Giant Band-Gap Reduction and Insulator-Metal Transition in Two

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C: Physical Processes in Nanomaterials and Nanostructures

Giant Band-Gap Reduction and Insulator-Metal Transition in Two-Dimensional InX (X= Cl, Br, I) Layers Zhen Ma, Fang Wu, Yunfei Liu, and Erjun Kan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04986 • Publication Date (Web): 14 Aug 2019 Downloaded from pubs.acs.org on August 14, 2019

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The Journal of Physical Chemistry

Giant Band‐Gap Reduction and Insulator‐Metal Transition in Two‐dimensional InX (X= Cl, Br, I) Layers

Zhen Ma,1 Fang Wu,1* Yunfei Liu,1 Erjun Kan2* 1College

of Information Science and Technology, Nanjing Forestry University,

Nanjing, Jiangsu 210037, P. R. China 2 Department

of Applied Physics, Nanjing University of Science and Technology,

Nanjing, Jiangsu 210094, P. R. China

Correspondence should be addressed to:

E. K ([email protected])

F. W. ([email protected])

ACS Paragon Plus Environment

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

ABSTRACT Manipulating the electronic structures of semiconductors by external electric field promises great potential in future electric technology. However, most of the explored low-dimensional systems only show weak response under external electric field, and the effective factor, which is defined as ΔEg/U (U is the induced electric potential difference, and ΔEg is the change of band gap), is very low. Here, we demonstrated that an unexpected giant band-gap modulation is realized in indium halides layers, and the effective factor is much higher than the reported results. Through comprehensive first-principles calculations, we found that two-dimensional (2D) InX (X= Cl, Br, I) monolayers are semiconductors with band gaps of 2.59, 2.30, and 2.08 eV, respectively. Remarkably, the band gaps of InX (X= Cl, Br, I) monolayers are dramatically reduced by an external electric field, and the band-gap reductions under an electric field of 0.5 V/Å found for InCl, InBr, and InI monolayers are 1.51, 1.50, and 1.38 eV, respectively. Furthermore, for InI bilayer (Eg = 1.78 eV) and four layers (Eg = 1.50 eV), the critical electric fields of closing the band gaps are only 0.3 V/Å and 0.1 V/Å, respectively. Our results revealed that such unexpected large band-gap modulations come from the weak electrostatic screening, benefited from the ionic bonds of Indium and halogen atoms. Thus, the mechanism presented here can be applied to design new semiconductor-based devices, such as field effect transistors or phase-transition materials.


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INTRODUCTION: In the low-dimensional semiconducting materials, such as nanotube1-2, nanoribbons3-4, and multilayers5-7, the electronic states can be effectively modulated when the electrons and holes are pulled in opposite directions in presence of an external electric field. Such effect has created plenty of new physical phenomena, such as boosting the solar-to-hydrogen efficiency8, creating skyrmions9, inducing superconductivity10 and topological insulator 7, tunable excitions11, ferroelectricity12, and optical modulators 13-16. Generally speaking, an additional electric potential will be induced when an external electric field is applied, which can be used for gate-controlled field effect transistors (FET)17-19. To quantitatively describe the effect of external electric field on the electronic structures modulation of semiconductors, we can define an effective factor ΔEg/U, where U is the induced electric potential difference, and ΔEg is the change of band gap. According to the definition, the effective factors in most of the previous explored systems are quite low. For example, our previous results have shown that the band gap of graphene nanoribbons can be tuned by the external electric field, but the estimated effective factor is smaller than 0.220. Thus, for most of the low-dimensional materials, the applied external electric field is always strongly screened, and only produces small band-gap modulation. On the other hand, to improve the performance of FET, new materials with large band-gap modulation under practical electric field are always highly desired. In this paper, we demonstrated the giant band-gap modulation in InX (X = Cl,



Br, I) layers through first-principles calculations. Our results show that the band gaps of InX (X = Cl, Br, I) monolayers can be significantly reduced by an external electric field. The largest effective factor is close to 1, which is much higher than any previous reports. Moreover, our results demonstrated that an insulator-metal transition is realized for InI bilayer with an electric field of 0.3 V/Å, and InI four layers with an electric field of 0.1 V/Å, respectively. The explored mechanism will benefit the further development of new semiconductor-based devices, such as high-performance field effect transistors (FET). COMPUTATIONAL DETAILS: Theoretical calculations were performed based on density functional theory (DFT) using the generalized gradient approximation (GGA) known as PW9121, implemented in the Vienna ab initio simulation package (VASP) code22. The projected augmented wave (PAW) method with a plane-wave basis set was used23-24. We applied periodic boundary conditions with a vacuum space of 18 Å in order to avoid interactions between the nearest neighbor unit cells in InX (X= Cl, Br, I) monolayers. Furthermore, the energy convergence criterion for the electronic wave function was set as 10-5 eV. The geometry optimization was considered to converge when the residual force on each atom was smaller than 0.01 eV/Å. During the optimization, 15×15×1 K-point is adopted, while 25×25×1 is used for total energy calculations. The 4×4×1 supercells were adopted to perform phonon calculations by using Phonopy. RESULTS


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Recently, one kind of layered semiconducting materials composed of indium and the group Ⅶ atoms (Cl, Br, I) have been synthesized in experiments25. Geometrically, InX (X= Cl, Br, I) materials are predominantly crystallized in a layered structure with space group cmcm (No. 63)25-26, and each In (halogen) atoms are surrounded by five halogen (In) atoms, and indium atom and halogen atoms are tightly bonded with an interlaced arrangement mode in one layer, as shown in Figure 1a and 1b. Moreover, the interactions between the neighbour layers are van der Waals force, which is similar with the known 2D nanomaterials27-30. Similar with graphene, the 2D counterparts may be exfoliation from 3D bulk materials because of the possibly low cleavage energies27-30. Our DFT calculations of band structure show that all InX materials are semiconductors, and the band gaps are 1.30 eV (InCl), 1.31 eV (InBr), 1.32 eV (InI), respectively. Micromechanical cleavage and liquid exfoliation are standard techniques to fabricate monolayer from layered materials if the cleavage energy is below 1 J m-2. To address the possibility of InX monolayer exfoliated from the bulk, the cleavage energy was defined as the following: 𝐸 Where 𝐸 , 𝐸

𝐸

and 𝐸

𝐸

𝐸

(1)

are the total energies of InX (X= Cl, Br, I)

monolayer, the total energy of the bulk after exfoliation, and the total energy of the bulk before exfoliation, respectively. Here, a 3L InX (X= Cl, Br, I) slab is used as a model of the bulk structure. As depicted in Figure 2a, our calculated cleavage



energy of InX (X= Cl, Br, I) monolayers are generally about 0.1 J m-2, which is even much smaller than those of ~ 0.37 J m-2 in graphite.31 To confirm the calculated cleavage energy, we also used the methods proposed by Jung et al.32, and found that the cleavage energy of InX (X= Cl, Br, I) monolayers are 0.08 J m-2, 0.12 J m-2 and 0.15 J m-2, respectively, which is consistent with our results. Thus, our results indicate that InX (X= Cl, Br, I) monolayers can be exfoliated from the bulk structures experimentally. To further verify the stability of 2D InX (X= Cl, Br, I), the phonon spectrum were investigated. As shown in Figure 2c, all the calculated phonon spectrum demonstrated that such monolayers are dynamic stable.

Figure 1. Geometric structures of InX (X = Cl, Br, I) (a) bulk and (b) monolayer. The green


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balls represent the indium atoms, the brown balls represent the group Ⅶ atoms (Cl, Br, I). (c) The calculated band structures for InCl, InBr and InI from the left to right sides.

For freestanding InX (X= Cl, Br, I) monolayers, all the calculated band dispersions show quasi-direct semiconducting characters. The calculated band gaps of InX (X= Cl, Br, I) monolayers are 2.59, 2.30, and 2.08 eV, respectively, which are much larger than those in bulk structures. Such effects are not surprised, which are caused by the quantum confinement effect as observed in many other similar systems.

Figure 2. (a) Cleavage energy, (b) electronic structures and (c) Harmonic phonon analysis of InX (X = Cl, Br, I) monolayers.

Previously, the band-gap modulation under an external electric field has been explored in many other one-dimensional or multilayers systems1-7,

20.

As we

know, such effect comes from the shift of energy level under an effective electric-potential difference, which is produced by a large vertical distances.



However, for a single monolayer of InX systems, the vertical distance is smaller than 5 Å. Thus, a large reduction of band gap in such monolayers is not expected. Interestingly, by applying an external electric field on such InX (X= Cl, Br, I) monolayers, the band gaps are sharply reduced as shown in Figure 3. The band-gap reductions under an electric field of 0.5 V/Å found for InCl, InBr, and InI monolayers are 1.51, 1.50, and 1.38 eV, respectively. Furthermore, under the external electric field of 0.5 V/Å, the estimated effective factors are 0.90, 0.88, and 0.78, respectively. It should be noted that in previous researches, such as graphene nanoribbons, the effective factor is smaller than 0.2. Thus, it is quite interesting why the effective factors in InX (X= Cl, Br, I) monolayers are so large.

Figure 3. (a) Geometric structures of InX monolayers under external electric field. (b) The calculated energy gaps of InX monolayers as a function of external electric field.

To explore the mechanism response for the band-gap reduction under the external electric fields, we plotted the band dispersion under external electric field in figure 4a. For pristine InX monolayers, the valence band maximum (VBM) and the conductive band minimum (CBM) have several subbands which are degenerated along the X-S-Y symmetry points. When the external electric field is


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applied, the degenerated subbands along the X-S-Y symmetry points are broken, and valence and conductive bands move towards each other, which leads to the reduction of the band gap. Interestingly, the band splitting of degenerated subbands under external electric field is largest in InCl monolayer, and is smallest in InI monolayer.

Figure 4. (a)The energy band structures of InCl, InBr and InI monolayers. (b) Plotted partial density of states (PDOS) for InCl, InBr and InI monolayers. Each figures contain the PDOS under electric field of 0.0, 0.3 and 0.5 V/Å from the top to the bottom, and the green arrows indicate the position of conductive and valence bands. The atomic positions are presented in Figure 3.

To explore the origin of band splitting under external electric field, we plot the partial density of states (PDOS) in figure 4b. Without external electric field,



the PDOS of In1 and In2 atoms are degenerated in all InX monolayers because of the crystal symmetry. By applying the external electric field, the crystal symmetry is broken, removing the degenerate states of In1 and In2 atoms. Under external electric field, the highest occupied states of In2 atoms and the lowest unoccupied states of In1 atoms are moved toward each other, which is response for the band-gap reduction. With the increasing of electric field, the energy interval between In1 atoms and In2 atoms is almost linearly reduced.

Figure 5. Plotted partial density of states of InI monolayer. The denotation of In1, In2, I3, and I4 is shown in Figure 3.

Figure 6. Electron localization function (ELF); ELF = 1 (red) and 0 (blue) indicate accumulated and vanishing electron density, respectively.

As we know, for InX monolayer, In atoms loose the outside p electrons, and


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leaving s orbitals fully occupied. For halogen atoms, p orbitals are fully occupied because of the charge transfer, as shown in Fig5. Consequently, the main character of In-X bonding is ionic, as demonstrated by the electron localization function (ELF) images of InX (X=Cl, Br, I) in Fig6. From the ELF, we can see two localization areas: one is located around the In and the other around the halogens. On the other hand, for InX monolayers, the valence bands are contributed by the In-s orbitals and X-p orbitals, while the conductive bands are composed of In-p orbitals. Once the external electric field is applied, both the highest occupied s states and lowest unoccupied p states of In1 ion are shifted to lower energy parts, while the highest occupied s states and lowest unoccupied p states of In2 ion are shifted to higher energy parts. Also, we noticed that both In1 and In2 ions keep the original charge states, implying the weak electrostatic screening. Thus, the significant response under external electric field indicates that ionic-bonds are more sensitive than covalence bands because of the weak electrostatic screening.



Figure7. Calculated band structures for InI bilayer (a) and InI four layers (b).

Since the InX monolayers show significant stark effect, it is expected that multilayers have an insulator-metal transition under a suitable electric field. To do so, we take the InI bilayer and four layers as examples, and perform the band structures calculations. For InI bilayer, the energy gap is about 1.78 eV, as shown in Figure 7. The critical electric field to induce insulator-metal transition is about 0.3 V/Å. Furthermore, for InI four layers, the intrinsic energy gap is 1.50 eV, while only an external electric field of 0.1 V/Å leads to the insulator-metal transition. Thus, our results demonstrate that InX multi-layers can be excellent candidates for phase-transfer materials or high-performance FET. DISSCUSSIONS Our results show that the band-gap modulation in ionic systems is more significant, compared with that in covalence systems. For covalence systems, both the valence and conductive bands are contributed by the delocalized orbitals. For example, in graphene nanoribbons, covalence bonds of carbon pz orbitals form delocalized states, and dominate the states around Fermi level. As a result, when the external electric field is applied, the charge of delocalized states can spontaneously screen the external electric potential, weakening the band-gap modulation. On the other hand, for ionic systems, partial occupied atomic orbitals are fully saturated by the charge transfer, making the atomic orbitals fully occupied


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(unoccupied). In our studied InX systems, In ions loose one p electron and keep the two s electrons, forming s2p0 electronic states. While halogen atoms get one electron, and lead to p6 electronic states. Therefore, all the electrons are tightly bound by the ions, preferring the localized electronic states. Once the external electric field is applied, electrons are not allowed to freely move. Thus, the screening of electric potential is much weaker than that in covalence systems, and the band-gap modulation is unexpected large. In this sense, to develop new phase transfer materials or high-performance FET, ionic-type semiconductors would be the best candidates. Conclusion In summary, we have systematically studied the electric properties of the InX (X= Cl, Br, I) layers by using first-principles calculations. Our results showed that the InX(X= Cl, Br, I) monolayer can be easily stripped from its 3D bulk structures due to the relatively low cleavage energy. The giant band-gap modulation was observed for all InX (X= Cl, Br, I) monolayers, which is due to the ionic character of In-X bonding and the resulted weak electrostatic screening, and the estimated effective factors are 0.90, 0.88, and 0.78 for InCl, InBr, and InI monolayers, respectively. Moreover, for InI bilayer and four layers, we demonstrated that the energy gap can be easily closed by a practical electric field. Our results not only explored the existence of giant stark effect in semiconductors, but also demonstrated that ionic-bonding semiconductors have promised potential in future high-performance devices.



Supporting Information Available: The calculated band structures of InX monolayer under external electric field, and the band structures of InI bilayer. This material is available free of charge via the Internet at http://pubs.acs.org. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS: This work was supported by the NSFC (11474165, 11774173), the Outstanding Youth Fund of Nanjing Forestry University (NLJQ2015-03). We also acknowledge the support from the Shanghai Supercomputer Centre.

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Giant Band-Gap Reduction and Insulator-Metal Transition in Two

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