Introduction

Wide-bandgap GaN-based power devices have been regarded as the great potential candidates for the next generation efficient power electronics and compact power systems, owing to the superior material properties such as high electron mobility, large breakdown field strength and high thermal stability [1,2,3,4,5]. Compared with high electron mobility transistors (HEMTs) [6,7,8,9,10,11] and current aperture vertical electron transistors (CAVETs) [12,13,14,15], GaN-based trench metal oxide semiconductor field effect transistors (MOSFETs) [16,17,18] are more competitive to realize intrinsically normally-off operation with higher current density, lower specific on-resistance (Ron,sp) and lower current collapse. Moreover, GaN-based trench MOSFETs possess relatively simple manufacturing process and do not need the regrowth of AlGaN/GaN layers [19, 20].

The development of lateral GaN-based MOSFETs has approximately come to saturation, due to the breakdown voltage (VBR) limited by the length of lateral drift region. Although the growth of length can increase VBR, the size of device enlarges, leading to reduction of the effective current density per unit chip area. In contrast, vertical GaN-based devices have been fully advanced. Under the same required VBR and amperage rating, smaller size and less cost can be realized on vertical GaN-based MOSFETs when make a contrast with lateral GaN MOSFETs [21]. In comparison with Si, Sapphire, SiC and Diamond substrate, the MOSFETs on free-standing GaN substrate can greatly reduce the probability of the high-density trap states and non-linearity contributed by lattice mismatch while operating at high power [22].

More studies have made great progress in VBR, Ron,sp and device reliability for GaN vertical MOSFETs in recent years. Floating P-body had been introduced in the N−-GaN drift region to form “P-body/N-drift” junction via TCAD simulation for the improvement of VBR of the enhancement-mode vertical GaN MOSFET [23]. Vertical GaN interlayer-based trench MOSFET (OG-FET) on a large-area in-situ oxide performed threshold voltage (Vth) of 2.5 V, Ron,sp of 0.98 mΩ·cm2 and VBR of 700 V with regrown 10-nm unintentional-doped-GaN interlayer as the channel and 50-nm in-situ Al2O3 as the gate dielectric [24]. Vertical GaN trench-MOSFETs with MBE regrown UID-GaN channel were investigated, which avoided the need to reactivate the buried body p-GaN and promised the same benefit on channel mobility compared to the MOCVD regrowth [25]. The device characteristics had been improved for vertical GaN trench MOSFETs by using Silvaco ATLAS 2-D simulation in order to get the best trade-off between VBR and Ron,sp [26].

In this work, we present vertical GaN-based trench gate MOSFETs (GaN TG-MOSFETs) on 4-inch free-standing GaN substrate exhibiting normally off operation for high power applications. We use Silvaco TCAD to simulate the structure and performance of GaN TG-MOSFETs based on semiconductor physics and advanced process. The simulation results obtained by Silvaco ATLAS simulation are consistent well with experiment data on the characteristic curves of transfer, output, and breakdown voltage, respectively. The device parameters are researched comprehensively by using TCAD for providing guide in actual fabrication and optimization. The design of the parameters includes the thickness of n−-GaN drift body layer (Ldrift), n−-GaN drift trench region (Ltrench), p-GaN channel layer (Lchannel) and gate dielectric layer (Ldielectric). The doping density of p-GaN channel layer (Na) and n−-GaN Drift layer (Nd) are included.

Experiment and Simulation Approach

High-quality, large-size and less-expensive GaN substrates are crucial for the progress of vertical GaN power devices. More techniques were proposed to optimize the growth of bulk GaN crystals, such as halide vapor phase epitaxy (HVPE), high nitrogen pressure solution (HNPS), basic and acidic ammonothermal, Na-flux method and near atmospheric pressure solution growth [27, 28]. HVPE is the main method for mass fabrication of GaN crystals, due to its high grow rate, high purity, high process repeatability and easy doping. The transparent 4-inch freestanding GaN wafer grown by HVPE with 13 points position for test is shown in Fig. 1a. We utilized a 420-μm-thick free-standing n+-GaN substrate in the device fabrication with the average mobility of 614 cm2·V−1·s−1 and the average dislocation density of 1.94 × 106 cm−2 at the top surface, as determined by contactless Hall measurement and cathodoluminescence (CL). The test result and CL image of the epitaxial layer are presented in Fig. 1b, c, respectively.

Fig. 1
figure 1

a Photograph of 4-inch freestanding GaN wafer, where the letters SZU can be clearly seen. b The mobility of GaN wafer. c The dislocation density and CL image of the epitaxial layer. d The fabrication process. e The schematic of energy band lined-up at the Al2O3/GaN heterointerface. f 3D drawing structure and g micrograph of the fabricated GaN TG-MOSFET

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The fabrication process of the GaN TG-MOSFETs discussed in this work is shown in Fig. 1d. The epitaxial growth began with 12-µm lightly doped 8.0 × 1015 cm−3 n−-GaN as the drift region. A 1.0-µm heavily doped p-GaN with a doping density of 1.0 × 1018 cm−3 was deposited as the channel region. Thereafter, a 0.2-µm-thick heavily doped n+-GaN with a doping density of 3 × 1018 cm−3 was grown as the source contact layer. The device fabrication process started with the formation of 0.2-μm-deep vertical trench and 1.7-μm-deep vertical mesa for p-body and gate contacts by using Cl2-based gases in reactive ion etching (RIE) at 15 W power, respectively. A 16-nm-thick Al2O3 film was deposited by atomic layer deposition (ALD) as gate dielectric. High-quality and stable MOS interface with low-density trap states is essential for GaN TG-MOSFETs. A two-step process, including simple acid cleaning and a following (NH4)2S passivation, was required to drastically reduce the interface states and border traps [29]. The source and drain electrodes with Ti/Al were annealed at 550 °C for 5 min in N2 ambient for ohmic contacts. The gate and p-body electrodes were composed of Ti/Au and Palladium, respectively. A 400-nm-thick SiO2 film was deposited by plasma enhanced chemical vapor deposition (PECVD) as the passivated isolation mesa. Finally, field plate termination was employed to impair the peak electric field crowded at the edge of PN junction around the isolation mesa. The Al-based field plate was connected to the source electrode.

The schematic of energy band lined-up at the Al2O3/GaN heterointerface in Fig. 1e. The forbidden band of GaN was exactly contained in that of Al2O3, where the deviations of the conduction band and valence band were 3.38 eV and 0.22 eV, respectively. It revealed that Al2O3 could maintain excellent insulation with GaN for electrons, which greatly reduced gate leakage current and improved device performance. The 3D drawing structure and parameters needed for optimization are shown in Fig. 1f. Figure 1g shows the micrograph of the device. The hexagonal crystal structure contained the outward vertical C axis, three horizontal axes a1, a2 and a3, and crystal planes in various directions.

The physical simulation models concerned for simulation were the parallel electric field-dependent mobility model, concentration-dependent mobility model, low field mobility model, Shockley–Read–Hall recombination model, Auger recombination model, impact ionization model, energy bandgap narrowing model and trap model [26, 29,30,31]. The main physical models and parameter values for simulation are shown in Table 1.

Table 1 The main model and parameter values for TCAD simulation
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For GaN simulation, Si donors and Mg acceptors were not completely ionized at room temperature since their high activation energies, especially for Mg-doped p-type GaN [32,33,34]. Thus, according to Fermi–Dirac distribution, the incomplete ionization model was incorporated in the simulation for accurately reproducing the breakdown voltage. The ionized donors and acceptors impurity concentrations were given as follows

$$N_{D}^{ + } = \frac{{N_{D} }}{{1 + g_{D} \cdot \exp (\frac{{\varepsilon_{Fn} + E_{D,0} - \theta_{n} \cdot \sqrt[3]{{N_{D}^{{}} }} - E_{C} }}{KT})}}$$
(1)
$$N_{A}^{ - } = \frac{{N_{A} }}{{1 + g_{A} \cdot \exp (\frac{{E_{V} + E_{A,0} - \theta_{p} \cdot \sqrt[3]{{N_{A}^{{}} }} - \varepsilon_{Fp} }}{KT})}}$$
(2)

Here, gD and gA are the appropriate degeneracy factors for conduction and valence bands. ED,0 and EA,0 are the donor and acceptor ionization energy at very low doping levels. θn and θp are constants accounting for geometrical factors as well as for the properties of the material. Low field mobility model is the result of fitting Caughey Thomas like model to Monte Carlo data [26, 32]. It can be defined as

$$\begin{aligned} \mu_{(n/p)} (T,N) & = \mu_{1(n/p)} \cdot (T/300)^{{\beta_{1(n/p)} }} + \\ & \frac{{(\mu_{2(n/p)} - \mu_{1(n/p)} ) \cdot (T/300)^{{\beta_{2(n/p)} }} }}{{1 + [\frac{N}{{N_{ref(n/p)} \cdot (T/300)^{{^{{\beta_{3(n/p)} }} }} }}]^{{\rho_{(n/p)} \cdot (T/300)^{{^{{^{{\beta_{4(n/p)} }} }} }} }} }} \\ \end{aligned}$$
(3)

where µ1, µ2 are the minimum and maximum mobility, ρ, β1, β2, β3, β4, are all temperature dependent fitting parameters, Nref is the reference doping level and N is the donor concentration.

The Poisson’s equations and Current continuity equation were essential for the analysis of simulation [35]. As in semiconductor PN junction, avalanche breakdown occurred when the impact ionization integral reached unity

$$I_{n} = \int {\alpha_{n} \exp \left(\int_{{}}^{w} {\alpha_{p} - \alpha_{n} {\text{d}}v} \right)} {\text{d}}w = 1$$
(4)

where In is the impact ionization integral of electrons. The utilized ionization rate model of electrons and holes are variation of the classical Chynoweth model [36], which based upon the following expressions,

$$\alpha_{n} = AN \cdot \exp \left[ { - \left( \frac{BN}{E} \right)^{BETAN} } \right]$$
(5)
$$\alpha_{p} = AP \cdot \exp \left[ { - \left( \frac{BP}{E} \right)^{BETAP} } \right]$$
(6)

Here, E is the electric field in the direction of current flow at the p-GaN channel layer in the structure. Various group has reported impact ionization coefficients to accurately predict the breakdown of GaN power devices in recent years [37,38,39,40,41]. The coefficients AN, AP, BN, BP, BETAN and BETAP of the impact ionization model in this work were determined by referring to the experiments above.

In this study, the work was mainly carried out by TCAD. The data obtained by simulation had been calibrated with the result of experiment on GaN TG-MOSFET shown in the third part. The comprehensive analysis and optimization design on Ldrift, Ltrench, Ldielectric, Lchannel, Na and Nd of devices were demonstrated in the fourth part, respectively.

Results and Discussion

The initial device parameters of simulation model were set as follows: Nd = 8.0 × 1015 cm−3, Na = 1.0 × 1018 cm−3, Ldrift = 12 μm, Ltrench = 0.5 μm, Lchannel = 1.0 μm, and Ldielectric = 16 nm. The interface state could capture the free electrons in the channel and formed the negative interface charge, leading to the decrease of the number of free electrons and the increase of Ron,sp. A low density of interface state was beneficial to reduce Ron,sp and switch loss. The interface state in the simulation was defined as 1011 cm−2·eV−1 by referring to the previous work [25]. The characteristic curves of transfer, output, and breakdown of GaN TG-MOSFET via experiment (Exp) and simulation (Sim) are shown in Fig. 2, respectively. This simulation results were consistent well with the data of experiment, which could verify the validity of the results obtained by simulation and calibrate the simulation model.

Fig. 2
figure 2

a Transfer I–V characteristics (ID–VG) at VDS = 0.5 V. b Output I–V characteristics (ID–VD) at VGS = 0 V, 5 V, 10 V, 15 V and 20 V, respectively. c Off-state I–V characteristics measured at VG = 0 V for fabricated GaN TG-MOSFET

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Figure 2a shows the ID–VG characteristics at VDS = 0.5 V. Several extraction methods were used to determine the value of Vth from the measured ID–VG characteristics [42]. Normally-off operation with Vth (defined at IDS = 1 μA/mm) of 3.15 V was observed. Figure 3a shows the current could not be conducted between the source and drain, since the channel was not yet formed a conduction path. In Fig. 3b, the inversion layer of electron was effectively generated in the channel only when VGS > Vth, hence generating the drain-to-source current. The distributions of energy band along line A and line B during off-state and on-state are shown in Fig. 3c and Fig. 3d, respectively. From off-state to on-state, the energy of conduction band (CB) obviously reduced until closing to the Quasi-Fermi level (QFL). Therefore, electrons could easily jump to CB and generate conduction current. Figure 2b exhibits the output I–V characteristics at VGS = 0 V, 5 V, 10 V, 15 V and 20 V, respectively. The Ron,sp estimated from the linear region was 1.93 mΩ·cm2 at VDS = 0.5 V and VGS = 20 V.

Fig. 3
figure 3

Electron concentration distributed at a VGS = 0 V, VDS = 0.5 V (off-state) and b VGS = 20 V, VDS = 0.5 V (on-state). The energy band distributed during c off-state and d on-state

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Figure 2c demonstrates the off-state I–V characteristics measured at VGS = 0 V. This work achieved the hard breakdown VBR of 1306 V when IDS > 50 mA/cm2 from experiment, while the VBR of simulation reached 2278 V. The insufficient activation of the Mg dopant existing in the p-GaN was considered as the reason for making the discrepancy in VBR between experiment and simulation. Finally, the corresponding figure of merit (FOM) obtained were 0.88 GW/cm2 and 1.68 GW/cm2 by experiment and simulation, respectively.

Two breakdown mechanisms, namely punch-through breakdown and avalanche breakdown, existed in the device, which were dominated by the product of Lchannel and Na (Lchannel · Na) of p-GaN. Taking the Na = 2.0 × 1017 cm−3 and various Lchannel for example by simulation as shown in Fig. 4a. Punch-through breakdown would occur when Lchannel · Na was lower than a certain value, such as Lchannel = 0.6 μm and Na = 2.0 × 1017 cm−3 in Fig. 4a. However, it would be changed to avalanche breakdown when Lchannel · Na was high enough, such as Lchannel = 0.8 μm and Na = 2.0 × 1017 cm−3. Moreover, the breakdown mechansims were studied in detail from the expansion of depletion region (DR), distributions of electric field and impact gen rate (IGR). Figure 4b shows the schematic of the device. Figures 4c–f and 5a–f show the expansion of DR of device with Lchannel = 0.4 μm and Lchannel = 1.2 μm, respectively. As drain voltage enlarged, the DR extended continually and was oriented toward the drain, which offered strong current blocking capability and suppressed the permature breakdown.

Fig. 4
figure 4

a Breakdown curves under Na = 2.0 × 1017 cm−3 and various Lchannel. b Schematic of GaN TG-MOSFET. c–f Depletion region at different reverse bias under Na = 2.0 × 1017 cm−3 and Lchannel = 0.4 μm, including VDS = 200 V, 400 V, 800 V and 1000 V. g Electric Field distributed along line A at VDS = 1000 V

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Fig. 5
figure 5

a–f Depletion region at different reverse bias under Na = 2.0 × 1017 cm−3 and Lchannel = 1.2 μm, including VDS = 200 V, 400 V, 800 V, 1000 V, 1500 V and 2000 V. g Electric Field distributed along line B at VDS = 2000 V

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Punch-through breakdown occured in the device with Na = 2.0 × 1017 cm−3 and Lchannel = 0.4 μm when VDS > 1000 V for Lchannel · Na was low. The EF along line A is shown in Fig. 4g. The peak EF was ~ 2.3 MV/cm and did not reach the critical electric field strength value of GaN. A high potential barrier prevents current flow. The barrier between source and drain significantly reduced for the expansion of DR when VDS increased. Since the current was an exponential function of barrier height, the current increased rapidly once the punch-through condition was satisfied. The number of electrons injected from source region into channel had greatly increased through EF. Large current flowed from drain directly to source as shown in Fig. 6a. In Fig. 6b, the peak IGR was located at the reverse biased PN junction between p-GaN and n−-GaN drift region as shown in the red circle.

Fig. 6
figure 6

a, b were the distributions of Total Current Density and Impact Gen Rate under Na = 2.0 × 1017 cm−3 and Lchannel = 0.4 μm, respectively. c, d were the distributions of Total Current Density and Impact Gen Rate under Na = 2.0 × 1017 cm−3 and Lchannel = 1.2 μm, respectively

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Avalanche breakdown happened in the device with Na = 2.0 × 1017 cm−3 and Lchannel = 1.2 μm when VDS > 2000 V for the Lchannel · Na was high. The EF along line B is shown in Fig. 5g. The peak EF was ~ 3.45 MV/cm and closed to the critical electric field of 3.3 MV/cm of GaN. The energy of electrons and holes was enhanced by EF when they pass through the space charge region. Since they collided with electrons of atoms in DR, large numbers of new electron–hole pairs were generated, causing the avalanche effect. Large electron and hole current were produced as shown in Fig. 6c. The electron current mainly flowed to drain, while hole current flowed to the source along p-GaN region. In the red circle of Fig. 6d, the peak IGR was located at the gate corner. It implied that the breakdown characteristic was similar to that of PN junction diode as long as punch-through did not occur. The simulation showed that device could achieve avalanche and avoid punch-through breakdown with enough value of Lchannel·Na. The effect of various Na on the breakdown mechanism was similar to that of Lchannel.

Analysis and Performance Evaluation

This simulation focused on studying the effects of various device parameters and obtaining the scheme of optimization design. Firstly, the thickness and doping density of n−-GaN drift layer were researched with different initial values. Then, we analysed the thickness and doping density of p-GaN channel layer based on the optimal parameters of n−-GaN drift layer. Finally, the impact of the thickness of gate dielectric was thoroughly studied. All the changes of the above parameters were discussed within a reasonable range. The power figure of merit FOM = VBR2/Ron,sp and Vth could be used as a criterion for optimization.

Analysis the Influence of n−-GaN Drift Layer

As shown in Fig. 7a, VBR increased and saturated at a certain value as Ldrift increased with different initial conditions. The phenomenon that DR extended and saturated with the growth of Ldrift caused the VBR increased and saturated. Conversely, VBR decreased with the growth of Nd. The situation was equivalent to the effect of the doping concentration in the low-doped side of the PN single junction diode on the VBR, which demonstrated that the value of Nd was inversely proportional to VBR. It implied that VBR prematurely saturated at thin Ldrift with high Nd. Low Nd had larger DR than high Nd due to the IGR of electron was low. Large DR could withstand high voltage and prevent electron absorbing electric field energy to reach breakdown. The change of Ron,sp was mainly caused by the variation of Rdrift (Ron,sp of n−-GaN drift layer). The Ron,sp decreased with the increase of Nd and decrease of Ldrift, respectively. Ron,sp decreased from 2.55 mΩ·cm2 to 1.56 mΩ·cm2 and VBR reduced from 2558 to 1997 V as Nd increased from 8.0 × 1015 cm−3 to 1.0 × 1016 cm−3 under Ldrift = 12 μm. In Fig. 7b, the obtained peak FOM were 2.76 GW/cm2, 2.69 GW/cm2 and 2.62 GW/cm2 under Ldrift = 16 μm, Ldrift = 12 μm, and Ldrift = 10 μm with the growth of Nd, respectively. It demonstrated that the optimal FOM could be obtained under the low Nd and thick Ldrift. In contrast, the change of Nd and Ldrift had no effect on Vth, and it remained at 3.15 V. The impact on Ron,sp and VBR were obvious by the change of Nd and Ldrift, while hardly influenced Vth.

Fig. 7
figure 7

a Simulated Ron,sp and VBR of the device versus Ldrift and Nd. b Vth and FOM as a function of Ldrift and Nd. c Simulated Ron,sp and VBR of the device versus Ltrench and Nd. d Vth and FOM as a function of Ltrench and Nd. In (a)–(d), the square, circle and triangle curves were simulated under Nd = 6.0 × 1015 cm−3, Nd = 8.0 × 1015 cm−3 and Nd = 1.0 × 1016 cm−3, respectively

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With the increase of Ltrench from 0.1 to 1.0 µm in Fig. 7c, d, Ron,sp continuously decreased. In contrast, VBR and FOM first increased and then decreased as the advance of Ltrench, finally reaching peak value at Ltrench = 0.2 µm. The obtained peak FOM were 3.15 GW/cm2, 3.45 GW/cm2 and 3.64 GW/cm2 under Nd = 6.0 × 1015 cm−3, Nd = 8.0 × 1015 cm−3, and Nd = 1.0 × 1016 cm−3, respectively. The impact of Ltrench on FOM was apparent when it was thin. The variety of Nd and Ltrench also made little difference on Vth. Vth showed independence for the change of Nd, Ldrift and Ltrench, due to the p-type channel region.

Analysis the Impact of p-GaN Channal and Dielectric

The effects of the Lchannel and Na of p-GaN channel layer were investigated based on Ldrift = 12 μm and Ltrench = 0.2 μm of n−-GaN drift layer. The change of Ron,sp was mainly caused by the variation of Rchannel (Ron,sp of p-GaN channel layer). The curves of Ron,sp showed continuous rising trend with the enhancement of Lchannel as shown in Fig. 8a. As Na increased from 2.0 × 1017 cm−3 to 3.0 × 1018 cm−3 under Lchannel = 1.0 μm, Ron,sp showed increasing trends from 1.94 mΩ·cm2 to 1.96 mΩ·cm2. The effect on the Ron,sp brought by the variety of Lchannel was little. The growth of Na could enlarge the VBR from 65 to 2632 V under 0.1 um. VBR increased and saturated at Lchannel = 0.8 μm under Na = 2.0 × 1017 cm−3. In contrast, VBR increased and saturated at Lchannel = 0.2 μm under Na = 8.0 × 1017 cm−3 and Na = 1.0 × 1018 cm−3, respectively. Moreover, VBR kept saturated from 0.1 μm to 1.0 μm of Lchannel under Na = 3.0 × 1018 cm−3. The high enough value of Lchannel · Na could achieve avalanche breakdown, which could be seen from the saturated VBR. On the contrary, the unsaturated VBR was known as punch-through breakdown. Similarly, the variation trend of FOM was the same as VBR. The peak FOM obtained was 3.59 GW/cm2. Vth grew from 1.19 V to 7.93 V under Lchannel = 1.0 μm with the increase of Na as shown in Fig. 8b. The change of Na had a marked effect on Vth, whereas the impact brought by the variety of Lchannel on Vth was negligible.

Fig. 8
figure 8

a Simulated Ron,sp and VBR of the device versus Lchannel and Na. b Vth and FOM as a function of Lchannel and Na. In (a) and (b), the square, rhombus, circle and triangle curves were simulated under Na = 2.0 × 1017 cm−3, Na = 8.0 × 1017 cm−3, Na = 1.0 × 1018 cm−3 and Na = 3.0 × 1018 cm−3, respectively. c Simulated Ron,sp and VBR of the device versus Ldielectric. d Vth and FOM as a function of Ldielectric

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The impact of the Ldielectric was researched based on Lchannel = 1.0 μm. The growth of Ldielectric would reduce Cox and electron concentration of channel layer under on-state condition, resulting in larger Ron,sp and Vth. Ron,sp increased from 1.92 mΩ·cm2 to 2.24 mΩ·cm2 and Vth enhanced from 1.87 V to 8.97 V for Ldielectric increasing from 8 to 50 nm as shown in Fig. 8c, d. Ldielectric had no effect on VBR, leading to the reduction of FOM from 3.63 GW/cm2 to 3.10 GW/cm2.

Conclusion

In this work, we analysed the performance of the fabricated GaN TG-MOSFET on 4-inch free-standing GaN substrate by Silvaco TCAD. The mechanisms of on-state and breakdown have been well studied. The key device parameters have been thoroughly researched considering the trade-off between Ron,sp and VBR. The normally off operation and high breakdown voltage show enormous potential to provide a bright future application for vertical GaN-based high power electronics.