## 2 Device Structure and Simulation Condition  
The cross-section device structure of the AlGaN/GaN SPD is schematically shown in Figure 1. Figure 1a introduces the diode with AlGaN/GaN/AlGaN hetero-epitaxial structure, and only one 2 DEG channel is introduced in the diode. The Al\({}_{0.1}\)Ga\({}_{0.9}\)N back barrier layer was introduced to enhance the confinement of the quantum well and avoid the formation of a parasitic channel. The trench anode was etched through at least the 2 DEG channel to ensure that the 2 DEG channel was divided into two individual channels. In order to further enhance the output characteristics of the trench anode Gunn diode, we also introduced a multi-2 DEG-channel structure in the diode, as shown in Figure 1b. The multi-2 DEG-channel structure mainly consisted of a 22 nm-thick un-doped Al\({}_{0.3}\)Ga\({}_{0.7}\)N barrier layer, multiple combinations of AlGaN/GaN hetero-epitaxial layers, and a 0.5 \(\upmu\)m-thick Al\({}_{0.1}\)Ga\({}_{0.9}\)N back barrier layer. The number of 2 DEG channels was controlled by the number of the combinations of the AlGaN/GaN hetero-epitaxial layers: one combination for two channels, two combinations for three channels. Furthermore, a combination of AlGaN/GaN hetero-epitaxial layer consists of a 15 nm-thick AlGaN barrier layer (10 nm-thick un-doped Al\({}_{0.1-0.3}\)Ga\({}_{0.3-0.7}\)N upper layer and a 5 nm-thick un-doped Al\({}_{0.3}\)Ga\({}_{0.7}\)N middle layer) and an 8 nm-thick undoped GaN channel layer (bottom layer). In the upper barrier layer, Al composition gradually changes from 10% to 30%. Theoretically, in one combination of AlGaN/GaN, higher Al composition of the barrier layer results in higher electron concentration of the 2 DEG channel in the GaN layer; however, this also leads to a shallower quantum well (that is, a lower electron concentration of the 2 DEG) in the upper AlGaN/GaN combination and a higher lattice mismatch between the AlGaN and the upper GaN layer. Therefore, we chose a composition gradient barrier layer in the first 10 nm, and 30%-Al-composition barrier in the second 5 nm.  
Similarly, in order to split all the 2 DEG channels into two parts, the trench should be etched through the bottommost GaN layer as shown in Figure 1b. In Figure 1a,b, the anode electrode is deposited inside the trench and two vertical cathode electrodes are fabricated beside the diode. There are three main reasons for the vertical electrodes. First, vertical electrodes bring less parasitic resistance. Second, vertical electrodes suppress the electric field peaks near the electrodes, which can easily result in the early breakdown of the diode. Third, in the multi-2 DEG-channel diode, all the electrodes should reach the bottom channel of the diode to ensure that each channel is able to work. The vertical cathode electrodes can be fabricated by MBE-regrown technology or ICP technology.  
In this paper, the design and simulation of the GaN-based SPD was done using the two-dimensional Silvaco Atlas software. For higher simulation accuracy, we adopted an EB (energy balance) model instead of a DD (drift diffusion) model. All the physical parameters were the same with [13]. We set the temperature as 300 K. To analyze the RF output characteristics of the devices, a sinusoidal voltage of form V\({}_{\text{DC}}\) + V\({}_{\text{RF}}\)sin(2\(\pi\)fft) was directly input to the SPD instead of using an RLC (Resistance Inductance Capacitance) resonant circuit, in order to increase calculating efficiency [17]. The DC-to-RF conversion efficiency \(\eta\) was defined as \(\eta=-\text{P}_{\text{RF}}/\text{P}_{\text{DC}}\) (P\({}_{\text{RF}}\) is the time-average RF power; P\({}_{\text{DC}}\) is the dissipated DC power).