Piezotronic probe modulates the piezoelectric-electric-thermal coupling field in GaN power electronics

Abstract

GaN high-electron-mobility-transistors (HEMTs) exhibit superior high-power and high-frequency characteristics; however, they generate a substantial amount of heat during operation. As quantum piezotronic devices, GaN HEMTs are of particular interest due to their strong coupling processes between piezoelectric, electrical and thermal fields, which are still being explored. For the first time, we built a theoretical framework combining piezotronics with an electrothermal model to reveal the thermal spatial distribution and temporal evolution of GaN HEMTs. Advanced infrared thermography shows that the heat source is localized near the gate in the fabricated GaN HEMTs, which aligns with our theoretical model. The dynamic temperature characteristics indicate that the substrate layer contributes to the main thermal resistance and capacitance. Notably, by introducing an external stress, piezoelectric polarization can act as a probe to locally modulate the thermal fields. A 10.1% decrease in temperature rise is realized during the dynamic modulation process, which further confirms the accuracy of the model. This work deepens the understanding and cognition of piezoelectric-electric-thermal coupling processes and offers a novel thermal management strategy for GaN HEMT devices.

---

New concepts

GaN HEMTs are widely used in power and radio frequency electronic devices, but they often generate significant heat, which can reduce the device lifespan. Therefore, thermal management is a critical issue. Piezotronics is an emerging interdisciplinary nanotechnology that utilizes external stress to modulate electrical properties. Due to the complex piezoelectric-electrical-thermal multi-field coupling effects in GaN HEMTs, there is potential to further regulate the thermal field through external stress based on piezotronics. Based on this, for the first time, we developed a piezoelectric–electrical–thermal coupling model and proposed a new concept of the piezotronic probe. First, we constructed a theoretical model by integrating piezotronics with the Joule heating model. Infrared camera measurements revealed that the highest temperature occurred on the gate side near the drain, which is consistent with our model. Dynamic temperature tests indicated that the substrate contributes to the majority of the thermal resistance and capacitance. Furthermore, we introduced the concept of a piezotronic probe. By applying external stress, we successfully modulated the temperature of the GaN HEMT devices, reducing it by 10.1%, which further validated the model. This model and piezotronic probe enhance the understanding of the piezoelectric-electrical-thermal coupling effect and provide a new dimension for thermal regulation in GaN power electronics.

Introduction

Gallium nitride (GaN) high-electron-mobility transistors (HEMTs) are widely applied in ultra-efficient electric-vehicle power electronics,^1,2 smart renewable energy grid³ and 5G/6G network architecture,^4,5 promising to fundamentally reshape the energy infrastructure and next-generation communication systems. Meanwhile, wide-bandgap semiconductor-based sensors have achieved significant development.^6–9 However, the large amount of heat generated in these high-power-density applications not only results in substantial efficiency degradation but also leads to reductions in the mean time to failure (MTTF).¹⁰ Therefore, thermal management is a critical issue for attaining performance and reliability improvement.^11–13 Traditional strategies based on heat conduction have been widely explored, such as incorporating heat spreaders,^10,14 adopting substrates with high-thermal-conductivity (HTC) materials,^15–17 and utilizing microfluidic channels.^18–20 However, heat generation mechanisms remains insufficiently understood.

Piezotronics, as an emerging field of multi-physical coupling, plays a pivotal role in piezoelectric nanogenerators (PENGs),^21,22 advanced sensing systems,^23,24 self-powered medical devices,^25,26 two-dimensional altermagnets,^27,28 and flexible electronic systems.^29–34 GaN HEMT is a unique quantum piezotronic device in which piezotronics serves as its fundamental design principle. Piezotronics elucidates the modulation of a two-dimensional electron gas (2DEG) by piezoelectric polarization fields. Meanwhile, the electrical transportation process has a direct influence on thermal fields. Proceeding from this point and utilizing piezoelectric polarization as a coupling bridge, a novel strategy for thermal field regulation can be established.

In this work, we build a theoretical model combining piezotronics with electrothermal models to reveal the thermal spatial distribution and temporal evolution of GaN HEMTs. Advanced infrared thermal imaging demonstrates that the main heat source is concentrated between the gate and drain regions, which aligns with the theoretical models. Dynamic temperature characteristics demonstrate that the substrate layer makes major contributions to thermal resistance and capacitance. Furthermore, we introduced the concept of piezotronic probe. The piezotronic probe strategy can achieve localized and site-specific modulation of the thermal field, and uniquely achieves a 10.1% reduction in temperature rise. This work provides critical insights into piezoelectric-electric-thermal coupling processes and offers guidance on employing novel thermal modulation strategies for GaN HEMT devices.

Results and discussion

Fig. 1(a) illustrates a schematic of the fabricated GaN HEMT in this work. Due to the spontaneous and piezoelectric polarization effects, a triangular quantum potential well is formed in the heterojunction interface and a high 2DEG density is generated with high electron mobility,³⁵ as shown in Fig. 1(b). Fig. 1(c) presents a high-resolution transmission electron microscopy (HR-TEM) image, revealing that the AlGaN/AlN/GaN interfaces have a high crystalline quality. The full width at half maximum (FWHM) of the rocking curve of the (002) plane of the GaN layer is 446 arcsec, while that of the (102) plane is 677 arcsec, as shown in Fig. S1. This indicates that the defect density is relatively low. Then, GaN HEMT devices were fabricated using advanced semiconductor micro-fabrication processing. Geometrically scaled-up devices were fabricated to adapt to the infrared camera resolution, and the proportional amplification model did not affect the results. The optical microscope image and device size are shown in Fig. 1(d). The detailed fabrication processes are provided in the Methods section. Then, the electrical characteristics were measured using a semiconductor parameter analyzer. Fig. 1(e) depicts the output characteristics of the device. The drain-source voltage (V_DS) ranges from 0 V to 12 V, and the gate-source voltage (V_GS) ranges from −3 V to 1 V. Under different biases, the maximum saturated drain-source current increases with an increase in V_GS, and no obvious current collapse occurs. Fig. 1(f) illustrates the transfer characteristic and transconductance curve under the conduction of V_DS = 8 V. The maximum current and transconductance of the device are 7.2 mA and 1.104 mS, respectively.

Fig. 1 Schematic and electrical characteristics of the fabricated GaN HEMT. (a) Structure of the fabricated GaN HEMT device. (b) Atomic model of the AlGaN/AlN/GaN heterojunction and its energy band structure. (c) Clear atomic micrograph of the AlGaN/AlN/GaN interface. (d) Optical microscope image of the fabricated GaN HEMT. (e) Output characteristic curve under V_GS from −3 V to 1 V with a step of 1 V. (f) Transfer characteristics and transconductance curve at V_DS = 8 V.

GaN HEMT devices exhibit complex thermal fields induced by piezoelectric–electric–thermal coupling. Noncontact emerging high-resolution infrared thermography is employed for temperature profile visualization. Fig. 2(a) displays the three-dimensional temperature distribution and corresponding isotherm mapping at V_DS = 80 V. The main thermal source is concentrated between the gate and drain electrode, with a peak occurring on the side of the gate near the drain. The peak temperature rise (ΔT = T_max − T₀) in the gate-drain region exceeds that in the gate-source region by 13.4%. Fig. 2(b) shows the temperature distribution along with the channel, revealing that the hotspot consistently localizes near the gate region across the 20–80 V range. Therefore, this phenomenon suggests prioritizing protection and designing heat dissipation in the gate-drain region, as this area constitutes the main heat generation. It is noteworthy that the temperature at the electrode is significantly lower than that at the GaN channel. There are two factors to consider: (i) the high thermal conductivity of the metal electrodes leads to efficient heat dissipation, resulting in a lower temperature relative to the channel region. (ii) Metal electrodes with lower infrared emissivity have a low sensitivity to temperature rise.³⁶ In addition, Fig. 2(c) shows that the highest temperature demonstrates an approximately linear increase with V_DS. Infrared thermography provides critical guidance for thermal dissipation optimization.

Fig. 2 Spatial thermal distribution and simulation of the fabricated GaN HEMT. (a) Three-dimensional diagram and isotherm mapping of the device temperature. (b) Temperature distribution along the channel direction (corresponding to the blue dashed line at V_DS = 20–80 V). (c) Variation in the maximum temperature with V_DS. (d) Simulated electrical potential profile near the gate position. (e)–(g) Distribution of the simulated device's electric potential, electric field in the Y direction (along with channel direction, positive direction from drain to source), and electric field in the Z direction (perpendicular to channel direction, positive direction from device bottom to top). (h) Simulated temperature profile near the gate position. (i) Device temperature distribution along the channel direction.

To reveal the mechanism of heat generation, a technology computer-aided design (TCAD) simulation was conducted at V_DS = 80 V. The simulated GaN HEMT structure is consistent with the fabricated device. Fig. 2(d) and (e) depict the electric potential of two-dimensional profiles and line-scan distribution near the 2DEG position, respectively. The electric potential exhibits an abrupt shift near the gate position, which causes a huge electric field according to the following formula: . Fig. 2f shows the electric field distribution along the channel direction, which drives carrier drift and generates current. According to the Joule heating formula,

where P is the Joule heat power density, is the current density and is the electric field. The region with a larger electric field generates greater Joule heat power, thereby generating localized hotspots. Meanwhile, a strong vertical electric field (vertical to channel direction) is generated on the gate side close to the drain, as illustrated in Fig. 2(g). This electric field depletes electrons near the gate, forming a space charge region, as shown in Fig. S2. The mobility of carriers is also reduced by a high electric field according to the high electric field saturation mobility mode.^37,38 Therefore, the differential resistance mode is employed to elucidate the heat distribution, as depicted in Fig. S3. According to σ = nqμ, the conductivity diminishes in the high electric field region due to depletion of electrons and reduction of mobility, resulting in an increase in differential resistance. According to the following formula

δP = δR × I², (2)

where δP is the differential heat power, δR is the differential resistance and I is the current; the position with higher differential resistance generates more Joule heat. Therefore, the heat source is located on the gate side close to the drain due to the combined influence of the drift electric field and the depletion region. Then, the temperature decays exponentially with the distance from the heat source, as shown in Fig. 2(h). Fig. 2(i) shows the simulated temperature distribution along the channel direction. The comparison with the experimental data demonstrates that the theoretical model matches the experimental results well. Notably, the difference between simulation and experiment is due to neglecting the large heat dissipation of metal electrodes, thermal generation from contact resistance, and localized defect-induced heating of epitaxial layers in the simulation.^11,36,39

Furthermore, we measured the characteristics of the thermal temporal evolution in GaN HEMT, which is important for high-frequency and high-power applications.^37,40 Fig. 3(a) and (b) illustrate the isothermal mapping when time = 1 s and 6 s after the application of a drain voltage of 40 V. The temperature first rises from the gate region and subsequently spreads across the entire device. More isotherm diagrams in 0–7 s are shown in Fig. S4. Fig. 3(c) displays the temporal evolution characteristics of the temperature linear distribution along the channel direction, indicating the hotspot persistently localized near the gate side. Furthermore, we determined that the peak temperature varies with time, as shown in Fig. 3(d). The device temperature rises quickly in about 7 s and reaches a relatively stable temperature of 38.73 ± 0.17 °C. When the voltage is removed, the temperature decreases rapidly to room temperature within 7 s. This curve exhibits temperature fluctuations within ±0.5%, as shown in the inset of Fig. 3(d). The device is thermally stable under high-voltage/high-frequency operation, as the kHz-range working frequency is lower than the thermal response time due to the absence of a device package and heat sink. Furthermore, a fitting analysis was performed on the heating and cooling processes, as shown in Fig. 3(e). The following formula, based on the Förster RC thermal network, fits the temperature curves:^37,41,42

where ΔT_h(t) is the rising temperature, P is the thermal dissipation power, and R_thi is the thermal resistance of the i-th network path and time constant τ_i = R_thi × C_thi, C_thi is the heat capacity. The Foster network can conveniently fit the temperature curve. The parameters of the Foster network have no actual physical significance, while the RC parameters of the Cauer network correspond to the actual thermal structural parameters of the device. The two networks can be converted into each other.^37,41,42 Fig. S5 demonstrates the schematic of the Foster and Cauer network models. The converted method can be found in the SI. The converted Cauer parameters of the rising process are presented as follows: R₁ = 3.4677, C₁ = 0.0123, R₂ = 10.2951, and C₂ = 0.1719. The physical meaning of the RC parameters can be determined through the heat transfer process, as illustrated in Fig. 3f. Joule heat is generated at a high electric field region, which is subsequently dissipated through the epitaxial layer and substrate due to no package and a heat sink. Due to the substrate exhibiting higher thermal resistance and capacitance, R₁ and C₁ represent the GaN epitaxial layer, while R₂ and C₂ represent the Si substrate. This analysis guides thermal optimization strategies: (i) reducing overall thermal resistance by improving epitaxial layer quality (e.g., defect density reduction) and adopting high-thermal-conductivity substrates (e.g., diamond or SiC); (ii) optimizing the thermal capacitance to delay sudden temperature increases under high electric power. In summary, the dynamic thermal model has deepened the understanding of the heat transfer process, providing critical guidance for device thermal dissipation optimization and stability design.

Fig. 3 Thermal temporal evolution process of the fabricated GaN HEMT. (a) and (b) Temperature distribution when the time is 1 s and 6 s, respectively. (c) Temporal evolution of the temperature linear distribution. (d) Variation in the highest temperature with time; the inset displays a temperature of 40–80 s. The orange dashed line represents the mean value. (e) Rise and drop temperature curves fitted by the Foster model. (f) Schematic of the heat conduction process and electrothermal coupling mechanism.

Piezotronics provides a novel way to modulate the electrical properties of GaN HEMT and could provide opportunities for further thermal field regulation. A customized fixture was fabricated to induce the piezotronic effect of GaN HEMT. When the movable module touches the backside of the sample and lifts upwards, an upward bending deformation is performed on the device. The lifting height can be precisely controlled by a spiral micrometer. The lifting height is 0, 10, 20 and 30 µm, corresponding to different external stress. Fig. 4(a) shows the output characteristics under external stress. At a lifting height of 30 µm, the saturation current decreases from 2.18 mA to 1.96 mA at V_GS = 1 V, which is caused by the reduction of the piezoelectric polarization charge under external stress.^43,44 The transfer curve exhibits an analogous decreasing trend, as shown in Fig. 4(b). The maximum current in the transfer curve decreases from 7.14 mA to 6.37 mA at V_DS = 8 V. In addition, the transfer curve reveals an increase in the device's threshold voltage (V_th) with lifting height, as illustrated in the inset of Fig. 4(b). The threshold voltage can be calculated as follows:⁴⁵

where the V_th is the threshold voltage, φ_b is the Schottky barrier height between the gate and barrier layer, ΔE_c is the conduction band offset at the AlGaN/GaN interface and σ_pol is the total polarization charge density. According to the formula, the threshold voltage exhibits a forward shift due to a reduction in the total piezoelectric polarization charge.^34,35,45 Fig. 4(c) displays a slight increase in gate current due to the external stress shifting the defect level toward the conduction band.⁴⁶ In addition, the transconductance slightly decreases, which indicates that the gate control capability of the device marginally decreases due to the diminution of the 2DEG density, as shown in Fig. 4(d). Based on the results, the piezotronic probe effectively regulates the electrical characteristics of GaN HEMT while paving the way for further modulation of the thermal field.

Fig. 4 Electrical properties of the fabricated GaN HEMT under external stress. (a) Comparison of output characteristic curves with lifting heights from 0 µm to 30 µm. (b) Transfer curves under different lifting heights at V_DS = 8 V; the inset is the change in the threshold voltage. (c) Gate current characteristics of the device. (d) Transconductance changes under external stress.

For the first time, we observed the modulation of the thermal field by the piezotronic effect. The induced temperature variations were visualized using a high-resolution infrared thermography camera. Fig. 5(a) illustrates the temperature distribution along the channel direction under varying voltage and lifting height conditions. A significant decrease in device temperature can be observed, indicating that external stress can efficiently modulate the thermal field. The reductions observed in both the gate-drain and gate-source regions reveal the stress impact of the global thermal field. Fig. 5(b) illustrates that the maximum temperature varies with the lifting height when the V_DS ranges from 20 V to 80 V. At V_DS = 80 V, the maximum temperature decreased from 42.9 °C to 41.4 °C, exhibiting a 10.1% reduction in the temperature rise. Moreover, the maximum temperature significantly decreases with an approximately linear relationship, demonstrating the linear modulation of Joule heating by external stress. We conducted tests on the stability and error of the piezotronic probe, as shown in Fig. S6. Twelve tests were conducted on a single device, and a total of 45 tests were carried out on 15 devices. The test results effectively demonstrate that the piezotronic-probe strategy exhibits excellent stability, which is described in the repeatability and error testing section of the SI. Fig. 5(c) and (d) display the device thermal profile under the conditions of 0 and 30 µm lifting height. It is observable that upon applying external stress to the device, the temperature at the hottest location decreases, accompanied by a general temperature reduction across the entire device. The four isotherms of 0–30 µm lifting height with the same temperature range are shown in Fig. S7 of the SI. As discussed above, the rules of piezotronics for thermal modulation have been comprehensively characterized by the piezotronic-probe strategy.

Fig. 5 Thermal modulation of the fabricated GaN HEMT under external stress. (a) Temperature distribution along the channel direction at different lifting heights and V_DS. (b) Variation in the maximum temperature with lifting heights. (c) and (d) Isotherm diagrams at 0 and 30 µm, respectively.

To elucidate the thermal field modulation mechanism under the piezotronic probe, a multi-physical coupled finite element simulation was established. First, external stress under different lifting heights was simulated. Fig. 6(a) illustrates the AlGaN/AlN/GaN heterojunction deformation and the corresponding σ_xx distribution. The σ_xx along the channel direction is depicted in Fig. S8. Raman spectroscopy can characterize the actual stress of a device. The actual stresses of lifting height from 0 to 30 µm are −82.1 MPa, −36.65 MPa, 13.33 MPa and 38 MPa, as shown in Fig. S9. Raman spectroscopy verifies the accuracy of the simulation model. Furthermore, through simulation, it was observed that the stress variation within the device range was less than 16%. Therefore, it is assumed that the stress applied to the device is uniform. The above results are incorporated into the simulated model as the stress component. Based on the self-consistent model of the Schrodinger and Poisson equations, the energy band and 2DEG concentration were calculated at the AlGaN/AlN/GaN heterojunction interface. As illustrated in Fig. 6(b), when the external stress reduces the total stress, the polarization intensity of the AlGaN/AlN/GaN interface decreases and the triangular potential well becomes shallower.^47–49 The shallower well exhibits a weakened capacity to confine electrons, thereby reducing the 2DEG concentration at the heterojunction interface, as shown in Fig. 6(c). Furthermore, we simulated the electric characteristics of the fabricated GaN HEMT under a piezotronic probe. A certain decrease in the saturation current is observed after applying external stress, as depicted in Fig. 6(d). Similarly, the drain current in the transfer curve exhibits a decline under external stress, as shown in Fig. 6(e). These current decreases are caused by the reduction in the 2DEG concentration. A forward shift of the threshold voltage is also presented in the inset due to the reduction in the total piezoelectric polarization charge. The change rules of output, transfer characteristics and threshold voltage are consistent with the experimental results. Finally, the temperature distribution under the piezotronic probe was simulated. The results demonstrate that applied external stress induces a reduction in device temperature, as shown in Fig. 6(f). The simulation results agree with the experimental observations, thereby further confirming the accuracy of the theoretical model. Detailed theoretical models and derivations are provided in the Theoretical Analysis section of the SI. Through the above analysis, the Joule thermal field could be effectively modulated by external stress via the bridge of piezoelectric polarization.

Fig. 6 Simulation of the electrical and thermal properties of the fabricated GaN HEMT using the piezotronic probe. (a) Schematic of external stress generated by material deformation and simulation of σ_xx stress distribution. (b) Energy band diagram under external stress. (c) Carrier concentration at the AlGaN/AlN/GaN interface. (d) Output characteristic curves. (e) Transfer characteristic curve; the inset is the threshold voltage change. (f) Temperature distribution curves obtained from simulation and experiment.

Conclusions

In summary, a systematic study was conducted on a theoretical framework combining piezotronics with an electrothermal model. The heat generation model under multi-field coupling reveals that the localized hotspot is generated by the drift electric field peak and electron depletion region. The advanced infrared thermography exhibited a 13.4% higher temperature in gate-drain region compared to the gate-source region and confirmed the accuracy of the model. Dynamic thermal analysis indicates that the substrate layer makes a major contribution to thermal capacitance and resistance. Furthermore, piezotronics serves as a probe to enable localized and site-specific thermal field modulation. A 10.1% decrease in temperature rise is observed during dynamic modulation, further confirming the accuracy of the model. The theoretical analysis reveals that piezoelectric polarization serves as a critical bridging role in a thermal field modulated by piezotronics. This study extends piezotronics to the domain of piezoelectric-electric-thermal multi-field coupling and provides critical insights into thermal optimization strategies in GaN power devices.

Methods

Device fabrication

The GaN epitaxial layer was deposited on the Si(111) substrate using the metal–organic chemical vapor deposition (MOCVD) method, with the layer from bottom to top as follows: Si substrate, 5 µm AlGaN buffer, 200 nm GaN channel, 1 nm AlN spacer, 18 nm Al_0.2Ga_0.8N barrier and 1 nm GaN cap layer. Then, micro processing is carried out on the epitaxial wafer to fabricate the device. All patterning definition processes use standard lithography processes with the lithography machine of SUSS MA/BA6. First, GaN wafers were etched by applying high-power ICP etching technology under the recipe of Ar/BCl₃/Cl₂ (5/15/30 sccm) to create the active region, using the equipment of Sentech SI 500. Then, the drain and source electrodes were fabricated using Denton Explore 14 EBE equipment with four metal Ti/Al/Ni/Au (20/120/45/55 nm). Subsequently, the metal electrodes were annealed for 30 s at 850 °C under nitrogen conditions to form ohmic contacts with low resistance using rapid thermal annealing equipment. Finally, a Ni/Au (80/50 nm) gate electrode was processed by EBE to form the Schottky contact. The device size is given below: the active area is 1 × 1 mm², the width of the metal electrode is 100 µm, and the spacing from gate to source and gate to drain is 350 µm. To further achieve piezotronic regulation, the silicon substrate of the device needs to be thinned. The Si substrate of GaN HEMT was thinned to a thickness of 500 µm utilizing ICP etching with O₂/SF₆ (20/60 sccm).

Device characterization

The DC electrical characteristics of the device are tested using a Keithley 1500 semiconductor parameter analyzer. The microscope image of the device was taken using the Optical Microscope of Lab.A1 Microscope and the Axiocam 208 color Microscopy Camera. The device temperature was tested using a microscopic infrared hot spot location measurement system (GMARG-A4), and the infrared band of the infrared camera is 8–14 µm. The Raman spectrum with a 532-nm laser under different stresses was measured using a micro-Raman spectrometer of Horiba LabRAM HR Evolution. All the measurements were tested at room temperature and atmospheric pressure conditions.

Author contributions

Z. D., Y. L. and W. H. conceived and designed the project. W. S. and B. J. planned experimental methods. D. L. and Y. W. performed the simulation and analyzed the data. Y. L., J. Z. and W. H. provided research resources. J. W., P. T. and W. H. supervised the project. Z. L., Y. L. and W. S. wrote the first draft of the manuscript. All authors participated in the discussion and revision of this manuscript.

Conflicts of interest

The authors declare no competing interests.

Data availability

The data supporting this article are included in the supplementary information (SI). Supplementary information includes the rocking curve of the GaN layer, the distribution of simulated electron mobility and density along the channel direction, schematic diagram of a differential resistance model, the isotherm diagram of the GaN HEMT in 0–7 seconds after voltage application, the equivalent transformation of parameters for Foster model and Cauer model, the repeatability and error testing, the isotherm diagram of the GaN HEMT at different lifting heights, the distribution of σ_xx along the channel direction, the Raman spectra, theoretical analysis. See DOI: https://doi.org/10.1039/d5nh00772k.

Acknowledgements

The authors thank for the support from the Beijing Natural Science Foundation (Z230024), the National Natural Science Foundation of China (Grant no. 52173298 and 52192611), and the National Key R & D Project from Minister of Science and Technology (2021YFA1201603).

References

1. Z. Zheng, L. Zhang, W. Song, S. Feng, H. Xu, J. Sun, S. Yang, T. Chen, J. Wei and K. J. Chen, Nat. Electron., 2021, 4, 595–603.
2. Y. Zhang, F. Udrea and H. Wang, Nat. Electron., 2022, 5, 723–734.
3. Y. Zhang, D. Dong, Q. Li, R. Zhang, F. Udrea and H. Wang, Nat. Rev. Electr. Eng., 2025, 2, 155–172.
4. H. Zhang, J. Li, D. Liu, S. Min, T.-H. Chang, K. Xiong, S. H. Park, J. Kim, Y. H. Jung, J. Park, J. Lee, J. Han, L. Katehi, Z. Cai, S. Gong and Z. Ma, Nat. Commun., 2020, 11, 3118.
5. L. Nela, J. Ma, C. Erine, P. Xiang, T.-H. Shen, V. Tileli, T. Wang, K. Cheng and E. Matioli, Nat. Electron., 2021, 4, 284–290.
6. Z. Li, Z. Li, C. Zuo and X. Fang, Adv. Mater., 2022, 34, 2109083.
7. W. Song, J. Lv, J. Wei, J. Ge, H. Qin, H. Duan, J. Li, X. He and Z. Li, Adv. Funct. Mater., 2025, 35, 2423881.
8. M. Deng, Z. Li, X. Deng, Y. Hu and X. Fang, J. Mater. Sci. Technol., 2023, 164, 150–159.
9. Z. Li, T. Yan and X. Fang, Nat. Rev. Mater., 2023, 8, 587–603.
10. Z. Yan, G. Liu, J. M. Khan and A. A. Balandin, Nat. Commun., 2012, 3, 827.
11. H. Jiang, T. Wang, Z. Zhang, F. Liu, R. Shi, B. Sheng, S. Sheng, W. Ge, P. Wang, B. Shen, B. Sun, P. Gao, L. Lindsay and X. Wang, Nat. Commun., 2024, 15, 9052.
12. B. Sun, G. Haunschild, C. Polanco, J. Ju, L. Lindsay, G. Koblmüller and Y. K. Koh, Nat. Mater., 2019, 18, 136–140.
13. Y. Cui, Z. Qin, H. Wu, M. Li and Y. Hu, Nat. Commun., 2021, 12, 1284.
14. Y. Zhang, H. Han, N. Wang, P. Zhang, Y. Fu, M. Murugesan, M. Edwards, K. Jeppson, S. Volz and J. Liu, Adv. Funct. Mater., 2015, 25, 4430–4435.
15. J. Wu, E. Zhou, A. Huang, H. Zhang, M. Hu and G. Qin, Nat. Commun., 2024, 15, 2540.
16. J. S. Kang, M. Li, H. Wu, H. Nguyen, T. Aoki and Y. Hu, Nat. Electron., 2021, 4, 416–423.
17. C. Perez, A. J. McLeod, M. E. Chen, S. Yi, S. Vaziri, R. Hood, S. T. Ueda, X. Bao, M. Asheghi, W. Park, A. A. Talin, S. Kumar, E. Pop, A. C. Kummel and K. E. Goodson, ACS Nano, 2023, 17, 21240–21250.
18. R. van Erp, N. Perera, L. Nela, I. Osama Elhagali, H. Zhu and E. Matioli, IEEE Trans. Power Electron., 2024, 39, 9717–9723.
19. R. van Erp, R. Soleimanzadeh, L. Nela, G. Kampitsis and E. Matioli, Nature, 2020, 585, 211–216.
20. W. Hong, L. Zhang, C. Zhang, F. Zhang, S.-Z. Yue, P.-B. Du, X.-F. Zheng, X.-H. Ma and Y. Hao, Appl. Phys. Lett., 2024, 124, 182203.
21. J. Hu, S. Liu, Y. Huo, B. Yang, Y. Yin, M. Tan, P. Liu, K. Cai and W. Ji, Adv. Mater., 2025, 37, 2417409.
22. A. A. Khan, A. Mathur, L. Yin, M. Almadhoun, J. Yin, M. H. Bagheri, M. F. Al Fattah, A. Rajabi-Abhari, N. Yan, B. Zhao, V. Maheshwari and D. Ban, Nat. Commun., 2024, 15, 9511.
23. C. Chen, Q. Yu, S. Liu and Y. Qin, ACS Nano, 2024, 18, 13607–13617.
24. Q. Yu, R. Ge, J. Wen, T. Du, J. Zhai, S. Liu, L. Wang and Y. Qin, Nat. Commun., 2022, 13, 778.
25. Q. Zheng, M. Peng, Z. Liu, S. Li, R. Han, H. Ouyang, Y. Fan, C. Pan, W. Hu, J. Zhai, Z. Li and Z. L. Wang, Sci. Adv., 2021, 7, 1–8.
26. W. Luo, R. Luo, J. Liu, Z. Li and Y. Wang, Adv. Funct. Mater., 2024, 34, 2311938.
27. W. Xun, X. Liu, Y. Zhang, Y.-Z. Wu and P. Li, Appl. Phys. Lett., 2025, 126, 161903.
28. X. Hu, W. Zhao, W. Xia, H. Sun, C. Wu, Y.-Z. Wu and P. Li, Appl. Phys. Lett., 2025, 127, 11905.
29. S. P. R. Mallem, J. Shim and S. J. An, Nano Energy, 2025, 135, 110618.
30. X. Song, B. Yi, Q. Chen, Y. Zhou, H. Cho, Y. Hong, S. Chung, L. You, S. Li and J. Hong, ACS Nano, 2024, 18, 16648–16657.
31. Z. Shi, L. Meng, X. Shi, H. Li, J. Zhang, Q. Sun, X. Liu, J. Chen and S. Liu, Nano-Micro Lett., 2022, 14, 141.
32. J. Zhu, X. Zhou, L. Jing, Q. Hua, W. Hu and Z. L. Wang, ACS Nano, 2019, 13, 13161–13168.
33. X. Chen, J. Dong, C. He, L. He, Z. Chen, S. Li, K. Zhang, X. Wang and Z. L. Wang, Nano-Micro Lett., 2021, 13, 67.
34. S. Zhang, B. Ma, X. Zhou, Q. Hua, J. Gong, T. Liu, X. Cui, J. Zhu, W. Guo, L. Jing, W. Hu and Z. L. Wang, Nat. Commun., 2020, 11, 326.
35. W. Wu and Z. L. Wang, Nat. Rev. Mater., 2016, 1, 16031.
36. Q. Guo, D. Li, Q. Hua, K. Ji, W. Sun, W. Hu and Z. L. Wang, Nano Lett., 2021, 21, 4062–4070.
37. N. Sahebghalam, M. Shalchian, A. Chalechale and F. Jazaeri, IEEE Trans. Electron Devices, 2022, 69, 4821–4827.
38. M. Wang, Y. Lv, Z. Wen, H. Zhou, P. Cui and Z. Lin, IEEE Electron Device Lett., 2022, 43, 2041–2044.
39. S. Yang, H. Song, Y. Peng, L. Zhao, Y. Tong, F. Kang, M. Xu, B. Sun and X. Wang, Nano Res., 2021, 14, 3616–3620.
40. J. Zhou, L. Zhong, X. Feng, W. Zhang, X. Liu, H. Zhou, Z. Liu, Y. Hao and J. Zhang, IEEE Trans. Electron Devices, 2025, 1–14.
41. X. Zheng, J. W. Pomeroy, G. Jindal and M. Kuball, IEEE Trans. Electron Devices, 2024, 71, 2367–2372.
42. X. Zheng, S. Feng, Y. Zhang and J. Li, IEEE Trans. Electron Devices, 2018, 65, 1734–1738.
43. J. Niu, J. Wang, W. Sha, Y. Long, B. Ma and W. Hu, Int. J. Extreme Manuf., 2025, 7, 012005.
44. F. Huang, J. Chen, Y. Ding and W. Huang, Nano Energy, 2022, 96, 107098.
45. W. Sha, Q. Hua, Y. Shi, J. Wang, X. Cui, Z. Dong, B. Wang, J. Niu and W. Hu, J. Mater. Chem. C, 2022, 10, 11783–11790.
46. X. Cui, K. Ji, L. Liu, W. Sha, B. Wang, N. Xu, Q. Hua and W. Hu, Mater. Today Phys., 2022, 28, 100870.
47. C. Jiang, T. Liu, C. Du, X. Huang, M. Liu, Z. Zhao, L. Li, X. Pu, J. Zhai, W. Hu and Z. Lin Wang, Nanotechnology, 2017, 28, 455203.
48. Y. Zhang, Y. Leng, M. Willatzen and B. Huang, MRS Bull., 2018, 43, 928–935.
49. Z. Cheng, Z. Huang, J. Sun, J. Wang, T. Feng, K. Ohnishi, J. Liang, H. Amano and R. Huang, Appl. Phys. Rev., 2024, 11, 041324.

---

Footnote

† These authors contributed equally.

---