## 2 Materials and Methods
Figure 1: T-shaped gate AlGaN/GaN high electron mobility transistor (HEMT) structure: (**a**) fabricated two-finger device; (**b**) simulated T-shaped unit structure. The S, D, and G stands for source, drain, and gate, respectively. The imbibed wurtzite structure of AlGaN/GaN heterostructures produces polarization in the device. Piezoelectric and spontaneous polarizations form a 2-DEG in the channel region via tensile and compressive stresses. Therefore, the modeling factors, such as polarization effect, energy bandgap, electron affinity, relative permittivity, mobility, saturation velocity, and Shockley-Read-Hall (SRH) recombination with fixed carrier lifetimes should be carefully considered, as presented in Table 2. The electron velocity is saturated in the 2-DEG region with a significant increase in electric field. This effect is because of a reduction in the effective mobility, since the magnitude of the drift velocity is the product of the mobility and the electric field. Therefore, a GaN-based saturation velocity model was used to find out the value of electron mobility (\(\upmu_{\text{n}}\)) as a function of applied parallel electric field (E), as denoted in Equation (2),  
\[\upmu_{\text{n}}(\text{E})=\frac{\upmu_{\text{n0}}+\text{VSATN}\frac{\text{E} ^{\text{NIN}\cdot\text{GANSAT}-1}}{\text{ECN}\cdot\text{GANSAT}^{\text{NIN} \cdot\text{GANSAT}}}}{1+\text{ANN}\cdot\text{GANSAT}\Big{(}\frac{\text{E}}{ \text{ECN}\cdot\text{GANSAT}}\Big{)}^{\text{N2N}\cdot\text{GANSAT}}+(\frac{ \text{E}}{\text{ECN}\cdot\text{GANSAT}}\Big{)}^{\text{N1N}\cdot\text{GANSAT}}} \tag{2}\]  
where \(\upmu_{\text{n0}}\) and VSATN are electron low-field mobility and saturation velocity, respectively, and N1N-GANSAT, ECN-GANSAT, ANN-GANSAT, and N2N-GANSAT are fitting parameters which were calculated with Monte Carlo methods [23; 24]. Furthermore, the Selberherr model was used to calculate the impact ionization process near the gate edge of the device [25; 26]. Figure 2 shows the overall characteristics of acceptor doping in the GaN buffer layer. Acceptor traps were exploited to minimize the electron punch-through effect via the GaN buffer layer, and the exact concentration of acceptor traps is shown in Figure 2a. The peak trap concentration was \(\sim\)10\({}^{18}\)/cm\({}^{3}\), where the doping concentration was reduced to below 10\({}^{15}\)/cm\({}^{3}\) at the AlGaN/GaN interface for higher carrier density in the 2-DEG channel layer. The conduction band energy level of the simulated device is presented in Figure 2b. The acceptor doping increased the conduction band energy of the GaN buffer layer, which improved the breakdown characteristics of the HEMT via an electron confinement effect. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **Units** & **GaN** & **AlGaN** \\ \hline Bandgap energy & eV & 3.4 & 3.87 \\ Electron affinity & eV & 3.8 & 3.47 \\ Relative permittivity & - & 9.38 & 9.5 \\ Low-field mobility(n) & cm\({}^{2}\)/V-s & 1000 & 300 \\ Low-field mobility(p) & cm\({}^{2}\)/V-s & 20 & 10 \\ High-field mobility model & - & GANSAT saturation velocity model \\ Saturation velocity & cm/s & \(1.4\times 10^{7}\) & \(1.1\times 10^{7}\) \\ SRH life time(e) & sec & \(1.0\times 10^{-7}\) & \(1.0\times 10^{-7}\) \\ SRH life time(p) & sec & \(2.0\times 10^{-7}\) & \(2.0\times 10^{-7}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation model parameters. (Gate metal work function, \(\upPhi_{\text{M}}\) = 5.0 eV). SHR: Shockley–Read–Hall. Figure 3 presents the electrical characteristics of the simulated device. The 2-DEG charge density based on spontaneous and piezoelectric polarizations is presented in Figure 3a. The 2-DEG charge carrier density at the AlGaN/GaN interface was 7.4354 \(\times\) 10\({}^{12}\)/cm\({}^{2}\). Figure 3b shows the threshold voltage (V\({}_{\text{th}}\)) and transconductance (g\({}_{\text{m}}\)) of the measured and simulated T-shaped gate AlGaN/GaN HEMTs, where the basic structures of both devices are already portrayed in Figure 1a,b.