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J. Semicond. > 2017, Volume 38 > Issue 3 > 033001
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SPECIAL TOPIC ON 2D MATERIALS AND DEVICES

Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2

Jimin Shang, Le Huang and Zhongming Wei

+ Author Affiliations

 Corresponding author: Jimin Shang,Email:sjm@zzuli.edu.cn

DOI: 10.1088/1674-4926/38/3/033001

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Abstract: Using first-principles calculations, including Grimme D2 method for van der Waals interactions, we investigate the tuning electronic properties of bilayer zirconium disulfides (ZrS2) subjected to vertical electric field and normal compressive strain. The band gap of ZrS2 bilayer can be flexibly tuned by vertical external electric field. Due to the Stark effect, at critical electric fields about 1.4 V/Å, semiconducting-metallic transition presents. In addition, our results also demonstrated that the compressive strain has an important impact on the electronic properties of ZrS2 bilayer sheet. The widely tunable band gaps confirm possibilities for its applications in electronics and optoelectronics.

Key words: vertical electric field, normal compressive strain, electronic properties, zirconium disulfides bilayer

Two-dimensional (2D) nanomaterials, layered transition metal chalcogenide family, recently have attracted much attention in nanoelectronics and optoelectronic devices, owing to the distinctive electronic and optical properties [1-5]. Bulk ZrS2, is held together with strong covalent in-plane bonds and weak van der Waals forces between the layers, and each layer consists of three atomic layers, forming the hexagonal structure. It is similar to graphene, easily using mechanical or chemical exfoliation to form monolayer and few layer sheets [6, 7]. Recently Zeng groups founded an effective approach to fabricate monolayer ZrS2 nanosheet [8]. Thus monolayer ZrS2 based field effect transistor (FET) devices are fabricated, which have higher electric sensitivity, and provide excellent semiconducting electronic properties [9]. Particularly, focused on the optical properties, two-dimensional (2D) ZrS2 are also suitable for solar cell applications, and present outstanding properties [10]. For the practical applications in optoelectronics, tunable electronic properties of 2D transition metal disulfide (TMD) materials are especially crucial. Recently Yan Li etc. reported many properties of monolayer ZrS2, such as strain effects on the monolayer band structure [11]. External electric field provides, besides strain and doping, another general route to tune the bandgap and crystal structure of the material, thereby inducing a novel physical phenomena. Current studies have confirmed that the electronic structure of graphene and MoS2 bilayer can be tuned in a large range by the applied external electric field [12-14]. Qihang Liu et al. systematically demonstrated the effect of vertical electric field on the electronic structure of MoS2 bilayer [14]. Recently further theoretical studies have been reported, such as applying an external electric field to a rippled MoS2 monolayer [15]. Current studies have confirmed that MoS2 bilayer undergoes semiconductor-metal transition by the applied external electric field [14]. However, about the bilayer ZrS2, the properties on applying external electric field, are rarely reported up to now. Another way of tuning the electronic structure could be by application of feasible normal compressive strain in experiment. Due to relatively weaker Van der Waals interlayer interactions normal compressive strain has been achieved as shown for other bilayer materials [16, 17]. In addition, ZrS2 thin sheets are easily grown with vertically aligned layers, so the vertical pressure is easy to realize in experiments. However, regarding the bilayer ZrS2 the result on applying normal strain has not been reported. The responses of electronic properties under electric field and external strain are interesting issues for discussion in band-gap engineering. In the following, the electronic structure of bilayer ZrS2 with applying the electric field and the compressive strain normal to the bilayer are respectively discussed using first-principles calculations. The physical mechanisms of the band gap decrease are discussed, increasing the applied electric field and strain. The application of electric field and strain on few-layered ZrS2 are expected to tune its electronic transport properties in nanoelectronics and nanophotonics.

The first-principles calculations were performed within the density-functional theory (DFT) using the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof for the exchange and correlation energy [18]. Numerical calculation was implemented by the Vienna ab initio simulation package (VASP). Van der Waals interactions in bilayer sheets, which are important in determining the electronic properties with the different interlayer distance, were included in the Grimme's DFT-D2 method [19]. On applying certain compressive strain, the distances between the layers were fixed using selective dynamics in Cartesian coordinates, and the atomic positions and lattice constants under each strain were optimized by using the conjugate gradient method. A plane-wave basis set with kinetic energy cutoff of 600 eV is used. Brillouin zone (BZ) sampling with Monkhorst-Pack(MP) method of 24×24×1 k-points were chosen. The convergence for energy was chosen as 10-6 eV/atom between two steps, and the maximum Hellmann-Feynman atomic force was less than 0.01 eV/Å upon ionic relaxation. The direction of the external electric field is normal to the plane of bilayers, and in VASP, the external uniform electric field is treated with adding an artificial dipole sheet (i.e., dipole correction) in the unit cell [20]. To avoid the interaction between periodic images of slabs in the z-direction, a vacuum of 20 Å is sufficient.

3.1 Electronic properties of bilayer ZrS2

ZrS2 compounds crystallize in the simplest 1T-CdI2 polytype, as shown in Fig. 1(a), and each layer consists of a chalcogen-metal-chalcogen sandwich structure. For ZrS2 bilayer, which can be constructed by pairing two ZrS2 monolayers together, as shown in Fig. 1(b), here we only investigate the AA stacking, which is the most stable configuration and it can be easily obtained by the mechanical exfoliation of bulk ZrS2. For bulk ZrS2, our results about the optimized lattice parameter a=3.680 Å agrees with previous calculations and experiment [8, 15]. For monolayer ZrS2, the band structure is shown in Fig. 2, which is in accord with previous calculations [11]. Up to now, the band structure of ZrS2 bilayer has not been reported as far as we know. Our results are displayed in Fig. 3. The conduction band minimum (CBM) is located at M, and the valence band maximum (VBM) is located between the Γ . With PBE method the result of indirect band gap is 1.09 eV. Comparing with the band structure of the monolayer in Fig. 2, the electronic properties of the bilayer are generally similar to the monolayer ZrS2, but it is different that a distinct feature of the bilayer is the slight energy level splitting of the VBM and the CBM. Furthermore, the double degeneracy at the M point of the conduction band is apparent in ZrS2 bilayer. What is the driving force that results in slight energy level splitting in both conduction band and valence band? The atoms within the same layer are strongly bonded covalently, while the two layers interact with each other through weak Van der Waals interactions, which induced the charge redistribution in two monolayers, and leads to the energy level splitting [13].

Figure  1.  (Color online) Top and side view of geometric structures of ZrS2 bilayer.
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Figure  2.  (Color online) Band structure of ZrS2 monolayer.
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Figure  3.  (Color online) Band structure of ZrS2 bilayer.
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3.2 Electronic properties of bilayer ZrS2 with external electric field

The vertical electric field is a powerful tool to achieve tunable electric properties in band gap engineering [21, 22]. To exploit the tunable electric properties of monolayer and bilayer ZrS2 with the external electric field, we have applied electric field perpendicular to the ZrS2 layers along the +z -direction. Interestingly, the electronic properties of the bilayer are similar to that of the monolayer ZrS2 under zero electric field, but the presence of electric field will lead to difference. Our theoretical studies indicate that ZrS2 monolayer is applied with an external electric field of even up to 3.6 V/Å, its band gap is almost unchanged, which shows that the electronic properties of ZrS2 monolayer are not easy to tune by applying external electric field.

In contrast, ZrS2 bilayer is sensitive to the external electric field. With the electric field increasing, the band gap of ZrS2 bilayer can be flexibly decreased, as shown in Fig. 4. Up to 1.4 V/Å, ZrS2 bilayer undergoes a semiconducting-metallic transition. Similar to MoS2, carbon nano-tubes [23] and boron nitride (BN) sheets [24], Stark effect, result in a shift of the bands and change the band structure when applying an external electric field, especially in the conduction region. As shown in Fig. 4, the energy bands such as band A and band B located at point M, are separated from each other entirely. The stronger the electric field is, the larger the band splitting is, as shown in Fig. 4(b), thus the band gap is smaller. With the electric field increasing, at a critical electric field, semiconducting metallic transition occurs.

Figure  4.  (Color online) (a) Band gaps of ZrS2 monolayer and bilayer as a function of vertical external electric field. (b) Band structure ZrS2 bilayer with electric field 0.2V/Å. (c) Band structure ZrS2 bilayer with electric field 1.4 V/Å.
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3.3 Electronic properties of bilayer ZrS2 with vertical compressive strain

Strain provides another general route to tune the bandgap and crystal structure of the material. For ZrS2 monolayer, tuning electronic properties with applying tensile strain has been discussed, with the small tensile strain, its bandgap increases [11, 25]. On the other hand, by application of compressive strain, it has been experimentally and theoretically demonstrated that the band structure of bulk TMDs can be modified. Thus, we also studied the effect of vertical strain on the electronic properties of ZrS2 bilayer. Here we applied compressive strain on the ZrS2 bilayer along the +z -direction. Our results demonstrated that the vertical compressive strain has a significant impact on the electronic properties of ZrS2 bilayer. The band gap of ZrS2 bilayer also decreases with the increase of compressive strain as shown in Fig. 5(a). Even a 2% compressive strain in z directions, can result in a 0.20 eV gap reduction, moreover, the VBM and CBM are still respectively located at the Γ and M points. When compressive strain in z-directions increases to 15% (Fig. 5(c)), the band structure is still indirect, whereas the shape of the VBM is different from the former, and compressive strain can result in a 0.80 eV gap reduction. The reduction of the band gap as a function of applied compressive strain is caused by interlayer interaction. With the compressive strain increasing, the interlayer interaction is enhanced, which results in charge transfer from the metal to the chalcogen, and moves the VBM and the CBM closer to the Fermi level.

Figure  5.  (Color online) (a) Band gaps of ZrS2 bilayer as a function of vertical compressive strain. (b) Band structure ZrS2 bilayer with compressive strain of 1.5%. (c) Band structure ZrS2 bilayer with compressive strain of 15%.
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By means of density functional theory with van der Waals correction, the influence of vertical electric field and compressive strain on the electronic properties of bilayer ZrS2 has been systematically investigated. The band gaps of the ZrS2 bilayer decrease monotonically with increasing electric field. At critical electric fields, semiconducting metallic transition occurs. We have also observed that the vertical compressive strain has a significant impact on the electronic properties of ZrS2 bilayer. Overall, the tuning of electronic properties due to external electric field and compressive pressure would promote their potential applications in electronics and optoelectronics.



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[2]
Mak K F, Lee C, Hone J, et al. Atomically thin MoS2:a new direct-gap semiconductor. Phys Rev Lett, 2010, 105(24):136805
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[6]
Li Y, Yang S, Li J. Modulation of the electronic properties of ultrathin black phosphorus by strain and electrical field. J Phys Chem C, 2014, 118(41):23970 doi: 10.1021/jp506881v
[7]
Kumar A, Ahluwalia P K. Mechanical strain dependent electronic and dielectric properties of two-dimensional honeycomb structures of MoX2(X D S, Se, Te). Physica B, 2013, 419:66 doi: 10.1016/j.physb.2013.03.029
[8]
Zeng Z, Yin Z, Huang X, et al. Single-layer semiconducting nanosheets:high-yield preparation and device fabrication. Angewandte Chemie Int Ed, 2011, 50(47):11093 doi: 10.1002/anie.v50.47
[9]
Li L, Fang X, Zhai T, et al. Electrical transport and highperformance photoconductivity in individual ZrS2 nanobelts. Adv Maters, 2010, 22(37):4151 doi: 10.1002/adma.v22:37
[10]
Li L, Wang H, Fang X, et al. High-performance Schottky solar cells using ZrS2 nanobelt networks. Energy Environ Sci, 2011, 4(7):2586 doi: 10.1039/c1ee01286j
[11]
Li Y, Kang J, Li J. Indirect-to-direct band gap transition of the ZrS2 monolayer by strain:first-principles calculations. RSC Adv, 2014, 4(15):7396 doi: 10.1039/c3ra46090h
[12]
Yu E K, Stewart D A, Tiwari S. Ab initio study of polarizability and induced charge densities in multilayer graphene films. Phys Rev B, 2008, 77(19):195406 doi: 10.1103/PhysRevB.77.195406
[13]
McCann E. Asymmetry gap in the electronic band structure of bilayer graphene. Phys Rev B, 2006, 74(16):161403 doi: 10.1103/PhysRevB.74.161403
[14]
Liu Q, Li L, Li Y, et al. Tuning electronic structure of bilayer MoS2 by vertical electric field:a first-principles investigation. J Phys Chem C, 2012, 116(40):21556 doi: 10.1021/jp307124d
[15]
Qi J, Li X, Qian X, et al. Bandgap engineering of rippled MoS2 monolayer under external electric field. Appl Phys Lett, 2013, 102(17):173112 doi: 10.1063/1.4803803
[16]
Manjanath A, Samanta A, Pandey T, et al. Semiconductor to metal transition in bilayer phosphorene under normal compressive strain. Nanotechnology, 2015, 26(7):075701 doi: 10.1088/0957-4484/26/7/075701
[17]
Huang L, Li Y, Wei Z, et al. Strain induced piezoelectric effect in black phosphorus and MoS2 van der Waals heterostructure. Sci Rep, 2015, 5:16448 doi: 10.1038/srep16448
[18]
Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater, 1996, 6(1):15 doi: 10.1016/0927-0256(96)00008-0
[19]
Grimme S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem, 2006, 27(15):1787 doi: 10.1002/(ISSN)1096-987X
[20]
Zywietz T, Neugebauer J, Scheffler M. Adatom diffusion at GaN (0001) and (0001) surfaces. Appl Phys Lett, 1998, 73(4):487 doi: 10.1063/1.121909
[21]
Ramasubramaniam A, Naveh D, Towe E. Tunable band gaps in bilayer transition-metal dichalcogenides. Phys Rev B, 2011, 84(20):205325 doi: 10.1103/PhysRevB.84.205325
[22]
Wu S, Ross J S, Liu G B, et al. Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2. Nat Phys, 2013, 9(3):149 doi: 10.1038/nphys2524
[23]
Jiang H. Structural and electronic properties of ZrX2 and HfX2(X D S and Se) from first principles calculations. J Chem Phys, 2011, 134(20):204705 doi: 10.1063/1.3594205
[24]
Greenaway D L, Nitsche R. Preparation and optical properties of group IV-VI2 chalcogenides having the CdI2 structure. J Phys Chem Solids, 1965, 26(9):1445 doi: 10.1016/0022-3697(65)90043-0
[25]
Guo H, Lu N, Dai J, et al. Phosphorene nanoribbons, phosphorus nanotubes, and van der Waals multilayers. J Phys Chem C, 2014, 118(25):14051 doi: 10.1021/jp505257g
Fig. 1.  (Color online) Top and side view of geometric structures of ZrS2 bilayer.

DownLoad: Full-Size Img PowerPoint
Fig. 2.  (Color online) Band structure of ZrS2 monolayer.

DownLoad: Full-Size Img PowerPoint
Fig. 3.  (Color online) Band structure of ZrS2 bilayer.

DownLoad: Full-Size Img PowerPoint
Fig. 4.  (Color online) (a) Band gaps of ZrS2 monolayer and bilayer as a function of vertical external electric field. (b) Band structure ZrS2 bilayer with electric field 0.2V/Å. (c) Band structure ZrS2 bilayer with electric field 1.4 V/Å.

DownLoad: Full-Size Img PowerPoint
Fig. 5.  (Color online) (a) Band gaps of ZrS2 bilayer as a function of vertical compressive strain. (b) Band structure ZrS2 bilayer with compressive strain of 1.5%. (c) Band structure ZrS2 bilayer with compressive strain of 15%.

DownLoad: Full-Size Img PowerPoint
[1]
Li Y, Tongay S, Yue Q, et al. Metal to semiconductor transition in metallic transition metal dichalcogenides. J Appl Phys, 2013, 114(17):174307 doi: 10.1063/1.4829464
[2]
Mak K F, Lee C, Hone J, et al. Atomically thin MoS2:a new direct-gap semiconductor. Phys Rev Lett, 2010, 105(24):136805
[3]
Splendiani A, Sun L, Zhang Y, et al. Emerging photoluminescence in monolayer MoS2. Nano Lett, 2010, 10(4):1271 doi: 10.1021/nl903868w
[4]
Wang Q H, Kalantar-Zadeh K, Kis A, et al. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nanotechnol, 2012, 7(11):699 doi: 10.1038/nnano.2012.193
[5]
Kuc A, Zibouche N, Heine T. Influence of quantum confinement on the electronic structure of the transition metal sulfide TS2. Phys Rev B, 2011, 83(24):245213 doi: 10.1103/PhysRevB.83.245213
[6]
Li Y, Yang S, Li J. Modulation of the electronic properties of ultrathin black phosphorus by strain and electrical field. J Phys Chem C, 2014, 118(41):23970 doi: 10.1021/jp506881v
[7]
Kumar A, Ahluwalia P K. Mechanical strain dependent electronic and dielectric properties of two-dimensional honeycomb structures of MoX2(X D S, Se, Te). Physica B, 2013, 419:66 doi: 10.1016/j.physb.2013.03.029
[8]
Zeng Z, Yin Z, Huang X, et al. Single-layer semiconducting nanosheets:high-yield preparation and device fabrication. Angewandte Chemie Int Ed, 2011, 50(47):11093 doi: 10.1002/anie.v50.47
[9]
Li L, Fang X, Zhai T, et al. Electrical transport and highperformance photoconductivity in individual ZrS2 nanobelts. Adv Maters, 2010, 22(37):4151 doi: 10.1002/adma.v22:37
[10]
Li L, Wang H, Fang X, et al. High-performance Schottky solar cells using ZrS2 nanobelt networks. Energy Environ Sci, 2011, 4(7):2586 doi: 10.1039/c1ee01286j
[11]
Li Y, Kang J, Li J. Indirect-to-direct band gap transition of the ZrS2 monolayer by strain:first-principles calculations. RSC Adv, 2014, 4(15):7396 doi: 10.1039/c3ra46090h
[12]
Yu E K, Stewart D A, Tiwari S. Ab initio study of polarizability and induced charge densities in multilayer graphene films. Phys Rev B, 2008, 77(19):195406 doi: 10.1103/PhysRevB.77.195406
[13]
McCann E. Asymmetry gap in the electronic band structure of bilayer graphene. Phys Rev B, 2006, 74(16):161403 doi: 10.1103/PhysRevB.74.161403
[14]
Liu Q, Li L, Li Y, et al. Tuning electronic structure of bilayer MoS2 by vertical electric field:a first-principles investigation. J Phys Chem C, 2012, 116(40):21556 doi: 10.1021/jp307124d
[15]
Qi J, Li X, Qian X, et al. Bandgap engineering of rippled MoS2 monolayer under external electric field. Appl Phys Lett, 2013, 102(17):173112 doi: 10.1063/1.4803803
[16]
Manjanath A, Samanta A, Pandey T, et al. Semiconductor to metal transition in bilayer phosphorene under normal compressive strain. Nanotechnology, 2015, 26(7):075701 doi: 10.1088/0957-4484/26/7/075701
[17]
Huang L, Li Y, Wei Z, et al. Strain induced piezoelectric effect in black phosphorus and MoS2 van der Waals heterostructure. Sci Rep, 2015, 5:16448 doi: 10.1038/srep16448
[18]
Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater, 1996, 6(1):15 doi: 10.1016/0927-0256(96)00008-0
[19]
Grimme S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem, 2006, 27(15):1787 doi: 10.1002/(ISSN)1096-987X
[20]
Zywietz T, Neugebauer J, Scheffler M. Adatom diffusion at GaN (0001) and (0001) surfaces. Appl Phys Lett, 1998, 73(4):487 doi: 10.1063/1.121909
[21]
Ramasubramaniam A, Naveh D, Towe E. Tunable band gaps in bilayer transition-metal dichalcogenides. Phys Rev B, 2011, 84(20):205325 doi: 10.1103/PhysRevB.84.205325
[22]
Wu S, Ross J S, Liu G B, et al. Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2. Nat Phys, 2013, 9(3):149 doi: 10.1038/nphys2524
[23]
Jiang H. Structural and electronic properties of ZrX2 and HfX2(X D S and Se) from first principles calculations. J Chem Phys, 2011, 134(20):204705 doi: 10.1063/1.3594205
[24]
Greenaway D L, Nitsche R. Preparation and optical properties of group IV-VI2 chalcogenides having the CdI2 structure. J Phys Chem Solids, 1965, 26(9):1445 doi: 10.1016/0022-3697(65)90043-0
[25]
Guo H, Lu N, Dai J, et al. Phosphorene nanoribbons, phosphorus nanotubes, and van der Waals multilayers. J Phys Chem C, 2014, 118(25):14051 doi: 10.1021/jp505257g
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    Jimin Shang, Le Huang, Zhongming Wei. Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2[J]. Journal of Semiconductors, 2017, 38(3): 033001. doi: 10.1088/1674-4926/38/3/033001
    J M Shang, L Huang, Z M Wei. Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2[J]. J. Semicond., 2017, 38(3): 033001. doi: 10.1088/1674-4926/38/3/033001.
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    Received: 15 August 2016 Revised: 24 November 2016 Online: Published: 01 March 2017

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      Article Navigation >  Journal of Semiconductors  > 2017  >  38(3): 033001
      Jimin Shang, Le Huang, Zhongming Wei. Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2[J]. Journal of Semiconductors, 2017, 38(3): 033001. doi: 10.1088/1674-4926/38/3/033001 ****J M Shang, L Huang, Z M Wei. Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2[J]. J. Semicond., 2017, 38(3): 033001. doi: 10.1088/1674-4926/38/3/033001.
      Citation:
      Jimin Shang, Le Huang, Zhongming Wei. Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2[J]. Journal of Semiconductors, 2017, 38(3): 033001. doi: 10.1088/1674-4926/38/3/033001 ****
      J M Shang, L Huang, Z M Wei. Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2[J]. J. Semicond., 2017, 38(3): 033001. doi: 10.1088/1674-4926/38/3/033001.
      shu

      Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2

      DOI: 10.1088/1674-4926/38/3/033001

      • Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

      Funds:

      Project support by the CAS/SAFEA International Partnership Program for Creative Research Teams and the Basic and Frontier Technology Research of Henan No.142300410244

      Project support by the CAS/SAFEA International Partnership Program for Creative Research Teams and the Basic and Frontier Technology Research of Henan (No.142300410244)

      More Information
      • Corresponding author: Jimin Shang,Email:sjm@zzuli.edu.cn
      • Received Date: 2016-08-15
      • Revised Date: 2016-11-24
      • Published Date: 2017-03-01

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