1 Introduction

Layered metal dichalcogenide materials have been topical recently owing to the tunability of their optical band gap. The optical band tunability property of metal dichalcogenides has been an explorative main quantity in the optoelectronics and energy harvesting space [1,2,3]. The formation of bi- and sandwiched layer configurations of metal dichalcogenides has offered the opportunity to harvest the intercalation effect between interlayer bond interactions [4, 5]. The introduction of other two-dimensional (2D) nanomaterials, such as graphene, as an ad hoc layer to form a bi- or sandwiched heterostructure has shown potential for improved material performance. Graphene is a 2D dimensionally atomic thin nanomaterial, which has been harvested for its outstanding properties, such as high electrical conductivity and optical properties [6]. For instance, the inclusion of graphene into SnS2 to form SnS2/graphene heterostructure has been established for improved transport properties for rechargeable battery storage [7, 8] and photocatalysis [9] applications. Furthermore, the enhanced electrochemical transport properties of sandwiched layered SnS2/graphene-based heterostructure have been suggested as a potential material for future photodetector and solar cell applications [1, 10] and are worth exploring.

Optimization of the interlayer separation distance in bi- and sandwich layered heterostructures offers a route to tuning the intercalation effect and electronic transport properties of layered heterostructures. The architecting of the interlayer spacing of dichalcogenides has been suggested to create layer decoupling [11]. Layer decoupling in metal dichalcogenides enables ease of band alignment and hybridization, which is crucial for electronic structural manipulation [12]. Hence, layer decoupling resulting from the interlayer spacing architecture creates the tendency to harvest individual layer capabilities, which can be significant for improved energy storage and conversion efficiencies [13]. The advantage of interlayer spacing engineering in layered SnS2-based heterostructure has been enormous. For instance, the recent report of Yang et al. [14] on interlayer engineering of cesium-doped SnS2 indicates improved NO2 gas sensing performance. The effect of interlayer spacing on the electronic properties of SnS2 was further iterated in the studies of Zhang et al. [15], where successful band gap tuning was achieved via interlayer spacing manipulation. This tunability of the band gap was attributed to interlayer coupling effects. Furthermore, the study of Xu et al. [16] showed interlayer spacing contributions in enhancing the electron/ion migration in planar SnS2/graphene heterostructure. While all these studies have proven useful for harvesting the benefits of layer intercalation, the formation of sandwiched-based heterogeneous configurations is still lacking. Meanwhile, SnS2-based heterostructure band gap alignment has been suggested to be consistent with type II heterostructure [17], which is recommended for improved optoelectronic-based acceptor–donor applications [18]. Since one of the crucial requirements for type II heterostructure is a high-conducting material [18], the inclusion of graphene in layered SnS2 configuration could prove significant for enhanced charge transport for optoelectronic applications. The current study explores the electronic and optical properties of graphene incorporated sandwiched SnS2 heterostructure with a focus on the effect of interlayer spacing on charge transport properties and optical response.

2 Computational details

The electronic structure and optical properties of the layered SnS2/graphene/SnS2 heterostructure were calculated using the density functional theory approach, as described in the Cambridge Serial Total Energy Package (CASTEP) [19] code. The exchange interaction of electron–electron was examined using the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) [20], while core-valence interactions were studied using the Vanderbilt ultrasoft pseudopotentials [21].

Initially, interlayer spacing from previous report [22] showed 3.25 Å as the optimum interlayer spacing. Based on this, the boundary limit of 1–5 Å was utilized, and the sandwiched SnS2/graphene/SnS2 heterostructures corresponding to different interlayer separations (1–5 Å) were constructed from individually optimized pristine SnS2 and graphene monolayer supercells of \(4 \times 4\) and \(3 \times 3\), respectively. The different supercell sizes were chosen so as to minimize lattice mismatch between graphene and SnS2 unit cells. Well-converged plane wave cutoff energy of \(500\,\hbox{eV},\) as well as optimized k-point sampling of 6 × 6 × 2 k-points, was utilized in structural geometry optimization of the heterostructure, with force and energy convergence criteria of 0.01 eV/Å and \({10}^{-4}\,\hbox{eV}\), respectively. A denser k-point mesh of 12 × 12 × 2 Monkhorst k-points was used for the calculation of electronic and optical properties for increased accuracy.

3 Results and discussion

Sandwich-like SnS2/graphene/SnS2 leads to the formation of a heterostructure, which can cause perturbations within its electronic structure due to system instability caused by lattice mismatch [23, 24]. Figure 1 shows the optimized structures of SnS2/graphene/SnS2 sandwich heterostructure for the different interlayer spacing.

Fig. 1
figure 1

Geometric optimized structure of SnS2/graphene/SnS2 sandwich heterostructure for different interlayer spacing distances

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We find that the interlayer spacing does not impact the heterostructures’ structural properties, specifically the bond lengths, except in the case of 5 Å, where the in-plane lattice undergoes a downward drift. This downward drift can be attributed to weak interlayer coupling resulting from the relatively large spacing [25].

Additionally, the stability of the heterostructures was examined using their cohesive energy, calculated expressed as:

$$E_{{\text{coh}}} = (E_{{\text{total}}} - E_{{\text{SnS}}_2 } - E_{{\text{graphene}}} )/ \sum\nolimits^n_i ,$$
(1)

where \({E}_{\text{total}}\) is the total energy of SnS2/graphene/SnS2 heterostructure, \({E}_{{\text{SnS}}_{2}}\) depicts the energy of a single-layer SnS2 structure, while \({E}_{\text{graphene}}\) and \({n}_{i}\) are the energy of the single-layer graphene structure and the total number of each atomic species in the supercell, respectively. Figure 2a and Table 1 show the calculated cohesive energy of the heterostructure for different interlayer spacings.

Fig. 2
figure 2

Calculated cohesive energies and band gap of the SnS2/graphene/SnS2 heterostructure for different interlayer spacing configurations

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Table 1 Calculated cohesive energies, band gap, and net charge transfer values of SnS2/graphene/SnS2 heterostructures for different interlayer spacing configurations
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As shown in Table 1, all the calculated values of the cohesive energy for the different interlayer spacings are relatively low, suggesting that SnS2/graphene/SnS2 can be achieved experimentally. The positive cohesive energy values in this case suggest non-spontaneous formation of the heterostructures. However, non-equilibrium techniques such as solidification and atmospheric pressure plasmas can be utilized for fabricating these heterostructures.

From Fig. 2a, an increase in the interlayer spacing results in a corresponding increase in the cohesive energies, reaching a maximum of 3–4 Å. However, a slight reduction in cohesive energy is observed at 5 Å, which can be attributed to inactive/weak coupling between the layers.

Figure 3 presents the calculated band structure of SnS2/graphene/SnS2 heterostructure for different interlayer spacing configurations. The band gap of the bulk layered SnS2 utilized for the building of the heterostructure was initially calculated as \(2.338\,\hbox{eV}\) and is consistent with experiment value [26]. As expected,

Fig. 3
figure 3

Band structure properties of SnS2/graphene/SnS2 heterostructure for different interlayer spacing configurations

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The calculated band gap values of the heterostructures values, as summarized in Table 1 and Fig. 2b, are relatively low owing to the electronic interactions as well as lattice mismatch effects. The high symmetry points at F and Q are consistent with K and M points, as reported in the literature [27]. The effect of the interlayer spacing results in a blue shift of both F and Z symmetry points. Additionally, the effect of the interlayer spacing leads to increased band gap widening at lower interlayer separations of 1–3 Å but decreases at larger separations of 4–5 Å, suggesting reduced interfacial coupling between the sandwiched layers. The increased bandgap for 3 Å (corresponds to the optimum interlayer spacing) suggests increased electron transport activities as depicted by previous report [22]. Additionally, another report [28] has suggested the increased band gap can be attributed to the conversion of excitons to partial charge-separated states.

The electron transport properties emanating from the electronic structure are crucial for understanding the electronic properties of the SnS2/graphene heterostructure. The insights from the electronic properties provide information on the electrical conductivity, which is important to the optoelectronic performance of the heterostructure. To clarify the charge transport properties of the SnS2/graphene/SnS2 heterostructure, Mulliken charge analysis was performed to elucidate the charge contributions and distributions arising from interlayer interactions. Figure 4 and Table 1 show the charge contributions from the individual elemental components and the total net charges for all the interlayer spacing configurations. For 1 Å, the net contribution originates from Sn atoms (\(15.25\,\hbox{e}\)), S (\(-14.76\,\hbox{e})\) and C (\(0.64\,\hbox{e}\)). Increasing the interlayer spacing to 2 Å leads to a reduction in the charge magnitude for both Sn (\(15.09\,\hbox{e}\)) and C (\(0.32\,\hbox{e}\)), with S remaining constant at \(-14.76\,\hbox{e}\). A subsequent increase in the interlayer spacing causes the net charge of Sn to reduce with the corresponding disappearance of contributions from C atoms. The net charges from S atoms remain constant regardless of the interlayer spacing distance. With respect to the net charges indicated in Table 1, the charge transfer implies a change from acceptor to donor behavior.

Fig. 4
figure 4

Charge contributions from individual elemental components in SnS2/graphene/SnS2 at different interlayer spacings obtained from Mulliken charge analysis

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Furthermore, the impact of graphene in the sandwiched SnS2-based heterostructure leads to increased electronegative charge transport for narrow interlayer space distance [29]. However, the electronegative transfer effect diminishes as the interlayer distance increases. Based on the charge transfer features, the interlayer distance tuning can be manipulated to harvest desired properties.

Further, the electron density difference was calculated to examine the charge transfer properties of the interlayer spacing effect. Figure 5 shows the color maps for the charge transfer properties of the sandwiched SnS2/graphene/SnS2 heterostructure for all the interlayer spacing configurations.

Fig. 5
figure 5

Electron density difference color maps for sandwiched SnS2/graphene/SnS2 heterostructure, where a interlayer 1 Å b interlayer 2 Å c interlayer 3 Å d interlayer 4 Å and e interlayer 5 Å. The blue region depicts an electron increase, whereas the yellow region indicates an electron decrease (Color figure online)

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As Fig. 5a indicates, the charge accumulation region (blue) is more prominent than the charge depletion region (yellow). As indicated in the Mulliken charge analysis, the increased accumulation can be attributed to the charge transfer from the Sn to C atoms. Considering the color map legends for the different interlayer spacing distances, the blue region’s magnitude decreases (\(-1.973 \to -1.967 \to 1.970\)) with a corresponding increase in the yellow region. The implication of the transfer is consistent with charge transfer analysis. Additionally, the color map legend does not extend to the extreme, suggesting electron transport localization and strong electron coupling between the layers [30].

The optical response properties of dichalcogenides are crucial for establishing the potential of the material for optoelectronic applications. The physical properties of light, such as absorption and index of refraction, are intrinsic features of materials, which can be tuned for desired applications. The fundamental representation of the propagation of light can be described in terms of light-matter interactions. The light-matter interaction in material can be described in the quantum mechanics regime, which provides insight into a more accurate approximation of the intrinsic properties of dichalcogenide materials [31]. The formalism of Kramers–Kronig given in Eq. 2 [32] is the real and imaginary part of the dielectric function, which enables the description of light-matter interaction in the sandwiched SnS2/graphene/SnS2 heterostructure

$$\varepsilon \left(\omega \right)= {\varepsilon }_{1} \left(\omega \right)+i{\varepsilon }_{2 }(\omega )$$
(2)

The relation describes the photon absorption leading to occupied and unoccupied wave functions. The real and imaginary parts can be extrapolated to describe the optical properties as:

$${\varepsilon }_{2 (\omega )}=\left(\frac{4{\pi }^{2}{e}^{2}}{{m}^{2}{\omega }^{2}}\right)\sum\nolimits_{i,j}\int {<i\left|M\right|j>}^{2}{f}_{i}\left(1-{f}_{j}\right)\delta \left({E}_{f}-{E}_{i}-\omega \right){\text{d}}^{3}k.$$
(3)

The real part \({\varepsilon }_{1 (\omega )}\) can be written as:

$${\varepsilon }_{1}\left(\omega \right)= 1+\frac{2}{\pi }P\underset{0}{\overset{\infty }{\int }}\frac{{\omega^{\prime}\varepsilon }_{2}\left({\omega }^{\prime}\right)d{\omega }^{\prime}}{({{\omega }^{\prime}}^{2}-{\omega }^{2})}$$
(4)

Based on the Kronig–Kramers relationship, the absorption coefficient \(\alpha (\omega )\) can be written as:

$$\alpha \left(\omega \right)= \sqrt{2\omega }{\left[\sqrt{{{\varepsilon }_{2}}^{2}+ {{\varepsilon }_{2}}^{2}(\omega )}- {\varepsilon }_{1}(\omega ) \right]}^{1/2}$$
(5)

The refractive index can be calculated using:

$$n\left(\omega \right)= \sqrt{\frac{|{\varepsilon }_{\text{1,2}}\left(\omega \right)+ {\varepsilon }_{1}(\omega )|}{2}}$$
(6)

The relationship between the absorption coefficient and the photon energy in the [100] polarization direction is shown in Fig. 6 for the different interlayer spacing configurations. Using 1 Å interlayer spacing as a reference, the threshold energy corresponding to the upper and lower levels of the valence band (VB) and conduction band (CB) is located at \(\sim 2.67\,\hbox{eV}\). The value is in close proximity to previous report [33] and is attributed to the M points at the VB and CB maximum of the electronic band structure of the SnS2/graphene/SnS2 heterostructure. The prominent optical plasmonic transition peak appearing at \(\sim 4.06\,\hbox{eV}\) suggests electronic inter-band transitions within the electronic band structure [34]. The effect of the interlayer spacing 2–4 Å does not shift the optical plasmonic transitions to higher energies; however, a decrease in absorption coefficient with interlayer spacing occurs and can be attributed to strong electronic coupling as indicated in the electron density difference analysis. The increased interlayer spacing of 5 Å indicates four additional plasmonic transitions, which could be attributed to the decoupling of the layers with corresponding weak intercalation layer effects [35].

Fig. 6
figure 6

Optical absorption coefficient of for sandwiched SnS2/graphene/SnS2 heterostructure for different interlayer spacing distances

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Figure 7 shows the imaginary part of the dielectric function represented by the energy loss function for the different interlayer spacing configurations. Using 1 Å interlayer spacing distance as a reference, six prominent plasmonic transitions are observed at approximately \(3.8\,\hbox{eV}\), \(5.3\,\hbox{eV}\), \(6.3\,\hbox{eV}\), \(7.4\,\hbox{eV}\), \(8.5\,\hbox{eV},\) and \(10.9\,\hbox{eV}\). The peaks \(3.8\,\hbox{eV}\) and \(7.4\,\hbox{eV}\) are consistent with the loss function profile for pristine SnS2. The \(3.8\,\hbox{eV}\) peak is attributed to the electronic transition from S 3p orbitals of S atom originating from the upper valence band to the 5 s orbitals from the lower conduction band of Sn atom [36]. The \(7.4\,\hbox{eV}\) peak is associated with the electronic transition between S 3p orbitals in the S atomic valence band and Sn 5p orbitals contributions from the Sn atom in the conduction band [36].

Fig. 7
figure 7

Dielectric loss function for sandwiched SnS2/graphene/SnS2 heterostructure at the different interlayer spacing distances

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The other peak positions can be attributed to the effect of intercalations and electronic coupling between the graphene and SnS2 layers. Moreover, the imaginary loss energy function indicates plasmonic transitions similar to graphene-based structures and are due to weakly bound excitonic/free carriers arising from optical excitation [37]. Hence, interlayer intercalation effects within the SnS2/graphene heterostructure lead to increased excitonic and plasmonic transitions and are consistent with the additional observed plasmonic transition peaks. Furthermore, the intercalation effect has been suggested to be associated with the interaction of spatial separation of the photoinduced electron and hole [38]. The impact of interlayer spacing on the loss function does not eradicate the plasmonic transitions; however, a decrease in the loss of energy is observed. The retention of the plasmonic transition is consistent with the strong intercoupling between the layers (1–4 Å) except for 5 Å interlayer spacing distance.

The refractive index properties of dichalcogenides are crucial for understanding the measure of the transparency to incident photon energy. The harvesting of the refractive index properties has led to potential surface plasmon resonance-based biosensors [39]. Figure 8 shows the calculated refractive index as a function of photon energy for sandwiched SnS2/graphene/SnS2 heterostructure at different interlayer spacing configurations. Using 1 Å as a reference interlayer, the refractive index shows a static magnitude of \(2.7\) and increases to \(3.3\) with a corresponding photon energy increase. The effect of incorporating graphene into SnS2-based dichalcogenides has been proven to create additional optical unoccupied states, as indicated in Fig. 8. A previous report on pristine layered SnS2 depicts two prominent peaks at \(3.8\,\hbox{eV}\) and \(\sim 6.1\,\hbox{eV}\) [40], which show consistency with the current study. However, additional peaks are observed at \(1.3\) and \(1.2\), corresponding to \(7.8\), \(8.3,\) and \(10.8\,\hbox{eV}\) photon energies, respectively. These values are consistent with contributions from graphene incorporation as suggested from previous report [41]. The effect of the interlayer spacing does not negate the refractive index peaks. However, the refractive index magnitude reduces as the interlayer spacing increases 1–4 Å, suggesting a possible reduction in the degree of photon energy transparency. The case of 5 Å interlayer spacing shows an increase in refractive index, which contrasts the other interlayer spacing. This outlying behavior is consistent with the decoupling of the layer, resulting in the anomaly.

Fig. 8
figure 8

Refractive index plot of sandwiched SnS2/graphene/SnS2 heterostructure at the different interlayer spacing distances

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The electronic density of state (DOS) is an important quantity that outlines the total unoccupied and occupied states per unit energy that are available within the electronic structure of the sandwiched SnS2/graphene material. The analysis of the DOS provides a picture of the electronic transport mechanism behind the sandwiched SnS2/graphene heterostructure system. The calculated DOS for the SnS2/graphene heterostructure is shown in Fig. 9. As indicated in Fig. 9a–d, the DOS and Fermi level remain unchanged irrespective of the interlayer spacing distance. The negligible change in the unoccupied states suggests the electron transport localization and strong electronic coupling between the layers, which was corroborated by the electron density difference analysis. Additionally, the valence region located at \(\sim 6\,\hbox{eV}\) from the Fermi level \({E}_{f}=0\) is associated with S and Sn atomic interactions [40].

Fig. 9
figure 9

Total density of state of sandwiched SnS2/graphene/SnS2 heterostructure at the different interlayer spacing distances, where a interlayer 1 Å b interlayer 2 Å c interlayer 3 Å d interlayer 4 Å and e interlayer 5 Å

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Figure 10 shows the partial density of state of the sandwiched SnS2/graphene heterostructure for the different interlayer spacing configurations. As indicated, the main unoccupied state located at \(\sim 2.1\,\hbox{eV}\) is attributed to the effect of hybridization between the Sn 5s and S 3p orbital states. The current study is consistent with a previous report, which suggested an s-p hybridization between the top valence band and bottom conduction band for both Sn 5s and S 3p orbital states [42]. The impact of the interlayer spacing does not impair the process of hybridization, which further supports the suggested strong interlayer coupling and electron transport localization.

Fig. 10
figure 10

Partial density of state of sandwiched SnS2/graphene/SnS2 heterostructure at the different interlayer spacing distances, where a interlayer 1 Å b interlayer 2 Å c interlayer 3 Å d interlayer 4 Å and e interlayer 5 Å

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The major contributors to the total density were considered by zooming into the Fermi level region (see Fig. 11). As indicated, the dominant contributions come from S 3p supersedes Sn 5s and C 2p in the SnS2/graphene heterostructures. The increased contribution from S 3p is expected since twice the number of S atoms are present in the sandwiched SnS2/graphene configuration. The trend of the Sn 3p contribution over Sn 5s and C 2p remains unchanged, irrespective of the interlayer spacing.

Fig. 11
figure 11

Zoomed-in region outlining the main contributors of the orbital states around the Fermi level. One interlayer spacing configuration was considered for ease of simplicity and presentation

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4 Conclusion

The current study focused on the effect of interlayer spacing on the electronic interactions and optical properties of layered SnS2/graphene/SnS2 heterostructures. The impact of graphene incorporation as a sandwich layer into SnS2 created additional unoccupied states with resultant potential for improved electronic transport and optical properties tunability. The tunability of the refractive index with corresponding interlayer spacing and strong electronic coupling between the layers is a suggestion for manipulating the optoelectronic properties. The effect of the interlayer spacing further creates the opportunity to harvest the features of the optoelectronic properties for applications such as energy harvesting and optical sensors.