Letter pubs.acs.org/JPCL
Theoretical Prediction of Carrier Mobility in Few-Layer BC2N Jiafeng Xie, Z. Y. Zhang, D. Z. Yang, D. S. Xue, and M. S. Si* Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, No. 222 South Tianshui Road, Lanzhou, Gansu 730000, China ABSTRACT: An ideal semiconducting material should simultaneously hold a considerable direct band gap and a high carrier mobility. A 2D planar compound consisting of zigzag chains of C−C and B−N atoms, denoted as BC2N, would be a good candidate. It has a direct band gap of 2 eV, which can be further tuned by changing the layer number. At the same time, our first-principles calculations show that few-layer BC2N possesses a high carrier mobility. The carrier mobility of around one million sqaure centimeters per volt-second is obtained at its three-layer. As our study demonstrated, few-layer BC2N has potential applications in nanoelectronics and optoelectronics.
SECTION: Molecular Structure, Quantum Chemistry, and General Theory
I
method in experiment.20 BC2N has a theoretical direct band gap of ∼1.6 eV in its monolayer19,21,22 compared with the value of 2.0 eV measured experimentally.23 Although it shares the honeycomb structure the same as graphene and h-BN, the actual atomic configurations have not been identified experimentally as three possible allotropes are involved.21,24 The electronic properties of these allotropes are inversionsymmetry-dependent. The one with inversion symmetry is found to be metallic. By contrast, the remaining two lacking inversion symmetry are semiconductors:19 one consists of C−C and B−N dimers with a narrow indirect band gap of ∼0.5 eV;19 the other is composed of C−C and B−N zigzag chains with a considerable band gap of ∼2 eV. The latter one is the focus of this work. In fact, the band gaps of BC2N have strikingly different experimental values of 23 meV,25 2.0 eV,23 or indirect band gap of 1.6 eV26 as several allotropes are usually involved. In 1996, Watanabe and coworkers studied the electrical properties of BC2N and reported the hole mobility of ∼10 cm2 V−1 s−1 on Ni substrate25 or 30 cm2 V−1 s−1 for thin films at room temperature.23 Those experimental products might be the compounds of BC2N allotropes. In 2011, Bruzzone and Fiori investigated the electron mobility of the narrow indirect gapped BC2N theoretically.27 The predicted electron mobility is ∼160 cm2 V−1 s−1. Up to now, no direct theoretical study has been addressed on the carrier mobility of the BC2N, which includes zigzag chains of C−C and B−N atoms. (Thereafter, we call it BC2N if without any specification.) We investigate the electronic structures of few-layer BC2N based on first-principles calculations. The direct band gap of 1.6 eV is obtained at the Γ point for its monolayer. When BC2N goes into multilayers in graphite-like AB stacking, the band gap
t is generally known that Moore’s law will no longer be sustained due to the continuous lowering of device dimensions.1 Thus, one of the most urgent tasks in the postsilicon era is to search for an alternative semiconducting material that has excellent performance in nanoelectronics and optoelectronics. An ideal candidate is expected to simultaneously have an appreciable band gap and a superior carrier mobility. The former is required by the capability of controlling the charge carrier on the external field. For example, a proper bandgap value of ∼2 eV responds directly to visible light. The latter takes into account the efficient manipulation of carrier in device applications. However, in realistic materials, the situation is not true. As for graphene, the carrier mobility approaches as high as 200 000 cm2 V−1 s−1,2 but the absence of a fundamental band gap makes it unsuitable for conventional digital applications in field-effect transistors.3 Many efforts have been devoted to open the band gap of graphene before its industrial synthesis. Hexagonal boron nitride sheet (h-BN) is a wide bandgap semiconductor.4 Unfortunately, the carrier mobility of h-BN is very low owing to the flat bands near the Fermi level.5 Although recently developed few-layer transition metal dichalcogenides (in particular MoS2)6−9 and monolayer black phosphorus (phosphorene)10−14 simultaneously satisfy the above two criteria, their puckered lattices cannot strictly confine the movement of the carrier within the 2D surface. Thus, a search for 2D planar semiconducting materials is still an ongoing task. Motivated by the ultrahigh carrier mobility of graphene and the insulating nature of h-BN, various hybrids of graphene and h-BN are investigated in hope of tuning the electronic properties.15−18 One material among them called BC2N, which is composed of C−C and B−N zigzag chains, has come to our attention. It is almost at the same time that BC2N is theoretically predicted by using first-principles calculations19 and successfully synthesized by the chemical vapor deposition © XXXX American Chemical Society
Received: September 21, 2014 Accepted: November 11, 2014
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Figure 1. (a) Crystal structure of bulk BC2N. The blue, green, and white balls represent the nitrogen, boron, and carbon atoms, respectively. (b) Brillouin zone with high-symmetry points and lines of bulk BC2N primitive cell. (c) Band structure of bulk BC2N calculated with the PBE-vdW functional. The dotted line denotes the Fermi energy level. The fitted effective masses along the Γ-M, Γ-K, and Γ-A directions are given as well.
Figure 2. (a) Top view of the atomic structure of monolayer BC2N. A 2 × 2 supercell is taken for brevity. (b) Brillouin zone with high-symmetry points and lines. (c) Top and (d) side views of the atomic structure of bilayer. Band structures of (e) monolayer and (f) bilayer BC2N. Two valence bands and two conduction bands are marked as VB1, VB2, CB1, and CB2 in panel f. (g) Spatial distributions of wave functions for the four marked states. The isovalue is set to 0.01 eÅ−3. (h) Evolution of the direct band gap as a function of layer number.
decreases and is close to 1.2 eV at five-layer. The carrier mobility of few-layer BC2N is predicted through the phononlimited scattered mode. Our results show that the carrier mobility can reach ∼800 × 103 cm2 V−1 s−1, suggesting that
few-layer BC2N would be considered a good candidate for nextgeneration electronic material. Few-layer BC2N can be easily isolated from its bulk counterpart through using the mechanical cleavage technique 4074
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values. (See Table 1 for details.) The only difference between them is the interlayer distance; namely, the interlayer distance
as the weak van der Waals (vdW) interaction holds them together.28,29 Here we begin our investigations on its bulk in the graphitic stacking.19 To compare with the previous work,19,22 we take an eight-atom supercell of hexagonal lattice in our calculations. The optimized configuration is depicted in Figure 1a. The obtained interlayer distance is 3.40 Å, in agreement with the experimental reports23,25 and theoretical predictions.19,22 The in-plane lattice constant is 2.54 Å, generating the in-plane covalent bond lengths as B−N of 1.46 Å, B−C of 1.55 Å, C−C of 1.45 Å, and C−N of 1.41 Å, which are consistent with that obtained by Lu and coworkers.30 The first Brillouin zone (BZ) of graphitic BC2N is given in Figure 1b. The calculated band structure is displayed in Figure 1c. It explicitly shows that bulk BC2N is a direct bandgap semiconductor at the Γ point. The band gap is ∼1.15 eV. If the layered structure is fabricated, the band gap should increase significantly (as discussed later). The chemical character in BC2N is anisotropic. This is because the C−B and C−N bonds only occur in the armchair chains but not in the zigzag chains. The chemical bonding of C−N and C−B bonds is stronger than that of the C−C and B− N bonds, which appear only in the zigzag chains. Thus, the bands along the Γ-M direction (armchair chain) are more dispersive than those along the Γ-K direction (zigzag chain), resulting in low effective masses and large carrier mobilities along the Γ-M direction. According to the nearly free electron model fitting those bands, we can estimate the effective mass of the hole as ∼0.24m0 (where m0 is the free electron mass), which is slightly larger than the electron’s 0.18m0. The effective masses of hole and electron are, respectively, 1.28 m0 and 0.44 m0 along the Γ-K direction, which are larger than those along the Γ-M direction. This finding is very insightful. In real space, the Γ-M direction corresponds to the armchair direction, while the Γ-K direction is responsible for the zigzag direction. It implies that carrier prefers to move along the C−N or C−B dimers. If we consider the metallic nature of graphene, the ultrahigh carrier mobility should propagate along the C−C dimers. Thus, if one wants to improve the carrier mobility in BC2N, the replacement of C−N or C−B dimers with C−C dimers by the substituting method will be a good approach. Future research can test this prediction. The bands along the ΓA direction are very flat. The much larger effective masses, 7.46 m0 for hole and 52.20 m0 for electron, are a natural consequence. Because it represents the interlayer direction, we ignore it. If the bulk BC2N is exfoliated to a monolayer, significant changes will occur. The unit cell of monolayer and its 2D BZ are shown in Figure 2a,b, respectively. The optimized in-plane lattice constant is 2.52 Å, which is slightly smaller than that of bulk previously discussed. As a result, the corresponding inplane covalent bonds shrink within the range of 0.1 to 0.2 Å. To verify its thermal stability, we calculate the phonon dispersion of monolayer BC2N (not shown for brevity). No imaginary frequency is observed in the vibration spectra, demonstrating monolayer BC2N kinetically stable. The optical branches are in the range of ∼1300−1700 cm−1, complying with the Raman15,31 and the infrared32 spectra and the previous theoretical report.33 This means that the strong in-plane sp2 bonds are formed, guaranteeing a planar lattice. When BC2N is in a bilayer with AB stacking, as shown in Figure 2c,d, the in-plane lattice constant is increased to be 2.54 Å, which is the same as the bulk phase. At the same time, the corresponding in-plane covalent bonds recover to the bulk’s
Table 1. Lattice Constants a and Δc (Interlayer Distance) and the in-Plane Covalent Bond Lengths of Few-Layer BC2N Calculated Using PBE-vdW Functionala
a
NL
a
Δc
B−N
B−C
C−C
C−N
1 2 3 4 5
2.52 2.54 2.54 2.54 2.54
3.35 3.44 3.39/3.49 3.34/3.52
1.45 1.46 1.46 1.46 1.46
1.53 1.54 1.54 1.54 1.55
1.43 1.45 1.45 1.45 1.45
1.40 1.41 1.41 1.41 1.41
All of them are in units of angstroms. NL represents the layer number.
of bilayer is 3.35 Å, which is smaller than that of bulk phase. This is because each layer in bilayer feels the vdW interactions from only its one neighboring layer, but two in the case of bulk phase. As the layer number increases, the interlayer distance increases. For example, Δc is 3.44 Å in trilayer, while in fourlayer or five-layer BC2N, Δc has two nonequivalent values in range of 3.34 to 3.52 Å. Another effect of layer increasing reflects on the band structures. The calculated band structure of monolayer BC2N is displayed in Figure 2e. The direct band gap is obtained to be 1.57 eV, a value 0.4 eV larger than that of bulk BC2N. As it goes to the bilayer, more bands appear in the band structure, as shown in Figure 2f. For example, two nearly degenerate bands emerge around the Γ point, corresponding to the two valence bands VB1 and VB2 and the two conduction bands CB1 and CB2. To demonstrate their effect on band gap explicitly, we plot their respective wave functions in Figure 2g. Although the four bands at the Γ point are extended throughout the bilayer, the detailed distributions of them behave in different manners. States VB1 and VB2 differ in the interlayer region (marked by red rectangles). The overlapping of wave functions is observed for VB1 but not for VB2. It demonstrates clearly that a bonding is formed for VB1, while an antibonding appears in VB2. This is why VB1 occupies the lower state compared with VB2. (See Figure 2f.) Similar bonding and antibonding features are also observed in CB1 and CB2. (See the red rectangles.) Unlike VB1 and VB2, some bondings parallel to the x axis are formed: right layer for CB1 but left one for CB2 (marked by aqua rectangles). Because of the overlapping of wave functions in the interlayer, the interlayer interactions play a role in the dispersion of bands, that is, pushing the VBs and CBs close to each. As a result, a reduction of bandgap by 0.3 eV is found from monolayer to bilayer. The thicker the few-layer BC2N, the stronger the interlayer interaction as more overlapped wave functions are involved. Thus, more dispersion of VBs and CBs occurs, giving rise to a smaller bandgap as the layer increases. The gap falls continuously on adding more layers to the bilayer, approaching 1.16 eV in five-layer, as displayed in Figure 2h. We note in passing that the effect of layers on band structure of BC2N is slightly different from that in multilayer graphene, where the electronic band dispersion near the Fermi level is sensitive to the number of layers and the stacking geometry.34−36 Actually, all of these systems are the so-called vdW heterostructures.37 The perturbed heteroatom plays a role in the variation of bands in those vdW heterostructures. Next, we focus our attention on the carrier mobility of fewlayer BC2N. In 2D materials, the carrier mobility can be calculated by the expression11,27 4075
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Table 2. Predicted Carrier Mobility in Few-Layer BC2Na type
NL
mM * /m0
mK*/m0
E1M
E1K
CM_2D
CK_2D
μM_2D
μK_2D
e
1 2 3 4 5 1 2 3 4 5
0.15 0.16 0.17 0.17 0.18 0.16 0.18 0.20 0.21 0.23
0.41 0.40 0.41 0.42 0.43 2.22 0.58 0.66 0.87 1.00
1.87 1.86 0.79 0.95 2.00 2.13 2.15 3.41 2.80 3.44
4.25 4.13 2.79 3.30 0.88 4.33 4.21 2.82 3.47 2.63
306.81 771.25 1023.28 1254.52 1856.08 306.81 771.25 1023.28 1254.52 1856.07
309.84 768.88 901.19 1285.37 1571.38 309.84 768.88 901.19 1285.37 1571.38
52.55 118.06 809.47 651.16 200.47 14.82 60.47 27.04 37.72 31.32
3.70 9.61 23.45 22.38 364.01 0.27 4.95 10.32 6.15 10.23
h
a Types “e” and “h” denote the “electron” and “hole”, respectively. mM * (mK*) (in unit of m0) represents the effective mass along the Γ-M (-K) direction. E1M (E1K) (in units of electronvolts) is the deformation potential at Γ point along the Γ-M (-K) direction. CM_2D (CK_2D) is the 2D elastic modulus for the Γ-M (-K) direction, which is in units of Jm−2. Carrier mobility μM_2D (μK_2D) (in units of 103 cm2 V−1 s−1) is along the Γ-M (-K) direction and is calculated using eq 1 with temperature T = 300 K.
μ2D =
eℏ3C2D kBTm*ma (Eli)2
0.4 eV. By contrast, the deformation potentials, for graphene of 5.0 eV,39 MoS2 of 3.9 eV,40 h-BN of 3.7 eV,27 AlGaAs of 3.9 eV,38 and phosphorene of ∼3 eV11 are relatively small. All of these make BC2N promising for applications in the semiconducting industry. In summary, we have investigated the carrier mobility of fewlayer BC2N from first-principles calculations. Our results show that few-layer BC2N possesses high carrier mobilities (around one million cm2V −1 s−1). Combining the high carrier mobility with the tunable bandgap around 2 eV, few-layer BC2N is an ideal semiconducting material that has significant potential for applications in nanaoelectronics and optoelectronics.
(1)
where e is the electron charge, ℏ is Planck’s constant divided by 2π, kB is Boltzmann’s constant, and T is the temperature. m* * or mK*) is the effective mass in the transport direction, and (mM ma is the averaged effective mass determined by ma = (m*Mm*K )1/2. Eil is the deformation potential constant of VBM for hole or CBM for electron along the transport direction, defined by Eil = ΔVi/(Δl/l0). Here ΔVi is the energy change of the ith band under proper cell compression and dilatation, l0 is the lattice constant in the transport direction, and Δl is the deformation of l0. The elastic modulus C2D of the longitudinal strain in the propagation directions (both zigzag and armchair) of the longitudinal acoustic wave is given by (E − E0)/S0 = C2D(Δl/l0)2/2, where E is the total energy and S0 is the lattice volume at equilibrium for a 2D system. It is noticed that eq 1 represents a phonon-limited scattering model.27,38 As described in eq 1, the carrier mobility of few-layer BC2N is not completely determined by the effective mass. The other two properties, the deformation potential, Eil, and the 2D elastic modulus, C2D, are also involved. All of these quantities are calculated by the PBE-vdW functional, and the corresponding values are summarized in Table 2. In monolayer BC2N, the electron mobility is ∼52.55 × 103 cm2 V−1 s−1 along the Γ-M direction, which is ∼15 times larger than that along the Γ-K direction. This is because the deformation potential along the Γ-K is much larger than that along the Γ-M direction, resulting in a strongly directional anisotropy. As the layer increases, the electron mobility appears a complex feature. The value of mobility first increases and then decreases along the Γ-M direction. The extrema is 809 × 103 cm2 V−1 s−1 and appears at three-layer. Surprisingly, the value of electron mobility increases with layer along the Γ-K direction and reaches 364 × 103 cm2 V−1 s−1 at five-layer. It is noticed that the directional anisotropy becomes weak as the layer increases for electron mobility. In the case of hole carrier, the directional anisotropy is small; namely, the hole mobility along the Γ-M direction is slightly larger than that along the Γ-K direction. The hole mobility is in the range of (∼0.27 to 60.47) × 103 cm2V−1s−1. More importantly, the hole mobility is ∼10−100 times smaller than that of electron, which stems from the larger deformation potential of hole carrier in comparison with electron. In fewlayer BC2N, the high carrier mobility mainly originates from their small deformation potential, which is in on the order of
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METHODS Our first-principles calculations are performed through using the SIESTA code within the framework of density functional theory.41 The generalized gradient approximation Perdew− Burke−Ernzerhof exchange-correction functional with vdW correction is used to consider the weak vdW interaction between the layers of BC2N.42−44 Core electrons are replaced by norm-conserving pseudopotentails45 in their fully separable form.46 The plane-wave energy cutoff is set to 250 Ry to ensure the convergence of total energy. The reciprocal space is sampled by a fine grid of 21 × 21 × 1 k-point in the Brillouin zone. The conjugate gradient algorithm is taken to fully relax the geometry until the force on each individual atom is
