2014 Annual IEEE India Conference (INDICON)
Threshold Voltage Modeling of GaN Based Normally-Off Tri-gate Transistor Chandan Yadav, Pragya Kushwaha, Harshit Agarwal, Yogesh Singh Chauhan Department of Electrical Engineering Indian Institute of Technology, Kanpur, V.P., India 208016 Email:
[email protected] Abstract-In this paper, a behavioral model of threshold voltage for normally-off (enhancement mode) AIGaN/GaN based tri-gate HEMT is proposed. AIGaN/GaN based tri-gate HEMT devices have additional sidewall gates and show threshold voltage variation with decreasing device width. The proposed model captures strain relaxation with reduction in device width , which is one of the primary reason for change in
vth
in AIGaN/GaN
tri-gate devices. Model shows excellent agreement with state-of the-art experimental and simulation data.
I.
devices for channel width scaling. In conventional AIGaN/GaN HEMT devices, threshold voltage becomes more negative as width becomes narrow [14] and reverse is observed for the trigate HEMT as width is reduced [5], [7], [13]. The difference in the behavior of the threshold voltage with respect to channel width (as width becomes narrow), indicates that we need different model for the trigate as compared to the conventional planar HEMT. The threshold voltage model for the conventional long channel and the wide width HEMT [15] is as follows:
INT RODUCTION
ALLIUM Nitride (GaN) is being used for high speed and
G high power applications because it has higher breakdown voltage, saturation velocity and high sheet carrier density [I).
In power electronics applications, normally-off (enhancement mode) devices with low on-resistance are required to avert the possible device destruction caused by short circuit at Vgs O.OV [2], [3). The normally-off FETs are also required for elimination of negative polarity power supply and to realize the simple cost effective logic circuit configuration [4]. =
Recently, AlGaN/GaN based tri-gate/FinFET (fin shaped) normally-off HEMT devices with and without gate oxide have been demonstrated by the Ohi et al. [5] and other research groups [6]-[lO). These AlGaN/GaN based tri-gate/FinFET have additional sidewall gates [11] compared to planer HEMT which enables them to have better electrostatic control on the channel resulting in better on- as well as off-state characteris tics [8], [9]. An important phenomena seen in these devices is increase in threshold voltage with decreasing channel width. The observed shift in threshold voltage with reduction in chan nel width is due to : a) sidewall gates assisted improved gate control on the channel [5], [7], and b) reduction in piezoelectric polarization due to strain relaxation [7], [12). A physical insight of threshold voltage dependency on channel-width is presented by Alsharef et al. [13] using numerical simulation. The normally-off mode device operation of AlGaN/GaN based tri-gate/FinFET makes it a promising candidate for the power electronics applications. To utilize the AlGaN/GaN based tri-gate in power elec tronics circuits, there is an urgent need of a compact model. Here, we are presenting a behavioral model for the threshold voltage variation with channel width. II.
MODEL DESCRIPTION
The AlGaN/GaN based trigate HEMT's threshold voltage behavior is different than the conventional planer HEMT 978-1-4799-5364-6/14/$31.00
©
2014 IEEE
where, x is the mole fraction of Al in AlxGa1-xN, 1Yms(x) is the Schottky barrier height, ,6,Ec(x) is AlGaN and GaN conduction band discontinuity, E ( x) is the dielectric constant of AlxGa1 -xN and CT ( X ) is the total polarization charge density and given as follows:
( )
CT X
=
Psp(AlxGa1-xN) - Psp(GaN) + Ppz(AlxGa1 -xN) -Ppz(GaN) (2)
Here, Psp denotes spontaneous polarization and Ppz de notes piezoelectric polarization in AlxGa1 -xN and GaN lay ers. Psp(AlxGa1-xN) and Ppz (AlxGa1-xN) can be calcu lated as [15], [16] follows:
(3)
Psp(AlxGa1 -xN)
=
X
· Psp(AlN) + (1 - x) . Psp(GaN) +0.019x· (1 - x) (4)
where, a(x) and a(O) are lattice constants, e33(x) and e31 (x) are piezoelectric constants and C33 (x) and C31 (x) are elastic constants. In (4), values for Psp(AlN) and Psp(GaN) is taken from [16). In the tri-gate HEMT devices, strain relaxation occurs with reduction in the channel width of the device. The variation of the degree of relaxation with channel width [13]
6.0x10·1
8.0x10·3
Simulation data [13) -- Model 0
5.0x10·1
.---........ .. ....... ... ---......... ... .... .. r-..., .....,... ... .,..,. .,.. ... .. ---......... ... .... ... ., --
Model
c:
0
� co X co
4.0x1O·1 c:
.�
Q) 3.0x10·1 0:::
en
-
0 2.0x10·1 Q)
�
g>
0
1.0x10·1 0.0 102
103
104
Channel Width (nm)
Channel Width (nm) Fig. 1. Verification of degree of relaxation behavior with data [13) against channel width. The behavior of degree of relaxation for wider width indicates zero relaxation (i.e. full strain condition) and for narrower width indicates partial relaxation.
is shown in Fig. 1 and is modeled using the channel width dependent function as follows:
Fig. 2. The expected decreasing behavior of strain due to lattice mismatch versus channel width. Decreasing behavior of strain for narrower width indicates partial relaxation condition compared to zero relaxation for wider width.
1.0x100
--
Model
�. � a.. -0 Q)
.�
7.5x10·1
co E .... where, X is the degree of relaxation, Wch is channel width (top gate width), f3 and A are the fitting parameters. After including the degree of relaxation, the effective piezoelectric polarization of AlxGal-xN layer can be written as follows [16]:
0 Z 5.0x10·1
2.5x10·1
L....... ..o .... ... .... ... _ ... ........ ... ........ ... _"--... ........ .. .... .. _ .. ........ .. .... ... .... .. ...
1�
1�
1�
1�
Channel Width (nm)
From (6), width dependency can be introduced in total sheet charge density. The width dependent sheet charge density can be written as follows:
Fig. 3. Normalized effective piezoelectric polarization of AlxGal-xN versus width variation. Normalization is done with Ppz of AlxGal-xN of planer HEMT. Decreasing behavior with narrower width indicates reduction in total polarization charge and positive shift in threshold voltage.
III.
CYeff(X)
=
Psp(AlxGal-xN) - Psp(GaN) + Ppz(GaN) -Ppz,eff(AlxGal-xN) (7)
Now the width dependent effective cy(x) from (7) can be used in (1) to capture the threshold voltage variation with width of the AIGaN/GaN based tri-gate devices. From the help of (1) and (7), threshold voltage for tri-gate devices can be written as follows:
In (8), CYeff(x) term introduces width dependency in Vth,eff and all other terms are same as in (1).
RESULTS AND DISCUSSION
The proposed threshold voltage model is verified with the data reproduced from [7] and [13]. The strain relaxation factor X is validated with the data reproduced from [13] as shown in Fig. 1. Model shows the consistent behavior with the data. The behavior of the strain due to lattice mismatch with decreasing width is shown in the Fig. 2. It shows the similar decreasing behavior of strain with channel width as observed in [12] and also shows that strain becomes independent from channel width above 500nm. The decreasing behavior of the normalized effective piezoelectric polarization due to strain relaxation with channel width [7], [13] is shown in Fig. 3. The validation of the proposed threshold voltage model for AIGaN/GaN based tri-gate HEMT with experimental data [7] is shown in Fig. 4. The proposed threshold voltage model shows expected behavior for a wide range of width and has excellent agreement with data. We have developed drain rv
1.0
0.05
Experimental data [7] -- Model
-
0.5
Line: Model
0.04
CO)
0> Cll -
Vgs= �.OV
Symbol: Experimental data
0
0.0
Vgs= 5.0V
'E0.03 E
'0 > -0.5
::c
Vgs= 4.0V
---: 0.02
'0
'0
'0
......
� (J)
0) -1.0
0
.... �
0
0
0
0
Vgs= 3.0V
0.01
I-
-1.5
0
10
0.00 0.0
5
Channel Width (nm) Fig. 4. Validation of the proposed threshold voltage model of the AIGaN/GaN based tri-gate HEMT device with the experimental data [7] with respect to the channel width of the device.
0
0
0
0
0
0
0
V 5= 2.0V 0
2.5
5.0
Vds(V)
7.5
10.0
Fig. 6. Comparison of the Ids Vs Vds of model with the experimental data [18] for the Wch annel = 80nm and Lg = 1.0{tm.
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0.05
[1]
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Line: Model Vds= IOOmV
0.04 -
E E 0.03
�
_-'B 0.02
0.01 W
Channel= 80nm
. A._____..!iiiIi_��_.J ii 0.00 1...___ -7.5 -2.5 7.5 -5.0 5.0 0.0 -10.0 2.5
Fig. 5. Comparison of the Ids Vs Vgs of model with the experimental data [18] for Wch annel = 80nm, Wch annel = 180nm and Lg = 1.0{tm at Vds =100mV .
current model for the tri-gate AlGaN/GaN finFET in [17]. The developed drain current model for tri-gate AlGaN/GaN finFET has excellent agrement with experimental data [18] as shown in Fig. 5 and Fig. 6. IV.
CONCLUSION
The proposed threshold voltage model for tri-gate AI GaN/GaN finFET has expected behaviour and shows excellent agrement with the data. ACKNOWLEDGMENT
This work was supported in part by Semiconductor Re search Corporation, in part by the Compact Model Coalition, in part by the IBM faculty award, in part by the DST Fast Track Scheme for Young Scientist, in part by Ramanujan Fellowship, in part by lIT Kanpurs initiation grant.
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