International Journal of Engineering & Technology IJET-IJENS Vol:14 No:04 33 I-V characteristics model for Carbon Nanotube Field Effect Transistors Rebiha Marki, Chérifa Azizi and Mourad Zaabat. Abstract-- The performance of carbon nanotube-based transistor is analyzed. The effect of geometrical parameters on the device performance is investigated as d tunnel. We have studied the influence of the material parameters, such as the height of the SB (ΦSB), and some other physical parameters like the nanotube chirality, the gate oxide thickness and the gate oxide dielectric permittivity Our results show clearly that device characteristics can be optimized by appropriately selecting geometrical and physical parameters. cylinders of SWCNTs (Figure 2). MWCNTs are less stable nanostructures with common structural defects. Thus SWCNTs are more suitable for practical applications. Index Term-- CNTFET, Schottky barrier, modeling. I. INTRODUCTION Air Carbon nanotubes CNTs have attracted great attention as potential materials for electronic devices because of their one-dimensional structure and tubular honeycomb network in the nanometer scale. They can be either metallic or semiconducting, depending on the chirality and the diameter of the CNTs [1],That s why they become key materials to envisage the future of BEYOND-CMOS nanoelectronics. Indeed, CNT shows the unprecedented ballistic transport ability, and a large charge mobility, which allow to fabricate CNT-based field effect transistors (CNTFET) with highly competitive performance. The switching of the CNTFETs is based on the bending of the nanotube bands [2]. II. CARBON NANOTUBES CNTs are cylindrical molecules formed from hexagonal structures of hybridized carbon atoms. They belong to the family of fullerenes, allotropic forms of carbon [10, 11]. CNTs are described as hollow cylinders arising from rolling individual or multiple layers of graphene in a joint less cylinders (Fig. 1). Fig. 1. Graphene sheets that shows the orientation of graphene hexagons Fig. 2. Structure of carbon nanotubes: a) SWCNT, b) MWCNT III. MODEL PRESENTATION The CNTFETs are modeled as Schottky barriers transistors (Fig 3). Those SB appear at the interfaces between the semiconducting nanotubes and the metallic leads (i.e., electrodes) when (i) the work function of the metal electrodes is higher than that of the nanotubes, and/or (ii) when the nanotube is supposed to behave as a p-type semiconductor (which is the case generally when operating under air). In a conventional CNTFET, the contacts between the metal electrode and the carbon nanotube channel are ohmic, the electrode metal contacts directly the nanotube, its principle of functioning is similar to MOSFET, when a gate voltage is applied C-CNTFET shows an unipolar characteristic[3]. For SBCNTFET, the contact is not ohmic but with an access resistance, it is a Schottky type with an energy barrier. The work function alignment of the leads with the nanotubes hence determines the extent of the Schottky barriers. A direct way to determine the presence of the Schottky barrier (SB) within the CNTFET is to point out the difference before/after approaching materials (the metal electrodenanotube) to align the Fermi level at the thermal equilibriumthe metallic and nanotube sides, respectively (Fig 3). Therefore, carriers with energies above the SB height reach the channel by thermionic emission. On the other hand, carriers with energies below the SB height have a tunnel probability to reach the channel [4]. There are two types of nanotubes: single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs), which are built of few centric
International Journal of Engineering & Technology IJET-IJENS Vol:14 No:04 34 Where is the nanotube diameter, is the gate oxide thickness, and are the dielectric permittivity of the nanotube and the gate oxide, respectively. The channel potential is given by [8]: Fig. 3. Formation of a Schottky barrier in the contact between the metal and the intrinsic nanotube materials. The height of the barrier For SBs of the valence band: is given by: { } The parameter is given as follows [9,10]: For SBs of the conduction band: Where : and are the work functions corresponding to the Fermi level of the carbon nanotube and the metal materials, respectively. The energy is the minimum of sub-band energy from the Fermi level of the carbon material. It is often called the lower sub-band, which is equal to. The index represents the order of the sub-band energy. IV. CURRENT CALCULATION The electrical current is expressed as [5]: V. RESULTS AND DISCUSSION In this work, we consider one sub-band. Figure 4 shows that the characteristic Ids versus Vgs is ambipolar (current of electrons and holes). Current of holes Current of electrons { ( ) ( )} This expression represents the sum of the energy sub-bands contributions of two terms: The first term represents the contribution of the source contact, and the second one represents the drain electrode contribution in terms of density of the current. With the effective barrier height of the source and drain respectively [6]: ( ) ( ) Where, is the screening length and is the tunneling distance. Fig. 4. for a SB-CNTFET with CNT. of SiO 2. =110 m ev, The influence of the height of the Schottky barrier is shown (Fig 5) on the characteristic Ids = f (Vgs) for three values of Vds=0.1 V Vds=0.3 V Vds=0.5 v Vds=0.7 V Vds=0.9 V Vds=1.2 V at Vds = 0.1 V. Indeed, by increasing the height of the barrier, the current Ids decreases. For a planar configuration, is given by [7]:
International Journal of Engineering & Technology IJET-IJENS Vol:14 No:04 35 10-8 SB height = 0.2 e. V SB height = 0.4 e. V SB height = 0.6 e.v 10-12 10-13 d tunnel = 8 nm d tunnel = 6 nm d tunnel = 4 nm 10-12 10-14 10-13 10-15. 10-14 Fig. 5. for a SB-CNTFET with a CNT for. =[0.2; 0,4; 0.6] e.v, We see clearly (Fig 6) that when Vgs increases Ids increases 4.5 5 x 10-9 4 Vgs=0.6 V Vgs=0.7 V Vgs=0.8 V Vgs=0.9 V 10-16 Fig 7. The effect of the tunneling distance d tunnel for a SB-CNTFET at Vds=0.1V. As shown in the output characteristics, the sourcedrain current (Ids) as a function of the source-drain voltage (Vds) taken at fixed gate voltage (Vgs) of figure 8, the saturation behavior of the drain current is significantly improved by reducing the SB height. As a matter of fact, Ids sat increases from 0.12 to 1.86 na when the SB height decreased from 0.2 to 0 e. V. 3.5 3 2.5 2 x 10-9 1.8 1.6 SB height=0 e.v 2 1.4 1.5 1.2 1 1 0.5 0.8 SB height=0.1 e.v 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vds (V) Fig. 6. for a SB-CNTFET with a CNT. of SiO 2.. =110 m ev. = 4.835 nm, =3.29 nm. On the other hand, we noticed (Fig 7) that Ids is better for d tunnel = 8 nm than that for d tunnel = 4 nm. 0.6 0.4 0.2 SB height=0.2 e.v 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vds (V) Fig.8. Output characteristics: Ids versus Vds for a SB-CNTFET with a CNT having a (13, 0) chirality, for three different SB heights at a fixed gate voltage of Vgs = 0.2V. On the other hand, we also noticed that the sourcedrain current (Ids) corresponding to the (25, 0) chirality is higher than that obtained from nanotubes having a (11, 0) chirality. Moreover, the best Ids performances were observed for the largest CNT diameters and hence for the lowest CNT gaps (fig 9). We note that the band gap of the semiconducting nanotubes is inversely proportional to their diameter.
International Journal of Engineering & Technology IJET-IJENS Vol:14 No:04 36 CNT(25,0) 10-8 CNT (11,0) CNT (17,0) dox= 10 nm dox= 70 nm -2-1.5-1 -0.5 0 0.5 1 1.5 2 Fig. 9. Ids as a function of the gate voltage Vgs for a fixed Vds of 0.1 V and for a fixed SB-CNTFET of 0.1 e.v and various CNT chiralities of (11, 0), (17, 0) and (25, 0), respectively. On figure 10, we see Ids as a function of two different gate oxide having two different dielectric permittivity. We have chosen the with, and the with. Simulations have shown that the drain current Ids is higher for higher dielectric permittivity..3.5.7.9 ZrO2 SiO2 Fig. 10. The effect of the gate oxide dielectric permittivity on the transfer characteristic for a SB-CNTFET with CNT having a (13, 0) chirality and for two different values of Figure 11 shows Ids as a function of Vgs measured at a fixed Vds of 0.1 V fro two different gate oxide thicknesses of 10 and 70 nm, respectively. We see clearly that when the thickness of the gate oxide layer decreases, the corresponding drain current Ids increases. This is mainly due to the fact that the confinement of carriers is more important. Fig.11. The effect of the gate oxide thickness on the transfer characteristic for a SB-CNTFET with CNT having a (13, 0) chirality. VI. CONCLUSION We have represented a SB-CNTFET model, we noticed that the characteristic Ids versus Vgs is ampipolar. The transistor has a symmetrical structure of energy band between the conduction and the valence band which implies matching contributions of electrons and holes in the current. The best performances are observed for the largest Vgs, We must increase the number of sub-bands in the calculations to obtain a suitable current. Ids is larger for the largest d tunnel. Thus, the saturation behavior of the drain current is significantly improved by reducing the SB height. Ids was is larger for the thinnest oxide layer and highest dielectric permittivity. We have seen that the diameter of the nanotube has a direct influence on the transport properties, where the best performances were observed for the largest CNT diameters and hence for the lowest nanotube band gaps. The obtained results enable us to optimize the geometrical and physical parameters to obtain the best performances of the device. REFERENCES [1] B.Aissa, and El Khani, M.A, The channel length effect on the electrical performance of suspended-single-wall-carbon-nanotubebased field effect transistors, Nanotechnology, 9pp, Vol. 20, No. 17, p.175203, 2009. [2] B.Aissa, D. Therriault, Electrical transport properties of single wall carbon nanotube/polyurethane composite based field effect transistors fabricated by UV-assisted direct-writing technology, Nanotechnology, 8pp, Vol. 23, No. 11, p.115705, 2012. [3] M. Najari and S. Frégonèse, Schottky barrier carbon nanotube transistor: compact modeling, scaling study, and circuit design applications IEEE, Trans. Electron Devices, vol. 58, no.1, pp. 205-215, Jan. 2011. [4] J. Goguet, Contribution à la modélisation physique et électrique compacte du transistor à nanotube, Ph.D. dissertation, Dept. Elect. Eng., Bordeaux 1 Univ,2009. [5] C. Maneux, J. Goguet, S. Fregonese, T. Zimmer, H. Cazin d Honincthun,and S. Galdin-Retailleau, Analysis of CNTFET physical compact model, in Proc. Int. Conf. DTIS Nanoscale Technol., pp. 40 45, 2006. [6] S. Fregonese, H. Cazin d Honincthun, J. Goguet, C. Maneux, T. Zimmer,J. Bourgoin, P. Dollfus, and S. Galdin-Retailleau, Computationally efficient physics-based compact CNTFET
International Journal of Engineering & Technology IJET-IJENS Vol:14 No:04 37 model for circuit design, IEEETrans. Electron Devices, vol. 55, no. 6, pp. 1317 1327, Jun. 2008. [7] J. Knoch and J. Appenzeller, Tunneling phenomena in carbon nanotube field-effect transistors, Phys. Stat. Sol. (A), vol. 205, pp. 679 694, 2008. [8] D. Rechem and S. Latreche, Nanotube diameter effect on the CNTFET performances, presented at the 5th Int. Conf. Sciences of Electronic, Technologies of Information and Telecommunications, Tunisia, Mar. 22 26,2009. [9] G Pennington, N Goldsman and A Akturk, A E Wickenden;"Deformation potential carrier-phonon scattering in semiconducting carbon nanotube transistors"; Applied Physics Letters 90, 062110 (2007). [10] Jie Deng, H. S Philip Wong; "A Compact SPICE Model for carbon nanotube field effect transistors including non-idealities and its application -Part I: Model of the intrinsic Channel region and Part 2: Full device model and circuit performance benchmarking"; IEEE Transaction on Electron Device, Vo1.54, No 12, December 2007.