and ID–VDS Kink in AlGaN/GaN HEMTs Due to Poole–Frenkel Effect

The kink effect in field-effect transistors (FETs) consists in a sudden increase in drain current, <inline-formula> <tex-math notation="LaTeX">${I}_{\text {D}}$ </tex-math></inline-formula>, during a drain voltage sweep and leading to a higher <inline-formula> <tex-math notation="LaTeX">${I}_{\text {D}}$ </tex-math></inline-formula> saturation value. We report new experimental data concerning the dynamic behavior of the “kink” in AlGaN/GaN HEMTs and correlate them with deep levels. The results demonstrate the role of the Poole–Frenkel effect in determining the occurrence of the kink and identify the experimental conditions that make it observable.

D RAIN current, I D , versus drain voltage, V DS , characteris- tics of field-effect transistors (FETs) can be affected by an instability called "kink effect," which consists in a sudden increase in I D during a V DS sweep, taking place over a narrow V DS range and leading to a higher I D saturation value [1].The kink effect has been observed in silicon-on-insulator and silicon-on-sapphire MOSFETs, where it has been attributed to accumulation of positive charge in the floating Si buffer due to holes generated by impact ionization [2], [3], [4].GaAs FETs can be affected by kink due to trapping/detrapping effects in the semi-insulating substrate or at the device surface [5], [6].
The kink effect can be associated with transconductance decrease and output conductance increase [14], [28], [29] and is therefore a relevant degradation mechanism for GaN HEMTs, which currently represent the most promising devices for RF power amplifier applications [29], [30].Recently, Grupen [1] has investigated kink effects in GaN HEMTs by means of simulations based on the Fermi kinetics transport and hot electron simulation method, including field-enhanced tunneling ionization of deep traps.Simulations in [1] were compared with experimental data reported in [12]; it was shown that the highly nonlinear field dependence of the electron tunneling probability into and out of traps located in the AlGaN barrier, along with hot electron effects, can explain the shape and bias dependence of the kink effect.
In this article, we report new experimental data concerning the dynamic behavior of the kink effect in GaN HEMTs, an aspect that has been neglected in the literature up to now.Results confirm the model proposed in [1] and provide new insights concerning the experimental characterization of kink effects.Devices under test, experimental setup, and experimental procedures are introduced in Section II; experimental results concerning direct current (dc) characteristics and dynamic threshold voltage, and V TH transient results are discussed in Section III.Finally, the results are reviewed and discussed in Section IV.Schematic of the measurment processes during (a) DC characterization: first, the V GS value is set, and after 30 ms (pink), the staircase V DS ramp starts; each step having a minimum duration of 40 ms (blue); at the end of the last step, when V DS reaches V DSmax , the drain voltage is turned off, after approximately 10 ms (black), the new V GS is applied (b) DP characterizations and (c) setup of the DP system.

II. EXPERIMENTAL DETAILS: DEVICES, QUASI-STATIC,
AND PULSED I D -V DS CHARACTERISTICS The devices analyzed in this article were fabricated on AlGaN/GaN heterostructures grown on SiC substrate, by using a 0.25-µm standard industry process.The GaN buffer was doped with carbon (C), in order to increase the charge confinement and reduce short-channel effects.MOCVD epitaxial growth of AlGaN/GaN ended with the growth of an in situ SiN passivation layer, which was subsequently selectively removed by an Ar plasma treatment before depositing the Pt/Ni/Au gate metallization.The devices under test have a total gate width of 2 × 50 µm and a gate-to-drain distance (L GD ) of 4 µm.A maximum current of 0.85 ± 0.03 A/mm, a maximum transconductance of 330 ± 20 ms/mm, and an OFF-state gate leakage current of 22 ± 6.1 µA/mm are achieved.A Keysight E5263A semiconductor device parameter analyzer was adopted to measure the dc device I D -V DS output characteristics, using step gate voltage (V GS ) and staircase drain voltage (V DS ) sweep.
During the dc measurement, a V GS value is set; after 30 ms, the staircase V DS ramp starts, each step having a minimum duration of 40 ms [one power line cycle (PLC)].At the end of the last step, with V DS at its maximum value V DSmax , the drain voltage is turned off (t fall < 0.5 ms), there is a waiting time of approximately 10 ms, and then, the new value of V GS is applied, as shown in Fig. 1(a).
As an alternative method to measure the I D -V DS characteristics, a "double-pulse" (DP) system [31] was used [Fig.1(b)], where V DS and V GS can be pulsed in order to measure the I -V device characteristics starting from a "stress" quiescent bias point, usually with a very low "measure" to "stress" duty cycle, keeping the measurement duration short in order to avoid selfheating and trapping/detrapping effects during measurement.A 1-/99-µs duty cycle was adopted in our case.The DP system is a custom system; based on arbitrary waveform generators (AWGs) and amplifiers (AMP), the drain current is recorded using a current probe, as shown in Fig. 1(c).
Hysteresis in I D -V DS characteristics is observed when V DS is swept toward higher values and back [Fig.2(a)]: when the characteristics are measured starting from the maximum drain voltage (V DSmax ) and decreasing V DS , the kink disappears.Considering the kink magnitude as the current difference before and after the sharp rise, the kink magnitude increases at increasing V DSmax applied during measurements [Fig.2(b)].
During the forward and reverse V DS sweep, ON-resistance (R ON ) showed no difference; by comparing various forward and reverse sweeps at different V GS , it is evident that the kink is caused by a ≈300-mV V GS difference, equivalent to a positive shift of threshold voltage V TH , as shown in Fig. 3(a).The peak of the output conductance, g D , corresponds to the position of the kink and occurs at an almost constant value of V DG ∼ = 6.5 V, see Fig. 3(b).
When the output characteristics are measured using the DP system, with a measurement time t M = 1 µs after a 99-µs quiescent phase at V GS,S = V DS,S = 0 V, the kink disappears.Pulsed curves also show reduced self-heating (smaller decrease of I DS at high V DS ) and slightly lower R ON in a linear region, see Fig. 4. DC and DP measurements confirm that the kink in our devices has the same features described in the previous papers.

III. DRAIN CURRENT AND THRESHOLD
VOLTAGE TRANSIENTS The analysis of drain current and threshold voltage transients provides a deeper insight into the origin of kink Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.effect in the tested devices.The stress/recovery experiment consists in applying a constant (V GS,F , V DS,F ) stress for a fixed duration of time ("filling" phase, up to 100 s typically), then observing the recovery of the device biased at V GS,B and V DS,B ("recovery" phase) for other 100 s.During both the stress and the recovery phases, a set of dynamic fast I D -V GS measurements at V DS,M , with V GS,M from −4.5 to 0 V were carried out with a 4-µs sweep time, at logarithmically spaced time intervals, in order to monitor the current and V TH variation over time, as shown in Fig. 5.
The emission time constant of the involved deep levels could be derived by fitting the current transient curves with stretched multiexponential functions as follows: where the fitting parameters A 0 and A 1 are amplitudes, τ 0 and τ 1 are the time constant, and β 0 and β 1 are the stretching factors.
Then, the measurements were repeated at different temperatures, from which the Arrhenius plots were extrapolated.
Fig. 6 shows drain current transients at various temperatures; filling was carried out in pinchoff condition (−6, 25 V); a (0, 0 V) bias was applied during recovery.During filling, a significant decrease of I D occurred within the first 10 µs, followed by a slower decrease.By fitting the transient using the two-stretched exponential function [black dashed lines in Fig. 6(b)], two trapping signatures were extracted during unbiased recovery measurement: the first one (E2) corresponds to the 10 µs-1 ms region observed during recovery and has an activation energy (E A ) equal to 0.8 eV and the second one   (E1) is extremely slow and its activation energy is 0.5 eV [Fig.6(c)].
The I D -V G curves during the recovery phase at RT showed that it takes more than 10 3 s to achieve a complete recovery of the drain current and V TH , as shown in Fig. 7. Due to the fact that the accuracy of the current probe is 1 mA, V TH was extracted as V GS when I DS is 1 mA from the experimental I D -V G curves.Fig. 8 shows the effect of V DS,F during the filling phase at OFF-sate, with V GS,F that is kept at −6 V, and V DS,F increases from 0 to 25 V: the |V TH | value decreases at increasing V DS,F , which is consistent with the increase of kink amplitude with V DS,max (Fig. 2).
When a nonzero bias is applied during the recovery phase, significant changes in the transient kinetics occur, see Fig. 9.The E2 transition (corresponding to 0.8-eV activation energy) is not affected by gate voltage; on the contrary, the emission Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.time constant of the E1 transition is reduced from 10 2 to 10 −2 s when V GS goes from 0 to −7 V with V DS,B = 0 V.
Notice that V GS < −5 V (in pinchoff) induces electron trapping during the recovery phase, leading to positive shift of threshold voltage, see Fig. 9(a); on the contrary, when V GS = −2 V (ON-state), a drain voltage value as high as V DS,B = 10 V is needed to move the E1 transition to 10 −2 s; no extra trapping occurs after 100 s at V GS,B = −2 V, V DS,B = 10 V, and V TH recovers to the value measured without stress, see Fig. 9(b).
The functional dependence on the electric field of the emission rate e = (τ ) −1 of E1 (the trap responsible for the kink effect) is determined by fitting the emission rate using a power law function (ln(e) = a +b * V p ).The fitting parameter p is 0.5 (Fig. 10), proving that e increases exponentially with the square root of the bias voltage, i.e., of the electric field, in agreement with the generally accepted model for Poole-Frenkel effect [32].
fitting e as a function of the zero field emission rate e(0) is determined to be around 10 −4 s −1 , which is in agreement with the experimental results showing that the emission time constant of E1 is almost 1000 s when no bias is applied during the recovery phase.α is a constant, which depends on the applied voltage and on trap potential lowering.Consistent with the Poole-Frenkel effect [32], the activation energy (E A ) of the detrapping time constant of E1 trap decreases with the square root of the applied gate voltage during recovery, see Fig. 11(a).Also, the dielectric constant was estimated to be 5.7, which is close to the dielectric constant of GaN and AlGaN at high frequency [33].Fig. 11(b) shows the V TH transients after filling V GS,F = −6 V, V DS,F = V for 100 s, with a bias of V GSB = −2 V, and V DSB = 5 V during the recovery phase, as a function of temperature.The detrapping process of E1 practically does not depend on temperature and its E A is reduced to almost zero.

IV. DISCUSSION AND CONCLUSION
The experimental results reported above can be explained as follows.During quasi-static measurements of the dc output I D -V DS (V GS ) characteristics, starting from pinchoff conditions, V DS is increased from 0 to V DSmax , Consistently, the value of V DG remarkably increases, and electron injection and trapping in deep donor levels in the AlGaN barrier and/or the GaN buffer occurs.The corresponding V TH dynamic transients suggest the presence of two deep levels (E1 and E2) having activation energies of 0.5 and 0.8 eV, respectively (Figs. 6 and 8).
After completing the first curve, the value of V GS is increased, and the V DS staircase starts again from 0 V.For V DG values lower than 4-5 V, the time constant for detrapping is longer than 1 s: since this time is much longer than the measurement time (40 ms), the negative charge under the gate shifts V TH toward positive values, thus inducing a decrease of I D with respect to the "detrapped" condition, see Fig. 2.However, as V GD is increased beyond approximately 5 V, the emission rate of electrons from donor states in the AlGaN increases exponentially due to the Poole-Frenkel effect, which reduces the activation energy of the traps from 0.5 eV to almost zero, see Figs. 9 and 11 [32].The detrapping time becomes shorter than the measurement time, V TH becomes more negative, and I D increases, thus originating a "kink" in the I D -V DS characteristics.When a reverse scan measurement (from V DS,max to 0 V) is carried out, Fig. 3(a), the high value of V DS makes detrapping time constant very short due to the PF effect so that the "detrapped" state is always measured; then, at low V DS , the electric field is insufficient to cause trapping, so a high value of current is measured along the entire reverse I -V curve.
In other words, the kink is due to a strong dependence of emission time on electric field or voltage (as it occurs for Poole-Frenkel effect [1], as shown in Fig. 12), coupled with a relatively slow sampling and measurement of the parameter analyzer.In fact, when I D -V DS characteristics are measured using a fast (1 µs) DP system, kink is not present since detrapping time is longer than 1 µs for any bias condition, see Figs. 4 and 9.
Several authors have attributed the appearance of the kink to Poole-Frenkel effects [1], [34], [35]; however, a detailed analysis of dynamic threshold voltage shift and its dependence on applied bias has not been reported.Our experimental data confirm the model reported in [1]; we attributed the kink to donor traps in the AlGaN, as emission time is more sensitive to V GS than V DS , see Fig. 9; moreover, the activation energy of traps responsible for the kink is around 0.50 eV, a value reported for traps in the AlGaN [36], [37], [38].Finally, even if we cannot exclude a role for deep acceptors introduced by carbon at nitrogen vacancies (C N defects), related to hole injection and transport [16] or hole redistribution [39], it should be stressed that the Poole-Frenkel effect on C-doping accelerates hole detrapping [40], leading to faster negative charge build-up due to ionized acceptors, contrarily to what has been observed in the present experiment.We cannot exclude that other mechanisms, not related to Poole-Frenkel effect and involving C traps in the buffer, can be responsible for the kink in other devices, but for the above reasons, we exclude them for the devices under study.
Previous investigations have also suggested that impact ionization [9], [20], [24] may be a possible cause of kink effects; nevertheless, it appears unlikely in the devices studied in this work.This is primarily because impact ionization is a nearly instantaneous process, and such rapid behavior does not align with the very long time constant detected in this work.Even if we assume that long time constants are somehow possible, an increase in temperature should theoretically result in a reduction of the number of hot electrons, consequently slowing down the recovery process.However, the experimental results showed the opposite trend (Fig. 6).
Earlier studies have also reported the presence of kink effects in Fe-doped devices.However, we exclude it, based on the emission time constant of the kink-responsible trap in the devices under study and its strong dependence on gate and drain voltage, both of which are different from the Fe trap.The latter is actually characterized by an emission time constant of ≈10 ms at room temperature with negligible Poole-Frenkel effects [41].Therefore, Fe-related traps do not play a role in the kink effects observed in the devices studied in this work.
Reported data demonstrate that, although the observation of the kink effect remains an indicator of charge trapping on deep levels or of charge accumulation in a floating, semi-insulating buffer, its occurrence or observation critically depends on measurement conditions; transient measurements are essential for correct understanding of physical phenomena originating the kink, which can be relevant for the operation and reliability of RF AlGaN/GaN HEMTs.Regarding HEMTs with different barrier materials, such as InAl(Ga)N, these can be affected by kink effects as well.In those devices also, if the kink effect is correlated to a voltage-dependent V TH dynamic shift (within the kink bias range), then it is reasonable to assume that barrier traps sensitive to the Poole-Frenkel effect are responsible for the kink.
In summary, new experimental evidence concerning the dynamic behavior of the "kink" phenomenon and its relation to deep levels in AlGaN/GaN HEMTs is presented in this article.This work demonstrates that the kink effect observed in AlGaN/GaN HEMTs is due to a strong dependence of emission time on electric field or voltage (as expected for Poole-Frenkel effect) coupled with a relatively slow sampling and measurement of the parameter analyzer.

Dynamic
Behavior of Threshold Voltage and I D -V DS Kink in AlGaN/GaN HEMTs Due to Poole-Frenkel Effect I. INTRODUCTION

Fig. 1 .
Fig. 1.Schematic of the measurment processes during (a) DC characterization: first, the V GS value is set, and after 30 ms (pink), the staircase V DS ramp starts; each step having a minimum duration of 40 ms (blue); at the end of the last step, when V DS reaches V DSmax , the drain voltage is turned off, after approximately 10 ms (black), the new V GS is applied (b) DP characterizations and (c) setup of the DP system.

Fig. 2 .
Fig. 2. (a) I D -V DS characteristics with forward (V DS from 0 to 15 V) and reverse (15 to 0 V) sweeps, 0.1-V steps.(b) Forward I D -V DS with V DS swept up to 5, 10, 15, and 20 V. Sweep speed 40 ms/V.V GS is swept from −5 V up to 0 V.

Fig. 3 .
Fig. 3. (a) I DS -V DS sweeps with different V GS 's during forward sweep (0 to 15 V) and reverse sweep (15 to 0 V) at different V GS 's.(b) Position of the kink (V DS,Kink V DG,Kink ) as a function of V GS and V DG .

Fig. 4 .
Fig. 4. Comparison of dc output I D -V DS characteristics with those measured by the DP system with a quiescent bias V GS = V DS = 0 V; measurement time t M = 1 µs and quiescent bias time t F = 99 µs.

Fig. 5 .
Fig. 5. (a) Bias sequence applied to the gate and drain contact.(b) Simplified schematic diagram of the V TH transient setup used in the work.

Fig. 6 .
Fig. 6.Repeated measurements at V GS,M = −1 V and V DS,M = 1 V without bias during recovery (V GS,B = V DS,B = 0 V).(a) During stress in pinchoff at V GS,F = −6 V and V DS,F = 25 V and (b) recovery after 1-s stress at (V GS,F = −6 V and V DS,F = 25 V), at baseplate temperature from 30 • C to 110 • C; color dot curves: experimental data and black dashed line: fit curves.(c) Arrhenius plots of E1 and E2 during the recovery phase.

Fig. 7 .
Fig.7.I -V G curves in linear scale at V DS,M = 7 V, V GS,M from −4.5 to 0 V, during the recovery phase, without bias during recovery (V DS,B = V GS,B = 0 V), after 100 s stress at V GS,F = −6 V and V DS,F = 25 V at RT.

Fig. 8 .
Fig. 8. Dynamic V TH transient with different filling voltage V DS,F in pinchoff at V GS,F = −6 V. (a) Filling transient.(b) Recovery at DS,B = V GS,B = 0 V at RT. V TH was extracted as V GS at I DS = 10 mA/mm.

Fig. Dynamic V
Fig. Dynamic V TH recovery transient of the device under test a 100-s filling at V GS,F = −6 V and V DS,F = 25 V with different (a) gate voltage V GS,B values applied during the recovery at V DS,B = 0 V and (b) drain voltage V DS,B values applied during the recovery at V GS,B = −2 V.

Fig. 10 .
Fig. 10.Emission rate (e) of E1 as a function of the applied V GS,B .

Fig. 11 .
Fig. 11.(a) Activation energy as a function of the square root of the absolute values of the applied gate voltage.(b) V TH transients measured with V G,F = −6 V and V D,F = 25 V at various temperatures, applying V GS,B = −2 V and V DS,B = 5 V.

Fig. 12 .
Fig. 12. Schematic electron energy diagram in equilibrium condition when no bias is applied during recovery (black) and in the presence of electric fields, where bias is applied during the recovery phase (red) showing the Poole-Frenkel emission process.