Simulation of AlGaN / GaN HEMTs ’ Breakdown Voltage Enhancement Using Gate Field-Plate , Source Field-Plate and Drain Field Plate

A 2-D simulation of off-state breakdown voltage (VBD) for AlGaN/GaN high electron mobility transistors (HEMTs) with multi field-plates (FPs) is presented in this paper. The effect of geometrical variables of FP and insulator layer on electric field distribution and VBD are investigated systematically. The FPs can modulate the potential lines and distribution of an electric field, and the insulator layer would influence the modulation effect of FPs. In addition, we designed a structure of HEMT which simultaneously contains gate FP, source FP and drain FP. It is found that the VBD of AlGaN/GaN HEMTs can be improved greatly with the corporation of gate FP, source FP and drain FP. We achieved the highest VBD in the HEMT contained with three FPs by optimizing the structural parameters including length of FPs, thickness of FPs, and insulator layer. For HEMT with three FPs, FP-S alleviates the concentration of the electric field more effectively. When the length of the source FP is 24 μm and the insulator thickness between the FP-S and the AlGaN surface is 1950 nm, corresponding to the average electric field of about 3 MV/cm at the channel, VBD reaches 2200 V. More importantly, the 2D simulation model is based on a real HMET device and will provide guidance for the design of a practical device.


Introduction
Gallium nitride (GaN)-based high electron mobility transistor (HEMT) has become an attractive candidate for high power applications, due to integrating lots of outstanding physical properties like high breakdown voltage, high frequency application and low on-resistance [1][2][3].For power devices, the property of high breakdown voltage is particularly significant.On account of the limit of technique process, the off-state breakdown voltage (V BD ) of AlGaN/GaN HEMTs is still far from the limitation of GaN material [4].
Field-plate (FP) technology is expected to be a feasible and effective way to increase the breakdown voltage by reducing the peak value of an electric field along the channel [5].From the perspective of field-plate position, FPs can be divided into gate field-plate (FP-G), source field plate (FP-S), and drain field plate (FP-D).Zhang, N.Q.et al. first proposed the FP-G and achieved a high V BD of 570 V, but resulting in severe degradation of frequency characteristics [6].Since then, multiple grating FP-G [7,8] and novel FP-G structures [9,10] have been invented to reduce the frequency degradation.Relevant analytical models [11,12] and reliability improvement [13] were also reported, providing a deeper insight into the relationship between FPs and V BD .In terms of FP-S, a T-shaped FP-S was designed by Mao Wei et al. and it attained high V BD and high efficiency remarkably [14].In order to enhance V BD more effectively, the combination of both FP-G and FP-S is inevitable [15][16][17].An extremely high V BD of 8300 V was achieved by using the thick poly-AlN passivation on HEMTs with both FP-G and FP-S [18].Toshiki Kabemura et al. made a 2-D analysis of breakdown characteristics of FP HEMTs with a high-k passivation layer, confirming that the V BD would increase with relative permittivity increasing [19].For investigating the impact of FP-G and FP-S on the capacitances, Aamir et al. modeled the bias dependence of terminal capacitances, and the proposed model is in excellent agreement with measured data [20].Meanwhile, the incorporation of FP-S and FP-D was considered to be an effective way to improve V BD and reduce the on-resistance to about 0.6 mΩ•cm 2 [21].However, in comparison with FP-G and FP-S, FP-D is rarely induced to enhance V BD but mostly induced to improve reverse breakdown voltage [22].In fact, FP-D can reduce the undesired electric field peak from the metal peak introduced by annealing [23].It is necessary to combine the three FPs.Up to now, the properties of HEMT with FP-G, FP-S and FP-D simultaneously are seldom discussed.At the same time, considering the complexity of structure, more structural parameters such as length of FPs, thickness of FPs and insulator layer are also needed to be optimized in detail.Hence, systematic simulation is necessary and will provide the guidance for experiment.
In this paper, the effect of geometrical variables of FP and insulator layer on field distribution and V BD were investigated systematically.The electric field distribution and V BD under different FP were compared by simulation using Silvaco TCAD [24].Moreover, the FP-G, FP-S and FP-D are employed simultaneously in an AlGaN/GaN HEMT to improve V BD effectively.The physical models are illustrated in Section 2. The parameters including length of FPs, thickness of FPs, and insulator layer of FPs were optimized for improving V BD .The breakdown characteristics of HEMT with FP-G, FP-S and FP-D were simultaneously discussed.

Physic Models
The two-dimensional numerical simulations were carried out by Silvaco TCAD.The simulated model was based on the experimental structure.Figure 1 shows a not-to-scale cross-section view of the device structure analyzed in this paper.The gate length L G was 3 µm, the source-to-gate distance L SG was 9 µm, and the gate-to-drain distance L GD was 22 µm.The field-plate length L FP-G ' was 2 µm.The insulator was assumed to be SiO 2 in this simulation, which was usually used in our lab.The permittivity of SiO 2 was set to 5, corresponding to the value of the experimental measurement.Likewise, Si 3 N 4 [25] and Al 2 O 3 [26] could also be selected as passivation, and the kind of insulator would not change the trend of V BD versus FPs [19].The thickness of insulator layer t 1 and t 2 ; length of FPs L FP-G , L FP-S and L FP-D ; and the thickness of FPs t FP-G and t FP-S are variable in the following Section.The leakage current [27], especially from the buffer layer, may result in electron injection from the channel into the buffer layer and a large drain current [28].Setting traps in the GaN buffer is a usual way to decrease the leakage current at pinch-off state [19,29,30], but it may cause a no-convergence problem.Moreover, we aimed to present the relevance between electric field distributions and FPs clearly and exclude the punch-through from the buffer layer.Therefore, with the purpose of simplifying calculation, we set the GaN buffer layer to be 200 nm, reducing the influence of buffer leakage current flow from source to drain [31].Besides, the thicknesses of the Al 0.23 Ga 0.77 N barrier and GaN channel are 25 nm and 10nm respectively.
Detailed simulation conditions are as follows.The 1×10 13 cm −2 positive charges were placed along the Al 0.23 Ga 0.77 N/GaN heterojunction to create the two-dimension electron gas, and the channel mobility was set to 1500 cm 2 /V•s [32].Also, the field-dependent mobility model and Shockley-Read-Hall (SRH) Recombination model were used.Thermal impact is common in the experiments [33,34], but we did not discuss it during the simulation.The breakdown voltage simulation in this paper was based on the Selberherr's impact ionization model.The ionization coefficients were AN = AP = 2.98 × 10 8 and 3 of 11 BN = BP = 3.44 × 10 7 [35].Moreover, simulations about breakdown performance were all carried out with the gate biased at −6 V, keeping devices on the off-state.Finally, V BD was defined as the drain voltage when the peak electric field in the channel reached 3 MV/cm [10,14,22].
Electronics 2019, 8, x FOR PEER REVIEW 3 of 11 breakdown performance were all carried out with the gate biased at −6 V, keeping devices on the off-state.Finally, VBD was defined as the drain voltage when the peak electric field in the channel reached 3 MV/cm [10,14,22].

Gate Field-Plate
We first discuss the influence of gate field-plate on VBD. Figure 2 shows the device structure only with FP-G.Three parameters are studied, including the insulator layer thickness t1, the FP-G length LFP-G and the FP-G thickness tFP-G.Figure 3a shows the distributions of electric field along the heterojunction interface for t1 from 100 nm to 300 nm when LFP-G is 4μm and tFP-G is 100 nm.For the sake of presenting the electric field peaks intuitively, we only display the electric field distributions partly around the region from gate to drain.As shown in Figure 3a, for thin insulator layer t1 (t1 <250 nm), the electric field at the FP-G edge is higher than the electric field at the gate edge.Due to the modulation of FP-G, the electric field at the FP-G edge reaches the breakdown standard first.Consequently, VBD increases with the increase of t1.However, when t1 further increases, the modulated effect of FP-G becomes weaker.Thus, the electric field peak shifts to the gate edge, which leads to the decrease of VBD.For the structure in Figure 2, the modulate effect induced by FP-G is optimal when t1 = 250 nm, as shown in Figure 3b.

Gate Field-Plate
We first discuss the influence of gate field-plate on V BD .Figure 2 shows the device structure only with FP-G.Three parameters are studied, including the insulator layer thickness t 1 , the FP-G length L FP-G and the FP-G thickness t FP-G .Figure 3a shows the distributions of electric field along the heterojunction interface for t 1 from 100 nm to 300 nm when L FP-G is 4µm and t FP-G is 100 nm.For the sake of presenting the electric field peaks intuitively, we only display the electric field distributions partly around the region from gate to drain.As shown in Figure 3a, for thin insulator layer t 1 (t 1 < 250 nm), the electric field at the FP-G edge is higher than the electric field at the gate edge.Due to the modulation of FP-G, the electric field at the FP-G edge reaches the breakdown standard first.Consequently, V BD increases with the increase of t 1 .However, when t 1 further increases, the modulated effect of FP-G becomes weaker.Thus, the electric field peak shifts to the gate edge, which leads to the decrease of V BD .For the structure in Figure 2, the modulate effect induced by FP-G is optimal when t 1 = 250 nm, as shown in Figure 3b.breakdown performance were all carried out with the gate biased at −6 V, keeping devices on the off-state.Finally, VBD was defined as the drain voltage when the peak electric field in the channel reached 3 MV/cm [10,14,22].

Gate Field-Plate
We first discuss the influence of gate field-plate on VBD. Figure 2 shows the device structure only with FP-G.Three parameters are studied, including the insulator layer thickness t1, the FP-G length LFP-G and the FP-G thickness tFP-G.Figure 3a shows the distributions of electric field along the heterojunction interface for t1 from 100 nm to 300 nm when LFP-G is 4μm and tFP-G is 100 nm.For the sake of presenting the electric field peaks intuitively, we only display the electric field distributions partly around the region from gate to drain.As shown in Figure 3a, for thin insulator layer t1 (t1 <250 nm), the electric field at the FP-G edge is higher than the electric field at the gate edge.Due to the modulation of FP-G, the electric field at the FP-G edge reaches the breakdown standard first.Consequently, VBD increases with the increase of t1.However, when t1 further increases, the modulated effect of FP-G becomes weaker.Thus, the electric field peak shifts to the gate edge, which leads to the decrease of VBD.For the structure in Figure 2, the modulate effect induced by FP-G is optimal when t1 = 250 nm, as shown in Figure 3b.breakdown performance were all carried out with the gate biased at −6 V, keeping devices on the off-state.Finally, VBD was defined as the drain voltage when the peak electric field in the channel reached 3 MV/cm [10,14,22].

Gate Field-Plate
We first discuss the influence of gate field-plate on VBD. Figure 2 shows the device structure only with FP-G.Three parameters are studied, including the insulator layer thickness t1, the FP-G length LFP-G and the FP-G thickness tFP-G.Figure 3a shows the distributions of electric field along the heterojunction interface for t1 from 100 nm to 300 nm when LFP-G is 4μm and tFP-G is 100 nm.For the sake of presenting the electric field peaks intuitively, we only display the electric field distributions partly around the region from gate to drain.As shown in Figure 3a, for thin insulator layer t1 (t1 <250 nm), the electric field at the FP-G edge is higher than the electric field at the gate edge.Due to the modulation of FP-G, the electric field at the FP-G edge reaches the breakdown standard first.Consequently, VBD increases with the increase of t1.However, when t1 further increases, the modulated effect of FP-G becomes weaker.Thus, the electric field peak shifts to the gate edge, which leads to the decrease of VBD.For the structure in Figure 2, the modulate effect induced by FP-G is optimal when t1 = 250 nm, as shown in Figure 3b.Then, we change the LFP-G from 0 μm to 20 μm and keep t1 fixed at 250 nm.Without a field plate at the drain side, the electric field at the gate edge increases rapidly and reaches the critical breakdown field 3 MV/cm at around VD = 55 V.For short LFP-G (LFP-G<4 μm), the modulate effect of field-plate is too small to reduce the electric field peak at the gate edge, so VBD increases slowly with the increase of LFP-G.As shown in Figure 3c,d, with the optimized t1, LFP-G from 4 μm to 8 μm, all can reduce the electric field peak value along the channel effectively, and the electric field peak value of the gate edge reaches 3 MV/cm until VD = 448 V.When the LFP-G is more than 20 μm, VBD will decrease.It is attribute to the narrower distance between the field-plate edge and the drain, which leads to the electric field at the FP-G edge reaches the critical breakdown electric field at around VD = 435 V.
The following parameter is FP-G thickness tFP-G.It is set to 100 nm, 300 nm, 400 nm, 800 nm and 8 μm, respectively.In previous researches, there were few studies on the relationship between breakdown characteristics and the thickness of the field-plate.As shown in Figure 3e, VBD increases with the increase of tFP-G.This phenomenon shows that thicker FP-G can reduce the electric field at the FP-G edge.However, the improvement of VBD is not obvious even when the tFP-G reaches 8 μm.In view of the highest VBD achievement with less changes in technology progress, we choose tFP-G = 100 nm as a suitable value for following researches.

Source Field-Plate
The FP-S is usually used in the GaN-based HEMTs in combination with the gate field-plate, with the aim of achieving a great improvement of VBD. Figure 4 shows the structure with FP-S.Firstly, the relationship between FP-S and VBD is studied in the HEMT without the FP-G.The thickness of the gate was fixed at 100 nm.From Figure 5, the effect of FP-S on VBD is similar to that of FP-G.With regard to t2, the optimum value of t2 is less than that of t1.Because in this device, when the FP-G is fixed to −6 V, the FP-S is fixed to 0 V, resulting in a higher electric field at the FP-S edge Then, we change the L FP-G from 0 µm to 20 µm and keep t 1 fixed at 250 nm.Without a field plate at the drain side, the electric field at the gate edge increases rapidly and reaches the critical breakdown field 3 MV/cm at around V D = 55 V.For short L FP-G (L FP-G <4 µm), the modulate effect of field-plate is too small to reduce the electric field peak at the gate edge, so V BD increases slowly with the increase of L FP-G .As shown in Figure 3c,d, with the optimized t 1 , L FP-G from 4 µm to 8 µm, all can reduce the electric field peak value along the channel effectively, and the electric field peak value of the gate edge reaches 3 MV/cm until V D = 448 V.When the L FP-G is more than 20 µm, V BD will decrease.It is attribute to the narrower distance between the field-plate edge and the drain, which leads to the electric field at the FP-G edge reaches the critical breakdown electric field at around V D = 435 V.
The following parameter is FP-G thickness t FP-G .It is set to 100 nm, 300 nm, 400 nm, 800 nm and 8 µm, respectively.In previous researches, there were few studies on the relationship between breakdown characteristics and the thickness of the field-plate.As shown in Figure 3e, V BD increases with the increase of t FP-G .This phenomenon shows that thicker FP-G can reduce the electric field at the FP-G edge.However, the improvement of V BD is not obvious even when the t FP-G reaches 8 µm.In view of the highest V BD achievement with less changes in technology progress, we choose t FP-G = 100 nm as a suitable value for following researches.

Source Field-Plate
The FP-S is usually used in the GaN-based HEMTs in combination with the gate field-plate, with the aim of achieving a great improvement of V BD .Figure 4 shows the structure with FP-S.Firstly, the relationship between FP-S and V BD is studied in the HEMT without the FP-G.The thickness of the gate was fixed at 100 nm.From Figure 5, the effect of FP-S on V BD is similar to that of FP-G.With regard to t 2 , the optimum value of t 2 is less than that of t 1 .Because in this device, when the FP-G is fixed to −6 V, the FP-S is fixed to 0 V, resulting in a higher electric field at the FP-S edge than that at the FP-G edge.Hence, to achieve the same effect of modulating the electric field by FP, the FP-S should be closer to the AlGaN surface.The variation trend of V BD with the length and thickness of FP-S is the same as that of FP-G.As we know, the electric field is in direct proportion to the electric potential difference, and the latter can be performed by the density of the potential line distribution.Therefore, the higher electric field corresponds to the narrower potential lines.From the potential line distributions of Figure 5g,h, we find that potential lines in (g) of FP-G edge are less crowded than that in (h) of FP-S edge even at high drain voltage, which is in accordance with electric field distributions [11].In a word, in order to enhance V BD , FP-G is more efficient than FP-S when the structure only has one FP.
than that at the FP-G edge.Hence, to achieve the same effect of modulating the electric field by FP, the FP-S should be closer to the AlGaN surface.The variation trend of VBD with the length and thickness of FP-S is the same as that of FP-G.As we know, the electric field is in direct proportion to the electric potential difference, and the latter can be performed by the density of the potential line distribution.Therefore, the higher electric field corresponds to the narrower potential lines.From the potential line distributions of Figure 5g,h, we find that potential lines in (g) of FP-G edge are less crowded than that in (h) of FP-S edge even at high drain voltage, which is in accordance with electric field distributions [11].In a word, in order to enhance VBD, FP-G is more efficient than FP-S when the structure only has one FP.than that at the FP-G edge.Hence, to achieve the same effect of modulating the electric field by FP, the FP-S should be closer to the AlGaN surface.The variation trend of VBD with the length and thickness of FP-S is the same as that of FP-G.As we know, the electric field is in direct proportion to the electric potential difference, and the latter can be performed by the density of the potential line distribution.Therefore, the higher electric field corresponds to the narrower potential lines.From the potential line distributions of Figure 5g,h, we find that potential lines in (g) of FP-G edge are less crowded than that in (h) of FP-S edge even at high drain voltage, which is in accordance with electric field distributions [11].In a word, in order to enhance VBD, FP-G is more efficient than FP-S when the structure only has one FP.

Drain Field-Plate
For FP-D, it is usually used to improve the reverse breakdown voltage.In fact, the electric field peak from the metal peak introduced by annealing could also be reduced by FP-D.However, the electric field peak does not appear on the drain edge in the Silvaco simulation, because of the flat and smooth edge of ohmic electros.Thus, single FP-D usually has little impact on electric field distribution along the channel.However, the electric field peak at the FP-S edge will increase if the distance between FP-S and FP-D is too close.Therefore, we only explored the relationship between FP-D length and VBD when the structure has both FP-S and FP-D, as shown in Figure 6. Figure 7 shows that when LFP-D>13 μm, VBD decreases due to the narrow distance between the two FPs.In consideration of passivation quality in the practical experiment, breakdown may occur between the two FPs.So, it may be more appropriate when LFP-D is set to 1 μm.

Drain Field-Plate
For FP-D, it is usually used to improve the reverse breakdown voltage.In fact, the electric field peak from the metal peak introduced by annealing could also be reduced by FP-D.However, the electric field peak does not appear on the drain edge in the Silvaco simulation, because of the flat and smooth edge of ohmic electros.Thus, single FP-D usually has little impact on electric field distribution along the channel.However, the electric field peak at the FP-S edge will increase if the distance between FP-S and FP-D is too close.Therefore, we only explored the relationship between FP-D length and V BD when the structure has both FP-S and FP-D, as shown in Figure 6. Figure 7 shows that when L FP-D >13 µm, V BD decreases due to the narrow distance between the two FPs.In consideration of passivation quality in the practical experiment, breakdown may occur between the two FPs.So, it may be more appropriate when L FP-D is set to 1 µm.

Drain Field-Plate
For FP-D, it is usually used to improve the reverse breakdown voltage.In fact, the electric field peak from the metal peak introduced by annealing could also be reduced by FP-D.However, the electric field peak does not appear on the drain edge in the Silvaco simulation, because of the flat and smooth edge of ohmic electros.Thus, single FP-D usually has little impact on electric field distribution along the channel.However, the electric field peak at the FP-S edge will increase if the distance between FP-S and FP-D is too close.Therefore, we only explored the relationship between FP-D length and VBD when the structure has both FP-S and FP-D, as shown in Figure 6. Figure 7 shows that when LFP-D>13 μm, VBD decreases due to the narrow distance between the two FPs.In consideration of passivation quality in the practical experiment, breakdown may occur between the two FPs.So, it may be more appropriate when LFP-D is set to 1 μm.

Devices Contained with FP-G, FP-S, and FP-D
For much higher VBD, there is no doubt that the FP-G should be combined with the FP-S [20].Figure 8 shows the structure of the device contained with FP-G, FP-S and FP-D simultaneously.The VBD is affected by seven variables, t1, t2, LFP-G, LFP-S, LFP-D, tFP-G, and tFP-S.Since many parameters should be optimized, the procedure is significant.Because the electric field peak at the gate edge is mainly affected by FP-G, it can be suppressed by a moderate value of t1, LFP-G and tFP-G.Therefore, we can fix these three parameters to adjust the electric field peak at the gate edge, close to but not higher than 3 M/cm.At the same time, less changes in the previous structure and little influence of FP thickness in enhancing VBD, tFP-S and LFP-D can be confirmed too.Thus, we can confirm five parameter values firstly, as shown in Table 1 Then we can focus on the other two parameters, t2 and LFP-S.As shown in Figure 9, for different LFP-S which vary from 18 μm to 28 μm, the moderated value (up to the highest VBD) of t2 is different.We can find the reason in Figure 10a.Only when three peaks are uniform and close to 3 MV/cm, could we achieve the highest VBD.Meanwhile, comparing Figure 11a with b, the potential lines distribution of the former are more crowded than that of the latter, resulting in a lower VBD [14].
However, no matter what the value of t2 is, there is the highest VBD of all lengths for a FP-S of 24 μm.When LFP-S is between 24 μm to 26 μm, combined with the optimal t2 = 1.7 μm, we can acquire the highest VBD of 2200 V.Then, when LFP-S is 28 μm, due to the narrow distance between FP-S and FP-D, the electric field peak of the FP-S edge will become higher, which makes VBD decrease.Figure 10b shows the electric field distributions for different t2 along the channel in HEMT when LFP-S is fixed to 24 μm.When t2 = 1950 nm, the two electric field peaks of FP-G edge and FP-S edge are approximate but not high enough to cause breakdown.So, when VBD is around 2200 V, the highest electric field peak appears at the gate edge.Hence, the crucial way to enhance breakdown voltage is

Devices Contained with FP-G, FP-S, and FP-D
For much higher V BD , there is no doubt that the FP-G should be combined with the FP-S [20].Figure 8 shows the structure of the device contained with FP-G, FP-S and FP-D simultaneously.The V BD is affected by seven variables, t 1 , t 2 , L FP-G , L FP-S , L FP-D , t FP-G , and t FP-S .Since many parameters should be optimized, the procedure is significant.Because the electric field peak at the gate edge is mainly affected by FP-G, it can be suppressed by a moderate value of t 1 , L FP-G and t FP-G .Therefore, we can fix these three parameters to adjust the electric field peak at the gate edge, close to but not higher than 3 M/cm.At the same time, less changes in the previous structure and little influence of FP thickness in enhancing V BD , t FP-S and L FP-D can be confirmed too.Thus, we can confirm five parameter values firstly, as shown in Table 1 Then we can focus on the other two parameters, t 2 and L FP-S .

Devices Contained with FP-G, FP-S, and FP-D
For much higher VBD, there is no doubt that the FP-G should be combined with the FP-S [20].Figure 8 shows the structure of the device contained with FP-G, FP-S and FP-D simultaneously.The VBD is affected by seven variables, t1, t2, LFP-G, LFP-S, LFP-D, tFP-G, and tFP-S.Since many parameters should be optimized, the procedure is significant.Because the electric field peak at the gate edge is mainly affected by FP-G, it can be suppressed by a moderate value of t1, LFP-G and tFP-G.Therefore, we can fix these three parameters to adjust the electric field peak at the gate edge, close to but not higher than 3 M/cm.At the same time, less changes in the previous structure and little influence of FP thickness in enhancing VBD, tFP-S and LFP-D can be confirmed too.Thus, we can confirm five parameter values firstly, as shown in Table 1 Then we can focus on the other two parameters, t2 and LFP-S.As shown in Figure 9, for different LFP-S which vary from 18 μm to 28 μm, the moderated value (up to the highest VBD) of t2 is different.We can find the reason in Figure 10a.Only when three peaks are uniform and close to 3 MV/cm, could we achieve the highest VBD.Meanwhile, comparing Figure 11a with b, the potential lines distribution of the former are more crowded than that of the latter, resulting in a lower VBD [14].
However, no matter what the value of t2 is, there is the highest VBD of all lengths for a FP-S of 24 μm.When LFP-S is between 24 μm to 26 μm, combined with the optimal t2 = 1.7 μm, we can acquire the highest VBD of 2200 V.Then, when LFP-S is 28 μm, due to the narrow distance between FP-S and FP-D, the electric field peak of the FP-S edge will become higher, which makes VBD decrease.Figure 10b shows the electric field distributions for different t2 along the channel in HEMT when LFP-S is fixed to 24 μm.When t2 = 1950 nm, the two electric field peaks of FP-G edge and FP-S edge are approximate but not high enough to cause breakdown.So, when VBD is around 2200 V, the highest electric field peak appears at the gate edge.Hence, the crucial way to enhance breakdown voltage is As shown in Figure 9, for different L FP-S which vary from 18 µm to 28 µm, the moderated value (up to the highest V BD ) of t 2 is different.We can find the reason in Figure 10a.Only when three peaks are uniform and close to 3 MV/cm, could we achieve the highest V BD .Meanwhile, comparing Figure 11a with Figure 11b, the potential lines distribution of the former are more crowded than that of the latter, resulting in a lower V BD [14].
However, no matter what the value of t 2 is, there is the highest V BD of all lengths for a FP-S of 24 µm.When L FP-S is between 24 µm to 26 µm, combined with the optimal t 2 = 1.7 µm, we can acquire the highest V BD of 2200 V.Then, when L FP-S is 28 µm, due to the narrow distance between FP-S and FP-D, the electric field peak of the FP-S edge will become higher, which makes V BD decrease.Figure 10b shows the electric field distributions for different t 2 along the channel in HEMT when L FP-S is fixed to 24 µm.When t 2 = 1950 nm, the two electric field peaks of FP-G edge and FP-S edge are approximate but not high enough to cause breakdown.So, when V BD is around 2200 V, the highest electric field peak appears at the gate edge.Hence, the crucial way to enhance breakdown voltage is to adjust relative FP parameters.By means of t 2 and L FP-S , the two electric field peaks at each FPs edge could be uniformed to be closely equal but less than 3 M/cm; and if the highest electric field peak appears at the gate edge, we would acquire the highest V BD .to adjust relative FP parameters.By means of t2 and LFP-S, the two electric field peaks at each FPs edge could be uniformed to be closely equal but less than 3 M/cm; and if the highest electric field peak appears at the gate edge, we would acquire the highest VBD.    to adjust relative FP parameters.By means of t2 and LFP-S, the two electric field peaks at each FPs edge could be uniformed to be closely equal but less than 3 M/cm; and if the highest electric field peak appears at the gate edge, we would acquire the highest VBD.    to adjust relative FP parameters.By means of t2 and LFP-S, the two electric field peaks at each FPs edge could be uniformed to be closely equal but less than 3 M/cm; and if the highest electric field peak appears at the gate edge, we would acquire the highest VBD.

Figure 1 .
Figure 1.Schematic of HEMT with FP-G, FP-S and FP-D.

Figure 2 .
Figure 2. Device structure with FP-G analyzed in this study.

Figure 1 .
Figure 1.Schematic of HEMT with FP-G, FP-S and FP-D.

Figure 1 .
Figure 1.Schematic of HEMT with FP-G, FP-S and FP-D.

Figure 2 .
Figure 2. Device structure with FP-G analyzed in this study.

Figure 2 .
Figure 2. Device structure with FP-G analyzed in this study.

Figure 1 .
Figure 1.Schematic of HEMT with FP-G, FP-S and FP-D.

Figure 2 .
Figure 2. Device structure with FP-G analyzed in this study.

Figure 3 .
Figure 3.The electric field distributions along the channel for different values of (a) t1, (c) LFP-G, and (e) tFP-G.The VBD for different values of (b) t1, (d) LFP-G, and (f) tFP-G.

Figure 3 .
Figure 3.The electric field distributions along the channel for different values of (a) t 1 , (c) L FP-G , and (e) t FP-G .The V BD for different values of (b) t 1 , (d) L FP-G , and (f) t FP-G .

Figure 4 .
Figure 4. Device structure with FP-S analyzed in this study.Figure 4. Device structure with FP-S analyzed in this study.

Figure 4 .
Figure 4. Device structure with FP-S analyzed in this study.Figure 4. Device structure with FP-S analyzed in this study.

Figure 4 .
Figure 4. Device structure with FP-S analyzed in this study.

Figure 6 .
Figure 6.Device structure with FP-S and FP-D analyzed in this study.

Figure 6 .
Figure 6.Device structure with FP-S and FP-D analyzed in this study.

Figure 6 .
Figure 6.Device structure with FP-S and FP-D analyzed in this study.

Figure 7 .
Figure 7.The electric field distributions along the channel for different values of (a) LFP-D.Off-state breakdown voltage VBD for different values of (b) LFP-D.

Figure 8 .
Figure 8. Device structure contained with FP-G, FP-S, and FP-D.

Figure 7 .
Figure 7.The electric field distributions along the channel for different values of (a) L FP-D .Off-state breakdown voltage V BD for different values of (b) L FP-D .

Electronics 2019, 8 , 11 Figure 7 .
Figure 7.The electric field distributions along the channel for different values of (a) LFP-D.Off-state breakdown voltage VBD for different values of (b) LFP-D.

Figure 8 .
Figure 8. Device structure contained with FP-G, FP-S, and FP-D.

Figure 8 .
Figure 8. Device structure contained with FP-G, FP-S, and FP-D.

Figure 9 .
Figure 9. VBD as a function of t2 and LFP-S.

Figure 10 .
Figure 10.(a) The electric field distributions along the channel in HEMT with different LFP-S under highest VBD; (b) the electric field distributions along the channel in HEMT when LFP-S = 24.

Figure 9 .
Figure 9. V BD as a function of t 2 and L FP-S .

Figure 9 .
Figure 9. VBD as a function of t2 and LFP-S.

Figure 10 .
Figure 10.(a) The electric field distributions along the channel in HEMT with different LFP-S under highest VBD; (b) the electric field distributions along the channel in HEMT when LFP-S = 24.

Figure 10 .
Figure 10.(a) The electric field distributions along the channel in HEMT with different L FP-S under highest V BD ; (b) the electric field distributions along the channel in HEMT when L FP-S = 24.

Figure 9 .
Figure 9. VBD as a function of t2 and LFP-S.

Figure 10 .
Figure 10.(a) The electric field distributions along the channel in HEMT with different LFP-S under highest VBD; (b) the electric field distributions along the channel in HEMT when LFP-S = 24.