Superlattices and Microstructures 113 (2018) 810e820

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Superlattices and Microstructures

journal homepage: www.elsevier.com/locate/superlattices

Current collapse modeling in AlGaN/GaN HEMT using small

signal equivalent circuit for high power application
D. Nirmal a, *, L. Arivazhagan a, A.S.Augustine Fletcher a, J. Ajayan b, P. Prajoon a
a
Department of Electronics and Communication Engineering, Karunya University, Coimbatore, India
b
SNS College of Technology, Coimbatore, India

a r t i c l e i n f o a b s t r a c t

Article history: In this paper, the drain current collapse in AlGaN/GaN High Electron Mobility Transistor
Received 31 October 2017 (HEMT) with field plate engineering is investigated. A small signal equivalent circuit of
Received in revised form 12 December 2017 AlGaN/GaN HEMT is developed and a new drain current model is derived. This model is
Accepted 12 December 2017
useful to correlate the impact of intrinsic capacitance and conductance on drain current
Available online 14 December 2017
collapse. The proposed device suppressed the current collapse phenomena by 10%
compared with the conventional AlGaN/GaN HEMT. Moreover, the DC characteristics of the
Keywords:
simulated device shows a drain current of 900 mA/mm, breakdown voltage of 291 V and
AlGaN
Current collapse
transconductance of 175 mS/mm. Besides, the intrinsic capacitance and conductance pa-
GaN rameters are extracted and its impact on drain current is analysed. Finally, the simulation
HEMT results obtained were in compliance with the derived mathematical model of AlGaN/GaN
HighPower HEMT.
Small signal model © 2017 Elsevier Ltd. All rights reserved.

1. Introduction

The superordinate material property of Gallium Nitride (GaN) increases the demand for AlGaN/GaN based HEMT in high
power and high frequency applications in current years [1e6]. The unique properties of GaN such as large band gap, higher
temperature stability, high electron mobility and good thermal conductivity makes it as a good alternative to silicon and GaAs
[7e11]. Although AlGaN/GaN HEMT offers many advantages, it still suffers from various effects such as current collapse, gate
leakage, junction heating, trap effect, etc. Among these various effects, currents collapse disrupts the linear property of the
amplifier and creates frequency dispersion at high operating voltages [12e21]. Several techniques are being adopted to
diminish this current collapse phenomenon in HEMT devices. The presence of high-k passivation, Field Plate (FP) and Fe
doped GaN buffer are a few techniques used to address this issue [22e28]. However, the current collapse is not fully scaled
down, which demands further investigation on current collapse effect in GaN based HEMT. Development of a virtual gate
between the gate and drain terminals is the primary cause for this effect. In this paper, the current collapse issue is being
addressed by carrying out structural modifications in the conventional AlGaN/GaN HEMT [15]. This is done by sandwiching an
AlN layer between SiN passivation and GaN-cap layer. The reduced lattice mis-matching by the incorporation of AlN layer
mitigates the surface traps at the SiN interface. The simulation result of the modified AlGaN/GaN HEMT shows a reduction in
current collapse effect at high drain to source voltage (Vds). Furthermore, the electrons in GaN cap are in equilibrium state at
low electric field. Increasing electric field transfer the electron from GaN cap to surface and starts accumulating at drain side-

* Corresponding author.
E-mail address: dnirmalphd@gmail.com (D. Nirmal).

https://doi.org/10.1016/j.spmi.2017.12.027
0749-6036/© 2017 Elsevier Ltd. All rights reserved.
 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820 811

gate edge. The accumulation of electron at gate edge is only contributed by the transferred electron from GaN cap layer, but
also by leakage of electron from gate. These surface electrons at gate edge deplete the sheet carrier density in channel at
higher forward drain DC bias and hence the current collapse occurs. The current collapse is proportion to the static (DC)
concentration accumulated electrons. The static concentration of electron can be reduced by stopping the electron transfer
from GaN cap layer to surface. One can prevent the electron transfer to the surface by increasing height of the energy barrier
between GaN cap layer and surface. The deployment of AlN layer over GaN cap to increase height of energy barrier and hence
reduces accumulation of electron at surface and current collapse. Besides the structural changes in the AlGaN/GaN HEMT, the
small signal equivalent circuit is probed [29e34]. The model is predominantly used to analyse and ascertain AC parameters
like cut off frequency, power gain, power added efficiency etc [35e43]. However, it has not been used previously to estimate
the non-linear effects in the drain current collapse. In this paper, we have implemented Miller's theorem to estimate the non-
linear effects. The Miller's theorem is applied in the small signal equivalent circuit to contemplate an efficient drain current
model. Furthermore, the small signal modeling has been used for showing the dependency of intrinsic elements on electrical
parameters such as drain voltage, drain current, gate current, etc. Huang et al. [29] introduced a novel inductance in small
signal model to describe the drain current increase with drain voltage. X - parameter based new modeling technique is
proposed by Essaada Li et al. [30] and demonstrated the nonlinear behaviour of intrinsic elements with bias voltage. Van Raay
et al. [31] have formulated a drain current by integral over transconductance and output conductance. Nsele et al. [32] showed
that output impedance is a strong function of drain voltage using capacitor behaviour in Y-parameter. Shealy et al. [33]
suggested to estimate the Gate-source capacitance and Gate-drain capacitance using Gate leakage current. Chen et al. [34]
demonstrated non-linear change in gate-drain capacitance for various drain current and drain voltage of the device. However,
all these approach does not represent the drain current in direct relation with intrinsic small signal model. The model
presented in this work have expressed the drain current in direct relation with small signal parameters. Hence the further
exploration of this model in future will accurately predict AC parameters dependency on bias voltage and current of the
device.

2. Device description

The conventional AlGaN/GaN HEMT exhibited higher current collapse effect at high current densities [15]. In the proposed
device, this current collapse is scaled down by employing a stack layer of AlN/GaN over the AlGaN barrier layer as depicted in
Fig. 1. In the proposed AlGaN/GaN HEMT, the epitaxial layer structure comprises of a 0.5 mm thick SiN passivation layer, 3 nm
thin AlN/GaN multi-cap layer, 20 nm thick Al0.3Ga0.7N barrier layer, a 30 nm thick GaN channel layer, 2 mm thick GaN buffer
layer with donor concentration of 5e16 cm
3 and a 5 mm thick SiC substrate layer [44]. On top of the gate layer, a field plate is
incorporated to reduce drain current collapse at higher Vds [45e47]. Silicon Carbide (SiC) material is chose as substrate due to
its higher thermal conductivity, temperature stability and good epitaxial lattice matching with GaN. The device has a gate
length (LG), Gate-Drain spacing (LGD), Gate-Source spacing (LSG) and Field Plate length are 0.25 mm, 2.7 mm, 0.8 mm, and 1 mm
respectively. The TCAD simulation uses the models from Ref. [15], the material parameters and physical dimensions are given
in Tables 1 and 2 respectively.

Fig. 1. Cross sectional schematic of AlGaN/GaN HEMT.

812 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820

Table 1
Material parameters used in the hemt simulation.

Atlas Parameters AlGaN GaN

eg300 (eV) 4.9 3.50
vsat (107 cm/s) 1.1 2.5
electron affinity (eV) 3.41 4.0
Nc300 (1018/cm3) 2.71 2.23
Nv300 (1018/cm3) 2.06 2.51
mn (cm2/V-s) 300 1200
permittivity ε 8.8 8.9

Table 2
Physical parameters used in the hemt simulation.

Layers Thickness Layers Thickness

SiN passivation 0.5 mm GaN channel 30 nm
AlN cap 1.5 nm GaN buffer 2 mm
GaN Cap 1.5 nm SiC Substrate 5 mm
AlGaN barrier 20 nm e e

3. Small signal model

The Small signal equivalent circuit of AlGaN/GaN HEMT is explored to render the influence of bias dependent components
on drain current. The equivalent circuit consist of extrinsic parasitic components (Lg, Ls, Ld, Rd, Rs, Rg, Cpg, Cpgd and Cpd) and the
intrinsic parasitic components (Cgs, Cgd, Cds, Rd, Ggd and Ri) as depicted in Fig. 2. In order to analyse capacitive effects of the
equivalent circuit using Y-parameter, the circuit is simplified into a capacitive p network as shown in Fig. 3.
The Y e parameter of the capacitive p network is derived as


Y11 ¼ ju Cpg þ Cgs þ Cpgd þ Cgd (1)


Y12 ¼
ju Cpgd þ Cgd (2)


Y21 ¼ ju Cpgd þ Cgd (3)


Y22 ¼ ju Cpd þ Cds þ Cpgd þ Cgd (4)

The capacitance in (1-4) are further simplified as input, output, and feedback capacitance. And it is expressed as

Ci ¼ Cpg þ Cgs (5)

Cfb ¼ Cpgd þ Cgd (6)

Co ¼ Cpd þ Cds (7)

By applying expression (5-7) in (1-4), Y - parameters becomes


Y11 ¼ ju Ci þ Cfb (8)

Y12 ¼
juCfb (9)

Y21 ¼ juCfb (10)


Y22 ¼ ju Co þ Cfb (11)

The expression (8) through (11) shows that Y - parameters possess the linear property with frequency. These Y-parameters
can be used in transconductance and drain current to analyse the current collapse phenomena in AlGaN/GaN HEMT.
Addressing gm in terms of Y-parameter [48],
 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820 813

Fig. 2. Small signal equivalent circuit of AlGaN/GaN HEMT.

Fig. 3. Capacitive p network of AlGaN/GaN HEMT.

 
jRe fY11 g
gm ¼ ðY21
Y12 Þ 1 þ (12)
ImfY11 g þ ImfY12 g

From (12), the drain current is given as

 
jRe fY11 g
IDS ¼ ðY21
Y12 Þ 1 þ V (13)
ImfY11 g þ ImfY12 g GS

By applying (8-11) in (13), the drain current is computed as,


 
jGgd
IDS ¼ 2 Cfb þ Ggd 1þ VGS (14)
Ci

The expression in (14) indicates the influence of capacitance and conductance in drain current of the device. In order to
increase the accuracy of drain current, Miller's theorem is used in small signal equivalent circuit of AlGaN/GaN HEMT. Fig. 4
shows a circuit of a two port network that has a feedback element between input and output port, where Ii, Io,Vi Vo, and Zfb are
input current,output current, input voltage, output voltage, and feedback element, respectively. The Miller's theorem splits
the feedback element Zfb into input element Zi and output element Zo. The Zi is derived from input current as

Vi
Vo 1
K
Ii ¼ ¼ Vi (15)
Zfb Zfb

Vo
Let K ¼ Vi , then (15) becomes
814 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820

Fig. 4. Two port model with miller feedback element.

Fig. 5. Two port model after Miller's theorem is applied.

1
K
Ii ¼ Vi (16)
Zfb

From, Ii ¼ VZii and (16), the input impedance Zi is written as

Zfb
Zi ¼ (17)
1
K

Similarly, output impedance Zo is derived from output current as

K
Zo ¼ Zfb (18)
K
1

The new derived circuit with input impedance Zi and output impedance Zo are shown in Fig. 5. Similarly, the feedback
capacitance and conductance in Fig. 2 are split into input and output elements, where Xfb is considered as feedback element
that consists of both Ggd and Cgd, Xi is the input element, and Xo is the output element. The Xi and Xo are derived as follows

Xfb
Xi ¼ (19)
1
K
and

K
Xo ¼ Xfb (20)
K
1

Since K ¼ VDS =VGS , K [ 1 at higher VDS. This unique property is used in (2), and Xo simplified further as

Xo ¼ Xfb (21)
 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820 815

Fig. 6. The modified intrinsic small signal model.

From Xi and Xo, the intrinsic part of the equivalent circuit in Fig. 2 is simplified as shown in Fig. 6. For DC analysis, extrinsic
elements are neglected in the simplified circuit in Fig. 3. The input element is assumed as Xi and output element is expressed
as Cgd and Ggd instead of Xo alone, because the drain current is to be derived at the output section.
The drain current is derived from Fig. 6 as
h
 i
IDS ¼ ju Cgd þ Cds þ Ggd Vds þ gm Vgs (22)

The magnitude of drain current is written as

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2
2
jIDS j ¼ u2 Cgd þ Cds V 2ds þ Ggd Vds þ gm Vgs (23)

This is the new efficient drain current model for current collapse effect and it is given in terms of intrinsic capacitance,
conductance and transconductance of the device. The transconductance gm does not vary with Vds at saturation region. This
makes the product of gm and Vgs constant in the drain current equation (23). The only varying part of drain current are the
intrinsic capacitance and conductance. We infer that the non-linear behaviour of drain current collapse is due to the collective
non-linear behaviour of capacitance and conductance.

4. Result and discussion

4.1. DC characterization of AlGaN/GaN HEMT

Fig. 7(a) shows the Id
Vgs characteristics of the proposed HEMT. From the figure, it is evident that the simulated drain
current result is well in agreement with experimental data reported in Ref. [15]. The proposed HEMT shows 6.26%
improvement in drain current compared with [15], which is mainly due to the use of AlN layer between SiN and GaN cap layer.
The sandwiched AlN layer minimize the lattice mismatch and trap charges at SiN/AlN interface which leads to the
enhancement of 2DEG and drain current of the proposed HEMT.
The change in the transconductance of the proposed HEMT with Vgs is shown in Fig. 7(b). It is apparent that the proposed
device exhibits a peak transconductance of 175 mS/mm which is 3% higher than the transconductance value reported in
Ref. [15]. The increase in transconductance mainly arises from the reduction of trap charges at the SiN/AlN interface which in
turn minimize the scattering effect and leads to improve electron mobility in the channel. A change in threshold voltage (Vth)
is also observed due to the higher bandgap (6.2 eV) AlN cap layer in the proposed HEMT device.
The drain leakage current variation with respect to Vds for the proposed HEMT is depicted in Fig. 7(c). For the LGD ¼ 2.7 mm,
the drain leakage current is lower than 1 (mA/mm) till it reaches a drain bias of 291 V and 252 V respectively for both proposed
and reported structures [15]. The breakdown voltage obtained for the proposed HEMT is 291 V which is 14% greater than the
simulated breakdown voltage (252 V) of the structure already reported. This is due to the higher heat handling capability of
AlN cap layer over GaN cap layer. Furthermore, the breakdown voltage of 370 V and 420 V are obtained in proposed HEMT for
LGD ¼ 4 mm and 6 mm, respectively.
The current collapse in proposed AlGaN/GaN HEMT is found to be 10% decrease in comparison with the AlGaN/GaN HEMT
[15], which is evident from Fig. 7(d). This reduction in current collapse is mainly due to incorporation of AlN cap layer which
has the higher thermal conductivity of 2 W/cm K. Further, the AlN layer suppress the self-heating effect and traps in the
interface of the device. The results of the new drain current collapse model is also found to be correlated with simulation. The
current collapse is further analysed by potential and electric field distribution in the following sections.

4.2. Energy band profile

The higher energy band gap of AlN cap layer in the proposed AlGaN/GaN HEMT bend its AlGaN barrier band more upward
than band of AlGaN/GaN HEMT [15] in Fig. 8. At the hetro-interface, this upward bent of AlGaN band in the proposed HEMT
816 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820

Fig. 7. a) The transfer and b) the transconductance characteristics of AlGaN/GaN HEMT. c) Drain leakage current versus Vds at Vgs ¼
10 V d) Ids
Vds charac-
teristics at Vgs ¼
1 V, 0 V.

Fig. 8. a) Energy band diagram of AlGaN/GaN HEMT [15] and b) proposed AlGaN/GaN HEMT at Equilibrium condition along the vertical axis.

gives the band edge of
0.28 (eV) which is lower than band edge of reported HEMT in Ref. [15] by
0.08 (eV). The lower value
of band edge improve the sheet carrier density of proposed device at equilibrium state (Vgs ¼ Vds ¼ 0 V).

4.3. Potential and electric field analysis

The potential distribution profile along the channel dimension for different Vds ¼ 4, 15, 30, 100 V is given in Fig. 9(a). It is
apparent from the figure that the potential profile at the drain end increase as the Vds increases. This is mainly due to the
 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820 817

Fig. 9. a) Potential and b) electric field distribution along the channel of the device.

enhanced electric field between the gate and drain end of the device. This subsequently reduces the density of 2DEG and
drain current. Moreover, there is an increase in the potential distribution under gate terminal, a shift in threshold voltage is
also observed in the analysis. Fig. 9(b) shows the electric field distribution for different drain voltages along the channel. At
high voltage, electric field shows two peaks; a peak at field plate and another at gate edge. For Vds of 4, 15, 30 V, electric field
shows only one peak at gate edge. As the voltage is increased further, the field plate peaks begins to appear. At Vds ¼ 100 V,
two peaks are observed at the gate and field plate edge, the peak field values are 2.9 MV/cm and 2.1 MV/cm respectively. As a
result, a growing trend has been seen in the field plate peak with increase in Vds. This leads to diminish the current collapse in
the Ids
Vds curve as in Fig. 7(d).

4.4. Intrinsic capacitance extraction

The values of intrinsic capacitance and conductance are extracted to analyse its impact on the DC performance of the
proposed HEMT. The bias dependent intrinsic capacitances (Cgd and Cgs) are shown in Fig. 10(a). The capacitance values are
found to be relatively low (0.5 pF) and shows an increasing fashion with Vgs. The values of the capacitance remain unchanged
at 0.5 pF till it reaches the threshold voltage of
5 V and attains its maximum value of 3 pF at Vgs ¼ 0 V. The obtained
maximum value of capacitance at Vgs ¼ 0 V is determined by the physical dimension of the gate and field plate of the device.
Also, the values of Cgd is 0.25 pF higher than Cgs, which is due to the small vertical extension of depletion charges under drain
end of gate terminal. Consequently, it reduces the effect of trap charges on drain current [9]. Further, a steep behaviour is
observed in Cgd and Cgs, which is the sign of enhanced lattice matching at the SiN/AlN interface [8].
Fig. 10(b) shows the drain voltage dependence of Cgd and Cgs. It shows that the Cgd and Cgs tail off for higher drain voltages
due to the expansion of depletion charges under gate terminal. It also observed that the value of Cgd shows a nonlinear
behaviour of 1 pF with higher drain voltages. This clearly shows that Cgd plays an important roll in non-linear decrease of

Fig. 10. a) Extracted intrinsic capacitances (Cgd and Cgs) Vs gate voltage. b) Extracted intrinsic capacitances (Cgd and Cgs) Vs drain voltage.
818 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820

Fig. 11. Extracted intrinsic conductance (Ggd) versus drain voltage.

drain current. Also, an increase in the value of Cgd is observed for Vds above 50 V, which is due to the more electric flux lines
established between the drain terminal and field plate. As a result, the surface trap charges are reduced in the SiN passivation
layer [48e53].

4.5. Intrinsic conductance extraction

Here the extraction of intrinsic conductance is carried out. As Vds increases, the conductance Ggd between gate and drain is
found to be decreasing as shown in Fig. 11. The result clearly shows the reduction in the minority carriers between gate and
drain [13], which in turn leads to decrease in gate leakage. Based on the investigations carried out above, it inferred that the
non-linear behaviour in drain current collapse over drain knee voltage is the collective sum of non-linear behaviour in ca-
pacitances and conductance.

4.6. Y - parameter extraction

The imaginary part of Y-parameter is extracted to analyse the intrinsic and extrinsic capacitances. The extracted values of
Y-parameters are shown in Fig. 12. The imaginary part of Y12 is decreasing from 0 to - 400 (Mho) for the frequency range of

Fig. 12. Extracted Y-parameters Vs frequency of 0e40 GHz.

 D. Nirmal et al. / Superlattices and Microstructures 113 (2018) 810e820 819

0e40 GHz. This clearly shows that the decreasing trend in Y12 is not linear, which leads to a variation in Cgd. Beyond 40 GHz,
the capacitance becomes more non-linear, which affects the current gain and stability of the device.

5. Conclusion

An accurate intrinsic small signal equivalent circuit has been developed for AlGaN/GaN HEMT. A new drain current model
is derived using the equivalent circuit and the current collapse effect is analysed. The analysis suggested that incorporation of
AlN cap layer helped to minimize the current collapse. And also the use of field plate supports to achieve a higher breakdown
voltage compared with convention HEMT structure. These devices are undoubtedly the most suitable candidates for future
high power and high speed applications.

Acknowledgment

This work is supported by Department of Research and Development Organization (DRDO), Govt. Of India (Grant No. ERIP/
ER/DG-MED&CoS/990616501/M/01/1646).

Appendix A. Supplementary data

Supplementary data related to this article can be found at https://doi.org/10.1016/j.spmi.2017.12.027.

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