Self-Hybridized Exciton-Polaritons in Sub-10-nm-Thick WS₂ Flakes: Roles of Optical Phase Shifts at WS₂/Au Interfaces

Abstract

Exciton–polaritons (EPs) can be formed in transition metal dichalcogenide (TMD) multilayers sustaining optical resonance modes without any external cavity. The self-hybridized EP modes are expected to depend on the TMD thickness, which directly determines the resonance wavelength. Exfoliated WS₂ flakes were prepared on SiO₂/Si substrates and template-stripped ultraflat Au layers, and the thickness dependence of their EP modes was compared. For WS₂ flakes on SiO₂/Si, the minimum flake thickness to exhibit exciton–photon anticrossing was larger than 40 nm. However, for WS₂ flakes on Au, EP mode splitting appeared in flakes thinner than 10 nm. Analytical and numerical calculations were performed to explain the distinct thickness-dependence. The phase shifts of light at the WS₂/Au interface, originating from the complex Fresnel coefficients, were as large as π/2 at visible wavelengths. Such exceptionally large phase shifts allowed the optical resonance and resulting EP modes in the sub-10-nm-thick WS₂ flakes. This work helps us to propose novel optoelectronic devices based on the intriguing exciton physics of TMDs.

1. Introduction

Transition metal dichalcogenides (TMDs) have long attracted the attention of researchers due to their fascinating physical properties for optoelectronic device applications, including sizable bandgap energies, large absorption coefficients, high electron mobility, and superior mechanical flexibility [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. In particular, it has been noted that the exciton–photon interactions dominate the optical responses of TMDs even at room temperature. In two-dimensional (2D) TMD layers, strongly bound electron-hole pairs (excitons) are generated by the weak dielectric screening and strong geometric confinement [1,2,3,4,5,6,7,8,9,10,11]. The exciton binding energy in TMDs is as large as hundreds of meV, which is one to two orders of magnitude larger than those of conventional semiconductors [1,2,3,4,5,6]. Integration of TMDs with photonic nanostructures can broaden our understanding of exciton physics, providing valuable insights into excitonic devices [4,5,6]. Moreover, strong coupling between excitons and photons leads to the formation of exciton–polaritons (EPs) in TMDs integrated with optical resonators [5,6]. These half-light half-matter quasiparticles allow us to investigate intriguing physical phenomena [16,17,18] and realize novel functional devices [19,20,21].

TMD multilayer flakes, with exceptionally large refractive indices, can sustain Fabry–Pérot (FP) resonance modes without any external cavity [8,9,10,11,12]. Consequently, a variation in the thickness significantly alters the apparent color of the TMD flakes due to the absorption and interference effects. Such unique optical characteristics enable the rapid and reliable determination of the TMD thicknesses using optical microscopy (OM) [13]. Moreover, coupling of excitons and the cavity photons in TMDs results in the formation of self-hybridized EPs [8,9,10,11,12]. Consequently, exciton–photon anticrossing behaviors appear at specific wavelengths along with splitting of the hybridized EP modes to upper and lower polariton branches (UPB and LPB, respectively) in TMD multilayer flakes on reflective substrates [6,8,9,10] The wavelength showing such cavity-free EP mode splitting depends on the thickness of the TMD flakes, since the flake thickness directly determines the optical resonance wavelength [8,9,10]. The integration of TMDs with optical resonators requires complicated time-consuming fabrication processes which are obstacles for active research works and the development of excitonic devices. Therefore, cavity-free self-hybridized EPs provide a versatile approach to investigate excitonic effects in the optical characteristics of TMDs.

Among numerous TMDs, WS₂ is one of the most intensively investigated materials. Monolayer WS₂ has a direct bandgap of ~2 eV, while the bulk counterpart has an indirect bandgap of ~1.3 eV [22,23,24]. Since the bandgap is appropriate for visible-range applications, WS₂ is a strong candidate to realize high-performance optoelectronic devices [23]. Additionally, WS₂ is a promising material for valleytronic devices, due to its broken inversion symmetry and strong spin–orbit coupling [24]. Earlier reports have shown that the minimum thickness of a WS₂ flake on dielectric SiO₂ substrates showing UPB-LPB splitting is approximately 40 nm, which is less than ~1/10 of the exciton resonance wavelength in vacuum [8]. To our surprise, exciton–photon anticrossing behaviors appear even in sub-20-nm-thick TMDs on metallic layers [10]. The EP mode formation boosts the optical absorption in thin TMD layers, which has stimulated the development of high-efficiency ultrathin photovoltaic devices [14,15]. Despite these noteworthy features, the physical origin to determine the minimum thickness for EP mode splitting in TMDs has not been explicitly investigated.

In this work, we prepared exfoliated WS₂ multilayer flakes and investigated their optical characteristics. The apparent colors and the measured reflectance spectra of the flakes showed significant variation depending on the flake thickness, which originated from the strong coupling between excitons and cavity photons. In particular, the thickness-dependent spectral responses of the flakes on SiO₂/Si substrates and Au thin films were compared to study how the metal underlayers affected the optical resonance and resulting EP mode splitting. Analytical and numerical calculations were also performed to elucidate the physical origins.

2. Materials and Methods

Exfoliated WS₂ flakes were prepared on SiO₂ (300 nm)/Si wafers and Au (100 nm) thin films, as illustrated in the schematic diagrams in Figure 1a,b. Hereafter, the former and latter samples will be called WS₂/SiO₂/Si and WS₂/Au, respectively. The Au thin films were deposited on SiO₂/Si substrates using e-beam evaporation and then were delaminated from the original substrates to slide glasses using UV-curable prepolymer (NOA63, Norland) [25]. The SiO₂/Si substrates serve as ultrasmooth templates, and the stripped Au thin films have very flat surface (typical root-mean-square roughness: 0.7 nm) (see Figures S1 and S2 of Supplementary Materials). Such template-stripped Au thin films are beneficial for minimizing the roughness at the interface between the WS₂ flakes and Au thin films [25].

Optical reflectance spectra of flakes were measured using a homemade setup with an optical microscope (LV100, Nikon, Tokyo, Japan) and a spectrometer (Maya 2000 Pro, Ocean Optics, Dunedin, FL, USA). Reflected light from sample surface was collected using a 50-μm-diameter optical fiber (M50L02S-A, Thorlabs, Newton, MA, USA), which enabled us to obtain the spectra from a selected area of several μm². The thickness of the flake was measured using an atomic force microscopy system (NX10, Park Systems, Suwon, Korea).

3. Results and Discussions

As shown in Figure 1a,b, the thickness of the WS₂ flake (d_WS2) significantly affects the apparent color of the flakes. It should be also noted that the flakes with identical d_WS2 values (e.g., 4, 7, and 20 nm) exhibit distinct colors depending on the underlying layers (SiO₂/Si and Au). Incident light undergoes reflection and transmission at the interface of two neighboring media in WS₂/SiO₂/Si and WS₂/Au. The amplitude and phase of light at each medium are determined by the Fresnel equations [13,26]. The superposition of all the reflected waves at the boundaries, i.e., the multiple-beam interference, determines the reflectance spectra and colors of the WS₂ flakes [26]. Even though the absorption coefficient of WS₂ is exceptionally large compared with those of conventional semiconductors, thin flakes allow the transmission of incident light [23]. As a result, the underlying layer as well as d_WS2 can affect the apparent color of the flake, as shown in Figure 1a,b.

Figure 2a–e shows the calculated and measured reflectance spectra of WS₂ flakes. The calculated spectra were obtained using transfer matrix method (TMM) based on the refractive indices of the materials in the literature [27,28]. The spectra of stand-alone WS₂ flakes are also calculated for comparison with those of WS₂/SiO₂/Si and WS₂/Au (Figure 2a). All the spectra exhibit local minima at 620 and 510 nm, which correspond to the A and B exciton resonance wavelengths of multilayer WS₂, respectively (see dashed lines in Figure 2a–e) [8,9,10,23] WS₂ flakes with d_WS2 > 40 nm exhibit thickness-dependent reflectance dips in addition to the exciton resonance dips (Figure 2a–c). These thickness-dependent reflectance dips originate from EP mode splitting since WS₂ multilayer flakes can work as optical cavities without external cavities [8,9,10]. The EPs can be formed when the wavelengths of the exciton resonances and cavity modes are close to each other. For an intuitive understanding, FP cavity modes in dielectric thin films can be regarded as standing waves. Thus, the minimum d_WS2 for the FP cavity mode is expected to be either λ/2n_WS2 or λ/4n_WS2 (n: real part refractive index of WS₂) [26]. Considering the large refractive index of WS₂, the minimum d_WS2 allowing the FP resonance can be less than 100 nm. Wang et al. reported the EP mode splitting from WS₂ flakes with d_WS2 > 40 nm on glasses [8]. Our results also show that the exciton–photon anticrossing occurs in sub-100-nm-thick WS₂ flakes (Figure 2a–c). Interestingly, the EP-mediated reflectance dips appear in WS₂/Au even with d_WS2 < 40 nm (Figure 2c). Zhang et al. reported similar thickness-dependent reflectance spectra from WS₂ multilayer flakes on Au thin films [10].

Figure 2d,e shows the measured reflectance spectra of WS₂/SiO₂/Si and WS₂/Au with several d_WS2 values, respectively. These experimental data well reproduce the key features of the calculation results in Figure 2b,c. The samples with d_WS2 of 50~60 nm show two EP-induced reflectance dips in both WS₂/SiO₂/Si and WS₂/Au, similar to others’ reports. [8,9,10] Hereafter, the dips at the wavelength (λ) < 600 nm and λ > 600 nm will be called as UPB- and LPB-related dips, respectively (see gray circles in Figure 2b–e). The UPB- and LPB-related reflectance dips also appear in the stand-alone flakes (Figure 2a). This suggests that the EP mode splitting observed in the flakes with d_WS2 of several tens of nm is originated from the self-hybridization of the excitons and the FP cavity photons [8,9,10] The reflectance spectra of WS₂/SiO₂/Si with d_WS2 = 8, 20, and 27 nm exhibit exciton resonance-mediated dips (see dashed lines in Figure 2d). These spectra show a gradual increase in the reflectance at long wavelengths above 700 nm, which depends on the thickness of the SiO₂ layer (see Figure S3 of Supplementary Materials). Thus, these long-wavelength features can be attributed to thin film interference in 300-nm SiO₂/Si substrates. In WS₂/Au with d_WS2 of 10 nm, a broad UPB-induced dip appears at 500 nm < λ < 600 nm and a LPB-induced dip appears slightly above the A exciton resonance wavelength (see gray triangles in Figure 2c,e). WS₂/Au with d_WS2 of 21 and 25 nm shows very broad UPB-mediated dips at λ~600 nm and weak LPB-related dips at λ > 600 nm (see gray triangles in Figure 2c,e). These measured reflectance dips of WS₂/Au agreed well with the calculation data (Figure 2c). This suggests that self-hybridized EP mode splitting can be formed in WS₂ flakes with d_WS2 much smaller than λ/4n_WS2.

Figure 3a,b shows that the measured and TMM-calculated reflectance spectra of WS₂/Au with d_WS2 ≤ 30 nm well agreed with each other. This suggests that the samples were well prepared, as intended. In particular, the good agreement between the experimental and calculated results should be attributed to the ultrasmooth surface of the template-stripped Au thin films. In the calculations, the refractive indices of the bulk WS₂ in Ref. [28] were used, since most of the flakes considered in this work were thicker than several layers. The UPB-related dips exhibit red-shift as increasing d_WS2 and they merge with the A-exciton dips. The LPB-related dips appear near the A exciton wavelength and exhibit red-shift as increasing d_WS2. From the measured and calculated data, the Rabi splitting energy of WS₂ flakes with d_WS2 < 50 nm on Au was estimated to be ~180 meV, which is somewhat smaller than those of flakes with d_WS2 > 50 nm reported in literature: ~270 meV in Ref. [8] and ~235 meV in Ref. [9] (see Figure S4 of Supplementary Materials). Figure 2c and Figure 3a,b clearly show that the EP mode dips can appear in even sub-10-nm-thick WS₂ flakes on Au. Such thickness is much smaller than λ/4n_WS2. Therefore, the simple analogy between the FP cavities and the standing waves in air columns cannot satisfactorily explain the minimum d_WS2 forming the EP modes in WS₂ flakes.

The electric field (E-field) distributions in WS₂/SiO₂/Si and WS₂/Au can be obtained using finite-difference time-domain (FDTD) simulation, as shown in Figure 4a–d. The horizontal axis, z, represents the position along the direction perpendicular to the sample surface. The origins of z were chosen at the WS₂/SiO₂ and WS₂/Au interfaces for WS₂/SiO₂/Si and WS₂/Au, respectively. The regions between the dashed lines represent the WS₂ flakes with d_WS2 = 70 nm for Figure 4a,b and d_WS2 = 20 nm for Figure 4c,d. The left sides of the WS₂ regions indicate the underlying SiO₂ (300 nm) and Au (100 nm) layers for WS₂/SiO₂/Si (Figure 4a,c) and WS₂/Au (Figure 4b,d), respectively. The right sides of the WS₂ flakes indicate air. The E-field distributions were obtained at wavelengths where the local minima of the reflectance appear (Figure 2b,c). The field distribution for WS₂(70 nm)/SiO₂/Si at λ = 580 nm, corresponding to UPB, is similar to the fundamental-mode standing wave in a pipe opened at both ends (Figure 4a). At λ = 650 nm, corresponding to LPB, the WS₂/SiO₂ interface looks like the antinode of a standing wave, but the other antinode is in air rather than the WS₂ surface. The field distribution for WS₂/Au can be compared to the standing wave pattern of a one-side-closed air column. In the cases of WS₂(70 nm)/Au at λ = 555 (UPB) and 630 nm (LPB), the WS₂/Au interface is similar to the node of a standing wave, but the antinode is in air (Figure 4b). The E-field exponentially decays in the Au layer due to the absorption and the decay length is determined by the penetration depth of light in Au (for example, 50 nm at λ = 600 nm) [29].

The d_WS2 of 20 nm is only ~1/10 of the wavelength of visible light, even if the large refractive index of WS₂ (4~5) is considered. Thus, the magnitude of the E-field does not change much in the 20-nm-thick WS₂ flakes (Figure 4c,d). As shown in Figure 4c, a large E-field appears in the 20-nm-thick WS₂ flake on SiO₂/Si under 600-nm-wavelength light illumination. Since the absorption is proportional to the square of the E-field, the large E-field increases (reduces) the absorption in the flake (reflectance), as shown in Figure 2b,d. In WS₂(20 nm)/Au, the local minima in the reflectance appear at λ = 600 and 700 nm (Figure 2c). The magnitude of the E-field in the flake at λ = 600 nm is smaller than that at λ = 700 nm (Figure 4d). Since the optical absorption depends on the imaginary part of the permittivity of the medium as well as the E-field, the smaller reflectance of WS₂ (20 nm)/Au at λ = 600 nm seems to result from the very large absorption coefficient of WS₂ near the exciton resonance wavelength. At λ = 700 nm (LPB), the relatively large E-field increases the absorption in the WS₂ flake, resulting in a broad reflectance dip at λ = 700 nm (Figure 2c). Obviously, the cavity modes in WS₂/Au with d_WS2 < 40 nm are distinct from typical FP resonance modes, which can be regarded as standing waves.

As illustrated in Figure 5a, three kinds of optical phase shifts need to be considered to understand the reflectance spectra of WS₂/SiO₂/Si and WS₂/Au. The spectra of the multilayers can be explained by superposition of light reflected at each interface, i.e., multiple-beam interference [26]. First, the propagation-related phase shift of light, φ_WS2, is given by $2\frac{2\pi }{\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$n_{\mathrm{WS}2}$}\right.}{d}_{\mathrm{WS}2}$, as shown in Figure 5b. Clearly, φ_WS2 increases with increasing d_WS2. Notably, φ_WS2 of a 50-nm-thick WS₂ flake becomes larger than 2π. n_WS2 is as large as 4~5 in the visible wavelength range and, therefore, the propagation of light in the WS₂ flake with a thickness of only about ~1/10 of the vacuum wavelength results in a large φ_WS2 [23]. The Fresnel coefficient of the reflected light, r_ij, is $\frac{n_i-n_j}{n_i+n_j}$ (n_i and n_j are the refractive indices of the two media at the interface) [26]. If n_i and n_j are real, then r_ij, is also real and the phase of r_ij can be either 0 (r_ij ≥ 0) or π (r_ij < 0). However, the phase of r_ij can differ from either 0 or π for complex n_i and n_j. The Fresnel coefficient-related phase shifts at the WS₂/air (φ_Air), WS₂/SiO₂ (φ_SiO2), and WS₂/Au (φ_Au) interfaces are shown in Figure 5c. The optical phase shifts largely vary as a function of wavelength, depending on the complex refractive indices of WS₂ and Au. The magnitude of φ_Au is much larger than that of φ_Air and φ_SiO2 over a broad wavelength range since the complex refractive index of Au is very large [27,29].

Figure 5d shows the total round-trip phase shift of light in WS₂/Au, φ_Total, which is the sum of the interfacial Fresnel coefficient-related contributions (φ_Air and φ_Au) as well as the propagation-related change (φ_WS2). When φ_Total is equal to integer multiples of 2π, WS₂/Au can form resonant cavity modes. Such resonant modes boost the optical absorption in the WS₂ flakes, as featured as local minima in the optical reflectance spectra. The intersection points of the φ_Total and 2π(integer) curves represent the resonant cavity mode wavelengths for WS₂/Au. The intersection points in Figure 5d agree well with the local minima in the calculated and measured spectra in Figure 2c,e. For d_WS2 > 40 nm, φ_WS2 is larger than 2π at a certain wavelength, giving rise to the FP resonance modes and resulting EP-induced reflectance dips. Figure 5d also shows that the resonant modes can appear for d_WS2 < 30 nm. For example, WS₂/Au of d_WS2 = 10 nm possesses intersection points near λ = 600 nm, close to the A exciton resonance wavelength of WS₂. As a result, the reflectance spectra of sub-10-nm-thick WS₂ flakes on Au exhibit clear features of UPB and LPB modes, as shown in Figure 2c and Figure 3a,b. It should be noted that φ_WS2 alone cannot enable the resonant cavity mode in WS₂/Au of d_WS2 < 10 nm (Figure 5b). Since the negative φ_Au can reduce φ_Total to zero at certain wavelengths, WS₂/Au enables the coupling of excitons and cavity photons (Figure 5c,d). The considerable contribution of the interface phase shift can explain why the E-field distributions in WS₂/Au are distinct from the waveforms of simple standing waves (Figure 4b,d).

Figure 6a,b shows the measured reflectance spectra of WS₂ flakes on SiO₂/Si substrates with d_WS2 < 30 nm before and after deposition of 30-nm-thick Au thin films, respectively. The top Au layers significantly modify the reflectance spectra of the WS₂ flakes. Such very thin flakes without Au thin films cannot exhibit the EP mode splitting, and there are only exciton-related dips in the reflectance spectra (Figure 2b and Figure 6a). However, the Au-coated flake exhibits additional reflectance dips in addition to the exciton-related dips, indicating the self-hybridized EP modes (Figure 6b). Since the penetration depth of Au at λ = 600 nm is 50 nm, the 30-nm-thick Au thin films allow the transmission of incident light to the WS₂ flakes and the formation of optical cavity modes [29]. The TMM-calculated 3D reflectance plots of Au(30 nm)/WS₂/SiO₂/Si samples in Figure 6c clearly show the exciton–photon anticrossing behaviors for not only d_WS2 > 40 nm but also d_WS2 < 40 nm, similar to WS₂/Au (Figure 2c and Figure 3a,b). The additional dips in the measured spectra (Figure 6b) agree well with those in the calculations (Figure 6c). These experimental and calculated results suggest that the contribution of the large optical phase shifts at the Au/WS₂ interface is crucial for the formation of EPs in WS₂ flakes with d_WS2 < λ/4n_WS2. Many TMDs possess large real and imaginary parts of refractive indices [11,12,13,14,15,30], and hence the EP modes are expected in other kinds of very thin TMD layers. Furthermore, strong electronic interactions [31] as well as remarkable plasmonic effects [7,10] at TMD/metal interfaces can give rise to emergent physical phenomena of TMD/metal systems.

4. Conclusions

We investigated the reflectance spectra of exfoliated WS₂ multilayer flakes on SiO₂/Si substrates and template-stripped Au layers. On such reflective layers, the exceptionally large refractive indices of WS₂ gave rise to optical resonance modes in the flakes without external cavities. The reflectance spectra of the flakes exhibited not only exciton-resonance-mediated dips but also EP mode-induced dips, resulting from hybridization of the excitons and the cavity photons. EP mode splitting appeared in WS₂/SiO₂/Si with d_WS2 > 40 nm, whereas WS₂/Au, even with d_WS2 < 10 nm, exhibited EP mode splitting. Such a notable difference in the minimum thickness for the formation of EPs could be attributed to the large optical phase shifts at the WS₂/Au interface. These results suggested that integration of metal thin films and nanostructures with TMDs enabled control of the EP behaviors and resulting optical characteristics of the TMD/metal systems.