**5. Performance analysis: numerical approach**

Different numerical studies of HEMTs have been performed to analyze the influence of inter‐ nal physical mechanisms. Some generalized numerical models reviewed from the literature are presented in this section.

#### **5.1. Fully coupled drift‐diffusion model**

**4.4. Gate capacitance including parasitic components**

52 Different Types of Field-Effect Transistors - Theory and Applications

**4.5. Thermal effects with complex structures**

Zhang et al. proposed a surface potential‐based analytical model for calculating capacitance including parasitic components for AlGaN/GaN HEMTs [6]. The sheet charge density is mod‐ eled solving charge control equations and capacitance is calculated based on the concept of surface charge potential, which is consistent with the sheet charge density model. The para‐ sitic components are further included in the model to provide a complete model. The devel‐

Although AlGaN/GaN HEMT is a promising device for high frequency and high power appli‐ cations, its performance can be degraded at high temperatures. Therefore, a thermal modeling is required to predict device performance at different temperatures. Bagnall et al. developed such a thermal model that incorporates thermal effects with closed form analytical solutions for complex multilayer structured HEMTs [7]. This structure consists of N number of layers (*j* = 1, 2, 3, …, N) and a heat source placed within the layers as shown in **Figure 8(a)**. The analytical modeling is carried out using Fourier series solution and validated using Raman thermography spectra. Distribution of temperature along AlGaN/GaN *x*‐axis interface includ‐

Apart from these models, many other analytical models have been proposed for noise elimi‐

oped model shows agreement with TCAD simulations and experimental data.

**Figure 7.** Comparison of transconductance with and without current collapse for AlGaN/GaN HEMTs.

ing heat source as presented by the model is shown in **Figure 8(b)**.

nation, loss calculation, estimation of polarization, small signal analysis, etc.

Yoshida et al. presented a two‐dimensional numerical analysis of HEMTs to simulate device performance [8]. Anderson's model is used to generate the equations of band‐edge lines and Boltzmann statistics is considered. Spatially continuous band‐edge variation is not justified in this model as current across the hetero interface is neglected. The hole current and the generation‐recombination current are also neglected. Finite difference approximation is used to discretize Poisson's equation and electron current continuity equation. After that, resultant equations are solved self consistently using Newton's method. This fully coupled model is traditionally known as drift‐diffusion model [14].

#### **5.2. Energy‐transport model: transport calculation**

Buot presented a two‐dimensional numerical simulator based on the analysis of the first three moments of the Boltzmann equation, known as the energy‐transport model [9]. It has been used to study various effects on the performance of AlGaAs/GaAs HEMTs [9]. The coupled trans‐ port equations (for details of energy transport equations, see Ref. [15]) were solved numerically using finite‐difference technique on a uniform mesh, using iterative scheme. Using HISSDAY, a computer simulator program, the transport equations for the energy transport model are numerically solved using implicit scheme for the continuity equations; Scharfetter‐Gummel method [16] for the current transport equation; and explicit forward differencing "marching" method for calculating the average energy. This model has an improvement over Widiger's energy transport model [17] where conduction is ignored in the AlGaAs layer [9].

### **5.3. Monte Carlo simulation**

Ueno et al. presented Monte Carlo simulation of HEMTs to analyze 2DEG electron transport [10]. The analysis is based on electron–phonon interaction model proposed by Price [18]. In this framework, the 2DEG electrons are assumed to be scattered by bulk phonons. Thus, wave func‐ tions calculated by self‐consistent analysis are used to evaluate the scattering rate. The chan‐ nel region is not considered uniform and electrons near drain region are considered as three dimensional and near‐source region are considered as two dimensional. In addition, electrons with high energy beyond the barrier height behave as three‐dimensional electrons and are not confined in the quantum well. In these simulations, the initial condition is first evaluated. Then the sheet electron density at each position between the source and the drain are estimated using the current continuity relation along the channel. Next, Monte Carlo simulation is car‐ ried out by dividing the channel into different meshes and evaluating the scattering rates of the electronic states in each mesh. Then taking the potential distribution of the given device from two‐dimensional Poisson equation, the steps are repeated until a steady state is obtained.

#### **5.4. Noise current using Green's function formalism**

Lee and Webb described a numerical approach to simulate the intrinsic noise sources within HEMTs [11]. A 2‐D numerical device solver is used in this model. Spectral densities for the gate and drain noise current sources and their correlation are evaluated by capacitive cou‐ pling. After solving Poisson's and the continuity equations using 2‐D numerical device solver, Green's functions are obtained. Here, Green's functions are used to determine local fluctua‐ tion (in terms of current or voltage at any point in the channel) at the gate and drain terminals. This approximate impedance field concept [19] helps determining the gate and drain noise sources and their correlation. For numerical simulation, the entire device is divided into some orthogonal areas and it is considered that 2‐D simulation results will be consistent with the 3D simulation result. Spontaneous polarization and strain‐induced piezoelectric polarization are also considered. It is assumed that the microscopic fluctuations in each segment are spatially uncorrelated which are originated from velocity fluctuation (diffusion) noise only.

#### **5.5. High temperature shear stress analysis**

Hirose et al. proposed a numerical model for AlGaN/GaN HEMT structures where shear stress due to the inverse piezoelectric effect is used to predict high‐temperature DC stress test results [12]. In this model, lattice plane slip in the crystal is assumed to be the initial stage of crack for‐ mation. Shear stress causes the slip, and slip deforms the crystal when the shear stress exceeds the yield stress. In GaN‐based HEMTs, the basal slip plane is (0001) and the slip direction is <1120>. The AlGaN layer is a wurtzite crystal grown in the <0001> direction [20]. Shear stress is assumed to be a result of the inverse piezoelectric effect. The mechanical stress and electric displacement occur due to the piezoelectric effect. Under the assumption of lattice mismatch in AlGaN layer, shear stress relates to the slip in the <1120> direction. However, to calculate shear stress, electric field is obtained from two‐dimensional device simulation based on Poisson's equation and drift‐diffusion current continuity equations. This model includes piezoelectric charges and the difference in spontaneous polarization charges in the AlGaN/GaN interface.

Among the numerical models, any one may have advantage over other models, but also have some limitations. For example, energy transport model can include hot electron effect [14]. Drift‐diffusion model cannot predict performances of submicron level gate devices [9]. Monte Carlo approach is one of the advanced approaches [21]. All of these numerical models provide unique insights into the device physics and create opportunity of performance improvement with TCAD before device fabrication.
