The electrical performance of HEMT depends on different device parameters such as temperature, channel height, thickness of oxide layer, and length of the channel. The analysis of HEMT is performed by several research groups to analyze its electrical performance using different techniques.^1,2,3 Huque et al.⁴ proposed an analytical model for AlGaN/GaN power HEMT to calculate the DC performance at higher temperatures. Turuvekere et al.⁵ analyzed the gate-leakage mechanisms of AlInN/GaN and AlGaN/GaN HEMTs considering thermionic emission (TE), Poole-Frenkel emission (PF), and Fowler Nordheim tunneling (FN). TE and PF mechanisms are dominant in AlGaN/GaN and FN is dominant in AlInN/GaN HEMT and predicted that Schottky barrier height increases with temperature. The temperature significantly effects the transconductance of both quadruple-gate (QG) and single-gate (SG) due to phonon scattering and mobility variation. The phonon scattering represents the interactions between the charge carriers and vibrations of the crystal lattice, which are quantized as phonons.^6,7,8,9,10 It is noticed that the transconductance is higher for low values of temperatures at higher values of gate voltage. He et al.¹¹ calculated the DC and AC characteristics of AlN/β-Ga²O³ HEMT, and reported that the drain current is reduced with increase in temperature that leads to the decrease in the transconductance. At lower temperature, the phonon scattering is reduced and carrier mobility increases significantly. At higher temperature, lower carrier mobility and increased interface trap activity is there. At higher gate voltage, stronger channel control and higher 2-DEG density is obtained due to which the cut-off frequency is reduced. In this work, the output conductance, transconductance generation factor, and early voltage of multi- gate and single gate AlInN/GaN MOS HEMT are compared. It is noticed that the QG AlInN/GaN MOS HEMT exhibits lower output conductance (g_d) as compared to single gate (SG) so QG can operate at higher currents with less variation. The effect of variation in temperature is also analyzed on different electrical parameters.

Figure 1 represents the 3D structure of AlInN/GaN MOS HEMT. The AlInN barrier layer provides lattice matching with GaN thus reduces the strain and damage at the hetero-interface thus improving the stability of the structure. The usage of oxide layer provides interesting significant features such as reducing gate leakage current and improving the breakdown voltage of the device. The GaN layer provides the confinement of the charge carriers and consists of the channel between source and drain.^6,7 The GaN layer belongs to wide bandgap material thus provides higher breakdown voltage and more voltage can be applied at the drain terminal.

In the present work, the analytical modeling of QG AlInN/GaN MOS-HEMT is performed. The method of equivalent number of gates is used. The parabolic potential expression is represented using Eqution (3). Tables 1 and 2 represent the device parameters and relations used in the present work. The boundary conditions are represented using Equations (4)–(9). The QG high electron mobility transistor (HEMT) can be viewed as two separate double gate (DG) HEMTs in zx and yz planes. So, we can analyze QG using the equivalent number of gates (ENG) method. The characteristics length λ_QG of QG can be calculated using:

where λ_DGzx and λ_DGyz are the characteristics length of the DG HEMTs in zx and yz planes.

Considering the DG HEMT of zx plane the characteristics length is calculated solving following 2D Poisson’s equation:

Where N_d is the donor concentration; ϕ (x, z) is the potential in the channel; ϕ_Gan is the permittivity of GaN; q is the unit charge in coulombs. Assuming the parabolic potential approximation in the x direction,

c₀ (z), c₁ (z)x, c₂ (z) are constants to be determined by using the following boundary conditions:

where Cox=εoxtox and V_FB = ϕ_M – ϕ_GaN which is flat band

voltage using Equation (4) which states that at x = 0 the potential is equal to the surface potential, gives

using Equation (7) which states at x = 0 the electric field can be written as

gives

using Equation (8) which states that at x = W_GaN the electric field can be written as

gives

c₀(z), c₁(z)x, c₂(z) are substituted in the Equation (3) and from this the centre potential can be calculated by putting x=WGaN2, gives

From Equation (13) the characteristic length of zx plane DG is λDGxz=8CoxwGaN(4εGaN+WGaNCox)   and similarly

characteristic length of yz plane DG can be calculated to be λDGyz=8CoxHGaN(4εGaN+WGaNCox)  

From Equation (1) we can calculate the λ_QG and the solution of Equation (2) is of the form

where βQG=λQG2(VGS−  VFB)−qNdεGaN. Constants A and B can

be calculated using the boundary conditions:

Potential at source terminal is V_s

Potential at drain terminal is V_D

Using Boundary conditions of (14a) and (14b) we get, constants A and B:

The results obtained using the proposed analytical model for center potential are compared with TCAD simulations. The Albrecht model is chosen to model the low field mobility using albrct parameter. The field-dependent mobility model (FLDMOB) is used to model velocity-saturation effect. The Shockley-Read-Hall (SRH) model is initiated in the model using the SRH parameter. The concentration dependent mobility (CONMOB) model is used to account for the mobility dependent on the concentration. In order to account for the strain due to lattice mismatch CALC.STRAIN model is incorporated so that the piezoelectric-polarization effects are also included in the analysis by setting the STRAIN and POLARIZATION parameters. Figures 2a–c represent the calculation of center potential for different channel height, channel length, and oxide thickness respectively.

It is analyzed that the transconductance (g_m1) of both QG and SG AlInN/GaN MOS HEMT reduces with increasing temperature due to the reduction in electron mobility and increase in the gate leakage current, similar to.⁹ The electron mobility reduces with the increase in temperature due increased lattice vibrations and hence increased phonon scattering. The transconductance of a semiconductor device quantifies how effectively the gate voltage controls the drain current. It is evident from Figure 3a that the magnitude of g_m1 is higher for QG as compared to SG due to better electrostatic control and enhanced carrier modulation. The electrostatic control is improved for QG as compared to SG because the gate surrounds the channel from all the surroundings. In SG, the gate modulates only the carriers near the top of the channel; however, for QG, the gate controls the channel over the entire distribution of electrons from all the surroundings. The calculation of the first and second order derivative of transconductance, i.e., g_m2 and g_m3 for different values of temperature are represented using Figures 3b and c. The g_m2 and g_m3 represent that how rapidly the magnitudes of g_m1 and g_m2 respectively changes with V_g. It is noticed that the magnitude of g_m2 and g_m3 remains more stable for QG thus indicating better linearity as compared to SG. It is observed using Figure 3d that the drain current is higher at lower values of temperature due to increased mobility of electrons and reduced access and contact resistances. The phenomenon of phonon scattering is reduced at lower temperature that results in the reduced interaction of phonons with the electrons, and because of this there occurs significant reduction in the lattice vibration, resulting in the increased mobility of the electrons.

The change in doping concentration significantly affects the electrical performance of AlInN/GaN MOS-HFET due to change in the charge concentration and ionized impurity scattering. Figure 4a represents the calculation of g_m1 for different doping concentration. It is analyzed that the QG device exhibits higher magnitude of g_m1 for different doping concentration as compared to SG, because the mobility degradation is more effective in SG at higher doping concentration. It is analyzed that the magnitude of g_m1 is higher at higher doping concentration due to increased charge density. Figure 4b represents the comparison of cut-off frequency (f_T) for different doping concentration. It is noticed that the magnitude of f_T is higher for higher doping concentration because the magnitude of g_m1 is increased due to increased carrier density at higher doping concentration, which leads to increase in f_T. Figure 4c represents the calculation of g_m2 for different doping concentration. The QG device is noticed to exhibit lower magnitude of g_m2 for different doping concentration as compared to SG due to uniform potential distribution which leads to minimal distortion. Figure 4d represents the TFP for different doping concentration. Figure 4e represents the calculation of g_m3 for different channel length. The QG device is noticed to exhibit lower magnitude of g_m3 for different doping concentration as compared to SG as the QG structure wraps the channel from all surroundings providing symmetric field control. Figure 4f represents the calculation of intrinsic gain. The magnitude of intrinsic gain is more in QG as compared to SG. The inversion charge is reduced more at lower doping concentration in SG than QG, thereby reducing g_m1, and consequently intrinsic gain is reduced more effectively as compared to QG. Figure 4g represents the comparison of IIP₃. It is noticed that QG exhibits higher IIP₃ because of the reduced magnitude of g_m3 and increased magnitude of g_m1 in QG as compared to SG with better electrostatic control. Figure 4h represents the comparison of VIP₂. Figure 4i represents the comparison of VIP₃. It is evident that the QG device exhibits more VIP₂ and VIP₃ as compared to SG.

In this work, the electrical performances of QG and SG AlInN/GaN MOS HEMTs are analyzed and compared. It is noticed that the magnitude of g_m2 is lower for QG as compared to SG because of better electrostatic control as channel is surrounded by the gate more effectively. The magnitude of g_m3 is calculated lower for QG as compared to SG, highlighting reduced non-linearity. It is analyzed that the QG exhibits higher intrinsic gain as compared to SG due to increased transconductance and reduced output conductance. It is noticed that QG exhibits higher IIP₃ for the analyzed device geometry because of the reduced magnitude of g_m3 and increased magnitude of g_m1 in QG as compared to SG making it suitable for highly linear analog applications.