A Novel Graphene Nanoribbon Field Effect Transistor for ... - IEEE Xplore

A Novel Grapphene Nanoribbon Field Effect Transistor fo for Integrated Circuit Design Yaser Moohammadi Banadaki* and Ashok Srivastava** School oof Electrical Engineering and Computer Science Louisiana State University Baton Rouge, LA 70803, U.S.A. * [email protected]; **[email protected] Abstract—In this work, we present a noovel structure of Graphene NanoRibbon Field-Effect Transistorr (GNR FET) to reduce short channel effects. In this structuree, two side metal gates with lower work-function than the main ggate are used in a conventional double-gate (DG) GNR FET top pology to provide virtual extensions to source/drain regions whilee these are biased constant, independent of the main gate. The prooposed GNR FET structure improves drain-induced barrier llowering (DIBL), which can reduce the short-channel effects (SCE) in device performance such as on/off current ratio, off-sstate current and subthreshold slope to make it a more suitable configuration than the normal GNR FET for digital integrated circuit design.

self-consistent solution of three-dimensional (3D) Poisson– Schrödinger equation, within the non-equilibrium Green’s he results demonstrate that function (NEGF) formalism [7]. Th SCEs are significantly reduced in our proposed II-GNR FET structure.

Keywords—Graphene NanoRibbon (GNR R); Field Effect Transistor (FET); drain-induced barrier lowerin ng (DIBL); shortchannel effects (SCEs);

The (13,0) GNR (W=1.48nm) haas a bandgap of Eg=0.86eV. The thickness of gate oxide is tox o =2nm and the dielectric constant of SiO2 is εr=4. Three adjaccent metallic gates are used, where the main gate and two side gaates have work functions of Φ1=4.8eV and Φ2=4.5eV, respectiv vely. The source and drain regions are doped with a molar fracttion of ionized donors equal to 5×10-3/cm3 while the channel iss intrinsic. In tight binding calculations, the nearest neighbor coupling c parameter of a pz orbital for the internal atoms and atoms along the edges are t=2.7eV and t(1 + δ) with δ=0.12, reespectively [1]. The length of the main gate is LM = 5nm and th hat of the side gates are LS = 3.5nm. The effects of edge bond d relaxation, third nearest neighbor coupling, and band to band d tunneling are neglected in the simulation of GNR band structurre.

I.

II.

Figure 1 depicts a 3D schematicc view of the II-GNR FET. The triple-gate structure is a modiification of a conventional DG GNR FET [8, 9], which sandwiiches an armchair graphene nanoribbon between two gates ass both channel and doped source/drain extensions [2].

INTRODUCTION

Graphene Nanoribbon (GNR) is one oof the promising materials for future non-classical devices annd nanoelectronic circuits because of its exceptional electronic pproperties such as the large carrier mobility, the possibilityy of band gap engineering, and planar structure [1]. On one hhand, GNR fieldeffect transistors (GNR FETs) can provide high on/off current ratio by introducing non-zero band gap at the expense of reducing the carrier mobility of graphene. Onn the other hand, GNR FETs still have a problem with low on/ooff current ratio in the case of wider graphene nanoribbon (high m mobility) with the channel length below 10nm as it has been reported theoretically [2] and experimentally [3]. Thhe short channel effects (SCEs) degrade the controllability of thhe gate voltage to drain current, which mainly arises from the baarrier lowering at the beginning of the channel due to the changee in drain voltage, known as the drain-induced barrier lowerinng (DIBL). The electrically induced extensions of source/drrain regions has been reported as an effective method to suuppress SCEs in MOSFETs as well as in nanometer devices [44-6]. However, to the best of our knowledge, this structure has not been applied to the GNR FETs. In this paper, we propose a structure whhich has two side gates with a lower work function than thee main gate and independent bias to induce the electricaally controllable inversion layers next to drain and source regioons. As such, we refer to the proposed GNR FET as inducedd inversion GNR FET (II-GNR FET). We have simulated II-GN NR FET using the

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NR FET STRUCTURE SIMULATION OF II-GN

Fig. 1. Schematic view off a II-GNR FET

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The GNR FET was simulated by converging an iterative procedure, where the 3D Poisson and the 1D Schrödinger equations are solved self-consistently, within the NEGF formulism. The NEGF formalism is a strength simulation approach to treat quantum-mechanical confinement as well as the effects of contacts on the carriers transport in the channel. The mean-free-path in nanoribbons is around hundreds of nanometers at room temperature due to the weak electronphonon interaction, which makes the carriers transport in GNR FETs near ballistic over the long distances. The simulation can be done by solving either an atomistic real space quantum transport [8, 9] or mode space approach [4, 7]. The latter needs less computational time and is accurate enough for the DG GNR FET structure, which permits the quantum problem to be divided in the transverse and longitudinal directions. Figure 2(a) shows the schematic view of an armchair edge nanoribbon graphene along with longitudinal and transverse directions. In the transverse direction, a tight binding Hamiltonian is used individually for each slab along the channel to find the energy subband profiles. In the longitudinal direction, the 1D transport equation can be solved within the NEGF formalism for every pair of subbands corresponding to conduction and valence bands [1]. Figure 2(b) shows the tight-binding (approximation) dispersion, which resulted from the first nearest-neighbor (1NN) interactions with a pz orbital basis. The elements in the Hamiltonian matrix are constructed between th and th th th atoms within the adjacent n and m slabs as follows,

Fig. 2. (a) The schematic sketch of an armchair edge (13,0) GNR as well as the quantities used in the NEGF formulism. Longitudinal and transverse directions correspond to x and z axis. The atom index within the slab used in tight binding approximation is also shown and (b) Energy dispersion relationships vs. normalized wavevector (π/∆x= π/3ac-c, where ac-c is spacing between carboncarbon atoms).

(1)

where h is the Plank constant. VDS, VM-GS and VS-GS are the drain-source voltage, the main gate-source voltage and the side gate-source voltage, respectively. The function f is the FermiDirac distribution, EFS and EFD are the Fermi energy levels in the source and drain regions. Details of the quantum transport calculation can be followed in [10, 11].

where Un and n m are the electrostatic potential energies at the (n ) atom site and the Kronecker Delta, respectively. The retarded Green’s function is given by (2) +

where E is the energy, is an infinitesimal positive value, I is the identity matrix, S and D are the self-energy matrices of the source and drain, respectively. H is the Hamiltonian matrix with the size of N×N, where N is the number of slabs in the GNR channel. U is the electrostatic potential matrix determined by the solution of a 3D Poisson equation as follows,

III.

RESULTS AND DISCUSSION

Fig. 3 shows the ID-VDS characteristics of a conventional GNR FET and the II-GNR FET structures. The simulation result of the GNR FET is in well agreement with that of [8], which applied an atomistic real space quantum transport. It can be noticed from the Fig. 3 that the II-GNR FET has lower drain current in comparison with that of the GNR FET in the same gate voltage. However, there is always a trade-off between increasing the on/off current ratio and value of the on current [2]. An increase in the voltage gain of II-GNR FET makes it suitable for analog applications.

(3) where r and 0 are the material permittivity and free space dielectric constant and is the net charge density distribution determined by the doping profile and the carriers distribution. The Poisson equation is solved using the finite element method in each iterative process to update the self-consistent potential matrix. After the convergence of the iterative process, the source–drain current can be calculated for each subband by expressing the channel transmission coefficient, T in terms of the Green’s function.

The ID-VGS characteristics of the II-GNR FET and a normal GNR FET structures are shown in Fig. 4. It can be noticed from the Fig. 4 that II-GNR FET has a much lower subthreshold current as well as lower leakage current in the off state. The ratio of ION to IOFF currents drastically increases in the II-GNR FET structure when compared with that of a GNR FET, making the proposed structure suitable for digital applications. The improvement in the ION/IOFF current ratio is about twenty orders of magnitude due to the ability of the IIGNR FET structure to suppress DIBL effect.

(4)

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wer values due to the higher shift the subthreshold swing to low control of the gate voltage over the channel. The DIBL can be quantitatively calculated as VTH/ VD by looking at the lateral shift in transconductance characterristics of II-GNR FET and GNR FET in subthreshold regions.. Fig. 7 shows the value of DIBL as a function of the channel length l for II-GNR FET and GNR FET structures. The DIBL dramatically increases by w the II-GNR FET has scaling down the channel length while superior attributes in comparison wiith that of GNR FET. There has been rapid progress in application of graphene transistors in recent years as the first graphene integrated circuit has been reported in radio-frequency analog applications [12]. However, these are not yet candidates to replace CMOS transistors in logic applications a because of the problem with high off-current in graphene-based integrated circuits. The problem is due to nott only narrow band gap of graphene transistors, but also high electrostatic SCE in short nm). In the latter case, the channel GNR FETs (less than 10n direct tunneling from the source to drain is significantly high, such that it operates like a conducto or rather than transistor [2]. The II-GNR FET transistor shows a significant improvement in on/off current ratio, off-state current and subthreshold slope, which makes it a more suitaable configuration than the normal GNR FET for digital integraated circuit design.

Fig. 3. I-V characteristics of II-GNR FET and G GNR FET.

Fig. 4. Transconductance characteristics of II-GNR FET aand GNR FET at VDS = 0.5V and VDS = 50 mV.

The advantage of II-GNR FET over the nnormal GNR FET can be observed by comparing the potential ddistribution along the channel in Fig. 5. In a normal GNR FET,, applying a high drain voltage can decrease the height of a potential barrier between the source and the channel regionn, leading to the DIBL effect and the increase in drain currentt. In other words, the drain current is controlled not only by the gate voltage, but NR FET potential also by the drain voltage. In contrast, the II-GN under the gate is unalterable by increasing VDS, consequently the barrier is significantly in control of the maiin gate voltage. It can be interpreted that the side gates provvide an effective screen for the main gate to prevent the changee in drain current due to the change in drain voltage.

Fig. 5. Potential profile along the channel of o GNR FET and II-GNR FET at VDS= 0.2 to 1 V with the step of 0.2 V.

The investigation of SCE immunity cann be studied by simulating the subthreshold swing and DIBL. Fig. 6 shows the variation of subthreshold swing with differentt channel lengths for both the normal GNR FET and II-G GNR FET. The subthreshold swing is calculated from S = V log(I ) in subthreshold region. It is noticeable from m the Fig. 6 that there is an undesirable increase in subthreeshold swing by decreasing the main channel length due to the loss of gate electrostatic controllability. It is obvious that II-GNR FET can GS

DS

Fig. 6. The Subthreshold Swing values as a function fu of main channel length for GNR FET and II-GNR FET at VDS=50 mV an nd VS-GS=0.7V.

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REFERENCES di, S. Reggiani, and G. Baccarani, R. Grassi, S. Poli, E. Gnani, A. Gnud "Tight-binding and effective mass modeling m of armchair graphene nanoribbon FETs," Solid-state electron nics, vol. 53, pp. 462-467, 2009. [2] Y. Ouyang, Y. Yoon, and J. Guo. "Scaling behaviors of graphene nanoribbon FETs: A three-dimensional quantum simulation study," IEEE Trans. Electron Devices, vol. 54, pp. 2223-2231, 2007. [3] Z. Chen, Y. Lin, M. Rooks and P. Avouris, A "Graphene Nano-Ribbon Electronics," Physica E: Low-dimensio onal Systems and Nanostructures, vol. 40, pp. 228-232, 2007. ntum simulation study of a new [4] Z Arefinia and A. A. Orouji. "Quan carbon nanotube field-effect transiistor with electrically induced source/drain extension," IEEE Trans. Device and Materials Reliability, vol. 9, pp. 237-243, 2009. [5] H. Hawaura, T. Sakamoto, T. Baba, Y. Y Ochiai, J. i. Fujita, S. Matsui, et al., "Transistor operation of 30-nm gatte-length EJ-MOSFETs," Electron Device Letters, IEEE, vol. 19, pp. 74-76, 1998. [6] S. Han, S. Chang, J. Lee, and H. Shin, "50 nm MOSFET with S/D) extensions,", IEEE Trans. electrically induced source/drain (S Electron Devices, vol. 48, pp. 2058-206 64, 2001. [7] P. Zhao and J. Guo. "Modeling edge effects in Graphene Nanoribbon Field-effect Transistors with real and d mode space methods," J. Appl. Phys., vol. 105, 034503, 2009. [8] H. Mohammadpour and A. Asgari, "Numerical study of quantum phene nanoribbon field effect transport in the double-gate grap transistors," Physica E: Low-dimensio onal Systems and Nanostructures, vol. 43, pp. 1708-1711, 2011. L and D. E. Nikonov, [9] G. Liang, N. Neophytou, M. S. Lundstrom, "Computational study of double-gate graphene g nano-ribbon transistors," Journal of Computational Electronics, vol. 7, pp. 394-397, 2008. [10] X. Guan, M. Zhang, Q. Liu, and Z. Yu, "Simulation investigation of ully self-consistent NEGF and TB double-gate CNR-MOSFETs with a fu method," IEDM Tech. Digest, pp. 761-7 764, 2007. [11] S. Datta, Quantum Transport: Attom to Transistor, Cambridge University Press, 2005. [12] J. Markoff. “I.B.M. Researchers Create High-Speed Graphene Circuits”. Internet: http://www.nytiimes.com/2011/06/10/technology/ 10chip.html?_r=0, Jun. 9, 2011. [1]

Fig. 7. The DIBL values as a function of main channel length for GNR FET and II-GNRFET at VDS=50 mV and VS-GS=0.7V.

IV.

CONCLUSION

In order to introduce a graphene nanoribbon field effect transistor as a high performance device in ddigital integrated circuits, a novel structure has been proposed tto reduce the offstate current because of short-channel effects. In this structure, two side gates are biased independent of the main gate as the virtual extensions to the source and the drain regions to shield the effect of drain voltage variation on the chaannel region. The device characteristics has been simulated using the selfconsistent solution of three-dimensional Poissson–Schrödinger equation, within the non-equilibrium G Green’s function (NEGF) for both the proposed II-GNR FET aand normal GNR FET for comparison. Although the structuree of the II-GNR FET is rather more complex than GNR FET T due to the two side gates, the results demonstrate that it significantly improves the device performance and reliabiliity.

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