**4. Performance analysis: analytical approach**

With rapidly growing popularity in high frequency and high power applications, HEMT devices have received extensive research attention in recent days. Many analytical models to study the characteristics of HEMTS as well as to improve device performance can be found in the literature. In this section, we present some of the eminent and effective analytical research works on AlGaN/GaN HEMTs.

### **4.1. Current‐voltage characteristics using charge control model**

An improved charge control model for *I‐V* characteristics of AlGaN/ GaN HEMTs was pre‐ sented in 2008 by Li et al. [3]. This model includes Robin boundary conditions in the solution of 1‐D Schrödinger equation and customizable eigen values in the solution of 2‐D Poisson's equation. Nonlinear polarization and parasitic resistance of source and drain have been incor‐ porated in this model. The model estimates drain current assuming second‐order continuity with analytical representation of transconductance. The device structure used in this model is almost similar to that of **Figure 2**. However, the only difference is that a doped AlGaN layer of 22 nm with doping concentration, *N*D = 2 × 1018 cm−3 is present above the undoped AlGaN layer to enhance polarization. The *I*‐*V* result plotted using this analytical model is shown here in **Figure 5** for different gate voltages.

#### **4.2. Dependence of 2DEG charge density on gate bias**

Khandelwal et al. proposed a physics‐based analytical model for 2DEG density in AlGaN/GaN HEMTs [4]. Using this model, they show the interdependence between 2DEG and Fermi lev‐ els. The proposed model does not require any fitting parameters. It models 2DEG considering charge concentration in two different regions. One has higher first subband energy, while the other has lower first subband energy compared to the Fermi level. Moreover, a unified model is also presented combining these two regions. It presents variation of 2DEG with gate bias volt‐ age as shown in **Figure 6**. The results show excellent agreement with numerical calculations.

#### **4.3. Short channel** *I‐V***characteristics with current collapse**

Current collapse is an undesirable but inevitable phenomenon in GaN‐based HEMTs. It is a short channel nonideal effect where current depends on the previous memory of gate volt‐ age. For *I‐V* characteristics of AlGaN/GaN HEMTS in presence of current collapse, another compact model was proposed [5]. It incorporates trapping mechanism and gate edges and is based on experimental data. Capacitance‐voltage (*C‐V*) characteristics of AlGaN/ GaN HEMTs can also be calculated using this model. This model analyses device transconductance vs. gate bias when current collapse occurs. A comparative plot of transconductance with and without current collapse as determined by this compact short channel model is shown in **Figure 7**.

High Electron Mobility Transistors: Performance Analysis, Research Trend and Applications http://dx.doi.org/10.5772/67796 51

the conduction band (Ec

works on AlGaN/GaN HEMTs.

in **Figure 5** for different gate voltages.

**4.2. Dependence of 2DEG charge density on gate bias**

**4.3. Short channel** *I‐V***characteristics with current collapse**

) and valence band (Ev

**4. Performance analysis: analytical approach**

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

**4.1. Current‐voltage characteristics using charge control model**

resulting in a quantum well filled with 2DEG and eventually, a conducting channel is formed.

With rapidly growing popularity in high frequency and high power applications, HEMT devices have received extensive research attention in recent days. Many analytical models to study the characteristics of HEMTS as well as to improve device performance can be found in the literature. In this section, we present some of the eminent and effective analytical research

An improved charge control model for *I‐V* characteristics of AlGaN/ GaN HEMTs was pre‐ sented in 2008 by Li et al. [3]. This model includes Robin boundary conditions in the solution of 1‐D Schrödinger equation and customizable eigen values in the solution of 2‐D Poisson's equation. Nonlinear polarization and parasitic resistance of source and drain have been incor‐ porated in this model. The model estimates drain current assuming second‐order continuity with analytical representation of transconductance. The device structure used in this model is almost similar to that of **Figure 2**. However, the only difference is that a doped AlGaN layer of 22 nm with doping concentration, *N*D = 2 × 1018 cm−3 is present above the undoped AlGaN layer to enhance polarization. The *I*‐*V* result plotted using this analytical model is shown here

Khandelwal et al. proposed a physics‐based analytical model for 2DEG density in AlGaN/GaN HEMTs [4]. Using this model, they show the interdependence between 2DEG and Fermi lev‐ els. The proposed model does not require any fitting parameters. It models 2DEG considering charge concentration in two different regions. One has higher first subband energy, while the other has lower first subband energy compared to the Fermi level. Moreover, a unified model is also presented combining these two regions. It presents variation of 2DEG with gate bias volt‐ age as shown in **Figure 6**. The results show excellent agreement with numerical calculations.

Current collapse is an undesirable but inevitable phenomenon in GaN‐based HEMTs. It is a short channel nonideal effect where current depends on the previous memory of gate volt‐ age. For *I‐V* characteristics of AlGaN/GaN HEMTS in presence of current collapse, another compact model was proposed [5]. It incorporates trapping mechanism and gate edges and is based on experimental data. Capacitance‐voltage (*C‐V*) characteristics of AlGaN/ GaN HEMTs can also be calculated using this model. This model analyses device transconductance vs. gate bias when current collapse occurs. A comparative plot of transconductance with and without current collapse as determined by this compact short channel model is shown in **Figure 7**.

) bend with respect to the Fermi level (EF

)

**Figure 5.** *I–V* characteristics for an Al0.15Ga0.85N/GaN HEMTs. The gate‐to‐source bias is swept from 1 to −2 V at a step of −1 V.

**Figure 6.** Comparison of 2DEG charge density, n<sup>s</sup> with numerical calculations as a function of gate voltage.

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

#### **4.4. Gate capacitance including parasitic components**

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‐ oped model shows agreement with TCAD simulations and experimental data.

### **4.5. Thermal effects with complex structures**

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

Apart from these models, many other analytical models have been proposed for noise elimi‐ nation, loss calculation, estimation of polarization, small signal analysis, etc.

High Electron Mobility Transistors: Performance Analysis, Research Trend and Applications http://dx.doi.org/10.5772/67796 53

**Figure 8.** (a) Complex multi‐layer HEMT structure with a heat source, and (b) Temperature distribution along *x* axis for AlGaN/GaN HEMTs including the heat source.
