- Email: [email protected]
N doping
Physics Letters A 379 (2015) 710–718
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Tailoring the electronic properties of a Z-shaped graphene field effect transistor via B/N doping Mohit Gupta a , Nitesh Gaur a , Puneet Kumar a , Sangeeta Singh a , Neeraj K. Jaiswal b,∗ , P.N. Kondekar a a b
Nanoelectronics and VLSI Lab., Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur 482005, India Discipline of Physics, Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur 482005, India
a r t i c l e
i n f o
Article history: Received 18 November 2014 Received in revised form 12 December 2014 Accepted 23 December 2014 Available online 30 December 2014 Communicated by R. Wu Keywords: Graphene nanoribbon Band structure Density of states I–V characteristics Transmission spectra
a b s t r a c t We performed first-principles calculations to reveal a viable way for tailoring the electronic properties of Z-shaped double gate graphene field effect transistor (Z-GFET). We used B/N impurities in channel region of Z-GFET. It is revealed that doping of channel region by B/N has a significant effect on its band gap which is directly reflected in the corresponding current–voltage characteristics. A semiconducting to metallic transition is also observed in selected configurations. For B–N co-doping (config. W), direct band gap of 1.84 eV is obtained which is 20% lower than that of pristine channel. Present results are useful for future electronic devices. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Owing to continuous exhaustive scaling, today’s Si based semiconducting technology is approaching its physical limitations because of prevailing short channel effects (SCEs). At the same time it has been observed that channel thickness plays a crucial role in affecting SCEs of a field effect transistor (FET). In this scenario, graphene based electronic devices with high mobility and controllable current densities can have wide potential applications [1, 2]. According to tight-binding calculations, graphene is intrinsically semi-metal [3]. Despite having remarkable electronic and magnetic properties [4–6], graphene cannot be used in semiconductor electronics due to its zero band gap [7]. The absence of band gap in graphene is due to free π electrons behaving as if they were massless charge carriers. The electronic band structure of graphene exhibits a linear dispersion with zero gap around the Dirac points [4]. The presence of this zero band-gap region restricts the suitability of graphene for future device applications. Researchers are seeking various techniques to introduce a band gap in graphene. Among these efforts, most promising are cutting large area graphene into thin strips known as graphene nanoribbons (GNRs) and biasing bilayer graphene [8–14]. In addition to this, various other techniques
*
Corresponding author. Tel.: +91 761 2632664x183. E-mail address: [email protected] (N.K. Jaiswal).
http://dx.doi.org/10.1016/j.physleta.2014.12.046 0375-9601/© 2014 Elsevier B.V. All rights reserved.
including (but limited to) chemical doping [15], edge modification, variation in chemical composition of the substrate and by application of external electric field have been used to introduce a band gap in graphene [16,17]. Based on edge termination, there are two main configurations of nanoribbons viz. armchair graphene nanoribbons (AGNR) and zigzag graphene nanoribbons (ZGNR) which naturally exhibit band gap varying inversely with their width ( E g ∝ 1/ w). This has already been proved through experiments and other theoretical investigations [18,19]. Further, AGNR behave as metal or semiconductor depending upon their width which is denoted by N a (number of carbon chains along its width). For N a = 3p and N a = 3p + 1, armchair nanoribbons are semiconducting, and for N a = 3p + 2 it is semi-metallic (where p is a positive integer) [20,21]. On the other hand, ZGNRs are more conductive and mainly behave as metals [22]. The band gap opening due to these nanoribbons is very less (0.5 eV in a 2.5 nm wide armchair ribbon), therefore to be utilized it in semiconducting devices, there must be sufficient band gap and it can be achieved via doping [23]. It is reported that impurities present in graphene nanoribbons significantly affect their electronic and transport properties [24–26]. Previously, Yan et al., reported a higher ION /IOFF ratio in the Z-shaped graphene nanoribbons FET [27]. The ability of B/N doping in graphene based nanomaterial is achieved experimentally [28,29] which makes it highly desirable to investigate the effect of these impurities on the electronic transport through graphene
M. Gupta et al. / Physics Letters A 379 (2015) 710–718
based novel electronic devices. In order to address aforementioned issues, we have investigated the electronic and transport properties of B/N doped Z-shaped FET and revealed some remarkable features. FETs performance parameter like drive current (I D ) has been investigated for the considered FET device configurations. Further, we have used double gate FET configuration in order to have a better control (than that of single gate) over the carrier flow through the channel region. 2. Computational details In this Letter, we have calculated the transport property of pristine and B/N doped double gated Z-shaped graphene FET (Z-GFET) with the help of first-principle calculations using Quantumwise (ATK-VNL) simulation package1 [32]. We utilized the density functional theory (DFT) within the limits of local density approximation (LDA) with Perdew–Zunger exchange correlation functional [30,31]. Valence electrons are expanded in a double zeta plus polarized basis set for all atomic species. Left and right electrodes are constructed using ZGNR whereas the central scattering region is made of AGNR. The width of the ZGNR and AGNR was classified by the number of atoms across the ribbon width. Each electrode is modeled by a supercell method with repeated carbon units along the transport direction. Doping is done via substitution in the central channel region by heteroatoms (B and N). An energy cut-off of 150 Rydberg is set to present the accurate charge density. The sampling for Brillouin zone integration was performed with a grid of 1 × 1 × 50 k-points. The bias dependent electron transmission spectrum and current were calculated using the non-equilibrium Green’s function (NEGF) method, as implemented in the ATK-VNL. The transmission probability of conducting channels available and current through the double gated FET system can be obtained as [33]
T ( E , V ) = Tr ΓL G R ( E , V )ΓR G A ( E , V ) I=
2e h
∞
(1)
dE T ( E , V ) f ( E − εL ) − f ( E − εR )
(2)
−∞
where, G R and G A are retarded and advanced Green’s R A functions of the central scattering region, ΓL,R = i [ L(R) ( E ) − R(L) ( E )] denotes the line width function. The εL and εR are electrochemical potentials of the left and right electrodes respectively under an external bias V . The transmission spectrum T ( E , V ) describes the quantum mechanical transmission probabilities for electrons. The semi-infinite effect of the right and left into acRelectrodes istaken A count by introducing the self-energy L(R) ( E ) and R(L) ( E ) in the effective Hamiltonian. 3. Results and discussion We have investigated the effect of substitutional edge doping of B and N impurities in a graphene based FET made of two metalsemiconductor junctions [27]. We used AGNR as the channel of Z-GFET and ZGNR as the contact material. The schematics and the convention adopted for defining the widths of considered ribbons and the transverse view of proposed double gate FET device have been depicted in Fig. 1(a)–(c). Different doping sites and corresponding device configurations are shown in Fig. 2. For a better visualization the upper gate of the device is not displayed. Different configurations are termed as config. P for pristine channel, config. Q for single N (at center site) doped channel, config. R for single B (at center site) doped channel, config. S for single N (at
1
http://www.quantumwise.com.
711
right site displaced) doped channel, config. T for single B (at right site displaced) doped channel. For double atom doping, we define config. U for double N doped channel, config. V for double B doped channel, config. W for B–N co-doped channel in which B is doped at one edge and N on the opposite edge of the channel ribbon. First we have analyzed the feasibility of the most favorable configuration by calculating the binding energy per atoms (BE). The BE is calculated as E B = E doped − E pristine − n( E impurity − E c ), where E doped is the total energy of the doped central region, E pristine is total energy of pristine central region, n is number of guest dopants atoms (B/N), E impurity is total energy of isolated impurity atom and E c is total energy of isolated C atom. For pristine central region, BE is calculated as ( E pristine /m) − E c , where m is number of C atoms [34]. The calculated BE are presented in Table 1. Perusal of Table 1 reveals that config. Q is the most feasible structure to obtain, followed by config. S. 3.1. Electronic properties 3.1.1. Band structure analysis The electronic band structure of a material serves as the signature for identifying its potential application in future electronic devices. Therefore, to understand the electronic properties of considered structures, we have calculated the band structures of channel region as shown in Fig. 3. Config. P shows the significant band gap of 2.30 eV [Fig. 3(a)] which is in consistent with previous results (2.53 eV) [34]. In config. Q and config. S, both the devices show an additional electronic state slightly overlapping the Fermi level. This additional state is due to charge transfer in chemical bond between C and N atom and indicates semi metallic behavior of the N doped channel [Fig. 3(b)]. It is observed that electronic behavior is not affected by displacing the N atom [Fig. 3(d)] which is due to the fact that charge transfer is same in both the configurations. Interestingly, as we increase the number of doped N atoms (config. U) in the channel region, an opening of small band gap (0.31 eV) [Fig. 3(f)] is observed which is due to small strain at both the edges of the ribbon. In config. R and config. T (center and displaced B doping site, Fig. 3(c) and Fig. 3(e)) shows the dispersive electronic state across the Fermi level. The charge transfer takes place from C to B owing to which extra electronic state is originated across the Fermi level. When the B concentration is increased to two atoms (config. V), there are two additional energy states in the vicinity of the Fermi level making it semi-metallic in nature as presented in Fig. 3(g). In the config. W, the observed band gap is about 20% lower than that of the pristine ribbon [Fig. 3(h)]. In B–N co-doped configuration one edge of the ribbon behaves as p-type doped while other as n-type. In this particular configuration, the highest valence band is shifted towards the Fermi level whereas the lowest conduction band remains unchanged resulting in a band gap of about 1.84 eV [Fig. 3(h)]. Therefore, it can be concluded that doping channel region with B/N at opposite edges could be a viable way to reduce the threshold voltage of the Z-shaped GNR FET. 3.1.2. Density of states analysis In order to have an in-depth understanding of observed electronic structures, we computed density of states (DOS) profiles of the considered configurations. The calculated DOS profiles for different configurations are shown in Fig. 4. The DOS for config. P [Fig. 4(a)] shows that no electronic states are available near the Fermi level and a clear energy gap of about 2.30 eV between the highest valence band and lower conduction band. The absence of electronic states across the Fermi level is in accordance with the observed pristine band structure and confirms its semiconducting behavior. The DOS profiles for B/N doped channel regions are depicted in Fig. 4(b)–(h). It is revealed that only N or only B doping always results in the semi metallic/metallic configurations whereas
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Fig. 1. Schematics of (a) AGNR channel region, (b) ZGNR electrode region and (c) transverse view of the proposed double gate ZGFET. The grey and white spheres represent carbon and hydrogen atoms respectively. Table 1 The calculated binding energy (eV) per atom in various configurations of AGNR. Configuration
Config. P
Config. Q
Config. R
Config. S
Config. T
Config. U
Config. V
Config. W
Binding energy
−7.05
−15.95
1.83
−10.79
14.55
4.14
14.82
−0.78
B and N co-doping results in a reduced band gap of about 1.84 eV. This reduction in the band gap is accompanied with the symmetry breaking at opposite edges of the ribbon. For the config. Q and config. S, DOS profiles show a sharp peak at the Fermi level indicating the high current for the FET made of this channel which can be validated with the current–voltage (I–V) curves. The single B doped channel DOS shows that pseudo gap is aligned with the Fermi level indicating unavailability of states for current conduction. These results are in accordance with the current observed in the I–V curves which are presented in the next section. 3.2. Transport properties To explore the potential of considered structures for device applications, we have investigated the transport properties of the various configurations by analyzing the I–V characteristics and transmission spectra (TS). Using the optimized geometries, the transmission coefficients are calculated using Eq. (1). The same approach has been previously used to calculate I–V characteristics of transition metal as well as B doped GNR [35,36]. Once the TS have been calculated, current through the channel region can be computed by integrating all the transmission values as given by Eq. (2). The computed drain to source current (I D ) versus the drain to source voltage (V DS ) relations for all device configurations (with a fixed top gate voltage V G = bottom gate voltage, V G = 1 V) are depicted in Fig. 5(a)–(h). Amongst all the structures, config. Q exhibits the highest current value with a magnitude of about 31 μA at 2 V [Fig. 5(b)]. It is followed by config. U and config. S with the highest magnitude of 28 μA and 27 μA respectively. It is noticed that for N doped channel, doping concentration and doping site does not have a significant influence on the observed I–V characteristics. On the other hand, current value is highly sensitive to the doping site of B atom. The highest current values are 4.8 μA
and 5.2 μA for config. R and config. V respectively, as compared to that of 16 μA for config. T. According to our expectations, the highest current in config. W (18 μA) is lying in between that of B or N doped configurations. The present analysis reveals that magnitude of current through the channel region is highly dependent upon the doping site of B/N atoms. Thus, it can be a viable way to control the flow of charge carriers in a Z-GFET. To further analyze the observed I–V behavior of the considered Z-shaped devices, we plotted TS as shown in Fig. 6. Regions εL and εR represent left and right electrodes respectively. In TS of config. P we noticed a transmission gap across the Fermi level [Fig. 6(a)], which in turn confirms the semiconducting behavior of pristine channel region. For config. Q, we observed a high transmission peak lying at the Fermi level [Fig. 6(b)]. The magnitude of this peak approaches to unity which indicates towards the possibility of ballistic transport through this configuration and confirms highest current magnitude as compared to others. The TS for the B doped structures exhibit a transmission gap in correspondence to the electronic band structures. This gap in the vicinity of Fermi level confirms the lowest current values of these configurations [Fig. 5]. For config. W, the TS shows a small peak in the valence band region just below the Fermi level and a decaying behavior at Fermi level is also noticed. This small finite value of transmission coefficient indicates toward small conduction taking place for this structure. The same we have noticed previously in the corresponding I–V characteristic depicted in Fig. 5(h). As the band gap of pristine AGNR is highly sensitive to their ribbon width, it is crucial to know whether the present results still hold for other members of AGNR family. In the present work, it is noticed that charge transfer between C and the guest atom takes place only at local level. Therefore, we expect no qualitative change in the electronic band structure or transport properties of the considered B/N doped AGNR as a function of their width. To verify this, we have
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Fig. 2. Different device configurations showing channel reagion. (a) Pristine (config. P), (b) with center N doping (config. Q), (c) with center B doping (config. R), (d) with displaced N doping (config. S), (e) with displaced B doping (config. T), (f) with double N doping (config. U), (g) with double B doping (config. V), (h) with both B–N doping (config. W). Grey, white, red and blue spheres represent C, H, B and N atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
also investigated the effect of N doping on other members of AGNR
4. Conclusion
family (width 5 and 6). To be concise, this time we have considered only the most stable geometry i.e. centre N doping. The calculated band structures of N a = 5 and N a = 6 are depicted in Fig. 7(a) and Fig. 7(b) respectively. An additional electronic state is noticed across the Fermi level in both of these structures. The similar band has been observed for N a = 4 (config. Q) [Fig. 3(b)]. Though, the degree of overlapping of this additional band with the Fermi level is slightly changed depending upon the ribbon width, the overall qualitative behavior is same for all family of AGNR. This is according to our expectations and we can conclude that present results qualitatively hold for other AGNR as well.
Conclusively, we have investigated different configurations of double gated B/N doped Z-GFET and compared the findings with that of pristine one. It is also noticed that band gap of the channel ribbons is highly sensitive to the presence of B/N dopants. This point towards the possibility of tailoring the band gap of Z-shaped GNR devices merely by controlling the doping sites which is eventually reflected in the performance of device under applied bias voltage. Analysis of BE reveals that config. Q is the most energetically feasible structure. This particular configuration also exhibits enhanced current conduction as compared to pristine and other doped structures. The obtained I–V characteristics are further sup-
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Fig. 3. Band structures of different configurations. (a) Config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W. (The red dotted line indicates Fermi level.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. The DOS of channel regions in various configurations. (a) Config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W. (The dotted line indicates the Fermi level.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. I–V characteristics of different configurations at top gate voltage = bottom gate voltage = 1 V in (a) config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W.
M. Gupta et al. / Physics Letters A 379 (2015) 710–718
Fig. 6. Transmission spectra of different configurations. (a) Config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W.
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Fig. 7. The band structures of centre N doping in AGNR for (a) N a = 5 and (b) N a = 6. The Fermi energy is set at 0 eV as highlighted by dashed line.
ported by the TS computations. Thus, the present study provides a viable way to alter the band gap of channel material to improve the performance of future graphene based devices. Acknowledgements Authors are thankful to Dr. Pankaj Srivastava faculty of Physics at Computational Nanoscience and Technology Lab. (CNTL), ABV – Indian Institute of Information Technology and Management, Gwalior, India, for providing computational resources. We also thank PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, for providing infrastructure facilities. 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] T. Ando, The electronic properties of graphene and carbon nanotubes, NPG Asia Mater. 1 (2009) 17–21. [3] G. Lu, K. Yu, Z. Wen, J. Chen, Semiconducting graphene: converting graphene from semimetal to semiconductor, Nanoscale 5 (2013) 1353–1368. [4] 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. [5] M.O. Goerbig, Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys. 83 (2011) 1193–1243. [6] A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109–162. [7] E. Rotenberg, A. Bostwick, T. Ohta, J.L. McChesney, T. Seyller, K. Horn, Origin of the energy bandgap in epitaxial graphene, Nat. Mater. 7 (2008) 258–259. [8] Young-Woo Son, M.L. Cohen, S.G. Louie, Energy gaps in graphene nanoribbons, Phys. Rev. Lett. 97 (2006) 216803. [9] T. Kawai, Y. Miyamoto, O. Sugino, Y. Koga, Graphitic ribbons without hydrogentermination: electronic structures and stabilities, Phys. Rev. B 62 (2000) R16349. [10] L. Ci, Z. Xu, L. Wang, W. Gao, F. Ding, K.F. Kelly, B.I. Yakobson, P.M. Ajayan, Controlled nanocutting of graphene, Nano Res. 1 (2008) 116–122. [11] S.S. Dutta, D.R. Strachan, S.M. Khamis, A.T.C. Johnson, Crystallographic etching of few-layer graphene, Nano Lett. 8 (2008) 1912. [12] Y. Fan, M. Zhao, Z. Wang, X. Zhang, H. Zhang, Tunable electronic structures of graphene/boron nitride heterobilayers, Appl. Phys. Lett. 98 (2011) 083103. [13] G. Fiori, G. Iannaccone, Ultralow-voltage bilayer graphene tunnel FET, IEEE Electron Device Lett. 30 (2009) 1096–1098. [14] G. Fiori, D. Neumaier, B.N. Szafranek, G. Iannaccone, Bilayer graphene transistors for analog electronics, IEEE Trans. Electron Devices 61 (2014) 729–733. [15] H. Liu, Y. Liu, D. Zhu, Chemical doping of graphene, J. Mater. Chem. 21 (2011) 3335–3345.
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Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Tailoring the electronic properties of a Z-shaped graphene field effect transistor via B/N doping Mohit Gupta a , Nitesh Gaur a , Puneet Kumar a , Sangeeta Singh a , Neeraj K. Jaiswal b,∗ , P.N. Kondekar a a b
Nanoelectronics and VLSI Lab., Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur 482005, India Discipline of Physics, Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur 482005, India
a r t i c l e
i n f o
Article history: Received 18 November 2014 Received in revised form 12 December 2014 Accepted 23 December 2014 Available online 30 December 2014 Communicated by R. Wu Keywords: Graphene nanoribbon Band structure Density of states I–V characteristics Transmission spectra
a b s t r a c t We performed first-principles calculations to reveal a viable way for tailoring the electronic properties of Z-shaped double gate graphene field effect transistor (Z-GFET). We used B/N impurities in channel region of Z-GFET. It is revealed that doping of channel region by B/N has a significant effect on its band gap which is directly reflected in the corresponding current–voltage characteristics. A semiconducting to metallic transition is also observed in selected configurations. For B–N co-doping (config. W), direct band gap of 1.84 eV is obtained which is 20% lower than that of pristine channel. Present results are useful for future electronic devices. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Owing to continuous exhaustive scaling, today’s Si based semiconducting technology is approaching its physical limitations because of prevailing short channel effects (SCEs). At the same time it has been observed that channel thickness plays a crucial role in affecting SCEs of a field effect transistor (FET). In this scenario, graphene based electronic devices with high mobility and controllable current densities can have wide potential applications [1, 2]. According to tight-binding calculations, graphene is intrinsically semi-metal [3]. Despite having remarkable electronic and magnetic properties [4–6], graphene cannot be used in semiconductor electronics due to its zero band gap [7]. The absence of band gap in graphene is due to free π electrons behaving as if they were massless charge carriers. The electronic band structure of graphene exhibits a linear dispersion with zero gap around the Dirac points [4]. The presence of this zero band-gap region restricts the suitability of graphene for future device applications. Researchers are seeking various techniques to introduce a band gap in graphene. Among these efforts, most promising are cutting large area graphene into thin strips known as graphene nanoribbons (GNRs) and biasing bilayer graphene [8–14]. In addition to this, various other techniques
*
Corresponding author. Tel.: +91 761 2632664x183. E-mail address: [email protected] (N.K. Jaiswal).
http://dx.doi.org/10.1016/j.physleta.2014.12.046 0375-9601/© 2014 Elsevier B.V. All rights reserved.
including (but limited to) chemical doping [15], edge modification, variation in chemical composition of the substrate and by application of external electric field have been used to introduce a band gap in graphene [16,17]. Based on edge termination, there are two main configurations of nanoribbons viz. armchair graphene nanoribbons (AGNR) and zigzag graphene nanoribbons (ZGNR) which naturally exhibit band gap varying inversely with their width ( E g ∝ 1/ w). This has already been proved through experiments and other theoretical investigations [18,19]. Further, AGNR behave as metal or semiconductor depending upon their width which is denoted by N a (number of carbon chains along its width). For N a = 3p and N a = 3p + 1, armchair nanoribbons are semiconducting, and for N a = 3p + 2 it is semi-metallic (where p is a positive integer) [20,21]. On the other hand, ZGNRs are more conductive and mainly behave as metals [22]. The band gap opening due to these nanoribbons is very less (0.5 eV in a 2.5 nm wide armchair ribbon), therefore to be utilized it in semiconducting devices, there must be sufficient band gap and it can be achieved via doping [23]. It is reported that impurities present in graphene nanoribbons significantly affect their electronic and transport properties [24–26]. Previously, Yan et al., reported a higher ION /IOFF ratio in the Z-shaped graphene nanoribbons FET [27]. The ability of B/N doping in graphene based nanomaterial is achieved experimentally [28,29] which makes it highly desirable to investigate the effect of these impurities on the electronic transport through graphene
M. Gupta et al. / Physics Letters A 379 (2015) 710–718
based novel electronic devices. In order to address aforementioned issues, we have investigated the electronic and transport properties of B/N doped Z-shaped FET and revealed some remarkable features. FETs performance parameter like drive current (I D ) has been investigated for the considered FET device configurations. Further, we have used double gate FET configuration in order to have a better control (than that of single gate) over the carrier flow through the channel region. 2. Computational details In this Letter, we have calculated the transport property of pristine and B/N doped double gated Z-shaped graphene FET (Z-GFET) with the help of first-principle calculations using Quantumwise (ATK-VNL) simulation package1 [32]. We utilized the density functional theory (DFT) within the limits of local density approximation (LDA) with Perdew–Zunger exchange correlation functional [30,31]. Valence electrons are expanded in a double zeta plus polarized basis set for all atomic species. Left and right electrodes are constructed using ZGNR whereas the central scattering region is made of AGNR. The width of the ZGNR and AGNR was classified by the number of atoms across the ribbon width. Each electrode is modeled by a supercell method with repeated carbon units along the transport direction. Doping is done via substitution in the central channel region by heteroatoms (B and N). An energy cut-off of 150 Rydberg is set to present the accurate charge density. The sampling for Brillouin zone integration was performed with a grid of 1 × 1 × 50 k-points. The bias dependent electron transmission spectrum and current were calculated using the non-equilibrium Green’s function (NEGF) method, as implemented in the ATK-VNL. The transmission probability of conducting channels available and current through the double gated FET system can be obtained as [33]
T ( E , V ) = Tr ΓL G R ( E , V )ΓR G A ( E , V ) I=
2e h
∞
(1)
dE T ( E , V ) f ( E − εL ) − f ( E − εR )
(2)
−∞
where, G R and G A are retarded and advanced Green’s R A functions of the central scattering region, ΓL,R = i [ L(R) ( E ) − R(L) ( E )] denotes the line width function. The εL and εR are electrochemical potentials of the left and right electrodes respectively under an external bias V . The transmission spectrum T ( E , V ) describes the quantum mechanical transmission probabilities for electrons. The semi-infinite effect of the right and left into acRelectrodes istaken A count by introducing the self-energy L(R) ( E ) and R(L) ( E ) in the effective Hamiltonian. 3. Results and discussion We have investigated the effect of substitutional edge doping of B and N impurities in a graphene based FET made of two metalsemiconductor junctions [27]. We used AGNR as the channel of Z-GFET and ZGNR as the contact material. The schematics and the convention adopted for defining the widths of considered ribbons and the transverse view of proposed double gate FET device have been depicted in Fig. 1(a)–(c). Different doping sites and corresponding device configurations are shown in Fig. 2. For a better visualization the upper gate of the device is not displayed. Different configurations are termed as config. P for pristine channel, config. Q for single N (at center site) doped channel, config. R for single B (at center site) doped channel, config. S for single N (at
1
http://www.quantumwise.com.
711
right site displaced) doped channel, config. T for single B (at right site displaced) doped channel. For double atom doping, we define config. U for double N doped channel, config. V for double B doped channel, config. W for B–N co-doped channel in which B is doped at one edge and N on the opposite edge of the channel ribbon. First we have analyzed the feasibility of the most favorable configuration by calculating the binding energy per atoms (BE). The BE is calculated as E B = E doped − E pristine − n( E impurity − E c ), where E doped is the total energy of the doped central region, E pristine is total energy of pristine central region, n is number of guest dopants atoms (B/N), E impurity is total energy of isolated impurity atom and E c is total energy of isolated C atom. For pristine central region, BE is calculated as ( E pristine /m) − E c , where m is number of C atoms [34]. The calculated BE are presented in Table 1. Perusal of Table 1 reveals that config. Q is the most feasible structure to obtain, followed by config. S. 3.1. Electronic properties 3.1.1. Band structure analysis The electronic band structure of a material serves as the signature for identifying its potential application in future electronic devices. Therefore, to understand the electronic properties of considered structures, we have calculated the band structures of channel region as shown in Fig. 3. Config. P shows the significant band gap of 2.30 eV [Fig. 3(a)] which is in consistent with previous results (2.53 eV) [34]. In config. Q and config. S, both the devices show an additional electronic state slightly overlapping the Fermi level. This additional state is due to charge transfer in chemical bond between C and N atom and indicates semi metallic behavior of the N doped channel [Fig. 3(b)]. It is observed that electronic behavior is not affected by displacing the N atom [Fig. 3(d)] which is due to the fact that charge transfer is same in both the configurations. Interestingly, as we increase the number of doped N atoms (config. U) in the channel region, an opening of small band gap (0.31 eV) [Fig. 3(f)] is observed which is due to small strain at both the edges of the ribbon. In config. R and config. T (center and displaced B doping site, Fig. 3(c) and Fig. 3(e)) shows the dispersive electronic state across the Fermi level. The charge transfer takes place from C to B owing to which extra electronic state is originated across the Fermi level. When the B concentration is increased to two atoms (config. V), there are two additional energy states in the vicinity of the Fermi level making it semi-metallic in nature as presented in Fig. 3(g). In the config. W, the observed band gap is about 20% lower than that of the pristine ribbon [Fig. 3(h)]. In B–N co-doped configuration one edge of the ribbon behaves as p-type doped while other as n-type. In this particular configuration, the highest valence band is shifted towards the Fermi level whereas the lowest conduction band remains unchanged resulting in a band gap of about 1.84 eV [Fig. 3(h)]. Therefore, it can be concluded that doping channel region with B/N at opposite edges could be a viable way to reduce the threshold voltage of the Z-shaped GNR FET. 3.1.2. Density of states analysis In order to have an in-depth understanding of observed electronic structures, we computed density of states (DOS) profiles of the considered configurations. The calculated DOS profiles for different configurations are shown in Fig. 4. The DOS for config. P [Fig. 4(a)] shows that no electronic states are available near the Fermi level and a clear energy gap of about 2.30 eV between the highest valence band and lower conduction band. The absence of electronic states across the Fermi level is in accordance with the observed pristine band structure and confirms its semiconducting behavior. The DOS profiles for B/N doped channel regions are depicted in Fig. 4(b)–(h). It is revealed that only N or only B doping always results in the semi metallic/metallic configurations whereas
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Fig. 1. Schematics of (a) AGNR channel region, (b) ZGNR electrode region and (c) transverse view of the proposed double gate ZGFET. The grey and white spheres represent carbon and hydrogen atoms respectively. Table 1 The calculated binding energy (eV) per atom in various configurations of AGNR. Configuration
Config. P
Config. Q
Config. R
Config. S
Config. T
Config. U
Config. V
Config. W
Binding energy
−7.05
−15.95
1.83
−10.79
14.55
4.14
14.82
−0.78
B and N co-doping results in a reduced band gap of about 1.84 eV. This reduction in the band gap is accompanied with the symmetry breaking at opposite edges of the ribbon. For the config. Q and config. S, DOS profiles show a sharp peak at the Fermi level indicating the high current for the FET made of this channel which can be validated with the current–voltage (I–V) curves. The single B doped channel DOS shows that pseudo gap is aligned with the Fermi level indicating unavailability of states for current conduction. These results are in accordance with the current observed in the I–V curves which are presented in the next section. 3.2. Transport properties To explore the potential of considered structures for device applications, we have investigated the transport properties of the various configurations by analyzing the I–V characteristics and transmission spectra (TS). Using the optimized geometries, the transmission coefficients are calculated using Eq. (1). The same approach has been previously used to calculate I–V characteristics of transition metal as well as B doped GNR [35,36]. Once the TS have been calculated, current through the channel region can be computed by integrating all the transmission values as given by Eq. (2). The computed drain to source current (I D ) versus the drain to source voltage (V DS ) relations for all device configurations (with a fixed top gate voltage V G = bottom gate voltage, V G = 1 V) are depicted in Fig. 5(a)–(h). Amongst all the structures, config. Q exhibits the highest current value with a magnitude of about 31 μA at 2 V [Fig. 5(b)]. It is followed by config. U and config. S with the highest magnitude of 28 μA and 27 μA respectively. It is noticed that for N doped channel, doping concentration and doping site does not have a significant influence on the observed I–V characteristics. On the other hand, current value is highly sensitive to the doping site of B atom. The highest current values are 4.8 μA
and 5.2 μA for config. R and config. V respectively, as compared to that of 16 μA for config. T. According to our expectations, the highest current in config. W (18 μA) is lying in between that of B or N doped configurations. The present analysis reveals that magnitude of current through the channel region is highly dependent upon the doping site of B/N atoms. Thus, it can be a viable way to control the flow of charge carriers in a Z-GFET. To further analyze the observed I–V behavior of the considered Z-shaped devices, we plotted TS as shown in Fig. 6. Regions εL and εR represent left and right electrodes respectively. In TS of config. P we noticed a transmission gap across the Fermi level [Fig. 6(a)], which in turn confirms the semiconducting behavior of pristine channel region. For config. Q, we observed a high transmission peak lying at the Fermi level [Fig. 6(b)]. The magnitude of this peak approaches to unity which indicates towards the possibility of ballistic transport through this configuration and confirms highest current magnitude as compared to others. The TS for the B doped structures exhibit a transmission gap in correspondence to the electronic band structures. This gap in the vicinity of Fermi level confirms the lowest current values of these configurations [Fig. 5]. For config. W, the TS shows a small peak in the valence band region just below the Fermi level and a decaying behavior at Fermi level is also noticed. This small finite value of transmission coefficient indicates toward small conduction taking place for this structure. The same we have noticed previously in the corresponding I–V characteristic depicted in Fig. 5(h). As the band gap of pristine AGNR is highly sensitive to their ribbon width, it is crucial to know whether the present results still hold for other members of AGNR family. In the present work, it is noticed that charge transfer between C and the guest atom takes place only at local level. Therefore, we expect no qualitative change in the electronic band structure or transport properties of the considered B/N doped AGNR as a function of their width. To verify this, we have
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Fig. 2. Different device configurations showing channel reagion. (a) Pristine (config. P), (b) with center N doping (config. Q), (c) with center B doping (config. R), (d) with displaced N doping (config. S), (e) with displaced B doping (config. T), (f) with double N doping (config. U), (g) with double B doping (config. V), (h) with both B–N doping (config. W). Grey, white, red and blue spheres represent C, H, B and N atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
also investigated the effect of N doping on other members of AGNR
4. Conclusion
family (width 5 and 6). To be concise, this time we have considered only the most stable geometry i.e. centre N doping. The calculated band structures of N a = 5 and N a = 6 are depicted in Fig. 7(a) and Fig. 7(b) respectively. An additional electronic state is noticed across the Fermi level in both of these structures. The similar band has been observed for N a = 4 (config. Q) [Fig. 3(b)]. Though, the degree of overlapping of this additional band with the Fermi level is slightly changed depending upon the ribbon width, the overall qualitative behavior is same for all family of AGNR. This is according to our expectations and we can conclude that present results qualitatively hold for other AGNR as well.
Conclusively, we have investigated different configurations of double gated B/N doped Z-GFET and compared the findings with that of pristine one. It is also noticed that band gap of the channel ribbons is highly sensitive to the presence of B/N dopants. This point towards the possibility of tailoring the band gap of Z-shaped GNR devices merely by controlling the doping sites which is eventually reflected in the performance of device under applied bias voltage. Analysis of BE reveals that config. Q is the most energetically feasible structure. This particular configuration also exhibits enhanced current conduction as compared to pristine and other doped structures. The obtained I–V characteristics are further sup-
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Fig. 3. Band structures of different configurations. (a) Config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W. (The red dotted line indicates Fermi level.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. The DOS of channel regions in various configurations. (a) Config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W. (The dotted line indicates the Fermi level.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. I–V characteristics of different configurations at top gate voltage = bottom gate voltage = 1 V in (a) config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W.
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Fig. 6. Transmission spectra of different configurations. (a) Config. P, (b) config. Q, (c) config. R, (d) config. S, (e) config. T, (f) config. U, (g) config. V, (h) config. W.
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Fig. 7. The band structures of centre N doping in AGNR for (a) N a = 5 and (b) N a = 6. The Fermi energy is set at 0 eV as highlighted by dashed line.
ported by the TS computations. Thus, the present study provides a viable way to alter the band gap of channel material to improve the performance of future graphene based devices. Acknowledgements Authors are thankful to Dr. Pankaj Srivastava faculty of Physics at Computational Nanoscience and Technology Lab. (CNTL), ABV – Indian Institute of Information Technology and Management, Gwalior, India, for providing computational resources. We also thank PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, for providing infrastructure facilities. 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] T. Ando, The electronic properties of graphene and carbon nanotubes, NPG Asia Mater. 1 (2009) 17–21. [3] G. Lu, K. Yu, Z. Wen, J. Chen, Semiconducting graphene: converting graphene from semimetal to semiconductor, Nanoscale 5 (2013) 1353–1368. [4] 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. [5] M.O. Goerbig, Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys. 83 (2011) 1193–1243. [6] A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109–162. [7] E. Rotenberg, A. Bostwick, T. Ohta, J.L. McChesney, T. Seyller, K. Horn, Origin of the energy bandgap in epitaxial graphene, Nat. Mater. 7 (2008) 258–259. [8] Young-Woo Son, M.L. Cohen, S.G. Louie, Energy gaps in graphene nanoribbons, Phys. Rev. Lett. 97 (2006) 216803. [9] T. Kawai, Y. Miyamoto, O. Sugino, Y. Koga, Graphitic ribbons without hydrogentermination: electronic structures and stabilities, Phys. Rev. B 62 (2000) R16349. [10] L. Ci, Z. Xu, L. Wang, W. Gao, F. Ding, K.F. Kelly, B.I. Yakobson, P.M. Ajayan, Controlled nanocutting of graphene, Nano Res. 1 (2008) 116–122. [11] S.S. Dutta, D.R. Strachan, S.M. Khamis, A.T.C. Johnson, Crystallographic etching of few-layer graphene, Nano Lett. 8 (2008) 1912. [12] Y. Fan, M. Zhao, Z. Wang, X. Zhang, H. Zhang, Tunable electronic structures of graphene/boron nitride heterobilayers, Appl. Phys. Lett. 98 (2011) 083103. [13] G. Fiori, G. Iannaccone, Ultralow-voltage bilayer graphene tunnel FET, IEEE Electron Device Lett. 30 (2009) 1096–1098. [14] G. Fiori, D. Neumaier, B.N. Szafranek, G. Iannaccone, Bilayer graphene transistors for analog electronics, IEEE Trans. Electron Devices 61 (2014) 729–733. [15] H. Liu, Y. Liu, D. Zhu, Chemical doping of graphene, J. Mater. Chem. 21 (2011) 3335–3345.
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