## 3 Results and Discussion  
As we changed the position of the trench anode electrode, L\({}_{1}\) and L\({}_{2}\) changed accordingly. We set L\({}_{2}\) = \(n\)L\({}_{1}\), and L\({}_{1}\) = L, where \(n\) is a positive integer. First we analyzed the samples as \(n\) = 1, that is, the anode contact was set at the center of the devices. The SPD with different numbers of 2 DEG channels from 1-3, were named sample A-C. For each sample, the channel length L ranged from 0.6 to 1.8 \(\upmu\)m, at a step of 0.2 \(\upmu\)m. The regular single-2 DEG-channel planar Gunn diode without a trench anode (sample D) was also analyzed as a reference, the channel length of which was also set to be L.  
The results (RF-to-DC efficiency \(\upeta\) versus the channel length L and RF output power P\({}_{\mathrm{RF}}\) versus L) are plotted in Figure 2. As shown in Figure 2, \(\upeta\) decreases with the number of the 2 DEG channels. The curves of \(\upeta\) versus L for all the samples show the same trend. Both \(\upeta\) and P\({}_{\mathrm{RF}}\) reach the value peaks at L = 1.0 \(\upmu\)m. When the channel length L is shorter than 1.0 \(\upmu\)m, the domain leaves the anode electrode before it grows mature, which results in lower \(\upeta\) and P\({}_{\mathrm{RF}}\). However, if the L is longer than 1.0 \(\upmu\)m, the domain grows mature before reaching the anode electrode, which results in invalid growing space and, therefore, deteriorates the noise performance. For the 1.0-\(\upmu\)m diode, the dipole domain grows to its mature size almost exactly as it reaches the anode electrode. Therefore, the highest operation performance is achieved in the diode of 1.0 \(\upmu\)m.  
The P\({}_{\mathrm{RF}}\) of 1.0-\(\upmu\)m-Sample A was 5.48 mW, nearly twice of that of Sample D. This is because the trench anode divided the single 2 DEG channel into two equal parallel channels. To further enhance the output power of SPD, we increased the number of AlGaN/GaN heterojunctions to achieve more parallel 2 DEG channels. Figure 3a,b gives the electron tracks derived at the same time steps inside one oscillation circle from 1.0 \(\upmu\)m-Sample B and Sample C respectively. Sample B contains two AlGaN/GaN heterojunctions, which can be equivalent to four 2 DEG channels. Similarly, Sample C is equivalent to six 2 DEG channels. As illustrated in Figure 3, all the 2 DEG channels were equal in length and independent of each other. In each channel, dipole domains form near the cathode contact and travel towards the anode contact without interfering with each other. Finally, all domains gradually disappear from anode contact at the same pace and a new oscillating circle repeats. The synchronization of electron domains inside each channel leads to a quasi-sine oscillating current wave; therefore, the fundamental frequency is enhanced. Ideally, since Sample B has four equal channels, its P\({}_{\mathrm{RF}}\) should be four times of that of 1.0-\(\upmu\)m-Sample D. However, based on Figure 2, P\({}_{\mathrm{RF}}\) of Sample B was 9.59 mW,  
Figure 1: The cross-section device structure of the AlGaN/GaN planar Gunn diode with trench anode electrode: (**a**) one 2D electron-gas (2 DEG)-channel diode; (**b**) triple-2 DEG-channel diode. only 3.2 times of that of Sample D. Furthermore, the efficiency \(\eta\) of sample B and C was also lower than Sample D. This is because in the multi-2 DEG-channel structure, the electron concentration deeper in the channel is lower than in the upper channel. This easily results in the inconsistency of the electron domain in each channel, which will increase the non-linearity of the quasi-sine oscillating current wave, and leads to lower \(\eta\) and lower total oscillation power. Figure 3: The schematic of the formation process of the electron domain in the 1.0 \(\upmu\)m-self-parallel planar Gunn diode with **(a)** two 2 DEG channels and **(b)** three 2 DEG channels.