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Akihiro Shimada, Haruna Shiomi, [Tetsuya Tohei](https://orcid.org/0000-0002-4113-2566), [Yusuke Hayashi](https://orcid.org/0000-0001-5672-1497), Masaya Yamaguchi, [Junpei Yamamoto](https://orcid.org/0009-0007-5684-0569), [Takeaki Hamachi](https://orcid.org/0000-0002-0631-1729), [Yasuhiko Imai](https://orcid.org/0000-0003-4686-2629), Kazushi Sumitani, [Shigeru Kimura](https://orcid.org/0000-0003-1064-7572), [Shota Kaneki](https://orcid.org/0000-0003-0806-8571), [Tamotsu Hashizume](https://orcid.org/0009-0004-8229-9460), [Akira Sakai](https://orcid.org/0000-0002-0654-504X)

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[<i>In situ</i> nanobeam x-ray diffraction of local strain in AlGaN/GaN high-electron-mobility transistors under operating condition](https://mdr.nims.go.jp/datasets/78cc2541-e4f5-45b0-9b7a-2883020c011e)

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1  In-situ nanobeam X-ray diffraction of local strain in AlGaN/GaN 1 MOS HEMT under transistor operation 2  3 Akihiro Shimada1, Haruna Shiomi1, Tetsuya Tohei1,a), Yusuke Hayashi1,b), 4 Masaya Yamaguchi1, Junpei Yamamoto1, Takeaki Hamachi1, Yasuhiko 5 Imai2, Kazushi Sumitani2, Shigeru Kimura2, Shota Kaneki3, Tamotsu 6 Hashizume3,c), and Akira Sakai1,a) 7  8 1Graduate School of Engineering Science, The University of Osaka, 1-3 Machikaneyama-9 Cho, Toyonaka, Osaka 560-8531, Japan 10 2Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan 11 3Research Center for Integrated Quantum Electronics, Hokkaido University, Sapporo 12 060-8628, Japan 13  14 a)Authors to whom correspondence should be addressed: tohei@ee.es.osaka-u.ac.jp 15 and sakai@ee.es.osaka-u.ac.jp 16 b)Present address: National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, 17 Ibaraki 305-0047, Japan 18 c)Present address: Institute of Materials and Systems for Sustainability, Nagoya 19 University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan  20  21   22 2  In-situ nanobeam X-ray diffraction of local strain in AlGaN/GaN 1 MOS HEMT under transistor operation 2  3  4 Abstract 5 We combined synchrotron radiation nanobeam X-ray diffraction technique with the 6 pump-probe method to perform in-situ measurements of local strain in a normally-ON 7 AlGaN/GaN metal-oxide-semiconductor high electron mobility transistor device under 8 transistor operation. The c-axis strain in the AlGaN barrier layer within the gate region 9 exhibited a clear position dependence, increasing as the gate voltage was increased in the 10 negative direction and as the measurement position moved from the center of the gate 11 electrode towards the drain-side gate edge. Based on the characteristics of the measured 12 c-axis and a-axis strains, we successfully extracted not only the strain component due to 13 the inverse piezoelectric effect but also the thermal expansion strain component, using 14 the constitutive equation for elastic bodies. From the characteristics of the device current 15 measured simultaneously with the strain measurements, it was revealed that the 16 temperature rise inducing the thermal expansion strain was caused by the transient and 17 steady-state drain currents.  18 3  I. INTRODUCTION 1 Power electronic devices based on Si are widely used in consumer electronics, 2 electric vehicles, and power generation plants. However, further performance 3 improvement to meet demands for high breakdown voltage and low on-resistance is 4 reaching limitation in terms of the material properties. Gallium nitride (GaN) has attracted 5 much attention as an alternative power device material because of its wider bandgap than 6 Si and its high breakdown voltage.1 Among those nitride-based devices, a high electron 7 mobility transistor (HEMT) involving AlGaN/GaN heteroepitaxial structures has been 8 developed and used practically in applications such as cellar phone base stations.2 A broad 9 range of power device applications are expected due to the merits of their low on-10 resistance and high-frequency operation, as well as their compact size and low power 11 consumption.3 In the AlGaN/GaN HEMT, a high concentration of carriers called two-12 dimensional electron gas (2DEG) is formed at the AlGaN/GaN interface by spontaneous 13 polarization of the group III-nitrides and piezoelectric polarization caused by the lattice 14 mismatch strain between AlGaN and GaN.4 On the other hand, there are problems to be 15 solved to further improve the performance and reliability of the devices. It has been 16 reported that a local electric field concentration at the drain-side gate edge increases the 17 stress due to the inverse piezoelectric effect and induces lattice defects such as pits, cracks, 18 etc.,5-15 which leads to degradation of device performance. Although various studies have 19 been conducted to clarify the degradation mechanisms associated with defect formation 20 in devices, few studies have focused on the lattice deformation dynamics in the local 21 region caused by the inverse piezoelectric effect and other relevant factors under device 22 operation. 23 An X-ray diffraction technique is one of the most effective methods to observe the 24 deformation of crystal structure and the related strain.16-20 Recently we have developed a 25 pump-probe measurement method based on synchrotron radiation nanobeam X-ray 26 diffraction (nanoXRD).19 Utilization of pulsed synchrotron radiation at the facility 27 SPring-8, enables non-destructive and in-situ observation of crystal structures in the 28 device under operation. Our previous report evaluated the local lattice deformation of 29 AlGaN/GaN metal-oxide-semiconductor (MOS) HEMTs, in which the inverse 30 piezoelectric response of AlGaN c-plane spacing to the gate voltage application was 31 clearly detected on a nanosecond time resolution.19 In the previous study, however, only 32 the gate voltage was applied to the device to verify the occurrence and detectability of the 33 piezoelectric effect, so strain distribution under the transistor operation of the HEMT has 34 been still elusive. In this study, we performed in-situ nanoXRD measurements of the local 35 lattice strain in the AlGaN/GaN MOS-HEMT under transistor operation, i.e., 36 4  simultaneous application of gate and drain voltages. Based on the systematic 1 measurements and the analysis using the constitutive equation for elastic bodies, 2 dominant factors inducing the strain in the device have been discussed. Results obtained 3 in the present study provide useful information on the underlying physical mechanisms 4 behind the device operation of GaN power devices with improved performance and 5 reliability. 6  7  8 II. EXPERIMENTAL 9 The stacked structure of the AlGaN/GaN MOS-HEMT sample21 evaluated in this 10 study, is shown in Fig. 1(a). First, a highly resistive C-doped GaN layer (600 nm) was 11 formed on the n-GaN substrate to prevent leakage current to the n-GaN substrate side. An 12 undoped-GaN layer (900 nm) and the AlGaN barrier layer were formed to induce 2DEG 13 at the interface. Considering the critical film thickness, the thickness and Al content of 14 the AlGaN layer were set to be 20 nm and 20%, respectively. The density and the mobility 15 of 2DEG were 6.5×1012 cm-2 and 1750 cm2 V-1 s-1, respectively. Ti/Al/Ti/Au as 16 source/drain electrodes were formed on the AlGaN layer by electron beam deposition 17 followed by annealing at 830 °C for 1 min to form an alloy. Al2O3 (30 nm) was then 18 deposited by atomic layer deposition as a gate insulator film. The Ni/Au was deposited 19 as a gate electrode using the same process as that for the source/drain electrodes. In this 20 measurement, we adopted the long gate structure to investigate the position dependence 21 and reproducibility in diffraction experiments and the gate length and width were 800 μm 22 and 400 μm, respectively. We carried out post-metallization annealing (PMA) at 300 °C 23 in N2 after the MOS-HEMT fabrication to improve interface state density between the 24 Al2O3/AlGaN. We confirmed that the PMA process reduced interface state densities at 25 the Al2O3/GaN interface, down to 4×1010 cm-1 eV-1 at energies near the conduction band 26 edge of GaN.22 The electrical characteristics of the device showing well-defined 27 normally-ON nature are described in detail in Ref 19. 28 The measurement geometry of nanoXRD (BL13XU beamline of SPring-8) is shown 29 in Fig. 1(b). The synchrotron X-ray beam was focused at 430 nm × 1030 nm using a 30 Fresnel zone plate and irradiated along the m-axis of the device under the drain and gate 31 voltage application using a function generator. The X-ray probe size is smaller than the 32 dimension of the gate and it allows the study of position dependence of lattice strain. The 33 diffracted X-rays from AlGaN symmetric 0004 and asymmetric 1-104 were detected by 34 two-dimensional photon-counting detector HyPix-3000 (Rigaku, Japan). In the present 35 experimental condition X-rays can penetrate the gate metal and diffraction from AlGaN 36 5  layer and GaN layer are acquired. Since AlGaN and GaN shows different peak positions 1 we can evaluate the strain of individual AlGaN layer. Three-dimensional (3D) ω–2θ–ϕ 2 mapping was performed for the diffraction16,19,20; to quantify the 2θ value corresponding 3 to the lattice spacing, the measured 3D diffraction profiles were integrated over the ω and 4 ϕ directions to obtain one-dimensional 2θ profiles. Representative data of ω–2θ intensity 5 map and 2θ-intensity profile are shown in Fig. S3. The lattice spacing was calculated from 6 the peak in 2θ profiles and Bragg’s equation. The strain resolution determined by the pixel 7 size (100 ×100 µm2) and the sample-detector distance (999.5652 mm) was 5.6×10-5. 8 Next, we describe the pump-probe method used in this study. We applied the voltage 9 as a pump pulse that was synchronized with the X-ray irradiation as a probe pulse and 10 measured the local lattice deformation of the device under transistor operation. The used 11 synchrotron X-rays have a period of 4.789 µs (frequency: 208.8 kHz) and consists of 12 continuous X-ray pulses with a period of 1.815 µs, called “train section”, and isolated X-13 ray pulses with a width of 60 ps, called “single bunch”. Synchronizing these X-ray pulses 14 with the applied voltage and changing the phase of the applied voltage pulses enables to 15 irradiate the probe X-ray pulses at any desired timing. In this study, only the train section 16 was selectively irradiated to the operating device. Schematic circuit diagram of the 17 experimental setup for the electrical measurement system are shown in Fig. S4. 18  19  20 III. RESULTS AND DISCUSSION 21 We applied a pulse voltage of -7, -5, -3, and 0 V as the gate voltage Vg and a pulse 22 voltage of 0 and 5 V as the drain voltage Vd and observed AlGaN 1-104 diffraction spots 23 to measure the voltage dependence of strains along the c- and a-axis. Although the AlGaN 24 layer of the sample used in this study has compressive strain along the c-axis in its non-25 operating state, the strain is defined based on the lattice spacing in the absence of an 26 applied voltage, specifically the initial spacings of the c- and a-planes that exhibit 27 compressive and biaxial tensile strains, respectively. The local strain was evaluated at 28 four measurement points of nanoXRD: 400, 200, 50, and 10 µm apart from the drain-side 29 gate edge (named as points A, B, C, and D, respectively). Results of the c- and a-axis 30 strains of the AlGaN layer measured at points A to D as a function of Vg with different Vd 31 are summarized in Fig. 2. We observed that the c-axis strain increases linearly with 32 increasing Vg in the negative direction. This indicates the applied external electric field 33 reduces the polarization of the AlGaN layer, and the pre-existing c-axis compressive 34 strain decreases accordingly with increasing the electric field.19 It is also notable that the 35 strain tended to be higher when Vd was set to 5 V (blue plots) compared to 0 V (red plots) 36 6  and higher strain was detected at the measurement points closer to the drain-side gate 1 edge. Meanwhile, the a-axis strain was below the detection limit, which is contrary to the 2 expectation of compressive strain due to the inverse piezoelectric effect. We assume that 3 this situation is due to the compressive strain being offset by the thermal expansion strain 4 caused by temperature rise, implying that the c-axis strain increases not only due to the 5 inverse piezoelectric effect but also due to thermal expansion strain. This assumption is 6 highly plausible because it has been frequently reported that when drain current flows in 7 HEMT devices, the temperature rise occurs from the gate to the drain regions in the device 8 due to the Joule heating effect.23-28 9 Based on this assumption, we attempt to estimate the temperature rise in the device 10 using the constitutive equation for elastic bodies. Given that the strain of the AlGaN layer 11 consists of three components such as constrained strain due to the substrate underneath 12 the AlGaN layer, inverse piezoelectric strain due to the voltage application, and thermal 13 expansion strain, the measured strains can be expressed by the following equation. 14 ⎝⎜⎜⎛𝜀𝜀𝑥𝑥𝑥𝑥𝜀𝜀𝑦𝑦𝑦𝑦𝜀𝜀𝑧𝑧𝑧𝑧𝜀𝜀𝑦𝑦𝑦𝑦𝜀𝜀𝑧𝑧𝑧𝑧𝜀𝜀𝑥𝑥𝑥𝑥⎠⎟⎟⎞=⎝⎜⎜⎛𝑠𝑠11 𝑠𝑠12 𝑠𝑠13 0 0 0𝑠𝑠12 𝑠𝑠11 𝑠𝑠13 0 0 0𝑠𝑠13 𝑠𝑠13 𝑠𝑠33 0 0 00 0 0 𝑠𝑠44 0 00 0 0 0 𝑠𝑠44 00 0 0 0 0 𝑠𝑠66⎠⎟⎟⎞⎝⎜⎜⎛𝜎𝜎𝑥𝑥𝑥𝑥𝜎𝜎𝑦𝑦𝑦𝑦𝜎𝜎𝑧𝑧𝑧𝑧𝜎𝜎𝑦𝑦𝑦𝑦𝜎𝜎𝑧𝑧𝑧𝑧𝜎𝜎𝑥𝑥𝑥𝑥⎠⎟⎟⎞+⎝⎜⎜⎛0000𝑑𝑑150000𝑑𝑑1500𝑑𝑑31𝑑𝑑31𝑑𝑑33000 ⎠⎟⎟⎞�𝐸𝐸𝑥𝑥𝐸𝐸y𝐸𝐸z�+⎝⎜⎜⎛𝛼𝛼11𝛥𝛥𝑇𝑇𝛼𝛼11𝛥𝛥𝑇𝑇𝛼𝛼33𝛥𝛥𝑇𝑇000 ⎠⎟⎟⎞(1) 15 where 𝜀𝜀  is the strain, 𝐸𝐸  is the electric field strength, 𝜎𝜎  is the stress, 𝑑𝑑  is the 16 piezoelectric constant, 𝛼𝛼  is the thermal expansion coefficient, and 𝛥𝛥𝑇𝑇  is the 17 temperature rise. The z-axis is parallel to the c-axis. The effect of shear stress can be 18 neglected and thus Eq. (1) can be simplified as 19 �𝜀𝜀𝑥𝑥𝑥𝑥𝜀𝜀𝑦𝑦𝑦𝑦𝜀𝜀𝑧𝑧𝑧𝑧� = �𝑠𝑠11 𝑠𝑠12 𝑠𝑠13𝑠𝑠12 𝑠𝑠11 𝑠𝑠13𝑠𝑠13 𝑠𝑠13 𝑠𝑠33��𝜎𝜎𝑥𝑥𝑥𝑥𝜎𝜎𝑦𝑦𝑦𝑦𝜎𝜎𝑧𝑧𝑧𝑧�+ �0 0 𝑑𝑑310 0 𝑑𝑑310 0 𝑑𝑑33��𝐸𝐸𝑥𝑥𝐸𝐸𝑦𝑦𝐸𝐸𝑧𝑧�+ �𝛼𝛼11𝛥𝛥𝑇𝑇𝛼𝛼11𝛥𝛥𝑇𝑇𝛼𝛼33𝛥𝛥𝑇𝑇� . (2) 20 Considering the plane stress condition (𝜎𝜎𝑥𝑥𝑥𝑥 = 𝜎𝜎𝑦𝑦𝑦𝑦, 𝜎𝜎𝑧𝑧𝑧𝑧 = 0), 𝜀𝜀𝑧𝑧𝑧𝑧 is expressed from Eq. 21 (2) as 22 𝜀𝜀𝑧𝑧𝑧𝑧 =2𝑠𝑠13𝑠𝑠11 + 𝑠𝑠12𝜀𝜀𝑥𝑥𝑥𝑥 + �𝑑𝑑33 − 𝑑𝑑312𝑠𝑠13𝑠𝑠11 + 𝑠𝑠12�𝐸𝐸𝑧𝑧 + �𝛼𝛼33 − 𝛼𝛼112𝑠𝑠13𝑠𝑠11 + 𝑠𝑠12�∆𝑇𝑇. (3) 23 The coefficient of 𝐸𝐸𝑧𝑧 in the second term on the right-hand side in Eq. (3), enclosed in 24 the parentheses, is the piezoelectric constant 𝑑𝑑′33, which accounts for the clamping effect 25 of the substrate.29,30 Therefore, 𝛥𝛥𝑇𝑇 is expressed as  26 ∆𝑇𝑇 = �𝜀𝜀𝑧𝑧𝑧𝑧 −2𝑠𝑠13𝑠𝑠11 + 𝑠𝑠12𝜀𝜀𝑥𝑥𝑥𝑥 − 𝑑𝑑33′ 𝐸𝐸𝑧𝑧� �𝛼𝛼33 − 𝛼𝛼112𝑠𝑠13𝑠𝑠11 + 𝑠𝑠12�� . (4) 27 Here we consider each of variable in Eq. (4) in accordance with the experimental 28 7  conditions. First, we estimate 𝐸𝐸𝑧𝑧  during device operation under the nanoXRD 1 measurement. The electric field applied to the AlGaN layer was estimated using a finite 2 element method (FEM) simulation (COMSOL Multiphysics). Details of the simulation 3 are provided in the supporting information. In the simulation, we constructed a geometric 4 model of the HEMT device (Fig. S1) and calculated 𝐸𝐸𝑍𝑍  exerted on the AlGaN layer 5 under the applied gate and drain voltages. The simulation results of the electric field 6 strength in the AlGaN layer at the moment of X-ray irradiation are shown in Fig. S2. The 7 results indicate that in the absence of drain voltage, the electric field Ez remains nearly 8 constant along the gate length, whereas with applied drain voltages, Ez varies from the 9 drain-side edge of the gate electrode towards the center. Furthermore, the influence of the 10 gate edge diminishes as the lateral geometry scale of the model increases. To estimate the 11 piezoelectric strains at each measurement points, we adopted Ez values at the scaled 12 positions corresponding to points A and D.  13 Second, the piezoelectric constant 𝑑𝑑33′   in Eq. (4) must be determined. Here we 14 adopted 𝑑𝑑33′   value (2.18 pm/V), obtained from the previous experiment that accounted 15 for the clamping effect.19 For the thermal expansion coefficients and elastic compliances 16 of Al0.2Ga0.8N, we used the following values obtained based on Vegard's law31,32: 𝛼𝛼11 =17 3.77 × 10−6 K−1 , 𝛼𝛼33 = 3.27 × 10−6 K−1 , 𝑆𝑆11 = 30.7 × 10−4 GPa , 𝑆𝑆12 = −9.70 ×18 10−4 GPa, and 𝑆𝑆13 = −5.68 × 10−4 GPa.  19 Using these determined variables, the experimental c-axis strain values, 𝜀𝜀𝑧𝑧𝑧𝑧 20 obtained at each measurement point, were analyzed using Eqs. (3) and Eq. (4) to derive 21 individual strain components and temperature change ∆𝑇𝑇, respectively. Figures 4(a-h) 22 show results of individual strain components for points A and D respectively, from left to 23 right: measured c-axis strain, constrained strain, inverse piezoelectric strain and thermal 24 expansion strain as a function of Vg at different Vd. At point A, i.e., on the center of the 25 gate electrode, the observed c-axis strain is approximately dominated by the contribution 26 of the inverse piezoelectric strain, since their values are similar to each other. On the other 27 hand, at point D, i.e. on the drain side of the gate electrode, the effect of not only the 28 inverse piezoelectric strain but also the thermal expansion strain is found to be strong, 29 particularly noticeable at a drain voltage of 5 V. 30 To elucidate the origin of the heat responsible for the thermal expansion strain, we 31 analyzed the correlation between ∆𝑇𝑇 and device characteristics, particularly focusing on 32 the drain current Id during transistor operation. During the in-situ nanoXRD 33 measurements, the time dependences of the applied Vd and Vg, as well as the Id flowing 34 through the device, were measured. The results at point A are presented as a representative 35 example in Fig. 4(a). It is noteworthy that, in the time profile of Id, a significant transient 36 8  drain current is observed at the rising edge of the applied pulse voltage, irrespective of Vd 1 or Vg. Furthermore, this transient current coincides with the period during which the X-2 ray irradiation for diffraction is conducted. Here, we define the average current flowing 3 through the device during X-ray irradiation as Id'. The value of Id' was evaluated by the 4 integration of the transient current part in the measured Id curve (red-filled area in Fig. 5 4(a)) divided by the time during which X-rays are irradiated. Figure 4(b) presents the 6 calculated results of Id’ under various voltage application conditions at point A. Even 7 when Vd is 0 V, Id’ increases with the increasing absolute value of Vg. This is because, 8 although the channel is cut off due to the application of a gate negative voltage exceeding 9 the threshold voltage, transient currents are generated due to the transient phenomena 10 associated with the rising edge of the pulse voltage of Vg, which increase with the 11 increment of Vg. On the other hand, when Vd is applied at 5 V, Id’ increases with the 12 decreasing absolute value of Vg, reflecting the tendency for not only the transient 13 component of the drain current but also the steady-state current to increase. 14 Figure 4(c) illustrates the correlation between Id’ and ∆𝑇𝑇 derived from Eq. (4) at 15 each measurement point. It is evident that, at all measurement points, there is a positive 16 correlation between Id’ and ∆𝑇𝑇. This indicates that both the steady-state and transient 17 components of the drain current, which constitute Id’, contribute to the temperature rise 18 during device operation. Additionally, there is a trend of increasing ∆𝑇𝑇  values with 19 respect to Id’ as the measurement point approaches the drain-side edge. We observe 20 negative values of ∆𝑇𝑇  for several points in Fig. 4(c), which is possibly attributed to 21 overestimation of piezoelectric strain component (𝑑𝑑33′ 𝐸𝐸𝑧𝑧) in eq. (4), but it doesn’t affect 22 overall trends in the ∆𝑇𝑇 - Id’ relation. This also implies that the error in temperature 23 measurement in this experiment is approximately 10 K. (We estimate that 20 percent 24 errors (overestimation) in simulated electric field strength and inverse-piezo electric 25 strain account for about 8 K difference (reduction) in the temperature estimation based 26 on eq.(4)) The degree of the temperature rise at each measurement point is determined by 27 the location of the heat source, assuming uniform heat dissipation characteristics near the 28 channel. It is well-established from numerous previous studies that the drain-side gate 29 electrode edge is a source of Joule heating due to electric field concentration, which 30 validates this observation.  31 Directly comparing the ∆𝑇𝑇 values obtained in the present experiment with those 32 obtained in previous studies using methods such as micro-Raman23,26-28 is difficult, since 33 the size of the present devices, the conditions of voltage application and the detected 34 current components are different from those previously reported. Nevertheless, the fact 35 that ∆𝑇𝑇 values of several K to several tens of K observed in this study is about an order 36 9  to half an order of magnitude smaller than previously reported results can be attributed to 1 the larger device size and smaller current and voltage values used. For example, a 2 previous paper reported that AlGaN/GaN HEMT on sapphire substrate shows temperature 3 rise of about 200 K at 5 W/mm power condition.33 This corresponds to temperature rise 4 of about 10 K at 250 mW/mm, this is comparable to our present experimental condition. 5 On the other hand, the successful detection of a temperature rise of only a few K clearly 6 demonstrates that in-situ nanoXRD possesses sufficient capability to detect this level of 7 temperature rise as a change in strain. The nanoXRD method is unique in that it can 8 observe both lattice structure and temperature changes, which is advantageous in 9 discussing the defect formation mechanism under nitride transistor operation. 10 Furthermore, given that many inorganic semiconductor materials have a thermal 11 expansion coefficient on the order of 10-6 K−1, it can be asserted that in-situ nanoXRD, 12 as demonstrated under the device operating conditions in this study, can also be applied 13 to measure local temperature rises during the operation of devices in other material 14 systems. 15  16  17 IV. CONCLUSION 18 We observed local lattice strain in the AlGaN/GaN MOS-HEMT by using in-situ 19 nanoXRD pump-probe method. Position-dependent strain in the AlGaN barrier layer 20 within the gate region was quantitatively measured under device operation with applied 21 gate and drain voltages. In the c-axis strain, a position-dependent increase in strain values 22 was observed as approaching from the center of the gate electrode to the drain-side gate 23 electrode edge. Among the strains predominantly observed due to the inverse 24 piezoelectric effect, the occurrence of thermal expansion strain was proposed as a 25 particularly non-negligible strain component. This was substantiated by the time 26 dependence of the transient and steady-state drain currents measured simultaneously with 27 the strain measurements. To the best of our knowledge, this study is the first to derive 28 temperature rise in an AlGaN/GaN HEMT device during operation by detecting thermal 29 expansion strain using nanoXRD. Many causes of harmful defects in devices are often 30 attributable to strain. Therefore, the findings of this study are significant as they 31 demonstrate that not only the inverse piezoelectric effect but also the temperature rise of 32 the device can be captured from the perspective of structural changes in the device. 33  34  35 10  Supplementary Material 1 Additional information about the FEM simulation of inverse-piezoelectric strain in 2 AlGaN/GaN HEMT device is included in the supplementary material. 3  4  5 ACKNOWLEDGMENTS 6 The nanoXRD measurements were performed at the BL13XU beamline at SPring-8 with 7 the approval of JASRI (Proposal Nos. 2019A1549, 2019B1009, 2019B1627, 2019B1797, 8 2019B2101, 2020A1136, 2020A1331, 2020A1402, 2020A1652, 2021A1207, 9 2021A1584, 2021B1345, 2021B1650, 2022B1567, 2022B1817, 2023A1695, 2023B1688, 10 2023B1052, 2024A1821, 2024A1929 and 2024B1651). This work was supported in part 11 by JSPS KAKENHI (Grant Nos. JP16H06423, JP16H06421, JP22KK0055, and 12 JP23H01447, JP23H05457) and Murata Science and Education Foundation. 13  14 DATA AVAILABILITY 15 The data that support the findings of this study are available from the corresponding 16 author upon reasonable request. 17   18 11  REFERENCES 1 1 N. Kaminski and O. Hilt, IET Circuits Devices Syst. 8, 227–236 (2014). 2 https://doi.org/10.1049/iet-cds.2013.0223 3 2 K. Husna Hamza and D. Nirmal, Int. J. Electron. Commun. (AEÜ) 116, 153040 4 (2020).  https://doi.org/10.1016/j.aeue.2019.153040 5 3 R. Sun, J. Lai, W. Chen, and B. Zhang, IEEE Access 8, 15529–15542 (2020). 6 https://doi.org/10.1109/ACCESS.2020.2967027 7 4 O. Ambacher, B. Foutz, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, A. 8 J. Sierakowski, W. J. Schaff, and L. F. Eastman, J. Appl. Phys. 87, 334–344 (2000). 9 https://doi.org/10.1063/1.371866 10 5 U. Chowdhury, J. L. Jimenez, C. Lee, E. Beam, P. Saunier, T. Balistreri, S.-Y. Park, T. 11 Lee, J. Wang, M. J. Kim, J. Joh, and J. A. del Alamo, IEEE Electron Device Lett. 29, 12 1098–1100 (2008). https://doi.org/10.1109/LED.2008.2003073 13 6 S.Y. Park, C. Floresca, U. Chowdhury, J. L. Jimenez, C. Lee, E. Beam, P. Saunier, T. 14 Balistreri, and M. J. Kim, Microelectronics Reliability 49, 478–483 (2009). 15 https://doi.org/10.1016/j.microrel.2009.02.015 16 7 M. Tapajna, U. K. Mishra, and M. Kuball, Appl, Phys. Lett. 97, 023503 (2010). 17 https://doi.org/10.1063/1.3460529 18 8 P. Makaram, J. Joh, J. A. del alamo, T. Palacios and C. V. Thompson, Appl. Phys. Lett. 19 96, 233509 (2010). https://doi.org/10.1063/1.3446869 20 9 M. Tapajna, N. Killat, J. Moereke, T. Paskova, K. R. Evans, J. Leach, X. Li, Ü. Özgür, 21 H. Morkoç, and K. D. Chabak, IEEE Electron Device Lett. 33, 1126–1128 (2012). 22 https://doi.org/10.1109/LED.2012.2199278 23 10 C-H. Lin, T. A. Merz, D. R. Doutt, J. Joh, J. A. del Alamo, U. K.Mishra, and L. J. 24 Brillson, IEEE Trans. Electron Devices 59, 2667–2674 (2012). 25 https://doi.org/10.1109/TED.2012.2206595 26 11 E. Zanoni, M. Meneghini, A. Chini, D. Macron, and G. Meneghesso, IEEE Trans. 27 Electron Devices 60, 3119–3131 (2013). https://doi.org/10.1109/TED.2013.2271954 28 12 Y. Wu, C.-Y. Chen, and J. A. del Alamo, J. Appl. Phys. 117, 025707 (2015). 29 https://doi.org/10.1063/1.4905677 30 13 A. Debnath, N. DasGupta, and A. DasGupta, IEEE Trans. Devices 67, 834–840 31 (2020). https://doi.org/10.1109/TED.2020.2965561 32 14 B. Shankar, A. Soni, S. Raghavan, and Mayank Shrivastava, IEEE Trans. Dev. Mater. 33 Rel. 20, 767–774 (2020). https://doi.org/10.1109/TDMR.2020.3033522 34 15 X. Cai, C. Du, Z. Sun, R. Ye, H. Liu, Y. Zhang, X. Duan, and H. Lu, J. Semicond. 42, 35 051801 (2021). https://doi.org/10.1088/1674-4926/42/5/051801 36 12  16 S. Kamada, S. Takeuchi, D. T. Khan, H. Miyake, K. Hiramatsu, Y. Imai, S. Kimura, 1 and A. Sakai, Appl. Phys. Express 9, 111001 (2016). 2 https://doi.org/10.7567/APEX.9.111001 3 17 Y. Ehara, S. Yasui, T. Oikawa, T. Shiraishi, T. Shimizu, H. Tanaka, N. Kanenko, R. 4 Maran, T. Yamada, Y. Imai, O. Sakata, N. Valanoor, and H. Funakubo, Sci. Rep. 7, 9641 5 (2017). https://doi.org/10.1038/s41598-017-09389-6 6 18 T. Sato, D, Ichinose, N. Oshima, T. Mimura, Y. Nemoto, T. Shimizu, Y. Imai, H. 7 Uchida, O. Sakata, and H. Funakubo, Jpn. J. Appl. Phys. 57, 0902B8 (2018). 8 https://doi.org/10.7567/JJAP.57.0902B8 9 19 H. Shiomi, A. Ueda, T. Tohei, Y. Imai, T. Hamachi, K. Sumitani, S. Kimura, Y. Ando, 10 T. Hashizume, and A. Sakai, Appl. Phys. Express 14, 095502 (2021). 11 https://doi.org/10.35848/1882-0786/ac1ee4 12 20 T. Hamachi, T. Tohei, Y. Hayashi, S. Usami, M. Imanishi, Y. Mori, K. Sumitani, Y. 13 Imai, S. Kimura, and A. Sakai, J. Appl. Phys. 135, 225702 (2024). 14 https://doi.org/10.1063/5.0199961 15 21 Y. Ando, S. Kaneki, and T. Hashizume, Appl. Phys. Express 12, 024002 (2019). 16 https://doi.org/10.7567/1882-0786/aafded 17 22 T. Hashizume, S. Kaneki, T. Oyobiki, Y. Ando, S. Sasaki, and K. Nishiguchi, Appl. 18 Phys. Express 11, 124102 (2018). https://doi.org/10.7567/APEX.11.124102  19 23 S. Choi, E. R. Heller, D. Dorsey, R. Vetury, and S. Graham, IEEE Trans. Electron 20 Devices 60, 159–162 (2013). https://doi.org/10.1109/TED.2012.2224115 21 24 B. M. Paine, T. Rust, and E. A. Moore, IEEE Trans. Electron Devices 63, 590–597 22 (2016). https://doi.org/10.1109/TED.2015.2510610  23 25 X. Chen, S. Boumaiza, and L. Wei, IEEE Trans. Electron Devices 66, 3748–3755 24 (2019). https://doi.org/DOI: 10.1109/TED.2019.2926742 25 26 A. Sarua, H. Ji, M. Kuball, M. J. Uren, T. Martin, K.P. Hilton, and R. S. Balmer, IEEE 26 Trans. Electron Devices 53, 2438–2447 (2006). 27 https://doi.org/10.1109/TED.2006.882274 28 27 K. R. Bagnall, E. A. Moore, S. C. Badescu, L. Zhang, and E. N. Wang, Rev. Sci. Inst. 29 88, 113111 (2017). https://doi.org/10.1063/1.5010225 30 28 M. Wu, X.-H. Ma, L. Yang, Q. Zhu, M. Zhang, L.-A. Yang, and Y. Hao, IEEE Trans. 31 Electron Devices, 65, 4792–4799 (2018). https://doi.org/10.1109/TED.2018.2868807 32 29 K. Lefki and G. J. M. Dormans, J. Appl. Phys. 76, 1764–1767 (1994). 33 https://doi.org/10.1063/1.357693  34 30 I. L. Guy, S. Muensit, and E. M. Goldys, Appl. Phys. Lett. 75, 4133–4135 (1999). 35 https://doi.org/10.1063/1.125560 36 13  31 I. Vurgaftman and J. R. Meyer, J. Appl. Phys. 94, 3675–3696 (2003). 1 https://doi.org/10.1063/1.1600519 2 32 R. R. Reeber and K. Wang, MRS Online Proceedings Library 622, 6351 (2000). 3 https://doi.org/10.1557/PROC-622-T6.35.1 4 33 S. Martin-Horcajo, A. Wang, M-F. Romero, M. J. Tadjer, F. Calle, IEEE Trans. El. 5 Dev. 60, 4105 (2013).  6 https://doi.org/10.1109/TED.2013.2284851  7 14  Figures 1  2  3  FIG. 1. (a) Schematic cross section of the AlGaN/GaN MOS-HEMT structure, (b) Schematic of the X-ray diffraction geometry in which each electrode is equipotential with Al wire, (c) The voltage application and X-ray irradiation protocol: Vd = 0 V and 5 V pulse, and (d) The X-ray irradiation points: 400, 200, 50, and 10 µm apart from the drain side gate edge (points A, B, C, and D).   4  5   6 15   1  2  3  FIG. 2. Measured strains in (a) the c-axis (Δc/c) and (b) the a-axis (Δa/a) of the AlGaN layer as a function of applied gate voltage Vg with different drain voltages Vd for points A to D.   4  5   6 16   1  2  3  FIG. 3. Results of decomposing the measured strains at (a-d) point A and (e-h) point D into the components of constrained strain (b,f), inverse piezoelectric strain (c,g), and thermal expansion strain(d,h), based on Eq. (3).   4  5   6 17   1  2  3  FIG. 4. (a) Voltage and current characteristics of the device as a function of time during nanoXRD measurements under two different voltage application condition. The green, purple, and red lines represent the drain voltage, the gate voltage, and the drain current, respectively. The duration of X-ray irradiation is shaded in light blue. (b) Drain current Id’ as a function of Vg for different Vd measured at point A. (c) Relationship between Id’ and the temperature rise ∆𝑇𝑇 at measurement points A to D (red and blue symbols show Vd= 0 and 5 V conditions, respectively).   4  5  6  a)Authors to whom correspondence should be addressed: tohei@ee.es.osaka-u.ac.jp and sakai@ee.es.osaka-u.ac.jp I. INTRODUCTION II. EXPERIMENTAL III. RESULTS AND DISCUSSION IV. CONCLUSION Supplementary Material ACKNOWLEDGMENTS DATA AVAILABILITY REFERENCES