Figure 3 shows the electron concentration distributions and conduction band of the DFF HEMT. When Vgs = 0, the electron density along AA’ line (in Fig. 1) is just 5 × 1014 cm−3 in Fig. 3a, and the conduction band is above the Fermi level in Fig. 3b. The E-mode is thus realized. When Vgs = 3 V > Vth, the conduction band along AA’ line has been pulled below the Fermi level, and electron density is as high as 2 × 1019 cm−3. The DFF HEMT has been turned on. Additional, the electron density along AA’ line at Vgs = 3 V is higher than that along BB’ line at Vgs = 0 V in Fig. 3a. It indicates that 2DEG has been restored owing to high positive-voltage biased to the double gate.

Fig. 3
figure 3

a Electron concentration distributions and b conduction band of DFF HEMT at Vgs = 0 V and Vgs = 3 V

Figure 4a shows the electron concentration distributions along the 2DEG channel in the on-state. The 2DEG concentration of the gate region of the DFF HEMT is much higher than those of the MIS HEMT and the MIS-FP HEMT. On one hand, the potential in the gate region of the DFF HEMT is much higher because both the BG and TG are applied to 3 V. The conduction band of the DFF HEMT is thus much lower as shown in Fig. 4b, which contributes to the higher 2DEG concentration. On the other hand, the polarization effect under the gate of the MIS HEMT and the MIS-FP HEMT is weakened because the AlGaN layer is etched partly to realize E-mode. Additional, it is normal that the 2DEG density under the right side of the gate is low for the three devices, because there is a higher electric potential of the semiconductor than that of the gate, as a depletion region. The field plate of the DFF HEMT is far away from the 2DEG channel and has smaller depletion effect on the 2DEG concentration than that of the MIS-FP HEMT. Therefore, the 2DEG concentration under the field plate of the DFF HEMT is higher, which contributes to higher current and lower specific on-resistance (Ron, sp).

Fig. 4
figure 4

a 2DEG distributions and b conduction band along AA’ line for three devices in the on-state

Figure 5 shows the output characteristic and transfer characteristic of the three devices. It can be seen from Fig. 5a that the DFF HEMT has the largest Id, sat and the smallest Ron, sp. The Id, sat of the MIS-FP HEMT is the smallest because the field plate assists in depleting 2DEG along the drift region (see Fig. 4a). For the DFF HEMT, on one hand, the 2DEG is recovered, and on the other hand, the double gates introduce electron accumulation layer. Figure 5c shows the electron current density along AA’ line. The DFF HEMT has a large current density in electron accumulation layer, in addition to the 2DEG channel current. The 2DEG channel still plays a dominant role in the transport. It can be seen from Fig. 5d that DFF HEMT has the highest transconductance owing to the double gates. The Vth of three devices is designed as 0.8 V.

Fig. 5
figure 5

a output I-V characteristics, b electron current density, c electron current density distributions along AA’ line and d transfer characteristics for three devices

Figure 6 shows the lateral component of the E-field (Ex) distribution and IV curves at breakdown. It indicates that the Ex for the DFF HEMT is effectively improved. Compared with the MIS HEMT, the field plate not only brings out new E-field peak, but also expands the depletion region for the MIS-FP and DFF HEMT. Particularly, for the DFF HEMT, the step field plate further uniforms the E-field distribution in the drift region. Meanwhile, the leakage current of the substrate has been suppressed by the poly-AlN substrate layer. Therefore, the DFF HEMT achieves the highest BV of 465 V (at Id = 10–6 mA/mm), and BV is 394 V for the MIS-FP HEMT, as shown in Fig. 6. Without the field plate and flip-structure for the MIS HEMT, the drift region cannot be completely depleted and leakage current is large, and thus the BV is just 75 V at the same drift region length.

Fig. 6
figure 6

Ex distributions and I-V curves for three devices at breakdown at y = 0.051 μm

Figure 7 shows the electron concentration distributions and conduction band at Vgs = 0 V along AA’ line with different T values. As T decreases, the conduction band rises and the electron density decreases. When T ≤ 50 nm, the depletion effect of the MIS structure on electrons is enhanced and the polarization effect is weakened. The whole conduction band is raised above EF. Consequently, E-mode is realized. When T > 50 nm, the depletion effect is weakened and the polarization effect is enhanced. Therefore, potential well of electrons is formed and the electron concentration rises to 1019 cm−3 order of magnitude, which is higher than the background charge concentration of 1018 cm−3. Figure 8 shows the transfer characteristic with different T values. The Vth increases as T decreases.

Fig. 7
figure 7

Electron concentration distributions and conduction band at Vgs = 0 V along AA’ line with the different T values

Fig. 8
figure 8

Transfer characteristics with the different T values

Figure 9 shows the output characteristic, electron concentration distributions and conduction band with the different T values at a constant of (Vgs − Vth). The Id, sat increases and the Ron, sp decrease as T decreases because the electron concentration increases, as shown in Fig. 9a and b. As T decreases, the Vth increases (in Fig. 8) and thus Vgs accordingly increases to maintain a constant of (Vgs − Vth), leading to the increase in electron concentration. Meanwhile, the conduction band is lower and the 2DEG concentration is higher owing to the lower T and higher Vgs, as indicated in Fig. 9b. Different from the conventional GaN HEMT, the DFF HEMT break through the tradeoff relationship between the high Vth and high Id, sat. As T decreases, both the Id,sat and the Vth increase.

Fig. 9
figure 9

a output characteristics and b electron concentration distributions and conduction band (Vgs − Vth = 3 V and Vds = 10 V along AA’ line) with the different T values

Figure 10 shows the influence of the L on the potential contours and Ex distribution of the DFF HEMT. The BV of the DFF HEMT firstly increases and then decreases as the L increases. When L = 0 μm means the DFF HEMT without the field plate, the BV is lower because the drift region has not been depleted. With the increase in L at L < 2.6 μm, the depletion region expands. The step field plate decreases the E-field peak at the gate edge (P1) and induces a new E-field peak below the end of the field plate (P2), so the BV increases as shown in Fig. 10b. P3 is the new E-field peak caused by the step field plate at y = 0.051 μm in Fig. 10b. At this time, the premature breakdown occurs at the right edge of the gate. When L = 2.6 μm, the Ex of the DFF HEMT is almost uniform and the BV of 465 V achieves the highest. When L = 3.0 μm, premature breakdown occurs owing to high P2, and BV decreases.

Fig. 10
figure 10

a Equipotential contours and b Ex distribution at breakdown at y = 0.051 μm with different L values

Figure 11 demonstrates the Ron,sp and BV values of the DFF HEMT and reported AlGaN/GaN HEMTs, the DFF-HEMT has a higher figure of merit (FOM = BV2/Ron,sp) than those of the AlGaN/GaN HEMTs in studies. As a result, when T = 40 nm, L = 2.6 μm, an excellent tradeoff between the on-state characteristics and the off-state characteristics is achieved.

Fig. 11
figure 11

Ron,sp and off-state BV in the DFF-HEMT and reported AlGaN/GaN HEMTs, together with the theoretical Si-, SiC- and GaN- limit

The fabrication process steps of the DFF HEMT are shown in Fig. 12, which is referred to the experiment in [16]. Key processes are given as follows: (a) Fabricate a conventional MIS HEMT on a Si (111)-based AlGaN/GaN heterojunction wafer. (b) form poly-AlN film on the device surface by physical vapor deposition (PVD), and bonding to the Si (100) wafer. (c) Remove the Si (111) substrate and part of the GaN epitaxial layer. (d) form the shallow trench of the field plate by inductively coupled plasma (ICP) etching. (e) ICP etch TG deep trench. (f) implement Al2O3 layer and the top gate metal. Compared with those of Ref. [16], the fabrication process of the DFF HEMT only add twice ICP etchings ((d) and (e)) to realize the E-mode and further improve the BV. The DFF HEMT simultaneously realizes E-mode, and achieves a higher BV and a smaller Ron.

Fig. 12
figure 12

Key fabrication process flows for the DFF HEMT

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