Temperature-Sensitivity of Two Microwave HEMT Devices: AlGaAs/GaAs vs. AlGaN/GaN Heterostructures

: The goal of this paper is to provide a comparative analysis of the thermal impact on the microwave performance of high electron-mobility transistors (HEMTs) based on GaAs and GaN technologies. To accomplish this challenging goal, the relative sensitivity of the microwave performance to changes in the ambient temperature is determined by using scattering parameter measurements and the corresponding equivalent-circuit models. The studied devices are two HEMTs with the same gate width of 200 µ m but fabricated using different semiconductor materials: GaAs and GaN technologies. The investigation is performed under both cooled and heated conditions, by varying the temperature from − 40 ◦ C to 150 ◦ C. Although the impact of the temperature strongly depends on the selected operating condition, the bias point is chosen in order to enable, as much as possible, a fair comparison between the two different technologies. As will be shown, quite similar trends are observed for the two different technologies, but the impact of the temperature is more pronounced in the GaN device. presents a comparative investigation of the temperature-dependent high-frequency behavior of two HEMTs based on AlGaAs/GaAs and AlGaN/GaN heterojunctions. enable this comparative investigation, a sensitivity-based analysis is developed. The assessment of the sensitivity of the two HEMTs to changes in the ambient temperature ( T a ) has been accomplished by using equivalent circuit models extracted from scattering ( S -) parameters. The ambient a wide range of values,


Introduction
High electron-mobility transistors (HEMTs, also known as a heterostructure or heterojunction FETs) based on AlGaAs/GaAs and AlGaN/GaN heterostructures have greatly evolved since their inception in the early 1980s [1] and early 1990s [2], respectively. The most evident difference between the GaAs and GaN technologies is that the former is more mature, whereas the latter is more suited for high-power applications, owing to its wide bandgap nature. Over the years, many studies have focused on the high-frequency characterization and modeling of the temperature-dependent behavior of both GaAs [3][4][5][6][7][8][9][10][11][12] and GaN [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] HEMTs. This is because the operating temperature can remarkably affect the device performance, reliability, and lifetime, which are key features in practical applications, especially those in harsh environmental conditions [28]. With the aim of contributing to the assessment of the impact of the temperature on GaAs and GaN technologies, this article presents a comparative investigation of the temperature-dependent high-frequency behavior of two HEMTs based on AlGaAs/GaAs and AlGaN/GaN heterojunctions. To enable this comparative investigation, a sensitivity-based analysis is developed. The assessment of the sensitivity of the two HEMTs to changes in the ambient temperature (T a ) has been accomplished by using equivalent circuit models extracted from scattering (S-) parameters. The ambient temperature has been swept over a wide range of values, going from −40 • C to 150 • C. The bias point has been selected in order to allow, as much as possible, a fair comparison between the two different transistor technologies. The GaAs and GaN HEMTs have the same gate width of 200 µm but differ in the gate lengths, which are 0.25 µm and 0.5 µm, respectively. For the first time, the challenging task of comparing the temperature-dependent performance of the two different semiconductor technologies is accomplished by reporting an extensive and systematic sensitivity-based analysis, which is carried out by using the drain current (I ds ), the equivalent-circuit parameters (ECPs), and the major RF figures of merit. The degradations of the device performance at a higher T a are found to be more pronounced for the GaN technology, which can be attributed to the higher dissipated power (P diss ). It is worth noting that the two tested technologies are inherently different and that this then clearly impacts on the achieved results. Given the widely different characteristics of the two tested technologies, it is really not feasible to distinguish each contribution arising from the different operating conditions (e.g., dissipated power) and peculiar device physics (e.g., thickness and thermal conductivity of the substrate). Hence, the reported comparative analysis has not aimed at distinguishing each contribution but at assessing the overall impact of the ambient temperature on the DC and microwave characteristics of the two tested technologies. Nevertheless, for the sake of completeness, it should be underlined that the channel temperature is higher than the ambient temperature because of the heat generated by the self-heating effects, which are strongly dependent not only on the dissipated power level but also on the thickness and thermal conductivity of the materials [13,[29][30][31][32][33][34][35][36]. Furthermore, it is worth mentioning that the extraction of the equivalent-circuit elements may be inevitable affected by the uncertainty inherent in measurements and that, in addition, the model topology itself is an approximation of the device physics [37][38][39][40][41][42][43], which in turn may impact on the achieved temperature-dependent findings.
The remainder of this article is organized as follows: Section 2 is focused on the description of the tested device and experiments, Section 3 is devoted to the sensitivitybased analysis and the discussion of the findings, and the last section summarizes the main conclusions of this study.

Devices and Experiments
The two studied devices are an AlGaAs/GaAs HEMT grown by molecular beam epitaxy (MBE) on a semi-insulating undoped GaAs substrate and an AlGaN/GaN HEMT grown by metal-organic chemical vapor deposition (MOCVD) on a SiC substrate. Figure 1 shows the schematic cross-sectional views and photos of the two tested HEMTs. The interdigitated layout of both devices is based on the connection in parallel of two fingers, each being 100-µm long, yielding to a total gate width of 200 µm. The gate lengths of the GaAs and GaN devices are 0.25 µm and 0.5 µm, respectively. The source-to-gate distance (L SG ) and the gate-to-drain distance (L GD ) are 0.5 µm and 2.0 µm for the GaAs device, while their values are equal to 1 µm and 2.75 µm for the GaN device.
The microwave experiment consists of S-parameters measured from 45 MHz to 50 GHz at nine different ambient temperatures: −40 • C, −25 • C, 0 • C, 25 • C, 50 • C, 75 • C, 100 • C, 125 • C, and 150 • C. The S-parameters were measured with a vector network analyzer (VNA HP8510C) in conjunction with a DC source (HP4142B) for biasing, a temperature control unit (Temptronic TP03200, Temptronic Corporation, Mansfield, MA, USA) for setting the ambient temperature, and a PC with a specialized software (IC-CAP) for controlling the full measurement procedure through the GPIB interface. The off-wafer calibration was performed using line-reflect-reflect-match (LRRM) standards on the alumina calibration substrate from Cascade Microtech and a commercial calibration software (WinCal). The comparative analysis is performed using S-parameters at the following two bias points in the saturation region: V ds = 3 V and V gs = −0.1 V for the GaAs HEMT and V ds = 9 V and V gs = −4 V for the GaN HEMT. This choice has been made based on the analysis of the DC output characteristics of the two transistors at different T a (see Figures 2 and 3), in order to enable, as much as possible, a fair comparison between the two different technologies. For the GaAs HEMT, two temperature-dependent effects contribute in opposite ways to Electronics 2021, 10, 1115 3 of 12 the resultant behavior of I ds with an increasing temperature: the degradation of the carrier transport properties and the threshold voltage (V th ) shift towards more negative values. Therefore, V gs is selected at −0.1 V, in order to minimize the contribution of the V th shift that plays a more dominant role at lower V gs . V ds is selected at 3 V, in order to avoid the pronounced positive slope of I ds at high V ds . For the GaN HEMT, the temperature-dependent behavior of I ds is mostly due to the degradation of the carrier transport properties and/or to a reduction in the carrier concentration in the two-dimensional electron gas (2DEG). Therefore, V ds and V gs are, respectively, selected at 9 V and −4 V, in order to avoid the pronounced negative slope of I ds (V ds ) at a high P diss . The microwave experiment consists of S-parameters measured from 45 MHz to 50 GHz at nine different ambient temperatures: −40 °C , −25 °C , 0 °C , 25 °C , 50 °C , 75 °C , 100 °C , 125 °C , and 150 °C . The S-parameters were measured with a vector network analyzer (VNA HP8510C) in conjunction with a DC source (HP4142B) for biasing, a temperature control unit (Temptronic TP03200, Temptronic Corporation, Mansfield, MA, USA) for setting the ambient temperature, and a PC with a specialized software (IC-CAP) for controlling the full measurement procedure through the GPIB interface. The off-wafer calibration was performed using line-reflect-reflect-match (LRRM) standards on the alumina calibration substrate from Cascade Microtech and a commercial calibration software (WinCal). The comparative analysis is performed using S-parameters at the following two bias points in the saturation region: Vds = 3 V and Vgs = −0.1 V for the GaAs HEMT and Vds = 9 V and Vgs = −4 V for the GaN HEMT. This choice has been made based on the analysis of the DC output characteristics of the two transistors at different Ta (see Figure 2 and Figure  3), in order to enable, as much as possible, a fair comparison between the two different technologies. For the GaAs HEMT, two temperature-dependent effects contribute in opposite ways to the resultant behavior of Ids with an increasing temperature: the degradation of the carrier transport properties and the threshold voltage (Vth) shift towards more negative values. Therefore, Vgs is selected at −0.1 V, in order to minimize the contribution of the Vth shift that plays a more dominant role at lower Vgs. Vds is selected at 3 V, in order to avoid the pronounced positive slope of Ids at high Vds. For the GaN HEMT, the temperature-dependent behavior of Ids is mostly due to the degradation of the carrier transport properties and/or to a reduction in the carrier concentration in the two-dimensional electron gas (2DEG). Therefore, Vds and Vgs are, respectively, selected at 9 V and −4 V, in order to avoid the pronounced negative slope of Ids (Vds) at a high Pdiss.    At the selected bias voltages (see Figure 4), the dimensionless relative sensi Ids with respect to Ta is calculated by normalizing the relative change in Ids to the change in Ta: where Ids0 is the value of Ids at the reference temperature (Ta0) of 25 °C. As can be o in Figure 4, RSIds is negative for both devices, as a consequence of the fact that an in Ta leads to a decrease in Ids, and is of greater magnitude for the GaN technolo consequence of the much higher Pdiss leading to a higher channel temperature (i.e. + RthPdiss where Rth is the thermal resistance). At the selected bias voltages (see Figure 4), the dimensionless relative sensitivity of I ds with respect to T a is calculated by normalizing the relative change in I ds to the relative change in T a : where I ds0 is the value of I ds at the reference temperature (T a0 ) of 25 • C. As can be observed in Figure 4, RSI d s is negative for both devices, as a consequence of the fact that an increase in T a leads to a decrease in I ds , and is of greater magnitude for the GaN technology, as a consequence of the much higher P diss leading to a higher channel temperature (i.e., T ch = T a + R th P diss where R th is the thermal resistance).  For the sake of completeness, we report the impact of the ambient temperature on the Ids-Vgs curves and the corresponding transconductance at Vds = 3 V for the GaAs device and at Vds = 9 V for the GaN device (see Figure 5). By increasing the temperature, the drain current and the transconductance are remarkably reduced for the GaN device, whereas operating bias points at which their values are temperature insensitive (the so-called current and transconductance zero temperature coefficient (CZTC and GZTC) points) can be observed for the GaAs device, owing to the counterbalancing of temperature-dependent effects contributing in opposite ways [12]. Figure 6 shows the impact of Ta on the measured S-parameters at the selected bias For the sake of completeness, we report the impact of the ambient temperature on the I ds -V gs curves and the corresponding transconductance at V ds = 3 V for the GaAs device and at V ds = 9 V for the GaN device (see Figure 5). By increasing the temperature, the drain current and the transconductance are remarkably reduced for the GaN device, whereas operating bias points at which their values are temperature insensitive (the so-called current and transconductance zero temperature coefficient (CZTC and GZTC) points) can be observed for the GaAs device, owing to the counterbalancing of temperature-dependent effects contributing in opposite ways [12]. and at Vds = 9 V for the GaN device (see Figure 5). By increasing the temperature, the drain current and the transconductance are remarkably reduced for the GaN device, whereas operating bias points at which their values are temperature insensitive (the so-called current and transconductance zero temperature coefficient (CZTC and GZTC) points) can be observed for the GaAs device, owing to the counterbalancing of temperature-dependent effects contributing in opposite ways [12]. Figure 6 shows the impact of Ta on the measured S-parameters at the selected bias points. By increasing Ta, the low-frequency S21 is reduced, due to the degradation of the carrier transport properties. Both devices are affected by the kink effect in S22 [44][45][46][47][48][49], which is more marked at a lower Ta because of the higher gm. As a matter of fact, it has been demonstrated that the kink effect is mainly due to high values of gm.  Figure 6 shows the impact of T a on the measured S-parameters at the selected bias points. By increasing T a , the low-frequency S 21 is reduced, due to the degradation of the carrier transport properties. Both devices are affected by the kink effect in S 22 [44][45][46][47][48][49], which is more marked at a lower T a because of the higher g m . As a matter of fact, it has been demonstrated that the kink effect is mainly due to high values of g m .

Sensitivity-Based Analysis
The S-parameters have been modelled using the equivalent-circuit model in Figure  7. The ECPs have been obtained by using a standard "cold" pinch-off approach [50]. As

Sensitivity-Based Analysis
The S-parameters have been modelled using the equivalent-circuit model in Figure 7. The ECPs have been obtained by using a standard "cold" pinch-off approach [50]. As illustrated in Figure 8, a good agreement between the measured and simulated S-parameter has been achieved for the two tested devices.
Electronics 2021, 10, x FOR PEER REVIEW illustrated in Figure 8, a good agreement between the measured and simulated S eter has been achieved for the two tested devices.    Table 1 reports the values of the drain current, the ECPs, the intrinsic input and feedback time constants (i.e., gs = RgsCgs and gd = RgdCgd), the unity current gain cut-off frequency (ft), and the maximum frequency of oscillation (fmax). The three intrinsic time constants (m, gs, and gd) model the intrinsic non-quasi-static (NQS) effects, which arise from the inertia of the intrinsic device in responding to rapid signal changes [51]. The values of ft and fmax are, respectively, determined from the measured short-circuit current gain (h21) and maximum stable/available gain (MSG/MAG). Although the GaAs HEMT has a shorter gate length that should result in a higher operation frequency, the GaN HEMT has smaller time constants (except for gd) and higher ft and fmax, which are desired in order to  Table 1 reports the values of the drain current, the ECPs, the intrinsic input and feedback time constants (i.e., τ gs = R gs C gs and τ gd = R gd C gd ), the unity current gain cut-off frequency (f t ), and the maximum frequency of oscillation (f max ). The three intrinsic time constants (τ m , τ gs , and τ gd ) model the intrinsic non-quasi-static (NQS) effects, which arise from the inertia of the intrinsic device in responding to rapid signal changes [51]. The values of f t and f max are, respectively, determined from the measured short-circuit current gain (h 21 ) and maximum stable/available gain (MSG/MAG). Although the GaAs HEMT has a shorter gate length that should result in a higher operation frequency, the GaN HEMT has smaller time constants (except for τ gd ) and higher f t and f max , which are desired in order to enable device applications at high frequencies. This is can be linked to the fact that the conventional scaling rules cannot be directly applied to make a straightforward comparison between devices that are based on different semiconductor materials, technologies, and layouts. As a matter of fact, this could be foreseen from the values of I ds , which are larger for the GaN HEMT, even if the GaAs HEMT has a shorter gate length that should result in a higher I ds . The same observation can be made for the intrinsic g m .
Likewise, in the case of I ds , the relative sensitivities of the other parameters in Table 1 are estimated by using Equation (1) and are then illustrated in Figures 9-11. Relative sensitivities of the extrinsic capacitances and inductances of close to zero were achieved (see Figure 9a-e), owing to their weak temperature dependence. On the other hand, the relative sensitivities of the extrinsic and intrinsic resistances are positive (see Figures 9f-h and 10d-f), due to the increase of the resistive contributions with an increasing T a . Contrary to the resistances, the transconductance shows a relative sensitivity that is negative (see Figure 11a), enlightening its degradation with an increasing T a . The relative sensitivities of the intrinsic capacitances can be positive or negative (see Figure 10a-c), depending on the considered device and capacitance. The relative sensitivities of the intrinsic time constants are positive (see Figure 11b-d), reflecting their increase at a higher T a and thus a shift of the onset of the NQS effects at lower frequencies. On the other hand, the relative sensitivities of the frequencies f t and f max are negative (see Figure 11e,f), reflecting their decrease at a higher T a and thus a reduction of the device operation frequencies. The analysis of the relative sensitivities of the crucial parameters such as g m , f t , and f max shows that larger negative values are observed for the GaN device compared to the GaAs counterpart (see Figure 11a,e,f), in line with what was seen for I ds (see Figure 4). Figure 9. Behavior of the relative sensitivities of the extrinsic parameters versus Ta for the two studied devices.

Conclusions
For the first time, an extensive and systematic comparative analysis of the GaAs and GaN HEMT technologies has been performed by investigating the impact of the temperature variations on the device performance in terms of the relative sensitivities of Ids, ECPs, and major RF figures of merit over a broad temperature range, spanning from −40 °C to 150 °C . By increasing Ta, performance degradations are observed for both devices but they are more pronounced for the GaN technology. This can be attributed to the higher Pdiss leading to a stronger degradation of the electron transport properties.
It is worth pointing out that establishing a fair comparison between the temperaturedependent performance of such inherently widely different semiconductor technologies is a very challenging task, since it is hard to define "homogeneous" operating conditions for devices exhibiting highly "heterogeneous" performances (e.g., the current density has to be referred to the tested technology) and to distinguish each contribution arising from the different peculiar features (e.g., different thermal conductivities of the substrates). In light of that, the selection of relatively balanced bias conditions has been based on the analysis of the specific DC output characteristics and then used as the benchmark for assessing the overall impact of Ta on the microwave characteristics of the two devices. The relative sensitivity has been chosen as an assessment indicator as this parameter allows one to evaluate quantitatively, systematically, and straightforwardly the impact of Ta on the microwave characteristics. Although the achieved findings are not of general validity as they can depend on the combined effects of ECPs whose values can change with the Figure 11. Behavior of the relative sensitivities of the intrinsic transconductance, the intrinsic time constants, and the RF figures of merit versus T a for the two studied devices. The illustrated bias points are: V ds = 3 V and V gs = −0.1 V for the GaAs HEMT and V ds = 9 V and V gs = −4 V for the GaN HEMT.

Conclusions
For the first time, an extensive and systematic comparative analysis of the GaAs and GaN HEMT technologies has been performed by investigating the impact of the temperature variations on the device performance in terms of the relative sensitivities of I ds , ECPs, and major RF figures of merit over a broad temperature range, spanning from −40 • C to 150 • C. By increasing T a , performance degradations are observed for both devices but they are more pronounced for the GaN technology. This can be attributed to the higher P diss leading to a stronger degradation of the electron transport properties.
It is worth pointing out that establishing a fair comparison between the temperaturedependent performance of such inherently widely different semiconductor technologies is a very challenging task, since it is hard to define "homogeneous" operating conditions for devices exhibiting highly "heterogeneous" performances (e.g., the current density has to be referred to the tested technology) and to distinguish each contribution arising from the different peculiar features (e.g., different thermal conductivities of the substrates). In light of that, the selection of relatively balanced bias conditions has been based on the analysis of the specific DC output characteristics and then used as the benchmark for assessing the overall impact of T a on the microwave characteristics of the two devices. The relative sensitivity has been chosen as an assessment indicator as this parameter allows one to evaluate quantitatively, systematically, and straightforwardly the impact of T a on the microwave characteristics. Although the achieved findings are not of general validity as they can depend on the combined effects of ECPs whose values can change with the specific device, the investigation methodology is technology-independent and straightforwardly applicable to other FETs in order to target a quantitative and systematic comparison.