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Study of Nitrogen terminated doped zigzag GNR FET exhibiting negative differential resistance
Superlattices and Microstructures 86 (2015) 355–362
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Study of Nitrogen terminated doped zigzag GNR FET exhibiting negative differential resistance Santosh Kumar Gupta ⇑, Girija Nandan Jaiswal Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology Allahabad, Allahabad 211004, Uttar Pradesh, India
a r t i c l e
i n f o
Article history: Received 29 July 2015 Accepted 30 July 2015 Available online 1 August 2015 Keywords: Graphene Zigzag GNR FET High-k dielectric Negative differential resistance
a b s t r a c t This paper presents the study of Gallium and Aluminum doped Nitrogen terminated zigzag Graphene Nano Ribbon (GNR) FET with high-k dielectric. The GNR FET structure has been designed and simulated using Quantumwise Atomistix Toolkit software package. The presented GNR FET with n-type (Nitrogen doped) electrodes and p-type (Gallium or Aluminum doped) scattering region are simulated and analyzed using Density Functional Theory combined with NEGF formalism and Device Density of States (DDOS). The device shows a negative differential resistance phenomenon which can be controlled by the gate of the zigzag GNR FET. It is found that doping of Gallium and Aluminum in scattering region provides higher drain current, higher ION/IOFF and IP/IV ratios as compared to that of Boron doped zigzag GNR FET. The potential applications of the device are in logical, high frequency, and memory devices. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The continuous miniaturization of Si devices based on CMOS technology is reaching its physical and geometrical limits so we are moving on other materials. Graphene, a two dimensional honey comb layer of carbon atoms in which carbon atoms form three r bonds in the plane of Graphene in sp2 configuration while another orbital pz, which is perpendicular to the Graphene plane makes p covalent bond, has shown the capability to become the novel material for nano-electronics because of its extraordinary properties [1–3]. This includes ultrahigh carrier mobility, thermal conductivity, electron–hole symmetry and quantum hall effect [4]. Graphene, being a zero band gap material, is not suitable for semiconductor electronics to fabricate FETs. However, formation of Graphene nanostructure of less than 10 nm can induce a band gap [5]. These nanostructures are called Graphene Nano Ribbon (GNR). Confining Graphene in one direction results in zigzag type GNR which shows metallic properties due to wave function localization at the zigzag edges and confining Graphene in other direction results in Arm chair type GNR which shows semiconducting properties due to both quantum confinement and the edge states. The induced band gap depends upon the width of the ribbon [6]. This band gap is not sufficient for Graphene to be used in digital logical applications. Arm chair type GNR has been used to simulate various high frequency GNR FETs [7]. Fabrication of GNRs requires atomically precise edges. Such a technique of fabricating GNRs has been proposed and this opens way for GNR to be used in future high-performance electronics applications [8].
⇑ Corresponding author. E-mail address: [email protected] (S.K. Gupta). http://dx.doi.org/10.1016/j.spmi.2015.07.069 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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Various methods have been reported to open a band gap in zigzag GNR e.g. selective doping [9], edge modulation (defective boundaries and edge disorder) [10,11], enabling each edge Carbon (C) atom to two Hydrogen (H) atoms [12], terminating the edge C atoms of the ribbon by Nitrogen (N) atoms [13]. In this paper we present a study on N (Nitrogen) terminated zigzag GNR FET. The binding energy created by the passivation of Nitrogen molecule (N2) on unpassivated zigzag GNR is always positive. Thus the formation of such ribbons is energetically favorable. The passivation of N can transform zigzag GNR (arm chair GNR) from metal (semiconductor) to semiconductor (metal). Band gap engineering by terminating edge C atoms with N atoms has the advantage that neither it requires any controlled manufacturing, which can be crucial in the case of defective boundaries nor it loses sp2 hybridization of edge C atoms, therefore, the resulting ribbon does not lose its planarity as is the case with H loading [12], where sp3 atoms are present along the edges [13]. In this paper we present a FET structure in which the scattering region (channel) is made of Nitrogen (N) terminated zigzag GNR and is doped with either Aluminum (Al) or Gallium (Ga), electrodes are made of N terminated zigzag GNR and are doped with Nitrogen. The device has been simulated and its electrical characteristics are described using Density Functional Theory (DFT) based on quantum transport calculations and device Density of States (DDOS). Based on these simulations we found that it exhibits negative differential resistance (NDR) in the voltage range of 0.1–0.25 V and provides better ON current compared to the N-passivated zigzag GNR proposed by Kumar et al. [13]. Negative differential resistance implies that for an increasing range of voltage the current will be decreasing. NDR can be either current controlled or voltage controlled. Due to ambipolar transport behavior of Graphene, NDR has been observed and reported in various three terminal GNR devices [14]. Previously single-gate Graphene sheet junctions have also shown negative differential resistance [15]. Negative differential resistance was also discovered in arm chair GNR junction [16,17], and the arm chair GNR junction has been examined for its suitability in tunneling diodes [17]. It has also been reported that p+/p zigzag GNR junction also exhibit NDR with high peak-to-valley current ratio (IP/IV) [18]. GNR FETs have been extensively investigated for their suitability at high frequency electronics [19,20]. Maximum frequency of oscillation (fmax) and cut off frequency (fc) of the proposed device is in the range of Giga-hertz; so, the NDR phenomenon in the proposed device is quite useful for high-frequency applications. 2. FET structure The semiconducting N-passivated zigzag GNR proposed in [13] has been used to realize GNR FET in the present work. The GNR FET is comprised of N-passivated (2, 2) zigzag GNR of which scattering region is doped with Al or Ga as shown in Fig. 1. The length and width of the scattering regions are 2.39 nm and 0.94 nm respectively. A high-k material has been used as gate dielectric to increase the gate control over the scattering region (channel). A typical dielectric constant of 24e0 corresponding to that of Hafnium oxide (HfO2) with thickness of 0.36 nm has been considered [21]. Since both the electrodes and the scattering region are parts of the same N-passivated (2, 2) zigzag GNR, such device structure can be useful for increasing the device density together with simplifying the fabrication process. The dopant atoms (N, Al, Ga) are substituted for C atoms in carbon materials similar to that of dopant added in Carbon Nano Tubes (CNTs) [22]. In the GNR FET, the two electrodes are doped using penta-valent N atoms with a doping concentration of 1 N atom for every 16 C atoms. Doping the N passivated zigzag GNR with N causes it to be n-type semiconductor. The scattering region is doped with trivalent Al or Ga atoms with a doping concentration of 1 dopant atom for every 80 C atoms. Doping the N passivated zigzag GNR with Al or Ga causes it to be p-type semiconductor. Doping with Aluminum (Al) and Gallium (Ga) is preferred because Al and Ga belong to the same group and also both Al and Ga are more reactive than Boron (B) [13]. The band structures of the N doped drain/source, scattering region doped with Al or Ga are shown in Fig. 2(a), (b) and (c) respectively. The Bloch functions for valance band maximum (VBM) and conduction band minimum (CBM) along with the projected density of states are analyzed to get the opening of band-gap. The band gap value for Nitrogen doped drain/source region is 0.62 eV, for Al doped scattering region is 0.35 eV, and for Ga doped scattering region it is 0.37 eV as shown by blue lines in
Fig. 1. Structure of the N-passivated (2, 2) zigzag GNR FET, where the box region at the two sides indicate the contacts region and blue (pink) ball represents the N (Ga/Al) atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. Band structure of (a) the smallest unit cell of N doped electrodes, (b) scattering region (Al doped) and (c) scattering region (Ga doped) of the N-passivated (2, 2) zigzag GNR FET, where the red line represents the Fermi level and region between blue lines represents the band gap. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2(a), (b) and (c) respectively. The source/drain electrodes Fermi level (red line) shifts toward conduction band minimum (CBM) thereby changing the Graphene Nano Ribbon into n-type. But in the scattering region the Fermi level (red line) shifts toward VBM thereby changing the Graphene Nano Ribbon into p-type.
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Since the site of doping also affects the band gap value [23], doping near the center is preferred because doping near the edges tends to suppress the band gap. The zigzag GNR FET consist of N doped source/drain electrodes and scattering region doped with either Al or Ga (shown in Fig. 1) is simulated using Quantumwise Atomistix. Density of States of the scattering region after forming the device is shown in Fig. 3(a) and (b). For both the Al and Ga doped zigzag GNRFET, the Fermi level lies well above in the band gap and hence indicates n-type nature of scattering region. The electrical characteristics of the devices are calculated using DFT-based quantum transport calculations and discussed in the next section.
3. Computational details All calculations have been performed using DFT with the local density approximation for the exchange correlation as incorporated in quantumwise Atomistix Toolkit (ATK) [24,25]. The device structure has been optimized using the Broyden– Fletcher–Goldfarb–Shanno method for optimization as incorporated in ATK. To study the transport properties of the proposed device, the fully self-consistent DFT combined with non-equilibrium Green’s function formalism [25] incorporated in ATK has been used. We took double-f polarized as basis set; the mesh cutoff is 100 Ry or 50 Ha. ATK can model accurately the electrical properties of nano scale devices consist of 3-D atomic arrangements and coupled with two semi-infinite
Fig. 3. Energy-DOS characteristics of (a) scattering region (Al doped) and (b) scattering region (Ga doped) of the N-passivated (2, 2) zigzag GNR FET.
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Fig. 4. Drain current (Id) versus drain voltage (Vds) variation for (a) Al doped zigzag GNR FET, (b) Ga doped zigzag GNR FET, at gate voltages (Vg) of 0.0, 0.2, 0.3, and 0.4 V and (c) comparison of drain current (Id) versus drain voltage (Vds) of Al doped zigzag GNR FET, Ga doped zigzag GNR FET and B doped zigzag GNR FET, at gate voltage (Vg) of 0.4 V.
electrodes. First of all the electronic structures of two electrodes are calculated separately using DFT to get the self-consistent Kohn–Sham potentials and Hamiltonian matrices. Then the current through the channel (scattering region) are calculated from the transmission spectrum using the Landauer–Buttiker formalism [26] as follows:
IðVÞ ¼
2q h
Z
þ1
ðf L ðE; VÞ f R ðE; VÞÞTðE; VÞdE
ð1Þ
1
where fL(E, V) and fR(E, V) are the Fermi functions for the left and right electrodes respectively, q is the magnitude of the charge on an electron, ⁄ is Planck’s constant, and T(E, V) is the energy (E) and bias voltage (V) dependent transmission spectrum.
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Fig. 5. Drain current (Id) versus gate voltage (Vg) variation for (a) Al doped zigzag GNR FET, (b) Ga doped zigzag GNR FET, at drain voltages (Vds) of 0.3, 0.4 and 0.5 V and (c) comparison of drain current (Id) versus gate voltage (Vds) variation of Al doped zigzag GNR FET, Ga doped zigzag GNR FET and B doped zigzag GNR FET at drain voltage (Vds) of 0.4 V.
4. Results and discussion The Id–Vds characteristic of the N passivated zigzag GNR FET is shown in Fig. 4(a) and (b) respectively. It is seen that doping with Al or Ga preserves the negative differential resistance phenomenon as was reported by Kumar et al. [13]. The device
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Table 1 Various parameters of zigzag GNR FET. Zigzag GNR FET parameters
Pmax (nW) fco (GHz) fmax (GHz) gm nX1 Rd (kX)
Doped with Al
Ga
525 340 113 2830 155
489 328 103 2740 144
exhibits negative differential region (NDR) for the gate to source biasing voltage (Vgs) 0.1–0.25 V. The NDR peak shifts toward lower values of Vds as Vgs is increased as is observed from Fig. 4(a) and (b). The peak drain current Id = 482 nA for Vds = 0.1 V occurs at Vgs = 0.4 V and Id = 435 nA for Vds = 0.12 V occurs at Vgs = 0.3 V for Al doped zigzag GNR FET. For Ga doped zigzag GNR FET the peak drain current for Vgs = 0.4 V is 459 nA at Vds = 0.1 V and Id = 412 nA for Vgs = 0.3 V at Vds = 0.12 V. The peak to valley drain current ratio (IP/IV) is 9.83 for Al doped device and 10.2 for the Ga doped device which is greater than that of the B doped zigzag GNR FET reported in [13]. It can also be seen from Fig. 4(a) and (b) that the beyond Vds = 0.3 V the current starts to increase monotonously. The maximum current for the Al and Ga doped zigzag GNR FET are 1051 nA and 978 nA respectively which is more than the maximum current obtained with B doped zigzag GNR FET. Fig. 4(c) shows the comparison among the Id–Vds characteristics of the three devices namely B doped, Al doped and Ga doped devices. Out of these three different zigzag GNR FETs, Al doped device provides 29% more drain current compared to the B doped zigzag GNR FET. The transfer curve of the Al doped and Ga doped devices are represented by Fig. 5(a) and (b). For the Al doped device the current at Vgs = 0.2 V and 0.5 V is 69 nA and 1347 nA respectively for Vds = 0.5 V and 17 nA and 804 nA at Vgs = 0.4 V. We can see from Fig. 5(a) and (b) that as the value of Vds increases from 0.4 to 0.5 V the current increase sharply. The device is ON at Vgs = 0.1 V and the value of Id at this point is 59 nA and 172 for Vds = 0.4 and 0.5 V respectively for the Al doped device. Similarly, for Ga doped device the value of Id at this point is 49 nA and 160 nA for Vds = 0.4 and 0.5 V respectively. For higher values of the drain voltage the current becomes a strong function of gate potential. This characteristic of the device can be utilized in sensing applications. Also, it can be noted that the ION/IOFF ratio is higher for the Al doped device compared to that of Ga doped device. The leakage current is also very small 100 nA. The cutoff frequency, maximum frequency of oscillation, and maximum power consumed by the GNR FETs are also computed at Vgs and Vds of 0.4 and 0.5 V respectively [27]. The maximum power consumed by the device is defined by P max ¼ Id V dsmax , the cutoff frequency is defined by f co ¼ g m =2pC gs and the maximum frequency of oscillation is defined by pffiffiffiffiffiffiffiffiffiffiffi f max ¼ ðf co =2Þ g m Rd and shown in Table 1. The values of transconductance g m ð¼ dId =dV g Þ and drain resistance 1
Rd ð¼ ðdId =dV d Þ Þ are also shown in Table 1. The gate to source capacitance C gs (=1.326 109 F) is same for both the devices. 5. Conclusion FET devices with N-passivated source/drain material and Al/Ga doped zigzag GNR as channel material have been proposed and the electrical characteristics (viz. Id–Vds and Id–Vgs) have been analyzed using DFT based quantum transport calculations. This device also exhibits NDR phenomenon which is explained and validated using energy DDOS characteristics of the channel region of the device. It has been found that the position of NDR peak can effectively be controlled by the applied gate voltage. This result can be used in nano-devices requiring variable or controlled NDR effect such as in memory and RF oscillators. The presented zigzag GNR FETs can also be used in other semiconducting applications by utilizing the presence of energy band gap. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (2004) 666–669. [2] J.S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P.L. McEuen, Coulomb oscillations and Hall effect in quasi-2D graphite quantum dots, Nano Lett. 5 (2005) 287– 290. [3] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (2005) 197–200. [4] A.K. Geim, K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183–191. [5] Y.W. Son, M.L. Cohen, S.G. Louie, Half-metallic graphene nanoribbons, Nature 444 (7117) (2006) 347–349. [6] Y.-W. Son, M.L. Cohen, S.G. Louie, Energy gaps in graphene nanoribbons, Phys. Rev. Lett. 97 (2006) 216803-1–216803-4. [7] Wonbong Choi, Jo-won Lee, Graphene: Synthesis and Applications, CRC Press, 2012. [8] J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Muoth, A.P. Seitsonen, M. Saleh, X. Feng, K. Müllen, R. Fasel, Atomically precise bottomup fabrication of graphene nanoribbons, Nature 466 (2010) 470–473. [9] B. Huang, Q. Yan, G. Zhou, J. Wu, B.L. Gu, W. Duan, F. Liu, Making a field effect transistor on a single graphene nanoribbon by selective doping, Appl. Phys. Lett. 91 (2007) 253122-1–253122-3. [10] A. Zhang, Y. Wu, S.H. Ke, Y.P. Fengand, C. Zhang, Band gap engineering of zigzag graphene nanoribbons by manipulating edge states via defective boundaries, Nanotechnology 22 (2011) 435702–435706.
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[11] D. Querlioz, Y. Apertet, A. Valentin, K. Huet, A. Bournel, S. Galdin-Retailleau, P. Dollfus, Suppression of the orientation effects on band gap in graphene nanoribbons in the presence of edge disorder, Appl. Phys. Lett. 92 (2008) 042108-1–042108-3. [12] S. Bhandary, O. Eriksson, B. Sanyal, Complex edge effects in zigzag graphene nanoribbons due to hydrogen loading, Phys. Rev. B 82 (2010) 165405-1– 165405-15. [13] A. Kumar, V. Kumar, S. Agarwal, A. Basak, N. Jain, A. Bulusu, S.K. Manhas, Nitrogen terminated semiconducting Zigzag GNR FET with negative differential resistance, IEEE Trans. Nanotechnol. 13 (1) (2014) 16–22. [14] Y. Wu, D.B. Farmer, W. Zhu, S.-J. Han, C.D. Dimitrakopoulos, A.A. Bol, P. Avouris, Y.-M. Lin, Three-terminal graphene negative differential resistance devices, ACS Nano 6 (3) (2012) 2610–2616. [15] V. NamDo, V. Hung Nguyen, P. Dollfus, A. Bournel, Electronic transport and spin-polarization effects of relativistic like particles in mesoscopic graphene structures, J. Appl. Phys. 104 (2008) 063708-1–063708-7. [16] H. Ren, Q.X. Li, Y. Luo, J. Yang, Graphene nanoribbon as a negative differential resistance device, Appl. Phys. Lett. 94 (2009) 173110-1–173110-3. [17] H. Teong, K.T. Lam, S. Bin Khalid, G. Liang, Shape effects in graphene nanoribbon resonant tunneling diodes: a computational study, J. Appl. Phys. 105 (2009) 084317-1–084317-6. [18] V. Nam Do, P. Dollfus, Negative differential resistance in zigzag-edge graphene nanoribbon junctions, J. Appl. Phys. 107 (2010) 063705-1–063705-5. [19] Y. Ming Lin, K.A. Jenkins, D. Farmer, Alberto Valdes-Garcia, P. Avouris, S. Chun-Yung, C. Hsin-Ying, B. Ek, Development of graphene FETs for high frequency electronics, in: IEEE Int. Electron Devices Meeting, vol. 1(4), 2009, pp. 7–9. [20] Y.M. Lin, C. Dimitrakopoulos, K.A. Jenkins, D.B. Farmer, H.-Y. Chiu, Alfred Grill, P. Avouris, 100-GHz transistors from wafer-scale epitaxial graphene, Science 327 (5966) (2010). 662–662. [21] G.D. Wilk, R.M. Wallace, J.M. Anthony, High-K gate dielectrics: current status and materials properties considerations, J. Appl. Phys. 89 (2001) 5243– 5275. [22] G. Zhou, W. Duan, Field emission in doped nanotubes, Nanotechnology 5 (2005) 1421–1434. [23] S.S. Yu, W.T. Zheng, Q. Jiang, Electronic properties of nitrogen-/boron- doped graphene nanoribbons with armchair edges, IEEE Trans. Nanotechnol. 9 (1) (2010) 78–81. [24] J. Taylor, H. Guo, J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B 63 (2001) 245407-1– 245407-13. [25] M. Brandbyge, J.L. Mozos, P. Ordej´on, J. Taylor, K. Stokbro, Density-functional method for nonequilibrium electron transport, Phys. Rev. B 65 (2002) 165401-1–165401-17. [26] M. Büttiker, Y. Imry, R. Landauer, S. Pinhas, Generalized many channel conductance formula with application to small rings, Phys. Rev. B 31 (1985) 6207–6215. [27] S.Y. Liao, Microwave Devices and Circuits, third ed., Pearson, Delhi, India, 2005 [Chapter 4 and 5].
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Study of Nitrogen terminated doped zigzag GNR FET exhibiting negative differential resistance Santosh Kumar Gupta ⇑, Girija Nandan Jaiswal Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology Allahabad, Allahabad 211004, Uttar Pradesh, India
a r t i c l e
i n f o
Article history: Received 29 July 2015 Accepted 30 July 2015 Available online 1 August 2015 Keywords: Graphene Zigzag GNR FET High-k dielectric Negative differential resistance
a b s t r a c t This paper presents the study of Gallium and Aluminum doped Nitrogen terminated zigzag Graphene Nano Ribbon (GNR) FET with high-k dielectric. The GNR FET structure has been designed and simulated using Quantumwise Atomistix Toolkit software package. The presented GNR FET with n-type (Nitrogen doped) electrodes and p-type (Gallium or Aluminum doped) scattering region are simulated and analyzed using Density Functional Theory combined with NEGF formalism and Device Density of States (DDOS). The device shows a negative differential resistance phenomenon which can be controlled by the gate of the zigzag GNR FET. It is found that doping of Gallium and Aluminum in scattering region provides higher drain current, higher ION/IOFF and IP/IV ratios as compared to that of Boron doped zigzag GNR FET. The potential applications of the device are in logical, high frequency, and memory devices. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The continuous miniaturization of Si devices based on CMOS technology is reaching its physical and geometrical limits so we are moving on other materials. Graphene, a two dimensional honey comb layer of carbon atoms in which carbon atoms form three r bonds in the plane of Graphene in sp2 configuration while another orbital pz, which is perpendicular to the Graphene plane makes p covalent bond, has shown the capability to become the novel material for nano-electronics because of its extraordinary properties [1–3]. This includes ultrahigh carrier mobility, thermal conductivity, electron–hole symmetry and quantum hall effect [4]. Graphene, being a zero band gap material, is not suitable for semiconductor electronics to fabricate FETs. However, formation of Graphene nanostructure of less than 10 nm can induce a band gap [5]. These nanostructures are called Graphene Nano Ribbon (GNR). Confining Graphene in one direction results in zigzag type GNR which shows metallic properties due to wave function localization at the zigzag edges and confining Graphene in other direction results in Arm chair type GNR which shows semiconducting properties due to both quantum confinement and the edge states. The induced band gap depends upon the width of the ribbon [6]. This band gap is not sufficient for Graphene to be used in digital logical applications. Arm chair type GNR has been used to simulate various high frequency GNR FETs [7]. Fabrication of GNRs requires atomically precise edges. Such a technique of fabricating GNRs has been proposed and this opens way for GNR to be used in future high-performance electronics applications [8].
⇑ Corresponding author. E-mail address: [email protected] (S.K. Gupta). http://dx.doi.org/10.1016/j.spmi.2015.07.069 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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Various methods have been reported to open a band gap in zigzag GNR e.g. selective doping [9], edge modulation (defective boundaries and edge disorder) [10,11], enabling each edge Carbon (C) atom to two Hydrogen (H) atoms [12], terminating the edge C atoms of the ribbon by Nitrogen (N) atoms [13]. In this paper we present a study on N (Nitrogen) terminated zigzag GNR FET. The binding energy created by the passivation of Nitrogen molecule (N2) on unpassivated zigzag GNR is always positive. Thus the formation of such ribbons is energetically favorable. The passivation of N can transform zigzag GNR (arm chair GNR) from metal (semiconductor) to semiconductor (metal). Band gap engineering by terminating edge C atoms with N atoms has the advantage that neither it requires any controlled manufacturing, which can be crucial in the case of defective boundaries nor it loses sp2 hybridization of edge C atoms, therefore, the resulting ribbon does not lose its planarity as is the case with H loading [12], where sp3 atoms are present along the edges [13]. In this paper we present a FET structure in which the scattering region (channel) is made of Nitrogen (N) terminated zigzag GNR and is doped with either Aluminum (Al) or Gallium (Ga), electrodes are made of N terminated zigzag GNR and are doped with Nitrogen. The device has been simulated and its electrical characteristics are described using Density Functional Theory (DFT) based on quantum transport calculations and device Density of States (DDOS). Based on these simulations we found that it exhibits negative differential resistance (NDR) in the voltage range of 0.1–0.25 V and provides better ON current compared to the N-passivated zigzag GNR proposed by Kumar et al. [13]. Negative differential resistance implies that for an increasing range of voltage the current will be decreasing. NDR can be either current controlled or voltage controlled. Due to ambipolar transport behavior of Graphene, NDR has been observed and reported in various three terminal GNR devices [14]. Previously single-gate Graphene sheet junctions have also shown negative differential resistance [15]. Negative differential resistance was also discovered in arm chair GNR junction [16,17], and the arm chair GNR junction has been examined for its suitability in tunneling diodes [17]. It has also been reported that p+/p zigzag GNR junction also exhibit NDR with high peak-to-valley current ratio (IP/IV) [18]. GNR FETs have been extensively investigated for their suitability at high frequency electronics [19,20]. Maximum frequency of oscillation (fmax) and cut off frequency (fc) of the proposed device is in the range of Giga-hertz; so, the NDR phenomenon in the proposed device is quite useful for high-frequency applications. 2. FET structure The semiconducting N-passivated zigzag GNR proposed in [13] has been used to realize GNR FET in the present work. The GNR FET is comprised of N-passivated (2, 2) zigzag GNR of which scattering region is doped with Al or Ga as shown in Fig. 1. The length and width of the scattering regions are 2.39 nm and 0.94 nm respectively. A high-k material has been used as gate dielectric to increase the gate control over the scattering region (channel). A typical dielectric constant of 24e0 corresponding to that of Hafnium oxide (HfO2) with thickness of 0.36 nm has been considered [21]. Since both the electrodes and the scattering region are parts of the same N-passivated (2, 2) zigzag GNR, such device structure can be useful for increasing the device density together with simplifying the fabrication process. The dopant atoms (N, Al, Ga) are substituted for C atoms in carbon materials similar to that of dopant added in Carbon Nano Tubes (CNTs) [22]. In the GNR FET, the two electrodes are doped using penta-valent N atoms with a doping concentration of 1 N atom for every 16 C atoms. Doping the N passivated zigzag GNR with N causes it to be n-type semiconductor. The scattering region is doped with trivalent Al or Ga atoms with a doping concentration of 1 dopant atom for every 80 C atoms. Doping the N passivated zigzag GNR with Al or Ga causes it to be p-type semiconductor. Doping with Aluminum (Al) and Gallium (Ga) is preferred because Al and Ga belong to the same group and also both Al and Ga are more reactive than Boron (B) [13]. The band structures of the N doped drain/source, scattering region doped with Al or Ga are shown in Fig. 2(a), (b) and (c) respectively. The Bloch functions for valance band maximum (VBM) and conduction band minimum (CBM) along with the projected density of states are analyzed to get the opening of band-gap. The band gap value for Nitrogen doped drain/source region is 0.62 eV, for Al doped scattering region is 0.35 eV, and for Ga doped scattering region it is 0.37 eV as shown by blue lines in
Fig. 1. Structure of the N-passivated (2, 2) zigzag GNR FET, where the box region at the two sides indicate the contacts region and blue (pink) ball represents the N (Ga/Al) atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. Band structure of (a) the smallest unit cell of N doped electrodes, (b) scattering region (Al doped) and (c) scattering region (Ga doped) of the N-passivated (2, 2) zigzag GNR FET, where the red line represents the Fermi level and region between blue lines represents the band gap. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2(a), (b) and (c) respectively. The source/drain electrodes Fermi level (red line) shifts toward conduction band minimum (CBM) thereby changing the Graphene Nano Ribbon into n-type. But in the scattering region the Fermi level (red line) shifts toward VBM thereby changing the Graphene Nano Ribbon into p-type.
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Since the site of doping also affects the band gap value [23], doping near the center is preferred because doping near the edges tends to suppress the band gap. The zigzag GNR FET consist of N doped source/drain electrodes and scattering region doped with either Al or Ga (shown in Fig. 1) is simulated using Quantumwise Atomistix. Density of States of the scattering region after forming the device is shown in Fig. 3(a) and (b). For both the Al and Ga doped zigzag GNRFET, the Fermi level lies well above in the band gap and hence indicates n-type nature of scattering region. The electrical characteristics of the devices are calculated using DFT-based quantum transport calculations and discussed in the next section.
3. Computational details All calculations have been performed using DFT with the local density approximation for the exchange correlation as incorporated in quantumwise Atomistix Toolkit (ATK) [24,25]. The device structure has been optimized using the Broyden– Fletcher–Goldfarb–Shanno method for optimization as incorporated in ATK. To study the transport properties of the proposed device, the fully self-consistent DFT combined with non-equilibrium Green’s function formalism [25] incorporated in ATK has been used. We took double-f polarized as basis set; the mesh cutoff is 100 Ry or 50 Ha. ATK can model accurately the electrical properties of nano scale devices consist of 3-D atomic arrangements and coupled with two semi-infinite
Fig. 3. Energy-DOS characteristics of (a) scattering region (Al doped) and (b) scattering region (Ga doped) of the N-passivated (2, 2) zigzag GNR FET.
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Fig. 4. Drain current (Id) versus drain voltage (Vds) variation for (a) Al doped zigzag GNR FET, (b) Ga doped zigzag GNR FET, at gate voltages (Vg) of 0.0, 0.2, 0.3, and 0.4 V and (c) comparison of drain current (Id) versus drain voltage (Vds) of Al doped zigzag GNR FET, Ga doped zigzag GNR FET and B doped zigzag GNR FET, at gate voltage (Vg) of 0.4 V.
electrodes. First of all the electronic structures of two electrodes are calculated separately using DFT to get the self-consistent Kohn–Sham potentials and Hamiltonian matrices. Then the current through the channel (scattering region) are calculated from the transmission spectrum using the Landauer–Buttiker formalism [26] as follows:
IðVÞ ¼
2q h
Z
þ1
ðf L ðE; VÞ f R ðE; VÞÞTðE; VÞdE
ð1Þ
1
where fL(E, V) and fR(E, V) are the Fermi functions for the left and right electrodes respectively, q is the magnitude of the charge on an electron, ⁄ is Planck’s constant, and T(E, V) is the energy (E) and bias voltage (V) dependent transmission spectrum.
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Fig. 5. Drain current (Id) versus gate voltage (Vg) variation for (a) Al doped zigzag GNR FET, (b) Ga doped zigzag GNR FET, at drain voltages (Vds) of 0.3, 0.4 and 0.5 V and (c) comparison of drain current (Id) versus gate voltage (Vds) variation of Al doped zigzag GNR FET, Ga doped zigzag GNR FET and B doped zigzag GNR FET at drain voltage (Vds) of 0.4 V.
4. Results and discussion The Id–Vds characteristic of the N passivated zigzag GNR FET is shown in Fig. 4(a) and (b) respectively. It is seen that doping with Al or Ga preserves the negative differential resistance phenomenon as was reported by Kumar et al. [13]. The device
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Table 1 Various parameters of zigzag GNR FET. Zigzag GNR FET parameters
Pmax (nW) fco (GHz) fmax (GHz) gm nX1 Rd (kX)
Doped with Al
Ga
525 340 113 2830 155
489 328 103 2740 144
exhibits negative differential region (NDR) for the gate to source biasing voltage (Vgs) 0.1–0.25 V. The NDR peak shifts toward lower values of Vds as Vgs is increased as is observed from Fig. 4(a) and (b). The peak drain current Id = 482 nA for Vds = 0.1 V occurs at Vgs = 0.4 V and Id = 435 nA for Vds = 0.12 V occurs at Vgs = 0.3 V for Al doped zigzag GNR FET. For Ga doped zigzag GNR FET the peak drain current for Vgs = 0.4 V is 459 nA at Vds = 0.1 V and Id = 412 nA for Vgs = 0.3 V at Vds = 0.12 V. The peak to valley drain current ratio (IP/IV) is 9.83 for Al doped device and 10.2 for the Ga doped device which is greater than that of the B doped zigzag GNR FET reported in [13]. It can also be seen from Fig. 4(a) and (b) that the beyond Vds = 0.3 V the current starts to increase monotonously. The maximum current for the Al and Ga doped zigzag GNR FET are 1051 nA and 978 nA respectively which is more than the maximum current obtained with B doped zigzag GNR FET. Fig. 4(c) shows the comparison among the Id–Vds characteristics of the three devices namely B doped, Al doped and Ga doped devices. Out of these three different zigzag GNR FETs, Al doped device provides 29% more drain current compared to the B doped zigzag GNR FET. The transfer curve of the Al doped and Ga doped devices are represented by Fig. 5(a) and (b). For the Al doped device the current at Vgs = 0.2 V and 0.5 V is 69 nA and 1347 nA respectively for Vds = 0.5 V and 17 nA and 804 nA at Vgs = 0.4 V. We can see from Fig. 5(a) and (b) that as the value of Vds increases from 0.4 to 0.5 V the current increase sharply. The device is ON at Vgs = 0.1 V and the value of Id at this point is 59 nA and 172 for Vds = 0.4 and 0.5 V respectively for the Al doped device. Similarly, for Ga doped device the value of Id at this point is 49 nA and 160 nA for Vds = 0.4 and 0.5 V respectively. For higher values of the drain voltage the current becomes a strong function of gate potential. This characteristic of the device can be utilized in sensing applications. Also, it can be noted that the ION/IOFF ratio is higher for the Al doped device compared to that of Ga doped device. The leakage current is also very small 100 nA. The cutoff frequency, maximum frequency of oscillation, and maximum power consumed by the GNR FETs are also computed at Vgs and Vds of 0.4 and 0.5 V respectively [27]. The maximum power consumed by the device is defined by P max ¼ Id V dsmax , the cutoff frequency is defined by f co ¼ g m =2pC gs and the maximum frequency of oscillation is defined by pffiffiffiffiffiffiffiffiffiffiffi f max ¼ ðf co =2Þ g m Rd and shown in Table 1. The values of transconductance g m ð¼ dId =dV g Þ and drain resistance 1
Rd ð¼ ðdId =dV d Þ Þ are also shown in Table 1. The gate to source capacitance C gs (=1.326 109 F) is same for both the devices. 5. Conclusion FET devices with N-passivated source/drain material and Al/Ga doped zigzag GNR as channel material have been proposed and the electrical characteristics (viz. Id–Vds and Id–Vgs) have been analyzed using DFT based quantum transport calculations. This device also exhibits NDR phenomenon which is explained and validated using energy DDOS characteristics of the channel region of the device. It has been found that the position of NDR peak can effectively be controlled by the applied gate voltage. This result can be used in nano-devices requiring variable or controlled NDR effect such as in memory and RF oscillators. The presented zigzag GNR FETs can also be used in other semiconducting applications by utilizing the presence of energy band gap. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (2004) 666–669. [2] J.S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P.L. McEuen, Coulomb oscillations and Hall effect in quasi-2D graphite quantum dots, Nano Lett. 5 (2005) 287– 290. [3] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (2005) 197–200. [4] A.K. Geim, K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183–191. [5] Y.W. Son, M.L. Cohen, S.G. Louie, Half-metallic graphene nanoribbons, Nature 444 (7117) (2006) 347–349. [6] Y.-W. Son, M.L. Cohen, S.G. Louie, Energy gaps in graphene nanoribbons, Phys. Rev. Lett. 97 (2006) 216803-1–216803-4. [7] Wonbong Choi, Jo-won Lee, Graphene: Synthesis and Applications, CRC Press, 2012. [8] J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Muoth, A.P. Seitsonen, M. Saleh, X. Feng, K. Müllen, R. Fasel, Atomically precise bottomup fabrication of graphene nanoribbons, Nature 466 (2010) 470–473. [9] B. Huang, Q. Yan, G. Zhou, J. Wu, B.L. Gu, W. Duan, F. Liu, Making a field effect transistor on a single graphene nanoribbon by selective doping, Appl. Phys. Lett. 91 (2007) 253122-1–253122-3. [10] A. Zhang, Y. Wu, S.H. Ke, Y.P. Fengand, C. Zhang, Band gap engineering of zigzag graphene nanoribbons by manipulating edge states via defective boundaries, Nanotechnology 22 (2011) 435702–435706.
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