Electronic and Transport Properties of Ti2CO2 MXene Nanoribbons

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Electronic and Transport Properties of Ti2CO2 MXene Nanoribbons Yuhong Zhou, Kan Luo, Xianhu Zha, Zhen Liu, Xiaojing Bai, Qing Huang, Zhansheng Guo, Cheng-Te Lin, and Shiyu Du J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06426 • Publication Date (Web): 11 Jul 2016 Downloaded from http://pubs.acs.org on July 14, 2016

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The Journal of Physical Chemistry

Electronic and Transport Properties of Ti2CO2 MXene Nanoribbons Yuhong Zhou 1, Kan Luo1, Xianhu Zha1, Zhen Liu1, Xiaojing Bai1, Qing Huang1 Zhansheng Guo2, Cheng-Te Lin3, and Shiyu Du1*

1

Engineering Laboratory of Specialty Fibers and Nuclear Energy Materials, Ningbo

Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo, Zhejiang, 315201, China 2

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China

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Key Laboratory of Marine Materials and Related Technologies, Zhejiang Key Laboratory

of Marine Materials and Protective Technologies, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China

*Corresponding author. E-mail: [email protected] Telephone: 086 0574-87602759

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ACS Paragon Plus Environment


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ABSTRACT

Using first-principles calculations, the electronic structures and electron transport properties of zigzag and armchair O-functionalized Ti2C MXene nanoribbons are examined in this work. We demonstrate that the energy gaps in patterned Ti2CO2 nanoribbons can be tuned by appropriate designs of crystallographic orientation and widths. The Ti2CO2 nanoribbons along the zigzag direction with width parameter larger than six show zero or very low band gaps, while band gaps are opened for Ti2CO2 nanoribbons with armchair shaped edges. The electronic transport properties for the devices of Ti2CO2 nanoribbons with various widths are investigated using nonequilibrium Green's Functions and the current-voltage characteristics of the devices are predicted. The current calculations reveal that some of these devices may have a nonlinear feature as well as negative differential resistance behaviors. The zigzag and armchair Ti2CO2 nanoribbon devices show different current-voltage curves. There are onset biases for armchair Ti2CO2 nanoribbons so that the current to be generated due to the band gaps, but not for most of the zigzag nanoribbons. The corresponding mechanisms for the variation of electronic band gaps and electronic transport properties are discussed. Based on their excellent carrier mobilities reported for the Ti2CO2 MXene and the negative differential resistance effect found in this work, the Ti2CO2 nanoribbon systems might find promising applications in nanoelectronic devices.

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1. INTRODUCTION Two dimensional (2D) materials have attracted increasing attention owing to their remarkable potential as building blocks for varieties of new functional materials.1-4 Graphene is well known as the most studied 2D materials in the recent decades. In the meantime, some new 2D materials consisted of different elements or compounds are also rising and become focus of current researches.5-7 As a good example, the new large family of 2D transition metal carbides and cabonitrides, called MXene (M=Ti, Sr, V, Cr, Ta, Nb, Zr, Mo, Hf; X=C, N, or both) have been synthesized from the layered metallic ceramics Mn+1AXn (n=1, 2, and 3) phases, i.e. MAX phases, where M is an early transition metal, A is mainly a group IIIA or IVA element, X is C and/or N, and n = 1, 2, or 3. Up to now, the fabricated MXene family include Ti3C2, Ti2C, Nb2C, V2C, (Ti0.5, Nb0.5)2C, (V0.5, Cr0.5)3C2, Ti3CN, Mo2C8 and Ta4C3.9 Since the selective etching of A atoms from Mn+1AXn, is achieved by exfoliation with HF solution in most instances, the MXenes are sometimes functionalized by the O, OH and/or F groups. With the advancement of experimental technologies and theories, the extraordinary properties of MXene materials have been widely investigated.4, 10, 11 The low-dimensional d-metal carbides or nitrides have been suggested to possess good electrical properties when the MXene elemental composition and/or their surface terminations are appropriately designed.4, 12-15 This can be seen from the MXenes’ band structure and electron density of states (DOSs) predicted by the density functional theory (DFT).10, 16-19 In general, bare MXene monolayers are shown to be metallic, with a high electron density near the Fermi 3



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level.20 MXenes have been shown to be promising for a variety of applications. However, the investigations on the potential applications of MXene nanoribbons in electronic devices are still in the start stage up to now. Recently, the electronic transport properties of conductive MXene have been found to be strongly influenced by surface terminations, 21, 22 which could make MXene a promising candidate material for the field-effect transistors (FET).23, 24 It was shown by theoretical computations that a sizable band gap can be opened for O-terminated Ti2C (Ti2CO2) monolayer. Also, some physical properties of MXenes are sensitive to their orientation.25 For example, in our previous work, it is determined that the Sc2CF2 MXene has a direct band gap and an anisotropic thermal conductivity and carrier mobility.14, 15 Besides the interest in 2D materials, the conversion of them to one dimensional (1D) nanostructure is also considered as a promising structural modification to expand their applicability on account of the quantum confinement effect and directionality.25 Currently, the fabrication of graphene naonoribbons with varying widths can be realized by different ways including cutting mechanically exfoliated graphenes, and patterning of grown graphenes.26-28 It has been found that structural variation of ribbons with nanometer sized widths can significantly change the characteristic of the electronic structures.25,

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Successful synthesis, novel properties and application prospects for graphene applications give an impetus to the search for non-carbon graphene-like materials. Therefore, it is reasonable to expect MXene may exhibit novel behaviors as well if MXene nanoribbons are applied in nanoelectronics. Unfortunately, the research on the devices assembled by 4


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semiconducting MXene nanoribbons has rarely been reported nor the mechanisms for their electronic transport are revealed. In this work, we chose Ti2CO2 nanoribbons as the representative semiconductor MXene and performed computational investigations on the electronic and transport properties. According to the current results, the band structures of Ti2CO2 nanoribbons with armchair and zigzag shaped edges show entirely different characteristics and the role of the edges is crucial for determining the values for the band gaps. In addition, we have studied the electronic transport properties of Ti2CO2 nanoribbon devices with different widths. Our findings may provide new clues for the design of practical nanoelectronic devices of MXenes.

2. MODEL AND METHOD When the MXene is patterned into a narrow ribbon, the carriers are confined to a quasi-one-dimensional (1D) system. Similar to graphene nanoribbon, the structure of MXene (Ti2CO2) nanoribbons are constructed by cutting a single layer MXene with the desired edges and widths. There are two types of Ti2CO2 nanoribbons: the armchair edged nanoribbons and the zigzag edged nanoribbons. The representative structures are as shown in Figure 1. In this work, the configurations of armchair MXene nanoribbons with various widths are labeled as from 6A to 15A; while for zigzag MXene nanoribbons, we have chosen 6Z, 8Z, 10Z, 12Z and 14Z as the model systems. Here Z and A indicate the zigzag and armchair edged nanoribbons, respectively, and the number indicates the width parameter, i.e. the number of Ti atom lines perpendicular to the periodic directions as 5



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illustrated in Figure 1. The models are used to study the effect of width on the electron transport and current-voltage (I-V) curves in the following sections. In the current models, for armchair nanoribbons, both asymmetric and symmetric armchair edges are considered with the corresponding width parameters being even (6, 8, 10, 12, 14) and odd (7, 9, 11, 13, 15) numbers, respectively. Figure 1(a) and 1(b) show armchair nanoribbons with width parameter 10 and 11, namely, 10A and 11A, respectively. In the case of the zigzag nanoribbons, previous reports have shown the TiTiC-CTiTi (the three atomic lines on each edge) type nanoribbon has the highest binding energy as well as negative edge energy, which means that the TiTiC-CTiTi edge structure is relatively stable4, 31. Therefore, the zigzag nanoribbon with TiTiC-CTiTi edge is adopted in this work. The resultant width parameter is an even number for zigzag nanoribbons (6, 8, 10, 12, 14). Figure 1(c) depicts the zigzag nanoribbon with CTiTi-TiTiC edge with width parameter 10, i.e. the structure of 10Z. For the current models, the width variation of nanoribbons is in the range from 9 Å to 24 Å for armchair nanoribbons and 9 Å to 22 Å for zigzag nanoribbons, respectively. For both zigzag and armchair nanoribbons, the vacuum spaces with the thickness of 20 Å are adopted in the aperiodic directions (perpendicular to the periodic directions) so that the system has no interactions with its mirror images. In this study, our calculations are carried out by using the Atomistix Toolkit (ATK) code.32 The exchange correlation energy is described by the generalized gradient approximation (GGA) in the scheme proposed by perdew-Burke-Ernzerhof (PBE). Hartwigsen-Goedeker-Hutter (HGH) norm-conserving pseudopotentials and the basis set of tier 0 are used. The k-point for the semi-infinite leads 6


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is sampled with a 1×1×30 Monkhorst-Pack k-grid for optimization. The optimized geometries were obtained by relaxing the whole system with a force tolerance 0.05 eV/Å. A plane wave kinetic energy cutoff of 400 Ry for the wave-function is used. Form the calculated band structures, 2D Ti2CO2 is a semiconductor with a narrow bandgap of 0.20 eV, which is in excellent agreement with the results of Khazaei et al. as well as our previous calculations.14,33

Figure 1. Optimized atomic configurations of Ti2CO2 nanoribbons. (a) Top and side view of armchair Ti2CO2 nanoribbons monolayer with the width parameter of 10; (b) Top and side view of armchair Ti2CO2 nanoribbons monolayer with the width parameter of 11; (c) Top and side view of zigzag Ti2CO2 nanoribbons monolayer with the width parameter of 10. The red balls present the oxygen atoms, the gray balls present the carbon atoms and the white balls present the titanium atoms.

After geometry optimization, the first-principles computation of transport properties is performed based on the nonequilibrium Green’s function (NEGF) approach combined the 7



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density functional theory (DFT) calculations, which is a ballistic limit calculation. The general model consists of three parts: the left electrode, the central scattering region, and the right electrode as shown in Figure 2. The left and right electrodes are semi-infinite periodic in the negative/positive z direction. Each lead is described by a supercell with two repeated Ti2CO2 unit cells along the transport direction (parallel to the z direction), and the scattering region is 24.4 Å (26.4 Å) in length for the zigzag (armchair) nanoribbons. To model the two-probe configuration, the NEGF-DFT self-consistency are employed controlled by the numerical tolerance of 10-5eV. The fineness of the real space grid is determined by an equivalent plane wave cutoff 400 Ry. The k-point samplings for the semi-infinite leads are performed with the 1×1×100 Monkhorst-Pack k-grids. The current through the transport systems are calculated by ATK-DFT with the range of a bias voltage from 0 V to 1.5 V. The current I(V) can be calculated by the Landauer-Buttiker formula34 given by Eq. (1). +∞

I (V ) =

2e ∫ [ f L ( E − U L ) − f R ( E − U R )]T ( E,V )dE h −∞

(1)

Here e is the electron charge, f is the Fermi function, h is Planck’s constant, T(E, V) is the transmission function of the system, and UL and UR are the electrochemical potentials of the left and right leads, respectively. Under the external bias V, the value of UL (or UR), will be shifted downward (or upward) by V/2 relative to the original electrochemical potentials, namely UL=EF–eV/2 and UR=EF+eV/2, where EF is average Fermi level. Thus, the region of the bias window is [–V/2, +V/2]. T(E, V) is estimated with the sum of the transmission 8


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probabilities of all channels available at energy E under the external bias voltage V, and can be calculated by the following formula.

T ( E , V ) = Tr éë Γ L ( E ) G R ( E , V ) Γ R ( E ) G A ( E , V ) ùû

(2)

Here ΓL ( E) and Γ R ( E) are the broadening functions derived from left and right electrode self-energies, respectively. G R ( E ,V ) and G A ( E ,V ) are the retarded and advanced Green’s functions, respectively.

Figure 2. The schematic diagram of an armchair Ti2CO2 device, taking 10A as the sample system.

3. RESULTS AND DISCUSSIONS In this work, both types of nanoribbons: zigzag and armchair nanoribbons are studied. Figure 3 shows the band structures of Ti2CO2 nanoribbons with armchair and zigzag shaped edges. The band gaps of 6A, 8A, 10A, 12A and 14A over the energy range are respectively 0.98 eV, 0.80 eV, 0.67 eV, 0.60 eV and 0.55 eV. Obviously, the band gaps of asymmetric edge armchair nanoribbons decrease monotonically with increasing width of nanoribbons. 9



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It is worth mentioning that the band gap of 8A configuration is in reasonable agreement with the previous results.5 The conduction band minimum (CBM) and the valence band maximum (VBM) are all located between the Γ and Z points and at the Γ point, respectively. In the case of symmetric edge armchair nanoribbons, the band gaps of 7A, 9A, 11A, 13A and 15A are 0.19 eV, 0.28eV, 0.38 eV, 0.42 eV 0.40eV, respectively. The CBM and the VBM are located at the Γ point. In general, this means that the band gap can be kept open if one cuts the 2D Ti2CO2 to nanoribbons along the armchair crystallographic orientation. These gaps are important to for semiconducting behavior in the device equipped with the 1D Ti2CO2 MXene. For the zigzag Ti2CO2 nanoribbons, our calculations indicate that they show versatile conductive characteristics, which can be indirect narrow-band gap semiconductors or metals, depending strongly on the width of the nanoribbons. The band gaps are 0.40 eV and 0.04 eV for 6Z and 8Z, the electronic structures of 10Z, 12Z, and 14Z exhibit metallic. Compared with the band gap of 2D Ti2CO2, 14,33 the band gap of 1D zigzag nanoribbon is small or zero unless the width is very narrow, which is in accord with the previous calculations.4 In addition, there exist energy intervals under the Fermi level for all zigzag nanoribbons. As we know, the armchair graphene nanoribbons are semiconducting with different band gaps depending on their width, while all zigzag graphene nanoribbons are metallic.35 These exhibit some similarities with MXene nanoribbons. Therefore, the crystallographic orientation and width of nanoribbons are also crucial parameter for the band gap engineering of the semiconducting MXene materials such as Ti2CO2. 10


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Figure 3. Band structures of various Ti2CO2 nanoribbons: (a)-(e) asymmetric armchair nanoribbons; (f) –(j) symmetric armchair nanoribbons; (k)-(p) zigzag nanoribbons. The Fermi energy is set at zero. The bands in green and red for the asymmetric armchair nanoribbons and zigzag nanoribbons are the bands closest to the Fermi level. The bands in red for the symmetric armchair nanoribbons are the bands lower than and closest to the

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Fermi level and the bands in bisque and green for the symmetric armchair nanoribbons are the two bands higher than but closest or second closest to the Fermi level.

Total Density of States (TDOS) and Projected Density of States (PDOS) of these Ti2CO2 nanoribbon models are shown in Figure 4. Overall, the TDOS present a number of continuous peaks correlated well with the corresponding band structures. For the armchair nanoribbons, the electron states are absent near the Fermi level as shown in Figure 4(a) and 4(b); as to the zigzag nanoribbons, Figure 4(c) shows TDOS peaks can be identified near the Fermi level. Along the zigzag direction, it can be seen the states near Fermi level are mainly contributed by the 3d orbitals of Ti atoms, which is probably a result of the edge Ti-Ti interaction of the CTiTi-TiTiC configuration. In regards to the armchair direction, the TDOS nearest to Fermi level is dominant by the 3d orbitals of Ti atoms and 2p orbitals of O atoms. Form the asymmetric armchair MXene nanoribbons, the band gap increases when the width parameter decreases, which can be readily understood by the quantum confinement effect. However, it is notable that the band gaps of symmetric armchair MXene nanoribbons rise with increasing widths from this work. The variation of band gaps with the widths of symmetric armchair MXene nanoribbons can be understood as follows. The band structures of nanoribbons 7A – 15A are shown in Figure 3(f)~3(j). From the figures, one can find that the edge bands (the bands in bisque) appear between the original conduction and valence bands when the nanoribbons are generated from the 2D MXene structure. This indicates that the edge of Ti2CO2 causes 12


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CBM energy downshift due to the existence of their electronic states and makes the apparent band gap become lower for the narrower nanoribbons. In fact, if ignoring the edge bands, the gaps of the original valence and conduction bands (shown in red and green in Figure 3(f)-3(j)) can be seen to be narrowed when the width number of the nanoribbons increases from 7 to 15, which is obviously a result of conventional quantum confinement effect. This phenomenon can also be seen from the DOS plots illustrated in Figure 4 (b). There exist TDOS peaks ranging from 0.1 to 0.3 eV for the nanoribbons 7A-15A. The PDOS analysis shows that these bands are dominant from the 3d orbital of Ti atoms and 2p orbitals of O atoms in the edges. The energies of these states can be found to increase when the width of nanoribbons increases, leading to the increase in apparent band gaps. Again, the gaps of the bands formed by the atoms other than edges of the nanoribbons can be found to be decreased, following the law of quantum confinement effect. Therefore, the edge effect of Ti2CO2 nanoribbons plays a significant role in determining their apparent band gaps and causes the enlargement when the widths increase.

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Figure 4. TDOS and the PDOS on atomic orbitals of Ti, C and O atoms of (a) asymmetric armchair; (b) symmetric armchair and (c) zigzag Ti2CO2 nanoribbons , respectively. The Fermi energy is at zero.

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Figure 5. The current-voltage (I-V) characteristics of (a) asymmetric armchair, (b) symmetric and (c) zigzag Ti2CO2 nanoribbons devices.

To examine the transport properties of pure Ti2CO2 nanoribbons devices, the self-consistently calculated I-V curves for these models in a bias range from 0 V to 1.5 V 16


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are shown in Figure 5; the nanoribbon devices with different orientations and widths present different I-V characteristics. As shown in Figure 5(a) and Figure 5(b), due to the semiconducting nature of armchair nanoribbons, onset voltages can be readily identified. The asymmetric nanoribbons show a higher onset voltage (0.6V vs. 0.5V between 14A and 15A; 1.0V vs. 0.4V between 6A and 7A), which is consistent with their higher band gaps. Notably, some of the devices also shows NDR phenomena. From Figure 5(a), take 6A for example, under a bias of 1.3 V, the current is 10.9 µA, but the current reduce to 8.4 µA when the bias is 1.4V, then the current increases again with the increasing applied bias voltage. The similar NDR behavior is also observed for 10A and 12A. As for the symmetric armchair nanoribbons, one can also find NDR effects as illustrated in Figure 5(b). For example, when the bias increases from 0.7 to 0.9 V, the current of 11A significantly drops from 8.2 µA to 2.5 µA, and then increases again with the increasing applied voltage. In these systems, we observed the NDR behaviors for 7A, 9A, 11A and 13A. It is interesting to point out that 7A, 11A and 13A all show negative dependence of current on voltage at 1.1 V~1.2 V. For zigzag Ti2CO2 nanoribbon devices, some substantial differences from the armchair ones exist as seen in Figure 5(c). There is no onset bias for all nanoribbons except 6Z due to their zero or very low band gaps. The currents all increase when the applied bias voltage from 0.0V to 0.5V except the configuration 8Z. These mean that the devices of Ti2CO2 nanoribbons along the zigzag direction may have only minor nonlinear effects in this bias range. When the bias is 0.6 V, 0.8V and 0.9V for 14Z, the current is respectively 37.0 µA, 20.9 µA and 13.9 µA, exhibiting strong NDR effects. In all these zigzag 17



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nanoribbon systems, the NDR behaviors can be observed. From the current work, NDR phenomena can be identified for a variety of MXene nanoribbons.

Figure 6. The transmission spectra and the corresponding TDOS at specified biases for (a) 10A, (b) 11A and (c) 12Z systems. The region in two vertical dash lines is the bias windows.

Since the current is determined by the transmission coefficient, in order to better understand the current-voltage curves of the MXene nanoribbons, we plot the TDOS and the energy-dependent transmission spectra at different applied biases in Figure 6 with 10A, 11A and 12Z as the examples. Detailed study on these curves provides further information on the current change with voltage. For zigzag nanoribbon devices of 12Z, the integration of the transmission function increases within the bias window from 0V to 0.5V as shown in Figure 6(c), reflected by the rising broad transmission peaks within the energy window -eV/2 to +eV/2.. Correspondingly, when the bias voltage increases to 0.5 V, the current increases to 29.7µA. When the voltage further increases 0.8 V, the transmission spectra in the bias window decreases significantly, thus, the current reduces to 18.4 µA. This implies 18


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the NDR effect can occur in zigzag nanoribbons. As to the armchair nanoribbons illustrated in Figure 6(a) and Figure 6(b), when the bias voltage increases to 0.4 V, no transmission peaks are found in the bias window for 10A and 11A. However, the TDOS in the bias window are nonzero for all cases. Since the transmission intensity is nonzero only when both leads have nonzero TDOS and the TDOS shown in the figure is for the whole device, it can be readily deduced that the filled states and empty states around the Fermi energy under a bias both exist and hinder the hopping of electron from the source to the drain. When the bias voltages is 0.9 V for 10A, there are available transmission spectra in the bias windows, causing the currents increase with the enhancement of the bias voltage. Moreover, the same pattern is found for 11A at the bias voltage of 0.7 V. However, when the bias increased to 1.1 V, the transmission peaks for 10A continue to increase while those for 11A drop evidently, which reflects that the configurations of 10A and 11A have different NDR feature at the bias near 1.1V. Overall, the current-voltage curves of the Ti2CO2 MXene devices can be well explained by the variation of the transmission spectra with the change of voltage in the bias window.

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Figure 7. (a)-(f): Combination plots for Band structure of the left lead (left panels), transmission spectra (middle panels), and band structure for the right lead (right panels). (a), (b) are for 10A devices at the bias voltage of 0.3 V and 0.9 V; (c), (d) are for 11A devices at the bias voltage of 0.3 V and 0.7V; (e), (f) are for 12Z devices at the bias voltage of 0.3 V and 0.5V; (g) The eigenstates of 11A at an eigenvalue of E=-0.04 eV at the bias of V=0.7 V; (h) The eigenstates of 11A at an eigenvalue of E=0 eV at the bias of V=0.7 V; (i) The eigenstates of 12Z at an eigenvalue of E=0 eV at the bias of V=0.3V; (j) The eigenstates of 12Z at an eigenvalue of E=0.04 eV at the bias of V=0.5 V.

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To understand the mechanism of the dependence of I-V curves on different crystallographic orientations in Ti2CO2 nanoribbons devices, detail investigations are performed on the bias-depended transmission spectra and band structures of both left and right leads for 10A, 11A and 12Z, respectively. The results are illustrated in Figure 7. For 10A, when the bias is 0.3 V, the energy bands move down and up by 0.15 eV for the left and right electrode, respectively. There are no bands that appear in the bias window shown by the bisque horizontal dash lines, and no transmission peaks appear in the energy range [-0.15 eV, 0.15 eV]. Therefore, the current is zero at the bias of 0.3 V, and the similar results are found for the case of 11A at the bias of 0.3V from Figure 7(c). When the bias is 0.9 V shown in Figure 7(b), there are some bands of the left lead in the energy range [-0.12 eV, -0.16 eV] that match the upper parts of the valence band of the right lead, therefore, the transmission spectra can be observed in the bias window. What’s more, for one of the largest transmission peaks located in -0.04 eV, the transmission coefficient is as high as 2.49. For 11A device, when the bias is 0.7 V, the match between the shifted bands of the two leads is in the energy range [-0.12 eV, 0.16 eV] leading to the transmission spectra located in the bias window as shown in Figure 7(d). The eigenstate of E= 0.04 eV which corresponds to the valley of the two transmission peaks is displayed in Figure 7(g). Obviously, the electronic state becomes more like a localized orbital with wave packets only appearing in part of the transmission region. This explains the reason that the corresponding transmission spectra are highly suppressed. So the transmission coefficient of E=0.04 eV is very small. Figure 7(h) shows the eigenstate of 11A at the an eigenvalue of 23



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E=0 eV, which is totally delocalized and spreads over the entire space of the scattering region, which implies enough channels are available for the transport of electrons in this eigenstate, in excellent agreement with the corresponding high transmission coefficient. As for 12Z device, when the bias is 0.3 V (0.5V), the transmission spectra can be seen in Figure 7(e) (7(f)). Figure 7(i) and 7(j) show the eigenstates that have delocalization feature in the scattering region at the an eigenvalue of E=0 eV (0.04eV) at the bias of 0.3V (0.5V). The notable difference in delocalization effect between these two states as seen in the figures is a reflection that the current with bias of 0.3V is lower than that of 0.5V. Here, with 14Z as an example, we also offer an explanation why the weak NDR phenomenon occurs for zigzag MXene nanoribbon. The transmission spectra of 14Z is shown in Figure 8. The yellow shadow area determines the current in the bias window. Obviously, transmission spectra have changed as the voltages change. When the bias voltage is 0.3V, the transmission spectra show the jagged peaks in the bias window, the current is 17.5µA, when the bias is increased to the 0.6 V, the transmission peaks are widened and the shaded area are larger as expected, so the current reaches 37.0 µA. When the bias voltage continuous to increase to the 0.8V, however, one should notice that a small transmission gap is generated，making the area of the transmission spectra within the bias window smaller and the current is thus decreased to only 20.9 uA, which is an indication of the NDR effect. When the bias voltage continues to increase to the 1.3V, the current increases again and reaches 56.1 µA. According to the current results, the NDR effect of different pure Ti2CO2 nanoribbons may show up in different voltage range. It is reasonable 24


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to expect that the NDR effect can be36 further amplified when the system is doped with heteroatoms or defects are considered as our previous work on graphene nanoribbons. This will be further examined in our future work.

Figure 8. The transmission spectra at specified biases of 0.3 V, 0.6V, 0.8V and 1.3 V for 14Z. The region in two vertical dash lines is the bias windows.

Finally, it is also interesting to compare the electron transport properties of MXene with other 2D materials. As the most well-known 2D material, graphene may have potential applications in electronic devices. Therefore, many studies have been performed to model the electron transport properties of graphene devices. For example, Cho et al has shown that the electronic transport properties of one dimensional devices such as graphene nanoribbons can be well modeled by the DFT method with appropriate application of dispersion corrections.36, 37 They also found both spin polarizations and orbital symmetries of the graphene nanoribbon with zigzag edges can be controlled by external magnetic field, 25



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leading to the novel design of spin-valve devices with significantly enhanced performances.38, 39 It has been found that the band gap of graphene can be opened in nanoribbons and the values of band gaps are strongly correlated with the widths and edges of the nanoribbons.2 The nanoribbons with the zigzag edges has been determined to be conductors. As to the nanoribbons with armchair edges, the band gap is dependent on the width. The structures with the width of 3N and 3N+1 carbon atoms are found to be semiconductor, but the structure with the width of 3N+2 carbon atoms is metallic.2 Accordingly, the edge and width may significantly influence the electron transport behavior of graphene nanoribbons, which has been discussed in recent works.30 Similarly, the band gap of Ti2CO2 MXenes is also determined to be dependent on the widths and edges from the current study. The nanoribbons of MXene with zigzag edges of width parameter larger than six resemble the conducting behavior of zigzag graphene nanoribbon and those with armchair edges behave like semiconductors whose band gaps change oscillatory with different widths and are also an analog to armchair graphene nanoribbons. Recently, it has been found graphene nanoribbon may have NDR effect with n- or p- type dopants.35 For MXene, the NDR effect can also be identified in this work. In summary, the MXene nanoribbons may have similarly promising electron transport features as graphene nanoribbons. Hence, the present work on the electron transport of different MXene nanoribbon may provide useful insight for the design of MXene based electronic devices.

4. CONCLUSIONS In summary, based upon ab initio calculations we examined the electronic structures of MXene (Ti2CO2) nanoribbons. It is demonstrated that the energy gaps in patterned MXene (Ti2CO2) nanoribbons can be tuned with the appropriate crystallographic orientation and 26


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widths. The results show that the armchair Ti2CO2 nanoribbons act as semiconductors while the zigzag nanoribbons show zero or little band gaps when the width parameter is larger than six. We also performed the computational study on the transport properties of MXene (Ti2CO2) nanoribbon devices, the calculations reveal that these devices have a striking nonlinear feature as well as NDR behaviors, which have been explained in detail. Altogether, our study on the charge transport of MXene nanorbbons structures can be regarded as a first step toward the development of semiconducting MXene-based electronic devices.

ACKNOWLEDGMENTS The authors acknowledge the financial support of the Division of Functional Materials and Nanodevices, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, ITaP at Purdue University for computing resources, the National Natural Science Foundation of China (Grant Nos. 51372046, 51479037 and 91226202), the Zhejiang Postdoctoral Sustentation Fund, China (Grant No.BSH1502165), the Ningbo Municipal Natural Science Foundation (No.2014A610006) and the key technology of nuclear energy, 2014, CAS Interdisciplinary Innovation Team.

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Electronic and Transport Properties of Ti2CO2 MXene Nanoribbons

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