Effect of an external electric field on the electronic properties of SnS₂/PbI₂ van der Waals heterostructures

Abstract

The future development of optoelectronic devices will require an advanced control technology in electronic properties, for example by an external electric field (E_field). Here we demonstrate an approach that the heterostructure based on van der Waals (vdW) heterobilayer built by monolayer SnS₂ and PbI₂ has a well-controlled electronic properties with E_field. A type-II staggered-gap band alignment is achieved from the SnS₂/PbI₂ vdW heterostructure with which SnS₂ dominated the lowest energy holes as well as the lowest energy electrons are separated in PbI₂. The charge redistribution with an E_field is mainly on the surface of SnS₂ layer and PbI₂ and the numbers of polarized electrons on the monolayers display a linear evaluation with external E_field. The band structure under different E_field experiences not only a transition from semiconductor to metal but also conversions between type-I straddling-band alignment and type-II staggered-gap, which results in different spatial distribution of the lowest energy electrons and holes. Moreover, when the E_field is between −0.06 V Å⁻¹ and −0.34 V Å⁻¹, the material manifests a varied direct bandgap which is more favor to optoelectronics and solar cell. Consequently, this vdW heterobilayer with well-controlled manner shows expectation for huge potential in optics and electronics.

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1. Introduction

Ever since the successful manufacture of isolated graphene was reported,¹ two dimensional (2D) materials have become the subject of extensive research because of their superior optical and electronic properties. Hence, a broad family of 2D materials like graphene, such as BN,² transition metal dichalcogenides^3–5 and topological insulators^6–8 etc., has been widely explored to solve that pristine graphene has a zero bandgap. Among them, recently, the SnS₂ 2D films^9,10 have been poured unordinary attentions due to environmentally friendly and earth-abundant. For instance, it was reported that SnS₂ can be used as advance materials for photocatalytic,¹¹ field effect transistors¹² and anode in lithium batteries.¹³ Meanwhile, previous studies on the lamellar semiconductor material of PbI₂ have reported that the freestanding single crystals PbI₂ could be prepared by a facile way.¹⁴ Furthermore, PbI₂ has been demonstrated to be an attractive candidate of thin film transistors and can play the role of a precursor for the organ PbI₂ perovskites employed in highly efficient hybrid solar cells.^15–17 Accordingly, SnS₂ and PbI₂ have promising potential applications in optics and electronics.

For the sake of exploring materials in electronics, optoelectronics and photovoltaics devices, 2D materials can be used as building blocks restacked layer-by-layer in precisely chosen sequences yielding composites with unusual properties.^18,19 A brand new discipline is provided to tailor electronic and optical properties of 2D materials into new physics and device applications owing to their unique crystal properties. For instance, an enterprising and insightful approach has been recently exhibited that an atomically thin p–n diode can be manufactured by a vertically stacked heterobilayer between n-type MoS₂ and p-type WSe₂ slices,^20,21 which will not lead to doping problems.²² Moreover, properties of vdW heterostructure would be more excellent than building blocks such as the SnS₂/MoS₂ vdW heterostructure exhibit an obvious photovoltaic effect and possess high mobility (27.6 cm² V⁻¹ s⁻¹), high on/off ratio (>10⁶) and high photoresponsivity (1.36 A W⁻¹), which is more outstanding than SnS₂ and MoS₂.²³ Thus, the vdW heterostructure with novel electronic and optoelectronic properties will reveal favorable properties and novel phenomena.

It is crucial to modify electronic properties of 2D materials for application in semiconductor devices and the two more effective ways are straining^24,25 and E_field.^26,27 In this article, we employed an external E_field to tunable the band structures because of reversibility and easy achievement. A quintessential example should be cited that the bandgap of bilayer graphene can be efficiently switched on via applications of electric field because the inversion symmetry of the structure was destroyed.^28,29 The fundamental bandgap of MoS₂, MoSe₂, MoTe₂ and WS₂ bilayer structures could be continuously modified with applied electric fields, eventually rendering them metallic.^30–32 Accordingly, utilization of E_field would lead to the realization of electronic properties engineering of the materials.

The bandgap of homobilayer SnS₂ could be continuously decreased with the electric field as well as different stacks³³ and a robust indirect band structure accompanied with the strength of increasing E_field. However, it is well known that the electron–hole recombination lifetime of the indirect bandgap semiconductor is longer than direct bandgap leading to lower the luminous efficiency, which is inappropriate for optoelectronic devices. Despite lots of researchers force on the modulation electronic properties of SnS₂ such as doping and strain,^10,12 there is no literature on SnS₂ with a direct bandgap.

In this work, we investigated the vdW heterostructure restacked by SnS₂ monolayer and PbI₂ monolayer to engineer an alternative type of advance optoelectronic material to realize any practical application of 2D vdW p–n junctions. The electronic properties have been systematically studied with external E_field by theoretical simulation and a well-behaved was found. The features make SnS₂/PbI₂ vdW heterobilayer a promising material for the advantage optoelectronic devices.

2. Theoretical methods

Our calculations were performed based on the density functional theory (DFT) in conjunction with the projector-augmented wave (PAW) potentials³⁴ as implemented in the Vienna Ab initio Simulation Package (VASP).^35,36 The exchange–correlation potentials was described through the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) formalism.³⁷ The valence electron configurations for Sn, S, Pb and I were 4d¹⁰5s²5p², 3s²3p⁴, 5d¹⁰6s²6p² and 5s²5p⁵, respectively. The heterobilayer was built by cells of SnS₂ and 2 × 2 cells of PbI₂. That a plane wave basis set with a cutoff energy of 480 eV and a 5 × 5 × 1 k-points grids determined by a fine grid of gamma-centered Monkhorst–Pack method³⁸ in the Brillouin zone was found to give good converged results. The atomic structures were relaxed using conjugate gradient algorithm as implemented in the VASP code until the forces on all unconstrained atoms were smaller than 0.01 eV Å⁻¹. Moreover, a more precise method for the on-site Coulomb repulsion of Sn 4d and Pb 5d was considered in all calculations for the sake of more accurate bandgap. A PBE+U approach³⁹ was employed to treat exchange–correlation energy and the choice of U = 9 eV for Sn as well as 8.5 eV for Pb can reproduce the experimental bandgap of SnS₂ and PbI₂, respectively. Additionally, spin-orbital-coupling⁴⁰ was expected to be significant influence on the heavy atoms of lead (Pb), therefore it was considered in all calculation. A vacuum layer of 20 Å along z direction was constructed to eliminate the interaction with spurious replica images. The zero damping DFT-D3 method of Grimme⁴¹ was used to account for long range vdW interaction between monolayer SnS₂ and PbI₂. All of structural figures and charge density drawings were produced by VESTA package.⁴²

3. Results and discussion

The schematic illustration of monolayer SnS₂ and PbI₂ is displayed in Fig. 1. Primitive cells are plotted by a black line and a brief look for the vector of lattices is marked. After the total energy optimization, the lattice constants of monolayer SnS₂ and PbI₂ are respectively collected as 3.61 Å and 4.67 Å as exhibited in Table 1, that the agreements with previous studies are preeminent.^8,22,32 The properties of monolayer SnS₂ and PbI₂ are intensely sensitive to in-plane strains^43,44 so that the impact of strain on electronic structure should be reduced. To minimize the lattice mismatch between the stacking blocks, the supercell of this heterostructure is built by of SnS₂ cells and 2 × 2 of PbI₂ cells, which the maximum mismatch for both SnS₂ and PbI₂ lattices is less than 2.3%.

Fig. 1 Schematic of the monolayers and the SnS₂/PbI₂ vdW heterobilayer. Top view of (a) SnS₂ and (b) PbI₂ monolayer. The top (c) and side view (d) of the heterobilayer. Silvery, yellow, dark grey and purple spheres represent Sn, S, Pb and I atoms, respectively.

Table 1 The lattice constants of SnS₂ monolayer, PbI₂ monolayer and the SnS₂/PbI₂ vdW heterostructure, respectively

		a (Å)	d (Å)	h (Å)
SnS2 monolayer		3.61	2.98
PbI2 monolayer		4.67	3.72
The heterostructure	SnS2 monolayer	9.45	3.03	3.49
	PbI2 monolayer		3.68

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The top and across views of the SnS₂/PbI₂ vdW heterostructure is presented in Fig. 1(c) and (d). The thicknesses of monolayers and the distance between SnS₂ and PbI₂ single-layer are respectively marked with d and h as displayed in Fig. 1(d). The optimized structural parameters and the binding energies are given in Table 1. After fully relaxed, the interlayer distance (h = 3.49 Å) is far greater than the sum of the covalent radii of I and S atom, indicating that the two building blocks are beyond the bonding range. To evaluate the stability, the binding energy (ΔE_b) of SnS₂/PbI₂ vdW heterobilayer was calculated and defined by,

ΔE_b = (E_SnS2/PbI2 − E_SnS2 − E_PbI2)/n, (1)

where E_SnS2/PbI2, E_SnS2 and E_PbI2 represent total energy of the SnS₂/PbI₂ vdW heterostructure, SnS₂ monolayer and PbI₂ monolayer, respectively. Meanwhile, [SnS₂] unit cells in the superlattice are marked as n which equals to seven in this article. By this definition, a negative ΔE_b is indicative of that the heterostructure is stable.

The binding energy of SnS₂ and PbI₂ vdW heterobilayer is −0.124 eV per SnS₂ unit, which is indicative of a rather weak but stable interaction between the layers. This could be just more evidence for that the interaction between SnS₂ monolayer and PbI₂ monolayer is mainly forced through van der Waals interactions because ΔE_b has the same order of magnitude as the other vdW substances, for example, graphite (ΔE_b = −0.10 eV per C atom),⁴⁵ bilayer SnS₂ (ΔE_b = −0.05 eV per SnS₂ unit),³³ the MoS₂/PbI₂ heterostructure (ΔE_b = −0.234 eV per MoS₂ unit)⁴⁶ and black phosphorus/MoS₂ heterobilayer (ΔE_b = −0.108 eV per MoS₂ unit).⁴⁷

We calculate the band structures of monolayer SnS₂ (Fig. 2(a)) and PbI₂ (Fig. 2(b)) as well as the SnS₂ and PbI₂ vdW heterostructure (Fig. 2(c)) to obtain the electronic properties based on PBE+U approach. For SnS₂ monolayer, the fundamental band structure is an indirect bandgap of about 2.22 eV that the valance band maximum (VBM) is extremely close to Γ point and the conduction band minimum (CBM) lies at M which is close to the reported values.^12,48 Additionally, the smallest gap of PbI₂ monolayer appears between the CBM at Γ and the VBM which medially lies between K and Γ that the agreements with previous studies are preeminent.⁴³

Fig. 2 Electronic band structures of (a) PbI₂, (b) SnS₂. (c) The projected band structure as well as schematic of band alignment of SnS₂/PbI₂ vdW heterostructure (blue and red lines respectively represent for SnS₂ and PbI₂ layer). The Fermi level is set to zero and marked by horizontal blue dotted line. The vacuum level is taken as a reference marked by green horizontal dash.

In Fig. 2(c), we present the projected band structure of the SnS₂ and PbI₂ in the vdW heterobilayer that the blue lines represent of SnS₂ monolayer and the red lines are for PbI₂, respectively. As can be seen in Fig. 2(c), the SnS₂ monolayer and PbI₂ monolayer compose a type-II staggered-gap band alignment that the CBM is contributed by SnS₂ whereas the VBM by PbI₂ with a bandgap of about 1.98 eV. In consequence, the Fermi level shifts to the CBM of SnS₂ and VBM of PbI₂ after they compose the heterobilayer. It can be looking forward that the photoelectric property will be improved distinctively because the lowest energy electron–hole pairs can separate in real space. Compared with the band structure, band alignment of heterostructure are even more important in material and device design. Meanwhile, the work function (Φ = E_Van − E_F, where the E_Van is the vacuum level and the E_F is the Fermi level, respectively) and band alignment is shown in Fig. 2(d). It is indicated that a type-II band alignment of vdW heterostructure is formed at the SnS₂/PbI₂ interface which will spontaneously separate the free electrons and holes, enabling the high efficiency optoelectronics and solar energy conversion.

To shed more lights on the nature of the charge transfer between the SnS₂ and PbI₂ layer, the averaged difference electron density of the heterostructure along the z direction was calculated by the formula

where the , and are the charge density at the (x, y, z) point in the SnS₂/PbI₂ bilayer, SnS₂ and PbI₂ monolayer, respectively. Accordingly, a positive value means electron accumulation and negative for depletion. The result is exhibited in Fig. 3(a), that the vertical blue short dash line means the intermediate position for the interface of the building blocks as well as the positions of Sn, S, Pb and I atomic layers are marked as purple, dark grey, yellow and silvery and short dot lines, respectively. As a result of the interlayer coupling effect, there is an obvious charge accumulation region as the SnS₂/PbI₂ heterointerface. Moreover, there is a small amount of electrons (about 0.453 × 10⁻³|e|) transferring from PbI₂ to SnS₂ layer, further indicating a weak interlayer coupling between SnS₂ layer and PbI₂ layer. Furthermore, a built-in electrical field formed intrinsic spontaneous of electric polarization is expected and directed from PbI₂ to SnS₂.

Fig. 3 (a) The averaged difference electron density of SnS₂/PbI₂ heterostructure along z direction. (b) and (c) The integrated charge density difference of the heterobilayer under different external E_field. (d) The transferred electrons as a function of E_field. The positive values of electrons in (d) indicate a transferred direction from SnS₂ to PbI₂ layer.

It is crucial to modify electronic properties of 2D materials for application in semiconductor devices so that an external E_field perpendicular to the heterobilayer is employed. The positive direction of E_field is set from PbI₂ layer to SnS₂ layer. To evaluate the influences of E_field modulating on the electronic properties of the heterostructure, the integrated charge density difference with E_field along z direction was employed and determined as,

where and are the charge density at (x, y, z) point of SnS₂/PbI₂ heterostructure with and without E_field. The results are displayed in Fig. 3(b) and (c). It is obvious that the charge redistribution is mainly on the surface of SnS₂ and PbI₂ layers. The positive charges (holes) tend to transfer from SnS₂ layer to PbI₂ layer and negative charges (electrons) transfer from PbI₂ layer to SnS₂ layer in the case of a negative E_field as well as positive E_field lead to the opposite direction of charge and hole transfers. Additionally, the amount of transferring electrons depends on the strength of the applied E_field.

To shed more lights on the charge redistribution with E_field, the numbers of polarized electrons on the building blocks were obtained through integrating the charge density from the vacuum layer to the intermediate position of the interface of the monolayers as exhibited in Fig. 3(d). The positive value means the electron transfers from SnS₂ layer to PbI₂ layer. The numbers of polarized electrons on the building blocks display a linear evaluation with external E_field and a transitional on the direction depends on the direction of E_field is found, which is identical with above analyses. The accumulation of electrons (holes) will lead to the Fermi level down (up)-shifted of SnS₂ and PbI₂ monolayer which thereby bring about modulation of the band structure. More charge transfer between SnS₂ and PbI₂ layer heralds a stronger interlayer interaction, indicating the shifts of band edges.

This could be graphically explained in Fig. 4(a), which manifests the evolution of the bandgap of SnS₂/PbI₂ heterostructure as a function of applied E_field. The bandgap is continuously tuned under the E_field, eventually achieving a mutation from semiconductor to metal at critical E_field. The bandgap varies linearly with E_field indicating a giant Stark effect.⁴⁹ It is almost lineally reduced with the strength of E_field reducing to zero bandgap at the E_field of about 0.28 V Å⁻¹ when a forward voltage is applied. For a negative E_field, the bandgap firstly increases reaching up to 2.19 eV which appears at an E_field of about −0.03 V Å⁻¹. The encouragement of bandgap is due to the presence of intrinsic spontaneous of electric polarization which is opposite to the E_field and has a superimposing effect on it. Further increases in strength of negative E_field (|E_field| > 0.06 V Å⁻¹) lead to linearly decreases in bandgap and the heterobilayer turns metallic at about −0.34 V Å⁻¹.

Fig. 4 (a) Bandgap variation with applied E_field of the SnS₂/PbI₂ vdW heterostructure. (b) Evolution of the band edges in SnS₂/PbI₂ heterostructure as a function of the E_field. CBM_SnS2(PbI2) and VBM_SnS2(PbI2) are the CBM and VBM of SnS₂(PbI₂) in the vdW heterobilayer.

To gain further insight, band edges dominated by SnS₂ and PbI₂ under various E_field are calculated and displayed in Fig. 4(b). The CBM and VBM of SnS₂(PbI₂) of the vdW heterobilayer are denoted by CBM_SnS2(PbI2) and VBM_SnS2(PbI2), respectively. Both the CBM and VBM of SnS₂ decrease linearly with E_field while the CBM and VBM of PbI₂ manifest a linear increase. The E_field exerts litter influence on the respective bandgaps of SnS₂ and PbI₂. The bandgap of SnS₂/PbI₂ heterostructure gives the same variation trend with Fig. 4(a). Additionally, the band alignment conversion from type-II to type-I heterostructure separated by the E_field about −0.03 V Å⁻¹ and then from type-I to type-II by about −0.06 V Å⁻¹, resulting in different spatial distribution of the lowest energy electrons and holes.

Energy dispersion with and without E_field is displayed in Fig. 5(a)–(d), respectively. With an E_field of −0.15 V Å⁻¹, the heterobilayer manifests a direct bandgap that both the CBM and VBM are located at Γ point. The direct bandgap semiconductor has a less electron–hole recombination lifetime with a high luminous efficiency which is overwhelmingly suitable for optoelectronic devices. The location of CBM changes from Γ to M point in the Brillouin zone but the VBM is still at Γ point leading to an indirect bandgap in the case of E_field = −0.05 V Å⁻¹ as shown in Fig. 5(b). When an E_field of 0.15 V Å⁻¹ is added to the vdW heterostructure, the band structure manifests an indirect bandgap that the CBM located at M point and VBM between K to Γ point (Fig. 5(d)).

Fig. 5 Band structures and partial charge densities plot for the CBM and VBM of the SnS₂/PbI₂ vdW heterostructure with and without E_field. (a) E_field = −0.15 V Å⁻¹, (b) E_field = −0.05 V Å⁻¹, (c) E_field = 0 V Å⁻¹, and (d) E_field = 0.15 V Å⁻¹. All isosurfaces of this text are set to 0.004 e Å⁻³.

The partial charge densities of the heterostructure from CBM and VBM with different E_field are calculated and summarized in Fig. 5. When the SnS₂/PbI₂ vdW heterobilayer subjected to a negative E_field of −0.15 V Å⁻¹, it is clearly shown that the partial charge density from CBM is dominated by Pb atoms and the VBM comes mainly from the SnS₂ layer, as shown in Fig. 5(a). That is to say, the staggered-gap band alignment be suggestive of a type-II heterojunction. Both the CBM and VBM of the heterobilayer, when the heterobilayer suffered by an E_field of −0.05 V Å⁻¹, are all straddled by SnS₂ layer (Fig. 5(b)) indicating a type-I heterojunction. When the heterobilayer suffered by the E_field of 0 V Å⁻¹ or 0.15 V Å⁻¹, the partial charge density from CBM is dominated by Sn atoms and the VBM by I atomical layer displayed in Fig. 5(c) and (d), respectively. Thus, a type-II staggered-gap band alignment is obtained with an alternation of CBM and VBM between the monolayer SnS₂ and PbI₂. Briefly, the band structures can be effectively modulated by an external electric field.

Similar evidence also comes from the band alignment of SnS₂/PbI₂ heterostructure under various E_field, as seen in Fig. 6. The E_f-SnS2(PbI2) indicate the quasi-Fermi level of SnS₂(PbI₂) in the vdW heterobilayer. V_D denote the conduction band offset in the SnS₂/PbI₂ heterostructure without an E_field as well as V = E_field × d is the external electric potential, which leads to the divergence of the quasi-Fermi levels. The interlayer distance is marked with d, which is a constant in this case. When the SnS₂/PbI₂ vdW heterostructure subjected to a negative E_field, the bandgap varies with E_field in the following function:

E_g = E_g(SnS2) − e(V_D − V) = E_g(SnS2) − eV_D + eE_field × d. (4)

Fig. 6 Band alignments of the SnS₂/PbI₂ vdW heterobilayer under different E_field.

The maximum bandgap is obtained when the E_field reaches to −0.03V Å⁻¹. Even the electric field increasing to −0.06V Å⁻¹, both the CBM and VBM of the heterobilayer are all straddled by SnS₂ layer. So, bandgap can be obtained as,

E_g = E_g(SnS2) ≈ 2.19 eV.

Under circumstances of E_field greater than 0.06 V Å⁻¹ along the negative direction, the bandgap varies as the function:

E_g = E_g(SnS2) − e(E_field − 0.06)d.

The linear evaluations of bandgap with the strength of E_field are obtained as the E_g(SnS2) and e is constant. Meanwhile, the varied relationship between bandgap and E_field shares the same evidence of the giant Stark effect.

4. Conclusions

In summary, a vdW heterostructure of SnS₂ and PbI₂ has been theoretically simulated and the heterobilayer has a well-behaved electronic property under an external E_field. A type-II staggered-gap band alignment is constituted which the spatial separation of the lowest energy electron–hole pairs can be actualized. When suffered under an external E_field, the charge redistribution is mainly on the surface of SnS₂ and PbI₂ layers and the numbers of polarized electrons on the building blocks display a linear evaluation with external E_field. Meanwhile, the transitional direction depends on the direction of E_field. The external E_field not only influences the band structure which changes from semiconductor to metal but also forces on band alignment which experiences a conversion between type-I straddling-band alignment type-II broken-gap, leading to a different spatial distribution of the lowest energy electrons and holes. A direct bandgap of the heterobilayer is found among −0.06 V Å⁻¹ and −0.34 V Å⁻¹. This work could bring forward a new perspective on advantage optoelectronics devices with a well-E_field-controlled manner by using SnS₂/PbI₂ vdW heterostructure.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant no. 61674053, 11504092 and 11504334), the Natural Science Foundation of Henan Province (Grant No. 162300410325) and by the High Performance Computing Center of Henan Normal University.

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