# Thermal Modeling of the GaN-based Gunn Diode at Terahertz Frequencies
## 3 Result and Discussion
As compared Figures 4c and 5d, we conclude that the joule heating generation accelerates the degradation of the domain under NEB model. Only transition domain formed under NEB model as Vdc = 50 V. When the operation voltage rises to 55 V, the domain completely degrades to accumulation domain. In theory, the dipole-domain mode oscillation is more stable and generates higher RF power compared with other oscillation modes in the Gunn diodes. As a result, no matter under EB model or NEB model, the RF output power PRF shows a downward trend, although the voltage increases, as shown in Figure 3b The dipole domain is composed of an excess electrons layer and a depleted electrons layer. However, there is only an excess electrons layer in the accumulation layer. Therefore, dipole-domain mode generates a lower frequency than the accumulation-layer mode does. As a conclusion, the degradation of the domain under both EB and NEB model incurs a decrease in conversion efficiency and RF output power and a slight increase in frequency. Figure 4: Lattice temperature profiles at different bias voltages under NEB model. Figure 3: **(a)** Simulation results of the oscillation frequency fosc and dc-to-ac conversion efficiency \(\eta\) versus the anode voltage Vdc and **(b)** RF output power PRF versus Vdc under EB and NEB models. The influence of different doping concentration of transit region N\({}_{\rm ac}\) on the output characteristics and physical mechanism of GaN Gunn diode is also investigated. We get the direct I-V and the global temperature characteristics for N\({}_{\rm ac}\) ranging from 1.5 \(\times\) 10\({}^{17}\) to 4 \(\times\) 10\({}^{17}\) cm\({}^{-3}\) under EB model and NEB model, as shown in Figure 6. Under EB model, the saturated current characterizing the generation of NDR oscillation exhibits a nearly uniform increase with a rising N\({}_{\rm ac}\). However the increase of the saturated current obtained under NEB model becomes smaller. At higher doping levels, anode current cannot become saturated as the voltage increases under NEB model, particularly, it presents obvious upward trend when N\({}_{\rm ac}\) is larger than 2 \(\times\) 10\({}^{17}\) cm\({}^{-3}\). This is because the increase of the lattice temperature with N\({}_{\rm ac}\) degrades the negative resistance effect. In Figure 6, the global lattice temperature can approach 1080 K when N\({}_{\rm ac}\) = 2.5 \(\times\) 10\({}^{17}\) cm\({}^{-3}\). Our simulation also presents the upper limit doping level of N\({}_{\rm ac}\) for stable oscillations is 3 \(\times\) 10\({}^{17}\) cm\({}^{-3}\) under EB model and 2.5 \(\times\) 10\({}^{17}\) cm\({}^{-3}\) under NEB model. Figure 7 shows the influence of N\({}_{\rm ac}\) on dc-to-ac conversion efficiency, oscillation frequency and RF output power. Under EB model, \(\eta\) decreases as doping level increases, however, there is an obvious increase of \(\eta\) under NEB model at N\({}_{\rm ac}\) of 2 \(\times\) 10\({}^{17}\) cm\({}^{-3}\). The same trend also appears on the curves of P\({}_{\rm RF}\)-N\({}_{\rm ac}\) as shown in Figure 7b. The increase of N\({}_{\rm ac}\) results in a larger proportion of N\({}_{\rm ac}\)/N\({}_{\rm notch}\) because we set an unchanged N\({}_{\rm notch}\) in this paper. The notch layer near cathode side aims to modulate the electric field of the cathode region and used as a nucleation point for the electron domain to reduce the dead zone length. However, a larger proportion of N\({}_{\rm ac}\)/N\({}_{\rm notch}\) leads a larger electric field and parasitic resistance at the notch layer as well as a smaller electric field in the active region. This is why the dipole domain gets mature within a smaller distance and the domain size becomes smaller when N\({}_{\rm ac}\) increases, which results in a decrease of \(\eta\) and P\({}_{\rm RF}\). In addition, when we take the self-heating effect into consideration, the lattice temperature distribution also plays an important role on the output characteristic of the device.