Monolayer PhosphoreneâMetal Contacts - ACS Publications

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Monolayer Phosphorene-Metal Contacts Yuanyuan Pan, Yangyang Wang, Meng Ye, Ruge Quhe, Hongxia Zhong, Zhigang Song, Xiyou Peng, Dapeng Yu, Jinbo Yang, Junjie Shi, and Jing Lu Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b04899 • Publication Date (Web): 12 Mar 2016 Downloaded from http://pubs.acs.org on March 14, 2016

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Chemistry of Materials

Monolayer Phosphorene  Metal Contacts Yuanyuan Pan1, Yangyang Wang1,3, Meng Ye1, Ruge Quhe1,4, Hongxia Zhong1, Zhigang Song1, Xiyou Peng1, Dapeng Yu1,2, Jinbo Yang1,2, Junjie Shi1, and Jing Lu1,2,* 1

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

2 3

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

Department of Nuclear Science and Engineering and Department of Materials Science

and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 , USA 4

Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, P. R. China *

Corresponding author: [email protected]

Abstract Recently, phosphorene electronic and optoelectronic prototype devices have been fabricated with various metal electrodes. We systematically explore for the first time the contact properties of monolayer (ML) phosphorene with a series of commonly used metals in a transistor by using both ab initio electronic structure calculations and more reliable quantum transport simulations. ML phosphorene undergoes a metallization under the checked metals, and the metallized ML phosphorene have an unnegligible coupling with channel ML phosphorene. ML phosphorene forms an n-type Schottky contact with Au, Cu, Cr, Al, and Ag electrodes and a p-type Schottky contact with Ti, Ni, and Pd electrodes upon inclusion of such a coupling. The calculated Schottky barrier heights are in good agreement with the available experimental data with Ni and Ti as electrodes. Our findings not only provide an insight into the ML phosphorene-metal interfaces but also help in ML phosphorene based device design.

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1. Introduction Two-dimensional (2D) materials with atomic thickness, such as graphene[1] and transition metals dichalcogenides[2] (TMDCs), have attracted tremendous attentions, due to their excellent properties and great potential for electronic and optoelectronic applications.[3-8] However, the zero band gap of graphene limits its application in digital logic devices despite of an extremely high carrier mobility of about 20000 cm V-1 s-1, and the relatively low mobility (200 cm V-1 s-1) of TMDCs (with a band gap of 1-2 eV) is difficult to meet the future request of high performance applications. Phosphorene, the youngest member of 2D materials,[9-11] has a finite band gap from 0.3 (in bulk) to 1.0 (monolayer) eV[12] and is mechanically exfoliated in the early of 2014.[9, 13-15] Monolayer (ML) and few-layer (FL) phosphorene field effect transistors (FETs) have been successfully fabricated with an on-off ratio of 105 and a mobility up to 1000 cm V-1 s-1, which make phosphorene a competitive candidate channel material for nanoelectronic devices. FL phosphorene photo-detector has been realized by Engel et al., which is capable of acquiring high-contrast (visibility V > 0.9) images both in the visible as well as in the infrared spectral regime.[16] FL phosphorene phototransistor was also demonstrated with a rise time of about 1 ms and responsivity of 4.8 mA/W.[17] P-n diode has been proposed based on p-type phosphorene and n-type MoS2 or graphene van der Waals heterojunction.[18-20] Therefore, phosphorene is also a promising material in photoelectronic devices.[21-22] In an actual electronic and photoelectronic device with 2D materials as the semiconducting channel, a contact with metal is usually required in order to inject appropriate types carrier into the conduction or valence band of 2D materials, and the formation of low-resistance metal contacts is the biggest challenge that masks the intrinsic exceptional electronic properties of semiconducting 2D materials.[23] In such a metal semiconductor contact, Schottky barrier is often formed at the interface, which decreases electron or hole injection efficiency and thus degrades the device performance. In order to win a high performance of the device, one can select a metal electrode with a small Schottky barrier height (SBH) at the metal-semiconductor interface. Unfortunately, the SBH is not simply determined by the difference between the work function of a metal and the conduction band

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minimum (CBM) or the valence band maximum (VBM) of semiconducting 2D materials due the complex Fermi level pinning.[24] Beside, a contact with metal also controls the polarity of semiconducting 2D materials due to a lack of controllable and sustainable substitutional doping scheme in 2D materials. Experimentally, Au, Cr, Ni, Ti, and Pd have been used as electrodes in phosphorene transistors.[9, 14-15, 17, 22, 25-31] So far, only the SBH between ML phosphorene and Ni has been measured with a value of 0.35 ± 0.02 eV for hole based on a transistor.[13] Theoretically the interfacial properties between ML phosphorene and Au, Ag, Al, Cu, Ti, Ta, Nb, Zn, In, and Pd based on a periodical system have been calculated (for Ag, Pd, and Cu, SBH = 0 due to an Ohmic contact feature).[32-34] However, a comprehensive SBH study of the contacts between ML-phosphorene and commonly used metal electrodes (such as Ni and Cr) based on a transistor configuration remains lacking. In this letter, we systematically explore the interfacial properties between ML phosphorene and the common metals (Al, Ag, Au, Cu, Ti, Cr, Ni, and Pd) in a transistor configuration based on ab initio electronic structure calculations and quantum transport simulations for the first time. ML phosphorene always underdoes a metallization under the eight metal electrodes as a result of formation of chemical bond. A big discrepancy in the calculated SBHs is frequently observed between the energy band calculations and quantum transport simulations. The SBHs obtained from the latter approach show a much better consistency with the available experiments because it takes into accounts the interactions between metal electrodes and channel ML phosphorene while the former does not. No Ohmic contacts are found between ML phosphorene and the eight metal interfaces in terms of the quantum transport simulations.

2. Methodology 2.1. Interface modeling We consider eight metals Al, Ag, Au, Cu, Ni, Ti, Pd, and Cr, which cover a wide range of work function. We choose six layers of metal atoms to simulate the metal surfaces and construct a supercell with ML phosphorene absorbed on one side of the metal surfaces, as shown in Figure 1(c). We fix the lattice constants of metal surface and change the optimized lattice constant of ML phosphorene a = 3.30 Å and b = 4.63 Å (the lattice constant are

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indicated in Figure 1(b)) to adjust to them. The

a2 + b2 × (2a)2 + b2

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ML phosphorene

matches 2 × 2 Al, Ag, Au, and Cr surface in the (110) orientation, and the 3a × b ML

phosphorene match 1 × 2 Ti surface in the (0001) orientation, respectively, and the 3a × b , the 3a × b , and the 5a × b ML phosphorene match 2 × 3 Ni surface, 4 × 2

6×

3

3

Cu surface and

Pd surface in the (111) orientation, respectively. The corresponding mismatches of

lattice constant are 0.59 ~ 2.65%, as given in Table 1. ML phosphorene mainly interacts with the top layers metal atoms, so the bottom three layers of metal atoms and the cell shape are fixed.

Figure 1. (a) Side and (b) top views of freestanding ML phosphorene. The rectangle indicates

the unite cell of ML phosphorene. (c) The initial configuration of ML phosphorene (purple ball) on metal surface (green ball). 2.2. Calculations methods

The geometry optimizations and electronic structure calculations are performed with the projector-augmented wave (PAW) pseudopotential[35] and plane-wave basis set with a cut-off energy of 400 eV, implemented in the Vienna ab initio simulation package (VASP) code.[36-37] The maximum residual force during geometry optimization is less than 0.01 eV/Å and energies are converged to within 1 × 10-5 eV per atom. The Monkhorst-Pack k-point mesh is sampled with a separation of about 0.02 Å-1 in the Brillouin zone during the relaxation and electronic calculation periods.[38] Van der Waals interaction is taken into account, with the

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vdW-DF level of optB88 exchange functional (optB88-vdW).[39] Since the slab is not symmetric, a dipole correction is used to eliminate the spurious interaction between the dipole moments of periodic images in the z direction. A vacuum buffer space of at least 12 Å is set. The total electron density is calculated by using ultrasoft pseudopotential plane-wave method implemented in CASTEP code, with a plane-wave cut-off energy of 280 eV.[40] A two-probe model (Figure 5(a)) is built to simulate phosphorene FET. The channel region along the transport direction consists of ~ 50 Å ML phosphorene. The electrodes adopt the optimized ML phosphorene-metal interfaces according to our above DFT results. 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) 11.2 package.[41-43] 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

T k// ( E) = Tr ΓLk// ( E) G k// ( E) Γ Rk// ( E) G k// † ( E) where, G k / /

(1)

k r,k a,k is the retarded (advanced) Green’s function and ΓL/R // ( E) = i ( ∑L/R// −∑L/R// )

represents the level broadening due to left electrode and right electrodes expressed in terms of the electrode self-energies ∑ kL / R , which reflects the influence of the electrodes on the //

scattering region[44]. The transmission function at a given energy different k// in the IBZ. Single- ζ

T

( E ) is averaged over

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–Pack[38] 50 × 1 × 50 and 50 × 1 × 1 k-point grid, respectively. GGA of PBE form[45] to the exchange-correlation functional is used.

3. Results and Discussions 3.1. ab initio electronic structure calculations results

We have optimized two different initial configurations of ML phosphorene-Al systems. One has the two adjacent phosphorus atoms in the lower layer (a layer) of phosphorene

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almost on the top of two adjacent Al atoms of A layer of metal (Initial configuration I with its side view shown in Figure 1(c)), and the other has one phosphorus atoms of the lower layer (a layer) on the interval of two adjacent Al atoms of A layer (Initial configuration II). The two initial configurations converge to the same structure (similar to initial configuration I) after relaxation. For other seven metal electrodes, we start structure relaxation from initial configuration I. The relaxed structures of ML phosphorene-metal contacts are depicted in Figure 2. The relaxed structures of ML phosphorene on Al, Ag, Au, and Cu electrodes are similar to the initial configuration I, and on Cu electrodes is consistent with ML phosphorene-Cu contacts reported in the previous work.[32] The original structure of ML phosphorene is preserved on Al, Ag, Au, and Cu electrodes, but destroyed seriously on Cr, Ni, Ti, and Pd electrodes.

Figure 2. Side view of the optimized structures and average electrostatic potentials in planes

normal to the interface of ML phosphorene-Al, Au, Ti, Cr, Ag, Cu, Ni, and Pd systems, respectively. The Fermi level is set to zero.

The primary parameters of ML phosphorene-metal contacts are listed in Table 1. The binding energy Eb of the ML phosphorene-metal contact is defined as Eb = (EP + EM – EP-M) / N

(2)

where EP, EM, and EP-M are the relaxed energy for pristine ML phosphorene, the clean metal surface, and the combined system, respectively, and N is the number of phosphorus atoms in the lower layer (a layer) of a supercell as shown in Figure 1(c). The equilibrium interlayer distance dP-M is defined as the average distance from the innermost layer of metal to the 6


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innermost ML phosphorene surface in the vertical direction of the interface as shown in Figure 1(c). The minimum interatomic distance dmin is defined as the minimum atomic distance from the innermost layer atom of metal to ML phosphorene surface atom. According to the bonding level, two categories of ML phosphorene-metal interfaces are classified. Weak bonding is formed for ML phosphorene-Al, Ag, Au, and Cu interfaces with smaller binding energy of 0.41 < Eb < 0.59 eV, and larger interlayer distance of 2.35 < dP-M < 2.57 Å and 2.30 < dmin < 2.46 Å, while strong bonding is formed for ML phosphorene-Cr, Ni, Pd, and Ti interfaces with lager binding energy of 0.85 < Eb < 1.62 eV, and smaller distance of 1.60 < dP-M < 2.19 Å, and 2.07 < dmin < 2.32 Å. The interactions between ML and metals are stronger

than those between graphene/graphdiyne and metals with ten times larger binding energy and smaller interfacial distances. The adsorption energies of the adatoms on ML phosphorene are also more than twice larger than those on graphene.[24,

46-48]

Therefore, the nonplanar

single-layer phosphorus material, ML phosphorene, is more active than the elemental single-layer plane carbon materials, such as graphene and graphdiyne. As shown in Figure 3, the band structures of ML phosphorene are destroyed on all the metal electrodes, suggestive of a covalent or chemical bonding between ML phosphorene and these metals. The Fermi level always crosses the ML phosphorene-derived band, leading to a metallization of ML phosphorene. The band hybridizations of ML phosphorene on Ti, Ni, Cr, and Pd electrodes are more intense than those on Al, Ag, Cu, and Au electrodes, a fact in line with their bonding level. By contrast, the band structures of ML graphene and graphdiyne absorbed on Ag, Al, Au, and Cu substrates not destroyed. This difference once more indicates that the interactions between ML phosphorene and metal surfaces are stronger than those between graphene/graphdiyne and metal surfaces.[24, 46-47]

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Figure 3. Band structures of ML phosphorene and ML phosphorene on Ag, Al, Au, Cu, Cr, Ti,

Pt, and Ni surfaces by the DFT method, respectively. The Fermi level is at zero energy. Gray line: band structure of the interfacial systems; red line: band structures of ML phosphorene. The line width is proportional to the weight. The band structure of freestanding ML phosphorene is calculated in

a2 + b2 × (2a)2 + b2 supercell.

To further confirm the metallization of ML phosphorene absorbed on metals, we calculate the partial density of states (PDOS) on P orbitals for ML phosphorene-metal systems as shown in Figure 4. A large amounts of P states appear in the original band gap of ML phosphorene in all the absorption systems, leading to a large PDOS of ML phosphorene at Ef on the eight metal surfaces, which is a typical criterion of metallization. In the case of weak bonding (i.e. ML phosphorene contacting with Al, Ag, Cu, and Au), the P pz orbital dominates the states in the original band gap of ML phosphorene, while in the case of strong bonding (i.e. ML phosphorene contacting with Ti, Ni, Cr, and Pd), the s, px, py, and pz orbital of P have almost the same contribution to the P states in the original band gap of ML phosphorene.

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Figure 4. Partial density of states (PDOS) (DOS on specified orbitals) of pure ML

phosphorene and ML phosphorene on the Ag, Al, Au, Cu, Cr, Ti, Pd, and Ni surfaces at the DFT level. The Fermi level is at zero energy. The PDOS of pure ML phosphorene is calculated in a primitive unit cell. The total electron distribution of ML phosphorene-metal interfacial systems can reflect the interaction between ML phosphorene and the metal surfaces. We calculated the electron density in the real space of ML phosphorene-Ag, Au, Pd, and Ni adsorbed systems and show the results in Figure 5. There is apparent electron accumulation in the ML phosphorene-Ag, Au, Ni, and Pd interfaces, indicating the formation of a covalent bond between them once more. The electron accumulation at ML phosphorene-Ni and Pd interfaces is more apparent than that at ML phosphorene-Ag and Au interfaces, as are in line with their bonding and hybridization levels.

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(a) Ag-phosphorene

(c) Ni-phosphorene

(b) Au-phosphorene

(d) Pd-phosphorene

3

0.0

0.8 e/Å

Figure 5. Contour plots of total electron distribution of (a) ML phosphorene-Ag system, (b)

ML phosphorene system, (c) ML phosphorene-Ni system, and (d) ML phosphorene-Pd systems. The purple, light blue, dark blue, yellow and green balls represent P, Ag, Ni, Au, and Pd atoms, respectively. The schematic diagram of a ML phosphorene FET is shown in Figure 6(a). Schottky barriers can appear on either of the two different interfaces in a ML phosphorene FET: One is between ML phosphorene and the contacted metal surface in the vertical direction (labeled interface B, and the corresponding SBH is labeled Φ V ) if the interaction between 2D material and metal is weak, and the other is between the contacted systems and the channel ML phosphorene in the lateral direction (labeled interface D, and the corresponding SBH is labeled Φ L ) if the contacted 2D material undergoes a metallization.[49] Besides, tunneling barrier can appear at interface B when electrons cross the gap (normally van der Waals gap) between metal and ML phosphorene. The frequently-used method to investigate contact barriers at 2D semiconductor-metals interfaces is electronic energy band calculation, in which contact barriers is decide by the distribution of the Fermi level (Ef) of metals and band structure of semiconductors. From Figure 3, the band hybridizations between ML

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phosphorene and all checked metals lead to a metallization of ML phosphorene under metal, and vertical Schottky barrier is absent.

Figure 6. (a). Right: Schematic diagram of a ML phosphorene FET. Left: Schematic

cross-sectional view of a typical metal contact to intrinsic ML phosphorene channel. A, C, and E denotes three regions, while B and D are the two interfaces separating them. Red rows show the pathway (ABCDE) of electron or hole injection from contact metal (A) to the ML phosphorene channel (E). (b - d). Three possible band diagrams of the ML phosphorene FETs in terms of the quantum transport calculations, depending on the type of metal. Examples are provided at the bottom of each diagram. EFm and EFc denote the Fermi level of the interfacial systems and channel ML phosphorene, respectively. First, we calculate the lateral SBH from the energy band scheme. Lateral electron SBH Φ Le (hole SBH Φ Lh ) is determined by the energy differences between the interfacial system Ef

and the CBM (VBM) of channel ML phosphorene. In the energy band scheme, the interfacial system and the channel are calculated separately, ignoring the possible coupling between. The size of the band gap of the channel semiconductor is critical to evaluate the SBH of a 2D semiconductor device. There are four kinds of commonly used band gap for a 2D

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semiconductor: transport gap (a sum of the electron SBH and hole SBH), quasi-particle band gap (dominated by many-electron effects), optical gap (dominated by exciton effects), and DFT band gap (single-electron approximation). For ML phosphorene, the four kinds of band gap are 1.0,[13] 2.0,[50] 1.3-1.45,[15, 51] and 0.91 (PBE functional) eV, respectively. Obviously, the DFT band gap is closest to the transport SBH because many-electron effects have been strongly suppressed due to charge doping of channel ML phosphorene by metal source/drain electrode or gate electrode. Hence, single-electron approximation is a good approximation to characterize the transport gap and SBH of ML phosphorene FET. The same case occurs in ML and BL MoS2-Ti contact, too. The experimentally extracted SBHs of ML and BL MoS2-Ti FET are 0.3 ~ 0.35[23] and 0.065 eV,[52] respectively, which are in agreement with the calculated values of 0.216 and 0.161 eV at the DFT level (PBE functional).[53] In terms of the energy band analysis, as shown in Figure 7, ML phosphorene forms an Schottky contacts with Al, Ag, and, and Ti (n-type), Cr, Au, Cu, and Ni (p-type) electrodes in the lateral direction, with lateral electron SBHs Φ Le = 0.23, 0.30, 0.40, 0.58, 0.71, 0.76, and 0.89 eV, respectively, while forms an Ohmic contact with Pd electrodes since the absorbed system EF is lower than the VBM of channel ML phosphorene. In experiments, it is not easy to form perfect Ohmic contact in 2D semiconductor FET, and caution must be taken for the Ohmic contact with Pd electrodes in ML phosphorene.

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Figure 7. Line-up of the work functions of the interfacial systems with the electronic band of

channel ML phosphorene in terms of separate electronic energy band calculations. The blue dash and the red solid present the work functions of the pure metals and ML phosphorene-metals systems, respectively.

The potential profiles at the vertical ML phosphorene-metal interfaces are shown in Figure 2. There are obvious tunneling barriers at the ML phosphorene-Cu, Al, Au, and Ag interfaces with barrier heights of 0.65, 1.26, 1.55, and 1.67 eV, respectively, while tunneling barrier vanishes at the ML phosphorene-Cr, Ni, Ti, and Pd interfaces due to the metallization of ML phosphorene. We assume a square potential barrier to replace the real potential barrier, and the barrier height (∆V) and width (wB) of the square potential barrier are the barrier height and full width at half maximum (FWHM) of the real potential barrier shown in Figure 2. The tunneling probabilities TB is calculated using equation:[54]   2m∆V TB = exp  −2 × wB  h  

(3)

where m is the massive of free electron and h is the reduced Plank’s constant. The resulting tunneling possibilities at ML phosphorene-Ag, Au, Al, Cu, Ti, Cr, Ni, and Pd are 59%, 61%, 67%, 85%, 100%, 100%, 100%, and 100%, respectively. The metallization between ML phosphorene and Cr, Ti, Ni, and Pd electrodes make electrons injecting from metal to ML phosphorene freely. Tunneling possibilities of weak bonding is smaller than that of strong bonding. 3.2. Quantum transport simulations

In above energy band method, the electronic properties of the electrode region and the channel are treated separately, ignoring the coupling between the two regions and thus possible Fermi level spinning. A more reliable to study the SBH of a transistor is to use ab initio quantum transport simulations within a two-probe model, in which the electrode

(including the metallized semiconductor under electrode) and the channel semiconductor are calculated as a whole, and the coupling between the electrode region and the channel are taken into account. The schematic model the ML phosphorene transistor is presented in Figure 6(a). The zero-bias transmission spectrums of ML phosphorene FETs with a channel 13



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h e length of L = 5 nm are plotted in Figure 8(a). The transport hole (electron) SBH Φ trans ( Φ trans )

is the difference from the Fermi level to the CBM (VBM) of channel ML phosphorene. When Au, Cu, Cr, Al, and Ag are chosen as electrodes, n-type ML phosphorene FET is formed with e of 0.30, 0.34, 0.37, 0.51, and 0.52 eV. While when Ti, Ni, and Pd are chosen as Φ trans

h electrodes, p-type Schottky ML phosphorene FET is formed with Φ trans of 0.30, 0.26, and

0.16 eV, respectively. The best n- and p- type contact metal for monolayer phosphorene is Al and Pd with the smallest Schottky barrier in our checked metals, respectively. Our calculation e with Cu as electrode is consistent with Zeng’s result that n-type Schottky is formed with Φ trans

of 0.37 eV[55]. It is noteworthy that the polarity and SBH difference of ML phosphorene under different metals cannot be predicted in terms of the work function of pristine metal at all. For example, Ti has a much smaller work function than Au (4.35 vs 5.00 eV in our calculation) and it appears to have a smaller electron SBH than Au. But actually Ti forms p-type Schottky barrier with a larger electron SBH of 0.75 eV while Au forms n-type Schottky barrier with ML phosphorene with the smallest electron SBH of 0.30 eV. The transport gap is a sum of electron and hole SBH:

h e , E gtrans = Φ trans + Φ trans

and the transport gap

E gtrans

for Ni, Ti, Cu, Al, Ag,

Au, Cr, and Pd as electrodes are 0.65, 1.05, 1.09, 1.11, 1.20, 1.20, 1.26, and 1.34 eV, respectively. Most of these transport gaps are close to the band gap (1.0 eV) of ML phosphorene except for Ni electrode with one exception of Ni contact (the cause will be discussed later).

Figure 8. (a) Zero-bias transmission spectra of the channel in ML phosphorene FET with Ag,

Cu, Cr, Al, Au, Ni, Ti, and Pd electrodes, the channel length L = 5 nm. (b) LDDOS in color

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coding for ML phosphorene FET with Al, Cu, Ni, and Pd electrodes, the channel length L = 5 nm. We calculate the local device density of state (LDDOS) in the ML phosphorene FETs with Au, Al, Ni, and Pd electrodes to visualize the energy band in real space and show them in Figure 8(b). ML phosphorene form n-type contact with Al and Cu electrode with electron SBHs of 0.52 and 0.31 eV, and p-type contact with Ni and Pd electrodes, with hole SBHs of 0.34 and 0.05 eV. The transport gap of ML phosphorene extracted from the LDDOS with Ni, Cu, Al, and Pd electrodes is 0.79, 0.93, 1.12, and 1.13 eV, respectively. Both the SBHs and transport gaps derived from the LDDOS calculation are generally consistent with those from the corresponding transmission spectrum calculations. Band bending away from the contact is an important property in a metal-semiconductor interface. In generally, the conduction band is bent downward due to an electron transfer from electrodes to channel ML phosphorene for n-type contact, while the valence band is bend upward due to an inverse electron transfer in p-type contact except for Pd-ML phosphorene interface where the hole Schottky barrier shape looks like a conventional one. Such a band bending picture in a metal-2D semiconductor interface where no impurity state exists in 2D semiconductor (lack of proper doping approach for 2D semiconductor)[23] appears different from an interfacial band bending picture in a common metal-n (p) type semiconductor interface where donor (acceptor) states exist and electrons (hole) are transferred from semiconductor to metal. 3.3. Comparison of the Schottky barriers between the two theoretical methods and the experiments

The calculated Schottky barriers in the two methods (the electronic band structure calculations and the quantum transport simulations) are compared in Figure 9. ML phosphorene FET with Al and Ag electrode form the same p-type FET in the two methods with similar hole SBHs (0.68/0.61 eV in the electronic band structure calculations vs 0.60/0.68 eV in the quantum transport simulations). When Ti, Cr, Au, and Cu are used as electrodes, the carrier polarity of ML phosphorene FET is completely reversed in the two methods. ML phosphorene FET with Ti electrode changes from n-type Schottky contact with a larger hole SBH of 0.51 eV (the electronic band structure calculations) to p-type Schottky 15



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contact with a smaller hole SBH of 0.30 eV (the quantum transport simulations). On the other hand, ML phosphorene FETs with Cr, Au, and Cu electrodes change from p-type Schottky (the electronic band structure calculations) to n-type Schottky (the quantum transport simulations) FET. The available experimental results shows that phosphorene FET with Ti electrode forms p-type Schottky FET, and FL phosphorene with Ti electrode has a hole SBH of 0.21 eV.[15] This result is in favor of the quantum transport simulations.[14] The smaller hole SBH obtained in experiment than obtained in the transport simulation is ascribed to a difference in layer number of phosphorene. FL phosphorene has a smaller band gap than ML phosphorene and generally has a smaller hole SBH. The carrier polarity of ML phosphorene-Ni and -Pd contacts are the same in the two methods. However, the hole SBH of ML phosphorene with Ni electrode from the transport simulation (0.26 eV) is much larger than that (0.02 eV) from the energy band analysis. The extracted experimental transport hole SBH of ML phosphorene with Ni electrode is 0.35 ± 0.02 eV, preferring the quantum transport simulation result once more. ML phosphorene forms an Ohmic contact with Pd electrode in the electronic band energy calculation. However, a small hole SBH (0.05 (LDDOS) ~ 0.16 (Transmission spectrum) eV) appears in quantum transport simulations, which reflects a Fermi level pinning to below the conduction band of ML phosphorene. An artificial Ohmic contact is also calculated for 2D MoS2-Sc contact in the energy band analysis as a result of ignoring the coupling between the electrode and channel region, and this deficiency can also be corrected by the quantum transport simulations.[53] Theoretically, Pd contact has the smallest hole SBH among all the checked metal electrodes. Consistently, phosphorene-Pd contact has the smallest contact resistance among Ti, Ni, and Pd contacts experimentally.[14, 25] In general, the differences in evaluating SBHs of ML phosphorene-metal contacts between the two theoretical methods are huge, and the quantum transport simulations that include the interaction between the electrode region and channel show a much better consistency with the experiment than the electronic band energy calculations. In other words, there is an unnegligible coupling between the electrodes and channel ML phosphorene in most of the checked ML phosphorene FETs, which highlights the importance of a high-level approach in treating the SBH beyond the electronic band calculations. 16


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Figure 9. Comparison of the Schottky barrier heights ( Φ

e SB

for electron and Φ

h SB

for hole)

of ML phosphorene-Al, Ag, Ti, Cr, Cu, Au, Ni, and Pd contacts obtained by the ab initio electronic band calculations, quantum transport calculations (the circled one by yellow is from Ref. 36 ), and experimental observations[13,15]. 3.4. Discussions

According to the tunneling barrier and the Schottky barriers obtained from the transport simulations, three kinds of ML phosphorene-metal contacts are identified and depicted in Figure 5(b-d). ML phosphorene forms an n-type Schottky contact with Al, Ag, Au, and Cu electrodes at the interface D with a tunneling barrier at the interface B, leading to type 1 contact. In type 2 contact, ML phosphorene-Cr system forms an n-type Schottky contact at the interface D with a vanishing tunneling barrier at the interface B. In type 3 contact, ML phosphorene-Ti, Ni, and Pd systems form a p-type Schottky contact at the interface D with a vanishing a tunneling barrier at the interface B. In all the ML phosphorene-metal systems, no SBH is formed at the interface B. The transport band gap with Ni electrode of 0.65 eV is underestimated to some extent, compared with the extracted experimental gap of 0.99 eV.[13] The 2D semiconductor material in a device includes two parts: one in the channel region and the other in the electrode region.

17



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In a real device, the lattice constant of the 2D semiconductor in the central region is close to that in the free-standing state, while the one in the electrode region is likely to be adapted to that of corresponding bulk metal. However, in a theoretical transport model, the lattice constants of the two parts of the 2D semiconductor have to be identical. In our above calculations, the lattice constant of phosphorene is adapted to that of metal electrodes (referred to as Model I). A problem arises in the selection of lattice adaption scheme in the case of a lattice constant-sensitive band gap[56-57] and a larger lattice mismatch. The calculated smaller transport gap of phosphorene FET with Ni electrode is ascribed to a larger strain of channel phosphorene 7.26 % in one direction though the average absolute lattice constant mismatch ε is only 2.65% (Table 1). We thus recalculate the transport spectrum of ML phosphorene FET with Ni electrode in terms of a different model (Model II) where the lattice constant of Ni is adapted to that of ML phosphorene. The two transport spectrums are compared in Figure S1. A transport gap of 1.17 eV is obtained in Model II, which is much closer to the experiment value of 0.99 eV. However, in model II, n-type Schottky contact is formed with electron and hole Schottky barriers of 0.50 and 0.67 eV, respectively, compared with p-type Schottky contact in Model I with electron and hole Schottky barriers of 0.39 and 0.26 eV, respectively. The experimental result is that p-type phosphorene FET is formed with electron and hole Schottky barriers of 0.63 and 0.35 eV, respectively.[13] A simple average of the two models give a hole SBH and transport gap of 0.45 and 0.91 eV, respectively. The real SBH and transport gap should be fall in between Model 1 and Model II, with the SBH in favor of Model I and the transport gap in favor of Model II. Actually, the obtained electron SBH from Model I and II for is 0.04 eV and 0.26 eV, respectively, for MoS2-Sc contact in our recent work,[53] and the former is also closer to the observed electron SBH of 0.03 eV in multilayer MoS2-Sc contact.[58] The preference of the SBH value to Model I suggests that the SBH formed at the interface is insensitive to the change of the band gap induced by the strain release because of partial Fermi level pinning to the VBM, as illustrated in Figure S2. There is a difference of the SBH between our results and the previous work.[34] For example, an Ohmic contact is predicted between ML phosphorene and Pd in that work, while a SBH of 0.16 eV is predicted in the present work. The differences are caused by the different methodology. We use both ab initio electronic structure calculations (periodical systems) and 18


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quantum transport simulations (transistor configurations), while the work only use ab initio electronic structure calculations for periodical systems. The measured Schottky barrier is often based on a transistor configuration. There are two possible interfaces to produce Schottky barrier in a transistor: the vertical interface and the lateral interface. The Schottky barrier calculated from the ab initio electronic structure calculations (periodical systems) actually corresponds to the Schottky barrier in the vertical interface of a transistor. However, in ML phosphorene transistor, the dominant interface is the lateral interface because a metallization of ML phosphorene leads to a disappearance of the Schottky barrier in the vertical interface. The Schottky barrier in the lateral interface can only be calculated by the transport simulation. Therefore, the Schottky barrier height calculated from the quantum transport simulations (transistor configurations) (corresponds to the Schottky barrier in the lateral interface) for ML phosphorene is different from that from the band calculations and is more in agreement with the experiments. Contact resistances are the more direct parameter to represent the nature of 2D semiconductor-metal interfaces. Total resistance of a transistor, which includes contact resistance and channel resistance, can be extracted from the I-V sweep. The channel resistance can be further extracted from the transfer curve as illustrated in the previous works.[13-14] Hence, in principle, the contact resistance can be calculated by the total resistance subtracting the channel resistance based on a transport simulation.

4. Conclusions In summary, we have investigated the interfacial properties between ML phosphorene and Al, Ag, Cu, Au, Cr, Ni, Ti, and Pd electrodes in a FET environment by using both ab initio electronic structure calculations and quantum transport simulations. Strong interactions are formed between ML phosphorene and all the checked metal surfaces and destroy the energy band structure of ML phosphorene. Compared with the energy structure calculations, the quantum transport simulations are more reliable in describing SBH because of including the interactions between the metal electrodes and channel ML phosphorene and indeed much better consistent with the experimental results. In terms of the quantum transport simulations, n-type Schottky contacts are formed between ML phosphorene and Au, Cu, Cr, Al, and Ag

19



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Page 20 of 27

electrodes, with electron SBHs of 0.30, 0.34, 0.37, 0.51, and 0.52 eV, respectively, and p-type Schottky contacts are formed between ML phosphorene and Ti, Ni, and Pd electrodes, with hole SBHs of 0.30, 0.26, and 0.16 eV, respectively. It is unexpected that Au forms n-type Schottky contact with ML phosphorene with the smallest electron SBH. Our results are well supported by the experimental SBH data with Ni and Ti as electrodes. The further design of ML phosphorene electronic devices can reference our results to choose an appropriate metal electrode.

Acknowledgement This work was supported by the National Natural Science Foundation of China (No. 11274016/

11474012),

the

National

Basic

Research

Program

of

China

(No.

2012CB619304/No. 2013CB932604), Fundamental Research Funds for the Central Universities, National Foundation for Fostering Talents of Basic Science (No. J1030310/No. J1103205), Program for New Century Excellent Talents in University of MOE of China

Supporting Information Zero-bias transmission spectra of ML phosphorene FET with Ni electrode obtained from different lattice match modes; Possible evolution of the hole SBH and band edges from the electrode to channel region.

20


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Table 1 Calculated interfacial properties of ML phosphorene-metal contacts. ε is the

average absolute ML phosphorene surface lattice constant mismatch. The equilibrium distance dP-M is the average distance between the contact ML phosphorene-metal interfaces in the vertical direction of it. The minimum interatomic distance dmin is the minimum atomic distance from the innermost layer atom of metal to ML phosphorene surface atom. The binding energy Eb is the energy of per phosphorus atom to remove ML phosphorene from metal surface. WM and W are the calculated work function for clean metals surface and adsorbed ML phosphorene-metal system, respectively. ∆V, wB, and TB are the tunneling barrier height, tunneling barrier width, and tunneling possibility, respectively. Φ Lh ( Φ Le ) and Φ

h tra n s

E gtrans

e ( Φ trans ) are the electronic and transport SBH of hole (electron) in the lateral direction.

is the transport gap, define as

e h E gtra ns = Φ tran s + Φ tra ns

. The calculated work function of ML

phosphorene is WP = 5.04 eV. Al

Ag

Cu

Au

Ti

Cr

Ni

Pd

ε (%)

0.52

1.12

2.58

1.00

2.58

1.02

2.65

0.96

dp-M (Å)

2.46

2.44

2.30

2.38

1.78

1.69

1.77

2.19

dmin (Å)

2.55

2.57

2.35

2.46

2.32

2.23

2.21

2.28

Eb (eV)

0.41

0.43

0.59

0.46

0.89

1.62

1.32

0.85

W (eV)

4.36

4.43

4.89

4.84

4.53

4.71

5.02

5.32

WM (eV)

3.86

4.20

4.77

5.00

4.35

4.69

5.16

5.27

∆V (eV)

1.26

1.67

0.65

1.55

0.00

0.00

0.00

0.00

wB (Å)

0.69

0.80

0.38

0.76

0.00

0.00

0.00

0.00

TB (%)

67.00 59.00 85.00 61.00

100.00

100.00

100.00

100.00

0.40

0.58

0.89

Φ Le (eV)

Φ

e trans

b

0.30

0.76

0.71

0.00 b

0.51

0.52

0.34

0.30

0.75

0.37

0.39 (0.64 )

1.18

Φ Lh (eV)

0.68

0.61

0.15

0.20

0.51

0.33

0.02

0.00

h (eV) Φ trans

0.60

0.68

0.75

0.90

0.30(0.21a)

0.89

0.26 (0.35b)

0.16

1.11

1.20

1.09

1.20

1.05

1.26

0.65 (0.99b)

1.34

Egtrans a

(eV)

0.23

(eV)

FL phosphorene experimental value from Ref. 13. Phosphorene experimental value from Ref. 15.

21



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Monolayer PhosphoreneâMetal Contacts - ACS Publications

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