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Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping
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Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping
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Yu-Cheng Ling, Feng Ning, Yan-hong Zhou, Ke-Qiu Chen ⇑
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Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410082, China
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Article history: Received 14 December 2014 Received in revised form 22 January 2015 Accepted 24 January 2015 Available online xxxx Keywords: Rectifying behavior Negative differential resistance Nonequilibrium Green’s functions
a b s t r a c t We investigate the electronic transport properties of triangular graphene systems with atoms B, N or both of them vertex doped based on non-equilibrium Green’s function approach combined with density functional theory. Interestingly, fine rectifying behavior and obvious negative differential resistance are observed in B–N vertex doped case. The origin of the rectification is that a barrier likes a p–n junction has been formed in B–N vertex doped junction. Moreover, weak interaction is considered by adjusting the distance between the two intermediate atoms. With the increase of the distance between them, the rectifying behavior and negative differential resistance weaken step by step. Our structure constructed by B–N vertex doped triangular graphene to realize fine rectification is constructive and is a promising candidate for the next generation nanoscale device. Ó 2015 Published by Elsevier B.V.
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1. Introduction
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In recent years, more and more microelectronic devices have been investigated through the development of unique properties of matter at the nanoscale, including nanostructures, molecules, and quantum dots [1–3]. Also, lots of interesting physical properties, for example, rectifying behaviors, negative differential resistance, and switching effects, have been investigated in molecular devices [3– 5]. Tailored by lithographic techniques, graphene nanostructures can be made to construct molecular devices [6–12]. And by selective tailoring graphene nanoribbon with high precision [7], fine rectification has been observed in graphene nanoribbon based systems with electron transfer from the vertex to the edge [8]. So far, varieties of molecular rectifiers have been explored and some possible mechanisms are also been suggested [10–16]. The rec-
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⇑ Corresponding author. Tel.: +86 0731 88820375. E-mail address: [email protected] (K.-Q. Chen).
tifying behavior can be realized by edge hydrogenated zigzag-edged graphene nanoribbon heterojunctions [12] or by weak intermolecular interaction on electronic bilayer graphene nanoribbon device [15]. Meanwhile, negative differential resistance has been found in molecular devices with specially designed [16–23]. For instance, by increasing the interaction length [17], by an external electric field [18] or using the high-bias properties of gold–carbon bonds, a family of diodes has been synthesized [21]. Moreover, doping is also the frequently adopted ways to research the new properties of matter [24–31]. The transmission conductance of single wall carbon nanotube and single wall boron nitride nanotube have been investigated [32], at the same time, the growth and interface formation of monolayer grapheme boron nitride heterostructures on ruthenium has been studied to investigate the graphene and hexagonal boron nitride, which offers an attractive system from which to build such 2D heterostructures [33]. Experiment on graphene doping shows that, with the C atoms substituted with B and N atoms respectively, the possibility of making p-type and n-type semiconducting
http://dx.doi.org/10.1016/j.orgel.2015.01.034 1566-1199/Ó 2015 Published by Elsevier B.V.
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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graphene has been improved [32]. Furthermore, negative differential resistance (NDR) behavior has been found with the change of doping position and the electronic transport properties are strongly related to the width of the ribbon and the position of the N dopant [22,23]. Therefore, in the present work, we investigated the electronic and transport properties of triangular graphene with different vertex doped. By first-principles calculations, rectifying behavior and NDR (negative differential resistance) are observed by changing the intermediate atoms and their mutual distance. These results are constructive for the study of molecular devices.
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2. Model and computational details
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The molecular device is illustrated in Fig. 1. The device model is divided into three parts: left electrode, right electrode, and the scattering region. The armchair graphene nanoribbons edges are used for the lead, while in the intermediate scattering region, triangular graphenes are used for the zigzag edges which are hydrogenated. Each electrode has been described as a supercell which contains two repeated carbon unit cells along the transport direction. For central molecule, the two vertex carbon atoms in trigonal graphenes are substituted with boron or nitrogen atom. The initial distance (Do) between two triangular graphene nanoribbons has been optimized. We consider the change of transport properties with the changing distance Dd increasing step by step from 0.1 Å to 0.2 Å and to 0.3 Å. The current has been calculated by using the Landauer formula [34]:
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IðV b Þ ¼
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2e h
Z
TðE; V b Þ f l ðE ll Þ f r ðE lr Þ dE
ð1Þ
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where llðrÞ are electrochemical potentials of the left and right electrodes. The difference of them is ll lr ¼ eV b . In the transmission spectrum, the energy region which contributes to the current has been known as the bias window. The total transmission probability:
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h i TðE; V b Þ ¼ Tr Cl GR Cr GA
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ð2Þ
where GRðAÞ is the retarded (advanced) Green functions of the central region. The geometrical optimization of the model structure and electron transport properties are all performed by using density functional theory (DFT) and non-equilibrium Green’s function (NEGF) method [35,36] and all residual forces on each atom are smaller than 0.05 eV/Å. The core electrons have been described with norm-conserving pseudopotentials and at the same time, the local-density approximation (LDA) has been used to the exchange-correlation potential. The k-point sampling is 1, 1, and 100 in the x, y, z direction, respectively, and the cutoff energy is set to 150 Ry. A single-zeta polarized (SZP) basis set is adopted for electron wave function and the convergence criteria for Hamiltonian and the electron density are 105.
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3. Results and discussions
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At first, all six configuration models show the same characteristics that the currents are nearly non-conducting in the bias range from 1.8 to 1.8 V, as can be seen from the Fig. 2(a). When the bias voltage exceeds 1.8 V, the current for all the models comes into being and the current for the model B–N increases obviously (see Fig. 2(a)). Second, the I–V curves of B–N, C–N, B–C vertex doped configurations show asymmetric behaviors where the current at positive bias is bigger than the corresponding negative bias, thus rectification emerges. The inset in Fig. 2(a) shows the rectification ratio. The rectification ratio is defined as:
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RðVÞ ¼ IðVÞ=jIðVÞj
ð3Þ
where I(V) and I(V) are the current at positive and negative voltages with the same voltage magnitude. Compared with models B–C and C–N, model B–N shows better rectification. The largest rectification ratio of model B–N reaches 87 at 1.84 V while for models C–N and B–C, the largest rectification ratios are 24 and 3 respectively. So the rectifying behaviors with one vertex carbon atom substituted with B atom and the other one with N atom simultaneously own the best effect. This behavior can be made as an electronic rectifier. In addition, the NDR behavior is also observed in model B–N at the bias range from 1.96 V to 2.2 V.
Fig. 1. Structure of a molecular device in our simulations, where B is a boron atom, C is a carbon atom, N is a nitrogen atom, and H is a hydrogen atom. Do + Dd is the distance between two triangular graphene nanoribbons.
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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Fig. 2. (a) The I–V characteristics and rectifying ratio changes with the applied bias for six triangular grapheme with different vertex doped models. (b) The I–V characteristics and rectifying ratio change with the applied bias for model B–N with four changing distance.
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In Fig. 2(b), we give the current–voltage (I–V) characteristics for B–N configuration with the B–N distance increases by Dd = 0.1 Å, 0.2 Å, 0.3 Å, respectively. As can be seen from Fig. 2(b), the rectifying behavior and NDR weaken step by step with the increase of the distance between the atoms B and N. For example, the biggest rectification ratio for models B–N with the Dd = 0.1 Å and Dd = 0.2 Å are 73 and 6 at 1.84 V, respectively, which are lower than that with Dd = 0 Å. To explain the big rectification ratio in the Fig. 2(a), we plot the transmission spectra of the models B–N, C–N, B–C at several voltages, as shown in Fig. 3. In the calculated bias region, the transmission peak at Fermi energy has a big impact on the molecular rectification, which display different shift tendency in the positive and negative bias window. With the increase of the positive bias voltage, the transmission spectra of models B–N and C–N show obviously transmission peak, while the transmission of model B–C is nearly zero in the energy range [2, 2] eV. And with the increase of the negative bias voltage, the transmission
spectra of all three models are nearly depressed. So model B–N and C–N have bigger rectification ratio than model B–C has. At the same time, as we can see in Fig. 3, under the positive bias, the transmission spectra of model B–N is bigger than model C–N at considered biases, which is the reason why the rectification ratio of model B–N is bigger than model C–N. As we known, the position of transmission peak is generally determined by the transmission channels and the delocalization of orbital. The first energy level below the average electrode Fermi energy is described as the highest occupied molecular orbital (HOMO) resonance, whereas that above the average is described as the lowest unoccupied molecular orbital (LUMO) resonance. When the bias voltage is 0 V, the HOMO and LUMO of models B–N, C–N and B–C are located between the two sides of the Fermi energy level and with the increase of positive bias voltage, the HOMO of three models shift to the right of the Fermi energy level as can be seen in Fig. 3. However, the HOMO1 of three models still lies near the Fermi energy
Fig. 3. Transmission spectra and HOMO and LUMO energy levels of models B–C, C–N and B–N at several bias. The HOMO and HOMO1 orbitals are label by blue lines. The energy origin is set to be the Fermi level of the system.
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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level. And with the increase of negative bias voltage, the HOMO1 of the three models shifts to the left of the Fermi energy level. It is noteworthy that the details of HOMO and HOMO1 are different for these three models. With the increase of the bias, the energy gap between the HOMO1 and HOMO for model B–N is smaller than that for model C– N, and that for model C–N is smaller than that for model B– C. For model B–N, these two orbitals together may contribute to a transmission peak, for example, at the bias of 1.84 V. However, the model C–N and B–C have only one molecular orbital (HOMO1) contribute to the transmission. In order to know the two orbitals’ contribution to the transmission, in Table 1, we present the molecular projected selfconsistent Hamiltonian (MPSH) distribution of these two orbitals at the bias voltage +1.84 V and 1.84 V for models B–N, C–N, and B–C, respectively, as an example to illustrastrate the above thought. From the table, we can see that at the bias +1.84 V, the MPSH distribution of orbitals HOMO and HOMO1 for Model B–N is spatially delocalized which results in obvious transmission peak at corresponding energy positions. For model C–N, the MPSH distribution of HOMO1 is also delocalized, but that of HOMO is localized, so the transmission peak is smaller than that for model B–N. For model B–C, both the MPSH distribution of orbitals (HOMO and HOMO1) are localized, so there is nearly no electron transmission. At the negative bias 1.84 V, the MPSH distribution of orbitals HOMO and HOMO1 for the three models are all localized, so the transmission of all of them are depressed. From above, we know why model B–N have the biggest current and rectification ratio at this bias. In addition, for model B–N, at the bias 1.96 V, the alignment of the HOMO1 and HOMO orbitals with the electrodes is good, which gives to a transmission peak. With the bias increasing, for example, at the bias of 2.2 V, the coupling between the two orbitals and the electrodes is weakened, so transmission coefficient is decreased in magnitude, and then NDR happens. So the origin of NDR is the alignment between the HOMO1 and HOMO orbitals of the central molecule and the electrodes [37,38]. To further understand the reason why rectifying behavior appeared, we show the electrostatic potential distribution and electron density for three models at zero bias in
Table. 2. As we know, the electron transfer from the lead to the central region could lead higher electrostatic potential barrier in central region, which will affect the charge redistribution on the molecule and impedes the flow of electrons across junction. It is obviously that the potential profile and electron density is asymmetric (see Table. 2): Boron shows higher electrostatic potential and lower electron density; meanwhile, Nitrogen shows lower electrostatic potential and higher electron density. Our result shows that the region of boron atom is positive charged (holes), just like the p-type semiconductor, and the region of nitrogen atom is negative charge (electrons), just like the n-type semiconductor. A barrier just likes the p–n junction has been formed in our molecules. Corresponding to ptype and n-type forms, the anion and cation have been compensated by charges. As positive bias appears, the carrier tends to the barrier, reducing the space charge, making the barrier thin, then the diffusion current is easy to transport and the avalanche breakdown happens. When the negative bias appears, the carrier moves away from the barrier, increasing the space charge, making the barrier layer thick and the diffusion current reduced. From the above results, it is easy to understand why rectifying behavior will occur in model B–N. In the following, in order to explain why the rectifying behavior and negative differential resistance in Model B– N weaken step by step with the increase of the distance between the atoms B and N, the transmission spectrum (see Fig. 4) at several representative biases and spatial distribution of MPSH of HOMO and HOMO1 at the bias of 1.84 V (see Table 3) for the models B–N with distance Dd = 0 Å, 0.1 Å, and 0.2 Å are presented. At the bias of 1.84 V, the MPSH of Model B–N with the Dd = 0 Å and Dd = 0.1 Å are delocalized which results in obvious transmission peaks at corresponding energy positions (see Table 3). However, the MPSH of HOMO and HOMO1 orbitals for model B–N with Dd = 0.2 Å and Dd = 0.3 Å become more localized, as a consequence, the corresponding transmission peaks are be extremely repressed. So the current become smaller and smaller with the increase of Dd at the bias and so the NDR nearly weaken step by step. And at the negative bias, the current do have the same tendency with the increase of Dd, but the current itself is
Table 1 Spatial distributions of HOMO1 at +1.84 V bias and 1.84 V bias for models B–N, C–N, and B–C, respectively. +1.84V
1.84V MPSH
HOMO1
HOMO
HOMO1
HOMO
B–C
C–N
B–N
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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Y.-C. Ling et al. / Organic Electronics xxx (2015) xxx–xxx Table 2 Electrostatic potential distributions and electron density distributions for three models at zero bias. B–C
C–N
B–N
Fig. 4. Transmission spectra, HOMO and LUMO energy levels for model B–N with three changing distance at several bias. The HOMO and HOMO1 orbitals are label by blue lines. The energy origin is set to be the Fermi level of the system.
Table 3 The MPSH distributions of HOMO1 and HOMO for model B–N at bias 1.84 V. B–N
Dd:0 Å
Dd:0.1 Å
Dd:0.2 Å
Dd:0.3 Å
HOMO1
HOMO
yet very small (see Fig. 2(a)), so distance change has little impact on the current at negative biases. So when the increase of the distance between the atoms B and N, the rectification effect is depressed. At last, we make an explanation why the currents are nearly non-conducting in the bias range from 1.8 to 1.8 V for all six configuration models in the Fig. 2. As we know, the armchair graphene nanoribbons are semiconductors with energy gaps decreasing as a function of the increasing ribbon width and the variations in band gaps exhibit three distinct family behaviors: D3pþ1 > D3p > D3pþ2 for all p’s where p is a integral number and N = 3p + 1, 3p or 3p + 2 is width of graphene nanoribbons. The band gap of 7-armchair graphene nanoribbon is about 1.73 eV. This rather large band gap results in the nearly depressed current in the bias range from 1.8 to 1.8 V for the six configuration models [39].
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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4. Conclusions
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The electronic transport properties of triangular graphene systems with atoms B, N or both of them vertex doped have been investigated by non-equilibrium Green’s function approach. Fine rectifying behavior and obvious NDR have been found in B–N vertex doped case. Moreover, weak interaction effect on the rectifying behavior and NDR was considered by adjusting the distance between the two intermediate atoms. With the increase of the distance between them, the rectification and negative differential resistance weakened step by step. The origin of the rectification was analyzed detailed. Structure made of B–N vertex doped triangular graphene is constructive to realize fine rectification and is a promising candidate for the next generation nanoscale device.
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Acknowledgements
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This work was supported by the National Natural Science Foundation of China (Nos. 11274105 and 91227125), by the National Basic Research Program of China (Nos. 2012CB932703 and 2011CB606405), by Hunan Provincial Natural Science Foundation of China (No. 12JJ2002), by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130161130004). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A).
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Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping
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Yu-Cheng Ling, Feng Ning, Yan-hong Zhou, Ke-Qiu Chen ⇑
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Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410082, China
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Article history: Received 14 December 2014 Received in revised form 22 January 2015 Accepted 24 January 2015 Available online xxxx Keywords: Rectifying behavior Negative differential resistance Nonequilibrium Green’s functions
a b s t r a c t We investigate the electronic transport properties of triangular graphene systems with atoms B, N or both of them vertex doped based on non-equilibrium Green’s function approach combined with density functional theory. Interestingly, fine rectifying behavior and obvious negative differential resistance are observed in B–N vertex doped case. The origin of the rectification is that a barrier likes a p–n junction has been formed in B–N vertex doped junction. Moreover, weak interaction is considered by adjusting the distance between the two intermediate atoms. With the increase of the distance between them, the rectifying behavior and negative differential resistance weaken step by step. Our structure constructed by B–N vertex doped triangular graphene to realize fine rectification is constructive and is a promising candidate for the next generation nanoscale device. Ó 2015 Published by Elsevier B.V.
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1. Introduction
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In recent years, more and more microelectronic devices have been investigated through the development of unique properties of matter at the nanoscale, including nanostructures, molecules, and quantum dots [1–3]. Also, lots of interesting physical properties, for example, rectifying behaviors, negative differential resistance, and switching effects, have been investigated in molecular devices [3– 5]. Tailored by lithographic techniques, graphene nanostructures can be made to construct molecular devices [6–12]. And by selective tailoring graphene nanoribbon with high precision [7], fine rectification has been observed in graphene nanoribbon based systems with electron transfer from the vertex to the edge [8]. So far, varieties of molecular rectifiers have been explored and some possible mechanisms are also been suggested [10–16]. The rec-
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⇑ Corresponding author. Tel.: +86 0731 88820375. E-mail address: [email protected] (K.-Q. Chen).
tifying behavior can be realized by edge hydrogenated zigzag-edged graphene nanoribbon heterojunctions [12] or by weak intermolecular interaction on electronic bilayer graphene nanoribbon device [15]. Meanwhile, negative differential resistance has been found in molecular devices with specially designed [16–23]. For instance, by increasing the interaction length [17], by an external electric field [18] or using the high-bias properties of gold–carbon bonds, a family of diodes has been synthesized [21]. Moreover, doping is also the frequently adopted ways to research the new properties of matter [24–31]. The transmission conductance of single wall carbon nanotube and single wall boron nitride nanotube have been investigated [32], at the same time, the growth and interface formation of monolayer grapheme boron nitride heterostructures on ruthenium has been studied to investigate the graphene and hexagonal boron nitride, which offers an attractive system from which to build such 2D heterostructures [33]. Experiment on graphene doping shows that, with the C atoms substituted with B and N atoms respectively, the possibility of making p-type and n-type semiconducting
http://dx.doi.org/10.1016/j.orgel.2015.01.034 1566-1199/Ó 2015 Published by Elsevier B.V.
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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graphene has been improved [32]. Furthermore, negative differential resistance (NDR) behavior has been found with the change of doping position and the electronic transport properties are strongly related to the width of the ribbon and the position of the N dopant [22,23]. Therefore, in the present work, we investigated the electronic and transport properties of triangular graphene with different vertex doped. By first-principles calculations, rectifying behavior and NDR (negative differential resistance) are observed by changing the intermediate atoms and their mutual distance. These results are constructive for the study of molecular devices.
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2. Model and computational details
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The molecular device is illustrated in Fig. 1. The device model is divided into three parts: left electrode, right electrode, and the scattering region. The armchair graphene nanoribbons edges are used for the lead, while in the intermediate scattering region, triangular graphenes are used for the zigzag edges which are hydrogenated. Each electrode has been described as a supercell which contains two repeated carbon unit cells along the transport direction. For central molecule, the two vertex carbon atoms in trigonal graphenes are substituted with boron or nitrogen atom. The initial distance (Do) between two triangular graphene nanoribbons has been optimized. We consider the change of transport properties with the changing distance Dd increasing step by step from 0.1 Å to 0.2 Å and to 0.3 Å. The current has been calculated by using the Landauer formula [34]:
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IðV b Þ ¼
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2e h
Z
TðE; V b Þ f l ðE ll Þ f r ðE lr Þ dE
ð1Þ
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where llðrÞ are electrochemical potentials of the left and right electrodes. The difference of them is ll lr ¼ eV b . In the transmission spectrum, the energy region which contributes to the current has been known as the bias window. The total transmission probability:
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h i TðE; V b Þ ¼ Tr Cl GR Cr GA
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ð2Þ
where GRðAÞ is the retarded (advanced) Green functions of the central region. The geometrical optimization of the model structure and electron transport properties are all performed by using density functional theory (DFT) and non-equilibrium Green’s function (NEGF) method [35,36] and all residual forces on each atom are smaller than 0.05 eV/Å. The core electrons have been described with norm-conserving pseudopotentials and at the same time, the local-density approximation (LDA) has been used to the exchange-correlation potential. The k-point sampling is 1, 1, and 100 in the x, y, z direction, respectively, and the cutoff energy is set to 150 Ry. A single-zeta polarized (SZP) basis set is adopted for electron wave function and the convergence criteria for Hamiltonian and the electron density are 105.
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3. Results and discussions
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At first, all six configuration models show the same characteristics that the currents are nearly non-conducting in the bias range from 1.8 to 1.8 V, as can be seen from the Fig. 2(a). When the bias voltage exceeds 1.8 V, the current for all the models comes into being and the current for the model B–N increases obviously (see Fig. 2(a)). Second, the I–V curves of B–N, C–N, B–C vertex doped configurations show asymmetric behaviors where the current at positive bias is bigger than the corresponding negative bias, thus rectification emerges. The inset in Fig. 2(a) shows the rectification ratio. The rectification ratio is defined as:
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RðVÞ ¼ IðVÞ=jIðVÞj
ð3Þ
where I(V) and I(V) are the current at positive and negative voltages with the same voltage magnitude. Compared with models B–C and C–N, model B–N shows better rectification. The largest rectification ratio of model B–N reaches 87 at 1.84 V while for models C–N and B–C, the largest rectification ratios are 24 and 3 respectively. So the rectifying behaviors with one vertex carbon atom substituted with B atom and the other one with N atom simultaneously own the best effect. This behavior can be made as an electronic rectifier. In addition, the NDR behavior is also observed in model B–N at the bias range from 1.96 V to 2.2 V.
Fig. 1. Structure of a molecular device in our simulations, where B is a boron atom, C is a carbon atom, N is a nitrogen atom, and H is a hydrogen atom. Do + Dd is the distance between two triangular graphene nanoribbons.
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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Fig. 2. (a) The I–V characteristics and rectifying ratio changes with the applied bias for six triangular grapheme with different vertex doped models. (b) The I–V characteristics and rectifying ratio change with the applied bias for model B–N with four changing distance.
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In Fig. 2(b), we give the current–voltage (I–V) characteristics for B–N configuration with the B–N distance increases by Dd = 0.1 Å, 0.2 Å, 0.3 Å, respectively. As can be seen from Fig. 2(b), the rectifying behavior and NDR weaken step by step with the increase of the distance between the atoms B and N. For example, the biggest rectification ratio for models B–N with the Dd = 0.1 Å and Dd = 0.2 Å are 73 and 6 at 1.84 V, respectively, which are lower than that with Dd = 0 Å. To explain the big rectification ratio in the Fig. 2(a), we plot the transmission spectra of the models B–N, C–N, B–C at several voltages, as shown in Fig. 3. In the calculated bias region, the transmission peak at Fermi energy has a big impact on the molecular rectification, which display different shift tendency in the positive and negative bias window. With the increase of the positive bias voltage, the transmission spectra of models B–N and C–N show obviously transmission peak, while the transmission of model B–C is nearly zero in the energy range [2, 2] eV. And with the increase of the negative bias voltage, the transmission
spectra of all three models are nearly depressed. So model B–N and C–N have bigger rectification ratio than model B–C has. At the same time, as we can see in Fig. 3, under the positive bias, the transmission spectra of model B–N is bigger than model C–N at considered biases, which is the reason why the rectification ratio of model B–N is bigger than model C–N. As we known, the position of transmission peak is generally determined by the transmission channels and the delocalization of orbital. The first energy level below the average electrode Fermi energy is described as the highest occupied molecular orbital (HOMO) resonance, whereas that above the average is described as the lowest unoccupied molecular orbital (LUMO) resonance. When the bias voltage is 0 V, the HOMO and LUMO of models B–N, C–N and B–C are located between the two sides of the Fermi energy level and with the increase of positive bias voltage, the HOMO of three models shift to the right of the Fermi energy level as can be seen in Fig. 3. However, the HOMO1 of three models still lies near the Fermi energy
Fig. 3. Transmission spectra and HOMO and LUMO energy levels of models B–C, C–N and B–N at several bias. The HOMO and HOMO1 orbitals are label by blue lines. The energy origin is set to be the Fermi level of the system.
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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level. And with the increase of negative bias voltage, the HOMO1 of the three models shifts to the left of the Fermi energy level. It is noteworthy that the details of HOMO and HOMO1 are different for these three models. With the increase of the bias, the energy gap between the HOMO1 and HOMO for model B–N is smaller than that for model C– N, and that for model C–N is smaller than that for model B– C. For model B–N, these two orbitals together may contribute to a transmission peak, for example, at the bias of 1.84 V. However, the model C–N and B–C have only one molecular orbital (HOMO1) contribute to the transmission. In order to know the two orbitals’ contribution to the transmission, in Table 1, we present the molecular projected selfconsistent Hamiltonian (MPSH) distribution of these two orbitals at the bias voltage +1.84 V and 1.84 V for models B–N, C–N, and B–C, respectively, as an example to illustrastrate the above thought. From the table, we can see that at the bias +1.84 V, the MPSH distribution of orbitals HOMO and HOMO1 for Model B–N is spatially delocalized which results in obvious transmission peak at corresponding energy positions. For model C–N, the MPSH distribution of HOMO1 is also delocalized, but that of HOMO is localized, so the transmission peak is smaller than that for model B–N. For model B–C, both the MPSH distribution of orbitals (HOMO and HOMO1) are localized, so there is nearly no electron transmission. At the negative bias 1.84 V, the MPSH distribution of orbitals HOMO and HOMO1 for the three models are all localized, so the transmission of all of them are depressed. From above, we know why model B–N have the biggest current and rectification ratio at this bias. In addition, for model B–N, at the bias 1.96 V, the alignment of the HOMO1 and HOMO orbitals with the electrodes is good, which gives to a transmission peak. With the bias increasing, for example, at the bias of 2.2 V, the coupling between the two orbitals and the electrodes is weakened, so transmission coefficient is decreased in magnitude, and then NDR happens. So the origin of NDR is the alignment between the HOMO1 and HOMO orbitals of the central molecule and the electrodes [37,38]. To further understand the reason why rectifying behavior appeared, we show the electrostatic potential distribution and electron density for three models at zero bias in
Table. 2. As we know, the electron transfer from the lead to the central region could lead higher electrostatic potential barrier in central region, which will affect the charge redistribution on the molecule and impedes the flow of electrons across junction. It is obviously that the potential profile and electron density is asymmetric (see Table. 2): Boron shows higher electrostatic potential and lower electron density; meanwhile, Nitrogen shows lower electrostatic potential and higher electron density. Our result shows that the region of boron atom is positive charged (holes), just like the p-type semiconductor, and the region of nitrogen atom is negative charge (electrons), just like the n-type semiconductor. A barrier just likes the p–n junction has been formed in our molecules. Corresponding to ptype and n-type forms, the anion and cation have been compensated by charges. As positive bias appears, the carrier tends to the barrier, reducing the space charge, making the barrier thin, then the diffusion current is easy to transport and the avalanche breakdown happens. When the negative bias appears, the carrier moves away from the barrier, increasing the space charge, making the barrier layer thick and the diffusion current reduced. From the above results, it is easy to understand why rectifying behavior will occur in model B–N. In the following, in order to explain why the rectifying behavior and negative differential resistance in Model B– N weaken step by step with the increase of the distance between the atoms B and N, the transmission spectrum (see Fig. 4) at several representative biases and spatial distribution of MPSH of HOMO and HOMO1 at the bias of 1.84 V (see Table 3) for the models B–N with distance Dd = 0 Å, 0.1 Å, and 0.2 Å are presented. At the bias of 1.84 V, the MPSH of Model B–N with the Dd = 0 Å and Dd = 0.1 Å are delocalized which results in obvious transmission peaks at corresponding energy positions (see Table 3). However, the MPSH of HOMO and HOMO1 orbitals for model B–N with Dd = 0.2 Å and Dd = 0.3 Å become more localized, as a consequence, the corresponding transmission peaks are be extremely repressed. So the current become smaller and smaller with the increase of Dd at the bias and so the NDR nearly weaken step by step. And at the negative bias, the current do have the same tendency with the increase of Dd, but the current itself is
Table 1 Spatial distributions of HOMO1 at +1.84 V bias and 1.84 V bias for models B–N, C–N, and B–C, respectively. +1.84V
1.84V MPSH
HOMO1
HOMO
HOMO1
HOMO
B–C
C–N
B–N
Please cite this article in press as: Y.-C. Ling et al., Rectifying behavior and negative differential resistance in triangular graphene p–n junctions induced by vertex B–N mixture doping, Org. Electron. (2015), http://dx.doi.org/10.1016/j.orgel.2015.01.034
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Y.-C. Ling et al. / Organic Electronics xxx (2015) xxx–xxx Table 2 Electrostatic potential distributions and electron density distributions for three models at zero bias. B–C
C–N
B–N
Fig. 4. Transmission spectra, HOMO and LUMO energy levels for model B–N with three changing distance at several bias. The HOMO and HOMO1 orbitals are label by blue lines. The energy origin is set to be the Fermi level of the system.
Table 3 The MPSH distributions of HOMO1 and HOMO for model B–N at bias 1.84 V. B–N
Dd:0 Å
Dd:0.1 Å
Dd:0.2 Å
Dd:0.3 Å
HOMO1
HOMO
yet very small (see Fig. 2(a)), so distance change has little impact on the current at negative biases. So when the increase of the distance between the atoms B and N, the rectification effect is depressed. At last, we make an explanation why the currents are nearly non-conducting in the bias range from 1.8 to 1.8 V for all six configuration models in the Fig. 2. As we know, the armchair graphene nanoribbons are semiconductors with energy gaps decreasing as a function of the increasing ribbon width and the variations in band gaps exhibit three distinct family behaviors: D3pþ1 > D3p > D3pþ2 for all p’s where p is a integral number and N = 3p + 1, 3p or 3p + 2 is width of graphene nanoribbons. The band gap of 7-armchair graphene nanoribbon is about 1.73 eV. This rather large band gap results in the nearly depressed current in the bias range from 1.8 to 1.8 V for the six configuration models [39].
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4. Conclusions
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The electronic transport properties of triangular graphene systems with atoms B, N or both of them vertex doped have been investigated by non-equilibrium Green’s function approach. Fine rectifying behavior and obvious NDR have been found in B–N vertex doped case. Moreover, weak interaction effect on the rectifying behavior and NDR was considered by adjusting the distance between the two intermediate atoms. With the increase of the distance between them, the rectification and negative differential resistance weakened step by step. The origin of the rectification was analyzed detailed. Structure made of B–N vertex doped triangular graphene is constructive to realize fine rectification and is a promising candidate for the next generation nanoscale device.
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Acknowledgements
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This work was supported by the National Natural Science Foundation of China (Nos. 11274105 and 91227125), by the National Basic Research Program of China (Nos. 2012CB932703 and 2011CB606405), by Hunan Provincial Natural Science Foundation of China (No. 12JJ2002), by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130161130004). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A).
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