Simulation of Gate Leakage Current of AlGaN/GaN HEMTs: Effects of the Gate Edges and Self-Heating

Thegateleakagecurrent( I G )ofAlGaN/GaNhighelectronmobilitytransistors(HEMTs)atvariousambienttemperaturesissimulated by considering its mechanism as domination of trap-assisted tunneling (TAT) and Poole-Frenkel (PF) emission for low electric ﬁeld in the AlGaN barrier, and domination of Fowler–Nordheim (FN) tunneling for high electric ﬁeld in the AlGaN barrier. Two bias cases are studied: V GS (gate voltage) variation while V DS (drain voltage) = 0 V without self-heating and V DS variation while V GS = 0 V with self-heating. For the ﬁrst case, FN tunneling current mainly concentrates near the gate edges and so it is not changed with the gate length. While PF emission and TAT current do not show big variation along the gate, they are affected by the gate length and show higher values for longer gate. For the second case, with V DS increasing the elevated device temperature caused by the self-heating obviously increases PF emission and also increases I G because PF emission is the dominant mechanism of I G . With V DS further increasing, although the higher device temperature presents, I G is not affected by the self-heating because the temperature-independent FN tunneling becomes the dominant mechanism of I G . Attribution

AlGaN/GaN high electron mobility transistors (HEMTs) present a big potential used in the field of high power, high temperature, and high frequency due to the wide bandgap of the materials as well as high electron mobility and saturation velocity in the transistors, which have attracted lot of researches in the past. Modelling/simulation and illustration of relevant mechanism of the gate leakage current (I G ) are important research aspects for AlGaN/GaN HEMTs, because usually I G can affect the device power efficiency and reliability. So far, some possible mechanisms of I G have been proposed: based on the fact of high density of traps locating in the AlGaN barrier or on the Al-GaN surface, I G could be formed by Poole-Frenkel (PF) emission 1 and phonon-assisted tunnelling; 2 due to the high electric field in the Schottky barrier, I G could be formed by Fowler-Nordheim (FN) tunneling 3 and thermionic field emission. 4,5 The electric field and also the leakage current near the gate edges have higher values than that in the other regions of the gate, 6 especially for the device under relative low V GS . Generally, the leakage current near the gate edges is considered to be negligible and so it is omitted in I G modelling for AlGaN/GaN HEMTs with long gate. While for the device with short gate, the leakage current near the gate edges is obvious and therefore it would be considered in the modelling. As far as we know, in the past, I G modelling has not addressed the self-heating effect since the studies were restricted to the device with V DS keeping zero (no self-heating). For the device with high power consumption, the self-heating could significantly increase the device temperature, 7,8 and any temperature-dependent I G should be influenced by the selfheating. In this paper, we will address the above mentioned effects of the gate edges and self-heating on I G for AlGaN/GaN HEMTs. We will perform numerical simulation of I G because of the complicated non-uniform distribution of electric field and leakage current near the gate edges.

Simulation Method
We study I G of AlGaN/GaN HEMTs for two bias cases: V GS variation while V DS = 0 V without the self-heating and V DS variation while V GS = 0 V with the self-heating. Mechanism of I G is considered as domination of TAT and PF emission for the device under high V GS or low V DS with low electric field in the barrier, namely the region of low z E-mail: ashuwang@126.com electric field (RLEF), and FN tunnelling for the device under low V GS or high V DS with high electric field in the barrier, namely the region of high electric field (RHEF). In the following, TAT, PF emission, and FN tunnelling as well as correspondent simulation methods will be introduced.
The AlGaN surface has negative piezoelectric and spontaneous polarization charge, while the AlGaN/GaN interface has correspondent positive charge. Large amount of donor-like traps concurrently exist on the AlGaN surface and the 2DEG in the channel comes from ionization of the donor-like traps. 9 The AlGaN surface negative charge is partially or even completely neutralized by positive charge from ionization of the donor-like traps. For the case that the AlGaN surface negative charge is partially neutralized, nonzero electric field should present in the AlGaN barrier which should lead to nonzero leakage current from the channel to the gate. To make total zero leakage current when V GS and V DS equal to zero, forward current from the gate to the channel namely trap-assisted tunneling current (J TAT ) was proposed. 1 J TAT has form similar to the thermionic emission and can be expressed as 10 where J 0 , V 0 , and η are parameters used to fit the experimental data, and q is the fundamental electronic charge, k is Boltzmann constant, and T is temperature. As aforementioned statement, J TAT is considered in RLEF. For the first studied case of high V GS (V DS = 0 V), V GS is approximated as constant along the gate and so Equation 1 can be directly used. For the second studied case of low V DS (V GS = 0 V), V GS along the gate is not a constant and so more derivations are needed. Because of low value of V DS , it can be approximated as linearly distributes in the channel between the source and drain contact, i. e., the electric field is constant in the channel. Therefore, the potential difference between any position of the gate contact and the source contact (V Gx ) can be expressed as V Gx = −V DS (L SG + L Gx )/(L SG + L G + L GD ), where L SG , L G , and L GD represent the distance of source-gate contact, gate length, and distance of gate-drain contact, respectively. L Gx is a variable denoting the position along the gate. L Gx = 0 and L Gx = L G denote the position of source-side and drain-side gate edge, respectively. Then V GS in Equation 1 should be replaced as V GS = V Gx . As a result, J TAT does not uniformly distribute along the gate.

S3026
ECS Journal of Solid State Science and Technology, 6 (11) S3025-S3029 (2017) PF emission means the electron emission from the trap also by thermal activation but with a lowered trap depth induced by the coulomb interaction, i.e., the emission rate is enhanced by the electric field. The current density J PF induced by the PF emission is expressed as 1 where C P F is a constant, E is the electric field across the barrier, φ t is the barrier height for the electron emission from the trap state, ε 0 is the permittivity of vaccum, and ε S is the relative permittivity of AlGaN at high frequencies. Equation 2 can be rearranged as where From Equation 3 ln(J P F /E) should be a linear function of √ E, and ε S as well as φ t can be extracted from m(T ) and c(T ). For the gate contact with large area, the leakage current near the gate edges is negligible. J PF can be calculated as I PF /A (I PF is the leakage current caused by PF emission and A is the gate contact area), then the above approach can be adopted to extract ε S as well as φ t . But for the devices studied in this paper, the leakage current near the gate edges is significant component so that J PF cannot be simply calculated as I PF /A and therefore ε S as well as φ t cannot be extracted by the above approach.
For AlGaN/GaN HEMTs, FN tunneling means the electron in the gate metal tunnels through a triangular barrier to the AlGaN conduction band, expressed as 11 where A is a constant, m e is the effective electron mass, φ b is the Schottky barrier height, and h is Planck constant. At last, as aforementioned illustration,J G is constituted by J TAT , J PF , and J FN , and it is calculated as Note that the leakage current I G , I TAT , I PF , and I FN are integral of the leakage current density J G , J TAT , J PF , and J FN along the gate metal/AlGaN interface, respectively. In principle, direction of E should be vertical to the gate metal/AlGaN interface and E should be constant across the AlGaN barrier in the expressions of J PF and J FN . The following approximations are adopted in our simulations. Although in the barrier near the gate edges significant horizontal component of electric field E x is presented, but it is much lower than the vertical component E y . 12 In the other areas of the barrier, E x is negligible. Especially, if the gate metal and AlGaN are considered as ideal metal and ideal dielectric, respectively, then the boundary conditions of Poisson equation determine that E at the gate metal/AlGaN interface has only E y but no E x , i.e., the direction of E is vertical to the interface. Therefore, E can be replaced by E y for calculations of J PF and J FN . As stated before, J PF is considered in RLEF, in which E y across the AlGaN barrier can be approximated as constant. So E y at the gate metal/AlGaN interface is used for J PF calculation. J FN is considered in RHEF and it mainly concentrates near the gate edges (see more illustrations in the next section) where E y does not keep constant. However, considering the tunneling barrier near the gate edges is very thin due to the relative high value of E y , it can be approximated as triangular barrier and then E y can be calculated as φ b /L, where L is the thickness of the tunneling barrier (see Figure 1). E (replaced by Ey) and T (the lattice temperature) needed for calculations of J TAT , J PF , and J FN are obtained by numerical simulations   (Figure 3b). Experimental I G is also shown for a comparison. In the simulations, the reasonable parameters of ε S = 10, m e = 0.222 m o , φ t = 0.6 eV, and φ b = 1.2 eV were selected. φ t = 0.6 eV is higher than the value of 0.3 eV reported in Ref. 1. This difference would be explained that the continuum of states formed by the dislocations may be influenced by the material properties and the device processing, which therefore may lead to uncertainty of φ t for different devices.

Results and Discussion
As shown in Figure 3a, with V GS decreasing from 0 to around −4.5 V the temperature-dependent I TAT and I PF dominate I G , and this  is the reason that higher ambient temperature leads to higher I G ( Figure  3b). With V GS further decreasing to −6 V, temperature-independent I FN becomes the dominant component of I G . As a result, I G will not affected by the ambient temperature. In order to deeply analyze the mechanism of I G , the distribution of E y (Figure 3c), J TAT , J PF , and J FN (Figure 3d) along the gate metal/AlGaN interface from source-to drain-contact for V GS = −3 V and −6 V are solely shown. E y near the gate edges continuously increases with V GS deceasing, while E y in the other areas of the interface saturates after V GS lower than the threshold voltage, which is a result from the depletion of 2DEG in the channel. Correspondingly, J PF and J FN show higher values near the gate edges than that in other areas. J FN is very sensitive to E y and so it shows pronounced variation along the interface. For V GS = −3 V, J PF along the whole interface is higher than J FN and so I PF is the dominant component of I G . For V GS = −6 V, J FN becomes higher than J PF near the gate edges, as a result I FN becomes the dominant component of I G .
The saturate E y far from the gate edges is not high enough to cause obvious J FN , meaning J FN mainly concentrates near the gate edges.
To investigate how I G is influenced by L G , I G for another device with L G = 3 μm is also simulated and compared with L G = 0.7 μm. Under the same V GS , E y (Figure 4b) and also J PF as well as J FN (Figure 4c) have almost same distributions along the gate metal/AlGaN interface for different L G . Although the same distributions of J PF , I PF shows higher value for L G = 3 um than that for L G = 0.7 um because of the larger gate area for longer L G ( Figure  4a). However, due to the concentration of J FN near the gate edges, I FN have same values for the different L G . Therefore, for the high V GS , device with longer L G should have higher I G because I TAT and I PF are the dominant components of I G . While for low V GS , I G should be L G -independent because I FN becomes the dominant component of I G .
We have studied I G for the device under V GS < 0 V (V DS = 0 V) without self-heating. In the following, I G for the device under V DS > 0 V (V GS = 0 V) with self-heating will be studied. I FN is temperatureindependent and I TAT is considered only for low V DS in which the self-heating is negligible. So only the simulated I PF with and without self-heating are compared as shown in the Figures 5a and 5b. For 5 V < V DS < 15 V, the elevated device temperature exhibiting the maximum value at the drain-side gate edge (Figure 5c) caused by the self-heating significantly increases I PF and also I G since I PF is the dominant component of I G . This increase of I G is more obvious for the device at low ambient temperature of 350 K. The SiC substrate of the studied device has high thermal conductivity. For the other two common Si and sapphire substrates having lower thermal conductivity compared to SiC, impact of the device self-heating on I G should be more significant. For V DS > 15 V, although stronger self-heating is presented, but it has no effect on I G because I FN becomes the dominant component of I G . Figure 5d shows the distributions of J PF and J FN along the gate metal/AlGaN interface. Due to the pinch-off of the drain current, E y near the drain-side gate edge is much higher than that in other areas of the interface. Similar to the aforementioned illustration, for the high V DS = 20 V J FN is higher than J PF near the drain-side gate edge and it mainly concentrates there.
In the following, we will illustrate that the simulations of I G are consistent with the reported experimental work about the increased I G for the degraded device. Mizuno et al. 15 illustrated that the plasma treatment before gate metal evaporation can reduce the positive charge locates in the vicinity of the AlGaN surface, meaning the electric field near the gate is reduced which therefore reduces the gate tunneling current. The increased I G for the degraded device could be attributed to two main aspects: one aspect is that the hot electrons can trigger traps in the device illustrated by Meneghesso et al., 16 this effect is more obvious especially for the device operation in semi-on state in which the hot electrons have both high energy and high density; another aspect is that, when the device operation under high V DS and low V GS with high electric field appearing at the drain-side gate edge, because of the piezoelectric property of AlGaN/GaN, high inverse piezoelectric stress may cause pits/cracks (mechanical failure) at the drain-side gate edge where large amount of traps should locate. 17 Overall, the device degradation regarding to the increase of I G was attributed to the increased traps caused by the hot electrons and pits/cracks. In our work, TAT, PF emission, and FN tunneling are considered for the simulations of I G . It is straight that increased traps should enhance the traps-based TAT and PF emission current. Additionally, increased traps can deplete the 2DEG in the channel and thus increases the electric field in the barrier, which finally increases TAT, PF emission, and also FN tunneling current. Therefore, our simulations of I G are consistent with the reported experimental results.

Conclusions
I G of AlGaN/GaN HEMTs considered as summation of I TAT , I PF , and I FN is simulated and compared to the experimental data. The TAT and PF emission are dominant mechanisms for low electric field in the AlGaN barrier, while FN tunneling is the dominant mechanism for high electric field in the AlGaN barrer. I TAT and I PF can be influenced by L G , while I FN is L G -independent due to the concentration of I FN near the gate edges. For the device at small values of V DS > 0 V (V GS = 0 V) with obvious power consumption, the self-heating can significantly increases I PF and also I G because I PF is the dominant component of I G . While for the device under high V DS , the self-heating has no influence on I G because temperature-independent I FN becomes the dominant component of I G .