# Thermal Modeling of the GaN-based Gunn Diode at Terahertz Frequencies
## 1 Introduction  
As one of the excellent candidates for terahertz radiation source, Gunn diodes have attracted much attention [1; 2; 3; 4; 5; 6; 7; 8]. Many recent researches demonstrate that the negative-differential-resistance (NDR) based GaN devices possess outstanding power performance at terahertz frequencies due to its unique electronic properties such as large band gap, high breakdown electric field, high electron drift velocity, and large NDR threshold voltage. Although theoretical works predict Gunn oscillations in the THz range in GaN diode [4; 5; 6; 7], experimental demonstrations of oscillations have not been achieved due to the technological bottleneck on GaN epitaxial growth and device fabrication. Besides, GaN material would face a serious self-heating problem when it is used for NDR device, because the threshold electric-field for NDR effect is almost 50 times larger than the value of GaAs material. For the Gunn diode, self-heating may trigger the weakening of the NDR effect and even the permanent failure of diode [8; 9; 10; 11]. As far as we know, there are many theoretical studies on Gunn diode recentyears, but without considering the self-heating effect. Some conclusions derived by these studies may not stand when taking the self-heating effect into consideration, particularly when the operation frequency approaches the terahertz regime. It is imperative to thoroughly investigate the relation between the thermal and electrical properties of terahertz Gunn diode in order to optimize the structure of the GaN Gunn diode and prevent or minimize the joule heating. There are great limitations to study the device thermal performance on the experimental method. Firstly, as we mention above, the fabrication and measurement of GaN Gunn diode are still very difficult because of bottlenecks on GaN epitaxial growth and device fabrication and the serious self-heating problem. Secondly, the self-heating effect deteriorates the output characteristics of the Gunn diode by affecting the motion of the electrons. However, it is difficult to provide a microscopic analysis on electron movements (especially the electron domain movements) by experimental method. Therefore, we choose the physical-based modeling and simulation method to achieve accurate device thermal management, which would guide the experiment research in turn.  
It is of difficulty to clarify the thermal effect on the electron domain in such a short transit region of Gunn diode at such a high electric field by means of traditional device transport theory. In this work, we use the energy balance transport model to explore the self-heating effect on characteristics of GaN vertical Gunn diode by means of a 2-D device simulation platform. The papers published on Gunn diode recent years have been mainly concentrated on the lateral high electron mobility transistor (HEMT)-like Gunn diode, due to its advantages over vertical ones [12; 13; 14]. However, the lateral structure still face reliability and integration challenges. Compared with the lateral diode, the vertical one also has its advantages, such as easier package, higher breakdown voltage, and so on [15; 16; 17]. Furthermore, the dc-to-ac dispersion induced by the surface states in lateral diode would be mitigated in the vertical one. Therefore, study on vertical Gunn diode is also needed. In this paper, we analyze the effect of the operation bias, the doping level and length of the active region on the performance and heating generation of the diode in detail. The geometry of the vertical diodes and physical model are described in Section 2, results and discussions are given in Section 3, and conclusions are given in Section 4. In order to better understand the thermal and electrical properties of GaN Gunn diode, two transport models, the non-isothermal-energy-balance model (NEB) and the energy-balance model (EB) are compared alternately in the simulation of each device sample.