Interface Trap-Induced Temperature Dependent Hysteresis and Mobility in β-Ga2O3 Field-Effect Transistors

Interface traps between a gate insulator and beta-gallium oxide (β-Ga2O3) channel are extensively studied because of the interface trap charge-induced instability and hysteresis. In this work, their effects on mobility degradation at low temperature and hysteresis at high temperature are investigated by characterizing electrical properties of the device in a temperature range of 20–300 K. As acceptor-like traps at the interface are frozen below 230 K, the hysteresis becomes negligible but simultaneously the channel mobility significantly degrades because the inactive neutral traps allow additional collisions of electrons at the interface. This is confirmed by the fact that a gate bias adversely affects the channel mobility. An activation energy of such traps is estimated as 170 meV. The activated trap charges’ trapping and de-trapping processes in response to the gate pulse bias reveal that the time constants for the slow and fast processes decrease due to additionally activated traps as the temperature increases.

Owing to these attractive characteristics, β-Ga 2 O 3 has attracted much interest in a variety of potential applications such as high power transistors [5,7,10], chemical sensors [20], solar-blind ultraviolet (UV) detectors [13,21,22], UV astronomy, and space communication which require practical operation in harsh environments [12]. Thus, in recent times, doping methods [11,23], metal contacts [11,24], and large-area film deposition [9,25,26] of β-Ga 2 O 3 have been actively investigated. In particular, the study of the interface characteristics between the gate insulator and the channel is of great significance because the charge trapping at the interface is a more fatal component in β-Ga 2 O 3 field-effect transistors (FETs) than bulk traps, and consequently inhibits the high performance and reliability of the devices [27]. Therefore, understanding and controlling the defects at the interface is a critical step in the application of β-Ga 2 O 3 -based devices. Recent studies have reported on the observation of interface traps in β-Ga 2 O 3 metal-oxide-semiconductor (MOS) capacitors and FETs using various gate insulators [8,27,28]. However, previous studies have not revealed the role of the interface traps in practical devices such as FETs or explicitly described their consequences on device operation.
Herein, we show that the interface trap induces hysteretic behavior in β-Ga 2 O 3 FETs at high temperatures and also mobility degradations at low temperatures. To analyze the mobility degradation and hysteresis, a bottom-gate β-Ga 2 O 3 FET was fabricated on SiO 2 in this study. The trapping/de-trapping processes at the interface between β-Ga 2 O 3 and SiO 2 and their effects on the mobility in the β-Ga 2 O 3 FET were studied by analyzing temperaturedependent electrical characteristics in the temperature range of 20-300 K. Additionally, trap-related parameters including the activation trap energy of the interface traps and the trapped charge densities were extracted by means of temperature-dependent hysteresis and transient analysis. This work will expand our understanding of the temperature-dependent characteristics and physical origin of the trap charges in β-Ga 2 O 3 FETs.

Device Fabrication
The (−201) surface β-Ga 2 O 3 bulk substrate with unintentional n-type doping was purchased from Tamura Corporation, Japan. Multi-layer β-Ga 2 O 3 flakes were mechanically transferred using a conventional scotch tape method from the β-Ga 2 O 3 bulk substrate onto a heavily doped p-type Si substrate with thermally grown 300 nm SiO 2 . The source and drain electrodes were defined on top of the Ga 2 O 3 flakes by photolithography, 20/100 nm Ti/Au electron-beam evaporation, and a conventional lift-off process. The fabricated device was annealed at 450 • C in nitrogen ambient for 1 min using a rapid thermal process to improve contact resistance.

Temperature-Dependent Electrical Measurements
The fabricated device was mounted in a liquid helium closed-cycle cryostat (Janis Research, CCS-150, Woburn, MA, USA). Temperature-dependent electrical characteristic measurements were carried out in a high vacuum (<10 −3 Pa) with a semiconductor parameter analyzer (Keithley, 4200A-SCS, Solon, OH, USA) to identify the intrinsic effects without ambient environmental effects like water and oxygen molecules. To obtain the transfer curves, the gate bias (V GS ) was swept from −40 to 10 V (forward sweep) and then back to −40 V (backward sweep) while maintaining drain bias (V DS ) values of 0.5 and 1 V. The output characteristics were measured by sweeping V DS from 0 to 10 V while varying the V GS (−15, −10, −5, 0, 5, and 10 V). The transient response was measured by the alternate V GS at a fixed V DS of 1 V. To reach equilibrium, we first applied V GS of 10 V for 600 s until I DS was saturated. Gate pulses were then changed from 10 V to 0 V and maintained for 150 s, and vice versa.

Contact Resistance, Mobility, and Threshold Voltage Extraction
The contact resistance (R C ) was calculated as follows: R C = L·θ/(W·C OX ·µ 0 ), where θ is the effective mobility attenuation factor, W is the channel width, L is the channel length, C OX is the capacitance of the SiO 2 , and µ 0 is the low-field mobility [29]. The low-field mobility was extracted from the Y-function, given by Y = (µ 0 ·C OX ·V DS ·W/L) 0.5 (V GS -V th,Y ), where V th,Y was the threshold voltage extracted from Y-function. The effective mobility attenuation factor was extracted as follows: We extracted the contact resistance and the mobility from the same transfer curve measured at V DS = 1 V. The mobility was extracted from the transfer characteristics. To observe the mobility except for the effect of contact resistance, we first extracted the actually applied drain voltage in the channel (V DS,CH ) as follows: V DS,CH = V DS -R C × I DS . Subsequently, the field-effect mobility was calculated as µ FE = L·g m /(W·C OX ·V DS,CH ), where g m is the transconductance. We estimated the threshold voltage as the x-intercept of the tangential line at the maximum slope on the transfer curve on a linear scale ( Figure S1 in Supplementary Materials).

The Interface Trap Density, the Amount of Charge, Time-Dependent Trapped Charge Density Changes, and Trap Parameter Extraction
The interface trap density is estimated from SS = ln(10)·kT/q·(1+(C S +C it )/C OX ), where SS is the subthreshold swing, C S is the capacitance of β-Ga 2 O 3 conducting channel and C it = q 2 × D it is the capacitance induced by the interface trap density [4,30]. The amount of charge trapped and de-trapped by the interface trap is extracted as ∆Q hy = C OX × ∆V. To determine the activation energy of the interface trap, ∆Q hy was fitted by ∆Q hy = Q m × exp(−E A /k B T) + Q fix , where Q m is the maximum charge density, k B is the Boltzmann constant, and Q fix is the temperatureindependent fixed charge density [30].
The time-dependent density of the trapped charges changes is expressed as Q it (t) -Q it (0) = -(I DS (t) -I DS (0))ε·ε 0 /q·t OX ·g m , where Q it (t) is the density of trapped charges (Q it ) as a function of time, Q it (0) is Q it at the time changed the gate pulses, I DS (t) is I DS as a function of time, I DS (0) is I DS at the edge of gate pulses, ε is the relative dielectric constant of the oxide, ε 0 is the permittivity of vacuum, and t OX is the thickness of the oxide. The where Q 1 and Q 2 are the density of trapped charges and τ it1 and τ it2 are the time constants [26].

Results and Discussion
The schematic in Figure 1a shows the fabricated β-Ga 2 O 3 FET on a heavily doped ptype Si substrate as the bottom gate with SiO 2 gate insulator. SiO 2 is potentially of a higher dielectric reliability in FETs due to the larger conduction band offset between SiO 2 and Ga 2 O 3 compared to Al 2 O 3 and Ga 2 O 3 [28]. Figure 1b shows an optical microscope image of the fabricated β-Ga 2 O 3 device, and we measured W as 3.3 µm and L as 15 µm. A thickness of the β-Ga 2 O 3 channel layer was measured as approximately 200 nm using atomic force microscopy (the inset in Figure 1b). A cross-sectional high resolution transmission electron microscopy (HR-TEM) image in Figure 1c represents the smooth interface between β-Ga 2 O 3 and SiO 2 . Mechanical exfoliation of β-Ga 2 O 3 and subsequent transfer on SiO 2 did not result in any damage or defect, and a high quality of crystalline was preserved in the fabricated device. The selective-area diffraction pattern was also characterized as shown in Figure 1d. [200] and [002] directions in monoclinic crystal structure were indicated, and the channel surface was confirmed as the β-Ga 2 O 3 (100) plane.
The fabricated β-Ga 2 O 3 FET was characterized by measuring its current-voltage characteristics. Figure 2a,b presents the measured transfer and output characteristics at room temperature, respectively. The fabricated device operates in depletion mode. We extracted the mobility, subthreshold swing, and threshold voltage of the device at room temperature from the transfer characteristics. At V DS = 1 V, maximum µ FE of the β-Ga 2 O 3 FET were 83.5 and 88.3 cm 2 /V·s, SS were 180 and 130 mV/dec, and threshold voltages (V th ) were −15.5 and −14 V for forward and backward sweeps, respectively, and an ON/OFF ratio (I ON /I OFF ) of approximately 10 7 was observed. Hysteresis (~1.5 V), a threshold voltage difference in the transfer curves depending on the sweep directions, was observed. The D it was estimated to be approximately 1.44 × 10 11 cm -2 eV -1 from SS at 300 K. The D it extracted in this work is similar to the previously other reports [27,28]. We also confirmed Ohmic contact behaviors from good linearity of the output curves near 0 V ( Figure S2 in Supplementary Materials). The fabricated β-Ga2O3 FET was characterized by measuring its current-voltage characteristics. Figure 2a,b presents the measured transfer and output characteristics at room temperature, respectively. The fabricated device operates in depletion mode. We extracted the mobility, subthreshold swing, and threshold voltage of the device at room temperature from the transfer characteristics. At VDS = 1 V, maximum μFE of the β-Ga2O3 FET were 83.5 and 88.3 cm 2 /V·s, SS were 180 and 130 mV/dec, and threshold voltages (Vth) were −15.5 and −14 V for forward and backward sweeps, respectively, and an ON/OFF ratio (ION/IOFF) of approximately 10 7 was observed. Hysteresis (~1.5 V), a threshold voltage difference in the transfer curves depending on the sweep directions, was observed. The Dit was estimated to be approximately 1.44 × 10 11 cm -2 eV -1 from SS at 300 K. The Dit extracted in this work is similar to the previously other reports [27,28]. We also confirmed Ohmic contact behaviors from good linearity of the output curves near 0 V ( Figure S2 in Supplementary Materials). The temperature-dependent hysteretic behaviors of two-dimensional materials were previously reported by our group [30], and in general, it is prevalent that the interface traps and associated charges are responsible for it. Therefore, to investigate the origin of the hysteresis in the β-Ga2O3 FET in detail, its temperature dependence was characterized. Figure 3a,b presents the respective transfer curves for forward and backward sweeps at various temperatures from 20 to 300 K, and two properties were observed from the temperature-dependent transfer curves. First, the drain on-current (above the threshold) decreased by approximately three orders of magnitude as the temperature varied from 300 to 20 K. Decreasing the temperature would have contributed to the mobility decrease, and a detailed discussion on this follows later on. Second, as the temperature increased, the threshold voltage in the forward sweep shifted more toward a negative value than the one in the backward sweep. In other words, the hysteresis increased as the temperature The temperature-dependent hysteretic behaviors of two-dimensional materials were previously reported by our group [30], and in general, it is prevalent that the interface traps and associated charges are responsible for it. Therefore, to investigate the origin of the hysteresis in the β-Ga 2 O 3 FET in detail, its temperature dependence was characterized. Figure  3a,b presents the respective transfer curves for forward and backward sweeps at various temperatures from 20 to 300 K, and two properties were observed from the temperaturedependent transfer curves. First, the drain on-current (above the threshold) decreased by approximately three orders of magnitude as the temperature varied from 20-300 K. Decreasing the temperature would have contributed to the mobility decrease, and a detailed discussion on this follows later on. Second, as the temperature increased, the threshold voltage in the forward sweep shifted more toward a negative value than the one in the backward sweep. In other words, the hysteresis increased as the temperature increased.
The temperature-dependent hysteretic behaviors of two-dimensional materials were previously reported by our group [30], and in general, it is prevalent that the interface traps and associated charges are responsible for it. Therefore, to investigate the origin of the hysteresis in the β-Ga2O3 FET in detail, its temperature dependence was characterized. Figure 3a,b presents the respective transfer curves for forward and backward sweeps at various temperatures from 20 to 300 K, and two properties were observed from the temperature-dependent transfer curves. First, the drain on-current (above the threshold) decreased by approximately three orders of magnitude as the temperature varied from 300 to 20 K. Decreasing the temperature would have contributed to the mobility decrease, and a detailed discussion on this follows later on. Second, as the temperature increased, the threshold voltage in the forward sweep shifted more toward a negative value than the one in the backward sweep. In other words, the hysteresis increased as the temperature increased. To analyze the hysteresis, we extracted the threshold voltage from the temperaturedependent transfer curves. Figure 3c shows the variations of the V th (left) in the forward (V THF , blue) and backward (V THB , red) sweeps. For consistency, we applied the same method to extract the threshold voltages for different temperatures. Thus, despite the monotonic left-shift of the transfer curves as the temperature increased, the additional change of slope on a linear scale made the variations of the extracted threshold voltage look more or less random and uncorrelated with temperature. Since the degree of hysteresis (∆V) is defined as the difference between V THF and V THB , any artifact made while obtaining an individual threshold voltage would be canceled out. As shown in Figure 3c, the variations in ∆V below 230 K were almost negligible but started to increase at around 230 K and rose sharply above 230 K due to the thermal activation of the interface traps and the associated charges responsible for the hysteresis. For a more quantitative analysis, the ∆Q hy trapped and de-trapped by the interface trap was extracted and then fitted by an Arrhenius plot, as shown in Figure 3d. The best fit of ∆Q hy was obtained with the fitting parameter values of Q m = 1.2×10 −5 C/cm 2 , E A = 170 meV, and Q fix = 2.3×10 −10 C/cm 2 (see the Methods section for more detail). The interface trap is partially active at room temperature even if the activation energy of 170 meV is six to seven times greater than the thermal energy at room temperature. Q fix , the charge density irrespective of the temperature, is five orders of magnitude smaller than Q m . In other words, most of the interface trap charges responsible for the hysteresis are governed by the temperature. In addition to the temperature-dependent hysteresis, the drain current (I DS ) decreased in the transfer curve because the mobility is reduced with decreasing temperature, and this temperaturedependent current drop was also observed in the output characteristics. As shown in Figure 4a, the saturation I DS decreased and the slope in the linear region decreased with decreasing temperature, due to an increase in contact resistance (R C ) and a decrease in mobility. As can be seen, the I DS no longer showed linear dependence on the bias near the low V DS as the temperature decreased, and the R C values were no longer negligible at low temperature. We extracted the R C from the modified Ghibaudo Y-function method [29] and the mobility by considering the finite R C (see the Methods section for more details). The temperature-dependent R C was calculated for forward and backward sweeps of the transfer curve, as shown in Figure 4b. R C was 6.3 kΩ at 300 K and then rapidly increased up to 100.8 MΩ as the temperature decreased, possibly because of the reduced thermal energies of carriers for thermionic emission over the Schottky barrier. contributed to the interplay between interface scattering and the effect of acceptor-like traps at the interface between β-Ga2O3 and SiO2 [27]. At temperatures below 230 K, the acceptor-like traps were frozen and electrically neutral, allowing more electrons to drift along the vicinity of the interface. The interface scattering became predominant over any other scatterings including ionized impurity scattering, and mobility steeply decreased. This can also be envisioned by the strong gate bias dependence of the channel mobility at low temperature, as discussed earlier (Figure 5b), and the previous reports of strong mobility degradation by the surface effects in β-Ga2O3 thin-films at low temperatures [33].  The maximum channel mobilities (µ CH ) at various temperatures considering the effect of the contact resistance are plotted on a log-log scale in Figure 5a. It is worth noting that the channel mobility steeply decreased as the temperature decreased below 230 K. At low temperature (generally below 100 K), the mobility reduced due to the impurity scattering and became proportional to T γ (γ = 1.5) as the reported Hall mobility [23,25,31,32] but here it decreased more quickly with γ at approximately 2.2 (T =~150 K) and 5.6 (T = 150-230 K). Thus we cannot explain this mobility degradation by the impurity scattering, and the surface related scattering would be responsible for it. In Figure 5b-e, the transfer curves at T = 100, 180, 260, and 300 K are plotted on a linear scale, respectively, and the extracted channel mobilities in each are also shown alongside. Implausibly, I DS at 100 K rapidly saturated at just above the threshold whereas that at 300 K increased linearly. That is to say, the channel mobility became less affected by the gate bias as the temperature increased. Interestingly, the channel mobility started to decrease below 230 K (the temperature that coincides with the hysteresis becoming invisible). Therefore, these trends contributed to the interplay between interface scattering and the effect of acceptor-like traps at the interface between β-Ga 2 O 3 and SiO 2 [27]. At temperatures below 230 K, the acceptor-like traps were frozen and electrically neutral, allowing more electrons to drift along the vicinity of the interface. The interface scattering became predominant over any other scatterings including ionized impurity scattering, and mobility steeply decreased. This can also be envisioned by the strong gate bias dependence of the channel mobility at low temperature, as discussed earlier (Figure 5b), and the previous reports of strong mobility degradation by the surface effects in β-Ga 2 O 3 thin-films at low temperatures [33].   We also carried out a time-domain analysis on the capture and release of charges by the traps at the interface by measuring the transient response to observe the behaviors of the traps [34]. As shown in Figure 6a, as soon as V GS dropped, I DS sharply dropped and then slowly increased because the captured carriers were released from the interface traps. At the rising edge of V GS , I DS popped up and then slowly decreased while maintaining V GS because of the electrons captured by the acceptor-like traps at the interface. As the temperature increased, these phenomena noticeably appeared because more of the acceptorlike traps were activated. We calculated the transient changes of the trapped charge density for the temperature from 240 to 320 K, as shown in Figure 6b; as the temperature increased, the changes of trapped and de-trapped charge density also increased. The transient changes were not observed below 240 K because of negligible variation by the trapped charge. Figure 6c shows temperature-dependent time constants extracted by fitting Figure 6b with a bi-exponential equation [35]. All of the time constants for the slow and fast processes decreased as the temperature increased because the activated traps were more abundant and the electrons were more thermally energized. We also observed that the charge trapping processes were faster than the charge de-trapping processes. The detailed time constants are available in the Supplementary Materials (Table S1). sient changes were not observed below 240 K because of negligible variation by the trapped charge. Figure 6c shows temperature-dependent time constants extracted by fitting Figure 6b with a bi-exponential equation [35]. All of the time constants for the slow and fast processes decreased as the temperature increased because the activated traps were more abundant and the electrons were more thermally energized. We also observed that the charge trapping processes were faster than the charge de-trapping processes. The detailed time constants are available in the Supplementary Materials (Table S1).

Conclusions
In summary, we investigated the effect of interface traps on the degradation of channel mobility and hysteresis in a bottom-gated β-Ga2O3 FET at low temperature. Temperature-dependent electrical characterizations were performed on the device in the temperature range of 20-300 K, and variations in threshold voltage and field-effect mobility and the degree of hysteresis were analyzed. The activation energy of the interface trap between β-Ga2O3 and SiO2 was estimated as 170 meV, and there was no observable hysteresis below 230 K. As the acceptor-like traps at the interface are frozen and inactive at low temperature, the hysteresis disappears and it was simultaneously found that the channel mobility sharply decreases. This was understood as the frozen charged traps allow the channel

Conclusions
In summary, we investigated the effect of interface traps on the degradation of channel mobility and hysteresis in a bottom-gated β-Ga 2 O 3 FET at low temperature. Temperaturedependent electrical characterizations were performed on the device in the temperature range of 20-300 K, and variations in threshold voltage and field-effect mobility and the degree of hysteresis were analyzed. The activation energy of the interface trap between β-Ga 2 O 3 and SiO 2 was estimated as 170 meV, and there was no observable hysteresis below 230 K. As the acceptor-like traps at the interface are frozen and inactive at low temperature, the hysteresis disappears and it was simultaneously found that the channel mobility sharply decreases. This was understood as the frozen charged traps allow the channel electrons to collide at the interface, which was also confirmed by the vulnerability of mobility to gate bias at low temperature. Furthermore, the charge trapping and detrapping processes at the interface were studied in the time-domain by switching the gate bias. At higher temperatures, the extracted time constants for the slow and fast processes became shorter due to more activated traps. We believe that understanding the role of the interface traps between the gate insulator and β-Ga 2 O 3 could help to optimize the fabrication and operation of β-Ga 2 O 3 -based devices in a variety of circumstances, particularly in harsh environments in space and military applications.
Supplementary Materials: The following are available online at https://www.mdpi.com/2079-499 1/11/2/494/s1, Figure S1. Transfer curve for V DS = 1 V in a linear scale at 180 K, Figure S2. Output curves of I DS -low V DS at room temperature, Table S1. The density of the trapped and de-trapped charges and the time constants.

Data Availability Statement:
The data presented in this study are available on request from thecorresponding author.