Schottky Barriers in Bilayer Phosphorene Transistors - ACS Applied

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Schottky Barriers in Bilayer Phosphorene Transistors Yuanyuan Pan, Yang Dan, Yangyang Wang, Meng Ye, Han Zhang, Ruge Quhe, Xiuying Zhang, Jingzhen Li, Wanlin Guo, Li Yang, and Jing Lu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b16826 • Publication Date (Web): 21 Mar 2017 Downloaded from http://pubs.acs.org on March 24, 2017

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ACS Applied Materials & Interfaces

Schottky Barriers in Bilayer Phosphorene Transistors Yuanyuan Pan1,†, Yang Dan1,†, Yangyang Wang3,*, Meng Ye1, Han Zhang1, Ruge Quhe4, Xiuying Zhang1, Jingzhen Li1, Wanlin Guo5, Li Yang6, and Jing Lu1,2,* 1

State Key Laboratory of Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, P. R. China

2

Collaborative Innovation Center of Quantum Matter, Beijing 100871, P. R. China

3

Nanophotonics and Optoelectronics Research Center, Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, P. R. China

4

State Key Laboratory of Information Photonics and Optical Communications & School of

Science, Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China 5

Key Laboratory for Intelligent Nano Materials and Devices of the Ministry of Education, P. R. China

6

Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, United States †

These authors contributed equally to this work.

*

Corresponding author: [email protected], [email protected] Abstract

It is unreliable to evaluate the Schottky barrier height (SBH) in monolayer (ML) 2D material field effect transistors (FETs) with strongly interacted electrode from the work function approximation (WFA) because of existence of the Fermi-level pinning. Here, we report the first systematical study of bilayer (BL) phosphorene FETs in contact with a series of metals with a wide work function range ( Al, Ag, Cu, Au, Cr, Ti, Ni, and Pd) by using both ab initio electronic band calculations and quantum transport simulation (QTS). Different from only one type of Schottky barrier (SB) identified in the ML phosphorene FETs, two types of SBs are identified in BL phosphorene FETs: the vertical SB between the metallized and the intact phosphorene layer, whose height is determined from the energy band analysis (EBA); the lateral SB between the metallized and the channel BL phosphorene, whose height is determined from the QTS. The vertical SBHs show a better consistency with the lateral SBHs of the ML phosphorene FETs from the QTS compared than the popular WFA. Therefore, we develop a better and general method than the WFA to estimate the lateral SBHs of ML semiconductor transistors with strongly interacted electrodes based on the EBA for its BL counterpart. In terms of the QTS, n-type lateral Schottky contacts are formed between BL phosphorene and Cr, Al, and Cu electrodes with electron SBH of 0.27, 0.31, and 0.32 eV, respectively, while p-type lateral Schottky contacts are formed between BL phosphorene and Pd, Ti, Ni, Ag, and Au electrodes with hole SBH of 0.11, 0.18, 0.19, 0.20, and 0.21 eV, respectively. The theoretical polarity and SBHs are in good agreement with available experiments. Our study provides an insight into the BL phosphorene-metal interfaces that are crucial for designing the BL phosphorene device. Keywords: bilayer phosphorene transistor, interface, Schottky barrier, energy band, quantum transport simulation 1

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Introduction Phosphorene, one of the youngest members of the two-dimensional (2D) material family, was successfully isolated from the layered black phosphorus crystals in early 2014.1-8 It has attracted tremendously renewed attentions because of its tunable direct band gap covering the visible to midinfrared range, high carrier mobility, and unique electronic, thermal, and electromechanical anisotropy.3, 9-15 Both monolayer (ML) and multilayer phosphorene field effect transistors (FETs), have been successively fabricated in experiments with a remarkable on/off ratio of ~105.1, 7 Forming low contact resistance in phosphorene FETs is a great challenge because a Schottky barrier (SB) always appears at metal and phosphorene interfaces.16-19 The quality of electrical contacts is even as crucial to the performance of the phosphorene device as phosphorene itself when the channel is in the nanoscale region.17 Thus, there is a need to clarify the interfacial properties of phosphorene and metals to facilitate the design of phosphorene FETs. Compared with ML phosphorene, multilayer phosphorene, which has a smaller band gap,9, 20-22 is expected to achieve a smaller SB or even an Ohmic contact. More importantly, multilayer phosphorene is more stable than ML phosphorene on exposure to ambient conditions, and actually most of the phosphorene FETs in experiments are multilayer FETs.14, 15 Several works have focused on the ML phosphorene-metal interfacial nature;23-26 but the nature of multilayer phosphorene-metal contacts is still vague. Bilayer (BL) phosphorene-metal contacts represent the simplest form of multilayer phosphorene contact with metals.27 To our knowledge, no systematic works have been carried out to analyze the interfacial properties of BL phosphorene and metal in a FET configuration. Due to the high activity, ML phosphorene tends to strongly interact with the metal electrodes and inevitably undergoes a metallization; as a result, the SB always appears in the lateral direction in a ML phosphorene FET.26 The popular theoretical method to evaluate the lateral Schottky barrier height (SBH) of 2D semiconductor FETs with strongly interacted electrodes is the work function approximation (WFA), in which the SBH is estimated by the difference of the Fermi level of metallized 2D materials and the conduction band minimum (CBM) or the valence band maximum (VBM) of the free-standing channel 2D material, completely ignoring the interaction between the metal electrodes and the channel semiconductors.26, 28 Unfortunately, such an approximation cannot give a reliable lateral SBH if there is a strong coupling between metallized 2D materials and metal electrodes.26, 28 Quantum transport simulation (QTS) based on the two-probe model is a more accurate method for evaluating the lateral SBH of 2D semiconductor FETs with strongly interacted electrodes 2


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because it includes the coupling between metal electrodes and channel semiconductors.26, 28 Our recent work clearly confirmed that the polarity and height of SB for the ML phosphorene FETs obtained from the QTS are indeed in much better agreement with measurements compared with the WFA.26 However, the QTS is much more complicated and time-consuming than the electronic band calculation. So far it is unclear whether there is a better way to estimate the lateral SBH of 2D semiconductor FETs with strongly interacted electrodes from the relatively simple electronic band calculation than the WFA without resort to the complicated QTS. In the paper, the interfacial nature of BL phosphorene with a series of metals spanning a wide work function range (Al, Ag, Cu, Au, Cr, Ti, Ni, and Pd) in a FET configuration has been systematically studied for the first time by using both the ab initio electronic band calculations and the ab initio QTS. Different from the ML phosphorene transistors, where only one type of SB (namely lateral SB) can be identified, there are two types of SB confirmed in BL phosphorene transistors: vertical SB is formed in the interfaces between the metallized and contacted phosphorene layer and the uncontacted phosphorene layer; lateral SB is formed in the interfaces between metallized BL phosphorene and the channel BL phosphorene. The vertical SBHs can be derived from the energy band analysis (EBA) of the BL phosphorene-metal interfacial system and they turn out to be in better accord with the lateral SBHs of the ML phosphorene transistor derived from the OTS compared with the lateral SBH of the ML phosphorene transistor derived from the WFA. Therefore, a new and better energy-band-based method is thus developed to estimate the SBH of a ML material transistor totally based on the EBA of its BL counterpart-metal interfacial system. According to the OTS, BL phosphorene forms n-type SB contacts with Cr, Al, and Cu electrodes and p-type SBs contact with Pd, Ti, Ni, Ag, and Au electrodes. Impressively, the observed polarity and SBHs of the phosphorene FETs from the QTS are consistent with the existing measurements. Methods The examined metals, Al, Ag, Cu, Au, Ti, Cr, Ni, and Pd, are commonly used as electrodes in experiments.1, 3, 4, 6, 7, 11, 29, The work functions of these metals vary greatly, which helps to control the carrier type in BL phosphorene when controllable and sustainable substitutional doping method in 2D materials remains inaccessible today. In our supercells, we use five layers of metal atoms to represent the metal surface, and put BL phosphorene on one side of it, with the initial distance between the two surfaces set to 3.5 Å, as indicated in Figure 1. The layer of BL phosphorene closer to metal is defined as the top phosphorene layer, while the layer farther to metal is defined as the bottom phosphorene 3



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layer. The lattice constants of the metal supercells are fixed and BL phosphorene, which has gone through geometry optimization with lattice constants a = 4.52 Å and b = 3.33 Å consistent with the previous works,20, 27 are strained to match them. Ni is an exception because we found that the transport gap and SBH are susceptible to the match way in the trial calculations. We have calculated the transport SBH for two match models: in model I, the lattice constant of BL phosphorene is adapted to that of Ni; in model II, the lattice constant of Ni is adapted to that of BL phosphorene. In model I, the electron and hole SBH is 0.18 and 0.13 eV, respectively, with a transport gap of 0.31 eV, while in model II, the electron and hole SBH is 0.52 and 0.19 eV, respectively, with a transport gap of 0.71 eV. The observed electron and hole SBH with Ni electrode is 0.23 and 0.48 eV, respectively, with a transport gap of 0.71 eV. Thus, adapting the lattice constant of Ni to that of BL phosphorene is more reasonable. The √(2𝑎)2 + 𝑏 2 × √𝑎2 + 𝑏 2 BL phosphorene matches 2 × 2 Al, Ag, Au and 2  2 Cr surfaces in the (110) orientation. The a × 3b, a × 3b, and a × 5b BL phosphorene

matches

3  4 Cu,

3  4 Ni and

3  6 Pd surfaces in the (111) orientation, respectively. The

a × 3b BL phosphorene matches 2 × 1 Ti surface in the (0001) orientation. The mismatches, as shown in Table 1, range from 1.39 % to 2.00 %. For each case, the length of the vacuum buffer space is at least 12 Å. The phosphorus atoms interact mainly with metal atoms at the top two layers, so the three layers at the bottom of the metal surfaces are fixed, and so does the cell shape. We use Vienna ab initio simulation package (VASP)30, 31 to perform geometry optimization and electronic structure calculation. The pseudopotential is projector-augmented wave (PAW), and planewave basis set is used, with the cut-off energy set to 400 eV.32,

33

The generalized gradient

approximation (GGA) with the Perdew−Burke−Ernzerhof (PBE) parameterization of the exchangecorrelation functional is employed.34 The criteria for convergence is 0.01eV/ Å for the residual force, and 1 × 10-5 eV per atom for the energy. K-points are sampled by the Monkhorst-Pack method with a separation of about 0.02 Å-1 in the Brillouin zone.35 Two corrections are introduced. The first one is concerned with Van der Waals interaction, which plays an important role in the cohesion between the layers of phosphorene, and here we use the vdW-DF level of optB88 exchange functional (optB88vdW).36 Besides, dipole correction is used to get rid of the spurious interaction caused by the dipole moments of periodic images in the z direction, which is the result of the asymmetry of the interfaces. Strong metallization occurs in the combined BL phosphorene-metal systems without considering spinorbit coupling and onsite U energy. Including spin-orbit coupling and onsite U energy will not affect 4


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the metallization. Including spin-orbit coupling and onsite U energy will indeed influence the work function of the combined BL phosphorene-metal systems. However, because of Fermi level pinning between the combined systems and channel BL phosphorene, spin-orbit coupling and onsite U energy are expected to have insignificant effect on the SBHs. A two-probe model (Figure 1(a)) is built to simulate a BL phosphorene FET. The channel region along the transport direction consists of ~ 50 Å ML phosphorene. The electrodes adopt the optimized BL phosphorene-metal interfaces and the channel adopts the free standing BL phosphorene. The lengths of the left electrode and right electrode are semi-infinite. The transport properties are calculated by using DFT coupled with nonequilibrium Green’s function (NEGF) method, which are implemented in Atomistix Tool Kit (ATK) 2016 package.37-39 The transmission coefficient 𝑇 𝒌∥ (𝐸) ( 𝒌∥ is a reciprocal lattice vector point along a surface-parallel direction (orthogonal to the transmission direction) in the irreducible Brillouin zone (IBZ)) is calculated as 𝒌

𝒌

𝑇 𝒌∥ (𝐸) = Tr [𝛤𝐿 ∥ (𝐸)𝐺 𝒌∥ (𝐸)𝛤𝑅 ∥ (𝐸)𝐺 𝒌∥ † (𝐸)] 𝒌

(1) 𝑟,𝒌

𝑎,𝒌

∥ (𝐸) = 𝑖 (∑𝐿/𝑅∥(𝐸) − ∑𝐿/𝑅∥ (𝐸)) where 𝐺 𝒌∥ (𝐸) is the retarded (advanced) Green’s function and 𝛤𝐿/𝑅

represents the level broadening due to left electrode and right electrodes expressed in terms of the 𝒌

∥ electrode self-energies ∑𝐿/𝑅 (𝐸) , which reflects the influence of the electrodes on the scattering

region.40 The transmission function at a given energy T (E) is averaged over different 𝒌∥ in the IBZ. Single-  plus polarization (SZP) basis set is employed, the real-space mesh cutoff is at least of 400 eV, and the temperature is set at 300 K. The electronic structures of electrodes and central region are calculated with a Monkhorst–Pack35 50 × 1 × 50 and 50 × 1 × 1 k-point grid, respectively. GGA of PBE form34 to the exchange-correlation functional is used.

Results and discussion Interfacial structure of the BL phosphorene-metal systems The main parameters of BL phosphorene-metal interfaces based on the ab initio electronic structure calculations and the ab initio QTS are listed in Table 1. Binding energy Eb is calculated as Eb = (EP + EM – EP-M)/N

(2)

where EP, EM, and EP-M are the total energies of the free standing BL phosphorene, free standing metal and the merged system, respectively, and N is the atom number of the phosphorene sublayer (indicated by letter Iʹ sublayer in Figure 1) that contacts the metal atoms directly in the supercell. The equilibrium interlayer distance dP-M is the average distance in the z direction between the metal sublayer I and the 5



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phosphorene sublayer Iʹ indicated in Figure 1. The minimum interatomic distance dmin is the minimum distance between a phosphorus atom and a metal atom. In terms of the binding energy and the two kinds of distances, the BL phosphorene-metal interfaces can be classified into two categories. The first category, consisting of the BL phosphorene-Ag, Al, Au, and Cu interfaces, belongs to weak bonding between BL phosphorene and the metal surface, with relatively small binding energies Eb ranging from 0.48 to 0.65 eV, and relatively greater distances dP-M and dmin, ranging from 2.30 to 2.49 Å, and from 2.36 to 2.58 Å, respectively. The second category, consisting of the BL phosphorene-Cr, Ti, Ni, and Pd interfaces, belongs to strong bonding, with relatively large binding energies Eb ranging from 1.44 to 2.76 eV, and relatively smaller distances dP-M and dmin, ranging from 1.61 to 2.17 Å, and from 2.07 to 2.39 Å, respectively. The different binding levels are related to the different occupied level of d-orbital of metals. Cr, Ti, Ni, and Pd have partially occupied d-orbitals, which form extra dorbital related covalent bonds with the orbitals of phosphorus atoms in addition to the s-orbital related covalent bond. While Ag, Al, Au, and Cu have unfilled or fully filled d-orbitals, they do not form extra d-orbital related covalent bonds with the orbitals of phosphorus atoms. The difference of the two categories is also reflected on the optimized configurations as shown in Figure 2. The structure of BL phosphorene is nearly invariable before and after weak bonding, while it is distorted after strong bonding, especially for Pd, Cr, and Ti metals. The binding degree and the distortion degree of the BL phosphorene-metal interfaces are consistent with those of the ML phosphorene-metal interfaces.26 The interactions between BL phosphorene and metals, while stronger than those between metals and the light IVA group 2D materials, such as graphene, graphdiyne, silicene, or germanene41-45, are weaker than those between metals and the heavy IVA group 2D materials, such as stanene46. Electronic band structure of the BL phosphorene-metal systems To further understand the coupling of metals with BL phosphorene, we extract the energy band structures of BL phosphorene (red line) and the phosphorene layer away from metals (green line) separately as shown in Figure 3. The band structures of BL phosphorene are seriously destroyed in all absorbed systems with the disappearance of band gap, which indicates strong hybridizations between metal and BL phosphorene. The energy band shapes of the phosphorene layer further away from metals are preserved in all systems, and the energy band gap are almost preserved in all systems except for the BL phosphorene-Cu and Au systems. Thus, the metal electrodes mainly interact with the top phosphorene layer and the other phosphorene layers are nearly intact. The decrease of the gap of the 6


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bottom phosphorene layer with Cu and Au metals are owing to the splitting of its CBM and VBM. The splitting of the CBM and the VBM of the uncontacted phosphorene with Cu and Au substrates results from the Van der Waals perturbation of the metallized phosphorene layer, which has many states around the CBM and the VBM. Partial density of states (PDOS) is another indicator reflecting the metallization of BL phosphorene. As shown in Figure 4, there is a large amount of states of BL phosphorene distributed around the Fermi level in all interfaces, which further indicates the metallization of BL phosphorene. We further extract the PDOS of the top and bottom phosphorene layer depicted in Figure S1 and Figure 5, respectively. There are states of the top phosphorene layer accumulated around the Fermi level, demonstrating the metallization of the top phosphorene layer and strong interactions between the top phosphorene layer and the metals. No states of the bottom phosphorene layer accumulate around the Fermi level and the band gap of the bottom phosphorene layer is consistent with the band gap of pristine ML phosphorene. The coupling of the metals with BL phosphorene from the DOS calculations is in accordance with the energy band analysis. Fermi level shift and charge transfer in the BL phosphorene-metal systems The work functions of BL phosphorene and metals differ. When BL phosphorene contacts with metals, electron will transfer from one to the other to equilibrate the Fermi levels. The calculated Fermi level shift of BL phosphorene ΔEf is defined as ΔEf = W - WP

(3)

Where W and WP are the work function of BL phosphorene-metal systems and free standing BL phosphorene, respectively. ΔEf as a function of the clean metal and BL phosphorene work function difference WM − WP is plotted in Figure 6(a). Charge transfers from BL phosphorene to metals with Ag and Al electrodes with the Fermi level shift ΔEf < 0; while charge transfers from metals to BL phosphorene with Ti, Cu, Cr, Au, Pd, and Ni electrodes with the Fermi level shift ΔEf > 0. The cross point between n- and p-type doping is found to for a metal with the work function WM = WP – 0.24 eV. Thus, in addition to the covalent interaction, there is charge transfer interaction between BL phosphorene and metals. To visualize the charge redistributions, we plotted the charge density difference of BL phosphorene-Al, Cr, Cu, and Au systems in Figure 6(b-e). The charge density difference is defined as Δρ = ρP-M – ρM – ρP

(4)

Where ρP-M, ρM, ρP is the charge density of BL phosphorene-metal systems, free standing metals, and 7



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free standing BL phosphorene, respectively. There is apparent charge loss for Al electrode when interacting with BL phosphorene, while there is apparent charge gain for Cr, Cu, and Au electrodes. Vertical Schottky barriers in the BL phosphorene-metal systems Charges injected from metal electrodes (region A) to the channel BL phosphorene (region G) come across three interfaces (B, D, and F) as shown in Figure 1(b): interface B is between the metal electrodes and the top phosphorene layer under the metal electrodes (region C); interface D is between the top phosphorene layer (region C) and the bottom phosphorene layer (region E); interface F is between the BL phosphorene under the metal electrodes and the channel BL phosphorene. SB can exist in all the three interfaces, while tunneling barrier can exist in the interface B and D. The tunneling barriers refer to the potential above the Fermi level in the distribution of the average electrostatic potentials in the direction perpendicular to the interfaces as shown in Figure 2. There are no potentials above the Fermi level in all the interfaces, so no tunneling barriers appear in both the interface B and D in the BL phosphorene FETs. The vertical electron (hole) SBH at the interface B is determined from the energy difference between the Fermi level and the CBM (VBM) of the top phosphorene layer. There is no SBH at the interface B owing to the total damage of the energy band structure of the top phosphorene layer (contact layer), as shown in Figure 3, and electrons can directly transfer across the interface B from the metal electrodes to the top layer phosphorene. The band structures of the bottom phosphorene layer (non-contact layer) are almost preserved in all the interfacial systems depicted in Figure 3. Therefore, a vertical electron (hole) SBH appears at the interface D (𝛷BL,V), which is determined by the difference of the Fermi level and the identifiable CBM (VBM) of the bottom phosphorene layer (we refer to it as EBA method). The values of 𝛷BL,V and the band gap of the bottom phosphorene layer away from metals are listed in Table S1. N-type Schottky contact is formed at the interface D with Cr, Al, Ag, and Ti with electron SBH of 0.39, 0.40, 0.42, and 0.50 eV, respectively, while p-type Schottky contact is formed with Cu, Au, Ni, and Pd with hole SBH of 0.19, 0.30, 0.43, and 0.45 eV, respectively. The band gap of the non-contact phosphorene layer with Cu, Au, Ag, Al, Pd, Ni, Ti, and Cr is 0.47, 0.70, 0.92, 0.93, 0.99, 1.05, 1.11, and 1.14 eV, respectively. The band gap of that phosphorene layer is in line with the free-standing ML phosphorene band gap of about 1.0 eV except for Cu and Au, which have smaller band gaps. Comparison with the lateral SBHs in the ML phosphorene FETs In the ML phosphorene FETs, SB only exists in the lateral direction between the ML phosphorene under metal electrodes and the channel ML phosphorene due to the metallization of ML phosphorene 8


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under metal electrodes.26 The lateral electron (hole) SBH is often estimated by the difference of the Fermi level of the metallized ML phosphorene and the CBM (VBM) of the free-standing ML phosphorene channel (namely WFA).16, 47, 48 Under the WFA, the coupling between the metallized ML phosphorene and the channel ML phosphorene is ignored. A more reliable approach to calculate the lateral SBH of the ML phosphorene FETs is the ab initio QTS based on a two-probe model, where the coupling is taken into consideration. The WFA gives a hole SBH of 0.02 eV for the ML phosphorene FET with Ni electrode. The extracted experimental transport hole SBH of ML phosphorene with Ni electrode is 0.35 ± 0.02 eV, which favors the QTS’s hole SBH of 0.26 eV. 26 The vertical SBHs of the BL phosphorene FETs from the EBA at the interface D and the lateral SBHs of the ML phosphorene FETs26 obtained from the WFA and the QTS are compared in Figure 7 and listed in Table S1. The vertical SBHs in the BL phosphorene FETs show a better consistency with the lateral SBHs of the ML phosphorene FET from the ab initio QTS compared with the WFA. For example, the vertical SB of the BL phosphorene FET with Cr electrode is n-type, in accordance with the lateral SB polarity of the ML phosphorene FET by the QTS, while the lateral SB of the ML phosphorene FET is p-type by the WFA. Artificial lateral Ohmic contact is obtained in the ML phosphorene FET with Pd electrode by the WFA, whereas SB exists in both the vertical direction in the BL phosphorene FET according to the EBA and the lateral direction in the ML phosphorene FET according to the QST. Therefore, the EBA of their BL counterparts is a better energy-band-based method to evaluate the lateral SBH of the ML phosphorene FETs than the popular WFA. The polarities of the vertical SB in the BL phosphorene FETs by the EBA are identical to the lateral SBs in the ML phosphorene FET from the QTS except for Ti electrode. The contrast of the n-type polarity in the vertical SB in the BL phosphorene FET from the EBA against the p-type character in the lateral SB in the ML phosphorene FET from the QTS reflects that the Fermi level pinning ability of the MIGS (metal induced gap states) in the vertical direction of the BL phosphorene FET are different from those in the lateral direction of the ML phosphorene FET with Ti electrode, and the latter have the stronger Fermi level pinning and pin the Fermi level to a position close to the valence band maximum. The schematic band alignments of the ML phosphorene FETs at the interface H and the BL phosphorene FETs at the interface D are shown in Figure S2. The better consistency between the vertical SBHs of the BL phosphorene FETs from the EBA and the lateral SBHs of the ML phosphorene FETs from the QTS is attributed to the fact that the coupling between the metallized ML phosphorene and the semiconducting ML phosphorene, which often leads to a Fermi level pinning, 28, 40, 42, 47, 49-52 9



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has been fully taken into consideration in the two schemes because the metal and semiconducting parts have been treated as a whole. The band alignments at these two interfaces are similar with each other if including the couplings, and thus the height and polarity of the SBs in these two kinds of interfaces are similar except that charge carriers will encounter a Van der Waals gap between the top and bottom phosphorene layer in the BL phosphorene FETs. By contrast, in the WFA, the coupling and thus the Fermi level pinning between the electrodes and the channel ML phosphorene are excluded, and thus poor results are obtained. The EBA can be extended to evaluate the lateral SBH in other ML semiconductor transistors with a strong coupling with electrodes only by analyzing their BL counterparts in a semi-infinite model, which avoids the more complicate QTS in a two-probe model. In the case of weak coupling between metal electrodes and the ML semiconductor, the band structure of the ML semiconductor is preserved. Charge carriers will just encounter a vertical SB, and the vertical electron (hole) SBH are directly extracted by the difference between the Fermi level and the CBM (VBM) of the ML semiconductors obtained from the semi-infinite interfacial model (namely the EBA) in agreement with those from the QTS for a two-probe model.26, 28 Lateral Schottky barriers of the BL phosphorene FETs tran In the QTS scheme, the lateral electron (hole) SBH 𝛷BL,L at the interface F is extracted from the

energy difference between the Fermi level and the CBM (VBM) of the transport gap in the zero-bias transmission spectra. Zero-bias transmission spectra of the channel in the BL phosphorene FETs are depicted in Figure 8(a-b) by using the ab initio QTS. BL phosphorene forms n-type Schottky contact with Cr, Al, and Cu with electron SBH of 0.27, 0.31, and 0.32 eV, respectively, and p-type Schottky contact with Pd, Ti, Ni, Ag, and Au with hole SBH of 0.11, 0.18, 0.19, 0.20, and 0.21 eV, respectively. Consistently, the previous experiments show that p-type phosphorene FETs are formed with Ni and Pd electrodes,7,29,53 and n-type phosphorene FETs transformed from pristine p-type FETs realize by employing Al contacts11 and Cu adatoms diffusion.54 The smaller hole SBH of Pd electrode (0.11 eV) than Ni electrode (0.19 eV) agrees well with the experimental result of a smaller contact resistance with Pd electrode than Ni electrode.53 More importantly, the available hole (electron) SBH of the BL phosphorene FET in experiment with value of 0.23 (0.48) eV is exceedingly consistent with our result that of 0.19 (0.52) eV with Ni electrode,7 and the observed hole SBH of 0.21 eV is in accordance with that of 0.18 eV with Ti electrode30 as shown in Figure 8(b).7 The transport gap is defined as 𝐸gtran = ℎ,tran 𝑒,tran 𝛷BL,L + 𝛷BL,L . The simulated transport gap with Ti, Cu, Al, Au, Ni, Ag, Cr, and Pd electrodes

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is 0.59, 0.68, 0.68, 0.69, 0.71, 0.74, 0.76, and 0.83 eV, respectively, which are in keeping with the observed transport gap of 0.71 eV with Ni electrode.7 we Local device density of states (LDDOS) of the BL phosphorene FETs with Al, Au, Cr, and Pd electrodes are depicted in Figure 8(c-f), which represent the energy distributions in the real space. Ntype BL phosphorene FETs are formed for Al and Cr electrodes with the electron SBH of 0.28 and 0.20 eV, respectively, while p-type BL phosphorene FETs are formed for Au and Pd electrodes with the hole SBH of 0.23 and 0.25 eV, respectively. The polarity and SBH from LDDOS calculations are consistent with those extracted from the transmission spectra. No apparent charge carriers transfer from electrodes to the channel BL phosphorene with Al, Au, and Pd electrodes, leading to the flat conduction and valance band. For BL phosphorene with Cr electrode, there is electron transfer from electrode to the channel BL phosphorene showing the conduction band bent downward. Apparent interfacial states emerge in these BL phosphorene FETs and are identified as MIGS as indicated in Figure 8 (c-f), which are responsible for the strong Fermi level pinning between the electrode and BL phosphorene (as shown in the next). The lateral SBHs are generally estimated by the WFA, and under this approximation, the coupling between the electrodes and the channel and thus the Fermi pinning are completely ignored. The 𝑒,WFA ℎ,WFA electron (hole) SBHs 𝛷BL,L (𝛷BL,L ) at the lateral interface F estimated by the WFA are shown in

Figure 9. Under the WFA, n-type SB is formed at the BL phosphorene-Al interface with the electron SBH of 0.26 eV; p-type SBs are formed at the BL phosphorene-Cu, Cr, Ti, and Ag interfaces with hole SBH of 0.10, 0.12, 0.34, and 0.40 eV, respectively; while Ohmic contacts are formed at the BL phosphorene-Pd, Au, and Ni interfaces. The p-type SB with Cu electrodes disagree with the n-type SB in experiment54 and by the QTS. What’s more, artificial Ohmic contacts formed with Ni and Pd electrodes are apparently unmatched with the experimental p-type Schottky contacts.7, 53, 55 Thus, the SBHs obtained by the ab initio QTS are more reasonable and precious than those by the WFA without including the coupling between electrodes and the channel BL phosphorene, same as that in the ML phosphorene FETs.26 If the Fermi level pinning is absent, the polarity and height of the SBs obtained from the two methods would be equal. The great difference between the polarity and height of the SBs obtained from the two methods reflects a strong Fermi level pinning between the electrodes and the channel BL phosphorene, which is caused by the MIGS shown in Figure 8. It is interesting to check the layer number dependence of the SBHs. Figure 10 shows the calculated and observed electron and hole SBHs as a function of the layer number of phosphorene with Ni and 11



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Cu electrodes (layer number n = 1, 2, and 3).7, 26 The observed SBHs always decrease with the increasing layer number with Ni electrode. The calculated SBHs are generally consistent well with the observed SBHs except that the electron SB of ML phosphorene with Ni electrode is underestimated. Conclusions In summary, we have systematically explored the SBHs in BL phosphorene FETs with a broad range of typical metal electrodes by using both the ab initio energy band calculations and the ab initio QTS. In terms of the ab initio QTS, BL phosphorene forms n-type Schottky contacts with Cr, Al, and Cu electrodes with lateral SBHs of 0.27, 0.31, and 0.32 eV, respectively, and p-type Schottky contacts with Pd, Ti, Ni, Ag, and Au electrodes with lateral SBHs of 0.11, 0.18, 0.19, 0.20, and 0.21 eV, respectively. The calculated polarity and SBHs of the BL phosphorene FETs are consistent with recent experiments. Moreover, we find that the vertical SBHs in BL phosphorene FETs derived from the EBA are in better agreement with the lateral SBHs in ML phosphorene FETs from the QTS than the widely used WFA because of the partial inclusion of the coupling between the electrodes and the channel semiconductors in the EBA method. Thus, we propose a better and general energy-band-based method to evaluate the lateral SBH of ML semiconductor transistors with strongly interacted electrodes (namely, the EBA of their BL counterpart-metal interfacial system) than the popular WFA. Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Tables of comparison of SBH, PDOS of the first phosphorene layer, Schematic configurations and band alignments of the ML phosphorene FETs.

Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 11674005/11274016/11474012/11274233), the National Basic Research Program of China (No. 2013CB932604/ 2012CB619304), the National Science Foundation Grant (1207141), National Foundation for Fostering Talents of Basic Science (No. J1030310/J1103205), National Materials Genome Project (2016YFB0700600), and Open Fund of Key Laboratory for Intelligent Nano Materials and Devices of the Ministry of Education of China (INMD-2016M03). We thank Kalpana Bodavula for the help in English modification.

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References 1. Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y., Black Phosphorus Field-effect Transistors. Nat. Nanotechnol. 2014, 9 (5), 372-377. 2. Reich, E. S., Phosphorene Excites Materials Scientists. Nature 2014, 506, 19. 3. Wang, H.; Wang, X.; Xia, F.; Wang, L.; Jiang, H.; Xia, Q.; Chin, M. L.; Dubey, M.; Han, S. J., Black Phosphorus Radio-frequency Transistors. Nano Lett. 2014, 14 (11), 6424-6429. 4. Xia, F.; Wang, H.; Jia, Y., Rediscovering Black Phosphorus as an Anisotropic Layered Material for Optoelectronics and Electronics. Nat. Commun. 2014, 5, 4458. 5. Ni, Z.; Liu, Q.; Tang, K.; Zheng, J.; Zhou, J.; Qin, R.; Gao, Z.; Yu, D.; Lu, J., Tunable Bandgap in Silicene and Germanene. Nano Lett. 2012, 12 (1), 113-118. 6. Liu, H.; A., N.; Zhu, Z.; Luo, Z.; Xu, X.; Toma´nek, D.; Ye, P. D., Phosphorene: an Unexplored 2D Semiconductor with a High Hole Mobility. ACS Nano 2014, 8 (4), 4033–4041. 7. Das, S.; Zhang, W.; Demarteau, M.; Hoffmann, A.; Dubey, M.; Roelofs, A., Tunable Transport Gap in Phosphorene. Nano Lett. 2014, 14 (10), 5733-5739. 8. Churchill, H. O.; Jarillo-Herrero, P., Two-dimensional Crystals: Phosphorus Joins the Family. Nat. Nanotechnol. 2014, 9 (5), 330-331. 9. Qiao, J.; Kong, X.; Hu, Z. X.; Yang, F.; Ji, W., High-mobility Transport Anisotropy and Linear Dichroism in Few-layer Black Phosphorus. Nat. Commun. 2014, 5, 4475. 10. Fei, R.; Yang, L., Strain-engineering the Anisotropic Electrical Conductance of Few-layer Black Phosphorus. Nano Lett. 2014, 14 (5), 2884-2889. 11. Perello, D. J.; Chae, S. H.; Song, S.; Lee, Y. H., High-performance n-type Black Phosphorus Transistors with Type Control via Thickness and Contact-metal Engineering. Nat. Commun. 2015, 6, 7809. 12. Favron, A.; Gaufres, E.; Fossard, F.; Phaneuf-L'Heureux, A. L.; Tang, N. Y.; Levesque, P. L.; Loiseau, A.; Leonelli, R.; Francoeur, S.; Martel, R., Photooxidation and Quantum Confinement Effects in Exfoliated Black Phosphorus. Nat. Mater. 2015, 14, 826–832. 13. Doganov, R. A.; O'Farrell, E. C.; Koenig, S. P.; Yeo, Y.; Ziletti, A.; Carvalho, A.; Campbell, D. K.; Coker, D. F.; Watanabe, K.; Taniguchi, T.; Castro Neto, A. H.; Ozyilmaz, B., Transport Properties of Pristine Few-layer Black Phosphorus by van der Waals Passivation in an Inert Atmosphere. Nat. Commun. 2015, 6, 6647. 14. Liu, H.; Du, Y.; Deng, Y.; Ye, P. D., Semiconducting Black Phosphorus: Synthesis, Transport Properties and Electronic Applications. Chem. Soc. Rev. 2015, 44 (9), 2732-2743. 15. Kou, L.; Chen, C.; Smith, S. C., Phosphorene: Fabrication, Properties, and Applications. J. Phys. Chem. Lett. 2015, 6 (14), 2794-805. 16. Kang, J.; Liu, W.; Sarkar, D.; Jena, D.; Banerjee, K., Computational Study of Metal Contacts to Monolayer Transition-metal Dichalcogenide Semiconductors. Phys. Rev. X 2014, 4 (3), 031005. 17. Allain, A.; Kang, J.; Banerjee, K.; Kis, A., Electrical Contacts to Two-dimensional Semiconductors. Nat. Mater. 2015, 14 (12), 1195-1205. 18. Fiori, G.; Bonaccorso, F.; Iannaccone, G.; Palacios, T.; Neumaier, D.; Seabaugh, A.; Banerjee, S. K.; Colombo, L., Electronics Based on Two-dimensional Materials. Nat. Nanotechnol. 2014, 9 (10), 768-79. 19. Wan, R.; Cao, X.; Guo, J., Simulation of Phosphorene Schottky-barrier Transistors. Appl. Phys. Lett. 2014, 105 (16), 163511. 20. Guo, H.; Lu, N.; Dai, J.; Wu, X.; Zeng, X. C., Phosphorene Nanoribbons, Phosphorus Nanotubes, and van der Waals Multilayers. J. Phys. Chem. C 2014, 118 (25), 14051-14059. 21. Low, T.; Roldán, R.; Wang, H.; Xia, F.; Avouris, P.; Moreno, L. M.; Guinea, F., Plasmons and 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Screening in Monolayer and Multilayer Black Phosphorus. Phys. Rev. Lett. 2014, 113 (10), 106802. 22. Tran, V.; Soklaski, R.; Liang, Y.; Yang, L., Layer-controlled Band Gap and Anisotropic Excitons in Few-layer Black Phosphorus. Phys. Rev. B 2014, 89 (23), 235319. 23. Gong, K.; Zhang, L.; Ji, W.; Guo, H., Electrical Contacts to Monolayer Black Phosphorus: A First-principles Investigation. Phys. Rev. B 2014, 90 (12), 125441. 24. Du, Y.; Ouyang, C.; Shi, S.; Lei, M., Ab Initio Studies on Atomic and Electronic Structures of Black Phosphorus. J. Appl. Phys. 2010, 107 (9), 093718. 25. Chanana, A.; Mahapatra, S., First Principles Study of Metal Contacts to Monolayer Black Phosphorous. J. Appl. Phys. 2014, 116 (20), 204302. 26. Pan, Y.; Wang, Y.; Ye, M.; Quhe, R.; Zhong, H.; Song, Z.; Peng, X.; Yu, D.; Yang, J.; Shi, J.; Lu, J., Monolayer Phosphorene–Metal Contacts. Chem. Mater. 2016, 28 (7), 2100-2109. 27. Dai, J.; Zeng, X. C., Bilayer Phosphorene: Effect of Stacking Order on Bandgap and its Potential Applications in Thin-film Solar Cells. J. Phys. Chem. Lett. 2014, 5 (7), 1289-1293. 28. Pan, Y.; Li, S.; Ye, M.; Quhe, R.; Song, Z.; Wang, Y.; Zheng, J.; Pan, F.; Guo, W.; Yang, J.; Lu, J., Interfacial Properties of Monolayer MoSe2–Metal Contacts. J. Phys. Chem. C 2016, 120 (24), 13063-13070. 29. Du, Y.; Liu, H.; Deng, Y.; Ye, P. D., Device Perspective for Black Phosphorus Field-effect Transistors: Contact Resistance, Ambipolar Behavior, and Scaling. ACS Nano 2014, 8 (10), 1003510042. 30. Kresse, G.; Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-energy Calculations Using a Plane-wave Basis Set. Phys. Rev. B 1996, 54 (16), 11169-11186. 31. Kresse, G.; Hafner, J., Ab Initio Molecular-dynamics Simulation of the Liquid-Metal– Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49 (20), 14251-14269. 32. Kresse, G.; Joubert, D., From Ultrasoft Pseudopotentials to the Projector Augmented-wave Method. Phys. Rev. B 1999, 59 (3), 1758-1775. 33. Blöchl, P. E., Projector Augmented-wave Method. Phys. Rev. B 1994, 50 (24), 17953-17979. 34. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865-3868. 35. Monkhorst, H. J. a. P., J.D, Special Points for Brillouin-zone Integrations. Phys. Rev. B 1976, 13, 5188-5192. 36. Klimes, J.; Bowler, D. R.; Michaelides, A., Chemical Accuracy for the van der Waals Density Functional. J. Phys. Condens. Matter. 2010, 22 (2), 022201. 37. Taylor, J.; Guo, H.; Wang, J., Ab Initio Modeling of Quantum Transport Properties of Molecular Electronic Devices. Phys. Rev. B 2001, 63 (24), 245407. 38. Brandbyge, M.; Mozos, J.-L.; Ordejón, P.; Taylor, J.; Stokbro, K., Density-functional Method for Nonequilibrium Electron Transport. Phys. Rev. B 2002, 65 (16), 165401. 39. ATOMISTIX Toolkit 2016 package; QuantumWise A/S: Copenhagen, Denmark, 2016. 40. Çakır, D.; Peeters, F. M., Dependence of the Electronic and Transport Properties of Metal-MoSe2 Interfaces on Contact Structures. Phys. Rev. B 2014, 89 (24), 245403. 41. Giovannetti, G.; Khomyakov, P.; Brocks, G.; Karpan, V.; van den Brink, J.; Kelly, P., Doping Graphene with Metal Contacts. Phys. Rev. Lett. 2008, 101 (2), 026803. 42. Pan, Y.; Wang, Y.; Wang, L.; Zhong, H.; Quhe, R.; Ni, Z.; Ye, M.; Mei, W. N.; Shi, J.; Guo, W.; Yang, J.; Lu, J., Graphdiyne-metal Contacts and Graphdiyne Transistors. Nanoscale 2015, 7 (5), 21162127. 43. Khomyakov, P. A.; Giovannetti, G.; Rusu, P. C.; Brocks, G.; van den Brink, J.; Kelly, P. J., Firstprinciples Study of the Interaction and Charge Transfer Between Graphene and Metals. Phys. Rev. B 14


Page 14 of 27

Page 15 of 27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2009, 79 (19), 195425. 44. Quhe, R.; Yuan, Y.; Zheng, J.; Wang, Y.; Ni, Z.; Shi, J.; Yu, D.; Yang, J.; Lu, J., Does the Dirac Cone Exist in Silicene on Metal Substrates? Sci. Rep. 2014, 4, 5476. 45. Wang, Y.; Li, J.; Xiong, J.; Pan, Y.; Ye, M.; Guo, Y.; Zhang, H.; Quhe, R.; Lu, J., Does the Dirac Cone of Germanene Exist on Metal Substrates? Phys. Chem. Chem. Phys. 2016, 18 (28), 19451-6. 46. Guo, Y.; Pan, F.; Ye, M.; Wang, Y.; Pan, Y.; Zhang, X.; Li, J.; Zhang, H.; Lu, J., Interfacial Properties of Stanene–metal Contacts. 2D Mater. 2016, 3 (3), 035020. 47. Gong, C.; Colombo, L.; Wallace, R. M.; Cho, K., The Unusual Mechanism of Partial Fermi Level Pinning at Metal-MoS2 Interfaces. Nano Lett. 2014, 14 (4), 1714-1720. 48. Kang, J.; Liu, W.; Banerjee, K., High-performance MoS2 Transistors with Low-resistance Molybdenum Contacts. Appl. Phys. Lett. 2014, 104 (9), 093106. 49. Wang, Y.; Yang, R. X.; Quhe, R.; Zhong, H.; Cong, L.; Ye, M.; Ni, Z.; Song, Z.; Yang, J.-B.; Shi, J.-j.; Li, J.; Lu, J., Does P-type Ohmic Contact Exist in WSe2-metal Interfaces? Nanoscale 2016, 8, 1179-91. 50. Zhong, H.; Quhe, R.; Wang, Y.; Ni, Z.; Ye, M.; Song, Z.; Pan, Y.; Yang, J.; Yang, L.; Lei, M.; Shi, J.; Lu, J., Interfacial Properties of Monolayer and Bilayer MoS2 Contacts with Metals: Beyond the Energy Band Calculations. Sci. Rep. 2016, 6, 21786. 51. Hwang, J. S.; Chang, C. C.; Chen, M. F.; Chen, C. C.; Lin, K. I.; Tang, F. C.; Hong, M.; Kwo, J., Schottky Barrier Height and Interfacial State Density on Oxide-GaAs Interface. J. Appl. Phys. 2003, 94 (1), 348-353. 52. Shen, H.; Dutta, M.; Fotiadis, L.; Newman, P. G.; Moerkirk, R. P.; Chang, W. H.; Sacks, R. N., Photoreflectance Study of Surface Fermi Level in GaAs and GaAlAs. Appl. Phys. Lett. 1990, 57 (20), 2118. 53. Das, S.; Demarteau, M.; Roelofs, A., Ambipolar Phosphorene Field Effect Transistor. ACS Nano 2014, 8 (11), 11730–11738. 54. Koenig, S. P.; Doganov, R. A.; Seixas, L.; Carvalho, A.; Tan, J. Y.; Watanabe, K.; Taniguchi, T.; Yakovlev, N.; Castro Neto, A. H.; Ozyilmaz, B., Electron Doping of Ultrathin Black Phosphorus with Cu Adatoms. Nano Lett. 2016, 16, 2145−2151. 55. Liu, H.; Neal, A. T.; Zhu, Z.; Luo, Z.; Xu, X.; Toma´nek, D.; Ye, P. D., Phosphorene: an Unexplored 2D Semiconductor with a High Hole Mobility. Acs Nano 2014, 8 (4), 4033-4041.

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Table 1. Calculated critical parameters characterizing the interfacial properties of BL phosphorenemetal contacts. 𝜀̅ represents the absolute mismatch of the lattice constants of the corresponding BL phosphorene surface on average. The equilibrium distance dP-M stands for the average distance between the contacting phosphorene and metal surfaces, while the minimum interatomic distance dmin denotes the minimum distance between a phosphorus atom and a metal atom from the two surfaces. Eb, the binding energy, is the energy per phosphorus atom needed to separate the two surfaces. W and WM are calculated work function of the BL phosphorene-metal interfaces and solitary metal surfaces, ℎ,tran 𝑒,tran respectively. 𝛷BL,L (𝛷BL,L ) is the transport SBH of hole (electron) in the lateral direction in the ℎ,tran 𝑒,tran BL phosphorene FETs. 𝐸gtran is the transport gap, which is defined as 𝐸gtran = 𝛷BL,L + 𝛷BL,L .

The calculated work function of pristine BL phosphorene is WP = 4.56 eV. Al

Ag

Cu

Au

Ti

Cr

Ni

Pd

𝜀̅ (%)

1.39

1.52

1.47

1.40

1.47

1.41

1.65

2.00

dP-M (Å)

2.49

2.45

2.30

2.38

1.96

1.76

1.72

1.88

dmin (Å)

2.58

2.58

2.36

2.48

2.39

2.22

2.19

2.31

Eb (eV)

0.48

0.50

0.65

0.60

1.58

2.03

1.47

1.22

W (eV)

4.38

4.53

4.83

4.96

4.59

4.81

5.03

4.93

WM (eV)

3.96

4.19

4.81

5.00

4.49

4.90

5.30

5.24

𝑒,tran 𝛷BL,L (eV)

0.31

0.54

0.32

0.48

0.41

0.27

0.52(0.48 a)

0.72

ℎ,tran 𝛷BL,L (eV)

0.37

0.20

0.36

0.21

0.18(0.21b)

0.49

0.19(0.23 a)

0.11

𝐸gtran

0.68

0.74

0.68

0.69

0.59

0.76

0.71

0.83

a

Experimental values.7

b

Experimental values.29

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(a)

(b) III II I I' II'

A dP-M

B

C

F

D

E

G

Figure 1. (a) Schematic diagram of a BL phosphorene FET. (b) Schematic cross-sectional view of a typical metal contact to the BL phosphorene channel. A, C, E, and G present four regions, B, D, and F denote three interfaces. Red rows show the pathway (A → B → C →F → G or A → B → C → D → E → G) of electrons or holes from contact metal (A) to the BL phosphorene channel.

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Figure 2. Side view of the optimized structures and the distribution of the average electrostatic potentials ranging in the direction perpendicular to the interfaces, corresponding to the Al, Au, Cu, Ag, Cr, Ti, Ni and Pd-BL phosphorene systems, respectively. The Fermi level is set to zero.

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Figure 3. Band structures of ML (blue lines) and BL (magenta lines) phosphorene in

 2a 

2

 b2  a 2  b2

supercell. Band structures of the BL phosphorene-Al, Au, Ag, Cu, Cr, Ti, Ni,

and Pd interfacial systems, respectively. The Fermi level is set to zero. Gray lines: band structures of the interfacial systems; Red lines: band structures of the layer of phosphorene close to the metal surface; Green lines: band structures of the layer of phosphorene away from the metal surface. The line width is proportional to the weight.

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Figure 4. Partial density of states (PDOS) (DOS on the special orbitals) of BL phosphorene on the Al, Ag, Au, Cu, Cr, Ti, Ni, and Pd surfaces, respectively. The Fermi level is at zero energy.

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Figure 5. Partial density of states (PDOS) (DOS on the special orbitals) of the bottom phosphorene layer in the BL phosphorene-Al, Ag, Au, Cu, Cr, Ti, Ni, and Pd systems, respectively. The Fermi level is at zero energy.

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Figure 6. (a) Calculated Fermi energy shift ΔEf (square) as a function of the clean metal and BL phosphorene work function difference WM − WP. (b-e) Charge density difference of BL phosphoreneAl, Cr, Cu, and Au systems, respectively. The light green and yellow surfaces represent charge loss and gain, respectively. The isosurface is 0.1 e/Bohr3.

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Figure 7. Comparison of the vertical SBHs of the BL phosphorene FETs obtained by the ab initio 𝑒/ℎ,EBA

EBA 𝛷BL,V

𝑒/ℎ,WFA

, the lateral SBHs of the ML phosphorene FETs obtained by the WFA 𝛷ML,L 𝑒/ℎ,tran

ab initio QTS 𝛷ML,L

𝑒/ℎ,exp

, and the observed SBHs7 𝛷ML,L

of the ML phosphorene FETs.

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, the


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Figure 8. (a-b) Zero-bias transmission spectra of the BL phosphorene FETs with Al, Cu, Cr, Au, Ti, Ni, Pd, and Ag electrodes. (c-f) LDDOS in color coding for the BL phosphorene FETs with Al, Au, Cr, and Pd electrodes, respectively. The channel length is L = 5 nm. The black circles indicate the MIGS at the interfaces.

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Figure 9. Comparison of the electron and hole lateral SBHs of the BL phosphorene FETs by using the 𝑒/ℎ,WFA

WFA 𝛷BL,L

𝑒/ℎ,tran

, the ab initio QTS 𝛷BL,L

𝑒/ℎ,exp 7 .

, and the experimental observations 𝛷BL,L

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Figure 10. (a and b) Calculated and observed7, 26 electron and hole SBHs as a function of layer number of phosphorene with Ni (a) and Cu (b) electrode.

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Schottky Barriers in Bilayer Phosphorene Transistors - ACS Applied

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