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ANALYTICAL MODELING OF ALGAN/GAN/INGAN
HIGH ELECTRON MOBILITY TRANSISTORS (HEMTS)
THROUGH POLARIZATION EFFECTS
V. Sandeep
Research Scholar, Centre for VLSI Design, Department of Electronics and Communication Engineering,
Kalasalingam Academy of Research and Education, Virudhunagar, (India).
E-mail: sandeep.vuud404@gmail.com
ORCID: https://orcid.org/0000-0002-0425-8688
J. Charles Pravin
Associate Professor, Centre for VLSI Design, Department of Electronics and Communication Engineering,
Kalasalingam Academy of Research and Education. Virudhunagar (India).
E-mail: charles@klu.ac.in
ORCID: https://orcid.org/0000-0002-9009-6274
Recepción: 28/11/2019 Aceptación: 15/01/2021 Publicación: 30/11/2021
Citación sugerida:
Sandeep, V., y Pravin, J. C. (2021). Analytical modeling of AlGaN/GaN/InGaN High Electron
Mobility Transistors (HEMTs) through polarization eects. 3C Tecnología. Glosas de innovación aplicadas
a la pyme, Edición Especial, (noviembre, 2021), 371-383. https://doi.org/10.17993/3ctecno.2021.
specialissue8.371-383
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ABSTRACT
High Electron Mobility Transistors (HEMTs) are high frequency hetero-junction transistors
used for various high-power applications like RF, radiation, space etc. AlGaN/GaN
HEMTs form Two-Dimensional Electron Gas (2DEG) when subject to stress between the
junction of a wide bandgap and low bandgap material. It is essential to evaluated the
charge denstiy induced due to polarization present in the 2DEG area, so the subsequent
number of electrons present in the quantum well can be evaluated. The polarization and
the sheet carrier density proles are investigated in the AlGaN/GaN hetero-structures
with an InGaN back-barrier layer (AlGaN/GaN/InGaN hetero-structure). The impact
of InGaN back-barrier on the polarization eects at the interfaces between AlGaN/GaN
as well as GaN/InGaN are studied here. An eective 2DEG density is obtained at a peak
value of 3.75 x 1013 cm-2. The graph is interpolated using linear interpolation. The carrier
concentration and the density in the 2DEG region has a signicantly enhanced value when
compared with the conventional AlGaN/GaN HEMTs. The sheet carrier concentration
of the proposed AlGaN/InGaN/GaN heterostructure attained 24% increase than the
one achieved with the conventional AlGaN/GaN structure. The outcomes prove that this
device could be potential candidate for microwave and power switching applications.
KEYWORDS
HEMT, AlGaN, GaN, InGaN, MATLAB, 2DEG, Polarization, Carrier concentration.
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1. INTRODUCTION
The group III-V nitride-based semiconductors has been essential materials for electronic
device applications that concern high power and high frequency applications. Over
the years, several III-V group semiconductors have been employed for these kinds of
applications. The Gallium Nitride High Electron Mobility Transistors (HEMTs) due to its
unique characteristics have found to be well suited for high power and Radio Frequency
applications (Fletcher & Nirmal, 2017). Various group III-nitrides like Gallium Nitride
(GaN), Aluminum Nitride (AlN), and Indium Nitride (InN), are used for the formation of
high mobility devices due to their above-mentioned properties such as High breakdown
eld and high velocity saturation. The bound charge of sheet charge strength of nitride
materials on the alloys of GaN, InN and AlN have been given in Foutz et al. (1999).
Due to their capability to handle large power at higher frequencies, the AlGaN/GaN
HEMT comes out as a next-generation RF and microwave power amplier. HEMT is a
hetero-structure device. Hetero- structure device generally satises the demands of high
speed, high power and high frequency. HEMT is widely utilized for applications that suit
very high frequencies. One of the main benets of the HEMT hetero-structure which
make it suitable for high-speed applications is the creation of Two-Dimensional Electron
Gas (2DEG).
The 2DEG is formed at the junction of the hetero-structure which enhances the electron
mobility of the device, which is caused due to the interfacing of wide bandgap (doped) and
the low bandgap (undoped) materials. 2DEG happens because of the polarization eects
formed in the hetero-junction. Simulated variation and lattice mismatch during formation
of the hetero-structure gives rise to polarization. When a doped (wide band-gap) material
is grown over an un-doped (narrow band-gap) material, due to dierence in their band
energies the lattice structure tends to adjust to each other’s atomic structures (Ambacher et
al., 2000; Ambacher et al., 1999).
The material properties of AlGaN make it a viable contender for high-speed applications.
The InGaN layer is mainly used for improving the electron mobility present in 2DEG.
Disorderly scattering of alloys could be reduced using the InGaN layer and it also helps in
improving the concentration of 2DEG in the hetero-junction (Kumar, Arya, & Ahlawat,
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2013; Bernardini, Fiorentini, & Vanderbilt, 1997). Due its increasing concentration property
and carrier mobility, it is used for high power applications.
The properties evaluated in the AlGaN/InGaN/GaN hetero-structure, which are compared
to existing AlGaN/GaN structure. The AlGaN/GaN has a wurtzite structure. The structure
of AlGaN/GaN is shown in Figure 2. Strain happening in the top layer causes piezoelectric
polarization which could be ve times of that happening in conventional AlGaAs/GaAs
structure which signicantly increases the carrier concentration of the interface (Baskaran
et al., 2013). In comparison to AlGaN/GaN, the addition of InGaN layer has higher
piezoelectric polarization. The total polarization induced charge density is evaluated by
adding both the spontaneous and piezoelectric polarization. By adding a hetero layer
in place of the existing one, the tensile and compressive strain gives rise to piezoelectric
polarization. The stress depends on the lattice parameter value of InGaN (Yu et al., 1997).
Liu et al. (2006) reported an AlGaN/GaN/InGaN/GaN double-heterojunction HEMT
(DH-HEMT) with high mobility 2DEG and reduced buer leakage. The electron mobility
obtained in this structure is 30% higher than in conventional AlGaN/GaN HEMT.
Replacement of AlGaN barrier layer in AlGaN/GaN HEMT with the InAlN layer with
varying Indium mole fractions is suggested in Kuzmik (2002). The n++GaN/InAlN/AlN/
GaN HEMT by eect of bulk and interface traps is studied in Molnár et al. (2014) using
Sentaurus TCAD simulation. Their result depicted the aect in free carrier concentration
in the channel by acceptor traps.
Two types of polarization eects exist in the region: piezoelectric polarization and
spontaneous polarization. Spontaneous polarization happens due to strong structural defects
in the lattice structure whereas the piezoelectric polarization is caused due to mismatch of
lattice structures happening in the device when the two hetero materials are grown one over
another. This paper concentrates on nding the polarization induced charge density and
sheet carrier concentration for the AlGaN/InGaN/GaN hetero-structure which is derived
from the self-consistent Poisson and Schrodinger equations. The remaining of the paper is
divided into the following sections. Section II depicts the proposed method used. Section III
shows the results and discusses the outcomes. Section IV concludes the paper.
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2. DEVICE STRUCTURE AND MODEL FORMULATION
The AlGaN/GaN layer could function at higher temperatures and voltages better than
other III-V group materials since it has a wide energy bandgap. The AlGaN/GaN/InGaN
structure is the proposed model as shown in Figure 1. The sheet carrier concentration
in Two-dimensional electron gas (2DEG) region of the AlGaN/GaN/InGaN structure
changes with change in polarization induced charge density.
Figure 1. AlGaN/GaN/InGaN Hetero-structure.
Source: own elaboration.
A. Spontaneous polarization
During zero strain state of the III-V semiconductor, a polarization eect takes place in the
equilibrium lattice known as spontaneous polarization. The ionicity of III-V group covalent
bond is much smaller than the ionicity of covalent bond. The spontaneous polarization of
GaN is higher than AlN, due to its dependency on the mole fraction of Al. The spontaneous
polarization of the AlGaN/GaN/InGaN is given below as described in Vetury et al. (2001).
(1)
B. Piezoelectric polarization
The strong iconicity present in the metal- nitrogen covalent bond changes the ideality of
the III nitride lattice thus bringing heavy modications lattice polarization. Strain is a way
through which the ideality of the crystal can be changed. Piezoelectric polarization in the
structure is caused due to the stress in the lattice. The applied stress changes the ideal lattice
parameters by varying a0 and c0 in the crystal structure. The strength of polarization varies
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accordingly, by change in lattice parameters a0 and c0. The total polarization decreases
with increase in a0/c0 ratio and vice versa.
(2)
The piezoelectric polarization PPE depends on the strain along the c axis εz, as well the
inplane stress εx and εy. Here e33 and e31 are termed piezoelectric coecients.
The relationship between lattices constant is given as (Kuzmik, 2002):
(3)
Here C0 is height of the crystal structure; C33 and C13 are elastic constants
Using both the equations the piezoelectric polarization is given as (Vetury et al., 2001):
(4)
This piezoelectric polarization is calculated in the c- axis.
C. Polarization sheet charge
Polarization eects lead to forming the bound charge density by attracting the bound sheet
charge. Positive bound charge leads to negative sheet charge. The total sheet charge due to
piezoelectric and spontaneous polarization is caused in both the structures: AlGaN/GaN
and AlGaN/GaN/InGaN (Yu et al., 1997).
(5)
The relaxation degree and the Aluminum concentration x is considered for calculating the
sheet carrier concentration. The degree of relaxation is calculated as (Vetury et al., 2001):
(6)
where a is the lattice constant.
The increase in relaxation degree leads to a linear increase in sheet charge. Since there
causes a maximum piezoelectric polarization in the junction, the strain relaxation could
restrict the induced sheet carrier density.
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D. Sheet carrier concentration
The carrier concentration ns(x) is formed due to several other factors including total charge
density σ(x) which is evaluated by
(7)
Where σ(x)/e is the polarization induced charge density, є is the Dielectric constant of
material, e is the charge, eФb (x) is the height of Schottky barrier, EF (x) is the Fermi level
energy and ΔEC is the oset for conduction band.
3. RESULTS AND DISCUSSION
Based on the equations obtained for Polarization sheet charge earlier, analytical modeling
was carried out in the AlGaN/GaN/InGaN structure for nding the sheet carrier
concentration.
Mathematical modeling was also performed for calculating the charge density and electron
concentration for the sheet carrier for the conventional AlGaN/GaN HEMT as given in
Ambacher et al. (2000).
The analytically modeled equations for the charge density and sheet carrier concentrations
were evaluated for the proposed AlGaN/GaN/InGaN hetero-structure using the MATLAB
software. It was later compared with the existing AlGaN/GaN HEMT.
The nal results show that the proposed AlGaN/GaN/InGaN hetero-structure displayed
improved performances in terms of both charge density as well as sheet carrier concentration
than the AlGaN/GaN HEMT.
3.1. SIMULATION RESULT OF POLARIZATION SHEET CHARGE
The sheet charge density is rst found out for the AlGaN/GaN/InGaN hetero-structure
which was solved self-consistently using the Poisson and Schrodinger equations.
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Figure 2. Polarization induced charge density of AlGaN/GaN Hetero-structure.
Source: own elaboration.
Figure 3. Polarization induced charge density of AlGaN/GaN/InGaN Hetero-structure.
Source: own elaboration.
Polarization charge is calculated in three regions:
• Region a - 0<x<0.42
• Region b - 0.43<x<0.68
• Region c - 0.69<x<1
where x is the Al concentration for Alx Ga1-x N structure.
The variation happening in sheet charge is observed in the region I i.e. x varies from 0 to
0.4 as shown in Figure 5. In this region the sheet charge of AlGaN/GaN/InGaN is about
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3.75 x 1013 cm-2 whereas in AlGaN/GaN it is about 1.7 x 1013 cm-2. In region II only slight
variation is observed. And in region III, it is similar to AlGaN/GaN HEMT.
3.1. SIMULATION RESULT OF SHEET CARRIER CONCENTRATION
Figure 4. Sheet carrier concentration of AlGaN/GaN Hetero-structure.
Source: own elaboration.
Figure 5. Sheet carrier concentration of AlGaN/GaN/InGaN Hetero-structure.
Source: own elaboration.
The above-mentioned outcomes display the Aluminum concentration x to the electron
concentration ns. The increase in sheet carrier concentration with increase in Al
concentration in examined. The maximum carrier concentration observed is 3.7 x 1013 cm-2.
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The addition of an InGaN layer has more eect on the increase in carrier concentration
than it has on the conventional AlGaN/GaN HEMT. The maximum value of carrier
concentration in AlGaN/GaN/InGaN exceeds the already existing structure of AlGaN/
GaN at about 3x1013 cm-2. The above results display better polarization induced charge
densities and sheet carrier concentrations for the proposed AlGaN/GaN/InGaN and
hence could be analyzed that it has a better mobility at the 2DEG region and has better
current owing through the region, making it even better and suitable for high frequency
applications like RF, space and radiations.
4. CONCLUSIONS
In conclusion, compared the sheet charges induced due to polarization eect has been
compared which is bound at the interface of AlGaN/GaN/InGaN by varying the value
of Aluminum concentration from 0 to 1. The variation in the aluminum concentraion
and piezoelectric constant was observed by considering the strain in the hetero-junction.
The nonlinear eect which is arising due to the strain in the piezoelectric polarization is
neglected. The sheet carrier concentration in 2DEG is increased by adding the InGaN layer.
The two-dimensional electron gas region increases with increase in electron concentration
at that area. The sheet carrier concentration and charge densities are improved when taken
in comparison with the existing AlGaN/GaN hetero-structure.
ACKNOWLEDGEMENT
The Authors are thankful to the management of Kalasalingam Academy of Research and
Education (KARE) for the provision of TCAD laboratory facilities during this research.
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