Electron-Transport Properties of Few-Layer Black Phosphorus - The

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Letter

Electron Transport properties of few-layer black phosphorus Yuehua Xu, Jun Dai, and Xiao Cheng Zeng J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b00510 • Publication Date (Web): 11 May 2015 Downloaded from http://pubs.acs.org on May 12, 2015

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The Journal of Physical Chemistry Letters

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Electron Transport Properties of Few-layer Black Phosphorus 4 5

Yuehua Xu1,2,3 , Jun Dai2 and Xiao Cheng Zeng2,* 7

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School of Mathematics and Physics, Changzhou University, Changzhou 213164, People’s Republic of China 2. Department of Chemistry and Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States 3 Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China *Email: [email protected]; 1.

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Abstract 2

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We perform the first-principles computational study of the effect of number of 24

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stacking layers and stacking style of the few-layer black phosphorus (BPs) on the 26

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electronic properties, including transport gap, current-voltage (i-v) relation and 28

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differential conductance. Our computation is based on the non-equilibrium Green’s 30

29

function approach combined with density functional theory calculations. Specifically, 32

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we compute electron transport properties of monolayer BP, bilayer BP and trilayer BP, 34

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as well as bilayer BPs with either AB-, AA- or AC-stacking. We find that the stacking 36

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number has greater influence to the transport gap than the stacking type. Conversely, 38

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the stacking type has greater influence to i-v curve and differential conductance than 40

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to the transport gap. This study offers useful guidance for determining the number of 42

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stacking layers and the stacking style of few-layer BP sheets in future experimental 4

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measurements and for potential applications in nanoelectronic devices. 46

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TOC: 47 48 49 50 51 52 53 54 5 56 57 58 60

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Keywords: interlayer interaction, two-probe configuration, transmission spectra, i-v curve,

differential conductance 1 ACS Paragon Plus Environment


1 2 4

3

The 6

5

recent successful exfoliation of another new two-dimensional atomic-layer

material, namely, layered black phosphorus (BP) or phosphorene from bulk black 8

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phosphorus1-5 has attracted immediate attention owing to their remarkable electronic 10

9

properties1, 12

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6-22

. Notably, the monolayer phosphorene possesses a desirable direct

bandgap of 1.5 eV18, 14

13

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and significant transport anisotropy within the monolayer

plane, as well as the linear dichorism24-26, rendering it a potential candidate for future 16

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nanoelectronic applications2, 6, 8, 14, 27-29. Few-layer BPs are predicted to have even 18

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richer electronic properties and higher tunability compared to the monolayer BP23, 25, 20

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30-34

2

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such as the high carrier mobility up to 1000 cm2V-1S-1 and layer-dependent direct

bandgaps, ranging from 1.51 eV for monolayer BP to 0.59 eV for five-layer BP. The 24

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reduction of bandgap in few-layer BPs is largely due to interlayer van der Waals 26

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interaction24. The predicted bandgap reduction with increasing the number of BP 28

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layers has been confirmed experimentally by Das et al35, evidenced by the 30

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layer-dependent transport gap. In turn, determination of the exact layer number of 32

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few-layer BP based on the measurement of the transport gap can be an effective tool 34

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for separation of different few-layer BPs. In addition to the stacking number, our 36

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recent calculation shows that the stacking type can also affect the bandgap of 38

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few-layer BPs31. For bilayer BPs, three possible stacking types were considered, 40

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namely AB-, AA- and AC-stacking, whose corresponding bandgaps are 1.04 eV, 0.95 42

eV, and 0.78 eV respectively31. Hence, it is expected that the transport gap of 4

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few-layer BP can be also affected by the stacking type. It would be useful to examine 46

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whether the transport gap of few-layer BP can be used as an indicator to distinguish 48

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different stacking type, at least for bilayer BPs. 50

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Besides the layer-dependent bandgaps, it is also important and timely to study the 52

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effect of different stacking number and stacking type on electron transport properties, 54

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such as current-voltage (i-v) curve and differential conductance. These properties are 56

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closely relevant to the design of practical nanoelectronic devices. Moreover, 58

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measurement of layer- and stacking-type-dependent i-v curve and differential 60

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conductance can be also used as supplemental information, besides the measurement 2 ACS Paragon Plus Environment

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of transport gap, to distinguish the stacking number and stacking types of few-layer 4 5

BPs. 6 7

A sensible modeling of a practical electron-transport device much meet the 9

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following requirements36-40: (1) Good contact with metallic electrodes; (2) three major 10 1

factors to determine the electronic transparency of contacts, i.e., favorable interface 12 13

geometry and bonding, the electronic density of states, and the potential barrier at the 14 15

interface; and (3) the top contact with electrode (because contacting a single layer 16 17

from side of electrodes is insufficient for good electron injection). We note that Guo 18 19

and coworkers investigated different metals as contact with monolayer BP for future 20 21

device application. They predicted that Cu (111) surface is the best candidate to form 2 23

an excellent ohmic contact with monolayer BP with a desirable modest binding 25

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energy per BP unit-cell of 1.30 eV41. We therefore adopt the Cu (111) surface as the 26 27

metal contact to support few-layer BPs in a two-probe configuration for modeling. 28 29

The first-principles computation of transport properties is based on the 31

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non-equilibrium Green’s function (NEGF) approach combined with the density 32 3

functional theory calculations. The monolayer, AB-stacking bilayer and ABA-stacking 34 35

trilayer BPs, as well as AB-, AA-, and AC-bilayer BPs are chosen as the model 36 37

systems to study the effect of stacking number and stacking type on the transport gap, 38 39

i-v curve, and differential conductance. The zigzag direction of few-layer BPs is 40 41

chosen as the transport direction because the electron mobility in the armchair 42 43

direction is expected to decrease much rapidly due to the strained effect. In the zigzag 45

4

direction, however, the electron mobility can be even enhanced by the strain25. 46 47

Besides the transport properties, our studies suggest possible strategies and 48 49

guiding rules for effective way to identify different stacking number and stacking type 50 51

of few-layer BPs. Specifically, we find that although both stacking number and 52 53

stacking type can affect the transport gap, i-v curve, and differential conductance of 54 5

few-layer BPs, the stacking number incurs greater influence than the stacking type, 56 57

while the stacking type has greater influence to the i-v curve and differential 58 60

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conductance than to the transport gap, especially for the AB- and AA-stacking bilayer 3 ACS Paragon Plus Environment


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BPs. Hence, the transport gap measured from the transmission spectra is best used to 4 5

identify the stacking number of BPs, but not the stacking type of BPs. 6 7 8 9

Computation of electronic structures and transport properties is carried out using 1

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the Atomistix Toolkit (ATK) code package based on the non-equilibrium Green’s 12 13

function (NEGF) approach combined with density functional theory (DFT) 15

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calcualtions42-43. 16 17

To model the two-probe configuration, a supercell is constructed from a slab of 18 19

three atomic layers of Cu with a few-layer BP sheet adsorbed on the Cu (111) surface. 20 21

A vacuum region of at least 20 Å is set in the supercell. Fig. 1 shows the two-probe 2 23

configuration with a monolayer BP. The system is divided into three regions: left 24 25

electrode, right electrode and scattering region. Here, the transport direction c(z) is set 26 27

along the zigzag direction of the BPs only, and the periodic boundary conditions are 28 29

applied in the transverse transport direction, i.e., the system extends infinitely along 30 31

the b(y) direction. The primitive cell of few-layer BP is taken from our previous 3

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studies30-31. The primitive cell of Cu has lattice constants of b = 4.496 Å and c = 2.596 35

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Å44. The lattice constants of the electrodes are chosen to be those of (1×1×3) strained 36 37

cell of few-layer BP as b = 4.496 Å and c = 10.382 Å, the same as those for a (1×1×4) 38 39

cell of Cu(111). The lattice-constant matching is reasonable since the mismatch from 40 41

the lattice parameters of Cu (111) surface is only about 1.8％ in the b direction and 42 43

4％ in the c direction. The effect of strained cell of few-layer BP on the electron 45

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mobility was discussed in detail in a previous study25. It was shown that when the 46 47

few-layer BP being under a biaxial strain of 6%, the electron mobility along the 49

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zigzag direction is even higher than unstrained ones25. So it is believed that strained 50 51

few-layer BP still possesses good electron transport properties in the zigzag direction. 52 53

A short channel device is considered with the length of the scattering region in the c(z) 54 5

direction being about 62 Å (see the two inner vertical white lines in Fig. 1 (a)) , 56 57

making the length of few-layer BP channel about 36 Å (see the red lines in Fig. 1(a)). 58 60

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This length is long enough to avoid the effect of metal-induced gap states for the 4 ACS Paragon Plus Environment

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few-layer BP (see Fig. 1(b)). 4 5 6 7

(a) 8 9 10 1 12 13 14 15 16 17 18 19 20 21 2 23 24 26

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(b) 27 28

60

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PDOS

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PDOS (arb.units)

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Fig. 1 (a) The optimized structure of two-probe configuration with monolayer BP (the 48

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lower panel is a top view of the two-probe configuration). The light purple balls 50

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denote phosphorus atoms and the gold balls denote Cu atoms. The length of the 52

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scattering region (between two inner vertical white lines) in the c(z) direction is about 54

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62 Å, while the length of the free-standing few-layer BP channel (between two 56

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vertical red dashed line) is about 38 Å. (b) the Partial density of states (PDOS) of 58

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phosphorus atoms in the channel. 59 60

5 ACS Paragon Plus Environment


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In the DFT calculation of electronic structures, we use a numerical basis set to 4 5

expand the wave function, i.e., the double zeta plus polarization basis set (DZP). The 6 7

generalized gradient approximation (GGA) is used for the electron exchange and 8 9

correlation and the Troullier-Martins pseudopotentials are used for the atomic cores. 10 1

The density mesh cut-off is chosen 150 Ry to achieve a balance between calculation 12 13

efficiency and accuracy. The k-point grids of 1 × 8 × 100 and 1 × 32 × 100 are used to 14 15

sample the Brillouin zone of the electrodes in the x, y and z direction for the geometry 16 17

relaxation and for computation of total energy, transmission spectra, and i-v curve, 18 19

respectively. The atomic structures of the junctions are fully optimized by minimizing 20 21

the atomic forces on the atoms to be smaller than 0.05 eV/Å. The separation between 2 23

the two electrodes is also optimized by minimizing the stress in the direction of the 24 25

junctions. 26 27 28 29

Upon DFT optimization, the average distance dz between the topmost layer of Cu 30 31

(111) surface and the bottom layer of few-layer BP is 2.27 Å, 2.26 Å and 2.26 Å for 32 3

the monolayer, AB-stacking bilayer and ABA-staking trilayer, respectively. These 34 35

values are slightly less than 2.31 Å for the monolayer BP obtained by Guo and 37

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coworkers.41 The shortest bond length dm between a topmost atom on Cu (111) and 38 39

the bottom-layer of BP is 2.34 Å for monolayer BP, 2.35 Å for AB-stacking bilayer 40 41

BP, and 2.35 Å for ABA-stacking trilayer BP, very close to 2.36 Å for the monolayer 43

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BP, obtained by Guo and workers.41 For the AA- and AC-stacking bilayer BPs, our 4 45

calculated dz is 2.23 Å and 2.26 Å, respectively, while dm is 2.36 Å and 2.35 Å, 46 47

respectively. 48 49

Next, we present results of computed transport gap, zigzag directional i-v curve, 50 51

normalized current (current per layer) and differential conductance in the two-probe 52 53

configuration, i.e., few-layer BP-Cu (111) junctions. First, we examine whether the 54 5

contact between BP and Cu is Omhic. Our calculation shows that the difference in the 56 57

work function b is -0.30 eV between Cu (111) and monolayer BP, which is quite 60

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close to the value -0.36 eV obtained by Guo and coworker41. In addition, we compute 6 ACS Paragon Plus Environment

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the electronic potential difference V between the lower P atoms and the Cu 4 5

substrate in the contact, which is -0.50 eV for monolayer BP. This result indicates that 6 7

the electrons can be easily injected from Cu to the BP without any energy barrier. 8 9

Hence, the contact between Cu (111) and monolayer BP is a good Ohmic contact. In 10 1

addition, we also check whether the electrons can be easily injected from the 12 13

combined BP-Cu contact to the freestanding part of BP channel (see Fig. 1(a)). 14 15

Computed PDOS of the freestanding part of BP channel can be used to estimate the 16 17

Schottky barrier, which is about 0.36 eV (see Fig. S1). Fig. 2(a) shows the 18 19

transmission spectra of monolayer BP, AB-stacking bilayer BP, and ABA-stacking 20 21

trilayer BP under zero bias. Note that the top layer in bilayer BP and the top two 2 23

layers in trilayer BP are electronically decoupled from the Cu (111) substrate. So their 24 25

contribution to the transmission spectra and to the i-v curves (see below) can be 26 27

deduced from subtraction (see Fig. 2(b)). 28 29

In Fig. 2(a), the transport gap decreases with increasing the layer number. More 30 31

specifically, the transport gap is 1.15 eV for monolayer BP, 0.71 eV for the bilayer BP, 32 3

and 0.63 eV for the trilayer BP. According to the DFT band-structure calculation, the 34 35

bandgap of bare monolayer, bilayer, and trilayer BP (all under a strain due to 36 37

lattice-constant matching) is 1.17 eV, 0.78 eV and 0.67 eV, respectively (see Fig. S2). 38 39

Hence, the computed transport gaps are largely consistent with computed bandgaps of 40 41

free-standing few-layer BP. Notably, these computed transport gaps are nearly the 43

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same as corresponding experimental values35, i.e., 1.0 eV for monolayer BP, 0.73 eV 4 45

for bilayer BP, and 0.60 eV for trilayer BP. Note also that the reduction of bandgap is 46 47

not linearly correlated with increasing the stacking number, suggesting that the 48 49

transport gap would become less effective to identify the stacking number for 50 51

many-layer BPs. 52 53 54 5 56 57 58 59 60



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monolayer BP bilayer BP trilayer BP

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(b) the 2nd layer of bilayer BP the 2nd and 3rd layers of trilayer BP

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T(E)

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Fig. 2 (a) Computed zigzag directional transmission spectra of monolayer BP, 2

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AB-stacking bilayer BP and ABA-stacking trilayer BP under zero bias, and (b) 24

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deduced contribution to the corresponding transmission spectra from the top layer of 26

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bilayer BP and top two layers of trilayer BP under zero bias. 27 28 30

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In Fig. 3, the computed zigzag directional transmission spectra of AB-, AA-, and 32

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AC-stacking bilayer BPs, as well as the contribution by the top layer to their 34

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transmission spectra are shown, where the corresponding transport gap is 0.71 eV, 36

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0.79 eV, and 0.57 eV, respectively. The transport gaps are also close to the computed 38

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bandgaps of bare AB-, AA, and AC-stacking bilayer BPs (under the same strain), 40

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which are 0.78 eV, 0.79 eV and 0.57 eV, respectively (see Fig. S3). The AC-stacking 42

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bilayer gives notably smaller bandgap than the AB- and AA-stacking bilayers, while 4

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the AA-stacking and AB-stacking bilayer BPs give nearly the same bandgap. So for 46

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bilayer BPs, it is easier to identify the AC-stacking based on the transport gap, but not 48

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so to differentiate AB- and AA-stacking. 49 50 51 52 53 54 5 56 57 58 59 60


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the 2nd layer of AB-stacking BP the 2nd layer of AA-stacking BP the 2nd layer of AC-stacking BP

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Fig. 3 (a) Computed zigzag directional transmission spectra of bilayer BP with AA-, 2

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AB-, and AC-stacking, under zero bias, and (b) the contribution by the top layer to 24

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their transmission spectra. 26

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Fig. 4 displays the computed zigzag directional i-v curves (based on the 27

Landauer-Buttiker formula45) for the monolayer BP, AB-stacking bilayer BP, and 30

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ABA-stacking trilayer BP under the bias ranging from 0 to 2 V. It can be seen that the 32

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amplitude of the current increases with increasing the stacking number. For example, 34

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under a bias of 2 V the current is 249 nA, 688 nA, and 936 nA for monolayer BP, 36

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bilayer BP, and trilayer BP, respectively. This behavior can be understood because the 38

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more stacking number for the few-layer BP, the more transmission channels would 40

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form. Besides the generic trend of i-v curves for all three cases, some special features 42

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can still be seen in each i-v curve. Specifically, for monolayer BP, a small decrease in 4

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current exists between bias 1.7 V and 1.8 V, and for bilayer BP, a similar decrease 46

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also exists between 1.6 V and 1.7 V. While for trilayer BP, no such decrease in 48

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current is observed in the bias range from 0 to 2 V. In addition, the deduced 50

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contribution from the top layer of bilayer BP and top two layer of trilayer BP to the 52

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current is shown in Fig. 4(b). Fig. 4(c) displays the normalized current (current per 54

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layer) for monolayer BP, bilayer BP and trilayer BP, respectively. It can be also seen 56

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that several special features in Fig. 4(b) and Fig. 4(c) also arise in their corresponding 58

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i-v curve. Hence, one may determine existence of monolayer, bilayer or trilayer BP in 60

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the sample, based on the amplitude of current as well as the presence and position of 9 ACS Paragon Plus Environment


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the decrease of current in i-v curve. 4 5 6 1000

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Fig. 4 Computed zigzag directional (a) i-v curves, (c) normalized current and (d) 37

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differential-conductance curve of the monolayer BP, bilayer BP, and trilayer BP. (b) 39

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The contribution from the top layer of bilayer BP and top two layers of trilayer BP to 41

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the corresponding i-v curves. 42 43 45

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Based on the computed i-v curve (with electron transport being in the zigzag 47

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direction), the differential conductance di/dv under bias 0 - 1.9 V can be computed 49

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(see Fig. 4(d)). One can see that the differences among the differential conductance 51

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are more pronounced compared to the i-v curve. Specifically, for the monolayer BP, a 52 53

valley in the differential conductance can be seen under bias ~1.5 V, whereas for the 54 5

bilayer BP and trilayer BP, a peak, rather than a valley, can be seen within this bias 56 57

region. Moreover, for the monolayer BP, there exists a peak under bias ~1.6 V, while 58 60

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for the bilayer BP and trilayer BP, there is a valley near this bias region. Hence, monolayer BP can be distinguished from the bilayer and trilayer BPs according to the 10 ACS Paragon Plus Environment

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characteristic valley in the differential conductance under bias ~1.5 V as well as the 4 5

peak under about 1.6 V in i-v curve. In addition, for the trilayer BP, there is a peak 6 7

under bias ~1.1 V while for the bilayer BP, no such characteristic peak is seen. 8 9

Furthermore, for the trilayer BP, the highest peak is located at bias ~1.8 V, while for 10 1

the bilayer BP, although a similar peak exists at this bias, the peak height is much 12 13

lower than that of the trilayer BP. Hence, the characteristic peaks at 1.1 V and 1.8 V 14 15

in the differential-conductance curve of trilayer BP are important features to 16 17

differentiate it from bilayer BP. 18 19

We have also studied the effects of different stacking type on i-v curve using the 20 21

two-probe configuration. The computed i-v curves for AB-, AA- and AC-bilayer 2 23

BP-Cu (111) junctions are shown in Fig. 5(a). In general, values of current under bias 24 25

0 - 2 V are close to one another among the three stacking types, although some 26 27

distinctive features can still be discerned. For the AB-stacking, as mentioned above, a 28 29

notable decrease in current exists between bias 1.6 V and 1.7 V, while the current 30 31

exhibits monotonic increase in this bias region for the AA-stacking. For the 32 3

AC-stacking, the maximum current (a peak) exhibits at about 1.9 V while for the 34 35

AB-stacking, the maximum is located under 2.0 V bias. Thus, although the amplitude 36 37

of current is more or less the same for the AB-, AA-, and AC-stacking bilayer BPs, 38 39

the decrease in current between 1.6 V and 1.7 V for AB-stacking and the decrease in 40 41

current between 1.9 V and 2.0 V for AC-stacking can be used as clear indicators to 42 43

differentiate the two stacking types from the AA-stacking type. In addition, the 4 45

deduced contribution from the top layer of AB-, AA-, and AC-stacking bilayer BPs to 46 47

the current is shown in Fig. 5(b). The normalized current is also calculated for the 48 49

AB-, AA-, and AC-stacking bilayer BPs (Fig. 5(c)). It can be seen that several main 50 51

features shown in Fig. 5(b) and 5(c) are also seen in the corresponding i-v curves (Fig. 52 53

5(a)). 54 5 56 57 58 59 60



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Current (nA)

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Current (nA)

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the 2nd layer of AB-stacking BP the 2nd layer of AA-stacking BP the 2nd layer of AC-stacking BP

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Fig. 5 Computed zigzag directional (a) i-v curve, (c) normalized current (d) 3

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differential conductance of bilayer BPs with AB-stacking, AA-stacking and 35

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AC-stacking, (b) the deduced contribution from the top layer of AB-, AA-, and 37

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AC-stacking bilayer BP to the current. 38 39 41

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The computed differential-conductance curves for AB-, AA-, and AC-stacking 43

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bilayer BPs under bias from 0 to 1.9 V is shown in Fig. 5(c). Again, the 45

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differential-conductance curves exhibit more striking differences compared to the 47

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corresponding i-v curves. Specifically, for the AA-stacking, a clear valley is seen 49

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under ~1.5 V bias, whereas for both the AB- and AC-stacking, a peak is seen near this 51

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bias. Moreover, for both AB- and AC-stacking, a deep valley is seen under ~1.6 V 53

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and ~1.7 V bias, respectively. Therefore, these valleys under 1.5 V, 1.6 V or 1.7 V 5

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bias can be used to distinguish the three stacking types from one another. 56 57 58 59 60


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-0.5

0.0

energy (eV)

0.5

1.0

1.7 V -0.5

0.0

energy (eV)

0.5

1.0

Fig.6 Computed zigzag directional transmission spectra of (a) monolayer BP under bias 1.7 V and 1.8 V; (b) AB-stacking bilayer BP under bias 1.6 V and 1.7 V; and (c) the AC-stacking bilayer BP under 1.9 V and 2.0 V. To highlight the integration of transmission spectra through the bias window, the integral areas are filled with different color.

31 3

32

We now discuss why these characteristic features arise for BPs with different 35

34

layer number or different stacking type. First, for the monolayer BP, the transmission 37

36

spectra under bias 1.7 V and 1.8 V are shown in Fig. 6(a). Clearly, under the bias 1.7 39

38

V, the integration of the transmission spectrum over the bias range [-0.85 V, 0.85 V] 41

40

is greater than that over the range [-0.9 V, 0.9 V]. Thus, the current is expected to 43

42

decrease within the bias range of 1.7 to 1.8 V. Likewise, for the bilayer BP, the 45

4

decrease in current between the bias 1.6 V and 1.7 V can be understood from 47

46

analyzing the corresponding transmission spectrum under bias 1.6 V and 1.7 V (see 49

48

Fig. 6(b)). Clearly, integration of the transmission spectrum over the bias range [-0.8 51

50

V, 0.8 V] is greater than that over the range [-0.85 V, 0.85 V]. In addition, for the 53

52

AC-stacking bilayer, again, the characteristic structures in i-v curve can be understood 5

54

from the corresponding transmission spectrum. The decrease in current between bias 57

56

1.9 V and 2.0 V, the corresponding spectrum under 1.9 V and 2.0 V is shown in Fig. 60

59

58

6(c). Integration of the transmission spectrum over the bias range [-0.95 V, 0.95 V] is greater than that over the range [-1.0 V, 1.0V]. 13 ACS Paragon Plus Environment


1 2 3

Second, characteristic features in the differential-conductance curves of few-layer 4 5

BPs can be understood through their corresponding i-v curves. For the monolayer BP, 6 7

the valley at ~1.5 V bias stems from the nearly unchanged current at 1.5 V bias (see 8 9

Fig. 4(a)). The peak at ~1.6 V bias can be understood from the trend of rapid increase 10 1

of current between bias 1.6 V and 1.7 V (Fig. 4(a)). For the bilayer BP, the valley at 12 13

~1.6 V bias can be understood from the decreasing current between 1.6 V and 1.7 V 14 15

(Fig. 4(a)). For the trilayer BP, the peaks under ~1.2 V can also be understood from 16 17

the fast increase of current from bias 0.9 V to 1.1 V. Similarly, the peak at ~1.8 V bias 18 19

can be understood from the even faster increase of current than that for bilayer BP. 20 21

Thus the amplitude of peak at 1.8 V bias is greater than that for bilayer BP. 2 23

Lastly, the characteristic features in the differential conductance of AB-, AA- and 24 25

AC-stacking bilayer BPs can be understood from their corresponding i-v curve. For 26 27

the AA-stacking, the valley at ~1.5 V bias is resulted from the slower increase of 28 29

current in this bias region compared to the current in the neighboring region. The 30 31

peaks at 1.5 V in both the AB- and AC-stacking cases are due to the faster increase of 32 3

current in this bias region compared to the current in the neighboring region. 34 35 36 37

We have performed, to our knowledge, the first systematic study of the effect of 38 39

stacking number and stacking type of few-layer BPs on the transport gap, zigzag 40 41

directional i-v curve, and differential conductance. We compute electron transport 42 43

properties of monolayer BP, bilayer BP and trilayer BP, as well as bilayer BPs with 4 45

either AB-, AA- or AC-stacking. We find that the stacking number has greater 46 47

influence to the transport gap than the stacking type. The characteristic features in i-v 48 49

curves of monolayer BP, bilayer BP, and trilayer BP are more pronounced, 50 51

particularly in their relative magnitude of current, than those of AA-, AB-, and 52 53

AC-stacking bilayer BPs. Moreover, the differential conductance deduced from i-v 54 5

curve is much more sensitive to the stacking number than to the stacking type. On the 56 57

other hand, the stacking type has greater influence to i-v curve and differential 58 60

59

conductance than to the transport gap. The difference in the transport gap between 14 ACS Paragon Plus Environment

Page 14 of 19

Page 15 of 19


1 2 3

AB- and AA-stacking bilayer BPs is merely 0.08 eV. A notable characteristic feature 4 5

in i-v curve is the decrease in the current between 1.6 V and 1.7 V for AB-stacking. 6 7

The valleys at 1.5 V and 1.6 V bias in the differential-conductance curves of AA- and 8 9

AB-stacking BPs are even more striking. These features can be useful indicators to 10 1

identify the AB-stacking from AA-stacking for bilayer BPs. 12 13

More importantly, our results may offer helpful guidance on how to identify 14 15

stacking number and stacking style of few-layer BP sheets for future experimental 16 17

measurements and applications in nanoelectronic devices. For example, for the 18 19

identification of the stacking number of 1 to 3, the transport gap in the transmission 20 21

spectrum appears to be an effective way, but not so effective for many-layer BPs. To 2 23

identify the AA- and AB-stacking for bilayer BPs, a combination of transport-gap 24 25

data along with zigzag directional i-v curve, and differential-conductance curve is a 26 27

much more effective approach. 28 29 30 31

ACKNOWLEDGMENTS. 32 3

We thank Dr. Anders Blom for valuable discussions. The work was supported by the 34 35

National Natural Science Foundation of China under Grant NO.11404038, the Special 36 37

Foundation for theoretical physics Research Program of China under Grant NO. 38 39

11347149, the Natural Science Foundation of the Jiangsu Higher Education 40 41

Institutions of China under Grant No. 13KJB140001, Jiangsu Government 42 43

Scholarship for Overseas Studies, the High Performance Computing Laboratory of 4 45

Changzhou University. XCZ was supported by the National Science Foundation (NSF) 46 47

through the Nebraska Materials Research Science and Engineering Center (MRSEC) 48 49

(grant No. DMR-1420645). 50 51 53

52

Supporting Information Available: Description of the material included. This material is available free of charge via the Internet 56

5

54

http://pubs.acs.org. 57 58 59 60



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Electron-Transport Properties of Few-Layer Black Phosphorus - The

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