Design Optimization of an Enhanced-Mode GaN HEMT with Hybrid Back Barrier and Breakdown Voltage Prediction Based on Neural Networks

Abstract

To improve the breakdown voltage (BV), a GaN-based high-electron-mobility transistor with a hybrid AlGaN back barrier (HBB-HEMT) was proposed. The hybrid AlGaN back barrier was constructed using the Al₀.₂₅Ga₀.₇₅N region and Al₀.₁G₀.9N region, each with a distinct Al composition. Simulation results of the HBB-HEMT demonstrated a breakdown voltage (1640 V) that was 212% higher than that of the conventional HEMT (Conv-HEMT) and a low on-resistance (0.4 mΩ·cm²). Ultimately, the device achieved a high Baliga’s figure of merit (7.3 GW/cm²) among reported devices of similar size. A back-propagation (BP) neural network-based prediction model was trained to predict BV for enhanced efficiency in subsequent work. The model was trained and calibrated, achieving a correlation coefficient (R) of 0.99 and a prediction accuracy of 95% on the test set. The results indicated that the BP neural network model using the Levenberg–Marquardt algorithm accurately predicted the forward breakdown voltage of the HBB-HEMT, underscoring the feasibility and significance of neural network models in designing GaN power devices.

1. Introduction

Gallium nitride high-electron-mobility transistors (GaN HEMTs) have a wide range of applications in power and RF electronics due to the favorable characteristics of high switching speed, high electron mobility, wide bandgap, and thermal stability [1,2,3,4,5,6]. It is necessary to design normally-off GaN HEMTs to increase safety and reliability in circuit design [7,8]. Several techniques have been reported to realize normally-off GaN HEMTs, including cascode structures [9], recessed gates [10,11], fluorine ion implantation [12], ultra-thin barrier layers [13], and p-(Al)GaN cap layers [14,15,16,17,18]. Among these techniques, the p-GaN cap layer structure stands out for its widespread adoption in commercial applications, attributed to its straightforward design, robustness, and superior performance. However, these devices have only achieved an average breakdown electric field of 1.4 MV/cm and Baliga’s figure of merit (FOM) of 3.9 GW/cm², respectively [17]. These figures are still significantly less than the critical breakdown electric field of 3 MV/cm.

The electric field distribution of the channel in a GaN HEMT is non-uniform during breakdown, with the electric field concentrating at the gate edges. This causes breakdown to occur first at the gate edges, which results in a lower average breakdown field. In addition, defects in the GaN material and interface states introduced during the fabrication process can lead to local electric field enhancement, further reducing the actual breakdown field of the device. Gate field plates or drain field plates are usually introduced to alleviate the local electric field enhancement problem [2]. However, the field plate structure introduces additional parasitic capacitance, which degrades the high-frequency characteristics of GaN HEMT devices [19]. GaN HEMTs with a back-barrier structure [20] can relieve electric field crowding without sacrificing high-frequency characteristics, but the balance between on-resistance (R_{on, sp}) and breakdown voltage (BV) is still not good enough.

Moreover, the BV of a GaN HEMT normally depends on multiple parameters such as barrier layer thickness, gate-to-drain distance, and specific parameters in special structures. These parameters are intricately coupled due to complex physical mechanisms within the GaN HEMT. Consequently, using simulation and experimental testing methods to continuously approach the target value requires significant time investment, leading to long optimization cycles and low efficiency in device design. The rise of the backpropagation neural network algorithm (BP) provides a more efficient solution for device design optimization. This algorithm employs a multidimensional nonlinear approximator to map input parameters to output parameters and possesses strong self-learning capabilities, making it particularly suitable for addressing the complex physical mechanisms within GaN HEMTs. Although there have been some studies reporting the use of neural networks for performance prediction in device design [21,22,23,24], there has been little research on the performance optimization of GaN HEMTs.

In this paper, a GaN-based high-electron-mobility transistor with a hybrid AlGaN back barrier (HBB-HEMT) is proposed to improve breakdown performance. The proposed HBB-HEMT was simulated with the Silvaco TCAD. Before the actual simulation, the simulation models [25,26,27,28,29,30] were calibrated by comparison with the experimental results [31], thus proving the correctness of the models. Based on simulation tools, the DC, breakdown, and CV characteristics of the HBB-HEMT were discussed and optimized. The final optimized results demonstrate that the HBB-HEMT has low R_{on, sp}, high BV, and high FOM, which shows significant potential in electronic power applications. Finally, L_gd (gate-to-drain distance), L_gi (gate-to-Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface distance), and T_buf (thickness of the GaN buffer) were selected as the neural network model inputs, while the breakdown voltage was designated as the output. The neural network model was trained using data obtained from TCAD simulations. The resulting predictions showed a low error rate compared to the simulation values, demonstrating the accuracy of the model.

2. Device Structure

The structure of the conventional p-GaN gate GaN HEMT (Conv HEMT) is shown in Figure 1a. The structures of the p-GaN gate GaN HEMT with a single AlGaN back barrier (B-HEMT) are depicted in Figure 1b,c, with the aluminum composition (Al.comp) of the AlGaN back barrier set to 0.1 and 0.25, respectively. Figure 1d illustrates the proposed HBB-HEMT, in which the hybrid AlGaN back barrier consists of an Al₀.₂₅Ga₀.₇₅N region and an Al₀.₁Ga₀.₉N region, and the Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface is set between the gate and the drain. The above four structures consist of a Si(111) substrate, GaN buffer layer, GaN channel layer, Al₀.₂₆Ga₀.₇₄N barrier layer, and p-GaN layer doped with 3 × 10¹⁷ cm⁻³.

Table 1. Key parameters of HBB-HEMT.

Parameter	Unit	Value	Parameter Caption
Lg	µm	1.4	Length of the gate region
Lgi	µm	1–6	Gate to the interface distance
Lgs	µm	1	Distance from gate to source
Lgd	µm	5~20	Distance from gate to drain
TP-GaN	nm	110	Thickness of p-GaN layer
Tbar	nm	15	Thickness of AlGaN barrier layer
Tch	nm	35	Thickness of GaN channel layer
Tbuf	µm	0.1~4	Thickness of GaN buffer layer
Tbb	nm	50	Thickness of AlGaN back barrier layer

provides the key structural parameters for the HBB-HEMT. For the HBB-HEMT, the Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface location (L_gi), the thickness of GaN buffer (T_buf), and gate-to-drain distance (L_gd) have been optimized.

3. Simulation Models

3.1. Simulation Models

In the simulation, various models were utilized, including the GaN polarization model, the mobility model, and the impact ionization model. The characteristics of the 2D electron gas are explained through the GaN polarization model. In the GaN polarization model, the total polarization (P_t) consists of spontaneous polarization (P_sp) and piezoelectric polarization (P_pe). Therefore, the P_t of GaN or Al_xGa_1−xN is [25]:

$${\mathrm{P}}_{\mathrm{t}}{=\mathrm{P}}_{\mathrm{sp}}{+\mathrm{P}}_{\mathrm{pe}}$$

(1)

For Al_xGa_1−xN, the spontaneous polarization intensity P_sp is given by [26]:

$${\mathrm{P}}_{\mathrm{sp}}{(\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}{\mathrm{N})=\mathrm{xP}}_{\mathrm{sp}}\left(\mathrm{AlN}\right)+(1-{\mathrm{x})\mathrm{P}}_{\mathrm{sp}}\left(\mathrm{GaN}\right)$$

(2)

In this context, the value for P_sp(AlN) is −0.09 and the value for P_sp(GaN) is −0.034. The piezoelectric polarization intensity P_pe is described as [27]:

$${\mathrm{P}}_{\mathrm{pe}}{(\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})=2\epsilon ({\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})({ \mathrm{e}}_{31}-{ \mathrm{e}}_{33}{\displaystyle \frac{{\mathrm{C}}_{13}}{{\mathrm{C}}_{33}}})$$

(3)

Let a(Al_xGa_1−xN) be the lattice constant of AlGaN. The strain ε(Al_xGa_1−xN) in AlGaN is described as follows:

$$\epsilon ({\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})={\displaystyle \frac{{\mathrm{a}}_{\mathrm{GaN}}-{\mathrm{a}(\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})}{{\mathrm{a}(\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})}}$$

(4)

$$\mathrm{a}({\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})=(1-{\mathrm{x})\mathrm{a}}_{\mathrm{GaN}}{+\mathrm{xa}}_{\mathrm{AlN}}$$

(5)

in which C₁₃ and C₃₃ represent elastic constants, e₃₁ and e₃₃ are piezoelectric constants of GaN, and a_GaN and a_AlN are the lattice constants of GaN and AlN, respectively. During the simulation, e₃₁, e₃₃, C₁₃, C₃₃, a_GaN, and a_AlN were set to −0.34, 0.67, 100, 392, 3.189, and 3.112, respectively. From the above formula, the strain ε(Al_xGa_1−xN) in AlGaN increases with Al composition. As the strain ε(Al_xGa_1−xN) increases, the piezoelectric polarization P_pe(Al_xGa_1−xN) in AlGaN also enhances. In this study, the Al composition was 0.26, and the tensile strain in AlGaN was approximately 0.63%.

In this study, the current characteristic of p-GaN HEMTs was described using the mobility model. During the simulation, the Albrecht model was chosen as the low-field mobility model, which was described as a function of doping concentration N and lattice temperature T [28]:

$$\begin{array}{l}{\displaystyle \frac{1}{\mathsf{\mu }\left({\mathrm{N},\mathrm{T}}_{ }\right)}}={\displaystyle \frac{\mathrm{a}\cdot \mathrm{N}}{{\mathrm{N}}_0}}{\left({\displaystyle \frac{{\mathrm{T}}_{ }}{{\mathrm{T}}_0}}\right)}^{-3/2}\ln \left(1+3{\left({\displaystyle \frac{{\mathrm{T}}_{ }}{{\mathrm{T}}_0}}\right)}^2{\left({\displaystyle \frac{\mathrm{N}}{{\mathrm{N}}_0}}\right)}^{-2/3}\right)\\ +\mathrm{b}{\left({\displaystyle \frac{{\mathrm{T}}_{ }}{{\mathrm{T}}_0}}\right)}^{3/2}+{\displaystyle \frac{\mathrm{c}}{\exp \left({\mathrm{T}}_1{/\mathrm{T}}_{\mathrm{L}}\right)-1}}\end{array},$$

(6)

In expression (6), a, b, c, N₀, T₀, and T₁ are set to 2.61 × 10⁻⁴ V·s·cm⁻², 2.9 × 10⁻⁴ V·s·cm⁻², 170.0 × 10⁻⁴ V·s·cm⁻², 1.0 × 10¹⁷ cm⁻³, 300 K, and 1065 K.

The high-field mobility μ(E) depends on the electric field E [29]:

$$\mathsf{\mu }\left(\mathrm{E}\right)={\displaystyle \frac{\mathsf{\mu }\left(\mathrm{N},\mathrm{T}\right){+\mathrm{V}}_{\mathrm{sat}}\frac{{\mathrm{E}}^{\mathrm{n}1-1}}{{{\mathrm{E}}_{\mathrm{c}}}^{\mathrm{n}1}}}{1+\alpha {\left(\frac{\mathrm{E}}{{\mathrm{E}}_{\mathrm{c}}}\right)}^{\mathrm{n}2}+{\left(\frac{\mathrm{E}}{{\mathrm{E}}_{\mathrm{c}}}\right)}^{\mathrm{n}1}}}$$

(7)

In this context, μ(N, T) is the low-field mobility in Equation (7). For Equation (7), V_sat, E_c, α, n1, and n2 are set to 1.9064 × 107 cm/s, 220.8936 kV/cm, 6.1973, 7.2044, and 0.7857, respectively.

In this study, the Selberherr impact ionization model was used to simulate the breakdown characteristic. In the model, the impact ionization rates for holes (α_p) and electrons (α_n) are described as [30]:

$${\mathsf{\alpha }}_{\mathrm{n}}{=\mathrm{a}}_{\mathrm{n}}\exp \left[-{\left({\displaystyle \frac{{\mathrm{b}}_{\mathrm{n}}}{\mathrm{E}}}\right)}^{\mathrm{m}}\right]$$

(8)

$${\mathsf{\alpha }}_{\mathrm{p}}{=\mathrm{a}}_{\mathrm{p}}\exp \left[-{\left({\displaystyle \frac{{\mathrm{b}}_{\mathrm{p}}}{\mathrm{E}}}\right)}^{\mathrm{m}}\right]$$

(9)

In Equations (8) and (9), the impact ionization rates of holes (α_p) and electrons (α_n) depend on the local electric field. According to the experimental results, the parameters at room temperature were set as follows: m = 1.1438 × 10⁷ cm⁻¹, a_n = 1.1438 × 10⁷ cm⁻¹, a_p = 23.8933 MV/cm, b_n = 23.8933 MV/cm, and b_p = 13.2.

3.2. Simulation Calibration

We fabricated a D-mode GaN HEMT to fit the simulation model [31]. The epitaxial structures with a dislocation density of 10⁹ cm⁻² were grown on Si substrates. The epitaxial structures consisted of a 4 nm thick GaN cap layer, a 21 nm thick AlGaN barrier layer, and a 3.2 µm thick GaN buffer layer. First, a 20 nm thick SiN_x was grown as the gate dielectric by low-pressure chemical vapor deposition (LPCVD), which was selectively etched into the gate pattern by inductively coupled plasma etching (ICP-RIE) using SF₆ mixed gas. Then, sputtered Ni/Au was deposited on the gate dielectric SiN_x as the gate electrode. The Ti/Al/Ni/Au stack was deposited and rapidly annealed at 870 °C to form the source and drain ohmic contacts. A 150 nm thick SiN_x was formed on the GaN cap layer for passivation and argon ion implantation for isolation. The gate width, gate length, gate-to-source distance, and gate-to-drain distance of the fabricated transistor were 250 µm, 2 µm, 2 µm, and 2 µm, respectively. The structural parameters used in the simulation were the same as those in the experiment. The fabricated D-mode GaN HEMT was tested by the Agilent B1505 and its test data were used to fit the models described above. The simulated threshold voltage (V_th) of GaN HEMT was −7.8 V, which is consistent with the experiment. Figure 2 presents the simulated output characteristics and the fabricated GaN HEMT output characteristics. The results demonstrate a good fitting, which proves the reliability of the simulation models for GaN HEMTs.

4. Results and Discussions

4.1. DC Properties

Figure 3a displays the transfer curves of the Conv HEMT, B-HEMTs, and HBB-HEMT. The simulation indicates that the V_th of the four devices is 1 V. Figure 3b shows that the saturation current of the four devices is 0.9 A/mm, and the on-resistance (R_{on, sp}) is 0.4 mΩ·cm² when the gate-source voltage V_gs is 4 V. Compared with Conv HEMT, the AlGaN back barrier does not affect the transfer and output characteristics of HEMT, which improves breakdown characteristics without sacrificing DC characteristics.

4.2. Breakdown Properties

The breakdown characteristics of four GaN HEMT devices were simulated. Figure 4 presents the contour plot of the electric field distribution during device breakdown. Electric field concentration occurs on the gate side in the buffer layers of Conv HEMT and B-HEMT (Al.comp = 0.1). Then, the electric field diminishes rapidly with increasing distance from the gate. However, the electric field displays a more uniform distribution for B-HEMT with an Al.comp of 0.25. Two-dimensional hole gas (2DHG) is formed at the interface between the GaN buffer layer and the AlGaN back-barrier layer due to piezoelectric polarization. The 2DHG generates an upward vertical electric field in the channel, which counteracts the downward vertical electric field caused by the positive polarization charges in the barrier layer. Consequently, by reducing the local electric field enhancement effect, the electric field distribution in the channel is more uniform. As the Al composition in the back-barrier increases, the concentration of the 2DEG also increases, which enhances the upward vertical electric field. Therefore, the electric field distribution in B-HEMT (Al.comp = 0.25) is more uniform than that in B-HEMT (Al.comp = 0.1) by further weakening the downward vertical electric field within the channel.

However, another electric field crowding region will occur near the drain electrode of B-HEMT (Al.comp = 0.25), which leads to early breakdown near the drain electrode. For the proposed HBB-HEMT, due to the modulation of the electric field by the hybrid AlGaN back-barrier structure, the electric field at the drain side is reduced, resulting in a more uniform electric field distribution across the buffer layer, channel, and passivation layer. The electric field reaches 3 MV/cm in the center of the buffer layer. The electric field modulation of the buffer layer in the hybrid AlGaN back-barrier structure primarily arises from the variance in relative permittivity between the Al₀.₂₅Ga₀.₇₅N and Al₀.₁Ga₀.₉N zones. The relative permittivity of Al_xGa_1−xN (where 0 ≤ x ≤ 1) can be computed using the following formula:

$${\mathsf{\epsilon }(\mathrm{Al}}_{\mathrm{x}}{\mathrm{Ga}}_{1-\mathrm{x}}\mathrm{N})=8.5\mathrm{x}+8.9(1-\mathrm{x})$$

(10)

The discrepancy in relative permittivity between the Al₀.₂₅Ga₀.₇₅N and Al₀.₁Ga₀.₉N zones stems from the distinct Al compositions, with relative permittivities of 8.5 and 8.9 for AlN and GaN, respectively. This variation in Al content influences the relative permittivity. Based on Gauss’s law, the electric fields of the Al₀.₂₅Ga₀.₇₅N zone (E₁) and the Al₀.₁Ga₀.₉N zone (E₂) are related as follows:

$${\mathsf{\epsilon }}_1{\mathrm{E}}_1{=\mathsf{\epsilon }}_2{\mathrm{E}}_2$$

(11)

The discrepancy in relative permittivity between the Al₀.₂₅Ga₀.₇₅N and Al₀.₁Ga₀.₉N zones is denoted by ε₁ and ε₂, respectively. This variance results in an electrical field discontinuity along the Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface. Such a discontinuity in the electrical field can then alter the electric field distributions between the gate and drain.

Figure 5a illustrates the one-dimensional electric field distribution in the channel of four devices when breakdown occurs. Electric field crowding occurs in the Conv HEMT and B-HEMTs. For Conv HEMT and B-HEMT (Al.comp = 0.1), the electric field peak is on the gate side. For B-HEMT (Al.comp = 0.25), another peak appears on the drain side, which is consistent with the results reported previously [18]. Figure 5b displays the breakdown curves of four GaN HEMTs, where V_gs is set to −3 V during the breakdown simulation. The BV of Conv HEMT is identified as 525 V, which is similar to the reported result of 510 V with similar dimensions [32]. The breakdown voltages are determined as follows: 615 V for B-HEMT (Al composition = 0.1), 940 V for B-HEMT (Al composition = 0.25), and 1225 V for the proposed HBB-HEMT, with BV defined as V_ds at I_ds = 1 μA/mm.

To improve the modulation ability of the hybrid AlGaN back barrier of the proposed HBB-HEMT, the thickness of the GaN buffer layer is optimized. Figure 6a illustrates the channel electric field distribution of the HBB-HEMT under breakdown conditions with different T_buf values. When T_buf is reduced to a minimal value (0.1 μm), the electric field peak on the gate side is eliminated, and a new electric field peak appears at the Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface. With the increase of T_buf, the electric field peak gathered on the drain side is reduced. However, when T_buf is larger than 1 μm, the electric field crowding near the gate increases. Therefore, when the GaN buffer thickness exceeds a certain threshold (1 μm), the modulation ability of the hybrid AlGaN back barrier decreases. Figure 6b shows the simulated BV of the HBB-HEMT with different T_buf values. Consistent with the results shown in Figure 6a, the highest BV (1640 V) is obtained when T_buf is 1 μm. Therefore, the optimized value of T_buf is determined to be 1 μm.

To further improve the withstand voltage capability of the HBB-HEMT, we optimized the position of the Al₀.₂₅Ga₀.₇₅N / Al₀.₁Ga₀.₉N interface. Figure 7a shows the distribution of the electric field in the channel for different L_gi values under breakdown conditions. For a given L_gd value, the electric field near the drain will decrease with a minuscule L_gi value, resulting in the overall average breakdown electric field in the channel far below the limit of the GaN. When the L_gi value is large, an electric field peak on the drain edge causes early breakdown, similar to what is seen in B-HEMT (Al.comp = 0.25) in Figure 5a. Figure 7b depicts the simulated breakdown voltage curves of HBB-HEMT with different L_gi values. As illustrated in Figure 7b, the breakdown voltage initially increases and then decreases as L_gi increases. The highest BV of 1640 V is achieved at L_gi = 4.5 μm.

Figure 8 illustrates the breakdown voltages, R_{on, sp}, and FOM of the HBB-HEMTs with different L_gd values, and for each device, the value of L_gi is set as L_gd-1.5 µm. Consistent with the GaN HEMTs reported in [17], the BV of the proposed HBB-HEMT increases with increasing L_gd. When L_gd is increased from 5 µm to 20 µm, BV is increased from 1350 V to as high as 4180 V. Compared to the results reported in [21], the proposed HBB-HEMT with the same L_gd exhibits a higher BV. Increasing L_gd can lead to a higher BV for HBB-HEMT, but also results in a higher specific on-resistance. When L_gd is increased to 20 µm, R_{on, sp} linearly increases to 2.2 mΩ·cm². Figure 8 also shows the calculated FOM for the proposed HBB-HEMT devices with different L_gd values. When L_gd is set to 10 µm, the highest FOM achieved is up to 9.3 GW/cm². When L_gd is set between 5 µm and 20 µm, the average breakdown electric field is larger than 2.6 MV/cm, and the highest average breakdown electric field (2.74 MV/cm) is obtained with a L_gd of 7 µm, which is very close to the GaN limit (3 MV/cm). The results indicate that the HBB-HEMT possesses high breakdown voltage with a large L_gd when the location of the Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface is properly designed.

Figure 9 presents the BV and R_{on, sp} values of this work and the other reported devices. Due to the effective electric field modulation capability of the hybrid AlGaN back barrier, the proposed HBB-HEMT devices demonstrate significant advantages in achieving a high BV and low R_{on, sp}. The performance of other reported GaN HEMT devices is included for comparison in Figure 9 [33,34,35,36,37,38,39]. The proposed HBB-HEMT devices exhibit a favorable balance between BV and R_{on, sp} relative to these previously reported results.

Table 2. Parameters of the device in simulations.

Year	Device	BV (V)	Ron,sp (mΩ·cm2)	FOM (MW/cm2)
2019	E-mode [33]	1000	2.8	357.1
2021	E-mode [34]	2154	2.58	1793.3
2021	E-mode [35]	1449	2.73	769.1
2022	E-mode [36]	723	1.80	290.4
2022	E-mode [37]	1781	4.4	720.9
2022	E-mode [38]	1205	2.22	654.1
2023	E-mode [39]	690	3.975	119
2024	This work	2623	0.74	9297.5

presents a comparison among various reported breakdown HEMTs. At L_gd = 10 µm, the proposed HBB-HEMT achieves a low on-resistance of 0.74 mΩ·cm² and a high breakdown voltage of 2623 V, yielding the best figure of merit (FOM) of 9.3 GW/cm² in the reported devices. Consequently, the HBB-HEMTs hold considerable promise for power electronics applications because of their high BV and low R_{on, sp}.

4.3. CV Properties

The CV characteristics of the HBB-HEMTs are shown in Figure 10. In the simulation process, we simulated the relationship between the input capacitance (C_iss), output capacitance (C_oss), reverse transfer capacitance (C_rss), and drain-source voltage (V_ds). At low drain-source voltage, the depletion region near the gate is small, resulting in a larger capacitance between the gate and drain. As the drain voltage increases, the depletion region near the gate starts to extend towards the drain, causing the channel charges between the gate and drain to be depleted. Consequently, the C_rss decreases with increasing drain voltage. This also applies to C_iss and C_oss, because both capacitances include C_rss:

$${\mathrm{C}}_{\mathrm{iss}}{=\mathrm{C}}_{\mathrm{gs}}{+\mathrm{C}}_{\mathrm{rss}}$$

(12)

$${\mathrm{C}}_{\mathrm{oss}}{=\mathrm{C}}_{\mathrm{ds}}{+\mathrm{C}}_{\mathrm{rss}}$$

(13)

However, for GaN HEMTs with a back barrier, due to a more uniform distribution of electric field in the channel, the depletion region extends further towards the gate, leading to a reduction in C_rss. From Figure 5a, it is evident that the Conv-HEMT exhibits the smallest depletion region area and thus the largest C_rss capacitance. The depletion region of the B-HEMT (Al.comp = 0.1) does not fully extend to the drain, resulting in a larger C_rss compared to the B-HEMT (Al.comp = 0.25) and HBB-HEMT. Furthermore, the presence of the back barrier enhances the confinement of the two-dimensional electron gas, thereby improving the gate’s control over the channel. Therefore, GaN HEMTs with a back barrier exhibit a slight increase in C_rss at V_ds = 0 V. In summary, C_rss decreases for the HBB-HEMT at high drain voltages, which effectively improves the device’s performance for high-frequency applications.

4.4. Neural Network Prediction

Predicting the performance of GaN HEMTs is a complex and important task. As shown in Section 4.2, traditional prediction methods normally rely on many experiments or simulations. The BP algorithm-based neural network is a feedforward neural network. It works by updating the network’s weights and biases using the backpropagation algorithm to minimize the loss function. The BP neural network has strong nonlinear modeling ability, parallel processing capability, and various optimization algorithms, making it advantageous for handling complex data from multiple physical mechanisms. To improve the efficiency of GaN HEMT performance prediction, a BP neural network model was trained in this paper and predicted the breakdown voltage of the HBB-HEMT.

4.4.1. Data Collection

For the HBB-HEMT, the distance of the gate to drain, the thickness of the GaN buffer, and the distance of the gate to the Al₀.₂₅Ga₀.₇₅N/Al₀.₁Ga₀.₉N interface significantly impacted the breakdown voltage. Consequently, these three parameters were set as input variables, with the breakdown voltage as the output parameter. The value of L_gi is closely related to L_gd. Based on the optimization results from the simulations, the buffer layer thickness range was set from 0.1 to 4 µm. Since the range of L_gi is dependent on L_gd, L_gi was set from 0 to L_gd, and L_gd was set from 5 to 20 µm.

Table 3. Parameters of devices in simulations.

Parameter	Value
Lgi	0, 2, 3, 4,……, Lgd
Lgd	5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Tbuf	0.1, 0.5, 1, 2, 3, 4

provides the specific values for each input parameter.

Simulations were conducted on 1296 different input parameter sets for the HBB-HEMT using TCAD Silvaco. After excluding some non-convergent results, a total of 1171 sets of breakdown voltage data with different input parameters was obtained. These simulation results were randomly divided into three groups: the training set, validation set, and test set, containing 937, 117, and 117 data points, respectively, corresponding to 80%, 10%, and 10% of the total data.

4.4.2. Establishment of Neural Network

To improve prediction accuracy, a BP neural network based on the Levenberg–Marquardt algorithm was constructed. As shown in Figure 11, the neural network architecture consisted of an input layer, a hidden layer, and an output layer. The input layer of the network had 3 neurons, representing L_gi, L_gd, and T_buf, respectively. The output layer had 1 neuron, representing the breakdown voltage of the HBB-HEMT. The hidden layer contained 10 neurons. During the training of the BP neural network, the maximum iterations were set to 1000, the error threshold to 0.0001, and the learning rate to 0.01.

All simulation data were fed into the initial BP neural network model for training. Figure 12 shows the loss during the training, validation, and testing processes. When the number of iterations was greater than 7, the loss tended to be stable as the number of iterations increased. The final R coefficient values of the trained BP neural network model are shown in Figure 13. In Figure 13, the correlation coefficients R for the training set and validation set are both 0.99, which is close to 1, indicating the accuracy of the neural network model without significant overfitting. The correlation coefficient R for the test set is also 0.99, demonstrating that the trained model has sufficient generalization capability and accurate prediction ability. Figure 14 compares the predicted data from the BP neural network model with the simulation data. The average prediction error of the data comparison is 4.59%. Therefore, the BP neural network using the LM algorithm predicts the breakdown voltage of the HBB-HEMT very close to the actual values.

5. Conclusions

A novel HBB-HEMT was designed and optimized in this work. The hybrid AlGaN back-barrier structure could effectively modulate the electric field distributions without sacrificing forward characteristics. After proper design and optimization, the proposed HBB-HEMT achieved a high BV (1640 V), which was 212% higher than the conventional HEMT, a low R_{on, sp} (0.4 mΩ·cm²) and a high FOM (7.3 GW/cm²). This performance was attained with an L_gd of 6 µm, an L_gi of 4.5 µm, and a T_buf of 1 µm. For the HBB-HEMT, the highest average breakdown electric field (2.73 MV/cm) was very close to the GaN limit, which was two times higher than that of the conventional GaN HEMT (0.88 MV/cm). Ultimately, the neural network model was used to predict the breakdown voltage of HBB-HEMTs. An average error of less than 5% indicates the accuracy of the predictive model, highlighting its significance for enhancing the efficiency of GaN HEMT design optimization.