van der Waals Stacking Induced Transition from Schottky to Ohmic

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Van der Waals Stacking Induced Transition from Schottky to Ohmic Contacts: 2D Metals on Multilayer InSe Tao Shen, Ji-Chang Ren, Xinyi Liu, Shuang Li, and Wei Liu J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 28 Jan 2019 Downloaded from http://pubs.acs.org on January 28, 2019

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Journal of the American Chemical Society

Van der Waals Stacking Induced Transition from Schottky to Ohmic Contacts: 2D Metals on Multilayer InSe Tao Shen, Ji-Chang Ren, Xinyi Liu, Shuang Li,* and Wei Liu* Nano and Heterogeneous Materials Center, School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China KEYWORDS: InSe, 2D metals, Schottky contact, Ohmic contact, Van der Waals, Density functional theory

ABSTRACT: Incorporation of two-dimensional (2D) materials in electronic devices inevitably involves contact with metals, and the nature of this contact (Ohmic and/or Schottky) can dramatically affect the electronic properties of the assembly. Controlling these properties to reliably form low-resistance Ohmic contact remains a great challenge due to the strong Fermi level pinning (FLP) effect at the interface. Herein, we employ density-functional theory calculations to show that van der Waals stacking can significantly modulate Schottky barrier heights in the contact formed between multilayer InSe and 2D metals by suppressing the FLP effect. Importantly, the increase of InSe layer number induces a transition from Schottky to Ohmic contact, which is attributed to the decrease of the conduction band minimum and rise of the valence band maximum of InSe. Based on the computed tunneling and Schottky barriers, Cd3C2 is the most compatible electrode for 2D InSe among the materials studied. This work illustrates a straightforward method for developing more effective InSe-based 2D electronic nanodevices.

INTRODUCTION Two-dimensional (2D) InSe was recently produced by mechanical exfoliation, and has been demonstrated to have high electron mobility (exceeding 103 cm2V-1s-1), comparable to black phosphorus, while remaining stable under ambient conditions.1-7 Practical use of 2D InSe in devices will require direct contact with metal electrodes to enable the injection of carriers.8 However, conventional metal-2D InSe contacts are often associated with the formation of a finite Schottky barrier which reduces carrier injection efficiency, increases contact resistance, and degrades device performance.3 Note that the contacts in InSe-based nanodevices are actually as important as InSe itself, whose excellent intrinsic properties would be masked by the high Schottky barrier at the hybrid interface.9 Therefore, the challenge of designing interfaces which form low-resistance Ohmic contact is of critical importance for the design, assembly, and fabrication of high-performance semiconductor devices. The Schottky barrier height (SBH), the energy barrier which must be overcome for charge carrier transport across the interface,10 is the parameter which differentiates Ohmic and Schottky junctions. Ohmic junctions have no such barrier. In modern silicon-based microelectronics, Ohmic contacts are achieved by either n- or p-type doping.11 Applying this scheme to improve contact properties in 2D materials, however, is not straightforward since their spatial confinement makes heavy doping challenging.12 One solution which has been deployed is the application of an electric field in a direction perpendicular to the metal-semiconductor junction (MSJ) can change the SBH to form an Ohmic contact.13 However, the required electric field for this transition is large making it infeasible for application to nanodevices. Due to the absence of effective doping methods for 2D semiconductors, the electrodes in 2D semiconductors-based transistors are usually bulk metals.8 For bulk metals, imperfections

such as dangling surface bonds contribute to large strains and chemical bonding of the semiconductor layer, altering the metalsemiconductor interface and resulting in the Fermi level pinning (FLP) effect. This effect hinders the tailoring of the SBH by varying the metal work function.14-15 As demonstrated by Kim et al.,16 a strong FLP effect results in the almost identical energy levels between MoS2 and different metal contacts, such as Ti, Cr, Au and Pd. Normally, FLP is induced by strong interface interactions, which results in localized density of states (DOS) at interfaces. Defect/Disorder-induced-gap-states (DIGS)17 and metal-inducedgap-states (MIGS)18 are the main contributions to FLP, by serving as reservoirs for electrons or holes and therefore pinning the Fermi level. The interfacial dipole10 formed by the redistribution of charge at the interface can also contribute to the FLP effect. In systems which exhibit FLP, the Schottky-Mott rule19-20 is violated and a large SBH is exhibited regardless of the metal work function thus obstructing the transport of electrons across the interface. Therefore, solving the contact problem essentially means controlling the SBH and reducing the FLP effect. For systems with weak interfacial interactions, the FLP effect can be largely surmounted21 and the Schottky-Mott limit, wherein the SBH is predictable by the innate properties of the metal and semiconductor, can be realized. Encouragingly, a very recent study has shown that the Schottky-Mott limit is closely approached by van der Waals (vdW) stacked Au film on layered MoS2.22 Conversely, chemically bonded interfaces exhibit strong FLP, which invalidates the Schottky-Mott rule. In such an interface, the chemical bonds cause charge scattering and reduce the carrier mobility. To achieve such a vdW contact of a 2D semiconductor with 3D metals requires careful treatment of defect free metal thin films laminated onto the semiconductors.22 In contrast to 3D metals, 2D metals have no surface dangling bonds, and thus vdW stacking can be more easily formed upon layering with 2D semiconductors. Graphene, a typical semimetal,

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is a promising candidate to realize pure 2D circuits.23 The graphene-MoS2 junction was recently found to exhibit low resistance Ohmic contact.24 In vdW stacked MSJ the weak interfacial interactions do not create localized DOS or potential puddles, and consequently FLP and potential scattering at the interface are reduced. The disappearance of lattice mismatching can further weaken the scattering. Therefore, it is more readily and straightforward to overcome the FLP effect and approach the Schottky-Mott limit in 2D-2D contacts. In this contribution we propose a new strategy to design lowresistance contacts. We use 2D metals (graphene; M3C225 (M = Cd, Hg, Zn); XA2 (X = Ta, V, Nb; A = S, Se)) as electrodes in contact with layered InSe to form MSJs. As the layer number of InSe increases, a transition from Schottky to Ohmic contact is achieved in several 2D metals-InSe systems. The vdW forces are found to dominate the bonding at the interface, which avoid chemical disorder, greatly suppress the interface dipole, and overcome the FLP effect. Comparison of the computed tunneling barrier and Schottky barrier suggests that Cd3C2 would be the best electrode for InSe among all 2D metals we studied.

RESULT AND DISCUSSION The optimized planar lattice constant of monolayer (ML) InSe is 4.07 Å from the optB88-vdW functional, which agrees with previous experimental and theoretical results.5, 7 The side and top views of InSe stacking on a 2D metal surface are illustrated in Figure 1a. We studied a wide range of 2D metals (Figure 1b) with chemically inert surfaces capable of binding with 2D InSe solely through vdW interactions. These metals can be roughly divided into two categories to form n-type or p-type contact. Graphene and M3C2 (M = Zn, Cd, and Hg) form n-type contact with InSe due to the low work functions (4.43 to 4.93 eV) of these 2D metals. Conversely, XA2 (X = Ta, V, and Nb, A = S and Se) possess higher work functions (5.65 to 6.44 eV) allowing them to form p-type contacts.

COMPUTATIONAL METHODS Density-functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP)26-27 and the Fritz-Haber-Institute ab initio molecular simulations (FHI-aims)28 code. We employed the optB88-vdW functional,29 as implemented in VASP, for the determination of relaxed structure, binding energy, and effective potential. This functional has been proven as a reliable method for describing vdW forces in 2D systems.30 For geometry relaxation, the shape and size of the supercell were fixed, and all the atoms were allowed to fully relax. All atomic positions were relaxed until the maximal residual forces per atom was less than 0.02 eV/Å and energy difference was smaller than 10-5 eV. A cutoff energy of 450 eV and the Monkhorst-Pack k-point sampling31 which is Γ-centered with 771 meshes were utilized. The distance of vacuum region was set to no less than 15 Å along z direction (vertical to the interface), to avoid the interaction between adjacent slabs. The band structure, work function, and DOS were calculated with the hybrid Heyd-Scuseria-Ernerhof (HSE06) functional,32 as implemented in the FHI-aims code. The hybrid functional was employed since it can remedy part of the self-interaction error in DFT. We used the “tight” setting for numerical atom-centered orbitals basis sets in FHI-aims. The convergence criteria of 10-5 electrons per unit volume for charge density and 10-6 eV for the total energy of the system were used. Note that the electronic properties of 2D heterojunctions were found to be sensitive to the vacuum settings.33 For this reason, the vacuum width was set to 100 Å for the determination of band structures and work functions. Our tests indicate that such vacuum setting gives well-converged band structures, work functions, and SBHs for our junction models (see Figure S1). To minimize the lattice mismatch (Table S1) as much as possible, the supercell matching patterns were set as follows: 1 × 1 Cd3C2 (Hg3C2) matches 3 × 3 InSe, 3 × 3 graphene matches 1 × 1 InSe,

3 × 3 Zn3C2 matches

7 × 7 InSe, 2 × 2 NbS2

(NbSe2, TaS2, TaSe2, and VSe2) matches 3 × 3 InSe, and 7 × 7 VS2 matches 2 × 2 InSe. We have computed MSJs with larger periodic cells, and found that the contact behaviors remain almost unchanged in small lattice-mismatched systems (Table S2). In addition, our calculations indicate that different stacking types have negligible perturbation on the stability and SBH values for vdW heterostructures (Figure S2, Figure S3, and Table S3).

Figure 1. (a) Side and top view of 2D metal-InSe junction, where the gray region represents 2D metals. (b) Top and side view of three types of 2D metals. (c) Computed band alignments between InSe (from 1 to 5 layers, 1L-5L) and work functions of 2D metals (Wm). Ec, Ev, Eg, and EEA represent conduction band edge, valence band edge, band gap, and electron affinities of multilayer InSe, respectively. G stands for graphene.

In the MSJs formed between these metals and InSe, the equilibrium interface distances (Deq), defined as the average out of plane distance between the Se atoms at the bottom of InSe and atoms at the top of 2D metals, are between 3.15 and 3.36 Å (c.f. Table 1) − typical distances for vdW interactions. That these interactions are vdW only is further evidenced by comparing their binding energies. Here, the binding energy (Eb) between 2D metals and ML InSe is defined as Eb = (EInSe + EM – Esys)/A, where EInSe, EM, and Esys are the total energies of ML InSe, the 2D metal, and the 2D metal-ML InSe junction, respectively; A is the interface area. According to this definition, positive value denotes favorite interface binding. The calculated Eb are in the range of 0.20 to 0.33 J/m2 (Table 1), which suggests that ML InSe is physisorbed on all the studied 2D metals. Note that for conventional MSJs, chemical bonding is normally formed at the interface, where DIGS can be hardly suppressed due to the commonly existed defects. In contrast, in our systems the vdW forces dominated interface can avoid chemical disorders. This would greatly suppress MIGS and interface dipole, finally overcome the FLP limitations. For most 3D metals (Al, Ti, Pd, Pt, Rh, and Hf) contact with ML InSe results in strong FLP at the interface.34 The FLP effect mainly originates from MIGS, DIGS, and interface dipole. The MIGS is described as a decay of metal wave function into the semiconductor, which induces localized gap states in the semiconductor. The existence of interface gap states pins Fermi energy to a certain level, making it hard to tune SBH to realize an Ohmic contact. The vdW stacking of layered InSe with 2D metals releases the lattice mismatch of the MSJ and enhances the decay of


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Journal of the American Chemical Society metal wavefunctions, thus in principle they do not suffer from disorder and the surface states of metal, and consequently avoid the the MIGS. For chemically bonded contacts, large charge transfer causes obvious interfacial dipoles, while vdW contact can significantly reduce interfacial dipoles due to the lesser charge transfer at the interface. Table 1. Equilibrium interface distance (Deq), binding energy (Eb), and Schottky barrier height (SB) of 2D metals-ML InSe junctions; work function of 2D metals (Wm), work function of 2D metals-ML InSe junctions (Wms), and their differences (EF). 2D metals graphene Cd3C2 Hg3C2 Zn3C2 TaSe2 VSe2 NbSe2 TaS2 VS2 NbS2

Deq (Å) 3.36 3.17 3.22 3.25 3.21 3.27 3.30 3.17 3.21 3.15

Eb (J/m2) 0.27 0.22 0.20 0.21 0.29 0.31 0.30 0.30 0.33 0.33

Wm (eV) 4.43 4.52 4.65 4.93 5.65 5.75 5.82 6.30 6.36 6.44

Wms (eV) EF (eV) SB (eV) 4.49 -0.06 0.01 4.57 -0.05 0.17 4.67 -0.02 0.36 4.96 -0.03 0.17 5.55 0.10 0.86 5.64 0.11 0.57 5.74 0.08 0.58 6.13 0.17 0.28 6.29 0.10 0.39 6.29 0.15 0.22

To provide a quantitative description of the FLP effect, we calculated Schottky barrier pinning factor S as35: S = d(EF)/dWm

(1)

where EF denotes the work function difference between the 2D metals (Wm) and 2D metals-ML InSe junctions (Wms). The Schottky-Mott limit is recovered when S = 0. Figure 2a illustrates that the magnitude of EF has a linear dependence on the work functions of 2D metals. In light of Eq. (1), the small S of 0.10 suggests a weak FLP. Therefore, the Fermi level of the MSJ can be varied largely with respect to the different 2D metals used, resulting in effectively tunable SBH. We further calculated the DOS of the Cd3C2-ML InSe system, and find that InSe has slight contribution to the DOS in the forbidden states (Figure 2b), exhibiting a weak MIGS at the interface.

Another factor contributing to FLP is the interfacial dipole. Figure 2c shows a plane averaged charge difference parallel to the interface between Cd3C2 and 2D InSe. The charge density difference () is estimated between entire and isolated systems, that is  = sys  M  InSe. We find that the electronic charge polarization is aggravated at the interface, which indicates the formation of an interface dipole. Since both the MIGS and the interfacial dipole are relatively small, the MSJs we studied here nearly approach the Schottky-Mott limit. This allows the tuning of the SBH by varying the 2D metals. As shown in Table 1, the SBHs can be tuned across a wide energy range (from 0.01 to 0.86 eV) in the studied systems. Based on the above analysis, 2D metals with different work functions can be employed to form a low SBH junction. By utilizing 2D metals with work function less than 4.37 eV or larger than 6.51 eV, Ohmic contact can be formed with ML InSe. However, it inevitably miss some prominent 2D metals such as graphene.36 As shown in Figure 1c, the conduction band minimum (CBM) and the valence band maximum (VBM) shift towards Fermi level as the layer number of InSe increases, rending an obvious decrease in the band gap. Notably, the layer dependent SBH for a given 2D metal-InSe contact is more dominant in the 2D limit (1-5 layers), since the InSe band-gap changes drastically only in the 2D regime. Since the SBH of the junction is determined by the energy difference between CBM (VBM) and Fermi level for n-type (ptype) doping, the decrease of SBH can be further enhanced by increasing the layers of InSe (c.f. Table S4). We applied SchottkyMott rule to estimate the SBH of our systems under the assumption that the FLP could be ignored. As shown in Figure S4, the magnitudes of SBH decrease consistently as the layer number of InSe increases. Moreover, the transition from Schottky to Ohmic contact can be found in our systems. In the case of graphene, Cd3C2, VS2, TaS2, and NbS2, Ohmic contacts can be realized with just two layers of InSe.

Figure 3. Schematic diagram of the Schottky barrier, tunneling barrier, and band structures of (a) Cd3C2-monolayer InSe and (b) Cd3C2-bilayer InSe junctions. The Schottky barrier heights (SB) are also indicated in the band structures, wherein the Fermi level is set to zero. Figure 2. (a), (d) Relative EF of the 2D metals-ML(BL) InSe junctions versus the work function values of 2D metals. The slope presents the FLP strength. (b), (e) Density of states (DOS) for Cd3C2-ML(BL) InSe. Gray lines present total DOS; pink and green lines represent the DOS projected on the Se and In, respectively. The Fermi level is set to zero. The regions between blue intervals indicate the forbidden states of InSe. (c), (f) Plane averaged charge difference along the vertical Z-direction to the Cd3C2-ML(BL) InSe interfaces. Red (blue) region represents charge accumulation (depletion) regions.

To further investigate the contact properties, we have systematically computed the band structure, work function, tunneling barrier, and SBH for all the ten MSJs that are considered in the current study (Table 1, Figure S5, and Figure S6). Here, we focus on the contact properties of the Cd3C2-InSe systems, because Cd3C2 was screened to be the most promising electrode based on



the computed tunneling barriers and Schottky barriers for 2D InSe among all materials we studied. As shown in Figure 2f, as the layer number of InSe increases, the charge accumulation/depletion is enhanced at the interface, indicating a growing interfacial dipole. The increase in the magnitude of interfacial dipole could shift the electronic levels and enhance the FLP effect. This can be seen in the value of S (0.13) of bilayer (BL) InSe system (Figure 2d), which is slightly larger than that of ML InSe (0.10). The analysis of the DOS plot (Figure 2e) shows that InSe has almost no hybridization with Cd3C2, indicating a vdW stacking of the junction. The value of SBH is 0.17 eV for Cd3C2-ML InSe junction (Figure 3a). For Cd3C2-BL InSe junction, the CBM drops to the Fermi level, indicating the disappearance of Schottky barrier at interface and thus the transition from Schottky to Ohmic contact (Figure 3b). The trade-off between the position of CBM and the extent of charge transfer indicates that it is superior to choose the junction with two layers of InSe.

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(2) 2mΦTB) ћ where ћ is the reduced Plancks constant, m is the mass of the free electron, and wTB is the width of the square potential barrier. For simplicity, we proposed a comprehensive factor C = w2TBTB to estimate the tunneling barrier (Table S5). The smaller C represents the larger tunneling probability and higher efficiency of electron injection. As shown in Figure 4b, Cd3C2 has the smallest C value, while NbS2 has the largest tunneling barrier due to the weak orbital overlaps (Figure S7). Based on the C values and SBH, the candidate materials we studied can be divided into three categories: type I, low Schottky barrier with small tunneling barrier; type Ⅱ, high Schottky barrier with large tunneling barrier; and type Ⅲ, low Schottky barrier with large tunneling barrier, as shown in Figure 4b. The work function of 2D metals in type Ⅰ (Ⅲ) mostly matches the CBM (VBM) of InSe thus form low SBH. M3C2 (M = Zn, Cd, and Hg) have a lower TB and slightly narrower wTB due to a weak interface interaction. Hence, the junctions between 2D InSe and Cd3C2, Hg3C2, and Zn3C2 show great potential for highperformance in electronic nanodevices. PTB = exp( ―

CONCLUSIONS We have systematically studied potential barriers for a series of vdW stacked metal-semiconductor junctions by combination of layered InSe with 2D metals. Tunable Schottky barrier height has been realized by selecting 2D metals with distinct work functions. The transition from Schottky to Ohmic contact occurs with the layer number of InSe increases. This contact transition is attributed to the vdW interlayer interactions between InSe layers. Two conditions, i.e., the absence of localized surface states and small interfacial dipole, should be fulfilled to design high performance 2D metal-semiconductor junctions. We find that Cd3C2-bilayer InSe performs best among all candidate materials we studied. Our study provides a new strategy to overcome the bottleneck of contact potential that exists in conventional metal-semiconductor junctions, and may promote the performance of electronic nanodevices.

Figure 4. (a) Effective potential profile of Cd3C2-ML InSe contact. The vacuum level is set to zero. (b) SB and C values of 2D metal-2D InSe junctions versus work function of 2D metals (Wm).

The transition from Schottky to Ohmic contact eliminates the Schottky barrier, and substantially improves the performance of the MSJ. However, since no strong orbital overlaps at the interface, the tunneling barrier always exists in vdW contact.8 To further increase the interface current in Ohmic contact, the tunneling barrier should be sufficiently small to enhance the transmission probability of the carriers. The tunneling barrier is characterized by two parameters: the tunneling barrier height (TB) and width (wTB).37 The magnitude of the tunneling barrier can be inferred from the effective potential (Veff) at the interface, which represents the carrier interaction with other electrons and the external electrostatic field. Low barrier height and narrow width indicate high electronic injection efficiency and thus low contact resistance. TB, the potential difference between the vdW gap (gap) and the potential energy of 2D InSe (InSe) can be characterized by the peak of Veff at the interface (Figure 4a). In our systems, obvious tunneling barriers exist at the vdW interface due to the weak interaction (Figure S6). The tunneling probability (PTB) can be calculated as38:

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Lattice mismatch of 2D metals-ML InSe junctions; computed work functions of graphene-InSe and VSe2-InSe with different lattice mismatches; total energy and Schottky barrier height of grapheneInSe and NbSe2-InSe with difference stacking types; Schottky barrier heights of 2D metal-ML(BL) InSe contacts; tunneling barrier height, tunneling barrier width and comprehensive factor of 2D metal-ML InSe contacts; band structures of Cd3C2-InSe with different vacuum widths; different stacking types of graphene-InSe and NbSe2-InSe; band structures of graphene-InSe and NbSe2-InSe with different stacking types; Schottky barrier height of Hg3C2InSe system as a function of InSe layer number; electron affinity and ionization potential of multilayer (1L-5L) InSe; band structures of Hg3C2-mutilayer (1L-3L) InSe; band structures of 2D metalsInSe junctions; effective potential profile of 2D metal-ML InSe contacts; density of states for Cd3C2-ML InSe and NbS2-ML InSe including Table S1-S5 and Figure S1-S7 (PDF).

AUTHOR INFORMATION


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Journal of the American Chemical Society Corresponding Author *[email protected] *[email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT We acknowledge supports from the NSF of China (51602155, 51722102, 21773120), the NSF of Jiangsu Province (BK20180448), the Fundamental Research Funds for the Central Universities (30918011340, 30917011201) and Jiangsu Key Laboratory of Advanced Micro&Nano Materials and Technology.

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van der Waals Stacking Induced Transition from Schottky to Ohmic

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