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Armchair α-graphyne nanoribbons as negative differential resistance devices: Induced by nitrogen doping
Organic Electronics xxx (xxxx) xxx–xxx
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Armchair α-graphyne nanoribbons as negative differential resistance devices: Induced by nitrogen doping Amin Mohammadia, Esmaeil Zaminpaymab,∗ a b
Department of Electrical, Biomedical, and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Iran Department of Physics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Armchair α-graphyne nanoribbon Nitrogen Doping Electronic transport properties Negative differential resistance
Using non-equilibrium Green's functions (NEGF) in combination with tight-binding (TB) model, the electronic transport properties of pristine and nitrogen (N) doped armchair α-graphyne nanoribbons (A-α-GYNRs) are studied under finite bias. Initially, we have calculated the total energy in order to find the most stable place for N atom. Then we have investigated the effect of width (W) and length (L) of the ribbon and also the position (edge and center of the ribbon) and concentration of doping on the electronic transport properties. Our results reveal that, doping changes the semiconducting behavior of 3n and 3n+1 A-α-GYNRs to semi metallic. Moreover, it is observed that the electronic transport properties are more affected by central doping rather than the edge doping. Interestingly, both edge and central doped ribbons show negative differential resistance (NDR) in all widths. Our results show that doping concentration and the NDR are inversely proportional to each other. We have also found that, as the length of the central region of the device gets longer, the NDR reaches up to 159. Transmission spectrum, bandstructure of the electrodes, Bloch wave functions and density of states (DOS) are analyzed subsequently to more elucidate the electronic transport properties. Our findings could be used to develop the nano-scale NDR devices.
1. Introduction Two-dimensional (2D) carbon based nano-materials have attracted tremendous attention due to their remarkable electronic properties. Carbon atoms can form different hybridized states (sp, sp2 and sp3) and thus an inexhaustible reservoir of high-performance synthetic carbon allotropes (nanotubes, graphene, graphdiyne, etc.) were prepared or predicted theoretically [1–4]. Graphyne (GY) which has the same symmetry as graphene is predicted by Baughman et al. [5]. GY is a family of carbon allotropes which consists both sp and sp2 hybridizations, modified by inserting a carbon triple bond (–C^C–) into the C–C bonds of graphene [6]. Although, in the case of graphyne just some finite-size flake building blocks have been synthesized [7] and single sheet of graphyne has still not been available, in 2010 graphdiyne (which is a graphyne substructure) was successfully synthesized on copper substrate and a semiconducting behavior was reported [8]. This experimental progress shows that GY will hopefully be obtained in future. The presence of acetylene linkages introduces a rich variety of properties for GY, including extreme hardness, high thermal resistance, good chemical stability, large surface area, high electrical conductivity, etc [9–14]. According to sp and sp2
∗
hybridization proportions and their arrangement in the lattice structure, α-graphyne, β-graphyne and γ-graphyne are formed [15]. α-graphyne and β-graphyne exhibit Dirac cone band structures, however, the γ-graphyne is predicted to be semiconducting with a direct band gap at the M point [16]. Due to its graphene like structure and symmetry, we have chosen α-graphyne for further studies. Alike graphene, cutting α-graphyne into quasi 1D nanoribbons (αGYNRs), is a way to adjust its band gap (Bg) [17]. According to their edge pattern, α-GYNRs divide into two main categories: 1) A-α-GYNRs and 2) zigzag (Z-α-GYNRs) [18]. All of A-αGYNRs are nonmagnetic, and Bg oscillates with a period of three when the ribbon width increases, while the Z-α-GYNRs are zero gap and have a stable antiferromagnetic configuration [19,20]. Introducing impurities is another way to adjust the electronic properties of carbon nano materials. Although experimental and theoretical studies have been conducted on doped α-GYNRs, but they mostly focus on doped Z-α-GYNRs and little information about doped A-αGYNRs has been reported [19–24]. Mingjun Li et al. [19]. have studied Z-α-GYNRs passivated with 3d transition-metal atoms at one of the ribbon edge. They found half-metallic behavior in response to the Fe-, Co- and Ni-doping at the edge of Z-α-GYNRs and also a large spin
Corresponding author. Tel.: +982833665275. E-mail addresses: [email protected], [email protected] (E. Zaminpayma).
https://doi.org/10.1016/j.orgel.2018.06.012 Received 24 March 2018; Received in revised form 16 May 2018; Accepted 9 June 2018 1566-1199/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Mohammadi, A., Organic Electronics (2018), https://doi.org/10.1016/j.orgel.2018.06.012
Organic Electronics xxx (xxxx) xxx–xxx
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Fig. 1. The optimized structure of devices based on A-α-GYNR. (a) Pristine (P) model, (b) Edge doped (E) model, (c) central doped model. In (a–c) L = 4 UC while W changes from 6 to 8. The doping atoms are nitrogen and the concentration of doping is about 1.92%. The vacuum pad along x and y directions are 25 and 65 Å, respectively.
Fig. 2. Schematic representation of (a) doping sites in a unit cell, (b, c) edge doped and (d, f) center doped A-α-GYNR unit cell. The most stable place for nitrogen atom is site-1 (sp) at the edge, and site-1ʹ (sp) in the center of the ribbon.
Table 1 Total energy of A-α-GYNR UCs with central or edge N doping at site −1, −2, −1ʹ and -2ʹ. N position
Total Energy (eV) Edge
Center
W
Site-1 (sp)
Site-2 (sp2)
Site-1ʹ (sp)
Site-2ʹ (sp2)
6 7 8
−2090.399 −2459.940 −2829.471
−2089.456 −2458.989 −2828.518
−2090.285 −2459.888 −2829.408
−2088.808 −2458.404 −2827.923
Xing Zhai et al. [22] have observed that magnetoresistance can be manipulated in a wide range by the dopants on the edges of Z-α-GYNRs. Sunkyung Kim et al. [6]. have seen that the structural, electronic, and magnetic properties of graphyne were changed according to the dopant
polarization on currents. Dan Zhang et al. [21]. have investigated the stability and spin-resolved electronic transport properties of Z-α-GYNRs with symmetric and asymmetric edge fluorinations. They have shown that edge fluorination can enhance the stability of Z-α-GYNRs. Ming2
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Table 2 The measured bond lengths of pristine and N-doped A-α-GYNRs after optimization.
effect is observed in current-voltage characteristics (I-V) at low bias voltages which could be practical in molecular devices. In the following, we have explored the effect of the width and length of the ribbon and doping concentration on this phenomenon. The underlying physics are studied in details by calculating the electrode band structures, transmission spectrums, Bloch wave functions and DOS. As you know, one of the most fascinating quantum electronic transport phenomena is NDR and it can be used as the basis in various device applications, such as high-frequency oscillators, memories, analog-to-digital converters, logic gates, etc. [25–27]. Although researchers have previously been able to create a negative resistance phenomenon in graphyne-based structures, their works are totally different from our method [28–30]. This paper is organized as the follows: In Section 2, the model and the simulation method are presented. In section 3 the results are discussed. At last, a summary of our results is given in Section 4. 2. Model and simulations Fig. 1 shows the optimized geometry of all devices. The systems are divided into three main regions: left electrode (LE), right electrode (RE) and the central scattering region (SR). Each electrode is described by a carbon unit cell (UC). The doping atoms are nitrogen. Initially, we place the doping atoms in the edge of the ribbon [see Fig. 1(b)] and then we place them in the central part of the width [see Fig. 1(c)] which are named as E and C models, respectively. Perfect structure is called P model in the following. W of the central scattering region changes while L is fixed (L = 4). Using SCC-DFTB combined with NEGF formalism, the electronic transport properties are studied. This method was used for many nano devices [31–34]. All the calculations are performed in DFTB + package with mio parameters set. According to Landauer–Büttiker formula: 2e μ I = h ∫μ R T (E , Vb)[f (E , μL ) − f (E , μR )] dE L Where e is the charge of electron and h is the Planck's constant.
Fig. 3. (a) The band gap of A-α-GYNR as a function of width of the ribbon, (b) the band structure of 6-, 7- and 8-A-α-GYNRs.
μR = Ef + e
atom site of doping and vacancy. Shengliang Zhang et al. [23] enhanced electrochemical properties of graphdiyne by introducing nitrogen atoms. Afshan Mohajeri et al. [24] have adjusted the electronic structure and optical properties of graphdiyne with N and S doping atoms. Additionally, reviewing the past literature, studies on α-GYNRs based devices, especially under finite bias, are extremely limited. Here in this paper, initially we investigate the effect of width on the electronic transport properties of perfect and nitrogen doped A-αGYNRs. It should be mentioned that the most stable place for nitrogen atom is determined by calculating the total energy. Then we study the effect of doping position (center or edge of the ribbon) on transport properties of presented A-α-GYNR based devices. Interestingly, an NDR
( ) , and μ V 2
L
= Ef − e
( ) are the chemical potentials of V 2
the right and left electrodes, Vb is the applied bias voltage across the electrodes, T (E , Vb) represents the transmission coefficient, and f (E , μ) is the Fermi–Dirac distribution. A k-point mesh of 1 × 1 × 100 within the Monkhorst–Pack scheme is used to sample the Brillouin zone of the electrodes. The cut off energy is set to 200 Ry. Geometry optimization is performed until the force becomes less than 0.05 eV/Å. The convergence criteria for Hamiltonian and the electron density is 10−5. The electron temperature is set to 300 K in transport calculations. The vacuum pad along x and y directions are 25 and 65 Å, respectively. The applied bias voltage is increased from 0 V to 1 V in steps of 0.1 V.
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Fig. 4. The current-voltage characteristics for P, E and C models at the bias range from 0 V to 1 V in steps of 0.1 V. (a) W = 6, (b) W = 7 and (c) W = 8.
have medium, large and small band gaps, respectively. Our results are in good agreement with those of [17]. For instance, the band structure of 6-, 7- and 8-A-α-GYNRs are shown in Fig. 3(b). The band gaps of 6-, 7- and 8-A-α-GYNRs are 0.43, 0.47 and 0.03 eV, respectively. Fig. 4 depicts the calculated I-V characteristics for all discussed molecular configurations (i.e. P, E and C models at the most stable sites) at the bias range from 0 V to 1 V in steps of 0.1 V. It is observed that, perfect 6- and 7-A-α-GYNRs have a threshold voltage (Vth) of about 0.43 and 0.47 V, respectively. In the other words, they have a semiconducting behavior [see Fig. 3(b)]. However, the I-V curve of perfect 8-A-α-GYNR have no Vth and it passes current as the bias voltage is applied to the device and shows a metallic behavior [see Fig. 3(b)]. After doping, in all widths, ribbons show a semi metallic behavior and no Vth is observed in the I-V characteristics. In the case of semiconductor A-α-GYNR based devices (W = 6 and 7), C models pass more current in a wide range of applied bias voltage. However metallic A-α-GYNR based device shows different characteristics. From Fig. 4(c) it is observed that up to 0.3 V, C model passes more current but after 0.3 V perfect device overtakes both doped models. As you see, I-V diagrams are nearly linear in lower bias voltages, but by increasing the applied bias voltage to C and E models, the linear behavior of I-V disappears and NDR phenomenon comes into sight. Peak to valley ratios and the impurity concentration are listed in Table 3. The best NDR effect refers to 7-C (W = 3n+1) model. Generally, it is found that the I-V characteristics of the presented models strongly depend on the width of the ribbons, doping and the position of them. According to the Landauer–Büttiker formula, current is proportional
Table 3 The NDR of 6-C/E, 7-C/E, 8-C/E models. The best NDR refers to 7-C model. W
6
7
8
Model
C
E
C
E
C
E
NDR
2
8.2
67
11
1.2
1.1
3. Results and discussions At first we should find the most stable place for nitrogen atoms. For this purpose we consider different sites [see Fig. 2(a)] for both central and edge impurity atoms and the total energy is calculated for each case. The calculated total energies for 6-, 7- and 8-A-α-GYNRs with central or edge dopants are listed in Table 1. As you know the most stable place is where the total energy gets minimum. The most stable place, in which the nitrogen atom prefers to be placed, is site-1 (sp) at the edge [see Fig. 2(b)] and site-1ʹ (sp) in the center [see Fig. 2(d)] of the ribbon. From Table 2 it is found that, when A-α-GYNRs get doped by nitrogen atom, a small change in adjoining bond lengths is observed. As you see, by doping A-α-GYNRs, bond lengths get smaller in optimized structures. Fig. 3(a) shows the Bg of A-α-GYNRs as a function of width of the ribbon (W = 3 to 11). As in armchair graphene nanoribbons (A-GNRs), increasing the width of A-α-GYNRs results in smaller Bg. Moreover, alike A-GNRs the Bg of A-α-GYNRs could be classified into three different groups: W = 3n, 3n + 1, 3n + 2 ribbons (n is a positive integer)
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Fig. 5. Transmission spectra and band structures of both left and right electrodes for (a–c) 7-P model, (b) 7-E model and (c) 7-C model. The Fermi level is set to be zero. Dashed lines represent the bias window.
V > 0.47 V, the conduction band of the left electrode gradually overlaps with the valance band of the right electrode and transmission occurs [see Fig. 5(c)]. Comparing the band structures of doped [see Fig. 5(d) and (g)] and perfect electrodes [see Fig. 5(a)], it is observed that an impurity subband, labeled as N, appears in the band structure of the doped electrodes. As you see this subband passes through the fermi level (Ef) and is the nearest subband to the Ef. On the other hand, π and π∗ subbands are located far away from Ef and thus N subband is the one which is responsible for transmission. At peaks, the N subbands of the right and left electrodes overlap with each other, but in valleys there is no
to the integral area of the transmission spectrum in the bias window (BW). So in order to understand the mechanism of the observed NDR behavior and its doping-position-dependence, we have illustrated the transmission spectrum of 7-P, 7-C and 7-E models (this can be done for W = 6 and 8 as well), at different bias voltages (see Fig. 5). Fig. 5(a) shows the bandstructure of pristine 7-A-GYNR. As you see in the bias window, 7-A-GYNR shows a semiconducting behavior and it passes no current in 0.47 eV of the bias window (like what emerged from Figs. 3 and 4(c), Bg = 0.47 eV). As you know, when the bias is applied to the electrodes, the chemical potential of the right and left electrodes go up and down, respectively and which is why at
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To further explain and elucidate the NDR effect, we have presented the transmission spectrum combined with DOS diagram for the central scattering region of 7-E (at 0, 0.2 and 0.5 V) and 7-C (at 0, 0.3 and 0.6 V) models [see Fig. (7)]. The non-zero amount of both T(E) and DOS around the fermi level at V = 0 V, shows the metallic behavior of 7-C and 7-E models. We know that where the peaks in DOS meet the peaks in the transmission spectrum, a resonant transmission is induced, but where T(E) is zero and DOS in non-zero, anti-resonant takes place. In order to understand the effect of doping concentration on the electronic transport properties, we consider four different doping concentrations for 7-C model which has the best NDR: 0%, 1.9%, 3.8% and 5.8% (see Fig. 8), and then the I-V characteristics is calculated for each case (see Fig. 9). In general, increasing doping concentration results in higher currents. Furthermore, it is observed that, a perfect device does not show any NDR effect, but all doped systems do. As you see, doping concentration and the peak to valley ratio are conversely proportional to each other. In the other words, increasing doping concentration makes the NDR smaller. The peak to valley ratio for 1.9%, 3.8% and 5.8% is 67, 1.88 and 1.13, respectively. It is clear that, as the doping concentration increases, the VValley moves down to the lower bias range. It is known that, length of the ribbon is another element which affects the electronic transport properties of the device. In order to more clarify this issue, we study the I-V characteristics of 7-C model with three different lengths, i.e. L = 3 UC, 4 UC and 5 UC (see Fig. 10). It is observed that at V < 0.6 V, length change does not affect the current remarkably but at V ≥ 0.6 V, as the length of the central region increases, the current decreases. On the other hand, the peak remains nearly fixed, while the valley of the curve shifts to the lower part and consequently the peak to valley ratio gets larger. The NDR value for 7-C model with L = 3 UC, 4 UC and 5 UC is listed in Table 4. Results reveal that, the best NDR refers to 7-C model with L = 5 UC.
Fig. 6. The Bloch wave functions of N and π∗ subbands of 7-E and 7-C models.
overlapped region between them. From Fig. 5(d) and (g) it is found that at V = 0 V, 7-E model has a semi metallic behavior. Fig. 5(e) and (f) show the transmission spectrum and band structures of the left and right electrodes of the 7-E model, at voltages in which the peak and valley of the NDR occurs. At V = 0.2 V, although the overlap region between the N subbands of the left and right electrodes decreases, but there is a non-zero T(E) in whole BW and the peak of the NDR appears. As the bias voltage increases to 0.5 V, the overlap area between the N subbands of the right and left electrodes becomes smaller and as a result the transmission in the BW decreases and the valley of the NDR appears. The same happens for 7-C model but at different voltages. The peak [see Fig. 5(h)] and valley [see Fig. 5(i)] appear at 0.3 V and 0.6 V, respectively. Comparing 7-E and 7-C models it is found that, 7-C has a larger NDR since its integral area of the transmission in the BW at V = VValley is nearly zero (The underlying physics will be more discussed in the following). As it is shown in Fig. 5(f), in the overlap region of the N and π∗ subbands, small peaks of transmission come into sight, but in Fig. 5(i), although N and π∗ subbands overlap with each other, the transmission is nearly zero. Here we show the Bloch wave functions of N and π∗ subbands of 7-E and 7-C models to more clarify the reason of this abnormal behavior (see Fig. 6). As you see in Fig. 6(a) and (b), the Bloch wave functions of N and π∗ subbands do not have a definite parity under the xz midplane mirror operation. As a result, there exists a weak coupling between these two subbands which results in small peaks of transmission in the bias window [see Fig. 5(f)]. On the contrary, the N and π∗ subbands of 7-C have even and odd parities, respectively, and consequently the tunneling between these two subbands is nearly forbidden [see Fig. 5(i)].
4. Conclusion We studied the electronic transport properties of pristine and N doped A-α-GYNRs under 0–1 V. At first we calculated the total energy to find the most stable place for nitrogen atoms. Furthermore we have compared the bond lengths of optimized prefect and doped structures. Fortunately a small change in adjoining bond lengths is observed. We found that, doping can close the band gap of semiconducting A-αGYNRs and define an NDR effect in the I-V characteristics of both C and E models with all widths. It should be mentioned that, among W = 6-C/E, 7-C/E and 8-C/E models, 7-C have the best NDR which is about 67. Comparing edge and central doped structures, we observed that the effect of central doping on the electronic transport properties is more than the edge doping. It stems from the parity of the subbands which contribute in transmission. We have also studied the effect of doping concentration and observed that doping concentration and the NDR are inversely proportional to each other. At last we studied the length effect on the I-V characteristics of 7-C model. Results revealed that, the longer the central region is, the larger NDR appears. 7-C model with L = 5 UC has the best NDR which is about 159. Our findings could be beneficial for designing and developing the nano scale NDR devices.
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Fig. 7. The transmission spectrum and DOS for 7-E at (a) V = 0 V, (b) V = 0.2 V, (c) V = 0.5 V, and for 7-C at (d) V = 0 V, (e) V = 0.3 V, (f) V = 0.6 V.
Fig. 8. 7-C model with four various doping concentrations: 0%, 1.9%, 3.8% and 5.8%.
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Fig. 9. The calculated I-V characteristics for 7-C model with four different doping concentrations: 0%, 1.9%, 3.8% and 5.8%.
Fig. 10. (a) The optimized structure of 7-C model in which W=7 (is fixed) while L changes from 3 UC to 5 UC. (b) The current-voltage characteristics of 7C model with L = 3 UC, 4 UC and 5 UC, at the bias range from 0 V to 1 V in steps of 0.1 V. Table 4 I Peak, I Valley and NDR of 7-C model with L = 3 UC, 4 UC and 5 UC. L
I
3 4 5
18.566 18.742 18.647
Peak
(μA)
I
Valley
0.527 0.280 0.117
(μA)
NDR 35 67 159
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Contents lists available at ScienceDirect
Organic Electronics journal homepage: www.elsevier.com/locate/orgel
Armchair α-graphyne nanoribbons as negative differential resistance devices: Induced by nitrogen doping Amin Mohammadia, Esmaeil Zaminpaymab,∗ a b
Department of Electrical, Biomedical, and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Iran Department of Physics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Armchair α-graphyne nanoribbon Nitrogen Doping Electronic transport properties Negative differential resistance
Using non-equilibrium Green's functions (NEGF) in combination with tight-binding (TB) model, the electronic transport properties of pristine and nitrogen (N) doped armchair α-graphyne nanoribbons (A-α-GYNRs) are studied under finite bias. Initially, we have calculated the total energy in order to find the most stable place for N atom. Then we have investigated the effect of width (W) and length (L) of the ribbon and also the position (edge and center of the ribbon) and concentration of doping on the electronic transport properties. Our results reveal that, doping changes the semiconducting behavior of 3n and 3n+1 A-α-GYNRs to semi metallic. Moreover, it is observed that the electronic transport properties are more affected by central doping rather than the edge doping. Interestingly, both edge and central doped ribbons show negative differential resistance (NDR) in all widths. Our results show that doping concentration and the NDR are inversely proportional to each other. We have also found that, as the length of the central region of the device gets longer, the NDR reaches up to 159. Transmission spectrum, bandstructure of the electrodes, Bloch wave functions and density of states (DOS) are analyzed subsequently to more elucidate the electronic transport properties. Our findings could be used to develop the nano-scale NDR devices.
1. Introduction Two-dimensional (2D) carbon based nano-materials have attracted tremendous attention due to their remarkable electronic properties. Carbon atoms can form different hybridized states (sp, sp2 and sp3) and thus an inexhaustible reservoir of high-performance synthetic carbon allotropes (nanotubes, graphene, graphdiyne, etc.) were prepared or predicted theoretically [1–4]. Graphyne (GY) which has the same symmetry as graphene is predicted by Baughman et al. [5]. GY is a family of carbon allotropes which consists both sp and sp2 hybridizations, modified by inserting a carbon triple bond (–C^C–) into the C–C bonds of graphene [6]. Although, in the case of graphyne just some finite-size flake building blocks have been synthesized [7] and single sheet of graphyne has still not been available, in 2010 graphdiyne (which is a graphyne substructure) was successfully synthesized on copper substrate and a semiconducting behavior was reported [8]. This experimental progress shows that GY will hopefully be obtained in future. The presence of acetylene linkages introduces a rich variety of properties for GY, including extreme hardness, high thermal resistance, good chemical stability, large surface area, high electrical conductivity, etc [9–14]. According to sp and sp2
∗
hybridization proportions and their arrangement in the lattice structure, α-graphyne, β-graphyne and γ-graphyne are formed [15]. α-graphyne and β-graphyne exhibit Dirac cone band structures, however, the γ-graphyne is predicted to be semiconducting with a direct band gap at the M point [16]. Due to its graphene like structure and symmetry, we have chosen α-graphyne for further studies. Alike graphene, cutting α-graphyne into quasi 1D nanoribbons (αGYNRs), is a way to adjust its band gap (Bg) [17]. According to their edge pattern, α-GYNRs divide into two main categories: 1) A-α-GYNRs and 2) zigzag (Z-α-GYNRs) [18]. All of A-αGYNRs are nonmagnetic, and Bg oscillates with a period of three when the ribbon width increases, while the Z-α-GYNRs are zero gap and have a stable antiferromagnetic configuration [19,20]. Introducing impurities is another way to adjust the electronic properties of carbon nano materials. Although experimental and theoretical studies have been conducted on doped α-GYNRs, but they mostly focus on doped Z-α-GYNRs and little information about doped A-αGYNRs has been reported [19–24]. Mingjun Li et al. [19]. have studied Z-α-GYNRs passivated with 3d transition-metal atoms at one of the ribbon edge. They found half-metallic behavior in response to the Fe-, Co- and Ni-doping at the edge of Z-α-GYNRs and also a large spin
Corresponding author. Tel.: +982833665275. E-mail addresses: [email protected], [email protected] (E. Zaminpayma).
https://doi.org/10.1016/j.orgel.2018.06.012 Received 24 March 2018; Received in revised form 16 May 2018; Accepted 9 June 2018 1566-1199/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Mohammadi, A., Organic Electronics (2018), https://doi.org/10.1016/j.orgel.2018.06.012
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Fig. 1. The optimized structure of devices based on A-α-GYNR. (a) Pristine (P) model, (b) Edge doped (E) model, (c) central doped model. In (a–c) L = 4 UC while W changes from 6 to 8. The doping atoms are nitrogen and the concentration of doping is about 1.92%. The vacuum pad along x and y directions are 25 and 65 Å, respectively.
Fig. 2. Schematic representation of (a) doping sites in a unit cell, (b, c) edge doped and (d, f) center doped A-α-GYNR unit cell. The most stable place for nitrogen atom is site-1 (sp) at the edge, and site-1ʹ (sp) in the center of the ribbon.
Table 1 Total energy of A-α-GYNR UCs with central or edge N doping at site −1, −2, −1ʹ and -2ʹ. N position
Total Energy (eV) Edge
Center
W
Site-1 (sp)
Site-2 (sp2)
Site-1ʹ (sp)
Site-2ʹ (sp2)
6 7 8
−2090.399 −2459.940 −2829.471
−2089.456 −2458.989 −2828.518
−2090.285 −2459.888 −2829.408
−2088.808 −2458.404 −2827.923
Xing Zhai et al. [22] have observed that magnetoresistance can be manipulated in a wide range by the dopants on the edges of Z-α-GYNRs. Sunkyung Kim et al. [6]. have seen that the structural, electronic, and magnetic properties of graphyne were changed according to the dopant
polarization on currents. Dan Zhang et al. [21]. have investigated the stability and spin-resolved electronic transport properties of Z-α-GYNRs with symmetric and asymmetric edge fluorinations. They have shown that edge fluorination can enhance the stability of Z-α-GYNRs. Ming2
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Table 2 The measured bond lengths of pristine and N-doped A-α-GYNRs after optimization.
effect is observed in current-voltage characteristics (I-V) at low bias voltages which could be practical in molecular devices. In the following, we have explored the effect of the width and length of the ribbon and doping concentration on this phenomenon. The underlying physics are studied in details by calculating the electrode band structures, transmission spectrums, Bloch wave functions and DOS. As you know, one of the most fascinating quantum electronic transport phenomena is NDR and it can be used as the basis in various device applications, such as high-frequency oscillators, memories, analog-to-digital converters, logic gates, etc. [25–27]. Although researchers have previously been able to create a negative resistance phenomenon in graphyne-based structures, their works are totally different from our method [28–30]. This paper is organized as the follows: In Section 2, the model and the simulation method are presented. In section 3 the results are discussed. At last, a summary of our results is given in Section 4. 2. Model and simulations Fig. 1 shows the optimized geometry of all devices. The systems are divided into three main regions: left electrode (LE), right electrode (RE) and the central scattering region (SR). Each electrode is described by a carbon unit cell (UC). The doping atoms are nitrogen. Initially, we place the doping atoms in the edge of the ribbon [see Fig. 1(b)] and then we place them in the central part of the width [see Fig. 1(c)] which are named as E and C models, respectively. Perfect structure is called P model in the following. W of the central scattering region changes while L is fixed (L = 4). Using SCC-DFTB combined with NEGF formalism, the electronic transport properties are studied. This method was used for many nano devices [31–34]. All the calculations are performed in DFTB + package with mio parameters set. According to Landauer–Büttiker formula: 2e μ I = h ∫μ R T (E , Vb)[f (E , μL ) − f (E , μR )] dE L Where e is the charge of electron and h is the Planck's constant.
Fig. 3. (a) The band gap of A-α-GYNR as a function of width of the ribbon, (b) the band structure of 6-, 7- and 8-A-α-GYNRs.
μR = Ef + e
atom site of doping and vacancy. Shengliang Zhang et al. [23] enhanced electrochemical properties of graphdiyne by introducing nitrogen atoms. Afshan Mohajeri et al. [24] have adjusted the electronic structure and optical properties of graphdiyne with N and S doping atoms. Additionally, reviewing the past literature, studies on α-GYNRs based devices, especially under finite bias, are extremely limited. Here in this paper, initially we investigate the effect of width on the electronic transport properties of perfect and nitrogen doped A-αGYNRs. It should be mentioned that the most stable place for nitrogen atom is determined by calculating the total energy. Then we study the effect of doping position (center or edge of the ribbon) on transport properties of presented A-α-GYNR based devices. Interestingly, an NDR
( ) , and μ V 2
L
= Ef − e
( ) are the chemical potentials of V 2
the right and left electrodes, Vb is the applied bias voltage across the electrodes, T (E , Vb) represents the transmission coefficient, and f (E , μ) is the Fermi–Dirac distribution. A k-point mesh of 1 × 1 × 100 within the Monkhorst–Pack scheme is used to sample the Brillouin zone of the electrodes. The cut off energy is set to 200 Ry. Geometry optimization is performed until the force becomes less than 0.05 eV/Å. The convergence criteria for Hamiltonian and the electron density is 10−5. The electron temperature is set to 300 K in transport calculations. The vacuum pad along x and y directions are 25 and 65 Å, respectively. The applied bias voltage is increased from 0 V to 1 V in steps of 0.1 V.
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Fig. 4. The current-voltage characteristics for P, E and C models at the bias range from 0 V to 1 V in steps of 0.1 V. (a) W = 6, (b) W = 7 and (c) W = 8.
have medium, large and small band gaps, respectively. Our results are in good agreement with those of [17]. For instance, the band structure of 6-, 7- and 8-A-α-GYNRs are shown in Fig. 3(b). The band gaps of 6-, 7- and 8-A-α-GYNRs are 0.43, 0.47 and 0.03 eV, respectively. Fig. 4 depicts the calculated I-V characteristics for all discussed molecular configurations (i.e. P, E and C models at the most stable sites) at the bias range from 0 V to 1 V in steps of 0.1 V. It is observed that, perfect 6- and 7-A-α-GYNRs have a threshold voltage (Vth) of about 0.43 and 0.47 V, respectively. In the other words, they have a semiconducting behavior [see Fig. 3(b)]. However, the I-V curve of perfect 8-A-α-GYNR have no Vth and it passes current as the bias voltage is applied to the device and shows a metallic behavior [see Fig. 3(b)]. After doping, in all widths, ribbons show a semi metallic behavior and no Vth is observed in the I-V characteristics. In the case of semiconductor A-α-GYNR based devices (W = 6 and 7), C models pass more current in a wide range of applied bias voltage. However metallic A-α-GYNR based device shows different characteristics. From Fig. 4(c) it is observed that up to 0.3 V, C model passes more current but after 0.3 V perfect device overtakes both doped models. As you see, I-V diagrams are nearly linear in lower bias voltages, but by increasing the applied bias voltage to C and E models, the linear behavior of I-V disappears and NDR phenomenon comes into sight. Peak to valley ratios and the impurity concentration are listed in Table 3. The best NDR effect refers to 7-C (W = 3n+1) model. Generally, it is found that the I-V characteristics of the presented models strongly depend on the width of the ribbons, doping and the position of them. According to the Landauer–Büttiker formula, current is proportional
Table 3 The NDR of 6-C/E, 7-C/E, 8-C/E models. The best NDR refers to 7-C model. W
6
7
8
Model
C
E
C
E
C
E
NDR
2
8.2
67
11
1.2
1.1
3. Results and discussions At first we should find the most stable place for nitrogen atoms. For this purpose we consider different sites [see Fig. 2(a)] for both central and edge impurity atoms and the total energy is calculated for each case. The calculated total energies for 6-, 7- and 8-A-α-GYNRs with central or edge dopants are listed in Table 1. As you know the most stable place is where the total energy gets minimum. The most stable place, in which the nitrogen atom prefers to be placed, is site-1 (sp) at the edge [see Fig. 2(b)] and site-1ʹ (sp) in the center [see Fig. 2(d)] of the ribbon. From Table 2 it is found that, when A-α-GYNRs get doped by nitrogen atom, a small change in adjoining bond lengths is observed. As you see, by doping A-α-GYNRs, bond lengths get smaller in optimized structures. Fig. 3(a) shows the Bg of A-α-GYNRs as a function of width of the ribbon (W = 3 to 11). As in armchair graphene nanoribbons (A-GNRs), increasing the width of A-α-GYNRs results in smaller Bg. Moreover, alike A-GNRs the Bg of A-α-GYNRs could be classified into three different groups: W = 3n, 3n + 1, 3n + 2 ribbons (n is a positive integer)
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Fig. 5. Transmission spectra and band structures of both left and right electrodes for (a–c) 7-P model, (b) 7-E model and (c) 7-C model. The Fermi level is set to be zero. Dashed lines represent the bias window.
V > 0.47 V, the conduction band of the left electrode gradually overlaps with the valance band of the right electrode and transmission occurs [see Fig. 5(c)]. Comparing the band structures of doped [see Fig. 5(d) and (g)] and perfect electrodes [see Fig. 5(a)], it is observed that an impurity subband, labeled as N, appears in the band structure of the doped electrodes. As you see this subband passes through the fermi level (Ef) and is the nearest subband to the Ef. On the other hand, π and π∗ subbands are located far away from Ef and thus N subband is the one which is responsible for transmission. At peaks, the N subbands of the right and left electrodes overlap with each other, but in valleys there is no
to the integral area of the transmission spectrum in the bias window (BW). So in order to understand the mechanism of the observed NDR behavior and its doping-position-dependence, we have illustrated the transmission spectrum of 7-P, 7-C and 7-E models (this can be done for W = 6 and 8 as well), at different bias voltages (see Fig. 5). Fig. 5(a) shows the bandstructure of pristine 7-A-GYNR. As you see in the bias window, 7-A-GYNR shows a semiconducting behavior and it passes no current in 0.47 eV of the bias window (like what emerged from Figs. 3 and 4(c), Bg = 0.47 eV). As you know, when the bias is applied to the electrodes, the chemical potential of the right and left electrodes go up and down, respectively and which is why at
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To further explain and elucidate the NDR effect, we have presented the transmission spectrum combined with DOS diagram for the central scattering region of 7-E (at 0, 0.2 and 0.5 V) and 7-C (at 0, 0.3 and 0.6 V) models [see Fig. (7)]. The non-zero amount of both T(E) and DOS around the fermi level at V = 0 V, shows the metallic behavior of 7-C and 7-E models. We know that where the peaks in DOS meet the peaks in the transmission spectrum, a resonant transmission is induced, but where T(E) is zero and DOS in non-zero, anti-resonant takes place. In order to understand the effect of doping concentration on the electronic transport properties, we consider four different doping concentrations for 7-C model which has the best NDR: 0%, 1.9%, 3.8% and 5.8% (see Fig. 8), and then the I-V characteristics is calculated for each case (see Fig. 9). In general, increasing doping concentration results in higher currents. Furthermore, it is observed that, a perfect device does not show any NDR effect, but all doped systems do. As you see, doping concentration and the peak to valley ratio are conversely proportional to each other. In the other words, increasing doping concentration makes the NDR smaller. The peak to valley ratio for 1.9%, 3.8% and 5.8% is 67, 1.88 and 1.13, respectively. It is clear that, as the doping concentration increases, the VValley moves down to the lower bias range. It is known that, length of the ribbon is another element which affects the electronic transport properties of the device. In order to more clarify this issue, we study the I-V characteristics of 7-C model with three different lengths, i.e. L = 3 UC, 4 UC and 5 UC (see Fig. 10). It is observed that at V < 0.6 V, length change does not affect the current remarkably but at V ≥ 0.6 V, as the length of the central region increases, the current decreases. On the other hand, the peak remains nearly fixed, while the valley of the curve shifts to the lower part and consequently the peak to valley ratio gets larger. The NDR value for 7-C model with L = 3 UC, 4 UC and 5 UC is listed in Table 4. Results reveal that, the best NDR refers to 7-C model with L = 5 UC.
Fig. 6. The Bloch wave functions of N and π∗ subbands of 7-E and 7-C models.
overlapped region between them. From Fig. 5(d) and (g) it is found that at V = 0 V, 7-E model has a semi metallic behavior. Fig. 5(e) and (f) show the transmission spectrum and band structures of the left and right electrodes of the 7-E model, at voltages in which the peak and valley of the NDR occurs. At V = 0.2 V, although the overlap region between the N subbands of the left and right electrodes decreases, but there is a non-zero T(E) in whole BW and the peak of the NDR appears. As the bias voltage increases to 0.5 V, the overlap area between the N subbands of the right and left electrodes becomes smaller and as a result the transmission in the BW decreases and the valley of the NDR appears. The same happens for 7-C model but at different voltages. The peak [see Fig. 5(h)] and valley [see Fig. 5(i)] appear at 0.3 V and 0.6 V, respectively. Comparing 7-E and 7-C models it is found that, 7-C has a larger NDR since its integral area of the transmission in the BW at V = VValley is nearly zero (The underlying physics will be more discussed in the following). As it is shown in Fig. 5(f), in the overlap region of the N and π∗ subbands, small peaks of transmission come into sight, but in Fig. 5(i), although N and π∗ subbands overlap with each other, the transmission is nearly zero. Here we show the Bloch wave functions of N and π∗ subbands of 7-E and 7-C models to more clarify the reason of this abnormal behavior (see Fig. 6). As you see in Fig. 6(a) and (b), the Bloch wave functions of N and π∗ subbands do not have a definite parity under the xz midplane mirror operation. As a result, there exists a weak coupling between these two subbands which results in small peaks of transmission in the bias window [see Fig. 5(f)]. On the contrary, the N and π∗ subbands of 7-C have even and odd parities, respectively, and consequently the tunneling between these two subbands is nearly forbidden [see Fig. 5(i)].
4. Conclusion We studied the electronic transport properties of pristine and N doped A-α-GYNRs under 0–1 V. At first we calculated the total energy to find the most stable place for nitrogen atoms. Furthermore we have compared the bond lengths of optimized prefect and doped structures. Fortunately a small change in adjoining bond lengths is observed. We found that, doping can close the band gap of semiconducting A-αGYNRs and define an NDR effect in the I-V characteristics of both C and E models with all widths. It should be mentioned that, among W = 6-C/E, 7-C/E and 8-C/E models, 7-C have the best NDR which is about 67. Comparing edge and central doped structures, we observed that the effect of central doping on the electronic transport properties is more than the edge doping. It stems from the parity of the subbands which contribute in transmission. We have also studied the effect of doping concentration and observed that doping concentration and the NDR are inversely proportional to each other. At last we studied the length effect on the I-V characteristics of 7-C model. Results revealed that, the longer the central region is, the larger NDR appears. 7-C model with L = 5 UC has the best NDR which is about 159. Our findings could be beneficial for designing and developing the nano scale NDR devices.
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Fig. 7. The transmission spectrum and DOS for 7-E at (a) V = 0 V, (b) V = 0.2 V, (c) V = 0.5 V, and for 7-C at (d) V = 0 V, (e) V = 0.3 V, (f) V = 0.6 V.
Fig. 8. 7-C model with four various doping concentrations: 0%, 1.9%, 3.8% and 5.8%.
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Fig. 9. The calculated I-V characteristics for 7-C model with four different doping concentrations: 0%, 1.9%, 3.8% and 5.8%.
Fig. 10. (a) The optimized structure of 7-C model in which W=7 (is fixed) while L changes from 3 UC to 5 UC. (b) The current-voltage characteristics of 7C model with L = 3 UC, 4 UC and 5 UC, at the bias range from 0 V to 1 V in steps of 0.1 V. Table 4 I Peak, I Valley and NDR of 7-C model with L = 3 UC, 4 UC and 5 UC. L
I
3 4 5
18.566 18.742 18.647
Peak
(μA)
I
Valley
0.527 0.280 0.117
(μA)
NDR 35 67 159
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