Ultrathin gold film modified optical properties of excitons in monolayer MoS2

Guang Yi Jia *ab, Qiang Zhang b, Zhen Xian Huang a, Shu Bin Huang a and Jing Xu a
aSchool of Science, Tianjin University of Commerce, Tianjin 300134, P. R. China. E-mail: gyjia87@163.com
bDepartment of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, P. R. China

Received 3rd August 2017 , Accepted 20th September 2017

First published on 22nd September 2017


Metal nanostructure plays an important role in tailoring the performance of various two-dimensional semiconductors. Herein, we theoretically study the optical properties of A, B and C excitons in monolayer MoS2 coated on ultrathin gold films less than 20 nm in thickness. We show that resonances of these three excitons occur at ∼660, ∼613 and ∼426 nm, respectively and each exciton maximizes absorption intensity at total reflection. However, because of the optical scattering effect induced by the ultrathin gold film, the maximum absorption of each exciton appears at the incident angle θm that is larger than its corresponding surface plasmon resonance angle θSPR. It is possible that due to the gradual approach between θm and θSPR, the maximum absorption intensity of the exciton gradually increases with thickening of the gold film. For external reflection, the C exciton maximizes absorption intensity around its corresponding quasi-Brewster's angle, whereas the incident angle, at which the A or B exciton gives the maximum absorption, gradually deviates from its corresponding quasi-Brewster's angle as the gold film thickness decreases. This discrepancy is explained by the dependencies of extinction coefficients of hybrid films on the excitonic resonance wavelength and gold film thickness.


Introduction

As a prototypical representative of the transition metal dichalcogenides, lamellar MoS2, due to its fascinating optoelectronic characteristics, has recently attracted tremendous research interest from both academic and applied communities.1–4 It usually undergoes a transition from an indirect bandgap material in its bulk counterpart to a direct bandgap semiconductor when confined in a monolayer, thereby enabling a broad optical bandgap tuning from 1.29 eV for bulk MoS2 to over 1.90 eV for monolayer MoS2.5 The prominent excitonic resonance features of MoS2 during interaction with excitation photons offer a flexible method to support various applications such as those in biosensors,6 hydrogen evolution reaction,7 photodetectors,8 and field effect transistors.9 Among these promising applications, construction of the coupling hybrid structures between MoS2 and various metal membranes is often used to modulate and improve the photoelectric performance of devices. For example, Yong et al. showed that the hybrid structure of graphene-MoS2 coated on Au substrate can detect molecules in an ultrasensitive manner.10 Mulpur et al. demonstrated that the emission intensity of rhodamine B fluorophore molecules, coated on a MoS2–Ag hybrid thin-film system, can be enhanced by a factor of up to 17-fold.11 Cronin et al. and Qi et al. found that the adhesion between metal (e.g., Au, Ag, Cu, Pt) and MoS2 films can modify the interface potential barriers; thus, the indirect bandgap emission of the MoS2 flake can be greatly enhanced by the hybrid structure.12,13

Despite the extensive research on MoS2–metal hybrid composites, the thickness of utilized metal film is usually comparable to or larger than the electron mean free path (EMFP), l, in bulk metal (l = 37.7, 39.9 and 53.3 nm for Au, Cu and Ag, respectively, at room temperature).14 However, when the metal film is far thinner than the l value, the carrier concentration and the mobility of free electrons will greatly decrease with a reduction in the thickness of the metal film, resulting in noticeable dependencies of physical factors, e.g., optical constant, photon dispersion, plasmon frequency, etc., on metal film thickness.15,16 Because of the mismatch of optical constant at the medium boundary induced by the ultrathin film, the interface scattering of photons is generally inevitable.17,18 Besides, from a preparation perspective, the crystallinity of metal films will become poor when the film thickness is lower than l.15,19 Thus, many grains and boundaries, which can strengthen the optical scattering effect, could appear in the ultrathin metal film. When the scattering coefficient is comparable to the absorption coefficient, the surface plasmon resonance (SPR) frequency of a metal nanomaterial could deviate from the maximum absorption frequency.16,20,21 Therefore, the combination of MoS2 with an ultrathin metal film may bring about several new phenomena. Moreover, previous studies on MoS2–metal hybrid structures have been mainly limited to using the normally incident excitation light.11–13,22–24 Under oblique incidence, evolutions of several optical factors including excitonic absorption, photon dispersion, SPR and Brewster's angles with structure factors such as the thicknesses of MoS2 and metal films remain elusive.

In this study, we simulate the optical absorption spectra of monolayer MoS2–Au hybrid structures using the transfer matrix method (TMM) and investigate the influence of ultrathin gold films less than 20 nm in thickness on the excitonic absorption, dispersion relation, SPR and Brewster's angles of the sapphire/Au/MoS2/air multilayer structure. Our results reveal that the ultrathin gold film can dramatically modify the excitonic optical properties of the MoS2 monolayer. The underlying mechanisms are discussed in detail.

Theoretical model and calculated method

In our model system, the monolayer MoS2–Au hybrid films are assumed to be deposited upon a sapphire prism, and the upper medium of the MoS2 is air, as shown in Fig. 1. The excitation wavelength changes from 400 to 800 nm. In this wavelength range, the sapphire is accepted as a non-absorbing substrate with a refractive index of ∼1.77.25 Thicknesses of gold films are set to 2.4, 4.4, 8.5, 13 and 19 nm. Their dielectric constants have been measured by Leung et al. and are significantly dependent on the film thickness.15 The height of monolayer MoS2 is 0.65 nm, and the complex refractive index published by Yu et al. is used.26 It is necessary to point out that the optical constants of gold films and monolayer MoS2 are measured under the conditions of being encapsulated between two ITO layers and deposited on the sapphire substrate, respectively. In the actual experiments, optical constants of the MoS2–Au hybrid films may be a little different. Owing to the lack of precise data, the theoretical model is arbitrarily constructed. Besides, the TMM leaves out several other affecting factors, e.g., interface doping as well as the possibly induced complexities of crystal structure and orientation. Even so, in actual comparison between theoretical and experimental results, some parameters, e.g., the dielectric function,27,28 could be optimized to offset the influences induced by non-optical factors. Thus, the TMM is a powerful tool to calculate and predict new optical phenomena in stratified 2D and/or metal materials.10,29,30
image file: c7cp05260j-f1.tif
Fig. 1 Schematic of the monolayer MoS2–Au hybrid films deposited on a sapphire prism.

Herein, we consider the incident light to be polarized in the incident plane, i.e., the transverse magnetic (TM) mode. Within the framework of TMM, N-layer films are stacked parallel along the normal direction z axis, and the jth layer has a complex refractive index ηj = nj + j and thickness dj. Refractive indices of incident and exit media are defined as n0 and nN+1, respectively. Then, the characteristic matrix of the multilayer system can be expressed by

 
image file: c7cp05260j-t1.tif(1)
with
 
image file: c7cp05260j-t2.tif(2)
Herein, δj = 2π/λ0ηjdj[thin space (1/6-em)]cos[thin space (1/6-em)]θj and pj = cos[thin space (1/6-em)]θj/ηj. The parameters λ0 and θj indicate the vacuum wavelength and refraction angle in the jth-layer medium, respectively. Accordingly, the four elements M11, M12, M21 and M22 of the matrix M can be derived. Then, the reflection and transmission coefficients of the multi-film system are given by r = M21/M11 and t = 1/M11, respectively. The reflectance and transmittance can be calculated by
 
R = |r|2(3)
 
image file: c7cp05260j-t3.tif(4)
where θ0 and θN+1 denote the incident and exit angles, respectively. According to energy conservation, the absorbance of the system can be obtained by A = 1 − RT.

Because the thicknesses of monolayer MoS2 and gold film are far smaller than the excitation wavelength, total reflection under the condition of n0 > nN+1 will occur when the incident angle θ0 exceeds the critical value θc = ∼34.4°. As a result, the incident optical beam will establish an evanescent electromagnetic field (named evanescent wave) in the exit medium but propagate in close proximity to the monolayer MoS2 or MoS2–Au hybrid films. When the evanescent wave vector kx matches with the surface plasmon wave vector ksp, the SPR phenomenon occurs with

 
kx = k0[thin space (1/6-em)]sin[thin space (1/6-em)]θ0 = ksp(5)
where the incident angle θ0 is known as the SPR angle θSPR.

To determine the SPR angle θSPR, a matrix formalism suitable for calculating the dispersion relation of plasmonic surface waves in an arbitrary multilayer system is employed.31 Within this method, it is assumed that there are two perpendicular magnetic field components with amplitudes Bjup and Bjdown to propagate up (positive z) and down (negative z) in the jth medium, respectively. In semi-infinite materials, there is only one wave going in positive z after the N + 1 boundary and negative z before the first boundary. Then, the boundary conditions of the electromagnetic field can be described using a matrix form as AB = 0 where

 
image file: c7cp05260j-t4.tif(6)
 
image file: c7cp05260j-t5.tif(7)
In the above expressions, A is a (2N + 2) × (2N + 2) matrix, and B is a vector of length (2N + 2). The complex wave vector kj has the momentum conservation kj2 = kx2 + kzj2 where kx is the tangential component (along the surface) for all materials, and kzj is the perpendicular component that varies depending upon the jth material. The eigenmode of the system occurs when the determinant of the matrix A equals 0 with a nonzero vector B. Then, it is possible to solve the kx value for each frequency of the plasmonic surface wave of interest. Thus, the dispersion relation is determined, and the θSPR value can be derived using eqn (5).

Results and discussion

We first consider the situation of internal reflection; i.e., the incident medium is the sapphire prism, as shown in Fig. 1. The optical absorption spectra of monolayer MoS2 and MoS2–Au composites are given in Fig. 2. One can see that all the samples present three extremum values at ∼660, ∼613 and ∼426 nm for each incident angle, which arise from the absorption of A, B and C excitons of MoS2, respectively. The break position of the vertical coordinate corresponds to the critical value θc. For the condition of θ0 < θc, the maximum absorption intensities of A, B and C excitons appear in the case of normal incidence, and their values as a function of the gold film thickness are shown in Fig. 3a with open symbols. It is found that the excitonic absorption of the MoS2–Au system gradually increases as the gold film decreases in thickness, and the hybrid structure with the thinnest gold film at 2.4 nm gives the most intensive absorption for each exciton. This could be ascribed to the optical scattering effect. Within this limitation of the ultrathin film, optical scattering becomes more and more pronounced as the gold film decreases in thickness.15 This increases the interaction probability between photons and the hybrid structure. Consequently, the MoS2–Au system with a thinner gold film favors a larger excitonic absorption.
image file: c7cp05260j-f2.tif
Fig. 2 Absorption spectra of MoS2–Au hybrid films as a function of the wavelength and incident angle for the internal reflection. The gold film thicknesses are set as (a) 0.0, (b) 2.4, (c) 4.4, (d) 8.5, (e) 13, and (f) 19 nm. Break positions of vertical coordinates indicate the critical value θc. Two color bars are given on the right. For all the figures of (a)–(f), refer to the upper (or bottom) color bar when the incident angles are larger (or smaller) than θc.

image file: c7cp05260j-f3.tif
Fig. 3 (a) Maximum absorption intensities of A, B and C excitons at normal incidence (open symbols) and total reflection (solid symbols). (b) SPR angles θSPR and incident angles θm where the excitons give their respective maximum absorption intensities at total reflection.

When the incident angle exceeds the critical value θc, total reflection occurs, and the incident angle θm at which each exciton gives its maximum absorption can be obtained according to Fig. 2. Fig. 3b shows the θm,A, θm,B and θm,C values for these three excitons at different gold film thicknesses. It is seen that the A, B and C excitons of monolayer MoS2 present the maximum absorption at almost the same incident angle of 48.4°. However, after the gold film is introduced, these three excitons exhibit maximum absorption at different incident angles, and their deviations from each other become increasingly clear with the thickening of the gold film (see Fig. 3b). Fig. 4 presents the dispersion curves of monolayer MoS2 and MoS2–Au hybrid films. The horizontal arrows indicate the positions of A, B and C excitonic resonance frequencies. We can see that the dispersion curve of monolayer MoS2 is nearly linear. As the gold film increases in thickness, the dispersion curve gradually deviates from the linear relation. In particular, the C exciton exhibits the largest deviation among these three excitons. According to the wave vector kx, the SPR angles θSPR,A, θSPR,B and θSPR,C can be derived viaeqn (5), as shown in Fig. 3b.


image file: c7cp05260j-f4.tif
Fig. 4 Dispersion curves of monolayer MoS2 (Au 0.0 nm) and MoS2–Au hybrid films. The horizontal arrows indicate the positions of A, B and C excitons. Note that the imaginary part of wave vector kx is neglected because it is smaller by more than 15 orders of magnitude than the real part.

It is seen that the incident angles of maximum excitonic absorption do not match with the SPR angles, and the deviation of θm from θSPR becomes larger and larger with reduced gold film thickness. This phenomenon is different from the results of Yong et al.10,32 Yong et al. recently reported the evolution of the SPR angle of the MoS2–Au (or WS2–Au) hybrid structure with the thicknesses of MoS2 (or WS2) and gold films. For monolayer MoS2 (or WS2) coated on gold films, the SPR angle is nearly unchanged with the gold film thickness, and it is consistent with the incident angle of minimum reflectivity (corresponds to the maximum absorption). These discrepancies could be ascribed to the fact that the thicknesses of gold films investigated by Yong et al. are thicker than 30 nm. In this thickness range that is comparable to or larger than the EMFP in bulk Au, the optical scattering effect is very weak such that the maximum absorption generally appears at the SPR position.16 Besides, the complex refractive index of gold film is calculated via the Drude model in the work of Yong et al., thus, the dielectric constant is less affected by the gold film thickness. Using the same model, we simulated the dispersion curves of monolayer MoS2–Au hybrid structures with gold film thickness changing from 35 to 55 nm (see Fig. S1 in the ESI). Moreover, Fig. S2 in the ESI shows the corresponding plots of absorption versus incident angles at these three excitonic resonance wavelengths by broken lines. For comparison, the variation of excitonic absorption with respect to incident angle for the hybrid structure consisting of ultrathin gold film and monolayer MoS2 is also shown by solid lines in Fig. S2 (ESI). One can see that the gold film thickness above 30 nm has less effect on the dispersion relation, and the incident angles of maximum excitonic absorption match the SPR angles. When the gold film thickness decreases to less than 20 nm, it is possible due to the optical scattering effect,15 the θm deviates from the θSPR and shifts towards a larger incident angle, whereas the θSPR shifts towards the critical angle as the gold film thickness decreases to 2.4 nm. These results are in accord with Fig. 3b.

Even if the θm value deviates from the SPR angle, the excitonic absorption intensity of MoS2–Au hybrid film is stronger than that of monolayer MoS2, as shown in Fig. 3a and Fig. S2 (ESI). Furthermore, for the same thickness of the gold film, the excitonic absorption at total reflection as depicted by solid symbols in Fig. 3a is stronger than that at normal incidence. In addition, the absorption intensity of each exciton at total reflection gradually increases with thickening of the gold film, which is contrary to the trend of excitonic absorption at normal incidence. Generally speaking, a larger extinction coefficient κ contributes to a larger excitonic absorption. For example, monolayer MoS2 gives the largest extinction coefficient κ at 426 nm (see Table 1), associating with the strongest C excitonic absorption among these three excitons. At the resonance wavelengths of A and B excitons, the thicker the gold film is, the larger the extinction coefficient κ of gold film is. Thus, thicker gold film contributes to a larger excitonic absorption in MoS2–Au hybrid films (see solid symbols in Fig. 3a). Nevertheless, the κ value of gold film at C excitonic resonance wavelength fluctuates with thickness, which cannot account for the increase of C excitonic absorption with thickening of the gold film (Fig. 3a). Hence, some other factor should be taken into account. Ideally, when the surface plasmon wave is excited, all the energy of incident light will be absorbed to support the resonant oscillations, giving rise to a dramatically enhanced evanescent field.32 Since the θSPR and θm values gradually draw near each other with thickening of the gold film (Fig. 3b), the evanescent field at the incident angle θm is gradually increased. As a result, the maximum absorption intensity of each exciton at total reflection gradually increases as the gold film thickness increases (Fig. 3a).

Table 1 Complex refractive indices n + of monolayer MoS2 and different thicknesses of gold films at three excitonic resonance wavelengths
n +
660 nm 613 nm 426 nm
Monolayer MoS2 4.93 + 1.02i 4.70 + 1.31i 4.73 + 3.45i
Au 2.4 nm 0.70 + 3.59i 0.63 + 3.25i 0.43 + 1.66i
Au 4.4 nm 0.30 + 3.94i 0.26 + 3.65i 0.13 + 2.44i
Au 8.5 nm 0.16 + 3.99i 0.14 + 3.70i 0.07 + 2.55i
Au 13 nm 0.11 + 4.13i 0.10 + 3.72i 0.07 + 1.88i
Au 19 nm 0.08 + 4.27i 0.07 + 3.83i 0.05 + 1.82i


Finally, we analyze the situation of external reflection; i.e., the incident and exit media are the air and the sapphire substrate, respectively. Fig. 5 shows the corresponding optical absorption spectra of monolayer MoS2 and MoS2–Au hybrid films. Fig. 6 gives the maximum absorption intensities of A, B and C excitons (panel a) as well as their corresponding incident angles (i.e., θm,A, θm,B and θm,C, panel b) by solid symbols. For an air–sapphire interface, the reflection of TM polarized light is extinguished at ∼60.53°, which is defined as the Brewster's angle. If, however, MoS2 or gold film is deposited onto the interface, the reflection of TM polarized light is inevitable due to the change in the electromagnetic boundary condition induced by surface conductivity.33 Thereby, the incident angle where the reflection reaches its minimum value is defined as the quasi-Brewster's angle. Fig. 6b shows the quasi-Brewster's angles θB at these three excitonic resonance wavelengths by open symbols.


image file: c7cp05260j-f5.tif
Fig. 5 Absorption spectra of MoS2–Au hybrid films as a function of the wavelength and incident angle for the external reflection; i.e., the incident and exit media are the air and the sapphire substrate, respectively. The gold film thicknesses are set as (a) 0.0, (b) 2.4, (c) 4.4, (d) 8.5, (e) 13, and (f) 19 nm.

image file: c7cp05260j-f6.tif
Fig. 6 (a) Maximum absorption intensities of A, B and C excitons as well as (b) their corresponding incident angles (solid symbols) for the external reflection. The quasi-Brewster's angles as a function of the gold film thickness are shown by open symbols in (b).

It is found from Fig. 6a that A and B excitons give the maximum absorption values at a gold film thickness of 2.4 nm, which is similar to that in the case of normal incidence of internal reflection (open symbols in Fig. 3a). Nevertheless, the C exciton exhibits a different variation trend with the gold film thickness. To unveil this discrepancy, Fig. S3 in the ESI gives the absorption and reflection spectra of different thicknesses of pure gold films. It is seen from Fig. S3a (or d) (ESI) that the absorption (or reflectance) of gold film at the A excitonic resonance wavelength of 660 nm gradually increases (or decreases) with decreasing thickness, which is in line with the optical scattering and antireflection effect.15 Accordingly, the MoS2–Au hybrid structure with a thinner gold film contributes to a stronger excitonic absorption. At the resonance wavelength of 613 nm (Fig. S3b in the ESI), the absorption of 13 nm gold film is a little larger than that of the 8.5 nm gold film. This may account for the fact that the B excitonic resonance absorption gives an extremum value at a gold film thickness of 13 nm (see Fig. 6a).

At the resonance wavelength of 426 nm, as shown in Fig. S3c (ESI), the absorption intensity decreases with thickening of the gold film up to 8.5 nm and increases thereafter. Even if the gold films at 13 and 19 nm have smaller absorption intensities than that at 2.4 nm, their reflection intensities are far stronger than that of the latter (Fig. S3f in the ESI). This would allow more reflected photons to participate in the interaction with the C exciton of monolayer MoS2. Besides, monolayer MoS2 has the largest extinction coefficient κ at 426 nm (Table 1), thus the absorption intensity of C exciton in Fig. 6a is increased when the gold film is thicker than 8.5 nm.

We can further observe from Fig. 6b that the θm,C value fluctuates around its corresponding quasi-Brewster's angles θB,C, whereas the θm,A (or θm,B) value gradually deviates from its corresponding quasi-Brewster's angles θB,A (or θB,B) with reduced gold film thickness. This change could be attributed to the dependencies of the extinction coefficient κ on wavelength and film thickness (Table 1). Taking the monolayer MoS2 as an example, we tentatively tuned the κ value of MoS2. It is found that the θm,C value decreases from 57.5° to 0° as the κ value at 426 nm reduces from 3.45 to be smaller than 2.45. When the κ value at 660 (or 613) nm is larger than 4.02 (or 3.91), the θm,A (or θm,B) value is no longer a zero but gradually approaches the quasi-Brewster's angle as the κ value increases to 5.52 (or 5.11). This change of θm induced by tuning the κ value of MoS2 is similar to that induced via the dependence of κ value on gold film thickness. We can see from Table 1 that the extinction coefficients κ of the gold film at resonance wavelengths of 660 and 613 nm gradually increase as the gold film increases in thickness. Nonetheless, the κ value of gold film at 426 nm fluctuates with thickness. Therefore, the θm,A (or θm,B) value of MoS2–Au hybrid films gradually approaches its corresponding quasi-Brewster's angles θB,A (or θB,B), whereas the θm,C value fluctuates around its corresponding quasi-Brewster's angles θB,C with thickening of the ultrathin gold film (see Fig. 6b). Because the excitation source in the calculation model is non-laser light, the above phenomena should not involve the thermal effects.

Conclusions

In summary, the impacts of ultrathin gold films on the excitonic optical properties of monolayer MoS2 have been studied. The A, B and C excitons in MoS2–Au hybrid films maximize their respective absorption peaks at total reflection. Because of the optical scattering effect induced by the ultrathin gold film, the incident angle of maximum excitonic absorption deviates from the SPR angle, and this deviation becomes smaller and smaller as the gold film increases in thickness. Accordingly, the maximum absorption intensity of each exciton at total reflection gradually increases with thickening of the gold film. For external reflection, the maximum absorption intensities of A and B excitons in hybrid films mainly decrease with thickening of the gold film, whereas that of the C exciton decreases with thickening of the gold film up to 4.4 nm and increases thereafter. Moreover, possibly due to the dependencies of extinction coefficients on the resonance wavelength and gold film thickness, the incident angle at which the C exciton gives its maximum absorption fluctuates around its corresponding quasi-Brewster's angle, while that of the A or B exciton gradually deviates from its corresponding quasi-Brewster's angle with reduced gold film thickness. These findings may provide insights into the interplay between monolayer MoS2 and ultrathin metal films and be useful to the material parameters for designing novel two-dimensional optoelectronic devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We acknowledge the financial support by the National Natural Science Foundation of China (No. 11647043) and the Tianjin University of Commerce (No. 2016ZT010328). We are also grateful to Dr Yong Liang Zhang from the Hong Kong Polytechnic University for helpful discussions.

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Footnote

Electronic supplementary information (ESI) available: Dispersion curves of hybrid structures with gold film thickness changing from 35 to 55 nm, variations of A, B and C excitonic absorption with respect to incident angle for the internal reflection, absorption and reflection spectra of different thicknesses of pure gold films for the external reflection. See DOI: 10.1039/c7cp05260j

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