Analysis of Conduction Path Dependent Off

advertisement
Advanced Science and Technology Letters
Vol.37(Electrical Engineering 2013), pp.29-33
http://dx.doi.org/10.14257/astl.2013.37.08
Analysis of Conduction Path Dependent Off-Current of
Double Gate MOSFET
Hakkee Jung1,Ohshin Kwon2
1
Department of Electronic Eng., Kunsan National University, 558 Daehak-ro, Kunsan-si,
Chonbuk, Republic of Korea
2
Department of Robot & Control Eng., Kunsan National University, 558 Daehak-ro,
Kunsan-si, Chonbuk, Republic of Korea
[email protected]
Abstract. This paper has presented the relationship of conduction path and
potential distribution for device parameters to analyze the off-current of double
gate(DG) MOSFET. The off-current has been analyzed for the change of
projected range and standard projected deviation of Gaussian function with
device parameters such as channel length and channel thickness. As a result,
this research shows the off-current has greatly influenced on forward and
backward conduction path and potential distribution for device parameters,
especially for the shape of Gaussian function for channel doping concentration.
Keywords: DGMOSFET, device parameter, off-current, conduction path,
potential distribution, Poisson equation
1
Introduction
The mobile processor needs to shrink power consumption and size. The smaller the
size of integrated circuits becomes, the better the yield becomes and the lower the
power consumption of device. The miniature of device offers the various limits to
device operation. The short channel effects (SCEs) are the most important obstacles to
occur with refinement of CMOSFET. Since the SCEs have been eventually happened
from short channel length, the structural modification of transistor has been studied to
increase the channel length, while the size of transistor becomes the smaller. The
multi gate FET (MugFET) is ultimately the transistor to lessen the SCEs by making
the gates of two above around channel of transistor. The double gate MOSFET
(DGMOSFET) is the simplest and representative MugFET[1,2]. Tiwari et al. have
used the Gaussian function as doping profile to solve the Poisson equation and
presented successfully the analytical potential and threshold voltage model, compared
with experimental results [3]. Since the DGMOSFET has two gates of forward and
backward contact, the two conduction path may be formed in the channel. Using
Tiwari’s potential model in this paper, the conduction path dependent off-current is
analyzed in subthreshold region. The two dimensional analytical current model is
presented using Tiwari’s model, and the influence on off-current with conduction path
and potential distribution is analyzed in the subthreshold region.
ISSN: 2287-1233 ASTL
Copyright © 2013 SERSC
Advanced Science and Technology Letters
Vol.37 (Electrical Engineering 2013)
This paper is organized as followings; In section 2, the off-current model derived
from Tiwari’s potential model and conduction path are presented. The section 3
shows the relation of off-current and conduction path for the projected range and the
standard projected deviation of Gaussian function, and conclusions are explained in
section 4.
2
Off-current and conduction path model
Fig. 1 Cross sectional view and potential energy of DGMOSFET
Figure 1 shows two dimensional cross sectional view and potential diagram of
DGMOSFET. Since DGMOSFET is symmetric for forward and backward gate and
potential is nearly constant for z -direction, the potential distributions φ ( x, y ) for
x - and y -direction is derived from Tiwari’s method[3] as followings;
φ (ς , y) =
VG −V fb +  E − Dς

+ ς erf (ς ) + exp(−ς 2 ) /
π




   E − Dς
 

φs −VG + V fb
+ Berf ( B) + exp(− B2 ) / π







(1)
where ς = ( x − R p ) / 2σ p in which R p is projected range , and σ p is standard
projected deviation of Gaussian function , erf is error function, and E, D, B is
constant referred in reference [3]. Note that φs = φs ( ymin ) represents the minimum of
f
b
φs ( y ) . The forward off-current I off and backward off-current I off could be derived
from surface potential when the minimum potential point for x -direction is xmin .
f
I off
=
30
 eφsf /Vt − eφmin /Vt 


WVt2 µn ni2 xmin
−VDS /Vt 

1− e
f
Lg N p
φs − φmin
(
) (
)
(2)
Copyright © 2013 SERSC
Advanced Science and Technology Letters
Vol.37 (Electrical Engineering 2013)
b
=
I off
WVt µn ni2 (tsi
2
− xmin )
Lg N p
(1 − e
() e
φsb /Vt
−VDS /Vt
(
− eφmin /Vt
φsb − φmin
)
)
(3)
where W is channel width, Vt is thermal voltage, µn is electron mobility, ni is
intrinsic concentration, VDS is drain voltage, and φsf and φsb are forward and
backward surface potential at y = ymin , respectively[4]. The φmin is minimum
potential at x = xmin and y = ymin , and N p is maximum doping concentration. To
obtain conduction path dependent off-current in this paper, the relationship of offcurrent and conduction path is analyzed for projected range and standard projected
deviation.
3
Relationship of off-current and conduction path
Fig. 2 Off-currents compared with experimental results.
To verify this off-current model of Eq. (4), our results are compared with
experimental ones for FinFET [5] as shown in Fig. 2, converted with
=
W 2 H fin + T fin where H fin is the thickness of FinFET and T fin is the width of
FinFET. As shown in compared results, the results of our model are good agreement
with those of experiment in the range of 8 nm ≤ R p ≤ 10 nm for projected range and
10 nm for standard projected deviation used in calculation of our model. Therefore
Eq. (4) could be reasonably used to calculate the off-current.
Figure 3 shows the contours of conduction path for forward and backward gate in
the range of 4 nm ≤ R p ≤ 10 nm and 4 nm ≤ σ p ≤ 10 nm in the case of tsi = 10 nm
and Lg = 50 nm . Note number of 0.5 is the center of channel. The inset shows
minimum x position of potential profile. The xmin goes toward backward gate with
increase of projected range and decrease of standard projected deviation. The forward
and backward conduction paths are changed toward center of channel according to the
trend for the change of xmin , but the change for forward conduction path is bigger than
Copyright © 2013 SERSC
31
Advanced Science and Technology Letters
Vol.37 (Electrical Engineering 2013)
one of backward. The movement of xmin toward backward gate from center of
channel causes the increase for the change rate of forward conduction path.
4
Conclusions
The off-current has been analyzed for the change of projected range and standard
projected deviation of Gaussian function with device parameters such as channel
length and channel thickness. Since the forward and backward conduction paths go
toward center of channel with the increase of projected range, the increase of channel
thickness, and the decrease of channel length, the off-current is increasing due to the
weakness of controllability of gate contact. As a result, this research shows the offcurrent of DGMOSFET has greatly influenced on forward and backward conduction
path for device parameters, especially for the projected range and the standard
projected deviation to decide the shape of Gaussian function for channel doping
concentration.
Fig. 3 Contours of conduction paths for forward and backward gate in the case of tsi = 10 nm
and Lg = 50 nm . The numbers notify position normalized from interface of forward gate and
oxide. The inset shows minimum x position of potential profile with same x - and y -axis
as contours graph of conduction path.
References
1. H. Agnihotri, A. Ranjan, P.K. Tiwari and S. Jit : An Analytical Drain Current Model for
Short-Channel Triple-Material Double-Gate MOSFETs, 2011 IEEE Computer Society
Annual Symposium on VLSI, pp.327--328 (2011)
32
Copyright © 2013 SERSC
Advanced Science and Technology Letters
Vol.37 (Electrical Engineering 2013)
2. S. Jandhyala and S. Mahapatra : An Efficient Robust Algorithm for the Surface-Potential
Calculation of Independent DG MOSFET, IEEE Trans. on Electron Devices, vol.58,
pp.1663--1671 (2011)
3. P.K. Tiwari, S. Kumar, S. Mittal, V. Srivastava, K.U. Pandey and S. Jit : A 2D Analytical
Model of the Channel Potential and Threshold Voltage of Double-Gate (DG) MOSFETs
With Vertical Gaussian Doping Profile, IMPACT-2009, pp.52--55 (2009)
4. R. Vaddi, S. Dasgupta and R.P. Agarwa : Two Dimensional Analytical Subthreshold
Current Model of a Generic Double Gate MOSFET with Gate Underlap, 2011 ICEDSA,
pp.246--249 (2011)
5. J. Kedzierski, D.M. Fried, E.J. Edward, T. Kanarsky, J.H. Rankin, H. Hanafi, W. Natzle, D.
Boyd, Y. Zhang, R.A. Roy, J. Newbury, C. Yu, Q. Yang, P. Saunders, C.P. Willets, A.
Johnson, S.P. Cole, H.E. Young, N. Carpenter, D. Rakowski, B.A. Rainey, P.E. Cottrell, M.
Ieong, H.P. Wong : High-performance symmetric-gate and CMOS compatible Vt
asymmetric-gate FinFET devices, IEDM Tech. Dig., pp.437--440 (2001)
Copyright © 2013 SERSC
33