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Structure and electronic properties of single-walled C3N nanotubes
Physica E 124 (2020) 114320
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Physica E: Low-dimensional Systems and Nanostructures journal homepage: http://www.elsevier.com/locate/physe
Structure and electronic properties of single-walled C3N nanotubes Zhanhai Li , Fang Cheng * Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha, 410004, China
A B S T R A C T
One-dimensional nanotubes have become an indispensable ideal candidate material for nano-device applications due to their excellent and unique electronic, mechanical, and thermal properties. By the first-principles method of density functional theory, we have theoretically investigated the structural stability, electronic properties, carrier mobility, and Poisson’s ratio of C3N single-walled nanotubes (C3NSWNT). We find that C3NSWNT is stable and the ground state of the system is non-magnetic. The electronic properties and carrier mobilities of C3NSWNT can be adjusted by diameter and edge engineering. The electron mobility of (n,n) armchair C3NSWNT (A-C3NSWNT) is lower than that of (n,0) zigzag C3NSWNT (Z-C3NSWNT), but the hole mobility of (n,n) A-C3NSWNT is higher than that of (n,0) Z-C3NSWNT. Moreover, both A-C3NSWNT and Z-C3NSWNT can transfer from semiconductor to metal by tuning the electric field, and Z-C3NSWNT is more sensitive to the applied electric field than A-C3NSWNT due to smaller energy gap. But only A-C3NSWNT can transfer from semiconductor to metal by tuning strain, and be more suitable to the application in nano electromechanical switching devices. These research results may provide some theoretical support for the potential application and development of nanoelectronic devices based on C3NSWNT.
1. Introduction Since the first discovery of multi-walled carbon nanotubes in 1991 [1] and the successful preparation of single-walled carbon nanotubes in 1993 [2,3], carbon nanotubes (CNTs) have rapidly become a research hotspot. Due to unique mechanical and thermal properties [4–10], they have a broad application prospects in the field of materials science, optics, nanoelectronics, nanotechnology [11–16]. Replacing some car bon atoms of CNTs by other elements like N can efficiently alter the electronic properties and come into being new applications. Multi-walled CNx nanotubes have been successfully prepared by pyro lyzing ferrocence/setminusmelamine mixtures in a high-temperature argon atmosphere at 1050 � C [17]. The relaxation structure of C3N single wall nanotubes (C3NSWNT) was reported to be independent of the chirality of nanotubes [18]. C3NSWNT has higher thermal conductivity and is affected by its length, chirality, and uniaxial strain [19,20]. And most of C3NSWNT are semiconductors with high Young’s modulus [21]. Zigzag C3NSWNT with vacancy defects exhibited ferromagnetic spin alignment [22]. The H atom adsorption have significant effects on the electronic structure of C3NSWNT [23]. The C3NSWNT is well suited for a hydrogen storage material [24,25]. As a member of the graphene-like materials, however, the research on the energetic, structure and electronic properties of C3NSWNT is not comprehensive enough. In this paper, we investigate the chirality index n -dependence of the electronic properties of two typical nanotubes, i. e., armchair C3NSWNT(A-C3NSWNT) and zigzag C3NSWNT(Z-C3 NSWNT),
in terms of the first principle method of density functional theory. The electron mobility of (n,n) A-C3NSWNT is lower than that of (n,0) Z-C 3NSWNT, but the hole mobility of (n,n) A-C3NSWNT is higher than that of (n,0) Z-C3NSWNT. The band gap can be modulated and the C3 NSWNT can transfer from semiconductor to metal by tuning electric field, strain and the zigzag and armchair edges. 2. Model and method The optimization of the structure, the evaluation of structural sta bility, and the calculation of electronic performance are all based on the density functional theory (DFT). All calculations are completed by using Atomistix ToolKit (ATK) package [26–28] developed by the first prin ciple, which has been widely used in the research of nanostructures [29–36]. To solve the Kohn-Sham equation, the spin-polarized Per dew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional was used to describe the exchange-correlation term of elec trons. It is accurate enough to calculate the total energy of atoms and the binding energy of small molecules. But the electronic band gap calcu lated in terms of the GGA functional would be slightly lower than the experimental value. And the elastic modulus calculated by GGA func tional is relatively soft. Taking into account the effect of atomic polar ization, the eigenfunction of electrons is a linear combination of atomic orbits. Double-zeta plus polarization (DZP) is used as the extended wave function of the basis function group for all atoms. The selection of base group determines the accuracy of calculation. C and N are light
* Corresponding author. E-mail address: [email protected] (F. Cheng). https://doi.org/10.1016/j.physe.2020.114320 Received 28 April 2020; Received in revised form 18 June 2020; Accepted 22 June 2020 Available online 10 July 2020 1386-9477/© 2020 Elsevier B.V. All rights reserved.
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Physica E: Low-dimensional Systems and Nanostructures 124 (2020) 114320
elements, thus it is completely sufficient to select the DZP base group for geometric optimization and property calculation. Troullier Martins norm-conserving pseudopotential is used to approximate the atomic kernel. 1 � 1 � 100 k-point samples are taken in the x-, y-, and z -axis directions of the first Brillouin zone, where the z-axis direction is the nanotube transmission direction. The value of the Mesh cut-off is mainly used to solve the Poisson equation and control the size of the real space integral network, and to ensure the balance of calculation accuracy and efficiency. We set it as 150 Ry (1 Ry ¼ 13.60 eV). The interaction be tween the model and its “image” is eliminated by selecting a vacuum cell larger than 1.5 nm in the x- and y-axis directions. All calculations are optimized by the Quasi Newton method until all residual forces on each atom are within 0.02 eV/Å. For research purposes, the Fermi energy levels of all nanotubes are set to zero. Similar to carbon nanotubes (CNTs), aC3NSWNT is formed by rolling a single layer of C3N nanoribbons into a cylinder. The atomic structure of C3NSWNT can be described by the chiral vector Ch ¼ na1 þ ma2, where a1 and a2 are unit vectors with the same head in the same hexagonal lattice and the tail at the adjacent zigzag end. The integer (n, m) is the number of steps of the zigzag bond. When m ¼ 0, C3NSWNT is a zigzag nanotube (Z-C3 NSWNT), then (n, 0) Z-C3NSWNT is used as the general term of all Z-C3NSWNT (chiral angle is 0� ). When n ¼ m, C3NSWNT is armchair nanotube (A-C3NSWNT). And (n, n) A-C3NSWNT is used as the general term of all A-C3NSWNT (chiral angle is 30� ). The rest of n and m values are all chiral C3NSWNT (C-C3NSWNT). We have selected two classical types of nanoribbons (zigzag and armchair nanoribbons), and rolled them into nanotubes as shown in Fig. 1. The shaded parts in Fig. 1 correspond to the nanoribbon used by the supercell during the coiling process. The actual research process is based on the nanotube extending infinitely along the transport direction. The band gap varies with diameter [37]. Due to the high hybridization caused by curvature [38], the tight binding method cannot accurately describe small diameter C3NNT. It is well known that the local density approximation(LDA) method is overly inclined to bind atoms, so bond lengths are usually underestimated by several percentage points [39].
shows that the energy difference between the ferromagnetic state (FM) and the antiferromagnetic state (AFM) is 0. This is because the magne tism of an isolated atom is mainly determined by the number of electrons in the outermost layer of the atomic orbital. The outermost 2p orbital of the C atom contains 2 electrons and the outermost 2p orbital of the N atom contains 3 electrons. After the formation of carbon-nitrobenzene ring, they all exist as a pair of covalent bonds. The system under study is a periodic nanotube, with both ends extending indefinitely, so there are no dangling bonds. To further determine whether the ground state of the system is magnetic (FM) or non-magnetic (NM), we calculated the magnetization energy (EM) of the system, which is defined as EM ¼ (EFM ENM)/Nt. Here, EFM and ENM are the total energy of the supercell in the FM and NM states, respectively, and Nt is the total number of atoms in the supercell. If the calculated magnetization energy is negative and its absolute value is sufficiently large, then the ground state of the system is a ferromagnetic (FM) state. However, the calculation results show that all infinitely extending nanotubes have a magnetization energy of 0 regardless of the value of the chiral index n. This indicates that the system is unlikely to be magnetic at limited temperatures. Therefore, the following research systems are all in the NM state. To test the thermal stability of the nanotubes, we have chose to perform the Born–Oppenheimer Molecular Dynamics (BOMD) simula tion in the NVT ensemble through the Nos�e thermal bath scheme. Fig. 2 (a) and (b) is a schematic diagram of the structure after (6,6) AC3NSWNT/(10,0) Z-C3NSWNT stays at 8ps in different temperature environments. It can be seen from Fig. 2(a) and (b) that the two types of nanotubes have basically not changed at a temperature of 500 K. When the temperature further increases, the C and N atoms all relax on the basis of their equilibrium positions, and the N atom relaxation is more significantly. From the left view of C3 NSWNT, we find that there will be a more obvious deformation at the position of each N atom, which will be more obvious with the increase of temperature. By observing the deformation degree of two kinds of nanotubes at different temperatures, it can be found that the deformation of nanotubes is more and more obvious with the increase of temperature, but the two kinds of nano tubes have never been reconstructed at 2000K, which proves that C3 NSWNT has better thermal stability. The band gap of C3NSWNT are plotted as the function of chirality
3. Results and discussion The spin-polarization exchange-correlation function calculation
Fig. 1. The structure of monolayer C3N sheet, in which the shaded part is the minimum periodic repeating unit nanoribbon required for the (a) (6,6) AC3NSWNT and (b) (10,0) Z-C3NSWNT supercell. The middle and right part of Fig. 1(a) and (b) are the left and front views of the nanotubes, respectively.
Fig. 2. (a) (6,6) A-C3NSWNT and (b) (10,0) Z-C3 NSWNT show the results of BOMD simulations at different temperatures (the left/right part is the left/front view of single-walled nanotubes at the same temperature). 2
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index n in Fig. 3. For the armchair-type nanotubes, the band gap is al ways 0 (metal) for an odd number n, but is always not equal to 0 (semiconductor) for even n. All semiconductors have direct band gaps, the band gap increases gradually in the range of small diameter (n ¼ 3–10), and decreases in the range of large diameter (n ¼ 10–14). For zigzag nanotubes, the band gap is always not equal to 0 (semiconductor) for odd n (n ¼ 3–9), but is zero (metal) for even n, which is opposite to that for armchair nanotubes. When n ¼ 5, 7, 11, 13, the band gap of ZC3NSWNT belongs to indirect band gap, the rest are all direct band gap. In the case of large zigzag nanotube diameter (n ¼ 9–14), the band gap decreases/increases with the increasing odd/even nanotube diameter n. By rolling up C3N nanoribbons the electron wave functions are subjected to an additional quantization condition, essentially ‘cutting’ one dimension slices out of the formerly two dimension band structure of C3N nanoribbons [40]. The binding energy is used to evaluate the structural stability of the studied system in isolated atomic states, which is defined as Eb ¼ (Etotal nNEN nCEC)/(nN þ nC). Here, Etotal is the total energy obtained by calculating the supercell system, nN/nC is the number of N/C atoms contained in the supercell, and EN/EC is the energy of one atom when the N/C atom is an isolated atomic state. As shown in Fig. 3(a) and (b), the binding energy of the armchair-type and zigzag-type nanotubes is al ways negative and less than 8.5 eV, which show that the system has good structural stability. The binding energy of the nanotubes decreases with the increase of the nanotube diameter. The smaller the negative value, the more stable the structure. Therefore the structural stability of the nanotubes will increase with the increase of the nanotube diameter. For the same chiral index n, the absolute value of the binding energy of A-C3NSWNT is larger than that of that of Z-C3NSWNT, so the stability of A-C3NSWNT is stronger than that of Z-C3NSWNT. The stability of the structure can also be described by the thermo dynamic properties of the material. The Gibbs free energy of the (6,6) AC3 NSWNT and (10,0) Z-C3NSWNT between 200 K ~ 1000 K are shown in Fig. 4(a). The Gibbs free energy of both (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT are negative, and shows a downward trend as the tem perature increases. Generally speaking, the lower the Gibbs free energy of the structure, the higher the thermodynamic stability. Thus both the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT have good stability. We have plotted the phonon dispersion spectra of both the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT as shown in Fig. 4(b) and (c). It can be seen that there is no virtual frequency in the entire Brillouin region, which
Fig. 4. (a) Temperature-dependent Gibbs free energy for (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT. The phonon dispersion of (b) (6,6) A-C3NSWNT, and (c) (10,0) Z-C3NSWNT, respectively.
indicates that C3NSWNTs are dynamically stable. Fig. 5 shows the gradual relationship between the bond length and the bond angle in the range of 3–14 for the chiral index n. The three bond lengths d1, d2, and d3 of A-C3NSWNT decrease with the increase of n from 3 to 8, and are basically stable at a certain value when n change from 9 to 14. The changes in three bond lengths are mainly affected by the bond strain on the curvature surface. The smaller the diameter, the larger the curvature. This effect is the most obvious for bonds parallel to the direction of curl, such as d3 in (n,n) A-C3NSWNT. As the diameter of the nanotube further increases, the curvature gradually decreases, and the bond length does not change. On the contrast, the bond lengths d1 and d3 of Z-C3NSWNT decrease with the increase of n from 3 to 14, but
Fig. 3. (a) and (b) indicate the change of bandgap and binding energy of A-C 3NSWNT and Z-C3NSWNT with n respectively. 3
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Fig. 5. The structure diagram of the mark, the relationship between the bond length and the bond angle with the chiral index n for (a) (6,6) A-C3NSWNT and (b) (10,0) Z-C3NSWNT, respectively.
the d2 bond of Z-C3NSWNT increases with the increase of n from 3 to 14. The d2 bond is perpendicular to the direction of curl, so it is independent of the bond strain on the curvature surface. From the Fig. 5, it can be seen that the bond angle always increases with the diameter of the nanotube n until it is consistent with the bond angle of two dimension materials. When the nanotube diameter is small, the curvature would be large, there would be a “folding” effect on the bond angles of the nanotubes. In the process of increasing nanotube diameter, it is equiv alent to the process of carbon nitrogen benzene ring slowly bending deformion and returning to the original state. Therefore the bond angle always increases with the increasing nanotube diameter. To understand the basic physical properties of the two types nano tubes, we need to explore their electronic structures. Fig. 6(a) and (c) show the band structure, total density of states (TDOS), and the pro jected density of states (PDOS) of elements and orbits of the intrinsic nanotubes. Obviously, both nanotubes are semiconductors. The con duction band minimum (CBM) and valence band maximum (VBM) of the two nanotubes are at the Γ point, so they are all direct band gaps. The band gap is 0.435 eV for (6,6) A-C3NSWNT and 0.096 eV for (10,0) ZC3NSWNT. For the (6,6) A-C3 NSWNT, the CBM and VBM bandwidths are sufficiently wide, which shows that the atomic orbital of the corre sponding energy band has a strong expansibility, a large degree of nonlocality and a small effective mass of electrons. Conversely, for the (10,0) Z-C3NSWNT, there is the relatively narrow band, so electrons have a very strong locality and the effective mass of electrons is rela tively large. This analysis results are consistent with the calculation results in Table 1. The density of states (DOS) is a visualization of the band structure. From the DOS diagrams of Fig. 6(a) and (c), it can be found that the Fermi energy levels are all in the range where the DOS value is zero, indicating that the system is a semiconductor. From the PDOS of atom, we can clearly see that the atomic orbital contribution mainly comes from the 2p orbital of C and N atoms, but the C-2p orbital contribution is more significant. The band structure of the studied sys tem is mainly determined by the orbital hybridization and electron transfer between the C and N atoms. We calculated the charge density difference in Fig. 6(b) and (d) where the increase and decrease of electrons relative to the isolated atomic state are represented by the magenta and blue areas. It can be clearly seen that electrons are always accumulated on the covalent bond formed by adjacent C and C (or C and N) atoms. The regular covalent bonds are formed between adjacent C atoms, but the electron cloud between N atom and C atom is obviously inclined to N atom, thus forming a polar covalent bond. According to Paulin’s calculation method, the electronegativity of C and N are 2.55 and 3.04, respectively.
Fig. 6. The calculated electronic band structure, DOS and PDOS of (a) (6,6) AC3NSWNT and (c) (10,0) Z-C3NSWNT. The charge density distribution of (b) (6,6) A-C3NSWNT and (d) (10,0) Z-C3 NSWNT, where magenta indicates an increase in electrons, and blue indicates a decrease in electrons. The dashed lines with arrows in the figure represent different atomic layers. The same atoms in the same color dashed layer have the same gain and loss electrons. The 3 isosurface value is 0.02jej� A . (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
The electronegativity of N atom is different from that of C atom, so there is charge transfer between adjacent C and N atoms. The data on the upper and lower sides of C3NSWNT in Fig. 6(b) and (d) indicates the number of gain and loss electrons of C or N. As we all know, according to electronegativity, N atom has a stronger ability to attract electrons than C atom. However, the large π bond formed in the C3N structure would increase the density of the electron cloud on the six-membered ring, resulting in an electrophilic behavior. This electrophilic behavior is more attractive to the N atom with two remaining electrons after sp2 hybridization, resulting in the loss of electrons in the N atom. Each N atom is connected with three C atoms, and the lost electrons of N atom are exactly equal to the sum of the gained electrons of the three C atoms 4
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lattice constants of the supercell before and after the strain, respectively. When ϵ is positive, the system is in a stretched state; conversely, if ϵ is negative, the system is in a compressed state. The calculation formula is E1 ¼ ∂Eedge/∂ϵ, in which Eedge is the band edge energy of CBM and VBM in the transport direction. For all 1D semiconductor nanotubes, the method for calculating carrier mobility is identical. Therefore, only the calcu lation process of carrier mobility for a (6,6) A-C3NSWNT is given here, as shown in Fig. 7(a) and (b). Fig. 7(a) shows the change of total energy with the strain, and a quadratic fitting is carried out. In terms of the definition of the tensile modulus, we obtain that C1 is equal to 271.60 eV/Å. The relationship between the energy of the CBM and VBM states as a function of the uniaxial strain in the transport direction is shown in Fig. 7(b). In terms of the deformation potential constant E1, we obtain that the deformation potential constant of electrons is 5.06 eV and that of holes is 1.46 eV. Thus in terms of Eq. (1), we obtain that electron and hole mobilities are 471.37 cm2V 1s 1 and 9656.36 cm2V 1s 1, respec tively. The electron mobility calculation data of two groups of semi conductor C3 NSWNT with similar diameters and different types are listed in Table 1. From the Table 1, we can see that the hole mobility is greater than the electron mobility except for (10,0) Z-C3NSWNT. The benzene ring-like structure has electron rich characteristics, which has obviously strong ability of hole transfer. The hole mobility reached 15878.70 cm2V 1s 1 for (8,8)A-C3NSWNT. The electron mobility of (n, n) A-C3NSWNT is lower than that of (n,0) Z-C3NSWNT, but the hole mobility of (n,n) A-C3NSWNT is higher than that of (n,0) Z-C3NSWNT. The carrier polarity of (n,n) A-C3NSWNT is relatively significant, and its hole mobility is more than 20 times that of electron mobility. In most cases, the mobility values of these carriers are larger than those of other nanotubes, such as carbon nanotubes [46], MoS2 nanotubes [47], WS2 nanotubes [48], phosphorene nanotubes [49] and black phosphorus nanotubes [50]. Therefore the C3NSWNT is a good candidate material for high performance nanodevices. The Bloch state of CBM and VBM corresponding to (6,6) A-C3NSWNT are shown in Fig. 7(c) and (d), which correspond to the transport ca pacity of electrons and holes. The wave function of the CBM state is relatively local. On the contrast, the wave function distribution of the VBM state shows a strong delocalization characteristic, and its wave
Table 1 Tensile modulus C1, deformation potential constant E1, effective mass m* and mobility μ of two groups of C3NSWNTs with similar diameters along the trans port direction. Structure
Type
C1 (eV� A )
|E1| (eV)
|m*| (me)
μ (cm2V 1s 1)
(6,6)
Electron Hole Electron Hole Electron Hole Electron Hole
271.60
5.06 1.46 1.20 1.34 5.08 1.51 2.76 1.02
0.317 0.222 0.649 0.832 0.314 0.180 0.469 0.913
471.37 9656.36 2720.80 1503.75 607.12 15878.70 1126.10 3065.83
(10,0) (8,8) (14,0)
1
259.14 348.11 347.38
connected with N atom, which satisfies the law of charge conservation. The edge characteristics of the highest valence band (HVB) and the lowest conduction band (LCB) are important to the transport of carriers along the C3NSWNT extension direction. Based on the theory of defor mation potential [41], we calculate the mobility of two groups of C3NSWNT with different types but similar diameters, in which phonon scattering is the main mechanism affecting carrier drift, and longitudinal wave is the most relevant factor determining carrier mobility [42]. For 1D semiconductor systems, the analytical expression of carrier mobility is [43–45] eℏ2 C
μ1D ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 1 3=2 2 ; 2πkB T jm� j E1
(1)
where μ1D is the mobility, e is the electronic charge, and ℏ is the reduced Planck constant, kB is Boltzmann constant, and T is temperature. In the calculation, we take T as 300 K m* is the effective mass of carriers in the transport direction. Based on the free electron model, it is defined as
m� ¼ ℏ2 ð∂2 EðkÞ=∂k2 Þ 1 in which E(k) is energy and k is wave vector. E1 is the deformation potential constant of the HVB corresponding to the hole and the LCB corresponding to the electron. C1 ¼ (∂2Etotal/∂ϵ2)/L0 is the tensile modulus under uniaxial strain, where Etotal is the total energy of a supercell, and ϵ ¼ (L L0)/L0 � 100% is strain in which L0 and L are the
Fig. 7. (a) The relationship between the total energy and the strain ϵ in the transport direction, and the red curve is derived from the quadratic fitting. (b) The energy of CBM and VBM varies with strain. The blue/ red line is a linear fit to CBM/VBM, respectively. The Bloch state of (c) CBM and (d) VBM corresponding to (6,6) A-C 3NSWNT. The isosurfaces value is 0.02 3 jej� A . (e) Poisson’s ratio as a function of the strain in the transport direction. (For interpretation of the ref erences to color in this figure legend, the reader is referred to the Web version of this article.)
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function in the stretching direction (transport direction) has a strong overlap, which means a higher carrier mobility [51]. For the selected (6, 6) A-C3 NSWNT supercell, the wave function of the CBM state is contributed by 24 C atoms, while the wave function of the VBM state is composed of 12 C atoms and 12 N atoms contribution. The electroneg ativity of the N atom is greater than that of the C atom, which means that VBM will generate more holes. Therefore hole transport is more likely to occur in the direction of cyclic extension of C3NSWNT, which results in hole mobility being 20.5 times larger than the electron mobility as shown in Table 1. The polarity of the carriers is very important in the photocatalytic process. We studied the elastic characteristics of C3N nanotubes with the analysis method of Poisson’s ratio [52]. Poisson’s ratio is defined as v ¼
ϵy/ϵz [53], in which ϵy and ϵz are deformation ratios in the y- and z-axis directions, respectively. The calculation results are shown in Fig. 7(e). When strain change from 0 to 0.04, the Poisson’s ratios of the A-C3 NSWNT and Z-C3NSWNT are negative, and have a consistent trend of increase from negative value to zero with the increasing strain. When the axial strain ratio is above 0.05, the Poisson ratio of two types of C3NSWNT show an oscillation mode and a similar trend of decrease with the increasing strain. Therefore, it is feasible to regulate C3NSWNT through deformation or strain. The most common method to tune the electronic properties of nanostructures is to apply an electric field or a strain. The effect of an external electric field perpendicular to the axial direction on the elec tronic properties of the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT are Fig. 8. The band structure of the (6,6) A-C3NSWNT under different external (a) electric field and (b) strain, respectively. The partial charge density of HVB for the (6,6) A-C3NSWNT at two different (c) field strengths and (d) strains, respectively. The band structure of the (10,0) Z-C3NSWNT under different external (e) electric field and (f) strain, respectively. The partial charge density of HVB for the (10,0) ZC3NSWNT at two different (g) electric field strengths and (h) strains, respectively. The isosurface value is 3 0.4 jej� A .
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shown in Fig. 8(a) and (e), respectively. Due to the structural symmetry of the two C3NSWNTs, the calculated results are the same when the voltage is applied up or down in the direction perpendicular to the axis. As the electric field increases from 0 to 0.5 V/Å, the LCB moves down and HVB moves up, the band gap decreases monotonically. When the electric field strength increases to 0.5 V/Å/0.4 V/Å, there is a semi conductor to metal transition occurs for (6,6) A-C3NSWNT as shown in Fig. 8(a)/(10,0) Z-C3NSWNT as shown in Fig. 8(e). The intrinsic band gap of (10,0) Z-C3NSWNT (Egap ¼ 0.096 eV) is smaller than that of (6,6) A-C3NSWNT (Egap ¼ 0.435 eV), so there is smaller electric field needed for semiconductor to metal phase transition in the case of (10,0) ZC3NSWNT. In order to illustrate the physical mechanism, we have plotted the partial charge density distributions of HVB at two typical electric fields 0 V/Å and 0.5 V/Å as shown in Fig. 8(c) and (g). In the absence of the external electric field, the partial charge density of HVB for the (6,6) A-C3NSWNT is mainly concentrated on the upper and lower sides of (6,6) A-C3NSWNT(see Fig. 8(c)), but the partial charge density of HVB for the (10,0) Z-C3 NSWNT is distributed on each N atom (see Fig. 8(g)), which results in the bandgap of (6,6) A-C3NSWNT is wider than that of (10,0) Z-C3NSWNT. When the electric field is 0.5 V/Å, there exists a potential energy difference between two edge of the C3NSWNT, which makes LCB moves down and HVB moves up with electric field. The change of Bloch state in nanotubes without and with electric field is caused by strong electric polarization induced by external electric field. The effect of strain in the axial direction on the electronic properties of the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT are shown in Fig. 8(b) and (f), respectively. Fig. 8(b) corresponds to (6,6) A-C3NSWNT. The band gap increases with the increase of compressive strain (strain ϵ is in the range of 10% ~0), but decreases with the increase of tensile stress (strain ϵ is in the range of 0 ~10%). When the tensile stress reaches 10%, there is the transition from semiconductor to metal. The partial charge density is mainly distributed on the upper and lower sides of (6,6) AC3NSWNT in the absence of the strain, then is transferred from the two sides of the nanotube to the middle of the nanotube when the tensile stress reached 10%, which is as shown in Fig. 8(d). The change in the atomic orbital distribution cause the phase transition. While for (10,0) Z-C3NSWNT, the band gap has never been reduced to 0 when the strain changes from 10% to 10% (see Fig. 8(f)). Under the effect of tensile stress, the band gap always increases with the increase of tensile strain. There is no significant change in the partial charge density distribution when the strain changes from 0% to 10%(see Fig. 8(h)). Therefore, (6,6) A-C3 NSWNT is more suitable to the application in nano electrome chanical switching devices.
All data generated or analyzed during this study are included in this article. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Zhanhai Li: Data curation, Writing - original draft. Fang Cheng: Conceptualization, Writing - review & editing. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No 11374002, Scientific Research Fund of Hunan Provincial Education Department 17A001, Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province and the construct program of the key discipline in hunan province. References [1] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56–58. [2] S. Iijima, T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature 363 (1993) 603–605. [3] D.S. Bethune, C.H. Kiang, M.S. De Vries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers, Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls, Nature 363 (1993) 605–607. [4] C.W. Padgett, D.W. Brenner, Influence of chemisorption on the thermal conductivity of single-wall carbon nanotubes, Nano Lett. 4 (2004) 1051–1053. [5] C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube, Nano Lett. 5 (2005) 1842–1846. [6] L. Chico, V.H. Crespi, L.X. Benedict, S.G. Louie, M.L. Cohen, Pure carbon nanoscale devices: nanotube heterojunctions, Phys. Rev. Lett. 76 (1996) 971. [7] T.W. Ebbesen, H.J. Lezec, H. Hiura, J.W. Bennett, H.F. Ghaemi, T. Thio, Electrical conductivity of individual carbon nanotubes, Nature 382 (1996) 54–56. [8] Jean-Paul Salvetat, et al., Elastic modulus of ordered and disordered multiwalled carbon nanotubes, Adv. Mater. 11 (1999) 161–165. [9] G. Overney, W. Zhong, D. Tomanek, Structural rigidity and low frequency vibrational modes of long carbon tubules, Z. Physik D Atoms, Mol. Clust. 27 (1993) 93–96. [10] E.W. Wong, P.E. Sheehan, C.M. Lieber, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes, Science 277 (1997) 1971–1975. [11] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Carbon nanotube functionalization with carboxylic derivatives: a DFT study, J. Mol. Model. 19 (2013) 391–396. [12] K.W. Lee, C.E. Lee, Antiferromagnetic edge states in carbon nanotubes with hydrogen line defect abundancy, Curr. Appl. Phys. 15 (2015) 163–168. [13] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Hydrogen dissociation on dienefunctionalized carbon nanotubes, J. Mol. Model. 19 (2013) 255–261. [14] Joo-Hyung Kim, et al., A flexible paper transistor made with aligned single-walled carbon nanotube bonded cellulose composite, Curr. Appl. Phys. 13 (2013) 897–901. [15] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Nitrate adsorption by carbon nanotubes in the vacuum and aqueous phase, Monatsh. Chem. Chem. Monthly 143 (2012) 1623–1626. [16] Dong-Lai Wang, et al., Comparative study of the electrostatic potential of perfect and defective single-walled carbon nanotubes, Comput. Theor. Chem. 966 (2011) 1–8. [17] R. Czerw, et al., Identification of electron donor states in N-doped carbon nanotubes, Nano Lett. 1 (2001) 457–460. [18] J. Hales, A.S. Barnard, Thermodynamic stability and electronic structure of small carbon nitride nanotubes, J. Phys. Condens. Matter 21 (2009), 144203. [19] Mohan SR. Elapolu, et al., Phononic thermal transport properties of C3N nanotubes, Nanotechnology 31 (2019), 035705. [20] X. Cheng, X. Wang, Thermal transport in C3N nanotube: a comparative study with carbon nanotube, Nanotechnology 30 (2019), 255401. [21] H. Wang, H. Wu, J.C.3N. Yang, A Two Dimensional Semiconductor Material with High Stiffness, Superior Stability and Bending Poisson’s Effect, 2017. arXiv: 1703.08754. [22] Seifollah Jalili, et al., Role of Defects on structural and electronic properties of zigzag C3N nanotubes: a first-principle study, Phys. E Low-dimens. Syst. Nanostruct. 56 (2014) 48–54. [23] A. Bafekry, C. Stampfl, S. Farjami Shayesteh, A first-principles study of C3N nanostructures: control and engineering of the electronic and magnetic properties of nanosheets, tubes and ribbons, ChemPhysChem 21 (2020) 164–174.
4. Conclusion In summary, we have investigated that the structure and electronic properties of (n,n) A-C3NSWNT and (n,0) Z-C3NSWNT in terms of the first-principles method of density functional theory. We find that the C3NSWNT system has high structural stability. The electronic properties of C3NSWNT is dependent of the chirality index n and the edge types. Both A-C3NSWNT and Z-C3NSWNT can transfer from semiconductor to metal by applying an electric field, and Z-C3NSWNT is more sensitive to the applied electric field than A-C3NSWNT due to smaller energy gap. But only A-C3NSWNT can transfer from semiconductor to metal by applying strain. The dramatic difference between the hole and electron mobilities also exists in C3NSWNTs. Moreover, our results suggest that the carrier mobility of C3NSWNTs can be adjusted by diameter and edge engineering. These results can provide some theoretical support for the development of nanodevices, and it is of great significance to explore the potential applications of nanomaterials based on C3NSWNT. Availability of data and materials The authors declare that materials and data are promptly available to readers without undue qualifications in material transfer agreements. 7
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Contents lists available at ScienceDirect
Physica E: Low-dimensional Systems and Nanostructures journal homepage: http://www.elsevier.com/locate/physe
Structure and electronic properties of single-walled C3N nanotubes Zhanhai Li , Fang Cheng * Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha, 410004, China
A B S T R A C T
One-dimensional nanotubes have become an indispensable ideal candidate material for nano-device applications due to their excellent and unique electronic, mechanical, and thermal properties. By the first-principles method of density functional theory, we have theoretically investigated the structural stability, electronic properties, carrier mobility, and Poisson’s ratio of C3N single-walled nanotubes (C3NSWNT). We find that C3NSWNT is stable and the ground state of the system is non-magnetic. The electronic properties and carrier mobilities of C3NSWNT can be adjusted by diameter and edge engineering. The electron mobility of (n,n) armchair C3NSWNT (A-C3NSWNT) is lower than that of (n,0) zigzag C3NSWNT (Z-C3NSWNT), but the hole mobility of (n,n) A-C3NSWNT is higher than that of (n,0) Z-C3NSWNT. Moreover, both A-C3NSWNT and Z-C3NSWNT can transfer from semiconductor to metal by tuning the electric field, and Z-C3NSWNT is more sensitive to the applied electric field than A-C3NSWNT due to smaller energy gap. But only A-C3NSWNT can transfer from semiconductor to metal by tuning strain, and be more suitable to the application in nano electromechanical switching devices. These research results may provide some theoretical support for the potential application and development of nanoelectronic devices based on C3NSWNT.
1. Introduction Since the first discovery of multi-walled carbon nanotubes in 1991 [1] and the successful preparation of single-walled carbon nanotubes in 1993 [2,3], carbon nanotubes (CNTs) have rapidly become a research hotspot. Due to unique mechanical and thermal properties [4–10], they have a broad application prospects in the field of materials science, optics, nanoelectronics, nanotechnology [11–16]. Replacing some car bon atoms of CNTs by other elements like N can efficiently alter the electronic properties and come into being new applications. Multi-walled CNx nanotubes have been successfully prepared by pyro lyzing ferrocence/setminusmelamine mixtures in a high-temperature argon atmosphere at 1050 � C [17]. The relaxation structure of C3N single wall nanotubes (C3NSWNT) was reported to be independent of the chirality of nanotubes [18]. C3NSWNT has higher thermal conductivity and is affected by its length, chirality, and uniaxial strain [19,20]. And most of C3NSWNT are semiconductors with high Young’s modulus [21]. Zigzag C3NSWNT with vacancy defects exhibited ferromagnetic spin alignment [22]. The H atom adsorption have significant effects on the electronic structure of C3NSWNT [23]. The C3NSWNT is well suited for a hydrogen storage material [24,25]. As a member of the graphene-like materials, however, the research on the energetic, structure and electronic properties of C3NSWNT is not comprehensive enough. In this paper, we investigate the chirality index n -dependence of the electronic properties of two typical nanotubes, i. e., armchair C3NSWNT(A-C3NSWNT) and zigzag C3NSWNT(Z-C3 NSWNT),
in terms of the first principle method of density functional theory. The electron mobility of (n,n) A-C3NSWNT is lower than that of (n,0) Z-C 3NSWNT, but the hole mobility of (n,n) A-C3NSWNT is higher than that of (n,0) Z-C3NSWNT. The band gap can be modulated and the C3 NSWNT can transfer from semiconductor to metal by tuning electric field, strain and the zigzag and armchair edges. 2. Model and method The optimization of the structure, the evaluation of structural sta bility, and the calculation of electronic performance are all based on the density functional theory (DFT). All calculations are completed by using Atomistix ToolKit (ATK) package [26–28] developed by the first prin ciple, which has been widely used in the research of nanostructures [29–36]. To solve the Kohn-Sham equation, the spin-polarized Per dew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional was used to describe the exchange-correlation term of elec trons. It is accurate enough to calculate the total energy of atoms and the binding energy of small molecules. But the electronic band gap calcu lated in terms of the GGA functional would be slightly lower than the experimental value. And the elastic modulus calculated by GGA func tional is relatively soft. Taking into account the effect of atomic polar ization, the eigenfunction of electrons is a linear combination of atomic orbits. Double-zeta plus polarization (DZP) is used as the extended wave function of the basis function group for all atoms. The selection of base group determines the accuracy of calculation. C and N are light
* Corresponding author. E-mail address: [email protected] (F. Cheng). https://doi.org/10.1016/j.physe.2020.114320 Received 28 April 2020; Received in revised form 18 June 2020; Accepted 22 June 2020 Available online 10 July 2020 1386-9477/© 2020 Elsevier B.V. All rights reserved.
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elements, thus it is completely sufficient to select the DZP base group for geometric optimization and property calculation. Troullier Martins norm-conserving pseudopotential is used to approximate the atomic kernel. 1 � 1 � 100 k-point samples are taken in the x-, y-, and z -axis directions of the first Brillouin zone, where the z-axis direction is the nanotube transmission direction. The value of the Mesh cut-off is mainly used to solve the Poisson equation and control the size of the real space integral network, and to ensure the balance of calculation accuracy and efficiency. We set it as 150 Ry (1 Ry ¼ 13.60 eV). The interaction be tween the model and its “image” is eliminated by selecting a vacuum cell larger than 1.5 nm in the x- and y-axis directions. All calculations are optimized by the Quasi Newton method until all residual forces on each atom are within 0.02 eV/Å. For research purposes, the Fermi energy levels of all nanotubes are set to zero. Similar to carbon nanotubes (CNTs), aC3NSWNT is formed by rolling a single layer of C3N nanoribbons into a cylinder. The atomic structure of C3NSWNT can be described by the chiral vector Ch ¼ na1 þ ma2, where a1 and a2 are unit vectors with the same head in the same hexagonal lattice and the tail at the adjacent zigzag end. The integer (n, m) is the number of steps of the zigzag bond. When m ¼ 0, C3NSWNT is a zigzag nanotube (Z-C3 NSWNT), then (n, 0) Z-C3NSWNT is used as the general term of all Z-C3NSWNT (chiral angle is 0� ). When n ¼ m, C3NSWNT is armchair nanotube (A-C3NSWNT). And (n, n) A-C3NSWNT is used as the general term of all A-C3NSWNT (chiral angle is 30� ). The rest of n and m values are all chiral C3NSWNT (C-C3NSWNT). We have selected two classical types of nanoribbons (zigzag and armchair nanoribbons), and rolled them into nanotubes as shown in Fig. 1. The shaded parts in Fig. 1 correspond to the nanoribbon used by the supercell during the coiling process. The actual research process is based on the nanotube extending infinitely along the transport direction. The band gap varies with diameter [37]. Due to the high hybridization caused by curvature [38], the tight binding method cannot accurately describe small diameter C3NNT. It is well known that the local density approximation(LDA) method is overly inclined to bind atoms, so bond lengths are usually underestimated by several percentage points [39].
shows that the energy difference between the ferromagnetic state (FM) and the antiferromagnetic state (AFM) is 0. This is because the magne tism of an isolated atom is mainly determined by the number of electrons in the outermost layer of the atomic orbital. The outermost 2p orbital of the C atom contains 2 electrons and the outermost 2p orbital of the N atom contains 3 electrons. After the formation of carbon-nitrobenzene ring, they all exist as a pair of covalent bonds. The system under study is a periodic nanotube, with both ends extending indefinitely, so there are no dangling bonds. To further determine whether the ground state of the system is magnetic (FM) or non-magnetic (NM), we calculated the magnetization energy (EM) of the system, which is defined as EM ¼ (EFM ENM)/Nt. Here, EFM and ENM are the total energy of the supercell in the FM and NM states, respectively, and Nt is the total number of atoms in the supercell. If the calculated magnetization energy is negative and its absolute value is sufficiently large, then the ground state of the system is a ferromagnetic (FM) state. However, the calculation results show that all infinitely extending nanotubes have a magnetization energy of 0 regardless of the value of the chiral index n. This indicates that the system is unlikely to be magnetic at limited temperatures. Therefore, the following research systems are all in the NM state. To test the thermal stability of the nanotubes, we have chose to perform the Born–Oppenheimer Molecular Dynamics (BOMD) simula tion in the NVT ensemble through the Nos�e thermal bath scheme. Fig. 2 (a) and (b) is a schematic diagram of the structure after (6,6) AC3NSWNT/(10,0) Z-C3NSWNT stays at 8ps in different temperature environments. It can be seen from Fig. 2(a) and (b) that the two types of nanotubes have basically not changed at a temperature of 500 K. When the temperature further increases, the C and N atoms all relax on the basis of their equilibrium positions, and the N atom relaxation is more significantly. From the left view of C3 NSWNT, we find that there will be a more obvious deformation at the position of each N atom, which will be more obvious with the increase of temperature. By observing the deformation degree of two kinds of nanotubes at different temperatures, it can be found that the deformation of nanotubes is more and more obvious with the increase of temperature, but the two kinds of nano tubes have never been reconstructed at 2000K, which proves that C3 NSWNT has better thermal stability. The band gap of C3NSWNT are plotted as the function of chirality
3. Results and discussion The spin-polarization exchange-correlation function calculation
Fig. 1. The structure of monolayer C3N sheet, in which the shaded part is the minimum periodic repeating unit nanoribbon required for the (a) (6,6) AC3NSWNT and (b) (10,0) Z-C3NSWNT supercell. The middle and right part of Fig. 1(a) and (b) are the left and front views of the nanotubes, respectively.
Fig. 2. (a) (6,6) A-C3NSWNT and (b) (10,0) Z-C3 NSWNT show the results of BOMD simulations at different temperatures (the left/right part is the left/front view of single-walled nanotubes at the same temperature). 2
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index n in Fig. 3. For the armchair-type nanotubes, the band gap is al ways 0 (metal) for an odd number n, but is always not equal to 0 (semiconductor) for even n. All semiconductors have direct band gaps, the band gap increases gradually in the range of small diameter (n ¼ 3–10), and decreases in the range of large diameter (n ¼ 10–14). For zigzag nanotubes, the band gap is always not equal to 0 (semiconductor) for odd n (n ¼ 3–9), but is zero (metal) for even n, which is opposite to that for armchair nanotubes. When n ¼ 5, 7, 11, 13, the band gap of ZC3NSWNT belongs to indirect band gap, the rest are all direct band gap. In the case of large zigzag nanotube diameter (n ¼ 9–14), the band gap decreases/increases with the increasing odd/even nanotube diameter n. By rolling up C3N nanoribbons the electron wave functions are subjected to an additional quantization condition, essentially ‘cutting’ one dimension slices out of the formerly two dimension band structure of C3N nanoribbons [40]. The binding energy is used to evaluate the structural stability of the studied system in isolated atomic states, which is defined as Eb ¼ (Etotal nNEN nCEC)/(nN þ nC). Here, Etotal is the total energy obtained by calculating the supercell system, nN/nC is the number of N/C atoms contained in the supercell, and EN/EC is the energy of one atom when the N/C atom is an isolated atomic state. As shown in Fig. 3(a) and (b), the binding energy of the armchair-type and zigzag-type nanotubes is al ways negative and less than 8.5 eV, which show that the system has good structural stability. The binding energy of the nanotubes decreases with the increase of the nanotube diameter. The smaller the negative value, the more stable the structure. Therefore the structural stability of the nanotubes will increase with the increase of the nanotube diameter. For the same chiral index n, the absolute value of the binding energy of A-C3NSWNT is larger than that of that of Z-C3NSWNT, so the stability of A-C3NSWNT is stronger than that of Z-C3NSWNT. The stability of the structure can also be described by the thermo dynamic properties of the material. The Gibbs free energy of the (6,6) AC3 NSWNT and (10,0) Z-C3NSWNT between 200 K ~ 1000 K are shown in Fig. 4(a). The Gibbs free energy of both (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT are negative, and shows a downward trend as the tem perature increases. Generally speaking, the lower the Gibbs free energy of the structure, the higher the thermodynamic stability. Thus both the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT have good stability. We have plotted the phonon dispersion spectra of both the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT as shown in Fig. 4(b) and (c). It can be seen that there is no virtual frequency in the entire Brillouin region, which
Fig. 4. (a) Temperature-dependent Gibbs free energy for (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT. The phonon dispersion of (b) (6,6) A-C3NSWNT, and (c) (10,0) Z-C3NSWNT, respectively.
indicates that C3NSWNTs are dynamically stable. Fig. 5 shows the gradual relationship between the bond length and the bond angle in the range of 3–14 for the chiral index n. The three bond lengths d1, d2, and d3 of A-C3NSWNT decrease with the increase of n from 3 to 8, and are basically stable at a certain value when n change from 9 to 14. The changes in three bond lengths are mainly affected by the bond strain on the curvature surface. The smaller the diameter, the larger the curvature. This effect is the most obvious for bonds parallel to the direction of curl, such as d3 in (n,n) A-C3NSWNT. As the diameter of the nanotube further increases, the curvature gradually decreases, and the bond length does not change. On the contrast, the bond lengths d1 and d3 of Z-C3NSWNT decrease with the increase of n from 3 to 14, but
Fig. 3. (a) and (b) indicate the change of bandgap and binding energy of A-C 3NSWNT and Z-C3NSWNT with n respectively. 3
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Fig. 5. The structure diagram of the mark, the relationship between the bond length and the bond angle with the chiral index n for (a) (6,6) A-C3NSWNT and (b) (10,0) Z-C3NSWNT, respectively.
the d2 bond of Z-C3NSWNT increases with the increase of n from 3 to 14. The d2 bond is perpendicular to the direction of curl, so it is independent of the bond strain on the curvature surface. From the Fig. 5, it can be seen that the bond angle always increases with the diameter of the nanotube n until it is consistent with the bond angle of two dimension materials. When the nanotube diameter is small, the curvature would be large, there would be a “folding” effect on the bond angles of the nanotubes. In the process of increasing nanotube diameter, it is equiv alent to the process of carbon nitrogen benzene ring slowly bending deformion and returning to the original state. Therefore the bond angle always increases with the increasing nanotube diameter. To understand the basic physical properties of the two types nano tubes, we need to explore their electronic structures. Fig. 6(a) and (c) show the band structure, total density of states (TDOS), and the pro jected density of states (PDOS) of elements and orbits of the intrinsic nanotubes. Obviously, both nanotubes are semiconductors. The con duction band minimum (CBM) and valence band maximum (VBM) of the two nanotubes are at the Γ point, so they are all direct band gaps. The band gap is 0.435 eV for (6,6) A-C3NSWNT and 0.096 eV for (10,0) ZC3NSWNT. For the (6,6) A-C3 NSWNT, the CBM and VBM bandwidths are sufficiently wide, which shows that the atomic orbital of the corre sponding energy band has a strong expansibility, a large degree of nonlocality and a small effective mass of electrons. Conversely, for the (10,0) Z-C3NSWNT, there is the relatively narrow band, so electrons have a very strong locality and the effective mass of electrons is rela tively large. This analysis results are consistent with the calculation results in Table 1. The density of states (DOS) is a visualization of the band structure. From the DOS diagrams of Fig. 6(a) and (c), it can be found that the Fermi energy levels are all in the range where the DOS value is zero, indicating that the system is a semiconductor. From the PDOS of atom, we can clearly see that the atomic orbital contribution mainly comes from the 2p orbital of C and N atoms, but the C-2p orbital contribution is more significant. The band structure of the studied sys tem is mainly determined by the orbital hybridization and electron transfer between the C and N atoms. We calculated the charge density difference in Fig. 6(b) and (d) where the increase and decrease of electrons relative to the isolated atomic state are represented by the magenta and blue areas. It can be clearly seen that electrons are always accumulated on the covalent bond formed by adjacent C and C (or C and N) atoms. The regular covalent bonds are formed between adjacent C atoms, but the electron cloud between N atom and C atom is obviously inclined to N atom, thus forming a polar covalent bond. According to Paulin’s calculation method, the electronegativity of C and N are 2.55 and 3.04, respectively.
Fig. 6. The calculated electronic band structure, DOS and PDOS of (a) (6,6) AC3NSWNT and (c) (10,0) Z-C3NSWNT. The charge density distribution of (b) (6,6) A-C3NSWNT and (d) (10,0) Z-C3 NSWNT, where magenta indicates an increase in electrons, and blue indicates a decrease in electrons. The dashed lines with arrows in the figure represent different atomic layers. The same atoms in the same color dashed layer have the same gain and loss electrons. The 3 isosurface value is 0.02jej� A . (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
The electronegativity of N atom is different from that of C atom, so there is charge transfer between adjacent C and N atoms. The data on the upper and lower sides of C3NSWNT in Fig. 6(b) and (d) indicates the number of gain and loss electrons of C or N. As we all know, according to electronegativity, N atom has a stronger ability to attract electrons than C atom. However, the large π bond formed in the C3N structure would increase the density of the electron cloud on the six-membered ring, resulting in an electrophilic behavior. This electrophilic behavior is more attractive to the N atom with two remaining electrons after sp2 hybridization, resulting in the loss of electrons in the N atom. Each N atom is connected with three C atoms, and the lost electrons of N atom are exactly equal to the sum of the gained electrons of the three C atoms 4
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lattice constants of the supercell before and after the strain, respectively. When ϵ is positive, the system is in a stretched state; conversely, if ϵ is negative, the system is in a compressed state. The calculation formula is E1 ¼ ∂Eedge/∂ϵ, in which Eedge is the band edge energy of CBM and VBM in the transport direction. For all 1D semiconductor nanotubes, the method for calculating carrier mobility is identical. Therefore, only the calcu lation process of carrier mobility for a (6,6) A-C3NSWNT is given here, as shown in Fig. 7(a) and (b). Fig. 7(a) shows the change of total energy with the strain, and a quadratic fitting is carried out. In terms of the definition of the tensile modulus, we obtain that C1 is equal to 271.60 eV/Å. The relationship between the energy of the CBM and VBM states as a function of the uniaxial strain in the transport direction is shown in Fig. 7(b). In terms of the deformation potential constant E1, we obtain that the deformation potential constant of electrons is 5.06 eV and that of holes is 1.46 eV. Thus in terms of Eq. (1), we obtain that electron and hole mobilities are 471.37 cm2V 1s 1 and 9656.36 cm2V 1s 1, respec tively. The electron mobility calculation data of two groups of semi conductor C3 NSWNT with similar diameters and different types are listed in Table 1. From the Table 1, we can see that the hole mobility is greater than the electron mobility except for (10,0) Z-C3NSWNT. The benzene ring-like structure has electron rich characteristics, which has obviously strong ability of hole transfer. The hole mobility reached 15878.70 cm2V 1s 1 for (8,8)A-C3NSWNT. The electron mobility of (n, n) A-C3NSWNT is lower than that of (n,0) Z-C3NSWNT, but the hole mobility of (n,n) A-C3NSWNT is higher than that of (n,0) Z-C3NSWNT. The carrier polarity of (n,n) A-C3NSWNT is relatively significant, and its hole mobility is more than 20 times that of electron mobility. In most cases, the mobility values of these carriers are larger than those of other nanotubes, such as carbon nanotubes [46], MoS2 nanotubes [47], WS2 nanotubes [48], phosphorene nanotubes [49] and black phosphorus nanotubes [50]. Therefore the C3NSWNT is a good candidate material for high performance nanodevices. The Bloch state of CBM and VBM corresponding to (6,6) A-C3NSWNT are shown in Fig. 7(c) and (d), which correspond to the transport ca pacity of electrons and holes. The wave function of the CBM state is relatively local. On the contrast, the wave function distribution of the VBM state shows a strong delocalization characteristic, and its wave
Table 1 Tensile modulus C1, deformation potential constant E1, effective mass m* and mobility μ of two groups of C3NSWNTs with similar diameters along the trans port direction. Structure
Type
C1 (eV� A )
|E1| (eV)
|m*| (me)
μ (cm2V 1s 1)
(6,6)
Electron Hole Electron Hole Electron Hole Electron Hole
271.60
5.06 1.46 1.20 1.34 5.08 1.51 2.76 1.02
0.317 0.222 0.649 0.832 0.314 0.180 0.469 0.913
471.37 9656.36 2720.80 1503.75 607.12 15878.70 1126.10 3065.83
(10,0) (8,8) (14,0)
1
259.14 348.11 347.38
connected with N atom, which satisfies the law of charge conservation. The edge characteristics of the highest valence band (HVB) and the lowest conduction band (LCB) are important to the transport of carriers along the C3NSWNT extension direction. Based on the theory of defor mation potential [41], we calculate the mobility of two groups of C3NSWNT with different types but similar diameters, in which phonon scattering is the main mechanism affecting carrier drift, and longitudinal wave is the most relevant factor determining carrier mobility [42]. For 1D semiconductor systems, the analytical expression of carrier mobility is [43–45] eℏ2 C
μ1D ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 1 3=2 2 ; 2πkB T jm� j E1
(1)
where μ1D is the mobility, e is the electronic charge, and ℏ is the reduced Planck constant, kB is Boltzmann constant, and T is temperature. In the calculation, we take T as 300 K m* is the effective mass of carriers in the transport direction. Based on the free electron model, it is defined as
m� ¼ ℏ2 ð∂2 EðkÞ=∂k2 Þ 1 in which E(k) is energy and k is wave vector. E1 is the deformation potential constant of the HVB corresponding to the hole and the LCB corresponding to the electron. C1 ¼ (∂2Etotal/∂ϵ2)/L0 is the tensile modulus under uniaxial strain, where Etotal is the total energy of a supercell, and ϵ ¼ (L L0)/L0 � 100% is strain in which L0 and L are the
Fig. 7. (a) The relationship between the total energy and the strain ϵ in the transport direction, and the red curve is derived from the quadratic fitting. (b) The energy of CBM and VBM varies with strain. The blue/ red line is a linear fit to CBM/VBM, respectively. The Bloch state of (c) CBM and (d) VBM corresponding to (6,6) A-C 3NSWNT. The isosurfaces value is 0.02 3 jej� A . (e) Poisson’s ratio as a function of the strain in the transport direction. (For interpretation of the ref erences to color in this figure legend, the reader is referred to the Web version of this article.)
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function in the stretching direction (transport direction) has a strong overlap, which means a higher carrier mobility [51]. For the selected (6, 6) A-C3 NSWNT supercell, the wave function of the CBM state is contributed by 24 C atoms, while the wave function of the VBM state is composed of 12 C atoms and 12 N atoms contribution. The electroneg ativity of the N atom is greater than that of the C atom, which means that VBM will generate more holes. Therefore hole transport is more likely to occur in the direction of cyclic extension of C3NSWNT, which results in hole mobility being 20.5 times larger than the electron mobility as shown in Table 1. The polarity of the carriers is very important in the photocatalytic process. We studied the elastic characteristics of C3N nanotubes with the analysis method of Poisson’s ratio [52]. Poisson’s ratio is defined as v ¼
ϵy/ϵz [53], in which ϵy and ϵz are deformation ratios in the y- and z-axis directions, respectively. The calculation results are shown in Fig. 7(e). When strain change from 0 to 0.04, the Poisson’s ratios of the A-C3 NSWNT and Z-C3NSWNT are negative, and have a consistent trend of increase from negative value to zero with the increasing strain. When the axial strain ratio is above 0.05, the Poisson ratio of two types of C3NSWNT show an oscillation mode and a similar trend of decrease with the increasing strain. Therefore, it is feasible to regulate C3NSWNT through deformation or strain. The most common method to tune the electronic properties of nanostructures is to apply an electric field or a strain. The effect of an external electric field perpendicular to the axial direction on the elec tronic properties of the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT are Fig. 8. The band structure of the (6,6) A-C3NSWNT under different external (a) electric field and (b) strain, respectively. The partial charge density of HVB for the (6,6) A-C3NSWNT at two different (c) field strengths and (d) strains, respectively. The band structure of the (10,0) Z-C3NSWNT under different external (e) electric field and (f) strain, respectively. The partial charge density of HVB for the (10,0) ZC3NSWNT at two different (g) electric field strengths and (h) strains, respectively. The isosurface value is 3 0.4 jej� A .
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shown in Fig. 8(a) and (e), respectively. Due to the structural symmetry of the two C3NSWNTs, the calculated results are the same when the voltage is applied up or down in the direction perpendicular to the axis. As the electric field increases from 0 to 0.5 V/Å, the LCB moves down and HVB moves up, the band gap decreases monotonically. When the electric field strength increases to 0.5 V/Å/0.4 V/Å, there is a semi conductor to metal transition occurs for (6,6) A-C3NSWNT as shown in Fig. 8(a)/(10,0) Z-C3NSWNT as shown in Fig. 8(e). The intrinsic band gap of (10,0) Z-C3NSWNT (Egap ¼ 0.096 eV) is smaller than that of (6,6) A-C3NSWNT (Egap ¼ 0.435 eV), so there is smaller electric field needed for semiconductor to metal phase transition in the case of (10,0) ZC3NSWNT. In order to illustrate the physical mechanism, we have plotted the partial charge density distributions of HVB at two typical electric fields 0 V/Å and 0.5 V/Å as shown in Fig. 8(c) and (g). In the absence of the external electric field, the partial charge density of HVB for the (6,6) A-C3NSWNT is mainly concentrated on the upper and lower sides of (6,6) A-C3NSWNT(see Fig. 8(c)), but the partial charge density of HVB for the (10,0) Z-C3 NSWNT is distributed on each N atom (see Fig. 8(g)), which results in the bandgap of (6,6) A-C3NSWNT is wider than that of (10,0) Z-C3NSWNT. When the electric field is 0.5 V/Å, there exists a potential energy difference between two edge of the C3NSWNT, which makes LCB moves down and HVB moves up with electric field. The change of Bloch state in nanotubes without and with electric field is caused by strong electric polarization induced by external electric field. The effect of strain in the axial direction on the electronic properties of the (6,6) A-C3NSWNT and (10,0) Z-C3NSWNT are shown in Fig. 8(b) and (f), respectively. Fig. 8(b) corresponds to (6,6) A-C3NSWNT. The band gap increases with the increase of compressive strain (strain ϵ is in the range of 10% ~0), but decreases with the increase of tensile stress (strain ϵ is in the range of 0 ~10%). When the tensile stress reaches 10%, there is the transition from semiconductor to metal. The partial charge density is mainly distributed on the upper and lower sides of (6,6) AC3NSWNT in the absence of the strain, then is transferred from the two sides of the nanotube to the middle of the nanotube when the tensile stress reached 10%, which is as shown in Fig. 8(d). The change in the atomic orbital distribution cause the phase transition. While for (10,0) Z-C3NSWNT, the band gap has never been reduced to 0 when the strain changes from 10% to 10% (see Fig. 8(f)). Under the effect of tensile stress, the band gap always increases with the increase of tensile strain. There is no significant change in the partial charge density distribution when the strain changes from 0% to 10%(see Fig. 8(h)). Therefore, (6,6) A-C3 NSWNT is more suitable to the application in nano electrome chanical switching devices.
All data generated or analyzed during this study are included in this article. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Zhanhai Li: Data curation, Writing - original draft. Fang Cheng: Conceptualization, Writing - review & editing. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No 11374002, Scientific Research Fund of Hunan Provincial Education Department 17A001, Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province and the construct program of the key discipline in hunan province. References [1] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56–58. [2] S. Iijima, T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature 363 (1993) 603–605. [3] D.S. Bethune, C.H. Kiang, M.S. De Vries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers, Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls, Nature 363 (1993) 605–607. [4] C.W. Padgett, D.W. Brenner, Influence of chemisorption on the thermal conductivity of single-wall carbon nanotubes, Nano Lett. 4 (2004) 1051–1053. [5] C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube, Nano Lett. 5 (2005) 1842–1846. [6] L. Chico, V.H. Crespi, L.X. Benedict, S.G. Louie, M.L. Cohen, Pure carbon nanoscale devices: nanotube heterojunctions, Phys. Rev. Lett. 76 (1996) 971. [7] T.W. Ebbesen, H.J. Lezec, H. Hiura, J.W. Bennett, H.F. Ghaemi, T. Thio, Electrical conductivity of individual carbon nanotubes, Nature 382 (1996) 54–56. [8] Jean-Paul Salvetat, et al., Elastic modulus of ordered and disordered multiwalled carbon nanotubes, Adv. Mater. 11 (1999) 161–165. [9] G. Overney, W. Zhong, D. Tomanek, Structural rigidity and low frequency vibrational modes of long carbon tubules, Z. Physik D Atoms, Mol. Clust. 27 (1993) 93–96. [10] E.W. Wong, P.E. Sheehan, C.M. Lieber, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes, Science 277 (1997) 1971–1975. [11] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Carbon nanotube functionalization with carboxylic derivatives: a DFT study, J. Mol. Model. 19 (2013) 391–396. [12] K.W. Lee, C.E. Lee, Antiferromagnetic edge states in carbon nanotubes with hydrogen line defect abundancy, Curr. Appl. Phys. 15 (2015) 163–168. [13] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Hydrogen dissociation on dienefunctionalized carbon nanotubes, J. Mol. Model. 19 (2013) 255–261. [14] Joo-Hyung Kim, et al., A flexible paper transistor made with aligned single-walled carbon nanotube bonded cellulose composite, Curr. Appl. Phys. 13 (2013) 897–901. [15] J. Beheshtian, A.A. Peyghan, Z. Bagheri, Nitrate adsorption by carbon nanotubes in the vacuum and aqueous phase, Monatsh. Chem. Chem. Monthly 143 (2012) 1623–1626. [16] Dong-Lai Wang, et al., Comparative study of the electrostatic potential of perfect and defective single-walled carbon nanotubes, Comput. Theor. Chem. 966 (2011) 1–8. [17] R. Czerw, et al., Identification of electron donor states in N-doped carbon nanotubes, Nano Lett. 1 (2001) 457–460. [18] J. Hales, A.S. Barnard, Thermodynamic stability and electronic structure of small carbon nitride nanotubes, J. Phys. Condens. Matter 21 (2009), 144203. [19] Mohan SR. Elapolu, et al., Phononic thermal transport properties of C3N nanotubes, Nanotechnology 31 (2019), 035705. [20] X. Cheng, X. Wang, Thermal transport in C3N nanotube: a comparative study with carbon nanotube, Nanotechnology 30 (2019), 255401. [21] H. Wang, H. Wu, J.C.3N. Yang, A Two Dimensional Semiconductor Material with High Stiffness, Superior Stability and Bending Poisson’s Effect, 2017. arXiv: 1703.08754. [22] Seifollah Jalili, et al., Role of Defects on structural and electronic properties of zigzag C3N nanotubes: a first-principle study, Phys. E Low-dimens. Syst. Nanostruct. 56 (2014) 48–54. [23] A. Bafekry, C. Stampfl, S. Farjami Shayesteh, A first-principles study of C3N nanostructures: control and engineering of the electronic and magnetic properties of nanosheets, tubes and ribbons, ChemPhysChem 21 (2020) 164–174.
4. Conclusion In summary, we have investigated that the structure and electronic properties of (n,n) A-C3NSWNT and (n,0) Z-C3NSWNT in terms of the first-principles method of density functional theory. We find that the C3NSWNT system has high structural stability. The electronic properties of C3NSWNT is dependent of the chirality index n and the edge types. Both A-C3NSWNT and Z-C3NSWNT can transfer from semiconductor to metal by applying an electric field, and Z-C3NSWNT is more sensitive to the applied electric field than A-C3NSWNT due to smaller energy gap. But only A-C3NSWNT can transfer from semiconductor to metal by applying strain. The dramatic difference between the hole and electron mobilities also exists in C3NSWNTs. Moreover, our results suggest that the carrier mobility of C3NSWNTs can be adjusted by diameter and edge engineering. These results can provide some theoretical support for the development of nanodevices, and it is of great significance to explore the potential applications of nanomaterials based on C3NSWNT. Availability of data and materials The authors declare that materials and data are promptly available to readers without undue qualifications in material transfer agreements. 7
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