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Tailoring electronic and transport properties of edge-terminated armchair graphene by defect formation and N/B doping
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Nabajyoti Baildya , Narendra Nath Ghosh , Asoke P. Chattopadhyay
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Department of Chemistry, University of Kalyani, Kalyani 741235, India b Department of Chemistry, University of Gour Banga, Mokdumpur 732103, India
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Article history: Received 28 October 2019 Received in revised form 18 November 2019 Accepted 4 December 2019 Available online xxxx Communicated by R. Wu Keywords: Graphene nanoribbon p-n junction Doping Defects Density functional theory
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First principle calculations based on Density Functional Theory and nonequilibrium Green’s function methods were carried out on a p-n junction device made of armchair graphene nanoribbons (GNR), with B and N doping and with defects, to examine transport properties of these systems. Doping and defects were found to lower band gap compared to pristine GNR. N-doping leads to the smallest band gap and the highest current (17.18 μA at 0.9 V bias, −12.82 μA at −1 V bias). B-doping shows the least current. Extensive delocalisation in N-doped system suggests a strong coupling between p and n parts, making the system a high rectifying diode. Linear correspondence between transmission coefficient and projected density of states suggest robust negative differential resistance effect. Tuning of efficiency of such p-n junction by doping and defect suggests the design of suitable nanoelectronic devices in future. © 2019 Published by Elsevier B.V.
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1. Introduction
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Graphene is a zero band gap two-dimensional honeycomb-like nanomaterial with some remarkable optical, thermal and electronic properties [1,3]. Its zero band gap makes it a typical electronic system with Dirac cones in band structure [2]. Theoretically, it has been found to have higher electronic mobility than copper [3]. Its lightweight and good strength make it an attractive nanomaterial for structural purposes. Transport properties of transition metal-doped graphene-metal nano-composites [4], hydrogenated borophene [5,6], BN-doped nanoribbon heterojunction [7], N-doped nanoribbon [8] etc. have been studied in some detail. Such properties of an armchair graphene nanoribbon with divacancy and two N-doped negative resistance devices were reported by Das et al. [9]. Kim et al. [10] discussed conductance of single boron, single nitrogen and one B and one N co-doped pristine graphene nano-ribbon (GNR). But the effect of doping GNR with multiple numbers of nitrogen and boron and co-doping with B-N in scattering region only in comparison with normal GNR and single vacant GNR on transport properties of graphene is not available so far. Doping with N and B makes graphene an n-type and p-type semiconductor respectively [11, 12].
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E-mail address: [email protected] (A.P. Chattopadhyay). https://doi.org/10.1016/j.physleta.2019.126194 0375-9601/© 2019 Published by Elsevier B.V.
Graphene [1,2] has attracted a great deal of attention for nanoelectronics and spintronics [3,4,9,10] due to its unique and exceptional properties. Currently, there exists many high-speed photodetectors in which prototypic graphene-based sensors are used [13] for the fabrication of transistors [14]. Here, graphene sheets are used as electrodes. Another important aspect of graphenebased nano-devices is the interface between graphene and other materials. There are many experimental [15–17] and theoretical works available on graphene-based nano-devices and heterojunctions [18–22]. The use of graphene as well as graphene-based nano-sensors, compared to metals such as Cu [23], increases every day, giving further impetus to the fabrication of graphene-based nanomaterials. It has thus become necessary for the deeper understanding of the transport properties of graphene-hetero junction in an atomistic level in order to fabricate efficient graphene based nanodevices. The graphene-metal interactions can occur in two forms [22]. One is chemisorption, which is generally observed between graphene and metals like Co, Ni etc [24]. The other is physisorption, where graphene interacts with Au, Ag etc [22,23]. Naturally, all armchair graphene nanoribbons (GNRs) behave like semi-conductors [25–27] having different band gaps that are controlled by the width of the ribbons. The semiconducting nature of normal semiconductor, or a p-type and n-type one, can be introduced into GNR by doping with B and N atom respectively in the sp2 carbon atom of GNR [28]. Doping in graphene nanoribbon modifies its transport properties [29]. Some results are available on
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Fig. 1. Optimised structure of GNR and doped GNR supercells with electrodes.
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the calculation of transport properties of single or multiple B or N doped GNR [30] and of GNR with defects [31]. The present work analyses the transport properties of armchair graphene nanoribbons (GNR), with multiple B and N doping and with defect formation.
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2. Model and computational details
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In the present work, a GNR of 4n width, where n is equal to the number of C-C pair (n=1) has been considered as a model having semiconducting nature [31]. Doping with B and N atoms, singly and together, have been carried out in such a symmetric manner in the scattering region to obtain a minimum energy configuration. Defects are also created in the scattering region in the usual way [32] to yield a minimum energy structure (see Fig. 1). All the GNRs are saturated with H-atoms at the edges. There are three parts in all the devices, viz. left-hand electrode (LHE, containing 60 atms), right-hand electrode (RHE, containing 60 atoms) and intermediate or scattering region (SR, containing 60 atoms). The scattering region only contains symmetric B, N distributions and the electrodes remain the same in all the cases. Good connectivity is ensured by this arrangement between the electrodes and the scattering region. Geometry optimization was performed using a double-ζ plus polarization function (DZP) basis set and the mesh cut-off is set at 300 Ry, with the electronic temperature set to 300 K. The Perdew-Burke-Ernzerhof (PBE) [29] type generalized gradient approximation (GGA) exchange-correlation functional is used in the calculations, as implemented in the SIESTA program suite [33]. The density matrix convergence criterion is set at 10−4 . The conjugate gradient method is used to stabilize all atoms until the maximum tolerance force reached a value less than 0.01 eV/Å. The k-point sampling for the semi-infinite leads was done with 1 × 1 × 12 Monkhorst-Pack k-grid and each electrode is semiinfinite long in z-direction and with super cell structure with a vacuum more than 20Å in x and y direction in order to decouple the adjacent mirror images. The entire system, including SR and electrodes, was optimized for each structure. The TranSIESTA module, as implemented in the SIESTA suite, was used to calculate transport properties. This package is composed of density functional theory and nonequilibrium Green’s function method [34,35]. The GGA in the PBE form is employed as the exchange-correlation functional, as the PBE exchange functional is very efficient [36–40] for both geometry optimizations and calculation of transport properties.
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Fig. 2. Band structure of (a) GNR (b) Defected GNR (c) B-doped GNR (d) BN-doped GNR (e) N-doped GNR. The Fermi energy is set to zero.
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The adopted mesh cut-off of 300 Ry is used with optimized basis sets of DZP type. The current passing through the contact region under a finite bias (Vb ), which was calculated by integrating the transmission function T(E, Vb ) within the energy bias window from −eVb /2 to +eVb /2 using the Landauer−Buttiker formula
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where f L(R) is the Fermi–Dirac distribution function for left (right) electrode and μL(R) is the electrochemical potential of the left (right) electrode such that eVb = μL − μR . A finite bias from −1 to 1 V was used with small grid of 0.1 V to investigate the current−voltage (I–V) characteristics as well as rectification ratio.
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3. Results and discussion
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Optimised geometries of all investigated GNRs are shown in Fig. 1. The corresponding band structures are shown in Fig. 2. It should be mentioned here that in GNR with defects and in B-doped GNR, the bands appear near Fermi level whereas, in Ndoped GNR, crossing of the dispersive bands at the Fermi level occurs as shown in Fig. 2e. Compared to pristine GNR, in GNR with defects, and in GNR doped with individual B and N atoms, lower-
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Fig. 3. Band gap of GNR’s.
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Fig. 4. HOMO and LUMO densities of GNR, defected and doped GNRs.
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metallic one. Introduction of B, N or both B and N in GNR lead to
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Fig. 5. Transmission function as a function of relative Fermi energy of (a) GNR, (b) defective GNR, (c) B-doped GNR, (d) BN-doped GNR, (e) N-doped GNR. PDOS as a function of relative Fermi energy of (f) GNR, (g) defective GNR, (h) B-doped GNR, (i) BN-doped GNR, (j) N-doped GNR.
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The band gaps of GNRs are shown in Fig. 3. This clearly indicates that individual doping with both nitrogen and boron leads to a decrease in the band gap, which is concordant with the band structure (Fig. 2b, 2c, 2e). Again, the boron nitrogen co-doped sys-
tem has a larger band gap which is also in accordance with Fig. 2d. However, one can predict that this band gap opening of the B or N co-doped GNR is due to the disorderedness induced by doping. It is noteworthy to mention here that both N and B doping convert semiconducting periodic GNR with width 4n (n= 1) to a metallic one as indicated by the dispersive π and π ∗ sub-bands crossing the Fermi level as shown in Figs. 2c and 2d respectively. Thus, they can be successfully used as semi-infinite leads. In pristine GNR, the HOMO-LUMO densities have symmetric distribution while in the case of defective and doped GNR, these densities are asymmetric in nature. In the case of B-doped and N-doped GNR, HOMO density is more prominent on heteroatomic sites. Compared to HOMO densities, the LUMO densities are much more localized. This localization is more prominent in case of N and B doped systems. With the application of different bias voltage, the density of states are changed accordingly. Compared to B-doped and B-N co-doped systems, in N-doped system, the HOMO and LUMO densities are more delocalised over the whole system. This type of delocalization indicates that there is a strong coupling between p and n parts which is also reflected by its lower band gap. Strong coupling between n and p parts makes the system a high rectifying diode. To investigate the mechanism of negative differential resistance (NDR) phenomena, the transmission function [T(E, Vb )] and the partial density of states (PDOS) were plotted as functions of relative Fermi Energy (E-Ef ) at different biases as shown in Fig. 5. (See Fig. 6.) For all the GNRs, the transmission function curves have two peaks: one below and other above the Fermi level, which correspond to HOMO and LUMO states respectively similar to the PDOS plots. The transmission function as represented in Fig. 5 (left panel) is in accordance with the PDOS plots as shown in Fig. 5 (right panel). The density of states for all the systems have more density at valence band than at conduction band. Also at negative bias, all transmission function plots show broad peaks. For nitrogen doping at both negative (−0.35 eV) and positive (+0.25 eV) bias, the transmission functions are much closer to Fermi level suggesting nitrogen doping decreases the bang gap, offering more metallic character. Compared to pristine graphene, doping and defects in
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Fig. 6. PDOS plot of (a) graphene, (b) defective graphene, (c) B-doped graphene, (d) BN-co-doped graphene, and (e) N-doped graphene. (For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.)
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GNR result in asymmetry in the transmission function, which is also reflected in the HOMO-LUMO densities as seen in Fig. 4. The B and N co-doped system has a transmission peak at the Fermi level, which suggests a strong mixing of HOMO and LUMO states. However, the current at the Fermi level is zero as the bias voltage is zero. On B doping, Fermi energy of the GNR is shifted downwards. On the other hand, on N doping it is shifted up and affects the pattern of the density of states of conduction band much more in comparison to valence band. The conjugate system remains a semiconductor still, with a shorter band gap between 0.083–0.013 eV. For N-doped GNR, the conduction band actually arises from nitrogen atom while for B-doped system both the conduction and valence bands arise from boron atom. Next, the current-voltage (I–V) characteristics are discussed of the GNRs studied. This is shown in Fig. 7 below. The asymmetric behaviour of all the system except graphene at positive and negative bias is clearly shown for all devices considered in the present calculations. All the systems are found to have zero current at zero bias, which is expected. By applying positive and negative bias, graphene shows symmetric current distribution. At bias 0.1 volt, the current reaches 5.47 μA and at bias −0.1 volt, this value reaches −5.55 μA. After that, change in current is negligibly small. In case of graphene with defects, the band gap is small, and some fluctuation in current is seen at bias −0.3 volt and at −0.5 volt. This feature is absent at positive bias. For boron doped GNR, changes in current at different bias is much smaller compared to other GNRs. But it also has some unsymmetrical behaviour at positive and negative bias. Due to small flow of current, the graph is not prominent for boron doped GNR compared to others. At −1 volt bias, it conducts more current but at +1 volt the current is much smaller. Again, at +0.5 volt it shows current of 0.0043 μA. In case of B-N co-doped GNR, at −0.7 volt bias there is a current of −0.705 μA which is absent at +0.7 volt. So there is again an unsymmetrical current flow. In N-doped GNR, the current flow is maximum compared to all other systems. The system shows a maximum current at bias 0.9 volt and the value of current is 17.18 μA. But at negative bias −1 volt, it also shows a high current of −12.82 μA. Hence in all systems (except pristine GNR), changes at both positive and negative bias are different. For boron doped graphene, the changes are much smaller compared to other systems, and hence not discernable in Fig. 7. But this system also shows some asymmetric nature of curve in both biases. For graphene with defects, B-N co-doped graphene, and also in N-doped graphene, the asymmetric nature of I-V curves are clearly shown. This asymmetry arises due to unsymmetrical distribution of electrons in HOMO and LUMO states. Asymmetry in the transmission function and PDOS plot for all GNR’s except pristine graphene is in accordance with the corresponding I vs V plots shown in Fig. 7.
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In summary, first-principle calculations based on density functional theory and nonequilibrium Green’s function method were carried out on a p−n junction device made of boron and nitrogendoped and defective armchair graphene nanoribbons of width 4n (n=1) to evaluate their transport properties. Symmetric distributions of doping give rise to minimum-energy configurations. Doping by individual B and N atoms and defective GNRs show lower band gap compared to pristine GNR. The N-doped system shows the smallest band gap, and the delocalised HOMO and LUMO densities over the system indicate that there is strong coupling between p and n parts. Such strong coupling between n and p parts makes the system a high rectifying diode. The transmission function and projected density of states show a linear correspondence
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Fig. 7. Comparison of I vs V characteristics for the studied GNR’s.
suggesting that the systems have robust negative differential resistance effect. In N-doped GNR, the current flow is maximum compared to other systems and the system shows a maximum current at bias 0.9 volt and the value of current is 17.18 μA. At negative bias −1 volt, it also shows a high current of −12.82 μA. For boron-doped GNR, current flow within the bias window is much smaller compared to other systems. Thus the efficiency of a single p−n junction tandem diode may be tuned by doping and defect formation. It is expected that the observations presented here are of some importance in the context of providing guidelines for the design of highly efficient devices in the field of graphene-based nanoelectronics.
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Data availability
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Relevant data files may be available on request to the corresponding author.
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Declaration of competing interest
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The authors declare no conflict of interest among themselves regarding the present work.
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Tailoring electronic and transport properties of edge-terminated armchair graphene by defect formation and N/B doping
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Nabajyoti Baildya , Narendra Nath Ghosh , Asoke P. Chattopadhyay
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Department of Chemistry, University of Kalyani, Kalyani 741235, India b Department of Chemistry, University of Gour Banga, Mokdumpur 732103, India
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Article history: Received 28 October 2019 Received in revised form 18 November 2019 Accepted 4 December 2019 Available online xxxx Communicated by R. Wu Keywords: Graphene nanoribbon p-n junction Doping Defects Density functional theory
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First principle calculations based on Density Functional Theory and nonequilibrium Green’s function methods were carried out on a p-n junction device made of armchair graphene nanoribbons (GNR), with B and N doping and with defects, to examine transport properties of these systems. Doping and defects were found to lower band gap compared to pristine GNR. N-doping leads to the smallest band gap and the highest current (17.18 μA at 0.9 V bias, −12.82 μA at −1 V bias). B-doping shows the least current. Extensive delocalisation in N-doped system suggests a strong coupling between p and n parts, making the system a high rectifying diode. Linear correspondence between transmission coefficient and projected density of states suggest robust negative differential resistance effect. Tuning of efficiency of such p-n junction by doping and defect suggests the design of suitable nanoelectronic devices in future. © 2019 Published by Elsevier B.V.
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1. Introduction
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Graphene is a zero band gap two-dimensional honeycomb-like nanomaterial with some remarkable optical, thermal and electronic properties [1,3]. Its zero band gap makes it a typical electronic system with Dirac cones in band structure [2]. Theoretically, it has been found to have higher electronic mobility than copper [3]. Its lightweight and good strength make it an attractive nanomaterial for structural purposes. Transport properties of transition metal-doped graphene-metal nano-composites [4], hydrogenated borophene [5,6], BN-doped nanoribbon heterojunction [7], N-doped nanoribbon [8] etc. have been studied in some detail. Such properties of an armchair graphene nanoribbon with divacancy and two N-doped negative resistance devices were reported by Das et al. [9]. Kim et al. [10] discussed conductance of single boron, single nitrogen and one B and one N co-doped pristine graphene nano-ribbon (GNR). But the effect of doping GNR with multiple numbers of nitrogen and boron and co-doping with B-N in scattering region only in comparison with normal GNR and single vacant GNR on transport properties of graphene is not available so far. Doping with N and B makes graphene an n-type and p-type semiconductor respectively [11, 12].
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E-mail address: [email protected] (A.P. Chattopadhyay). https://doi.org/10.1016/j.physleta.2019.126194 0375-9601/© 2019 Published by Elsevier B.V.
Graphene [1,2] has attracted a great deal of attention for nanoelectronics and spintronics [3,4,9,10] due to its unique and exceptional properties. Currently, there exists many high-speed photodetectors in which prototypic graphene-based sensors are used [13] for the fabrication of transistors [14]. Here, graphene sheets are used as electrodes. Another important aspect of graphenebased nano-devices is the interface between graphene and other materials. There are many experimental [15–17] and theoretical works available on graphene-based nano-devices and heterojunctions [18–22]. The use of graphene as well as graphene-based nano-sensors, compared to metals such as Cu [23], increases every day, giving further impetus to the fabrication of graphene-based nanomaterials. It has thus become necessary for the deeper understanding of the transport properties of graphene-hetero junction in an atomistic level in order to fabricate efficient graphene based nanodevices. The graphene-metal interactions can occur in two forms [22]. One is chemisorption, which is generally observed between graphene and metals like Co, Ni etc [24]. The other is physisorption, where graphene interacts with Au, Ag etc [22,23]. Naturally, all armchair graphene nanoribbons (GNRs) behave like semi-conductors [25–27] having different band gaps that are controlled by the width of the ribbons. The semiconducting nature of normal semiconductor, or a p-type and n-type one, can be introduced into GNR by doping with B and N atom respectively in the sp2 carbon atom of GNR [28]. Doping in graphene nanoribbon modifies its transport properties [29]. Some results are available on
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Fig. 1. Optimised structure of GNR and doped GNR supercells with electrodes.
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the calculation of transport properties of single or multiple B or N doped GNR [30] and of GNR with defects [31]. The present work analyses the transport properties of armchair graphene nanoribbons (GNR), with multiple B and N doping and with defect formation.
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2. Model and computational details
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In the present work, a GNR of 4n width, where n is equal to the number of C-C pair (n=1) has been considered as a model having semiconducting nature [31]. Doping with B and N atoms, singly and together, have been carried out in such a symmetric manner in the scattering region to obtain a minimum energy configuration. Defects are also created in the scattering region in the usual way [32] to yield a minimum energy structure (see Fig. 1). All the GNRs are saturated with H-atoms at the edges. There are three parts in all the devices, viz. left-hand electrode (LHE, containing 60 atms), right-hand electrode (RHE, containing 60 atoms) and intermediate or scattering region (SR, containing 60 atoms). The scattering region only contains symmetric B, N distributions and the electrodes remain the same in all the cases. Good connectivity is ensured by this arrangement between the electrodes and the scattering region. Geometry optimization was performed using a double-ζ plus polarization function (DZP) basis set and the mesh cut-off is set at 300 Ry, with the electronic temperature set to 300 K. The Perdew-Burke-Ernzerhof (PBE) [29] type generalized gradient approximation (GGA) exchange-correlation functional is used in the calculations, as implemented in the SIESTA program suite [33]. The density matrix convergence criterion is set at 10−4 . The conjugate gradient method is used to stabilize all atoms until the maximum tolerance force reached a value less than 0.01 eV/Å. The k-point sampling for the semi-infinite leads was done with 1 × 1 × 12 Monkhorst-Pack k-grid and each electrode is semiinfinite long in z-direction and with super cell structure with a vacuum more than 20Å in x and y direction in order to decouple the adjacent mirror images. The entire system, including SR and electrodes, was optimized for each structure. The TranSIESTA module, as implemented in the SIESTA suite, was used to calculate transport properties. This package is composed of density functional theory and nonequilibrium Green’s function method [34,35]. The GGA in the PBE form is employed as the exchange-correlation functional, as the PBE exchange functional is very efficient [36–40] for both geometry optimizations and calculation of transport properties.
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Fig. 2. Band structure of (a) GNR (b) Defected GNR (c) B-doped GNR (d) BN-doped GNR (e) N-doped GNR. The Fermi energy is set to zero.
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The adopted mesh cut-off of 300 Ry is used with optimized basis sets of DZP type. The current passing through the contact region under a finite bias (Vb ), which was calculated by integrating the transmission function T(E, Vb ) within the energy bias window from −eVb /2 to +eVb /2 using the Landauer−Buttiker formula
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where f L(R) is the Fermi–Dirac distribution function for left (right) electrode and μL(R) is the electrochemical potential of the left (right) electrode such that eVb = μL − μR . A finite bias from −1 to 1 V was used with small grid of 0.1 V to investigate the current−voltage (I–V) characteristics as well as rectification ratio.
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3. Results and discussion
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Optimised geometries of all investigated GNRs are shown in Fig. 1. The corresponding band structures are shown in Fig. 2. It should be mentioned here that in GNR with defects and in B-doped GNR, the bands appear near Fermi level whereas, in Ndoped GNR, crossing of the dispersive bands at the Fermi level occurs as shown in Fig. 2e. Compared to pristine GNR, in GNR with defects, and in GNR doped with individual B and N atoms, lower-
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Fig. 3. Band gap of GNR’s.
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Fig. 4. HOMO and LUMO densities of GNR, defected and doped GNRs.
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metallic one. Introduction of B, N or both B and N in GNR lead to
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Fig. 5. Transmission function as a function of relative Fermi energy of (a) GNR, (b) defective GNR, (c) B-doped GNR, (d) BN-doped GNR, (e) N-doped GNR. PDOS as a function of relative Fermi energy of (f) GNR, (g) defective GNR, (h) B-doped GNR, (i) BN-doped GNR, (j) N-doped GNR.
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The band gaps of GNRs are shown in Fig. 3. This clearly indicates that individual doping with both nitrogen and boron leads to a decrease in the band gap, which is concordant with the band structure (Fig. 2b, 2c, 2e). Again, the boron nitrogen co-doped sys-
tem has a larger band gap which is also in accordance with Fig. 2d. However, one can predict that this band gap opening of the B or N co-doped GNR is due to the disorderedness induced by doping. It is noteworthy to mention here that both N and B doping convert semiconducting periodic GNR with width 4n (n= 1) to a metallic one as indicated by the dispersive π and π ∗ sub-bands crossing the Fermi level as shown in Figs. 2c and 2d respectively. Thus, they can be successfully used as semi-infinite leads. In pristine GNR, the HOMO-LUMO densities have symmetric distribution while in the case of defective and doped GNR, these densities are asymmetric in nature. In the case of B-doped and N-doped GNR, HOMO density is more prominent on heteroatomic sites. Compared to HOMO densities, the LUMO densities are much more localized. This localization is more prominent in case of N and B doped systems. With the application of different bias voltage, the density of states are changed accordingly. Compared to B-doped and B-N co-doped systems, in N-doped system, the HOMO and LUMO densities are more delocalised over the whole system. This type of delocalization indicates that there is a strong coupling between p and n parts which is also reflected by its lower band gap. Strong coupling between n and p parts makes the system a high rectifying diode. To investigate the mechanism of negative differential resistance (NDR) phenomena, the transmission function [T(E, Vb )] and the partial density of states (PDOS) were plotted as functions of relative Fermi Energy (E-Ef ) at different biases as shown in Fig. 5. (See Fig. 6.) For all the GNRs, the transmission function curves have two peaks: one below and other above the Fermi level, which correspond to HOMO and LUMO states respectively similar to the PDOS plots. The transmission function as represented in Fig. 5 (left panel) is in accordance with the PDOS plots as shown in Fig. 5 (right panel). The density of states for all the systems have more density at valence band than at conduction band. Also at negative bias, all transmission function plots show broad peaks. For nitrogen doping at both negative (−0.35 eV) and positive (+0.25 eV) bias, the transmission functions are much closer to Fermi level suggesting nitrogen doping decreases the bang gap, offering more metallic character. Compared to pristine graphene, doping and defects in
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Fig. 6. PDOS plot of (a) graphene, (b) defective graphene, (c) B-doped graphene, (d) BN-co-doped graphene, and (e) N-doped graphene. (For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.)
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GNR result in asymmetry in the transmission function, which is also reflected in the HOMO-LUMO densities as seen in Fig. 4. The B and N co-doped system has a transmission peak at the Fermi level, which suggests a strong mixing of HOMO and LUMO states. However, the current at the Fermi level is zero as the bias voltage is zero. On B doping, Fermi energy of the GNR is shifted downwards. On the other hand, on N doping it is shifted up and affects the pattern of the density of states of conduction band much more in comparison to valence band. The conjugate system remains a semiconductor still, with a shorter band gap between 0.083–0.013 eV. For N-doped GNR, the conduction band actually arises from nitrogen atom while for B-doped system both the conduction and valence bands arise from boron atom. Next, the current-voltage (I–V) characteristics are discussed of the GNRs studied. This is shown in Fig. 7 below. The asymmetric behaviour of all the system except graphene at positive and negative bias is clearly shown for all devices considered in the present calculations. All the systems are found to have zero current at zero bias, which is expected. By applying positive and negative bias, graphene shows symmetric current distribution. At bias 0.1 volt, the current reaches 5.47 μA and at bias −0.1 volt, this value reaches −5.55 μA. After that, change in current is negligibly small. In case of graphene with defects, the band gap is small, and some fluctuation in current is seen at bias −0.3 volt and at −0.5 volt. This feature is absent at positive bias. For boron doped GNR, changes in current at different bias is much smaller compared to other GNRs. But it also has some unsymmetrical behaviour at positive and negative bias. Due to small flow of current, the graph is not prominent for boron doped GNR compared to others. At −1 volt bias, it conducts more current but at +1 volt the current is much smaller. Again, at +0.5 volt it shows current of 0.0043 μA. In case of B-N co-doped GNR, at −0.7 volt bias there is a current of −0.705 μA which is absent at +0.7 volt. So there is again an unsymmetrical current flow. In N-doped GNR, the current flow is maximum compared to all other systems. The system shows a maximum current at bias 0.9 volt and the value of current is 17.18 μA. But at negative bias −1 volt, it also shows a high current of −12.82 μA. Hence in all systems (except pristine GNR), changes at both positive and negative bias are different. For boron doped graphene, the changes are much smaller compared to other systems, and hence not discernable in Fig. 7. But this system also shows some asymmetric nature of curve in both biases. For graphene with defects, B-N co-doped graphene, and also in N-doped graphene, the asymmetric nature of I-V curves are clearly shown. This asymmetry arises due to unsymmetrical distribution of electrons in HOMO and LUMO states. Asymmetry in the transmission function and PDOS plot for all GNR’s except pristine graphene is in accordance with the corresponding I vs V plots shown in Fig. 7.
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4. Conclusion
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In summary, first-principle calculations based on density functional theory and nonequilibrium Green’s function method were carried out on a p−n junction device made of boron and nitrogendoped and defective armchair graphene nanoribbons of width 4n (n=1) to evaluate their transport properties. Symmetric distributions of doping give rise to minimum-energy configurations. Doping by individual B and N atoms and defective GNRs show lower band gap compared to pristine GNR. The N-doped system shows the smallest band gap, and the delocalised HOMO and LUMO densities over the system indicate that there is strong coupling between p and n parts. Such strong coupling between n and p parts makes the system a high rectifying diode. The transmission function and projected density of states show a linear correspondence
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Fig. 7. Comparison of I vs V characteristics for the studied GNR’s.
suggesting that the systems have robust negative differential resistance effect. In N-doped GNR, the current flow is maximum compared to other systems and the system shows a maximum current at bias 0.9 volt and the value of current is 17.18 μA. At negative bias −1 volt, it also shows a high current of −12.82 μA. For boron-doped GNR, current flow within the bias window is much smaller compared to other systems. Thus the efficiency of a single p−n junction tandem diode may be tuned by doping and defect formation. It is expected that the observations presented here are of some importance in the context of providing guidelines for the design of highly efficient devices in the field of graphene-based nanoelectronics.
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Data availability
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Relevant data files may be available on request to the corresponding author.
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Declaration of competing interest
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The authors declare no conflict of interest among themselves regarding the present work.
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