# Thermal Modeling of the GaN-based Gunn Diode at Terahertz Frequencies
## 3 Result and Discussion  
Figure 2 gives direct current I-V characteristics of the GaN Gunn diode under the EB model and NEB model, respectively. A serious drop of the saturate current appears when taking the self-heating problem into consideration in NEB model, which is attributed to the decrease of the electron velocity in the transit region due to the increased lattice temperature. At smaller V\({}_{\text{dc}}\), however, the differences in the anode current are almost negligible, because the increment of the lattice temperature is small. The heat generation in the transit region is caused by an energy transferring from the electron to the lattice, which is related to inelastic phonon scattering processes of the electron. As reported in [26], the scattering processes mainly responsible for the heat generation are the intra-valley scatterings of the electron in the \(\Gamma\)1 and the U valley. The heat generation originated from the intra-valley scattering in the \(\Gamma\)1 valley builds up near the cathode side. The electric field peak at the notch layer increases the scattering rate and accelerates the electrons to attain sufficient energy to transfer to the upper U-valley. Therefore, as the electrons travel towards the anode side, the heat generation originated from the intra-valley scattering in the U and other upper valleys begins to predominate. The variation of lattice temperature throughout the transit region can be investigated by using NEB model. Our simulations shown that the peak lattice temperature occurs near the notch-doped region where the electric field has a maximum, approaching 820 K at V\({}_{\text{dc}}\) = 50 V and 1015 K at V\({}_{\text{dc}}\) = 60 V, respectively. Therefore, we suggest using a pulsed bias operation to reduce the self-heating generation, in consistent with the fact that short bias pulses are normally applied instead of dc biases in order to avoid possible joule in the experiments of GaAs Gunn diode and HEMT devices [15; 27; 28; 29; 30]. In the instantaneous simulation, stable oscillations generate when the bias voltage of GaN Gunn diode ranges from 50 V to 75 V under EB model. However, stable oscillations can only be obtained at a narrow voltage range of 50-55 V under NEB model, which attributes to influence of thermal generation. For both models, the dc-to-ac conversion efficiency \(\eta\) decreases with V\({}_{\text{dc}}\), as shown in Figure 3, which gives the results of \(\eta\), f\({}_{\text{osc}}\) (oscillation frequency) and P\({}_{\text{RF}}\) versus V\({}_{\text{dc}}\). Under NEB model, as the operation voltage rises from 50 to 55 V, there is an obvious increase of lattice temperature throughout the whole diode, especially near the anode side, as manifested in Figure 4. The increase of the electric field greatly enhances the phonon scatterings of the electrons, which leads to the increase of the lattice temperature with V\({}_{\text{dc}}\), and accordingly the subsequent decrease of the anode current and the conversion efficiency. The serious heat accumulation even prevents the formation of stable oscillation when the bias voltage becomes higher than 55 V. At the bias voltage of 50 V, we extract the oscillation frequency f\({}_{\text{osc}}\) of around 207.0 GHz and 178.1 GHz from stab  
Figure 2: Simulated direct I-V characteristics of [PERSON] diode under NEB (non-isothermal-energy-balance model) model and EB (energy-balance model) model. under EB and NEB model, respectively. We can also find from Figure 3 that fosc shows an uptrend under both models as the voltage increases, which can be explained by Figure 5, the electric field profiles derived inside one oscillation period. At the operation voltage of 50 V, diode operates at dipole domain mode under EB model, as manifested in Figure 5a. Figure 5b shows that under EB model, the electron domain degrades into the mode between dipole domain and accumulation domain at Vdc = 75 V, and we call it a transition domain mode for the first time.