## 3 Results and Discussion
Figure 2: (**a**) The RF-to-DC efficiency \(\eta\) versus the channel length L; (**b**) the RF output power \(\mathrm{P_{RF}}\) versus L.  
In addition, the results of frequency f versus channel length L for all the samples are plotted in Figure 4. All the curves have the same trend and almost overlap, which basically follows the empirical formula: f = v\({}_{\text{ave}}\)/L, where v\({}_{\text{ave}}\) is the average velocity for the electron domain. For Sample A, the frequency is about 270.64 GHz when L = 0.6 \(\upmu\)m and 172.94 GHz when L = 1.0 \(\upmu\)m.  
We also studied the asymmetric self-parallel diodes with different L\({}_{1}\) and L\({}_{2}\), where L\({}_{2}\) should be an integral multiple (\(n\)) of L\({}_{1}\), that is, L\({}_{2}\) = \(n\)L\({}_{1}\) (\(n\)\(\geq\) 2). In order to ensure that the electric field along the 2 DEG-channel stays within the normal operating range, an appreciate voltage of V\({}_{1}\) should be applied across the cathode electrode C\({}_{1}\) and anode electrode A, and accordingly a voltage of \(n\)V\({}_{1}\) should be applied across C\({}_{2}\) and A. We first studied the devices with L\({}_{1}\) = 0.6 \(\upmu\)m and L\({}_{2}\) = 1.2 \(\upmu\)m = 2 L\({}_{1}\). Figure 5a,b gives the schematic of the formation process of the electron dipoles in asymmetric single-2 DEG-channel SPD and the triple-channel SPD respectively, from which we can see that the electron domains in the shorter channels repeated two circles, while the electron domains in the longer channels complete one circle. More specifically, from Figure 5(a1-a3), we can see that the electron domain in the left channel has disappeared from the anode, while the domain in the right channel just approached the central position of the channel. In Figure 5a4, a new dipole domain forms inside the left channel and the domain in the right channel continues to grow up as moving to the anode. Figure 5(a5,a6) shows the process of disappearing of the two domains in both channels as they approach the anode side. The disappearance of the electron domain in the long channel represents a complete oscillation circle. The unsynchronized electronic domain motion results in the non-linearity of the RF current, as shown in Figure 6, and the oscillation current wave and frequency spectrum of the 0.6-1.2-\(\upmu\)m asymmetrical single-2 DEG-channel and triple-2 DEG-channel SPDs. Figure 6 shows that there are two peaks in the oscillation current wave in both diodes and the second-harmonics are greatly enhanced. As shown in Figure 6a,b, the smaller current peak is generated by the disappearance of the domain in the shorter channel, while the larger peak is due to the disappearance of the domain in the longer channel. For the single-2 DEG-channel SPD, f of 280.77 GHz, \(\upeta\) of 1.79%, and P\({}_{\text{RF}}\) of 2.19 mW is achieved at the second harmonic. Correspondingly, P\({}_{\text{RF}}\) increases to 6.02 mW, while f changes slightly at second harmonic in the triple-2 DEG-channel SPD. Figure 4: Frequency of the output signal f versus the channel length L.  
We further verified the motion of the electron domains in the multi-2 DEG-channel SPD as L\({}_{2}\) = 1.8 \(\upmu\)m = 3L\({}_{1}\). Similarly, before the dipole domain of the right channels leaves the anode electrode, the formation and movement of the electron domain repeat almost three circles in the shorter channel, which results in three current peaks in the oscillation current waves. Therefore, as shown in Figure 7, the third harmonic component is greatly enhanced in both SPDs at the frequency of around 280 GHz. Figure 5: The schematic of the formation process of the electron domain in the asymmetric self-parallel planar Gunn diode (SPD) where L\({}_{2}\) = 1.2 \(\upmu\)m = 2L\({}_{1}\): (**a1–a6**) single-2 DEG-channel SPD and (**b1–b6**) triple-2 DEG-channel SPD.