# Thermal Modeling of the GaN-based Gunn Diode at Terahertz Frequencies
## 3 Result and Discussion
A stable oscillation hardly generates under NEB model but there is still oscillation generating under EB model when L\({}_{\text{ac}}\) increases to 1.4 \(\upmu\)m.  
If the thermal generation is suppressed in the long transit region diode, non-unique dipole domains would appear particularly at higher doping level of N\({}_{\text{ac}}\). By using EB model we have found two dipole domains formed in the diode with L\({}_{\text{ac}}\) of 1.4 \(\upmu\)m and N\({}_{\text{ac}}\) of 3 \(\times\) 10\({}^{17}\) cm\({}^{-3}\), as illustrated in Figure 11a,b. The dual-dipole-domain phenomenon is attributed to two reasons. Firstly, dipole domain easily generates in the device which has higher N\({}_{\text{ac}}\)\(\times\) L\({}_{\text{ac}}\). Secondly, the increase of the N\({}_{\text{ac}}\)/N\({}_{\text{n notch}}\) enhances the fluctuation of the electric field in the transit region, which promotes the formation of two  
Figure 2:1 Electric field profiles of the diode derived inside one oscillation circle at the same time steps, when L\({}_{\text{ac}}\) = 1.2 \(\upmu\)m, under (**a**) EB and (**b**) NEB models. Figure 2:2 Simulation results of the oscillation frequency f\({}_{\text{osc}}\) and dc-to-ac conversion efficiency \(\upeta\) versus the active region length L\({}_{\text{ac}}\) under EB and NEB models. dipole domains inside one oscillation circle. However, the domain near the notch layer differs from the traditional dipole domain. Normally, the dipole domain consists of an excess electrons layer and a depleted electrons layer, but we cannot find an obvious excess electrons layer near the cathode side, as shown in Figure 11a. In order to demonstrate it is a dipole domain we extract electron concentration and electron velocity profiles at 12.6 ns, as shown in Figure 12a. Theoretically, the excess electrons part of the dipole domain forms as the trailing electrons behind the dipole arriving with a higher velocity. By the same token, the region of depleted electrons also grows because electrons ahead of the dipole leave at a higher velocity [30]. The correspondence between the electron concentration and electron velocity shown in Figure 12a excellently supports this opinion. The electrons inside the notch layer experience a velocity overshoot, as illustration in the region 1 of the Figure 12a. So the electrons of the excess electrons layer comes from the notch layer initially. One on hand, the electron concentration of notch layer is greatly lower than that of the active channel; on the other hand, the excess electrons layer part comes into being immediately inside the notch layer. Therefore, it results in the formation of an obscure excess electrons layer. At the same time, the electrons in region 2 speed up, ahead of which formed a depleted electrons layer. Due to the dual-dipole-domain phenomenon inside one oscillation circle, the harmonic frequency is greatly enhanced, as shown in Figure 12b where the frequency spectrum is extracted by means of the fast Fourier transformation (FFT) algorithm. The excellent frequency multiply would find a promising application in terahertz technology. Figure 2:3 Electron concentration (**a**) and electric field (**b**) profiles derived inside one oscillation circle at the same time step, when L\({}_{\text{ac}}\) = 1.4 \(\upmu\)m and N\({}_{\text{ac}}\) = 3 \(\times\) 10\({}^{17}\) cm\({}^{-3}\) under EB model. Figure 2:4 (**a**) The relationship of the electron velocity and electron concentration derived inside on oscillation circle at 12.6 ns, when L\({}_{\text{ac}}\) = 1.4 \(\upmu\)m, N\({}_{\text{ac}}\) = 3 \(\times\) 10\({}^{17}\) cm\({}^{-3}\); (**b**) and its frequency spectrum diagrams.