# Thermal Modeling of the GaN-based Gunn Diode at Terahertz Frequencies
## 4 Conclusion  
In this paper, we present a numerical analysis on self-heating effect in GaN vertical n\({}^{+}\)-n\({}^{-}\)-n\({}^{-}\)n\({}^{+}\) Gunn diode based on Silvaco-Atlas, by emphasizing the microscopic analysis of the electron domain mode. In order to better understand the thermal and electrical properties of GaN Gunn diode, two models--the non-isothermal energy balance model (NEB) and energy balance model (EB)--are solved and analyzed alternately in the implementation of each sample. Our simulations have demonstrated that self-heating effect degrade the electron domain model and output characteristics of GaN Gunn diode. There is an obvious decrease of the saturation current in the direct I-V characteristics of each sample under NEB model, and peak lattice temperature in the notch region and reaches more than 1015 K at the operation voltage of 60 V. In order to avoid the serious heat generation, pulsed current is suggested instead of direct current. We have also explored the influence of the various parameters, viz. operation bias, the doping level and length of the active region on the heating generation and distribution. The increase of these parameters increases the inelastic phonon scattering processes of the electron, and further enhances the heat generation of the lattice, which weakens the NDR effect and degrades the electron domain as well as the output characteristics. In addition, with self-heating effect taken into consideration, the normal operation range of device is greatly limited, as compared with the ideal situation. We propose the transition domain for the first time, which is in between the dipole domain and accumulation layer, and stands for the degradation of the electron domain. A proper N\({}_{\text{ac}}\)/N\({}_{\text{n notch}}\) not only makes the notch layer a nucleate layer but also provides a more uniform temperature distribution, which results in higher output characteristics of the device. As demonstrated in our simulation, best performance is obtained in the sample with a doping level of \(2\times 10^{17}\) cm\({}^{-3}\). Dual-domain phenomenon is formed under EB model in the device with longer active region length and higher N\({}_{\text{ac}}\)/N\({}_{\text{n notch}}\), which enhances the harmonic frequency. However, we have not found dual-domain phenomenon under NEB model. The simulation of the structure parameters makes it possible to optimize the device and reduce the self-heating effect. Other engineering approaches to alleviate the heating like using an effective heat-sinking are our future work.  
Conceptualization, Y.W. and J.A.; methodology, Y.W.; software, Y.W.; validation, Y.W., J.A. and S.L.; formal analysis, Y.W.; investigation, W.Y.; resources, Y.H.; data curation, Y.W.; writing--original draft preparation, Y.W.; writing--review and editing, S.L., Y.H.; visualization, J.A.; supervision, J.A., Y.H.; project administration, J.A.; funding acquisition, J.A., Y.H.  
This work was partially supported by the National Key Research and Development Program (Grant No. 2017 YFB043000) and the National Natural Science Foundation of China (Grant No. 61274092). The author [PERSON] thanks the colleagues and her teachers who help her in her research work. The authors declare no conflict of interest.