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Transport properties of doped zigzag graphene nanoribbons
Chinese Journal of Physics 57 (2019) 47–52
Contents lists available at ScienceDirect
Chinese Journal of Physics journal homepage: www.elsevier.com/locate/cjph
Transport properties of doped zigzag graphene nanoribbons Xue Peia,b, Chen Aqingc, Zhang Juana,b,d, Shao Qingyia,b,
⁎
T
a
Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China Guangdong Engineering Technology Research Center of Efficient Green Energy and Environmental Protection Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China c College of Materials & Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, PR China d School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China b
A R T IC LE I N F O
ABS TRA CT
Keywords: Interconnect Zigzag graphene nanoribbons Doping Electronic transport property Density functional theory Non-equilibrium Green's function
Numerous studies on materials have driven the development of modern nanoelectronic devices. And research also shown that the integrated circuits have entered the era of the nanoelectronic scales from the scale of microelectronics. But the limitations of copper as a traditional connection, such as the resistivity increases a lot, further causing a lot of heat in the interconnect, have been highlighted. Therefore, we need new materials as the substitution of copper. The metallic properties exhibited by the zigzag graphene nanoribbons (ZGNRs) can be controlled by the edge states, doping and different widths of the nanoribbons. In this paper, we applied simulation to dope copper atom chains on ZGNRs. We found an energetic phenomenon that after doping the nanoribbons conductivity have increased significantly than the original. In addition, the transmission channels are mainly concentrated near the doping position, and the width used for transmission is greatly reduced after doping. It is expected to be used as an inter-connect application in nano-integrated circuits in the future.
1. Introduction Current development of integrated circuit has entered the era of nano-integrated circuits [1,2]. The copper is widely used in most of the interconnection processes. However, in nanoscale, copper interconnection have to face many problems, such as size effect, stability and reliability [3]. In nano-integrated circuits technology, interconnects have also became a difficulty in designing integrated circuits that need to be overcomed. So, we need to find a new type of material to replace the copper as interconnection in integrated circuits. In addition, the emergence of two-dimensional materials has made it possible to make integrated circuits of several nanometers in thick [4]. After the discovery of graphene in 2004, both experimentalists and theoreticians have shown a strong interest in it [5]. Cutting graphene in the transverse direction can make it into a finite size graphene nanoribbon (GNR). The GNR has excellent physical properties such as high electrical conductivity [6], high thermal conductivity [7], etc. There are two unique types of GNRs, respectively, armchair graphene nanoribbons (AGNRs) and zigzag graphene nanoribbons (ZGNRs), different in the atomic arrangement of the nanoribbon edges. It has been extensively studied that AGNRs can be metallic or semiconducting depending on their widths [8,9]. ZGNRs are metallic and have a special edge states on both sides of the ribbon, regardless of its widths [10,11]. These striking characteristics have made GNRs a possible alternative to copper for integrated circuit interconnect [12]. Now, there are many
⁎ Corresponding author at: Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China. E-mail address: [email protected] (Q. Shao).
https://doi.org/10.1016/j.cjph.2018.12.014 Received 18 September 2018; Received in revised form 23 November 2018; Accepted 13 December 2018 Available online 29 December 2018 0577-9073/ © 2018 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
Chinese Journal of Physics 57 (2019) 47–52
P. Xue et al.
Fig. 1. Optimized geometric structures of n-ZGNRs and different positions of doped copper atoms, the width n = 8 is shown in (a) and n = 10 in (f). (b)–(e) depict the models optimized after doping at P1–P4 respectively; (g)–(k) depict the doping models that have been optimized for L1–L4 positions, respectively. All graphene nanoribbons are edge-passivated with one hydrogen atom. Gray, red, and white balls denote carbon, copper, and hydrogen atoms, respectively. The black rectangle shows primitive cell for the nanoribbon.
methods have been used for manufacturing GNRs, for example, cutting graphene [13], patterning epitaxially grown graphene [14], or unzipping carbon nanotubes [15]. As early as in 2009, Jiao et al. [16] have obtained GNRs by unzipping carbon nanotubes and fabricated GNRs devices. In the past few years, theoretical research on producing electronic devices with GNRs (including zigzag or armchair type) has become more and more popular. Llinas et al. have used bottom-up to synthesized AGNRs and successfully manufactured high-performance short channel field effect transistors [17]. Different elements have been doped in the single-atom form through create vacancies by highenergy atom/ion bombardment and fill these vacancies with desired dopants [18]. All of these provide the basis for the fabrication of electronic devices using graphene nanomaterials. With the deepening of research on GNRs and nanomaterials, its broad application and desirable prospects in electronic device have been continuously demonstrated. In this paper, we have an idea to enhance their conductivity by doping some atoms such as copper, and then we study the properties of the model of ZGNRs with copper atom chains. In order to fabricate interconnection wires for electronic devices. In our work, the transport properties are studied by the density functional theory (DFT) combined with non-equilibrium Green's function (NEGF) [8,19].
2. Material and methods 2.1. Models and geometric optimization According to previous report [20], we define the width parameter N ‘as’ the number of zigzag lines of GNRs, as shown by the black dashed line in the Fig. 1a, across the nanoribbon, denoted by n-ZGNGs. We used hydrogen atoms to modify the GNRs edge as the contrast group because of its stable structure [20–22]. We replaced the carbon atoms in one dashed black line with copper atoms. We take four substitution positions (P1-4, as shown in Fig. 1a) for 8-ZGNRs, the optimized structures are shown in Fig. 1(b–e) respectively. And five substitution locations (L1-5) for 10-ZGNRs as indicated in the Fig. 1f, the optimized structures are shown in Fig. 1(g–k), respectively. The nanoribbons after doping are denoted by n-8-ZGNRs and m-10-ZGNRs (n from 1 to 4, m from 1 to 5). At first, we conducted a comparative study of the stability of the doped structures to prove the possibility of their stable existence. Then we calculated the band structure and density of states (DOS) of the nanoribbons. Consistent with the previous research results, they all can exist stably and show good properties [11,23,24]. Geometric optimization and energy calculation (including band structure and DOS) utilized the DOML3 [25,26] module in material studio (MS). For processing the electronic exchange-correlation energy, the generalized gradient approximation (GGA) proposed by Perdeu, Burke, and Ernzerhof (PBE) [27,28] is used, which is often used in DFT calculations. The sampling for Brillouin 48
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Fig. 2. (a) The optimized geometric structure of 4-8-ZGNRs; (b) the I–V curves of 8-ZGNRs and n-8-ZGNRs.
zone integrations is performed using the Monkhorst-Pack Scheme [29] with a regular k-point grid of 1*1*30 for the electronic relaxation. To prevent the interaction between adjacent nanoribbons, we modeled the supercell of the nanoribbons in a very large vacuum which regions of 30 (20) Å in (perpendicular to) its plane. 2.2. Non-equilibrium Green's function In this calculation, this two-probe device consists of three parts as shown in Fig. 6a and b: left electrode (L), right electrode (R) and central scattering region (C). Since the working environment is at room temperature, the electron temperature set in our calculation is 300 K. By utilizing the non-equilibrium Green's function, we obtained the current–voltage (I–V) characteristics of the device. And meanwhile we applied a bias voltage varies from 0.0 to 1.0 V in a step of 0.2 V, as shown in Fig. 2b. The density mesh cutoff was chosen as 150 Ry and the Brillouin zone of the electrode was sampled with 1*1 *100 points [30]. 3. Results and discussion 3.1. Structure and stability Firstly, we studied the structure and stability of the ZGNRs and copper chain-ZGNRs model which are geometrically optimized and compared the binding energy of each structures. The banding energy of the doping ZGNRs can be calculated as follows [31]:
B. E = Edoped − EWithout impurity − n Eisolatedimpurityatom where Edoped is the total energy of the doped system, Ewithout impurity is the total energy of the system without cooper atom doping, n is the number of impurity atoms, Eisolated impurity atom is the total energy of the isolated cooper atom. We found that when we doping at the edge position the binding energy is the largest, indicating that the structure is the most stable. This result is also consistent with previous research [32]. By comparing the optimized structures, it can be seen that the influence of different doping positions on the structural deformation is basically the same. The lattices which is close to the dopants deformed largely, nevertheless, far ones still remain in hexagonal. We use 4-8-ZGNRs as an example to analyze the change in bond length and bond angle before and after doping. We label the four atoms in the hexagon with A, B, C, and D, respectively, as shown in Fig. 2a. The original carbon atoms are replaced by copper atoms at the A, C, and D positions. It can be clearly seen from Fig. 2a that the AB, AC, and AD bonds are all significantly increased, the AB is increased by 36.7%, and the AC is increased by 79.6%, the ∠BAC increasing by 26.12%, and the ∠ACD decreasing by 51.96%. After doping, the width of the entire nanoribbon increased. 3.2. Current–voltage characteristics We took graphene nanoribbons with a width of n = 8 as an example to explore the transport properties of copper-doped and pristine nanoribbons. Since the structure of the GNR device is symmetrical in the direction of transmission, we only consider the circumstance which only a positive 0–1 V bias is applied. It can be seen from the Fig. 2b that the current increases along with the bias, except 1-8-ZGNRs. However, while operating in low bias regime (below 0.2 V), all the considered structures exhibited linear I–V characteristics. In addition, the devices with different dopant position have different I–V curves. All of them exhibited a stronger conductivity than ZGNRs. At the same bias, the nanoribbons doped at P2 have the largest current. It is due to the participation of the edge hydrogen atoms and copper atoms in the conduction. Moreover, after our research calculations, for the ZGNR with width n = 10, it also has the best conductivity when doping at the L2 (The calculation results are not put in this article). 49
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Fig. 3. The transmission spectrum of (a) 8-ZGNRs and (b) 1-8-ZGNRs under the bias voltage. The bias voltage varies from 0.0 to 1.0 V in a step of 0.2 V.
3.3. Transmission spectrum of the 8-ZGNRs and 1-8-ZGNRs In order to gain a deeper and intuitive understanding of the conductivity of nanoribbons after doping, we have also studied their transmission spectrum under different bias. We cited the transmission spectrum of 8-ZGNRs (Fig. 3a) and 1-8-ZGNGs (Fig. 3b) under different bias voltages for analysis. At 0 bias, it can be seen from Fig. 3a that the transmission spectrum of 8-ZGNR appeared a transmission peak at the Fermi level and the quantum platform is observed. These two characteristics of the transmission spectrum have been known [33]. Once the bias is applied in the 8-ZGNRs, the edge of the transport platform begins to enter the bias window. As the bias voltage increases, we did not find a significant threshold of bias. This phenomenon is due to the fact that the symmetrical ZGNRs have a conductance gap near the Fermi level, and this gap increases with increasing bias voltage but is slightly less than the bias voltage, which causes symmetrical ZGNRs to have a small current at a certain bias voltage [34]. The transmission spectrum of 18-ZGNRs under different bias voltages is shown in Fig. 3b. In Fig.b, we can observe a significant threshold of bias in the bias window. The magnitude of the integral area enclosed by the transmission curve and the bias window increased with the bias increased. Moreover, when the bias is less than 0.6 V, the increase is more obvious, and when it is less than 0.6 V, it is slow. Therefore, it illustrated the change of I–V curve of 1-8-ZGNRs in the range of 0–1 V bias in Fig. 2b. And then we calculated the projected PDOS of the atoms in the nanoribbons. We selected the PDOS at the P1-4 positions of the 8ZGMRs and 1-8-ZGNRs in the black dotted rectangle in Fig. 1b to illustrate the transmission characteristics, as shown in Fig. 4a and b. Figs. 4c and d show the transmission spectra of 8-ZGNR and 1-8-ZGNR, respectively. Comparing Figs. 4a and c, we can see that the peak near the Fermi level corresponds to that at PDOS and is mainly provided by the edge carbon atoms. It can be seen from Fig. 4b and Fig.d that the characteristic peak of the doped graphene nanoribbons at 0.45 eV are mainly caused by the carbon atom. And corresponding to the energy band structure indicated by the red arrow in Fig. 5b. From Fig. 3b, we can observe that all important quasi-boundary state features around the edge of the subband disappear. It can be explained from PDOS in the Fig. 4b that this phenomenon is caused by the effect of doping with copper [35]. And, the major conduction channel around the Fermi energy is mainly provided by the dopant. Therefore, the doping of copper atoms contributes to the high density state of the Fermi energy.
Fig. 4. The PDOS of C atoms in 8-ZGNRs (a). The PDOS of Cu atom at P1 and C atoms at in 1-8-ZGNRs. Transmission spectrum of (c) 8-ZGNRs and (d) 1-8-ZGNRs under 0 V. 50
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Fig. 5. Band structures of 8-ZGNRs and 1-8-ZGNRs as shown in (a) and (b), respectively. Position EF is set to 0 eV, as indicated by the green dotted line. (c) density of states of the 8-ZGNRs and 1-8-ZGNRs.
3.4. Band structures of H-passivated and copper-doped ZGNRs To deepen the understanding of the electronic properties of the 8-ZGNRs and 1-8-ZGNRs, we calculated the band structure, DOS and positions of the Fermi levels. As shown in Figs. 5a, b and c, the 1-8-GNRs showed more energy bands and increased DOS near the Fermi level compared to 8-GNRs. The energy band gap of 8-ZGNRs we calculated is 0.001 eV. The calculation results are basically consistent with the previous [36]. The Fermi level also decreased from −4.155 eV (8-ZGNRs) to −4.746 eV (1-8-GNRs); this decreased of the Fermi level is as expected from a comparison of the band structure. From the DOS (Fig. 5c), we can know that more electrons are introduced around the Fermi level which contributed by copper atoms. The change of band structure, DOS and Fermi level indicated that the ZGNRs doped Cu atom chain can improve the conductivity of the original GNR and are consistent with the calculated I–V characteristics and transmission spectrum.
3.5. Transmission pathway The structure of device constructed for the research of transmission characteristics is shown in Fig. 6. We calculated the transmission pathway of pristine ZGNRs (as shown in Fig. 6a) under 0.5 V bias. As can be seen from Fig. 6a, the main path of the electrons is the edge of the nanoribbon. According to previous studies [37], the reason of this phenomenon is due to the edge effect. The magnitude of the transmission channel can directly reflect the probability of electron passing through. Moreover, it can be seen from the transmission pathway of 1-8-ZGNRs (as shown in Fig. 6b) that the transmission channel is concentrated around the doping position. Compared to the pristine nanoribbon, the transmission performance of the nanoribbons after doped is enhanced and concentrated. After measurement and calculation, we can get an atomic-scale current channel with a line width of 0.223 nm. This is exactly what we want to achieve experimentally. It can be seen that Cu have an important influence on the transport properties of ZGNRs.
Fig. 6. The transmission pathway of 8-ZGNRs (a) and 1-8-ZGNRs (b). 51
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4. Summary In conclusion, using the first principle calculation [38–40], we calculated the voltage–current characteristics, transmission pathway, band structure and DOS of undoped and doped with a row of copper atoms ZGNRs passivated by hydrogen atoms. Our calculations shown that the doped ZGNRs are energy-stable, although they have a deformed structure and the structure of 1-8-ZGNRs are the most stable. The I–V curve and transmission spectrum indicated that, at the same voltage, the doped nanoribbons have bigger current, which means a better conductivity. The increase in conductivity is due to the improve in the number of energy bands and DOS near the Fermi level. After doping a row of copper atoms, we have achieved the goal of increasing the transmission channel and reducing the width occupied by the transmission channel. Our results suggest that ZGNRs doped with copper atoms have a good potential for application in the interconnection of nanodevices. 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52
Contents lists available at ScienceDirect
Chinese Journal of Physics journal homepage: www.elsevier.com/locate/cjph
Transport properties of doped zigzag graphene nanoribbons Xue Peia,b, Chen Aqingc, Zhang Juana,b,d, Shao Qingyia,b,
⁎
T
a
Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China Guangdong Engineering Technology Research Center of Efficient Green Energy and Environmental Protection Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China c College of Materials & Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, PR China d School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China b
A R T IC LE I N F O
ABS TRA CT
Keywords: Interconnect Zigzag graphene nanoribbons Doping Electronic transport property Density functional theory Non-equilibrium Green's function
Numerous studies on materials have driven the development of modern nanoelectronic devices. And research also shown that the integrated circuits have entered the era of the nanoelectronic scales from the scale of microelectronics. But the limitations of copper as a traditional connection, such as the resistivity increases a lot, further causing a lot of heat in the interconnect, have been highlighted. Therefore, we need new materials as the substitution of copper. The metallic properties exhibited by the zigzag graphene nanoribbons (ZGNRs) can be controlled by the edge states, doping and different widths of the nanoribbons. In this paper, we applied simulation to dope copper atom chains on ZGNRs. We found an energetic phenomenon that after doping the nanoribbons conductivity have increased significantly than the original. In addition, the transmission channels are mainly concentrated near the doping position, and the width used for transmission is greatly reduced after doping. It is expected to be used as an inter-connect application in nano-integrated circuits in the future.
1. Introduction Current development of integrated circuit has entered the era of nano-integrated circuits [1,2]. The copper is widely used in most of the interconnection processes. However, in nanoscale, copper interconnection have to face many problems, such as size effect, stability and reliability [3]. In nano-integrated circuits technology, interconnects have also became a difficulty in designing integrated circuits that need to be overcomed. So, we need to find a new type of material to replace the copper as interconnection in integrated circuits. In addition, the emergence of two-dimensional materials has made it possible to make integrated circuits of several nanometers in thick [4]. After the discovery of graphene in 2004, both experimentalists and theoreticians have shown a strong interest in it [5]. Cutting graphene in the transverse direction can make it into a finite size graphene nanoribbon (GNR). The GNR has excellent physical properties such as high electrical conductivity [6], high thermal conductivity [7], etc. There are two unique types of GNRs, respectively, armchair graphene nanoribbons (AGNRs) and zigzag graphene nanoribbons (ZGNRs), different in the atomic arrangement of the nanoribbon edges. It has been extensively studied that AGNRs can be metallic or semiconducting depending on their widths [8,9]. ZGNRs are metallic and have a special edge states on both sides of the ribbon, regardless of its widths [10,11]. These striking characteristics have made GNRs a possible alternative to copper for integrated circuit interconnect [12]. Now, there are many
⁎ Corresponding author at: Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China. E-mail address: [email protected] (Q. Shao).
https://doi.org/10.1016/j.cjph.2018.12.014 Received 18 September 2018; Received in revised form 23 November 2018; Accepted 13 December 2018 Available online 29 December 2018 0577-9073/ © 2018 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
Chinese Journal of Physics 57 (2019) 47–52
P. Xue et al.
Fig. 1. Optimized geometric structures of n-ZGNRs and different positions of doped copper atoms, the width n = 8 is shown in (a) and n = 10 in (f). (b)–(e) depict the models optimized after doping at P1–P4 respectively; (g)–(k) depict the doping models that have been optimized for L1–L4 positions, respectively. All graphene nanoribbons are edge-passivated with one hydrogen atom. Gray, red, and white balls denote carbon, copper, and hydrogen atoms, respectively. The black rectangle shows primitive cell for the nanoribbon.
methods have been used for manufacturing GNRs, for example, cutting graphene [13], patterning epitaxially grown graphene [14], or unzipping carbon nanotubes [15]. As early as in 2009, Jiao et al. [16] have obtained GNRs by unzipping carbon nanotubes and fabricated GNRs devices. In the past few years, theoretical research on producing electronic devices with GNRs (including zigzag or armchair type) has become more and more popular. Llinas et al. have used bottom-up to synthesized AGNRs and successfully manufactured high-performance short channel field effect transistors [17]. Different elements have been doped in the single-atom form through create vacancies by highenergy atom/ion bombardment and fill these vacancies with desired dopants [18]. All of these provide the basis for the fabrication of electronic devices using graphene nanomaterials. With the deepening of research on GNRs and nanomaterials, its broad application and desirable prospects in electronic device have been continuously demonstrated. In this paper, we have an idea to enhance their conductivity by doping some atoms such as copper, and then we study the properties of the model of ZGNRs with copper atom chains. In order to fabricate interconnection wires for electronic devices. In our work, the transport properties are studied by the density functional theory (DFT) combined with non-equilibrium Green's function (NEGF) [8,19].
2. Material and methods 2.1. Models and geometric optimization According to previous report [20], we define the width parameter N ‘as’ the number of zigzag lines of GNRs, as shown by the black dashed line in the Fig. 1a, across the nanoribbon, denoted by n-ZGNGs. We used hydrogen atoms to modify the GNRs edge as the contrast group because of its stable structure [20–22]. We replaced the carbon atoms in one dashed black line with copper atoms. We take four substitution positions (P1-4, as shown in Fig. 1a) for 8-ZGNRs, the optimized structures are shown in Fig. 1(b–e) respectively. And five substitution locations (L1-5) for 10-ZGNRs as indicated in the Fig. 1f, the optimized structures are shown in Fig. 1(g–k), respectively. The nanoribbons after doping are denoted by n-8-ZGNRs and m-10-ZGNRs (n from 1 to 4, m from 1 to 5). At first, we conducted a comparative study of the stability of the doped structures to prove the possibility of their stable existence. Then we calculated the band structure and density of states (DOS) of the nanoribbons. Consistent with the previous research results, they all can exist stably and show good properties [11,23,24]. Geometric optimization and energy calculation (including band structure and DOS) utilized the DOML3 [25,26] module in material studio (MS). For processing the electronic exchange-correlation energy, the generalized gradient approximation (GGA) proposed by Perdeu, Burke, and Ernzerhof (PBE) [27,28] is used, which is often used in DFT calculations. The sampling for Brillouin 48
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Fig. 2. (a) The optimized geometric structure of 4-8-ZGNRs; (b) the I–V curves of 8-ZGNRs and n-8-ZGNRs.
zone integrations is performed using the Monkhorst-Pack Scheme [29] with a regular k-point grid of 1*1*30 for the electronic relaxation. To prevent the interaction between adjacent nanoribbons, we modeled the supercell of the nanoribbons in a very large vacuum which regions of 30 (20) Å in (perpendicular to) its plane. 2.2. Non-equilibrium Green's function In this calculation, this two-probe device consists of three parts as shown in Fig. 6a and b: left electrode (L), right electrode (R) and central scattering region (C). Since the working environment is at room temperature, the electron temperature set in our calculation is 300 K. By utilizing the non-equilibrium Green's function, we obtained the current–voltage (I–V) characteristics of the device. And meanwhile we applied a bias voltage varies from 0.0 to 1.0 V in a step of 0.2 V, as shown in Fig. 2b. The density mesh cutoff was chosen as 150 Ry and the Brillouin zone of the electrode was sampled with 1*1 *100 points [30]. 3. Results and discussion 3.1. Structure and stability Firstly, we studied the structure and stability of the ZGNRs and copper chain-ZGNRs model which are geometrically optimized and compared the binding energy of each structures. The banding energy of the doping ZGNRs can be calculated as follows [31]:
B. E = Edoped − EWithout impurity − n Eisolatedimpurityatom where Edoped is the total energy of the doped system, Ewithout impurity is the total energy of the system without cooper atom doping, n is the number of impurity atoms, Eisolated impurity atom is the total energy of the isolated cooper atom. We found that when we doping at the edge position the binding energy is the largest, indicating that the structure is the most stable. This result is also consistent with previous research [32]. By comparing the optimized structures, it can be seen that the influence of different doping positions on the structural deformation is basically the same. The lattices which is close to the dopants deformed largely, nevertheless, far ones still remain in hexagonal. We use 4-8-ZGNRs as an example to analyze the change in bond length and bond angle before and after doping. We label the four atoms in the hexagon with A, B, C, and D, respectively, as shown in Fig. 2a. The original carbon atoms are replaced by copper atoms at the A, C, and D positions. It can be clearly seen from Fig. 2a that the AB, AC, and AD bonds are all significantly increased, the AB is increased by 36.7%, and the AC is increased by 79.6%, the ∠BAC increasing by 26.12%, and the ∠ACD decreasing by 51.96%. After doping, the width of the entire nanoribbon increased. 3.2. Current–voltage characteristics We took graphene nanoribbons with a width of n = 8 as an example to explore the transport properties of copper-doped and pristine nanoribbons. Since the structure of the GNR device is symmetrical in the direction of transmission, we only consider the circumstance which only a positive 0–1 V bias is applied. It can be seen from the Fig. 2b that the current increases along with the bias, except 1-8-ZGNRs. However, while operating in low bias regime (below 0.2 V), all the considered structures exhibited linear I–V characteristics. In addition, the devices with different dopant position have different I–V curves. All of them exhibited a stronger conductivity than ZGNRs. At the same bias, the nanoribbons doped at P2 have the largest current. It is due to the participation of the edge hydrogen atoms and copper atoms in the conduction. Moreover, after our research calculations, for the ZGNR with width n = 10, it also has the best conductivity when doping at the L2 (The calculation results are not put in this article). 49
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Fig. 3. The transmission spectrum of (a) 8-ZGNRs and (b) 1-8-ZGNRs under the bias voltage. The bias voltage varies from 0.0 to 1.0 V in a step of 0.2 V.
3.3. Transmission spectrum of the 8-ZGNRs and 1-8-ZGNRs In order to gain a deeper and intuitive understanding of the conductivity of nanoribbons after doping, we have also studied their transmission spectrum under different bias. We cited the transmission spectrum of 8-ZGNRs (Fig. 3a) and 1-8-ZGNGs (Fig. 3b) under different bias voltages for analysis. At 0 bias, it can be seen from Fig. 3a that the transmission spectrum of 8-ZGNR appeared a transmission peak at the Fermi level and the quantum platform is observed. These two characteristics of the transmission spectrum have been known [33]. Once the bias is applied in the 8-ZGNRs, the edge of the transport platform begins to enter the bias window. As the bias voltage increases, we did not find a significant threshold of bias. This phenomenon is due to the fact that the symmetrical ZGNRs have a conductance gap near the Fermi level, and this gap increases with increasing bias voltage but is slightly less than the bias voltage, which causes symmetrical ZGNRs to have a small current at a certain bias voltage [34]. The transmission spectrum of 18-ZGNRs under different bias voltages is shown in Fig. 3b. In Fig.b, we can observe a significant threshold of bias in the bias window. The magnitude of the integral area enclosed by the transmission curve and the bias window increased with the bias increased. Moreover, when the bias is less than 0.6 V, the increase is more obvious, and when it is less than 0.6 V, it is slow. Therefore, it illustrated the change of I–V curve of 1-8-ZGNRs in the range of 0–1 V bias in Fig. 2b. And then we calculated the projected PDOS of the atoms in the nanoribbons. We selected the PDOS at the P1-4 positions of the 8ZGMRs and 1-8-ZGNRs in the black dotted rectangle in Fig. 1b to illustrate the transmission characteristics, as shown in Fig. 4a and b. Figs. 4c and d show the transmission spectra of 8-ZGNR and 1-8-ZGNR, respectively. Comparing Figs. 4a and c, we can see that the peak near the Fermi level corresponds to that at PDOS and is mainly provided by the edge carbon atoms. It can be seen from Fig. 4b and Fig.d that the characteristic peak of the doped graphene nanoribbons at 0.45 eV are mainly caused by the carbon atom. And corresponding to the energy band structure indicated by the red arrow in Fig. 5b. From Fig. 3b, we can observe that all important quasi-boundary state features around the edge of the subband disappear. It can be explained from PDOS in the Fig. 4b that this phenomenon is caused by the effect of doping with copper [35]. And, the major conduction channel around the Fermi energy is mainly provided by the dopant. Therefore, the doping of copper atoms contributes to the high density state of the Fermi energy.
Fig. 4. The PDOS of C atoms in 8-ZGNRs (a). The PDOS of Cu atom at P1 and C atoms at in 1-8-ZGNRs. Transmission spectrum of (c) 8-ZGNRs and (d) 1-8-ZGNRs under 0 V. 50
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Fig. 5. Band structures of 8-ZGNRs and 1-8-ZGNRs as shown in (a) and (b), respectively. Position EF is set to 0 eV, as indicated by the green dotted line. (c) density of states of the 8-ZGNRs and 1-8-ZGNRs.
3.4. Band structures of H-passivated and copper-doped ZGNRs To deepen the understanding of the electronic properties of the 8-ZGNRs and 1-8-ZGNRs, we calculated the band structure, DOS and positions of the Fermi levels. As shown in Figs. 5a, b and c, the 1-8-GNRs showed more energy bands and increased DOS near the Fermi level compared to 8-GNRs. The energy band gap of 8-ZGNRs we calculated is 0.001 eV. The calculation results are basically consistent with the previous [36]. The Fermi level also decreased from −4.155 eV (8-ZGNRs) to −4.746 eV (1-8-GNRs); this decreased of the Fermi level is as expected from a comparison of the band structure. From the DOS (Fig. 5c), we can know that more electrons are introduced around the Fermi level which contributed by copper atoms. The change of band structure, DOS and Fermi level indicated that the ZGNRs doped Cu atom chain can improve the conductivity of the original GNR and are consistent with the calculated I–V characteristics and transmission spectrum.
3.5. Transmission pathway The structure of device constructed for the research of transmission characteristics is shown in Fig. 6. We calculated the transmission pathway of pristine ZGNRs (as shown in Fig. 6a) under 0.5 V bias. As can be seen from Fig. 6a, the main path of the electrons is the edge of the nanoribbon. According to previous studies [37], the reason of this phenomenon is due to the edge effect. The magnitude of the transmission channel can directly reflect the probability of electron passing through. Moreover, it can be seen from the transmission pathway of 1-8-ZGNRs (as shown in Fig. 6b) that the transmission channel is concentrated around the doping position. Compared to the pristine nanoribbon, the transmission performance of the nanoribbons after doped is enhanced and concentrated. After measurement and calculation, we can get an atomic-scale current channel with a line width of 0.223 nm. This is exactly what we want to achieve experimentally. It can be seen that Cu have an important influence on the transport properties of ZGNRs.
Fig. 6. The transmission pathway of 8-ZGNRs (a) and 1-8-ZGNRs (b). 51
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4. Summary In conclusion, using the first principle calculation [38–40], we calculated the voltage–current characteristics, transmission pathway, band structure and DOS of undoped and doped with a row of copper atoms ZGNRs passivated by hydrogen atoms. Our calculations shown that the doped ZGNRs are energy-stable, although they have a deformed structure and the structure of 1-8-ZGNRs are the most stable. The I–V curve and transmission spectrum indicated that, at the same voltage, the doped nanoribbons have bigger current, which means a better conductivity. The increase in conductivity is due to the improve in the number of energy bands and DOS near the Fermi level. After doping a row of copper atoms, we have achieved the goal of increasing the transmission channel and reducing the width occupied by the transmission channel. Our results suggest that ZGNRs doped with copper atoms have a good potential for application in the interconnection of nanodevices. 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