Analytical Design and Modelling of GaN Vertical Trench Junction Barrier Schottky Diodes


 We report GaN vertical trench junction barrier Schottky (TJBS) diodes and systematically investigate the impacts of the key design parameters on the reverse and forward characteristics of GaN-based TJBS diodes by numerical simulation. Compared with conventional planar junction barrier Schottky (PJBS) diodes, the TJBS structure can suppress the electric field at the Schottky interface more effectively by taking advantage of the electric field shielding effect. We found that the electric field profile can be influenced by the doping concentration, thickness and spacing of p-GaN, as well as the depth and angle of the trench sidewalls. Furthermore, the effect of the cross-sectional profile on the forward characteristics of the TJBS diodes are investigated and the analytical model of the forward conduction is also developed. The results can pave the way towards a high-power, high-voltage, and low-loss GaN vertical Schottky barrier diodes for high-efficiency power system applications.


Device architectures and principles
distribution into the drift layer. Thanks to the combined effect by the trench and p-GaN 90 structures, a stronger electric field shielding effect can be observed from the TJBS structure in 91 Figure 1(b), which allows a substantial reduction of the electric field at the Schottky surface, 92 compared to the PJBS structure. Meanwhile, the electric field peak moves further into the drift 93 layer due to the adoption of the trench and allows the formation of deeper pn junction. 94 The reverse blocking capability of TJBS diodes is dominated by the electric field distribution, 95 which is closely correlated with the electric field shielding effect from the pn junction and the 96 vertical trench structure. Therefore, the influence of the key design parameters on the device 97 performance is investigated by varying the doping concentration and the thickness of the p-98 GaN (Tp), the width of the channel (Wc) between adjacent p-GaN, the depth of the trench (Dtr), 99 and the angle (θ) of the trench slope. The breakdown voltage is defined as the reverse bias value 100 corresponding to a current density of 1 A/cm 2 . 101 We conduct the numerical investigation based on the Advanced Physical Models of 102 (3) 117 where is the acceptor degeneracy factor, and EF is the Fermi level, EA is the acceptor level. 118 Furthermore, the concentration of ionized Mg acceptors is considered to be much higher in the 119 simulation procedure under non-equilibrium condition than under equilibrium condition, as 120 experimentally reported in Reference [42]. 121   To explore the breakdown mechanism of the TJBS diodes with different p-doping 139 concentrations, we extracted the lateral 1D electric field profiles from the bottom interface 140 between p-GaN and the n --GaN drift layer, as shown by the dash line in the inset of the Figure  141 2(b). With a high p-doping concentration of 2×10 18 cm -3 and above, a high electric field can be 142 observed at the corner of the p-GaN structure, which exceeds the critical breakdown field of 143

Results and discussion
GaN and leads to premature breakdown. A more uniform distribution of the electric field can 144 be observed with p-doping concentration of 2×10 17 cm -3 , which can result in an improved 145 breakdown voltage compared to that at a higher p-doping concentration. With a p-doping 146 concentration of 2×10 16 cm -3 , a further reduction in the electric field value is recorded at the 147 bottom of the p-GaN. However, the corresponding breakdown voltage of the TJBS diodes is 148 lower, which cannot be explained with the 1D electric field profile in Figure 2 leads to an accumulation of the electric field at the p-GaN corner and thus a premature  Figure  191 4(a). 192

TJBS diodes 194
After addressing the effects of the p-GaN related design parameters (p-doping concentration 195 and thickness), we then look into the influence of the geometrical dimensions (p-GaN spacing 196 and trench depth) on the reverse characteristics of the TJBS diodes, as presented in Figure 5  distinction in the breakdown voltage is more pronounced between the TJBS diodes with a trench 206 depth of 1 μm and 2 μm, respectively, which can be further enlarged with a larger Wc. 207 The breakdown mechanism of the TJBS diodes is investigated by analyzing their 1D electric 208 field profiles at different Wc and Dtr. Figure 5 (

P-GaN
diodes based on the optimized structure. As is shown in Figure 6, as θ increases from 40° to 233 100°, the reverse breakdown voltage increases monotonously from 1000 V to 1260 V, with a 234 concomitant increase in on-resistance (Ron). Specially, when the value of θ changes from 90° to 235 100°, a sharp increase of the Ron can be observed from 1.8 mΩ·cm 2 to 3.5 mΩ·cm 2 , which can 236 be attributed to a narrower current conduction channel. 237 The reason for the increased breakdown voltage with a larger θ can be derived from the 2D 238 electric field distribution in Figure 7. At a small θ of 40° in Figure 7 The overall resistance Ron of device is determined by the resistive components, which can be 255 given by 256   where ФB is the Schottky barrier height, q is the electron charge, k is the Boltzmann constant, T 273 is the Kelvin temperature, and A * is the Richardson constant.
represents the current density 274 through the Schottky surface, which is proportional to the cell current density ( ) by the 275 following expression 276 where D is the width of the Schottky interface under the conduction path, which is related to 278 the width of the channel (Wc) and the junction depletion region (Wd) 279 Wd can be derived from the following equation: 281 where , , and are the dielectric constant, the built-in potential difference, the applied 283 forward bias and the drift layer doping concentration, respectively. Furthermore, the simulated 284 Ron of the TJBS diodes with θ of 60° in terms of Wc is presented in Figure 9, in which the curve 285 of Ron calculated according to the proposed analytical calculation model is also shown. It can 286 be seen that there is a favorable agreement between the calculation values and the simulation 287 results, confirming the validity of the proposed analytical calculation model. 288 The analytical model can be used for intuitively analyzing the variation of Ron and calculate 289 the forward voltage drop (VFS) of the TJBS diodes, which can pave the way for the design of

Conclusion 293
In summary, we report GaN-based trench junction barrier Schottky diodes and systematically 294 analyzed the effects of the key design parameters on the reverse and forward characteristics of 295 the devices. By taking advantage of the charge coupling effect with the TJBS structure, the 296 barrier lowering effect at the Schottky junction at can be effectively suppressed. With an 297 optimal set of design parameters, the locally concentrated electric field at either the corner of 298 the trench or the edge of the p-GaN can be effectively alleviated, resulting in a boosted 299 breakdown performance in the TJBS diodes. In addition, an analytical model is explored and 300 developed to explain physical mechanism behind the forward conduction behaviors. We believe 301 that the results can provide a systematical design strategy for the development of low-loss, high-302 voltage, and high-power GaN power diodes towards an efficient power system. 303 Authors' contributions 304

Availability of data and materials 316
All data generated or analyzed during this study are included within the article. 317 318