Charge Transport in Borophene: The Role of Intrinsic Line Defects

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C: Physical Processes in Nanomaterials and Nanostructures

Charge Transport in Borophene: The Role of Intrinsic Line Defects Jing Zeng, and Keqiu Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12559 • Publication Date (Web): 26 Feb 2019 Downloaded from http://pubs.acs.org on February 27, 2019

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The Journal of Physical Chemistry

Charge Transport in Borophene: The Role of Intrinsic Line Defects Jing Zenga, c and Ke-Qiu Chenb a

College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang 421002, People's Republic of China

b

Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China c

Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang 421002, People's Republic of China

 

Corresponding author. Tel: +86 15211898336. E-mail address: [email protected] (J. Zeng) Corresponding author. Tel: +86 0731-88820375. E-mail address: [email protected] (K. Q. Chen) 1

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ABSTRACT Very recently, the borophene line defects assembled with 1/6 and 1/5 rows were experimentally observed. As a lightest 2D metal sheet, borophene may realize applications in transparent electronic interconnects and electrodes. It is very important and timely to reveal the effects of line defects on quantum transport, which is directly related to borophene-based applications. By using the nonequilibrium Green’s functions and the density-functional theory, here we investigate the charge transport of borophene line defects observed by ultrahigh vacuum scanning tunnelling microscopy in the experiment. It is shown that the presence of 1/6  1/5 boundary weakens the  transmission, but almost completely blocks the  transmission. Furthermore, line defects is found to give rise to quasibound states that strongly hinder propagating electrons in a wide energy region, which is confirmed to originate from strong backscattering and quantum interference effects. This result indicates that borophene with line defects has profound potential for developing novel types of switching devices.

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1. INTRODUCTION Graphene, composed of single-layer carbon atoms, caused a new technology and new industrial revolution in the field of electronics. Inspired by the broad application prospect of graphene, other single-element 2D materials were also successfully synthesized, such as silicene,1 germanene,2 stanene,3 black phosphorene,4 blue phosphorene,5 etc. These new 2D sheets with atomic thickness have been proven to have potential applications in electronic devices and integrated circuits in the future. However, they are prone to oxidize when exposed to ambient environment, which limits their application in electronics. Recently, borophene as a 2D monolayer of boron atoms was successfully grown following theoretical predictions. 6, 7 At present, several borophene structures have been experimentally prepared by epitaxial growth of boron atoms on Ag(111) and Ag(110) surfaces, including 12 (   1/ 6 ),

 3 (   1/ 5 ), and  (   1/ 9 ) sheets.6-8 Experiment results showed that borophene is not easy to be oxidized, which is beneficial to build freestanding 2D electronic device in the future.7 Moreover, borophene sheets ( 12 and  3 sheets) are also found to host Dirac cone by using angle-resolved photoemission spectroscopy together with theoretical calculations.9,

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These outstanding electronic properties

make borophene a suitable candidate for building high-speed low-dissipation electronic devices with practical application value.9 So far, borophene with perfect crystalline structures has attracted extensive attention due to its potential for integration into future electronic circuits.11-15 Similar to graphene, however, borophene may contain defects when it is fabricated under

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certain conditions.16 Very recently, the intrinsic defects of borophene have been studied by Liu et al.17 applying ultrahigh vacuum scanning tunnelling microscopy and first-principles simulations. Line defects are observed in borophene, which displays an atomic-scale characterization that the 1/6 sheet contains the structure of 1/5 and vice versa. In particular, the new borophene phases with periodic line defects can be produced by mixing the ratios of 1/6 and 1/5 units. It is known that borophene is the lightest 2D metal sheet ever discovered, and may have broad prospect in transparent electronic interconnects and electrodes.18 Understanding the effects of line defects on quantum transport is very important for realizing borophene-based applications. 2. MODEL AND COMPUTATIONAL DETAILS In the present work, we studied the charge transport of borophene line defects observed experimentally by using the ATOMISTIX TOOLKIT package, which adopts density-functional theory combined with the Keldysh nonequilibrium Green's technique.19-27 Figure 1 displays the geometrical models that demonstrate borophene line defects. Figure 1a shows a model that 1/6 and 1/5 sheets are coupled seamlessly, where a smooth-phase boundary is observed [see the purple shadow region]. The purple shadow region of Figure 1b [Figure 1c] displays an atomic structure that the 1/6 [ 1/5 ] sheet contains a row of the 1/5 [ 1/6 ]. At last, we also present the geometrical structure of  4/ 21 phase borophene which is produced by the period assembly of 1/6 and 1/5 rows. To explore the quantum transport of these models, two-probe systems need to be constructed. In the present work, 1/6 or 1/5

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rows are used to build electrodes and electrode extensions, as shown in gray shadow regions. The transmission is computed using the double-  polarized basis set, the generalized gradient approximation, the density mesh cut-off 75 Hartree, and the Monkhorst–Pack k-points grid 1×13×200. The atomic structure are relaxed until all residual force on each atom is smaller than 0.02 eV﹒Å-1.

Figure 1. The purple shadow regions of (a)-(d) display geometrical structures that describe the

1/6 -1/5 boundary, line defect in 1/6 , line defect in 1/5 , and 4/21 phase, respectively. Their corresponding scanning tunnelling microscopy images can be found in Ref. 17. The dark (light) grey regions are the electrodes (electrode extensions) parts of the corresponding two-probe systems.

The currents through the borophene-based two-probe systems are computed by the Landauer-Büttiker formula28

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I (Vb ) 

2e T ( E , Vb )[ f l ( E  l )  f r ( E   r )]dE , h 

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(1)

where Vb and l ( r ) are the external bias voltage and the electrochemical potential of the left (right) electrode, respectively.

f l ( r ) is the Fermi-Dirac distribution

functions of the left (right) electrode. 3. RESULTS AND DISCUSSION In previous works, many feasible ways have been adopted to introduce magnetism in the low dimensional systems, such as doping,29 hybrid connection,30 defect,31 edge modification,32 and adsorption.33 Many interesting spin-transport properties, including thermal giant magnetoresistance,29 nearly 100% spin polarization,29 colossal magnetoresistance,30 perfect spin Seebeck effect,30 spin negative differential resistance,34 etc., have been observed. However, calculations show that the ground state of borophene sheets with line defects is non-magnetic state, we thus explore their charge transport properties in the following discussion. I-V curves of all models are displayed in Figure 2a. Furthermore, the I-V curves of the pristine 1/6 and 1/5 sheets are also presented for comparison. It is interesting to find that they are divided into three groups with respect to the pristine 1/6 and 1/5 systems. It is found that the conductivity has been affected when 1/6 and 1/5 sheets are assembled into a smooth 1/6 -1/5 boundary model, which acts as a low-resistance resistor in the borophene-based 2D circuit.35 For the 1/6 ( 1/5 ） sheet inserted with a row of the

1/5 (1/6 ）structure, the resistance rises due to the increase of the number of the 1/6 -1/5 boundary. While for the 4/21 sheet, its conductivity is significantly suppressed compared with that of the pristine 1/6 and 1/5 sheets, which behaves

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like a high-resistance resistor in the borophene circuit.

Figure 2. The I -V curves and transmission spectra of pristine borophene sheets and those with line defects. The Fermi level has been set to be zero. 7



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Figure 2b-d present the transmission functions corresponding to the pristine sheets and geometrical models depicted in Figure 1. It is noted that clear conductance plateaus occur in the pristine 1/6 and 1/5 sheets. However, the introduction of line defects in borophene gives rise to the occurence of backscattering, leading to the suppression of the transmission coefficients near the Fermi level. As shown in Figure 2b-d, the conductance values G at the Fermi energy show a decrease as the number of the 1/6 -1/5 boundary increases. Clearly, the conductance values G for one, two, and five 1/6 -1/5 boundaries have been reduced to about 1 G0 ( G0  2e 2 / h ), 0.85 G0 , and 0.38 G0 , respectively. In addition, for the 4/21 sheet, the full suppression of conductance is observed on the occupied side, which is in striking contrast to the other cases. This means that the  4/ 21 sheet may be a suitable candidate for developing novel types of switching devices.36

Figure 3. The transmission eigenstates of the pristine one

1/6 sheet, the 1/6 sheet inserted with

1/5 unit, and the 4/21 sheet at a selection of energies and - point.

To understand the influence of lines defects on transmission coefficients, the transmission eigenvalues of the pristine 1/6 sheet, the 1/6 sheet inserted with one

1/5 unit, and the 4/21 sheet at a selection of energies are calculated, and their corresponding transmission eigenstates are plotted in Figure 3. 8


For the pristine 1/6

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sheet, there are two eigenchannels at the Fermi energy and - point. For the first channel, the phase cancellation leads to a vanishing eigenstate amplitude in six fold coordinated B atoms. Thereforce, wave functions of the remaining boron atoms can be considered as two sublattices, which is similar to graphene.9,

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Here these two

sublattices can simultaneously contribute to the first transmission eigenstate, forming

 transmission. For the second eigenchannel, eigenstate amplitude is dominated by the coupling of 2p orbitals between four (fivefold) coordinated atoms. As shown in Figure 3, conduction in the second channel mainly comes from the contribution of  transmission. The  transmission and the  transmission in the pristine 1/6 sheet show almost the same weight in percentage of their contributions to the conductance, as shown in Table 1. However, obvious changes have taken place when line defects occur in borophene. For the 1/6 sheet inserted with one 1/5 unit, its first channel has a similar characteristic with that of the pristine 1/6 sheet, but its eigenstate amplitude shows an obvious difference on both sides of the 1/6 -1/5 boundary. This indicates that the 1/6 -1/5 boundary can weaken eigenchannel wave functions in the

 transmission. Similar to the pristine 1/6 sheet, the second channel is still dominated by the  transmission. However, the  transmission parallel to the direction of electron transport is almost completely blocked by the 1/6 -1/5 boundary, leading to the disappearance of the transmitted states in the right side of the scattering region [see Figure 3]. As a consequence, here the first channel is of significant weight (～99.6%), as displayed in Table 1.

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TABLE 1. The contribution ratio of the first and second eigenchannels of the pristine the

1/6 sheet,

1/6 sheet inserted with one 1/5 unit, and the 4/21 sheet to the transmission (at the Fermi

energy and - point).

1/6 sheet

Line defect in 1/6

4/21 sheet

Channel 1 (%)

51%

99.6%

100%

Channel 2 (%)

49%

0.4%

0

Similar results can be also found in the  4/ 21 sheet. Scanning tunnelling microscopy images indicate that the  4/ 21 sheet is constructed by the periodic assembly of

1/6 and 1/5 units. Thus, for the  transmission, reflection of the

scattering wave occurs at all boundary regions, and amplitude of wave functions gradually decays when they pass through the 1/6 -1/5 boundary. Thus, amplitude of wave functions exhibits an oscillation characteristic along the transport direction, forming localized scattering states. Both localization and reflection obviously weaken the  transmission. For the  transmission, however, it is almost completely blocked by the first 1/6 -1/5 boundary. So the conductance mainly comes from the contribution of the first eigenchannel (see Table 1). To further reveal the transport mechanisms of borophene with lines defects observed in the experiment, we resolve the transmission path between boron atoms. It is found from Figure 4a that for the pristine 1/6 sheet, the transmission mainly originates from two aspects: electron transfer via chemical bonds and through hopping between the fourfold and fivefold coordinated boron atoms. However, when the 1/6 sheet is inserted with a row of the 1/5 structure, the transmission through 10


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chemical bond channels and electron hopping channels shows the reversal of ring currents near the 1/6 -1/5 boundary, as shown by blue, purple and red arrows. This gives rise to a vortex current near the boundary, which disrupts the electron transport in the system. This phenomenon is particularly evident in the 4/21 sheet. In the mean time, it is interesting to note that for the 4/21 sheet, the transmission path through electron hopping channels almost disappears in the right side of the central scattering region after multiple vortex current regions disrupt the electron transport path.

Figure 4. The electron transmission pathways at the Fermi energy for the pristine the

1/6 sheet,

1/6 sheet inserted with one 1/5 unit, and the 4/ 21 sheet. The arrow color represents the

direction of electron transmission. The arrow volume represents the magnitude of the pathway.

For the 4/21 sheet, another impressive phenomenon is that on the occupied side, transmission coefficients are significantly suppressed by the quasibound states induced by the line defects. This characteristic may be useful for developing novel

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types of switching devices.36 In order to reveal the corresponding mechanism, in Figure 3, we also present the transmission eigenstates of the 4/21 sheet at -0.88 eV. Generally, the amplitude of eigenstate should have a relatively large weight in the left side of the device due to the incoming wave functions coming from the left electrode. For the first eigenstate, however, here the amplitude of the wave functions is obviously lower in the first and third 1/6 unit cells, indicating that the incoming and reflected wave functions form destructive interference in these regions. Thus, the quantum interference effect in combination with backscattering of the 1/6 -1/5 boundary give rise to a nearly vanishing transmitted state in the right side of the  4/ 21 sheet, yielding a full suppression of transmission coefficients in the corresponding energy region. By applying a gate voltage, it is possible to provide control over the energy position of this characteristic, and thus realizing the transition between on and off states. 36, 37 The presence of line defects in borophene is found to give rise to quasibound states that strongly backscatter propagating electrons at certain energy region. However, whether this interesting physical phenomenon is dependent on periodic self-assembly of borophene line defects remains an open question. Liu et al.17 have showed that line defects may be produced by arbitrary combinations of 1/6 and 1/5 rows, and has a local periodicity. We thus construct an atomic model that consists of one 1/6 row assembled with two 1/6 units, as shown in Fig 5(a). Clearly, the transmission coefficient near -0.97 eV decays exponentially with the increase of repeat line defect units [see the black dotted frame in Figure 5b], which is significantly different from

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Figure 5. (a) An atomic model that consists of repeat line defect units, where a line defect unit is made up of one

1/6 row assembled with two 1/5 rows. N indicates the number of repeat line

defect units (N=1-4). (b) Transmission spectra for all systems. The Fermi level has been set to be zero. (c) The first transmission eigenstates of N repeat line defect units (N=1 and 4) at -0.97 eV and - point.

the rule of conductance variation at the Fermi energy. Therefore, increasing the repeat line defect units may be an effective way to enhance the performance of the 13



gate-regulated borophene-based switching devices. To explore the corresponding transport mechanism, we plot the first eigenchannel scattering states of N repeat line defect units (N=1 and 4) at -0.97 eV. The quantum interference phenomenon can be observed in these two systems, which is characterized by the scattering states having a relatively small amplitude in the far left of the system. Clearly, the presence of one line defect unit weakens wave functions amplitude, and the transmitted state is still found in the right side of device region. In comparison, the increase of the lines defect units obviously enhances backscattering efficiency, leading to a full suppression of electron transport in a wide energy region. 4. CONCLUSIONS In summary, we investigate the charge transport properties of borophene-based electronic devices assembled with 1/6 and 1/5 rows by using the nonequilibrium Green’s functions and the density-functional theory. We find that at low bias region, borophene sheets can act as low-resistance or high-resistance resistors by the change of line defects. As electronic devices driven by low bias can save energy consumption, borophene sheets with line defects have the broad application prospect in a new generation of electronic circuitry. Meanwhile，mechanism analysis shows that the

1/6 -1/5 boundary weakens eigenchannel wave functions of the  transmission, but almost completely blocks the  transmission. For the  4/ 21 sheet, we find that transmission coefficients on the occupied side can be significantly suppressed by the quasibound states induced by the line defects, which originates from strong backscattering and quantum interference effects. Moreover, our results also indicate

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that increasing lines defect units can make the transmission coefficient decay exponentially in a wide energy region, showing a rule of conductance variation different from that at Fermi level. These results indicate the important role of line defects in the charge transport in borophene. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant No. 61401151 and 11674092), by the National Key Research and Development Program of China (Grant No. 2017YFB0701602), by the Science and Technology Plan Project of Hunan Province (Grant No. 2016TP1020), and by the Science and Technology Development Plan Project in Hengyang City (Grant No. 2017KJ159). REFERENCES (1) Vogt, P.; Padova, P. D.; Quaresima, C.; Avila, J.; Frantzeskakis, E.; Asensio, M. C.; Resta, A.; Ealet, B.; Lay, G. L. Silicene: Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon. Phys. Rev. Lett. 2012, 108, 155501. (2) Li, L.; Lu, S.; Pan, J.; Qin, Z.; Wang, Y.; Wang, Y.; Cao, G.; Du, S.; Gao, H. J. Buckled Germanene Formation on Pt (111). Adv. Mater. 2014, 26, 4820-4824. (3) Zhu, F.; Chen, W.; Xu, Y.; Gao, C.; Guan, D.; Liu, C.; Qian, D.; Zhang, S.-C.; Jia, J. Epitaxial Growth of Two-Dimensional Stanene. Nature Mater. 2015, 14, 1020-1025. (4) 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. Nature Nanotechnol. 2014, 9, 372-377.

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Charge Transport in Borophene: The Role of Intrinsic Line Defects

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