Two port network based Scattering parameter, Modelling and Simulation of GaN/AlGaN HEMT

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Two port network based Scattering parameter, Modelling and Simulation of GaN/AlGaN HEMT

1Vidyashree. L, ²P. Vimala

1,2 Dayananda Sagar College of Engineering/ECE, Bangalore, India

Abstract—An Analytical modelling of Admittance Parameters(Y-parameters) are obtained by using the Two port network Concepts applied to the Small Signal Equivalent Circuit of GaN/AlGaN based HEMT. In This paper we have determined the scattering parameters using the analytical modelling of Admittance parameters. We have simulated the Analytical modelling result of Admittance parameters and Scattering parameters in Matlab tool and Also We have designed the GaN/AlGaN based HEMT using Comsol tool.

Index Terms—Comsol tool, Matlab tool, Scattering parameters, Y-Parameters,

I. INTRODUCTION

The Applications of GaN/AlGaN HEMT is used in Space applications, Radar and in satellites because of their High efficiency, High Power and High Frequency applications. Generally, HEMT are designed by using either GaAs Semiconductor material or GaN Semiconductor material. GaN based HEMT will have more advantages than GaAs based HEMT because of their good Breakdown voltage, less power dissipation, can operate at High temperature and it is having more power density and can operate at High voltage compared to GaAs based HEMT. For that purpose, we are talking about GaN/AlGaN HEMT here. Analytical modelling of admittance parameters are determined using 3-port equivalent circuit for separate gate InAlAs/InGaAs DG- HEMT [1[,[2]. The admittance parameters are obtained in terms of Real and Imaginary part [3]. The scattering parameters are determined using 2-port equivalent circuit for tied gate InAlAs/InGaAs DG-HEMT [4-6].

The Extrinsic scattering parameters are determined by using the intrinsic Y-Parameters and Extrinsic parameters [7],[8].

AlGaN/GaN high-electron mobility transistor (HEMT) devices are considered to be very promising candidates for high-speed and high-power applications [9]. These devices offer advantages such as high breakdown voltage, high charge density, and good electron mobility [10]. The formation of the 2-D electron gas (2DEG) in these devices is the heart of the device operation and has been studied in great detail in the literature.

In this paper we have designed the GaN/AlGaN HEMT and Analyzed the small signal equivalent circuit of GaN/AlGaN HEMT to obtain the analytical modelling of Admittance parameters and Scattering Parameters in terms of Real and Imaginary parts. and the Analytical

II. MODEL FORMATION

GaN/AlGaN HEMT is as shown in the “Fig. 1”. It has 5 layers, such as Doped AlGaN layer, AlGaN Spacer layer, GaN layer, nucleation layer and SIC layers. The Some portion of AlGaN is doped to increase the drain current. Spacer layer is used to increase the electron mobility in 2DEG.Above the GaN layer 2DEG is formed and the AIN nucleation layer is used to match the crystal structure of GaN with the Crystal structure of SIC material. SIC can withstand at high thermal operation, so it is used in GaN/AlGaN HEMT.

Fig 1: GaN/AlGaN HEMT structure designed in Comsol tool

III. ANALYTICAL MODELLING

In this paper we are analyzing the Small signal equivalent circuit of GaN based HEMT. The SSEC of GaN HEMT is as shown in “Fig. 2”. The HEMT is having 3-Terminals, source, drain and gate. Intrinsic parameters(Y-Parameter) can be find out by considering the Gate to source Capacitance (Cgs), Input Resistance (Ri), Gate to drain capacitance (Cgd), Output conductance (Gd) parameters. Ym is the Current source generator and it is always equal to the g_mexp(j).

Fig 2: Small Signal Equivalent circuit for HEMT Apply the Two Port Network Concepts to Fig. 2.

According to 2-port analysis we have 2 ports, Input Port and Output Port. Input Port is taken between Gate with

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Respect to Source. _V₁and I₁ are the voltage and current of Input port.

V2and

I2are the voltage and current of Output port. Generally, we will supply the voltage and measure the current in 2-port network.so we can calculate the admittance parameter of the circuit easily.

Apply the Nodal Analysis of Current I₁at input port and Current

I2at output port are evaluated as follows.

2 1

1 i i

I   (1)

2 3 4

2 i i i

I    (2)

Represent

i

₁_,

i

₂

, i

₃_,

i

₄_,

i

₅ in the form of R

V. we will get _I₁ and _I₂as follows.

1 I

1

1 i

gs gs

R C j

V C j



 ₊

2

1 j C V

V C

j gd   gd (3)

I2= gd

V₂ +

1 )

1 exp(





i gs m

R C j

j g V



 -

2

1 j C V

V C

j _gd   _gd (4) A. Intrinsic Y-Parameter

In 2-port Equivalent circuit of GaN based HEMT, we will get four admittance parameters, they arey₁₁,y₁₂,y₂₁,y₂₂. Each parameter is represented in terms of Real part and imaginary part. Analytical modelling of Y-parameters obtained bellow.

i. y₁₁ is the Input admittance parameter which is the ratio of the current at input port to the voltage at input port,when output port is short circuited. i.e

y₁₁

1 1

V

I keeping _V₂=0. (5)

Apply (3) to (5) and also make ₀

2

V in (3). Finally, we will get

_y₁₁_

1

i gs gs

R C j

C j



 +

Cgd

j (6)

ii. y₁₂ is the Reverse transfer admittance parameter which is the ratio of the current at input port to the voltage at output port, when input port is short circuited.

i.e y₁₂

2 1

V

I keeping

V1=0. (7)

1

_y₁₂_- Cgd

j (8) iii.

y21 is the Forward transfer admittance parameter which is the ratio of the current at output port to the voltage at input port, when output port is short circuited.

i.e

21 y

1 2

V

I keeping

V2=0. (9)

2

21 y

1 ) exp(





i gs m

R C j

j g



 - Cgd

j (10)

iv. y₂₂ is the output admittance parameter which is the ratio of the current at output port to the voltage at output port, when input port is short circuited. i.e

22 y

2 2

V

I keeping

V1=0. (11)

1

22

y g_d jC_gd (12)

B. Intrinsic (S)Scattering Parameter S-Parameters are used to determine the RF

characteristics of GaN HEMT. In this paper we have used the analytical modelling of Y-parameters such asy11,y12,y21,y22to determine the S-Parameters such ass₁₁,s₁₂,s₂₁,s₂₂.The bellow expressions shows Intrinsic Y-parameters are converted into Intrinsic S-parameters.

11 S

) (

)) 1 )(

1 ((

) (

)) 1 )(

1 ((

21 12 2 0 22 0 11 0

y y Z y Z y Z





 (13)

12 S

) ( ) 1 )(

1 (

2

21 12 2 0 22 0 11 0

12 0

y y Z y Z y Z

y Z





 (14)

21 S

) ( ) 1 )(

1 (

2

21 12 2 0 22 0 11 0

21 0

y y Z y Z y Z

y Z





 (15)

22 S

) ( )) 1 )(

1 ((

) ( )) 1 )(

1 ((

21 12 2 0 22 0 11 0

21 12 2 22 0 11 0

y y Z y Z y Z







 (16)

We have compared the Analytical modelling result of Y and S-parameters with Matlab tool Simulation results.

The Parameters used to find out the simulation results are shown in “Table 1”.In Ref [4] they have done parameter extraction using these values.

“Table 1”- List of Parameters and values used for simulation.

Parameters Name Used Values C_gd(fF)

C_gs(fF) C_ds(fF) G_ds(ms) R_i(ohm) G_m(ms) R_gd(ohm) Tau(ps)

8.2 20.8 3.2 22.1 5.6 10.9 114.1 0.41

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IV. RESULTS AND DISCUSSIONS

The intrinsic set of admittance parameters for the 2- port network is shown from Fig 3 to Fig 6 with the variation of Frequency upto 100GHZ.

y11Parameter have both the imaginary part and the real part. Fig 3(a)shows the imaginary part of _y₁₁ Vs frequency. and Fig 3(b)shows the real part of

y11Vs frequency. In both graphs we can see_y₁₁admittance increases with increasing frequency.

(a)

(b)

Fig 3: (a) shows the imaginary part of _y₁₁ Vs frequency.

And (b)shows the real part of

y11Vs frequency

y

12Parameter has only imaginary part. Fig. 4 shows the imaginary part of

y12 Vs frequency. In this graph we can seey₁₂admittance decreases with increasing frequency.

y21Parameter have both the imaginary part and the real part. Fig 5(a)shows the imaginary part of

y21 Vs frequency and Fig 5(b)shows the real part of y₂₁Vs frequency. In both graphs we can see

y21admittance decreases with increasing frequency.

Fig. 4 shows the imaginary part of y₁₂ Vs frequency (a)

(b)

Fig 5:(a) The imaginary part of

y21 Vs frequency and (b)shows the real part of y₂₁Vs frequency.

y

22parameter has both Real part and Imaginary part.

Real part of

y

₂₂is constant and it will not vary with respect to frequency so Fig. 6 shows the imaginary part of y₂₂ Vs frequency. In this graph we can seey₂₂admittance decreases with increasing frequency.

Intrinsic Y-parameters are used to determine the intrinsic S-parameters. All the S-parameters are having

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modelling of S-parameters are compared with the Ref.

[3]. Fig. 7 to Fig. 11 shows the S-parameters with the variation of frequency(GHZ).

s11 parameter is called Input Reflection Coefficient In this graph we can see

s11admittance decreases with increasing frequency.

Fig. 6 shows the imaginary part of y₂₂ Vs frequency (a)

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Fig. 7:(a) Imaginary part of

s11Vs frequency(GHZ) and (b) is the Real part of

s11Vs frequency(GHZ).

s12 parameter is called the Reverse Transmission Coefficient. Fig. 8:(a) shows Imaginary part of

s12Vs frequency(GHZ) and 8 (b) is the Real part of

s12Vs frequency (GHZ )Fig. 8(a) and 8(b) shows that the scattering parameters value changes by varying the frequency. In

s12,The Scattering values increases by increasing frequency.

(a)

(b)

Fig. 8:(a) Imaginary part of s₁₂Vs frequency(GHZ) and (b) is the Real part of

s12Vs frequency(GHZ)

s21 parameter is called the Forward Transmission Coefficient. Fig. 9(a) and 9(b) shows that the scattering parameters value changes by varying the frequency.

Thes₂₁Parameter, increases by increasing frequency.

s22 parameter is called the Output Reflection Coefficient. Fig. 10(a) and 10(b) shows that the scattering parameters value changes by varying the frequency.

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(a)

(b)

Fig. 9:(a) Imaginary part of s₂₁Vs frequency(GHZ) and (b) is the Real part of

s21Vs frequency(GHZ) (a)

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Fig. 10:(a) Imaginary part of s₂₂Vs frequency(GHZ) and (b) is the Real part of

s22Vs frequency(GHZ)

V. CONCLUSION

Small signal analysis is done by using the Small signal equivalent circuit of GaN HEMT. We have applied the two port network concepts to SSEC to do the analytical modelling of admittance parameters and Obtained admittance parameters are used to determine the S- Parameters. The Analytical modelling of Y-Parameter is compared with respect to Ref. [1] and The Analytical modeling of S-Parameters are compared with reference to Ref [3]. Both the analytical modelling results are simulated using Matlab tool.

REFERENCES

[1] Parveen, Intrinsic Admittance Parameter for Separate Gate InAlAs/InGaAs DG-HEMT for 100 nm Gate length, IEEE conference, New Delhi, India, ICT 2013.

[2] Parveen RF characteristics of 100-nm separate gate InAlAs/InGaAs DG-HEMT, IEEE Vol 55, No.11, pages 5, November 2013.

[3] M. Bhattacharya, scattering parameters based modelling and simulation of Symmetric tied gate HEMT for millimetre application, solid state Electronics 63 ,2011.

[4] Du jiangfeng, Small signal modelling of AlGaN/GaN HEMT with consideration of CPW Capacitance, IEEE Vol 33, No.3, pages 4 march 2015.

[5] Mazhar B Tayer, Parameter Extraction for Pseudo orphic HEMTS using Genetic Algorithms -IEEE Vol:3, No.2, published in 2009.

[6] Ma Teng, Topic - A new small signal model of asymmetric AlGaN/GaN HEMT. Xidian university, Vol 31, No. 06, june 2010

[7] Ronan G Brady, An improved small signal parameter extraction algorithm for GaN HEMT devices, IEEE Transaction on microwave and technology, Volume:56, June 2008.

[8] Parveen Modeling of InAlAs/InGaAs/InAlAs DG-HEMT Mixer for microwave applications.

IOSR Vol 10, issue 4,2015

[9] Niraj man shresta, Simulation study of AIN spacer layer thickness on AlGaN/GaN HEMT, Himalayan physics, Vol 4, No.4,2013

[10] K. Feblets, Influence of undoped spacer layer thickness on GaAs/AlGaAs HEMT Semiconductor science technology,13,1998

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