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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