Device Design Assessment of GaN Merged P-i-N Schottky Diodes

Device characteristics of GaN merged P-i-N Schottky (MPS) diodes were evaluated and studied via two-dimensional technology computer-aided design (TCAD) after calibrating model parameters and critical electrical fields with experimental proven results. The device’s physical dimensions and drift layer concentration were varied to study their influence on the device’s performance. Extending the inter-p-GaN region distance or the Schottky contact portion could enhance the forward conduction capability; however, this leads to compromised electrical field screening effects from neighboring PN junctions, as well as reduced breakdown voltage. By reducing the drift layer background concentration, a higher breakdown voltage was expected for MPSs, as a larger portion of the drift layer itself could be depleted for sustaining vertical reverse voltage. However, lowering the drift layer concentration would also result in a reduction in forward conduction capability. The method and results of this study provide a guideline for designing MPS diodes with target blocking voltage and forward conduction at a low bias.


Introduction
In recent decades, extensive research efforts have been put into developing III-N-based optoelectronic and electronic devices for future lighting and high-power systems because of the III-N semiconductor's wide energy bandgap, large critical electrical field, and good thermal dissipation capability [1][2][3][4]. For high-frequency rectifying applications, a variety of GaN-based two-terminal devices have been developed, including Schottky barrier diodes (SBDs, or Schottky diode for short), P-i-N diodes, and so on.
A Schottky diode could be formed by several-micron-thick n-type GaN films and a highly doped contact layer, for Schottky contact and ohmic contact, respectively. The Schottky barrier height is typically designed to be 1 eV or less, which translates into a turn-on voltage of no larger than 1 V, and a small conduction loss. However, the GaN SBD demonstrated so far exhibited a relatively inferior breakdown voltage when compared with GaN P-i-N diodes, partly due to the relatively high leakage current and the occurrence of peak electrical fields at the device's surface [5][6][7][8][9].
GaN-based P-i-N diodes have been demonstrated for a number of substrates, including GaN [10][11][12][13][14], SiC [15], sapphire [16][17][18], and Si [19][20][21][22]. So far, GaN P-i-N diodes with breakdown As shown in Figures 1 and 2, one fabricated GaN SBD using Ni/GaN as Schottky contact and three GaN P-i-N diodes with various drift layer thicknesses [24] were utilized to extract key material parameters, such as low field mobility, saturation velocity, and carrier lifetime, which are highly correlated to the forward characteristics. The best experimental match was found with electron low-field mobility at 400 cm 2 /v-s and electron lifetime at 0.7 ns [43][44][45]. The total number of grid points were 80,000, while 170,000 triangles were used in calculations. Device simulations were executed by solving the Poisson, continuity, and current density equations, considering incomplete ionization, the Auger recombination model, and the Shockley-Read-Hall (SRH) recombination model. In addition, all the simulations were carried out using Fermi-Dirac statistics [43]. Traps were not taken into account for the simulation process, although traps are believed to be sources of leakage current and would lead to pre-breakdown of devices, such as P-i-N diodes [20,24].  [24] were utilized to extract key material parameters, such as low field mobility, saturation velocity, and carrier lifetime, which are highly correlated to the forward characteristics. The best experimental match was found with electron lowfield mobility at 400 cm 2 /v-s and electron lifetime at 0.7 ns [43][44][45]. The total number of grid points were 80,000, while 170,000 triangles were used in calculations. Device simulations were executed by solving the Poisson, continuity, and current density equations, considering incomplete ionization, the Auger recombination model, and the Shockley-Read-Hall (SRH) recombination model. In addition, all the simulations were carried out using Fermi-Dirac statistics [43]. Traps were not taken into account for the simulation process, although traps are believed to be sources of leakage current and would lead to pre-breakdown of devices, such as P-i-N diodes [20,24].  Table 1.
The theoretical critical electrical field for GaN was reported to be as high as 3.3 MV/cm; however, the practical breakdown occurred at a relatively lower electrical field due to imperfect material properties, especially for GaN grown on foreign substrates. The realistic critical electrical field at which the breakdown occurred was determined by a set of fabricated GaN P-i-N diodes on Si substrates with drift layer thicknesses from 2.0 to 3.0 μm, as shown in Figure 2a. The basic device structure consists of a 0.8 μm thick n-GaN layer (electron concentration n = 1 × 10 19 cm -3 ), a 2/2.6/3 μm-thick i-GaN layer (electron concentration n = 2 × 10 16 cm -3 ), and a 0.5 μm thick p-GaN (hole concentration p = 2 × 10 17 cm -3 ). Figure 2b shows the extracted experimental data for fabricated devices with diameters of 100 μm. The corresponding breakdown voltage was increased from 390 to 515 V, respectively. The electrical field distribution of three devices at the point of breakdown was plotted  Table 1. electrical fields for depleted GaN layer and Ni/GaN Schottky contact, respectively, and will be used as criteria for breakdown determinations in the study of MPS structure.  Table 1.

P-i-N Diode with 5 µm Drift Layer and MPS Diode Design Assessment
To meet higher breakdown voltage applications, such as the 600 V breakdown voltage rate that is widely used in power applications, the drift layer thickness is typically increased to sustain a higher breakdown voltage. Figure 3a shows the schematic cross-sectional view of a GaN P-i-N diode with a 5 μm thick drift layer. The fully vertical MPS structure can be fabricated using a substrate removal technique, which has been well-developed and reported in our previous work [20]. It was found that the device's characteristics were highly related to the drift layer background concentration. In practice, the background concentration of the unintentionally doped i-GaN layers was in the range of 7 × 10 15 cm -3 to 2 × 10 16 cm -3 , depending on substrate choices, thin film thickness, and growth methods [5,19,46,47]. The background concentration could be lowered by doping carbon or iron [48] during the growth. Alternatively, one may slightly tune the concentration by altering growth temperature and pressure.
When the drift layer i-GaN background concentration was n = 2 × 10 16 cm -3 , the critical electrical field inside the device reached the breakdown criteria of 2.1 MV/cm, given 600 V reverse bias. When the i-GaN background concentration was reduced to 1 × 10 16 cm -3 , the blocking voltage was increased to 860 V, using the same critical breakdown criteria: 2.1 MV/cm.
A comparison of the electrical field distribution ( Figure S2. Supplementary Materials) showed that the decrease of the background concentration would greatly enlarge the space charge region, which could thus help to hold relatively larger blocking voltages. The results implied that high blocking voltage could only be achieved when the drift layer could be depleted to a great extent.  Table 1.
The theoretical critical electrical field for GaN was reported to be as high as 3.3 MV/cm; however, the practical breakdown occurred at a relatively lower electrical field due to imperfect material properties, especially for GaN grown on foreign substrates. The realistic critical electrical field at which the breakdown occurred was determined by a set of fabricated GaN P-i-N diodes on Si substrates with drift layer thicknesses from 2.0 to 3.0 µm, as shown in Figure 2a. The basic device structure consists of a 0.8 µm thick n-GaN layer (electron concentration n = 1 × 10 19 cm −3 ), a 2/2.6/3 µm-thick i-GaN layer (electron concentration n = 2 × 10 16 cm −3 ), and a 0.5 µm thick p-GaN (hole concentration p = 2 × 10 17 cm −3 ). Figure 2b shows the extracted experimental data for fabricated devices with diameters of 100 µm. The corresponding breakdown voltage was increased from 390 to 515 V, respectively. The electrical field distribution of three devices at the point of breakdown was plotted through TCAD-based tools, and it was found that the peak electrical field was all 2.1 MV/cm, despite the variation of the drift layer thicknesses, as shown in Figure 2c. A recently reported SBD device [5] revealed a high breakdown voltage of 1 kV using 11 µm thick drift layer, and the critical electrical field for Schottky contact was about 1.60 MV/cm according to our fitting results (see Figure S1, Supplementary Materials). In short, 2.1 and 1.6 MV/cm were determined as critical breakdown electrical fields for depleted GaN layer and Ni/GaN Schottky contact, respectively, and will be used as criteria for breakdown determinations in the study of MPS structure.

P-i-N Diode with 5 µm Drift Layer and MPS Diode Design Assessment
To meet higher breakdown voltage applications, such as the 600 V breakdown voltage rate that is widely used in power applications, the drift layer thickness is typically increased to sustain a higher breakdown voltage. Figure 3a shows the schematic cross-sectional view of a GaN P-i-N diode with a 5 µm thick drift layer. The fully vertical MPS structure can be fabricated using a substrate removal technique, which has been well-developed and reported in our previous work [20]. It was found that the device's characteristics were highly related to the drift layer background concentration. In practice, the background concentration of the unintentionally doped i-GaN layers was in the range of 7 × 10 15 cm −3 to 2 × 10 16 cm −3 , depending on substrate choices, thin film thickness, and growth methods [5,19,46,47]. The background concentration could be lowered by doping carbon or iron [48] during the growth. Alternatively, one may slightly tune the concentration by altering growth temperature and pressure. The GaN MPS, which aims to combine the merits of GaN SBDs and GaN P-i-N diodes, was assessed by TCAD tools (Figure 3b). In this structure, the i-GaN drift layer thickness was kept as 5 µ m. The p-GaN (p = 2 × 10 17 cm -3 , 800 nm thick) boxes and i-GaN boxes (with the same background concentration as i-GaN layer underneath, 800 nm thick) were alternatively placed above the i-GaN layer. Nickel and titanium were selected to form ohmic contact and Schottky contact with p-GaN and i-GaN, respectively [8,24]. Wp and Wd denote the p-GaN box width and inter-p-GaN box distance, respectively.  Figure 4 showed electrical field distribution of MPSs at -400 V, with inter-p-GaN layer distance Wd from 0.5 to 6 µ m, while keeping the p-GaN box width Wp 1 µ m, depth Dp 800 nm, and i-GaN concentration 2 × 10 16 /cm 3 . When the MPS was reverse biased, the space charge region in the PN junction was expanded outwards. In the case of Wd-Wp = 0.5-1 µ m, the space charge region of the neighboring PN junction would merge together to help hold vertical voltage under the Schottky contact, resulting in a reduced electrical field at the Schottky contact surface, compared with a pure SBD. In this case, the Schottky contact was protected from a high electrical field. When increasing the reverse bias up to 550 V, the peak E-field inside the MPS could reach its critical value, at which the MPS reached breakdown. One may find the blocking voltage 550 V was only slightly lower than that of pure P-i-N diodes (600 V). When increasing Wd from 0.5 to 4 and 6 µ m, one may find that at the same reverse 400 V, the fusion effect of two neighboring space charge regions was mitigated, or in other words, the screening effect from the space charge region to protect the Schottky contact was weakened, as shown in Figure 4b,c. There needs to be a higher voltage drop for the space charge region of the PN junction to expand to the extent that two neighboring space charge regions could merge with each other. Additionally, it is possible that before the space charge region could get the charge to fuse, a breakdown may already occur at the Schottky contact interface which is determined as the breakdown hot spot, as is the case in Figure 4c. Table 2 summarizes extracted device characteristics at the breakdown for various inter-p-GaN regions (distance Wd), while keeping the p-GaN lateral dimension fixed at 1 μm. One may find a monotonously decreased breakdown voltage as Wd was increased, as a result of continuously mitigated E-field screening effects. Correspondingly, the hot spot of the breakdown was shifted from inside the GaN space charge region to the Schottky contact surface. When the drift layer i-GaN background concentration was n = 2 × 10 16 cm −3 , the critical electrical field inside the device reached the breakdown criteria of 2.1 MV/cm, given 600 V reverse bias. When the i-GaN background concentration was reduced to 1 × 10 16 cm −3 , the blocking voltage was increased to 860 V, using the same critical breakdown criteria: 2.1 MV/cm.

Reverse Characteristics
A comparison of the electrical field distribution ( Figure S2. Supplementary Materials) showed that the decrease of the background concentration would greatly enlarge the space charge region, which could thus help to hold relatively larger blocking voltages. The results implied that high blocking voltage could only be achieved when the drift layer could be depleted to a great extent.
The GaN MPS, which aims to combine the merits of GaN SBDs and GaN P-i-N diodes, was assessed by TCAD tools (Figure 3b). In this structure, the i-GaN drift layer thickness was kept as 5 µm. The p-GaN (p = 2 × 10 17 cm −3 , 800 nm thick) boxes and i-GaN boxes (with the same background concentration as i-GaN layer underneath, 800 nm thick) were alternatively placed above the i-GaN layer. Nickel and titanium were selected to form ohmic contact and Schottky contact with p-GaN and i-GaN, respectively [8,24]. W p and W d denote the p-GaN box width and inter-p-GaN box distance, respectively. Figure 4 showed electrical field distribution of MPSs at −400 V, with inter-p-GaN layer distance W d from 0.5 to 6 µm, while keeping the p-GaN box width W p 1 µm, depth Dp 800 nm, and i-GaN concentration 2 × 10 16 /cm 3 . When the MPS was reverse biased, the space charge region in the PN junction was expanded outwards. In the case of W d -W p = 0.5-1 µm, the space charge region of the neighboring PN junction would merge together to help hold vertical voltage under the Schottky contact, resulting in a reduced electrical field at the Schottky contact surface, compared with a pure SBD. In this case, the Schottky contact was protected from a high electrical field. When increasing the reverse bias up to 550 V, the peak E-field inside the MPS could reach its critical value, at which the MPS reached breakdown. One may find the blocking voltage 550 V was only slightly lower than that of pure P-i-N diodes (600 V). When increasing W d from 0.5 to 4 and 6 µm, one may find that at the same reverse 400 V, the fusion effect of two neighboring space charge regions was mitigated, or in other words, the screening effect from the space charge region to protect the Schottky contact was weakened, as shown in Figure 4b,c. There needs to be a higher voltage drop for the space charge region of the PN junction to expand to the extent that two neighboring space charge regions could merge with each other. Additionally, it is possible that before the space charge region could get the charge to fuse, a breakdown may already occur at the Schottky contact interface which is determined as the breakdown hot spot, as is the case in Figure 4c. Table 2 summarizes extracted device characteristics at the breakdown for various inter-p-GaN regions (distance W d ), while keeping the p-GaN lateral dimension fixed at 1 µm. One may find a monotonously decreased breakdown voltage as W d was increased, as a result of continuously mitigated E-field screening effects. Correspondingly, the hot spot of the breakdown was shifted from inside the GaN space charge region to the Schottky contact surface.   The MPS with an i-GaN concentration of 1 × 10 16 /cm 3 was also simulated as shown in Figure 5. Similar to the MPS with an i-GaN layer concentration of 2 × 10 16 /cm 3 , the Schottky contact was wellprotected for short Wd, such as Wd-Wp = 0.5-1 µ m (Figure 5a). As Wd increased, the screening effect was mitigated. Additionally, it was found that a critical point (simultaneous breakdown) occurred at a combination of Wd-Wp = 8-1 µ m, which is quite different from the MPS with an i-GaN layer concentration of 2 × 10 16 /cm 3 . The simultaneous breakdown point can be regarded as an indicator that the breakdown hot spot shifted from inside the MPS to be at the Schottky contact surface. In the latter case, the E-field screening effect from PN junctions was compromised, such that the Schottky contact was not well-screened from the high electrical field. A further comparison of Tables 2 and 3 suggested that for an MPS with the same device dimensions, the breakdown voltage could be well  The MPS with an i-GaN concentration of 1 × 10 16 /cm 3 was also simulated as shown in Figure 5. Similar to the MPS with an i-GaN layer concentration of 2 × 10 16 /cm 3 , the Schottky contact was well-protected for short W d , such as W d -W p = 0.5-1 µm (Figure 5a). As W d increased, the screening effect was mitigated. Additionally, it was found that a critical point (simultaneous breakdown) occurred at a combination of W d -W p = 8-1 µm, which is quite different from the MPS with an i-GaN layer concentration of 2 × 10 16 /cm 3 . The simultaneous breakdown point can be regarded as an indicator that the breakdown hot spot shifted from inside the MPS to be at the Schottky contact surface. In the latter case, the E-field screening effect from PN junctions was compromised, such that the Schottky contact was not well-screened from the high electrical field. A further comparison of Tables 2 and 3 suggested that for an MPS with the same device dimensions, the breakdown voltage could be well enhanced by reducing the drift layer background concentration, as a result of the larger space charge region generated. was mitigated. Additionally, it was found that a critical point (simultaneous breakdown) occurred at a combination of Wd-Wp = 8-1 µ m, which is quite different from the MPS with an i-GaN layer concentration of 2 × 10 16 /cm 3 . The simultaneous breakdown point can be regarded as an indicator that the breakdown hot spot shifted from inside the MPS to be at the Schottky contact surface. In the latter case, the E-field screening effect from PN junctions was compromised, such that the Schottky contact was not well-screened from the high electrical field. A further comparison of Tables 2 and 3 suggested that for an MPS with the same device dimensions, the breakdown voltage could be well enhanced by reducing the drift layer background concentration, as a result of the larger space charge region generated.

Forward Characteristics
The role of inter-p-GaN distance W d and of drift layer concentration plays on the forward characteristics was also simulated and studied. Figure 6a presented the forward current density for five cases of W d from 0 to 8 µm, while keeping W p 1 µm wide and an i-GaN concentration of 1 × 10 16 /cm 3 . All the MPSs shared similar turn-on voltages of around 0.8 V, which was determined by the concentration of i-GaN and the work function of the metal selected. It could be found that MPSs exhibit better forward characteristics than pure P-i-N at a low bias range, typically below 5 V. As the ratio of W d /W p was increased, the current density was increased for voltages ranging from 0.8 to around 8 V, as a result of the higher portion of Schottky contact as a conduction channel. On the other hand, the pure P-i-N diode, which had a relatively large turn-on voltage, showed a relatively lower differential on resistance (due to conductivity modulation), meaning that the current density could overrun that of the MPS at a relatively large bias, typically over 7 V. Figure 6c,d shows a comparison of the current density for MPSs (i-GaN concentration of 1 × 10 16 /cm 3 ) with Wd-Wp = 1-1 μm and Wd-Wp = 4-1 μm at 5 V. The current was mainly concentrated in and dominated by the Schottky contact region at 5 V. The larger Wd is, the larger the portion of the device (Schottky contact part) that was activated for conduction, as well as the current density through the device. As is illustrated in Figure 4 and Table 3, the better conduction induced by larger portions of Schottky contact was achieved at the cost of a reduction of more than 100 V in the breakdown voltage. Figure 6b shows the comparison of forward current density among MPSs with various i-GaN concentrations and physical dimensions. It could be observed that the MPSs with relatively high background concentrations tend to exhibit higher currents after turn-on, due to the higher intrinsic carrier concentration for conduction. (More results about MPSs with i-GaN concentrations of 2 × 10 16 /cm 3 can be found in Figure S3, Supplementary Materials.)

Conclusions
The influence of lateral physical dimensions and of drift layer background concentration was assessed and studied. The model parameters used in the simulation study were carefully calibrated with fabricated GaN SBD and GaN P-i-N diodes to ensure the parameters' authenticity. Extending inter-p-GaN region distance Wd enhanced the forward conduction capability, especially at a low bias range. At the same time, the electrical field screening effects were compromised so that a reduced breakdown voltage was observed. When reducing the drift layer background concentration, a higher breakdown voltage is expected for each combination of Wd-Wp, as larger portions of the drift layer Figure 6c,d shows a comparison of the current density for MPSs (i-GaN concentration of 1 × 10 16 /cm 3 ) with W d -W p = 1-1 µm and W d -W p = 4-1 µm at 5 V. The current was mainly concentrated in and dominated by the Schottky contact region at 5 V. The larger W d is, the larger the portion of the device (Schottky contact part) that was activated for conduction, as well as the current density through the device. As is illustrated in Figure 4 and Table 3, the better conduction induced by larger portions of Schottky contact was achieved at the cost of a reduction of more than 100 V in the breakdown voltage. Figure 6b shows the comparison of forward current density among MPSs with various i-GaN concentrations and physical dimensions. It could be observed that the MPSs with relatively high background concentrations tend to exhibit higher currents after turn-on, due to the higher intrinsic carrier concentration for conduction. (More results about MPSs with i-GaN concentrations of 2 × 10 16 /cm 3 can be found in Figure S3, Supplementary Materials).

Conclusions
The influence of lateral physical dimensions and of drift layer background concentration was assessed and studied. The model parameters used in the simulation study were carefully calibrated with fabricated GaN SBD and GaN P-i-N diodes to ensure the parameters' authenticity. Extending inter-p-GaN region distance W d enhanced the forward conduction capability, especially at a low bias range. At the same time, the electrical field screening effects were compromised so that a reduced breakdown voltage was observed. When reducing the drift layer background concentration, a higher breakdown voltage is expected for each combination of W d -W p , as larger portions of the drift layer itself could be depleted by sustaining higher reverse voltage. However, lower drift layer concentration would also lead to a trade-off in forward conduction capabilities. The design of MPS diodes has to take both forward and reverse characteristics into account. The simulation method and results in this study provide a guideline for designing MPSs and assessing GaN MPS performance, which combines the merits of both SBD and P-i-N diodes for high-voltage and low-loss applications.