Nearly perfect and broadband optical absorption by TMDCs in cover/TMDC/spacer/Au/substrate multilayers

Abstract

Two-dimensional transition metal dichalcogenides (TMDCs) with direct bandgap and high optical absorption have opened a new horizon in photonics and optoelectronics. Increasing their absorption could greatly benefit their application, a subject still under debate. Thus, this study was focused on the plasmonic effect mediated by a thin gold layer and the role of individual spacer and cover layers or their combination in structures that include TMDC monolayers, namely, cover/TMDC/spacer/Au/substrate multilayers. The optical properties of these structures were investigated via the transfer matrix method in the visible wavelength region, revealing absorption values up to 99%. Such structures could be applied in the design of efficient optical absorbers for high-performance photovoltaic devices.

1 Introduction

Two-dimensional transition metal dichalcogenides (TMDCs) with chemical formula MX₂ (M = Mo or W and X = S or Se) have attracted increasing attention in optoelectronics due to their high optical absorption [1,2,3,4,5,6]. Among them, MoS₂ and MoSe₂ monolayers are particularly important because of their unique electronic and optical properties, useful for applications in transistors, detectors, solar cells, biosensors, waveguides, Raman scattering, etc. [5,6,7,8,9]. The exceptional absorption in the visible range of such ultrathin TMDC structures comes from their direct bandgap [10, 11]; however, to achieve a noticeable optoelectronic response in any TMDC-based devices, an even higher absorption in a wide wavelength range is required.

In recent years, different theoretical and experimental techniques have been proposed to realize TMDC structures with high absorption in a wide optical range [12, 13]. Among many designs, the presence of TMDC monolayers in one-dimensional optical structures has attracted special attention because of their simplicity [14]. In such elements, the presence of a substrate affects the absorption. The use of well-known substrates such as Si and SiO₂ may reduce their absorption relative to that when the substrate is absent. However, for Si/SiO₂ dual substrate, the sequential light reflections in the SiO₂ layer and the light returning to the TMDC monolayer result in absorption increase [11]. Using a spacer, a cover or both (as shown in Fig. 1) are other conventional methods for increasing the absorption [14, 15]. Another approach for its further enhancement is to utilize a plasmonic layer having a metal nanostructure, which has been used as a substrate [16,17,18] or a thin layer within a structure [19,20,21], increasing the absorption within a given wavelength range or at a certain wavelength. Moreover, the combination of the two last mentioned methods, i.e., the use of a spacer, a cover, or both along with a plasmonic layer, has also been examined [22,23,24]. Nevertheless, the designs suggested so far are complicated and simplifications in either their theory or experiments are still required.

Fig. 1

a Three-dimensional schematic of the structure, air/cover/TMDC/spacer/Au/substrate. b Cross-sectional view of the designed structure

For further development, in the present study, we investigated the absorption in structures consisting of a TMDC monolayer and plasmonic, cover, and spacer layers to attain high absorption in a broad wavelength. We found that the role of the individual spacer layer in the absorption increase was more pronounced than that of the cover one. In addition, the absorption was roughly equal between the combined spacer and cover configuration and the one with only the spacer layer. In the latter one, which is experimentally more desirable than the former one due to the less number of constituted layers, the absorption reached 99% as an optimal design for application in photovoltaics and optoelectronics.

2 Modeling

Figure 1a schematizes the proposed air/cover/TMDC/spacer/Au/substrate structure; light is transmitted from air to the structure. Since the substrate material plays a role in the overall absorption, three different substrates were tested (Si, SiO₂, and SiO₂ (50 nm)/Si) to investigate its effect. The spacer and cover layers were chosen of SiO₂ and polymethylmethacrylate (PMMA), respectively; their thicknesses were accordingly denoted as d_s and d_c. Two different TMDC monolayers were used: 0.615 nm MoS₂ and 0.664 nm MoSe₂. The complex refractive index values of Si, SiO₂, PMMA, Au, MoS₂, and MoSe₂ in the visible wavelength region were taken from literature [11, 25,26,27,28,29] and are plotted in Fig. 2.

Fig. 2

Real and imaginary refractive index of a MoSe₂ monolayer, b MoS₂ monolayer, c PMMA, SiO₂ and Si layer, and d Au layer

The absorption is calculated based on the transfer matrix method (TMM) [30]; the transfer matrix of each layer for the transverse electric (TE) and transverse magnetic (TM) polarizations is

$$M_{j} = \left( {\begin{array}{*{20}c} {\text{Cos} \left( {2\pi n_{j} d_{j} \frac{{\cos \theta_{j} }}{\lambda }} \right)} & { - i \varGamma \text{Sin} \left( {2\pi n_{j} d_{j} \frac{{\cos \theta_{j} }}{\lambda }} \right)} \\ { - i \varGamma \text{Sin} \left( {2\pi n_{j} d_{j} \frac{{\cos \theta_{j} }}{\lambda }} \right)} & {\text{Cos} \left( {2\pi n_{j} d_{j} \frac{{\cos \theta_{j} }}{\lambda }} \right)} \\ \end{array} } \right),$$

(1)

where λ, n_j, $\theta_{j}$, and d_j are the wavelength, refractive index, light propagation angle, and thickness of the jth layer, respectively, and for TE and TM polarizations is correspondingly defined as $\frac{1}{{\cos \left( {\theta_{j} } \right)n_{j} }}$ and $\frac{{\cos \left( {\theta_{j} } \right)}}{{n_{j} }}.$

The final transfer matrix M for the whole structure is obtained by multiplying those of each constituent layer. The tangential electric and magnetic fields can be expressed for the first ($E_{{0{\text{t}}}}$, $H_{{0{\text{t}}}} )$ and last ($E_{\text{st}}$, $H_{\text{st}}$) surroundings, according to the matrix relation as follows:

$$\left( {\begin{array}{*{20}c} {E_{\text{st}} \left( r \right)} \\ {H_{\text{st}} \left( r \right)} \\ \end{array} } \right) = \left( M \right) \left( {\begin{array}{*{20}c} {E_{{0{\text{t}}}} \left( r \right)} \\ {H_{{0{\text{t}}}} \left( r \right)} \\ \end{array} } \right).$$

(2)

These fields can be expressed in terms of amplitudes of the transmitted (c⁺) and reflected (c⁻) fields in each layer as

$$\left( {\begin{array}{*{20}c} {E_{{0{\text{t}}}} \left( r \right)} \\ {H_{{0{\text{t}}}} \left( r \right)} \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {\psi {\text{e}}^{{i2r\pi n_{0} \frac{{\cos \theta_{0} }}{{\lambda_{0} }}}} } & {\psi {\text{e}}^{{ - i2r\pi n_{0} \frac{{\cos \theta_{0} }}{{\lambda_{0} }}}} } \\ {n_{0} \varphi {\text{e}}^{{i2r\pi n_{0} \frac{{\cos \theta_{0} }}{{\lambda_{0} }}}} } & { - n_{0} \varphi {\text{e}}^{{ - i2r\pi n_{0} \frac{{\cos \theta_{0} }}{{\lambda_{0} }}}} } \\ \end{array} } \right) \left( {\begin{array}{*{20}c} {c_{0}^{ + } } \\ {c_{0}^{ - } } \\ \end{array} } \right),$$

(3)

$$\left( {\begin{array}{*{20}c} {E_{\text{st}} \left( r \right)} \\ {H_{\text{st}} \left( r \right)} \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {\psi {\text{e}}^{{i2r\pi n_{s} \frac{{\cos \theta_{s} }}{{\lambda_{s} }}}} } & {\psi {\text{e}}^{{ - i2r\pi n_{s} \frac{{\cos \theta_{s} }}{{\lambda_{s} }}}} } \\ {n_{s} \varphi {\text{e}}^{{i2r\pi n_{s} \frac{{\cos \theta_{s} }}{{\lambda_{s} }}}} } & { - n_{s} \varphi {\text{e}}^{{ - i2r\pi n_{s} \frac{{\cos \theta_{s} }}{{\lambda_{s} }}}} } \\ \end{array} } \right) \left( {\begin{array}{*{20}c} {c_{s}^{ + } } \\ 0 \\ \end{array} } \right),$$

(4)

where 0 and s refer to air and substrate, and ψ and φ for the TE (TM) polarization are equal to $\cos \theta_{\text{J}}$ (1) and 1 ($\cos \theta_{\text{J}}$), respectively. Finally, transmission, reflection, and absorption are calculated as follows:

$$T \, = \frac{{n_{s} \cos \theta_{s} }}{{n_{0} \cos \theta_{0} }}\left| {\frac{{c_{s}^{ + } }}{{c_{0}^{ + } }}} \right|^{2} ,\,R \, = \left| {\frac{{c_{0}^{ - } }}{{c_{0}^{ + } }}} \right|^{2} ,\,{\text{and}}\,A = 1{-}T{-}R.$$

3 Results and discussion

To identify the structure with maximum absorption, the absorption spectra of various designs including different gold thicknesses, suspended MoS₂ and MoSe₂ monolayers, and the proposed TMDC layers on Si, SiO₂, and SiO₂(50 nm)/Si substrates are plotted in Fig. 3a (for MoS₂) and c (for MoSe₂). Since the absorption of the gold layer increases with its thickness up to 60 nm, above which no significant changes could be seen, this threshold value was chosen as its optimal thickness. According to the Snell’s law and the high refractive index of the single substrates (Si and SiO₂) compared to air, the presence of a substrate reduces the absorption with respect to its absence. However, in the dual substrate (SiO₂(50 nm)/Si) configuration, the absorption increased due to the sequential light reflections in the middle SiO₂ layer and the light returning to the TMDC layer, as mentioned above.

Fig. 3

Absorption spectra of various gold thicknesses (dashed line), suspended TMDC (green line) and TMDC on three substrates of Si (blue line), SiO₂ (red line) and SiO₂ (50 nm)/Si (black line), for a MoS₂ and c MoSe₂. The gold layer is placed between the TMDC and the substrate for b MoS₂ and d MoSe₂ TMDCs

To investigate the plasmonic effect, a gold layer with thickness 60 nm is placed between the TMDC monolayer and the substrate. The results obtained by such a structure with different substrates (Si, SiO₂, and SiO₂(50 nm)/Si) are plotted in Fig. 3b (for MoS₂) and d (for MoSe₂). The absorption value and width of the air/TMDC/Au/SiO₂(50 nm)/Si structure for both tested TMDC monolayers were slightly greater than those found using the single substrates. Moreover, the plasmonic effect in the gold layer resulted in an absorption increase for both TMDC layers in comparison with those shown in Fig. 3a, c.

For further optimization, the impacts of the individual cover and spacer layers with different thicknesses were investigated; their optimal values were found to be 50 and 40 nm, respectively. The absorption spectra obtained using the air/TMDC/spacer/Au/substrate and air/cover/TMDC/Au/substrate structures with these optimized thicknesses are shown in Fig. 4a, b for MoS₂ and Fig. 4c, d for MoSe₂, respectively.

Fig. 4

Absorption spectra of the air/TMDC/spacer (50 nm)/Au/substrate structure for a MoS₂ and c MoSe₂ and for air/cover (40 nm)/TMDC/Au/substrate structures for b MoS₂ and d MoSe₂

The calculated absorption values and widths of the investigated structures are also listed in Tables 1 and 2, respectively. The structure with the SiO₂(50 nm)/Si substrate exhibited much better results than those using the individual Si and SiO₂ ones; thus, this dual substrate configuration was identified as the best choice. The maximum absorption values at 429 nm for the MoS₂-based structures with the individual spacer and cover layers were 99% and 90%, respectively, and those for the corresponding MoSe₂-based ones were accordingly 96% and 88%, respectively. This indicates that the spacer layer has a more pronounced effect than the cover one in the absorption increase.

Table 1 Maximum absorption of structures at 429 nm without spacer and cover (air/TMDC/Au/substrate), with individual spacer (air/TMDC/spacer (50 nm)/Au/substrate), individual cover (air/cover (40 nm)/TMDC/Au/substrate) and the combined spacer and cover (air/cover (40 nm)/TMDC/spacer(50 nm)/Au/substrate

Table 2 Absorption width of structures without spacer and cover (air/TMDC/Au/substrate), with individual spacer (air/TMDC/spacer(50 nm)/Au/substrate), individual cover (air/cover(40 nm)/TMDC/Au/substrate) and and the combined spacer and cover (air/cover(40 nm)/TMDC/spacer(50 nm)/Au/substrate)

The effect of the thicknesses of both spacer and cover layers on the absorption by air/cover/TMDC/spacer/Au/SiO₂(50 nm)/Si at a chosen maximum absorption wavelength, i.e., 429 nm, is illustrated in Fig. 5a for MoS₂ and b for MoSe₂. The maximum absorption reached was 95% and 93% for MoS₂ and MoSe₂, when using d_s = 44 nm and d_c = 4 nm, respectively. The absorption spectra of the air/cover/TMDC/spacer/Au/SiO₂(50 nm)/Si structures having three different combinations of spacer and cover thicknesses (d_s = 50 nm and d_c = 40 nm, d_s = 44 nm and d_c = 4 nm, and d_s = 50 nm and d_c = 0 nm) are displayed in Fig. 5c, d for MoS₂ and MoSe₂, respectively, showing that the d_s = 44 nm and d_c = 4 nm configuration exhibited almost identical results as the structure with the individual spacer layer. Therefore, the structure with only the spacer layer was chosen as the best choice, since it has a lower layer number with maximum absorption values of 99% and 96% for MoS₂ and MoSe₂, respectively.

Fig. 5

Effect of thicknesses of both spacer and cover layers on the absorption at 429 nm are shown for air/cover/TMDC/spacer/Au/SiO₂(50 nm)/Si for a MoS₂ and b MoSe₂. Absorption spectra vs. wavelength are plotted for the structure air/cover/TMDC/spacer/Au/SiO₂(50 nm)/Si for three different thicknesses of spacer and cover layers, d_s = 50 nm and d_c = 40 nm (blue color), d_s = 44 nm and d_c = 4 nm (red color), d_s = 50 nm and d_c = 0 nm (black color) for c MoS₂ and d MoSe₂

The increase in absorption is due to localization of light and also enhancement of the light intensity in the TMDC monolayer [28]. The intensity at 429 nm vs. position for air/cover/TMDC/spacer/Au/substrate structure is shown in Fig. 6. This is determined for four different thicknesses of spacer and cover layers using MoS₂ and MoSe₂ with d_s = 0 nm and d_c = 40 nm (a and b), d_s = 50 nm and d_c = 0 nm (c and d), d_s = 44 nm and d_c = 4 nm (blue color, e and f) and d_s = 50 nm and d_c = 40 nm (red color, e and f). The intensity in the TMDC monolayer for thicknesses of spacer and cover layers being d_s = 50 nm, d_c = 0 nm and d_s = 44 nm, d_c = 4 nm is greater than using other thicknesses of spacer and cover layers; dictating the maximum absorption.

Fig. 6

Intensity vs. position for structure air/cover/TMDC/spacer/Au/substrate for four different thicknesses of spacer and cover layers, d_s = 0 nm and d_c = 40 nm (a, b), d_s = 50 nm and d_c = 0 nm (c, d), d_s = 44 nm and d_c = 4 nm (blue color, e, f), d_s = 50 nm and d_c = 40 nm (red color, e, f) for MoS₂ and MoSe₂

The strong plasmonic resonances in metallic nanostructures have been widely utilized to boost the light absorption of TMDC [31]. Here, we demonstrate an enhancement of light absorption in monolayer TMDC using plasmonic Au layer. Obtained results show that the enhancement of localized electromagnetic field in the TMDC monolayer caused by plasmonic Au layer enhances the local absorption of TMDC.

The incident light angle can also affect absorption. Thus, the absorption of both TE and TM polarizations should be considered not only for the normal incidence but also for the oblique incidence in such structures. Hence, the effect of the incident angle for both the TE and TM polarizations on the absorption by the air/TMDC/spacer/Au/SiO₂(50 nm)/Si structure was examined as well (Fig. 7).

Fig. 7

Effect of the incident angle on the absorption in air/TMDC/spacer(50 nm)/Au/SiO₂(50 nm)/Si structure, using the MoS₂ layer for a TE and b TM polarization. The absorption for the structure using the MoSe₂ layer for c TE and d TM polarization

By increasing the incident angle, the upper edge of the bandwidth in both polarizations shifted toward shorter wavelengths (i.e., red shift). For both the investigated TMDCs, the absorption was above 78%, in the TE polarization from 0° to 80° and in the TM polarization from 0° to 70°. The maximum absorption was 99% for both TMDCs.

The absorption vs. angle of incidence at 429 nm is plotted in Fig. 8a, b for MoS₂ and MoSe₂ layers, respectively. It can be seen that for both TE and TM polarizations, the reduction of absorption with increasing incidence angle is obvious. The light intensity vs. position calculated at 429 nm for both TMDCs for incident angles of 30°, 45°, 60°, and 70° and their results are shown in Fig. 8c, d (TE polarization) and Fig. 8e, f (TM polarization). Obviously, when the angle was increased to 45° in TE polarization and when the angle was increased to 70° in TM polarization, the maximum intensity did occur at the TMDC monolayer position for both TMDCs. Hence, by increasing angle, a systematic decrease in absorption can be observed.

Fig. 8

Absorption in terms of angle for a MoS₂ and b MoSe₂. The intensity of the wave in terms of location in λ_peak in TE polarization for c MoS₂ and d MoSe₂ and TM polarization for e MoS₂ and f MoSe₂ for incident angle 30° (red), 45° (blue), 60° (black), and 80° (green)

4 Conclusions

In the pursuit of perfect light absorption, structures based on a TMDC monolayer were investigated. The effects of plasmonic gold, spacer, and cover layers play important roles in this viewpoint. We found that an individual spacer layer is more effective than a cover one in improving the absorption response, providing results similar to those from structures with both the spacer and cover layers. We achieved absorption values of 99% and 96% using MoS₂ and MoSe₂ as TMDC monolayers, respectively, in an air/TMDC/spacer/Au/SiO₂/Si configuration. The influences of light incident angle and polarization on the best design were also studied; the absorption was at least 78% for the TE polarization from normal up to 80° and for the TM polarization from normal up to 70°. The results of this work can be useful for achieving broadband and broad-angle absorption via TMDC monolayers in optoelectronic applications.