Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM VIII-O-4 SIMULATION OF GRAPHENE NANORIBBON FIELD EFFECT TRANSISTOR Dinh Sy Hien University of Science, VNU-HCM ABSTRACT Graphene has been one of the most vigorously studied research materials Graphene nanoribbon material has been briefly reviewed Top-gate graphene nanoribbons field effect transistor used for digital IC applications is modeled Self-consistent atomistic simulations based on the non-equilibrium Green’s function method are employed The current-voltage characteristics of the graphene nanoribbon field-effect transistor are studied The effects of the geometrical parameters of channel material on the current-voltage characteristics of the graphene nanoribbon FET are explored Especially, the room temperature on-off current ratio by top-gate voltage of GNR-FET has been calculated and reached 104 Key words: Graphene, Graphene nanoribbon FET, non-equilibrium Green’s function, currentvoltage characteristics INTRODUCTION Graphene [1-8] has been one of the most vigorously studied research materials since its inception in 2004 Graphene has attracted considerable attention from scientific community due to its excellent electronic properties, such as high electron and hole mobilities even at room temperature and at high doping concentration [9], high thermal conductivity [10], and its interesting optical properties [11] 2D graphene is a gapless material, which makes it unsuitable for digital IC applications However, an energy bandgap can be induced by tailoring a graphene sheet into graphene nanoribbons (GNR) called 1D graphene (GNR) [12] Depending on the orientation of the ribbon edges, GNR can have edges with zigzag shape, armchair or a combination of these two [13] In order to obtain a suitable bandgap for transistor applications, the width of GNR must be scaled to extremely small values Bandgap energy of narrow GNR is inversely proportional to the width of the GNR In narrow GNR, line-edge roughness plays an important role in the device characteristics [14-20] The effect of line-edge roughness on the device performance of GNR field-effect transistor (GNR-FET) has been numerically studied in [14-15, 21] In this paper, using top-gate GNR-FET model, device performances are investigated The electronic transport in the GNR-FET used narrow GNR as channel of sub-10 nm is studied The device characteristics are explored by using the non-equilibrium Green’s function method Basing on the obtained results, on-off current ratio of the GNR-FET for digital IC applications has been calculated This work is organized as follows: section describes channel materials used for GNR-FET, simulation method, and results of simulations Concluding remarks are drawn in section MATERIAL AND SIMULATION METHOD Graphene channel materials Bandgap engineering In modern electronics, bandgap formation is the key concept for switching current, and thus, for processing electric signals Although graphene has great advantages for use in electronics applications, including atomically thin channels, high mobility, and large electric field effects, its semi-metallic electronic band structure makes the creation of a graphene transistor quite challenging So far, several methods have been proposed for introduction of bandgap in graphene Among them the most promising are graphene nanoribbons In this section, we briefly review theoretical predictions, experimental results, and the major challenges of the formation of bandgap in graphene Graphene nanoribbons In quantum mechanical systems, the confinement of carriers leads to discrete energy levels This also the case in graphene; however, some diffences are seen because of its peculair lattice structure Thin graphene wires are called graphene nanoribbons Two common structures, armchair and zigzag nanoribbons (Figure 1), have been intensely studied theoretically Theoretical predictions In the following theoretical treatment of graphene nanoribbons, the graphene edges are assumed to be passivated by hydrogen, as illustrated in Figure ISBN: 978-604-82-1375-6 29 Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM In the tight binding (TB) approximation for π-electrons in graphene, armchair graphene nanoribbons are metallic when the number of carbon atoms in the ribbon width, N a satisfies the relation, Na = 3p+2 (where p is a positive integer), and are semiconducting otherwise The energy gap Δ Na is inversely proportional to the width in each group, Na = 3p or Na = 3p+1 Zigzag nanoribbons in the TB approximation are metallic and have flat bands at = In the first-principles calculation using the local spin density approximation (LSDA), the result is significantly different from that discussed above Specially, all of the armchair and zigzag nanoribbons are semiconducting with gaps depending on the ribbon width The energy gap of zigzag nanoribbons in the LSDA calculation, Δ, is well fitted by (1) for the ribbons width w > nm Figure Two kinds of graphene nanoribbons: a) armchair and b) zigzag N a and Nz denote the number of carbons in ribbon width in armchair and zigzag nanoribbons, respectively White circles indicate hydrogen atoms passivating the graphene edges The magnitude of the gaps is presented in Figure Figure Energy gaps in graphene nanoribbons Experiments Graphene nanoribbons have been made by various methods, including electron beam lithography followed by oxygen plasma etching [22-25], and chemical derivation [26-29] The main challenge in gap formation in graphene nanoribbons is suppression of structural disorder Structural disorder causes weak localization and the Coulomb blockade effect, and suppresses the mobility Lithographically defined graphene nanoribbons were first reported by Han et al in 2007 [22] After contacting a graphene flake with Cr/Au (3/50 nm) electrodes, they produced a graphene nanoribbon from the flake by oxygen plasma etching They estimated the magnitude of the energy gap, and found that the energy gap g is well fitted by ISBN: 978-604-82-1375-6 30 Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM (2) where w is the ribbon width, a = 0.2 eVnm, and w* = 16 nm Han et al attributed inactive width w* to contribution from localized edge state near the ribbon edge caused the structural disorder from etching process Graphene nanoribbons have also been made by chemical exforliation Li et al [26] obtained graphene nanoribbons with edges that appeared smoother than those obtained lithographically Graphene nanoribbons with various widths ranging from 50 nm down to sub-10 nm scale were obtained by this method The room temperature on-off current ratio Ion/Ioff induced by the back-gate voltage increased exponentially with decreasing ribbon width; it reached 10 in sub-10 nm ribbons Here, the on (off) current I on (Ioff) is defined as the maximum (minimum) value of the source-drain current I for a fixed bias (source-drain) voltage V within a measured gate voltage range The energy gap g estimated from relationship (3) was converted into an empirical form (4) and falls between the limits of theoretical results (Figure 2) Wang et al [28] reported that even in smooth, chemically graphene nanoribbons with widths of sub-10 nm, the mobility was limited to 200 cm2/Vs and the mean free path was limited These values are significantly smaller than those for wider graphene devices These values were attributed to scattering at the edges caused by edge roughness Top-gate graphene nanoribbons FET In this sub-section, the effect of the geometrical parameters on the transfer characteristics and performance of GNR-FET is investigated A top-gate GNR-FET with gate oxide of Al2O3 with relative dielectric constant, r = 9.8 is assummed [30] Graphene monolayer flake is exfoliated from bulk natural graphite crystals by the micromechanical cleavage The substrate consists of a highly-doped, n-type Si(100) wafer with an arsenic doping concentration of ND > 1020 cm-3, on which a 300 nm-thick SiO2 layer is grown by thermal oxidation Metal contacts on the sample is defined by using electron beam lithography (EBL) followed by a 50 nm-thick metal (Ni) layer evaporation and a lift-off process A graphene FET with source-drain separation and top-gate length is shown in Figure [30] Figure Structure of top-gate graphene field-effect transistor [30] is used in our simulations For all simulation, the widths of source and drain contacts of nm, the length of channel of 10 nm, room temperature are assummed The top-gate GNR-FET having channel of a highly-doped, n-type with NH3 doping concentration is also assummed for suppressing Schottky effect in the source-semiconducting-drain contacts of the device The flow of current is due to the difference in potentials between the source and the drain, each of which is in a state of local equilibrium, but maintained at different electro-chemical potentials 1, and hence with two distinct Fermi functions [31]: f1 E f E 1 ISBN: 978-604-82-1375-6 (5) expE 1 / kBT 31 Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM f E f E (6) expE 2 / kBT by the applied bias V: 2 1 qV Here, E- energy, kB - Boltzmann constant, T- temperature The density matrix is given by dE n dE 2 G E 2 A1E f1E A2 E f2 E (7) The current ID flows in the external circuit is given by Landauer formula: I D q / h dETE f1 E f E (8) The quantity T(E) appearing in the current equation (4) is called the transmission function, which tells us the rate at which electrons transmit from the source to the drain contacts by propagating through the device Knowing the device Hamiltonian [H] and its coupling to the contacts described by the self-energy matrices 1, , we can calculate the current from (8) For coherent transport, one can calculate the transmission from the Green’s function method, using the relation T E Trace 1G2G Trace 2G1G (9) The appropriate NEGF equations are obtained: A f E A f E , A iG G A A G EI H 1 , 1, i 1, 1, , A1 E G1G , A2 E G2G , 1 Gn (10) 2 where H is effective mass Hamiltonian, I is an identity matrix of the same size, 1, are the broadening n functions, A1,2 are partial spectral functions, A(E) are spectral function, G is correlation function We use a discrete lattice with N points spaced by lattice spacing ‘a’ to calculate the eigenenergies for electrons in the channel Results and discussion The main goal of the project was to make a user-friendly simulation program that provides as much control as possible over every aspect of the simulation Flexibility and ease of use are difficult to achieve simultaneously, but given the complexity of quantum device simulations became clear that both criteria were vital to program success Consequently, graphic user interface development was major part of the program We start by simulating ID-VD characteristics of top-gate GNR-FET Figure shows the schematic of the device used in our simulations Top-gate GNR-FET with one-dimensional graphene as the channel is simulated The device is simulated with Al2O3 as the dielectric which has been predicted to be one of the promising dielectrics for GNR-FETs in recent experiment [30] All the simulations have been done for channel length of GNR-FET, L = 10 nm Figure shows the ID-VD characteristics of the GNR-FET having the length of 10 nm versus different gate voltages It can be noted that when the gate voltage is increased the saturated drain current exponentially increased This behavior is in agreement with experimental results [31] ISBN: 978-604-82-1375-6 32 Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM Figure The ID-VD characteristics of the top-gate GNR-FET at different gate votage, VG = 0.1 V, 0.4 V, 0.6 V, 0.8 V (bottom to up) Figure shows the ID-VD characteristics of the top-gate GNR-FET having the length of 10 nm under ballistic transport and that with phonon scattering It is shown that scattering can have an appreciable affect on the on-current At VGS = 0.8 V, the on-current is reduced by 9% due to the phonon scattering Figure The ID-VD characteristics of the gate top GNR-FET at VG = 0.8 V for ballistic, scattering, where the length of the gate is LG=10 nm Figure shows ID-VD characteristics of GNR-FET versus the gate voltage, VG When the gate voltage is small, the drain current is gradually increased When the gate voltage is greater than VG = 0.3 V, the drain current is exponentially increased The modeling results agree well with experimental data [31] Figure The 3D plot of ID-VD characteristics of the top gate GNR-FET versus VG, where the length of the gate is LG=10 nm Figure shows the 3D plot of ID-VD characteristics of the GNR-FET versus the temperature, T It can be noted that as the temperature increases the saturated drain current gradually increases We also observe that the off-current is about 1×10-9 nA at very low temperature and the low gate voltage, V g = 0.1 V From Figure and we can calculate on/of-current ratio, Ion/Ioff = 1×10-5 nA/1×10-9 nA = 104 ISBN: 978-604-82-1375-6 33 Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM Figure The 3D plot of the ID-VD characteristics of the top-gate GNR-FET versus temperature The GNR-FET parameters are: material, Al2O3, the gate length is LG = 10 nm, the gate thickness is tox = nm, at the gate voltage, VG = 0.1 V The effect of the channel length scaling on the device characteristics is investigated ID-VD characteristics of GNR-FET versus the length of the gate layer at room temperature are shown in Figure Apparently, as the length of the GNR-FET decreases, the saturated drain current gradually increases Figure The 3D plot of the ID-VD characteristics versus the gate length of the top-gate GNR-FET at room temperature, T = 300 K The parameters of the GNR-FET: material, Al2O3, the gate thickness, tox= nm Figure shows ID-VD characteristics of the top-gate GNR-FET versus the gate thickness at room temperature Apparently, as the gate thickness, tox of the GNR-FET is increased, the saturated drain current is gradually decreased Figure The 3D plot of ID-VD characteristics of the top-gate GNR-FET versus the gate thickness, tox at room temperature, T = 300 K The parameters of the GNR-FET: material, Al2O3, the gate length is LG = 10 nm ISBN: 978-604-82-1375-6 34 Báo cáo toàn văn Kỷ yếu hội nghị khoa học lần IX Trường Đại học Khoa học Tự nhiên, ĐHQG-HCM CONCLUSION A model for the top-gate GNR-FET using NEGF written in GUI of Matlab has been reported The top-gate GNR-FET has been simulated Typical simulations is then successfully performed for various parameters of the GNR-FET or the electronic transport of GNR-FET has been investigated The model is not only able to accurately describe ID-VG, ID-VD characteristics of the GNR-FET, but also effects of channel materials, gate materials, size of GNR-FET, temperature on the characteristics The obtained results indicate that the performance of GNR-FET in terms of on/off-current ratio is improved in narrow ribbons, while the conductance is degraded in longer channel We also observe that the on/off-current ratio of the GNR-FET is 104 as the GNRwidth of nm and the GNR-length of 10 nm MÔ PHỎNG TRANSISTOR HIỆU ỨNG TRƯỜNG DẢI NANO GRAPHENE Đinh Sỹ Hiền Đại học Khoa học Tự nhiên, ĐHQG-HCM TÓM TẮT Graphene vật liệu nghiên cứu sôi động Trong báo này, vật liệu dải nano graphene tổng quan cách ngắn gọn Transistor hiệu ứng trường cổng sử dụng cho ứng dụng vi mạch số mô hình Những mô mức nguyên tử tự-tương thích dựa phương pháp hàm Green không cân sử dụng Đặc trưng dòng transistor hiệu ứng trường dải nano graphene nghiên cứu Những ảnh hưởng thông số hình học vật liệu kênh lên đặc trưng dòng transistor hiệu ứng trường dải nano graphene nghiên cứu kỹ Đặc biệt tỷ số dòng on-off nhiệt độ phòng theo cổng GNR-FET tính toán đạt tới 104 Từ khóa: 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