*Article* **Enhanced Operational Characteristics Attained by Applying HfO<sup>2</sup> as Passivation in AlGaN/GaN High-Electron-Mobility Transistors: A Simulation Study**

**Jun-Hyeok Choi <sup>1</sup> , Woo-Seok Kang <sup>1</sup> , Dohyung Kim <sup>1</sup> , Ji-Hun Kim <sup>1</sup> , Jun-Ho Lee <sup>1</sup> , Kyeong-Yong Kim <sup>1</sup> , Byoung-Gue Min <sup>2</sup> , Dong Min Kang <sup>2</sup> and Hyun-Seok Kim 1,\***


**Abstract:** This study investigates the operating characteristics of AlGaN/GaN high-electron-mobility transistors (HEMTs) by applying HfO<sup>2</sup> as the passivation layer. Before analyzing HEMTs with various passivation structures, modeling parameters were derived from the measured data of fabricated HEMT with Si3N<sup>4</sup> passivation to ensure the reliability of the simulation. Subsequently, we proposed new structures by dividing the single Si3N<sup>4</sup> passivation into a bilayer (first and second) and applying HfO<sup>2</sup> to the bilayer and first passivation layer only. Ultimately, we analyzed and compared the operational characteristics of the HEMTs considering the basic Si3N<sup>4</sup> , only HfO<sup>2</sup> , and HfO2/Si3N<sup>4</sup> (hybrid) as passivation layers. The breakdown voltage of the AlGaN/GaN HEMT having only HfO<sup>2</sup> passivation was improved by up to 19%, compared to the basic Si3N<sup>4</sup> passivation structure, but the frequency characteristics deteriorated. In order to compensate for the degraded RF characteristics, we modified the second Si3N<sup>4</sup> passivation thickness of the hybrid passivation structure from 150 nm to 450 nm. We confirmed that the hybrid passivation structure with 350-nm-thick second Si3N<sup>4</sup> passivation not only improves the breakdown voltage by 15% but also secures RF performance. Consequently, Johnson's figure-of-merit, which is commonly used to judge RF performance, was improved by up to 5% compared to the basic Si3N<sup>4</sup> passivation structure.

**Keywords:** AlGaN/GaN; high-electron-mobility transistor; passivation; HfO<sup>2</sup>

### **1. Introduction**

Generally, AlGaN/GaN high-electron-mobility transistors (HEMTs) are widely adopted in power electronics because of their outstanding electronic and material properties, such as high-critical electric field (~3.3 MV/cm) and wide energy bandgap (3.4 eV). Interestingly, these remarkable characteristics make GaN more practicable for high-power and high-frequency applications compared to other materials [1]. Hence, due to these material characteristics, AlGaN/GaN HEMTs exhibit high electron saturation velocity as well as high current density, high thermal reliability, and high breakdown voltage (VBD) [2–4]. In addition, HEMTs based on the AlGaN/GaN heterostructure show admirable performances via a two-dimensional electron gas (2-DEG) in the channel generated by the spontaneous and piezoelectric polarization effects [5,6]. Nevertheless, to sufficiently satisfy the market requirements, GaN-based HEMTs require further research for high-voltage and highfrequency applications [7–9]. It has been demonstrated that the field-plate structures in GaN-based HEMTs are commonly used to increase the VBD, resulting in operational stability and reliability. However, the frequency characteristics are degraded due to the increase in parasitic capacitances, such as the gate-to-source capacitance (Cgs) and gate-to-drain

**Citation:** Choi, J.-H.; Kang, W.-S.; Kim, D.; Kim, J.-H.; Lee, J.-H.; Kim, K.-Y.; Min, B.-G.; Kang, D.M.; Kim, H.-S. Enhanced Operational Characteristics Attained by Applying HfO<sup>2</sup> as Passivation in AlGaN/GaN High-Electron-Mobility Transistors: A Simulation Study. *Micromachines* **2023**, *14*, 1101. https://doi.org/ 10.3390/mi14061101

Academic Editors: Zeheng Wang and Jingkai Huang

Received: 27 April 2023 Revised: 22 May 2023 Accepted: 22 May 2023 Published: 23 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

capacitance (Cgd) [10,11]. This clearly shows the advantages and disadvantages of applying field-plates in GaN-based HEMTs due to trade-off between DC and RF characteristics. Additionally, many studies are being conducted to improve the devices' performance [12,13]. As an alternative to HEMTs with field-plate structure, we employed HfO<sup>2</sup> as the passivation to enhance VBD. Interestingly, HfO<sup>2</sup> has a high dielectric constant (~25) and large bandgap energy (5.7 eV), both of which may be exploited to improve the devices' performance in comparison with the basic GaN-based HEMTs with Si3N<sup>4</sup> passivation [14]. Based on these material properties, it is anticipated that the leakage current and VBD characteristics can be improved. However, HfO<sup>2</sup> passivation in HEMTs also produces additional parasitic capacitances, which may degrade their frequency characteristics. Thus, we suggested the additional structures to secure RF performance while applying HfO<sup>2</sup> as a passivation layer.

In this article, we compare and analyze three different passivation structures which use the basic Si3N4, only HfO2, and HfO2/Si3N<sup>4</sup> (hybrid), respectively, as passivation materials. Compared to the basic Si3N<sup>4</sup> passivation structure, we confirmed that the VBD of the HfO<sup>2</sup> passivation structure improved by approximately 18.8%, but its frequency characteristics were significantly degraded. Meanwhile, the hybrid passivation structure exhibited a slightly reduced VBD, but its frequency characteristics were improved to approximately twice that of the HfO<sup>2</sup> passivation structure. Thus, we optimized the second Si3N<sup>4</sup> passivation thickness in the hybrid passivation structure to further increase its RF performance. Consequently, the various passivation structures in terms of VBD, on-resistance (Ron), and cut-off frequency (fT) were evaluated using the standard lateral figure-of-merit (LFOM) (=VBD <sup>2</sup>/Ron) and Johnson's figure-of-merit (JFOM) (=f<sup>T</sup> <sup>×</sup> <sup>V</sup>BD) [15–17].

#### **2. Materials and Methods**

To obtain a reasonable simulation criterion, we first analyzed the fabricated HEMT with a 0.15-µm planar-gate structure [18]. The AlGaN/GaN HEMTs were grown on a 4-inch SiC substrate by using metal–organic chemical vapor deposition. More precisely, the epitaxial layers were composed of a 0.2-µm-thick nucleation layer, a Fe-doped 2-µm-thick GaN buffer layer, and a 25-nm-thick Al0.25Ga0.75N barrier layer. Additionally, the Ohmic metallization of the device was formed by Ti/Al/Ni/Au evaporation followed by rapid thermal annealing at 775 ◦C for 30 s, and device isolation was achieved by P<sup>+</sup> ion implantation. Next, a 50-nm-thick 1st Si3N<sup>4</sup> passivation layer was deposited by using plasma-enhanced chemical vapor deposition (PECVD). The first metal interconnections with the Ohmic contacts were formed by the Ti/Au evaporation after etching the 1st Si3N<sup>4</sup> passivation layer. Further, a planar gate was formed by using single-layer electron beam lithography. More precisely, a gate foot length of 0.15 µm was obtained by electron-beam exposure using poly methyl methacrylate resist, and the 1st Si3N<sup>4</sup> passivation layer underneath the gate pattern was removed by inductively coupled plasma dry etching. Ni/Au planar-gate metal stack was deposited by electron-beam evaporation and lift-off processes. After this, a 250-nm-thick 2nd Si3N<sup>4</sup> PECVD film was deposited for device passivation. A sourceconnected field-plate was formed by using the Ti/Au metal and lift-off process. Finally, the wafer-thinning and backside via-hole process was performed. The scanning electron microscope (SEM) image of the fabricated planar gate AlGaN/GaN HEMT is shown in Figure 1a.

Figure 1b shows the schematic diagram of the basic Si3N<sup>4</sup> passivation structure of the HEMT. Based on the fabricated device, we determined the structural and material parameters to be utilized for modeling without any other structural changes, such as changes to the planar-gate electrode structure, and while retaining the same gate footlength of 0.15 µm, including the epitaxial layer. Table 1 provides the specific geometrical parameter information of the basic Si3N<sup>4</sup> passivation structure used in the simulation.

**Figure 1.** A cross-sectional schematic of the fabricated planar gate AlGaN/GaN high-electron-mobility transistor (HEMT) structure: (**a**) scanning electron microscope (SEM) image; and (**b**) an illustration used in modeling. The S, D, G, and S-FP represent the source, drain, gate, and source-connected field-plate, respectively; each number (1–6) is explained in Table 1. **Figure 1.** A cross-sectional schematic of the fabricated planar gate AlGaN/GaN high-electronmobility transistor (HEMT) structure: (**a**) scanning electron microscope (SEM) image; and (**b**) an illustration used in modeling. The S, D, G, and S-FP represent the source, drain, gate, and sourceconnected field-plate, respectively; each number (1–6) is explained in Table 1.



⑥ Lୋୟ୲ୣିୌୣ୧୦୲ 0.44 Field-plate thickness 0.44 1st passivation 0.05 2nd passivation 0.25 AlGaN barrier 0.025 GaN buffer 2 Nucleation layer 0.2 In this simulation study, it is essential to initialize the material and simulation parameters in order to accurately confirm the operating characteristics of the device. The specific material parameters of GaN and AlGaN used for simulation are summarized in Table 2. As shown in Table 2, we subdivided the FMCT (Farahmand-modified Caughey – Thomas) and GANSAT electron mobility models based on the electric field within the device [19]. Additionally, heat models were applied in the simulation to implement the actual device performance for accurate simulation results. Additionally, acceptor-trap dop-In this simulation study, it is essential to initialize the material and simulation parameters in order to accurately confirm the operating characteristics of the device. The specific material parameters of GaN and AlGaN used for simulation are summarized in Table 2. As shown in Table 2, we subdivided the FMCT (Farahmand-modified Caughey–Thomas) and GANSAT electron mobility models based on the electric field within the device [19]. Additionally, heat models were applied in the simulation to implement the actual device performance for accurate simulation results. Additionally, acceptor-trap doping in Al-GaN/GaN HEMTs is generally used to improve the VBD by reducing the substrate leakage current [20]. However, current-collapse phenomena such as drain-lag and gate-lag inevitably occur [21]. Therefore, a properly controlled acceptor-trap doping is essential to achieve high-performance HEMTs. The Gaussian acceptor doping profile is applied in the simulation by using Fe (iron). More precisely, the peak acceptor-trap doping concentration is set to 1018/cm<sup>2</sup> in the GaN buffer layer and gradually decreases according to the Gaussian distribution, resulting in an acceptor-trap doping concentration below 1015/cm<sup>2</sup> at the interface between AlGaN and GaN.

ing in AlGaN/GaN HEMTs is generally used to improve the Vୈ by reducing the substrate leakage current [20]. However, current-collapse phenomena such as drain-lag and gate-lag inevitably occur [21]. Therefore, a properly controlled acceptor-trap doping is essential to achieve high-performance HEMTs. The Gaussian acceptor doping profile is applied in the simulation by using Fe (iron). More precisely, the peak acceptor-trap doping concentration is set to 1018/cm2 in the GaN buffer layer and gradually decreases according


**Table 2.** Material parameters used in the simulation at a temperature of 300 K (SRH: Shockley–Read–Hall).

In order to conduct an accurate device simulation by considering the self-heating effect (SHE), we applied physical models to calculate the heat generation within the device [22,23]. First, we used the lattice heat flow equation,

$$\mathbf{C}\frac{\partial \mathbf{T}\_{\mathrm{L}}}{\partial \mathbf{t}} = \nabla(\kappa \nabla \mathbf{T}\_{\mathrm{L}}) + \mathbf{H} \tag{1}$$

where C is the heat capacitance per unit volume, κ is the thermal conductivity coefficient, H is the heat generation, and T<sup>L</sup> is the local lattice temperature. More precisely, the thermal conductivity, which is important to calculate the SHE in a device simulation, is commonly temperature-dependent. Therefore, we applied the thermal conductivity model,

$$\kappa(\mathbf{T}) = (\mathbf{TC.CONST}) / (\mathbf{T\_L}/300)^{\mathbf{TC.NPOW}} \tag{2}$$

where TC.CONST is the thermal conductivity constant at 300 K and TC.NPOW is the calibration factor which is an experimental value. The applied TC.CONST and TC.NPOW parameters of GaN, AlGaN, and SiC-4H are summarized in the Table 3 [24].


**Table 3.** Thermal parameters used for the thermal conductivity model.

We investigated the relationship between parasitic capacitances and frequency characteristics. The capacitance equation can be expressed by:

$$\mathbf{C} = \frac{\varepsilon\_{\partial} \varepsilon\_{r}}{d} A \tag{3}$$

where C is the capacitance, *ε<sup>o</sup>* is the permittivity of free space (constant value), *ε<sup>r</sup>* is the dielectric constant of the material, *A* is the area of overlap of the two electrodes, and *d* is the electrode separation distance. As expressed in Equation (3), *ε<sup>r</sup>* and *d* have a significant influence on the change in capacitance.

Next, f<sup>T</sup> and maximum oscillation frequency (fmax) were explained by Equations (4) and (5):

$$\mathbf{f\_T} = \frac{\mathbf{g\_m}}{2\pi \left(\mathbf{C\_{gs}} + \mathbf{C\_{gd}}\right)} \approx \frac{\mathbf{g\_m}}{2\pi \mathbf{C\_{gs}}} \tag{4}$$

$$\mathbf{f\_{max}} = \frac{\mathbf{f\_{\Gamma}}}{2\sqrt{\pi \mathbf{f\_{\Gamma}} \mathbf{C\_{gd}} (\mathbf{R\_{\\$}} + \mathbf{R\_{\\$}} + \mathbf{R\_{\\$}} + 2\pi \mathbf{I\_{s}}) + \mathbf{G\_{ds}} (\mathbf{R\_{\\$}} + \mathbf{R\_{\\$}} + \mathbf{R\_{\\$}} + \pi \mathbf{f\_{\Gamma}} \mathbf{L\_{s}})} \approx \sqrt{\frac{\mathbf{f\_{\Gamma}}}{8\pi \mathbf{R\_{\\$}} \mathbf{C\_{gd}}}} \tag{5}$$

where gm, Cgs, and Cgd represent the transconductance, gate-to-source capacitance, and gate-to-drain capacitance, respectively. As described in Equation (4), decreasing the parasitic capacitances, such as Cgs and Cgd, increases the fT. The Rs, Rg, Rgs, Ls, and Gds are the source resistance, gate resistance, gate-to-source resistance, parasitic source inductance, and output conductance, respectively [25]. Equation (5) shows that R<sup>g</sup> and Cgd must be reduced to achieve a higher fmax. Additionally, as f<sup>T</sup> increases, fmax also increases, as shown in Equation (5). sitic capacitances, such as Cୱ and Cୢ , increases the f . The Rୱ , R , Rୱ , ୱ , and Gୢୱ are the source resistance, gate resistance, gate-to-source resistance, parasitic source inductance, and output conductance, respectively [25]. Equation (5) shows that R and Cୢ must be reduced to achieve a higher f୫ୟ୶ . Additionally, as f increases, f୫ୟ୶ also increases, as shown in Equation (5).

where g୫, Cୱ, and Cୢ represent the transconductance, gate-to-source capacitance, and gate-to-drain capacitance, respectively. As described in Equation (4), decreasing the para-

<sup>≈</sup> <sup>ඨ</sup> f

8πRCୢ (5)

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2ටπfCୢ(Rୱ + R + Rୱ + 2πLୱ)+Gୢୱ ൫Rୱ + R + Rୱ + πfLୱ൯

#### **3. Results 3. Results**

f୫ୟ୶ <sup>=</sup> f

*3.1. Basic Si3N<sup>4</sup> Passivation Structure of HEMT Modeling Verified by Matching the Simulation's Results with the Measured Data 3.1. Basic Si3N4 Passivation Structure of HEMT Modeling Verified by Matching the Simulation's Results with the Measured Data* 

In this work, we matched the simulated drain current-gate voltage (IDS-VGS) transfer and f<sup>T</sup> with the measured data of the fabricated basic Si3N<sup>4</sup> passivation structure of the HEMT to ensure the simulation's reliability. The measured datum of the drain current at a gate voltage of 0 V (Idss) was 898.71 mA/mm, which was similar to the simulated datum of 914.90 mA/mm. Furthermore, the measured maximum transconductance (Gm) was 344.17 mS/mm, which corresponds to the simulated value of 349.60 mS/mm. The above results for maintaining the threshold voltage (Vth) at −3.8 V were confirmed. Therefore, by adjusting the simulation's parameters, Idss, Gm, and Vth values of the simulation and the corresponding measured results were matched within 1.8% of the maximum error rate, as shown in Figure 2a. A dip of the simulated transconductance around-gate voltage of −2.4 V was found, since two different field-dependent electron mobility models were used, as represented in Table 2. The exact criterion for determining the field within the device as low or high remains unknown, but a slight dip in simulated transconductance can occur at an obscure boundary of these models. The IDS–VGS transfer of the fabricated device was measured by using a Cascade Microtech Summit 12,000 probe station and a HP4142B Modular DC Source/Monitor probe station. In this work, we matched the simulated drain current-gate voltage (Iୈୗ-Vୋୗ) transfer and f with the measured data of the fabricated basic Si3N4 passivation structure of the HEMT to ensure the simulation's reliability. The measured datum of the drain current at a gate voltage of 0 V (Iୢୱୱ) was 898.71 mA/mm, which was similar to the simulated datum of 914.90 mA/mm. Furthermore, the measured maximum transconductance (G୫ ) was 344.17 mS/mm, which corresponds to the simulated value of 349.60 mS/mm. The above results for maintaining the threshold voltage (V୲୦) at −3.8 V were confirmed. Therefore, by adjusting the simulation's parameters, Iୢୱୱ, G୫, and V୲୦ values of the simulation and the corresponding measured results were matched within 1.8% of the maximum error rate, as shown in Figure 2a. A dip of the simulated transconductance around-gate voltage of −2.4 V was found, since two different field-dependent electron mobility models were used, as represented in Table 2. The exact criterion for determining the field within the device as low or high remains unknown, but a slight dip in simulated transconductance can occur at an obscure boundary of these models. The Iୈୗ–Vୋୗ transfer of the fabricated device was measured by using a Cascade Microtech Summit 12,000 probe station and a HP4142B Modular DC Source/Monitor probe station.

**Figure 2.** (**a**) The measured and simulated drain current-gate voltage (Iୈୗ– Vୋୗ) transfer characteristics of a basic Si3N4 passivation structure of the HEMT at a drain voltage (Vୈୗ) of 10 V. The black and blue arrows represent drain current and transconductance, respectively; and (**b**) the measured and simulated current gain of a basic Si3N4 passivation structure of the HEMT as a function of frequency at Vୈୗ = 20 V and gate voltage (Vୋୗ) = −2.6 V. **Figure 2.** (**a**) The measured and simulated drain current-gate voltage (IDS–VGS) transfer characteristics of a basic Si3N<sup>4</sup> passivation structure of the HEMT at a drain voltage (VDS ) of 10 V. The black and blue arrows represent drain current and transconductance, respectively; and (**b**) the measured and simulated current gain of a basic Si3N<sup>4</sup> passivation structure of the HEMT as a function of frequency at VDS = 20 V and gate voltage (VGS ) = −2.6 V.

The simulated and measured f<sup>T</sup> of the basic Si3N<sup>4</sup> passivation structure of HEMT are shown in Figure 2b. As regards the RF characteristics, the bias points of the simulated results and the measured data were a drain voltage of 20 V and gate voltage of −2.6 V, which were selected since the frequency characteristics were outstanding in comparison to other bias points. More specifically, the f<sup>T</sup> was defined as the intersection of the x-axis and the extension line at the point of current gain (H21), with a slope of −20 dB/decade [26]. The measured and simulated values of the f<sup>T</sup> were 25.19 GHz and 24.64 GHz, respectively. This

clearly shows that the simulated f<sup>T</sup> was accurate enough when compared to the measured values, as the error rate was only 2.2%. PNA-X N5245A network analyzer was used to analyze the f<sup>T</sup> of the device within the frequency range from 0.5 to 50 GHz. the measured values, as the error rate was only 2.2%. PNA-X N5245A network analyzer was used to analyze the f of the device within the frequency range from 0.5 to 50 GHz. *3.2. Comparative Analysis between HEMTs with Si3N4, HfO2, and Hybrid Passivation* 

The simulated and measured f of the basic Si3N4 passivation structure of HEMT are shown in Figure 2b. As regards the RF characteristics, the bias points of the simulated results and the measured data were a drain voltage of 20 V and gate voltage of −2.6 V, which were selected since the frequency characteristics were outstanding in comparison to other bias points. More specifically, the f was defined as the intersection of the x-axis and the extension line at the point of current gain (H21), with a slope of −20 dB/decade [26]. The measured and simulated values of the f were 25.19 GHz and 24.64 GHz, respectively. This clearly shows that the simulated f was accurate enough when compared to

#### *3.2. Comparative Analysis between HEMTs with Si3N4, HfO2, and Hybrid Passivation Structures Structures*

To enhance the operational characteristics, we suggested two structures, as shown in Figure 3. Figure 3a shows the HfO<sup>2</sup> passivation structure of the HEMT. As shown in Figure 3b, the hybrid passivation structure consists of first and second passivation layers, which are composed of HfO<sup>2</sup> and Si3N4, respectively. Specifically, these passivation structures will exhibit enhanced DC characteristics, including the VBD, as compared to the basic Si3N<sup>4</sup> passivation structure, because of the material properties of HfO2. The other structural parameters excluding the passivation material were not changed in the simulation. To enhance the operational characteristics, we suggested two structures, as shown in Figure 3. Figure 3a shows the HfO2 passivation structure of the HEMT. As shown in Figure 3b, the hybrid passivation structure consists of first and second passivation layers, which are composed of HfO2 and Si3N4, respectively. Specifically, these passivation structures will exhibit enhanced DC characteristics, including the Vୈ, as compared to the basic Si3N4 passivation structure, because of the material properties of HfO2. The other structural parameters excluding the passivation material were not changed in the simulation.

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**Figure 3.** The schematics of various passivation structures for the AlGaN/GaN HEMT: (**a**) HfO2 passivation structure; and (**b**) hybrid passivation structure. **Figure 3.** The schematics of various passivation structures for the AlGaN/GaN HEMT: (**a**) HfO<sup>2</sup> passivation structure; and (**b**) hybrid passivation structure.

#### 3.2.1. Analysis of DC Characteristics 3.2.1. Analysis of DC Characteristics

First, we analyzed the DC characteristics of the HfO2 and hybrid passivation-structures, and then compared them to the basic Si3N4 passivation-structure. Figure 4a shows the Iୈୗ– Vୋୗ transfer characteristics of all three structures at a drain voltage of 10 V. Among them, the HfO2 passivation structure slightly improved not only the drain current, but also the transconductance, in comparison with the basic Si3N4 passivation structure. Interestingly, these results show that R୭୬ decreases as HfO2 is employed in passivation [27]. The drain current-drain voltage (Iୈୗ– Vୈୗ) characteristics were simulated at the gate voltages of −5, −4, −3, −2, −1, and 0 V, respectively, as shown in Figure 4b. As the higher gate voltage was applied, the electron concentration in the channel region increased, resulting in a large drain current. However, a decrease in drain current was observed as the drain voltage increased. These results may be explained by SHE, since applying a higher voltage leads to a higher heat generation, resulting in the degradation of the DC characteristics [28–30]. When the applied drain voltage increased, a strong electric field was generated within the device. Due to the large electric field, phonon scattering was observed to reduce the electron mobility and current density. Although the SHE occurred in all three structures, the HfO2 passivation and hybrid passivation structures exhibited a higher drain current than did the basic Si3N4 passivation structure. In addition, R୭୬ was First, we analyzed the DC characteristics of the HfO<sup>2</sup> and hybrid passivation-structures, and then compared them to the basic Si3N<sup>4</sup> passivation-structure. Figure 4a shows the IDS–VGS transfer characteristics of all three structures at a drain voltage of 10 V. Among them, the HfO<sup>2</sup> passivation structure slightly improved not only the drain current, but also the transconductance, in comparison with the basic Si3N<sup>4</sup> passivation structure. Interestingly, these results show that Ron decreases as HfO<sup>2</sup> is employed in passivation [27]. The drain current-drain voltage (IDS–VDS) characteristics were simulated at the gate voltages of −5, −4, −3, −2, −1, and 0 V, respectively, as shown in Figure 4b. As the higher gate voltage was applied, the electron concentration in the channel region increased, resulting in a large drain current. However, a decrease in drain current was observed as the drain voltage increased. These results may be explained by SHE, since applying a higher voltage leads to a higher heat generation, resulting in the degradation of the DC characteristics [28–30]. When the applied drain voltage increased, a strong electric field was generated within the device. Due to the large electric field, phonon scattering was observed to reduce the electron mobility and current density. Although the SHE occurred in all three structures, the HfO<sup>2</sup> passivation and hybrid passivation structures exhibited a higher drain current than did the basic Si3N<sup>4</sup> passivation structure. In addition, Ron was calculated to be 4.02, 3.84, and 3.97 Ω-mm for the basic Si3N4, HfO2, and hybrid passivation structures, respectively.

Figure 5a shows the electric field distribution in the channel layer under a drain voltage of 200 V. In comparison with the basic Si3N<sup>4</sup> passivation structure, the HfO<sup>2</sup> and hybrid passivation structures demonstrated that the peak electric field in the channel layer was reduced and dispersed due to the high dielectric constant of HfO2. As the peak electric field increased, impact ionization, which causes the generation of electron-hole pairs, became severe. Thus, the redistribution of the electric field effectively improved the VBD. Specifically, the VBD values of the Si3N4, HfO2, and hybrid passivation structures were 232.47, 276.27, and 268.41 V, respectively, as shown in Figure 5b. After applying a

voltage of −7 V to the gate to completely turn off the device, the drain voltage when the drain current exceeded 1 mA/mm was defined as the VBD. Figure 5c compares the drain leakage current for the three different passivation structures. Particularly, the structures where HfO<sup>2</sup> is applied to the passivation layer can show that the 2-DEG confinement in the channel region can be improved due to the wide bandgap energy of HfO2, reducing the leakage current. Therefore, the HfO<sup>2</sup> passivation structure exhibited the least drain leakage current among the three [31,32]. *Micromachines* **2023**, *14*, x FOR PEER REVIEW 7 of 14 calculated to be 4.02, 3.84, and 3.97 Ω-mm for the basic Si3N4, HfO2, and hybrid passivation structures, respectively. (**a**) (**b**)

**Figure 4.** The DC simulation results of Si3N4, HfO2, and hybrid passivation structures: (**a**) Iୈୗ– Vୋୗ

calculated to be 4.02, 3.84, and 3.97 Ω-mm for the basic Si3N4, HfO2, and hybrid passivation

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structures, respectively.

**Figure 4.** The DC simulation results of Si3N4, HfO2, and hybrid passivation structures: (**a**) Iୈୗ– Vୋୗ transfer at Vୈୗ = 10 V. The black and blue arrows represent drain current and transconductance, respectively; (**b**) drain current-drain voltage (Iୈୗ-Vୈୗ) characteristics at Vୋୗ = −5, −4, −3, −2, −1, and 0 V. **Figure 4.** The DC simulation results of Si3N<sup>4</sup> , HfO<sup>2</sup> , and hybrid passivation structures: (**a**) IDS–VGS transfer at VDS = 10 V. The black and blue arrows represent drain current and transconductance, respectively; (**b**) drain current-drain voltage (IDS -VDS ) characteristics at VGS = −5, −4, −3, −2, −1, and 0 V. HfO2 is applied to the passivation layer can show that the 2-DEG confinement in the channel region can be improved due to the wide bandgap energy of HfO2, reducing the leakage current. Therefore, the HfO2 passivation structure exhibited the least drain leakage current among the three [31,32].

**Figure 5.** *Cont*.

(**a**) (**b**)

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**Figure 5.** The DC simulation results of Si3N4, HfO2, and hybrid passivation structures: (**a**) electric field distribution in the channel region; (**b**) off-state breakdown voltage; and (**c**) off-state drain leakage current. **Figure 5.** The DC simulation results of Si3N<sup>4</sup> , HfO<sup>2</sup> , and hybrid passivation structures: (**a**) electric field distribution in the channel region; (**b**) off-state breakdown voltage; and (**c**) off-state drain leakage current. **Figure 5.** The DC simulation results of Si3N4, HfO2, and hybrid passivation structures: (**a**) electric field distribution in the channel region; (**b**) off-state breakdown voltage; and (**c**) off-state drain leakage current.

#### 3.2.2. Analysis of the RF Characteristics 3.2.2. Analysis of the RF Characteristics 3.2.2. Analysis of the RF Characteristics

Figure 6 shows the parasitic capacitance characteristics for Si3N4, HfO2, and hybrid passivation structures. Specifically, the Cୱ and Cୢ were obtained at a drain voltage of 20 V and a gate voltage of −2.6 V. As shown in Figures 6 (a) and (b), the HfO2 passivation structure shows the highest Cୱ and Cୢ, since the dielectric constant of HfO2 is larger than that of Si3N4, which is explained by Equation (3). In addition, the parasitic capacitance values of the hybrid passivation structure were smaller than that of the HfO2 passivation structure. This is because the HfO2 passivation thickness was thinner in the hybrid passivation structure compared to the HfO2 passivation structure. Therefore, the parasitic ca-Figure 6 shows the parasitic capacitance characteristics for Si3N4, HfO2, and hybrid passivation structures. Specifically, the Cgs and Cgd were obtained at a drain voltage of 20 V and a gate voltage of −2.6 V. As shown in Figure 6a,b, the HfO<sup>2</sup> passivation structure shows the highest Cgs and Cgd, since the dielectric constant of HfO<sup>2</sup> is larger than that of Si3N4, which is explained by Equation (3). In addition, the parasitic capacitance values of the hybrid passivation structure were smaller than that of the HfO<sup>2</sup> passivation structure. This is because the HfO<sup>2</sup> passivation thickness was thinner in the hybrid passivation structure compared to the HfO<sup>2</sup> passivation structure. Therefore, the parasitic capacitances tended to increase as more HfO<sup>2</sup> was used in the passivation layer. Figure 6 shows the parasitic capacitance characteristics for Si3N4, HfO2, and hybrid passivation structures. Specifically, the Cୱ and Cୢ were obtained at a drain voltage of 20 V and a gate voltage of −2.6 V. As shown in Figures 6 (a) and (b), the HfO2 passivation structure shows the highest Cୱ and Cୢ, since the dielectric constant of HfO2 is larger than that of Si3N4, which is explained by Equation (3). In addition, the parasitic capacitance values of the hybrid passivation structure were smaller than that of the HfO2 passivation structure. This is because the HfO2 passivation thickness was thinner in the hybrid passivation structure compared to the HfO2 passivation structure. Therefore, the parasitic capacitances tended to increase as more HfO2 was used in the passivation layer.

pacitances tended to increase as more HfO2 was used in the passivation layer.

(**a**) (**b**) **Figure 6.** The parasitic capacitance characteristics of Si3N4, HfO2, and hybrid passivation structures: **Figure 6.** The parasitic capacitance characteristics of Si3N4, HfO2, and hybrid passivation structures: (**a**) gate-to-source capacitance; and (**b**) gate-to-drain capacitance. **Figure 6.** The parasitic capacitance characteristics of Si3N<sup>4</sup> , HfO<sup>2</sup> , and hybrid passivation structures: (**a**) gate-to-source capacitance; and (**b**) gate-to-drain capacitance.

Figure 7 represents the simulated f and f୫ୟ୶ of the three different passivation structures. Similarly, as the capacitance simulations, f and f୫ୟ୶, were obtained at a drain voltage of 20 V and a gate voltage of −2.6 V. More precisely, the f values are 24.64, 10.17, and 20.50 GHz for the basic Si3N4 passivation, HfO2 passivation, and hybrid passivation Figure 7 represents the simulated f and f୫ୟ୶ of the three different passivation structures. Similarly, as the capacitance simulations, f and f୫ୟ୶, were obtained at a drain voltage of 20 V and a gate voltage of −2.6 V. More precisely, the f values are 24.64, 10.17, and 20.50 GHz for the basic Si3N4 passivation, HfO2 passivation, and hybrid passivation structures, respectively. The f values of the HfO2 and hybrid passivation structures were decreased by 58.7% and 16.8% compared to the basic Si3N4 passivation structure, respec-Figure 7 represents the simulated f<sup>T</sup> and fmax of the three different passivation structures. Similarly, as the capacitance simulations, f<sup>T</sup> and fmax, were obtained at a drain voltage of 20 V and a gate voltage of −2.6 V. More precisely, the f<sup>T</sup> values are 24.64, 10.17, and 20.50 GHz for the basic Si3N<sup>4</sup> passivation, HfO<sup>2</sup> passivation, and hybrid passivation structures, respectively. The f<sup>T</sup> values of the HfO<sup>2</sup> and hybrid passivation structures

structures, respectively. The f values of the HfO2 and hybrid passivation structures were decreased by 58.7% and 16.8% compared to the basic Si3N4 passivation structure, respec-

tively. According to Equation (4), the f values of the three passivation structures may

(**a**) gate-to-source capacitance; and (**b**) gate-to-drain capacitance.

were decreased by 58.7% and 16.8% compared to the basic Si3N<sup>4</sup> passivation structure, respectively. According to Equation (4), the f<sup>T</sup> values of the three passivation structures may have been influenced by the g<sup>m</sup> and Cgs. In addition, the fmax values of the basic Si3N<sup>4</sup> passivation, HfO<sup>2</sup> passivation, and hybrid passivation structures are 110.28, 48.72, and 88.53 GHz, respectively. It can be seen that fmax value of HfO<sup>2</sup> passivation structure significantly decreased as f<sup>T</sup> decreased according to Equation (5). Particularly, the fmax, which is obtained from the extension line with a slope of −20 dB/decade at the intersection of the maximum stable/available gain (MSG/MAG), becomes 0 dB [33,34]. have been influenced by the g୫ and Cୱ. In addition, the f୫ୟ୶ values of the basic Si3N4 passivation, HfO2 passivation, and hybrid passivation structures are 110.28, 48.72, and 88.53 GHz, respectively. It can be seen that f୫ୟ୶ value of HfO2 passivation structure significantly decreased as f decreased according to Equation (5). Particularly, the f୫ୟ୶ , which is obtained from the extension line with a slope of −20 dB/decade at the intersection of the maximum stable/available gain (MSG/MAG), becomes 0 dB [33,34].

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 9 of 14

**Figure 7.** The cut-off frequency (f) and maximum oscillation frequency (f୫ୟ୶) for different passivation structures: (**a**) Si3N4 passivation structure; (**b**) HfO2 passivation structure; and (**c**) hybrid passivation structure. **Figure 7.** The cut-off frequency (fT) and maximum oscillation frequency (fmax ) for different passivation structures: (**a**) Si3N<sup>4</sup> passivation structure; (**b**) HfO<sup>2</sup> passivation structure; and (**c**) hybrid passivation structure.

Interestingly, these results clearly show that the ratio of HfO2 in passivation is important for DC and RF performances. As the ratio of HfO2 increases, the DC characteristics are improved, but the RF characteristics, such as parasitic capacitances and frequency characteristics, are degraded due to the material properties of HfO2. To improve both DC and RF characteristics, we selected the hybrid passivation structure and then simulated four different 2nd Si3N4 passivation thicknesses, i.e., 150, 250, 350, and 450 nm, which will be discussed in Section 3.3. More precisely, to optimize the second Si3N4 passivation thickness and calculate the figure-of-merit, we analyzed the operational characteristics including Vୈ, parasitic capacitances, and frequency characteristics. Interestingly, these results clearly show that the ratio of HfO<sup>2</sup> in passivation is important for DC and RF performances. As the ratio of HfO<sup>2</sup> increases, the DC characteristics are improved, but the RF characteristics, such as parasitic capacitances and frequency characteristics, are degraded due to the material properties of HfO2. To improve both DC and RF characteristics, we selected the hybrid passivation structure and then simulated four different 2nd Si3N<sup>4</sup> passivation thicknesses, i.e., 150, 250, 350, and 450 nm, which will be discussed in Section 3.3. More precisely, to optimize the second Si3N<sup>4</sup> passivation thickness and calculate the figure-of-merit, we analyzed the operational characteristics including VBD, parasitic capacitances, and frequency characteristics.

Figure 8a shows the electric field distribution in the channel region at a drain voltage of 200 V and a gate voltage of −7 V. The peak electric field was not significantly affected

*3.3. Determination of the Optimum Second Passivation Thickness for Hybrid Structure* 

3.3.1. Analysis of the DC Characteristics

#### *3.3. Determination of the Optimum Second Passivation Thickness for Hybrid Structure* 3.3.1. Analysis of the DC Characteristics *Micromachines* **2023**, *14*, x FOR PEER REVIEW 10 of 14

Figure 8a shows the electric field distribution in the channel region at a drain voltage of 200 V and a gate voltage of −7 V. The peak electric field was not significantly affected by the second passivation thickness. Additionally, the overall electric field distribution also showed no significant difference. Therefore, the VBD values of the various second passivation thickness structures were not changed significantly. As shown in Figure 8b, the VBD was simulated to be 262.00, 268.41, 267.57, and 262.30 V for the hybrid passivation structure with second passivation thicknesses of 150, 250, 350, and 450 nm, respectively. As the field-plate gradually deviates from the channel region, the electric field in the channel cannot be dispersed, resulting in the decrease of VBD. Meanwhile, as the passivation thickness increases, it is expected that VBD would increase, because the passivation can prevent the electric field in the channel region spread by the high electric field adjacent to the gate electrode. For these two reasons, the VBD were slightly enhanced in the second passivation thicknesses of 250 and 350 nm, compared with other structures. by the second passivation thickness. Additionally, the overall electric field distribution also showed no significant difference. Therefore, the Vୈ values of the various second passivation thickness structures were not changed significantly. As shown in Figure 8b, the Vୈ was simulated to be 262.00, 268.41, 267.57, and 262.30 V for the hybrid passivation structure with second passivation thicknesses of 150, 250, 350, and 450 nm, respectively. As the field-plate gradually deviates from the channel region, the electric field in the channel cannot be dispersed, resulting in the decrease of Vୈ. Meanwhile, as the passivation thickness increases, it is expected that Vୈ would increase, because the passivation can prevent the electric field in the channel region spread by the high electric field adjacent to the gate electrode. For these two reasons, the Vୈ were slightly enhanced in the second passivation thicknesses of 250 and 350 nm, compared with other structures.

**Figure 8.** The DC simulation results of hybrid passivation structure with various second passivation thicknesses: (**a**) electric field distribution in the channel region; and (**b**) off-state breakdown voltage. **Figure 8.** The DC simulation results of hybrid passivation structure with various second passivation thicknesses: (**a**) electric field distribution in the channel region; and (**b**) off-state breakdown voltage.

#### 3.3.2. Analysis of the RF Characteristics 3.3.2. Analysis of the RF Characteristics

Figure 9 shows the Cୱ and Cୢ of the hybrid passivation structure with various second passivation thicknesses, at a drain voltage of 20 V and a gate voltage of −2.6 V. The second passivation thickness affected the parasitic capacitance values. Specifically, the 150-nm-thick second passivation structure showed the largest Cୱ, due to the decrease in distance between the gate and source, as shown in Figure 9a. According to Equation (3), as the distance among the electrodes increased, the parasitic capacitances decreased. Therefore, compared to Cୱ , there is no significant change in Cୢ , because the gate-tosource distance is much shorter than the gate-to-drain distance. In addition, the 450-nmthick second passivation structure exhibited a slightly larger Cୢ than did the other structures, as shown in Figure 9b. The change in materials from air to Si3N4 led to an increase in Cୢ due to dielectric constant of the materials, which is explained by Equation (3). Figure 9 shows the Cgs and Cgd of the hybrid passivation structure with various second passivation thicknesses, at a drain voltage of 20 V and a gate voltage of −2.6 V. The second passivation thickness affected the parasitic capacitance values. Specifically, the 150-nm-thick second passivation structure showed the largest Cgs, due to the decrease in distance between the gate and source, as shown in Figure 9a. According to Equation (3), as the distance among the electrodes increased, the parasitic capacitances decreased. Therefore, compared to Cgs, there is no significant change in Cgd, because the gate-to-source distance is much shorter than the gate-to-drain distance. In addition, the 450-nm-thick second passivation structure exhibited a slightly larger Cgd than did the other structures, as shown in Figure 9b. The change in materials from air to Si3N<sup>4</sup> led to an increase in Cgd due to dielectric constant of the materials, which is explained by Equation (3).

Figure 10 shows the simulated f<sup>T</sup> and fmax values for the different second passivation thicknesses at a drain voltage of 20 V and a gate voltage of −2.6 V. When the second passivation thicknesses were 150, 250, 350, and 450 nm, the f<sup>T</sup> values in the simulations were 17.92, 20.50, 22.64, and 24.97 GHz, respectively. A decrease in the Cgs due to a change in the second passivation thickness led to an increase in fT, according to Equation (4). Therefore, f<sup>T</sup> tended to increase by about 14.4~39.3% as the second passivation thickness was extended by each 100-nm-step. The fmax values were simulated to be 78.50, 88.53, 91.47, and 106.39 GHz for the hybrid passivation structure with the second passivation

thicknesses of 150, 250, 350, and 450 nm, respectively. Comparing the fmax values of the hybrid passivation structures based on the different second passivation thicknesses, it can be demonstrated that the fmax values increased by 12.8~35.5% with each 100-nm-step increase in the second passivation thickness. According to Equation (5), the fmax values were mainly influenced by the increase in f<sup>T</sup> because there was no significant change in Cgd. Throughout these results, we confirmed the dependence of frequency characteristics in relation to the second passivation thickness. *Micromachines* **2023**, *14*, x FOR PEER REVIEW 11 of 14 (**a**) (**b**)

*Micromachines* **2023**, *14*, x FOR PEER REVIEW 11 of 14

**Figure 9.** The parasitic capacitance characteristics of the hybrid passivation structure with various second passivation thicknesses: (**a**) gate-to-source capacitance; and (**b**) gate-to-drain capacitance. **Figure 9.** The parasitic capacitance characteristics of the hybrid passivation structure with various second passivation thicknesses: (**a**) gate-to-source capacitance; and (**b**) gate-to-drain capacitance. in Cୢ. Throughout these results, we confirmed the dependence of frequency characteristics in relation to the second passivation thickness.

tics in relation to the second passivation thickness. **Figure 10.** The simulated f and f୫ୟ୶ as a function of the second passivation thicknesses at Vୈୗ = 20 V and Vୋୗ = −2.6 V. **Figure 10.** The simulated f<sup>T</sup> and fmax as a function of the second passivation thicknesses at VDS = 20 V and VGS = −2.6 V.

#### **4. Discussion 4. Discussion**

20 V and Vୋୗ = −2.6 V.

**4. Discussion** 

In this article, we simulated the DC and RF characteristics of various passivation structures. Additionally, we analyzed the hybrid passivation structure by changing the second passivation thickness. Based on these results, we first calculated the LFOM and In this article, we simulated the DC and RF characteristics of various passivation structures. Additionally, we analyzed the hybrid passivation structure by changing the second passivation thickness. Based on these results, we first calculated the LFOM and JFOM to investigate the performance of the device for the various passivation structures. Table 4 provides a summary of the DC and RF characteristics, including the figure-of-merit for the four different passivation structures. More precisely, the LFOM and JFOM of the basic Si3N<sup>4</sup> passivation structures were 13.44 MW/mm and 5.73 THz-V, respectively. The HfO<sup>2</sup> passivation structure increased the LFOM by 48% and decreased the JFOM by 39% compared with the basic Si3N<sup>4</sup> passivation structure. In comparison with the basic Si3N<sup>4</sup>

**Figure 10.** The simulated f and f୫ୟ୶ as a function of the second passivation thicknesses at Vୈୗ =

In this article, we simulated the DC and RF characteristics of various passivation structures. Additionally, we analyzed the hybrid passivation structure by changing the second passivation thickness. Based on these results, we first calculated the LFOM and

passivation structure, analysis of the hybrid passivation structure showed that the LFOM was increased by up to 35% and the JFOM was decreased by up to 4%.


**Table 4.** A summary of the DC and RF characteristics of various passivation structure HEMTs.

Subsequently, the LFOM values for the hybrid passivation structure of different second passivation thicknesses were estimated to be 17.93, 18.15, 17.68, and 15.53 MW/mm, respectively. In addition, except for the hybrid passivation structure with 450-nm-thick second Si3N<sup>4</sup> passivation, the LFOM values of the other hybrid passivation structures had improved by more than 28%, compared to the basic Si3N<sup>4</sup> passivation structure. Further, we measured the JFOM values for the hybrid passivation structures of different second passivation thicknesses, which were 4.70, 5.50, 6.06, and 6.55 THz-V, respectively. As the second passivation thickness increased, the JFOM values also increased.

### **5. Conclusions**

In this study, using TCAD simulation, we analyzed the operational characteristics of AlGaN/GaN HEMTs in accordance with changes of passivation materials and thicknesses. Before analyzing the various passivation structures, all the simulation and material parameters were precisely set through mapping with the measurement data of the fabricated device to ensure the reliability of the simulated data. Based on the simulation results, we suggest an optimized hybrid structure of HEMT which adopts a 50-nm-thick first HfO<sup>2</sup> passivation and a 350-nm-thick second Si3N<sup>4</sup> passivation. Unlike other general structures such as the field-plate in the HEMT, we confirmed that the hybrid passivation structure of the HEMT with suitable passivation thickness could enhance both the DC and RF performances, including the LFOM and JFOM. Consequently, the simulation results clearly show that HfO<sup>2</sup> as a passivation material with a second passivation thickness suitable for the AlGaN/GaN HEMTs can be a promising candidate for future high-power and high-frequency applications.

**Author Contributions:** Conceptualization and writing—original draft preparation, J.-H.C.; software and investigation, W.-S.K.; formal analysis and data curation, D.K.; validation and formal analysis, J.-H.K.; formal analysis and investigation, J.-H.L.; validation and investigation, K.-Y.K.; validation and formal analysis, B.-G.M.; resources and investigation, D.M.K.; supervision, funding acquisition, resources, and writing—review and editing, H.-S.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partly supported by an Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the government of the Republic of Korea (MSIT) under grant No. 2021-0-00760, as well as the Institute of Civil Military Technology Cooperation, funded by the Defense Acquisition Program Administration and the Ministry of Trade, Industry and Energy of the government of the Republic of Korea, under grant No. 22-CM-15.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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