MoS2 flakes have attracted much attention due to their attractive properties. Optical reflectance techniques can prove to be very powerful techniques to study some of the thickness dependent physical properties, e.g. A and B excitonic peaks. Here, we measured reflection spectra of MoS2 flakes on SiO2/Si substrate in the broad wavelength range of 400-800 nm and studied the emission wavelength of A and B excitons as a function of the layer number. Moreover, we calculated the optimized SiO2 thickness to avoid the substrate-related interference effect influencing the investigation of exciton properties.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
With the exfoliation technique for preparing atomically thin sheets , layered two dimensional (2D) materials have attracted great interest due to their excellent physical properties and remarkable device prospects [1,2]. There is a kind of representative 2D materials, transition metal dichalcogenides (TMDs), with representative materials as molybdenum disulphide (MoS2) [3,4]. A single monolayer of MoS2 consists of an atomic plane of a Mo sandwiched between two S atomic planes. Multilayer MoS2 have layers weakly stacked by van der Waals force with a S-Mo-S covalently bonded sandwich in each layer. Such stacked layer structure makes properties of MoS2 flakes dependent on its thickness, or layer number (denoted as N) [5–7].
Several optical techniques have been used to probe N-dependent optical properties of MoS2 flakes, such as Raman spectroscopy [6–8] and photoluminescence (PL) . Raman spectrum consists of E12g and A1g modes with a peak distance between these two modes used to identify the layer number of 1L-4L MoS2 layers [6,7], meanwhile contains ultralow-frequency shear (S) and breathing (B) modes with their frequencies used to identify the layer number of 1L-10L MoS2 layers [7,8]. PL spectrum shows the strong contrast of PL efficiency between 1L and multilayer MoS2 sheets due to the feature of transferring from indirect-bandgap in bulk material to direct-bandgap in 1L sheet . Although A and B exciton emission peaks can be also displayed in PL spectrum, they coincide with the direct-bandgap PL peak in 1L sheet and separate from the indirect-bandgap PL peak with increasing layer number but with reduction in strength of 102-103 orders of magnitude , which are all not conducive to studying exciton properties. Recently, optical reflection and transmission spectra have proven to be another powerful technique to study 2D materials [9–14]. Frisenda R et al  showed a versatile optical microscope setup to carry out differential reflectance and transmittance spectroscopy in TMDs to determine their number of layers and to characterize their fundamental optical properties such as excitonic resonances. In this paper, we measured reflection spectra of NL MoS2 flakes on SiO2/Si substrate in the broad wavelength range of 400-800 nm and studied their exciton properties as a function of N by utilizing the experimental setup with higher spectral resolution for samples with sizes in the micron range. Moreover, we noticed that the substrate-related interference effect influenced excitonic features collected from MoS2 flakes. Here, we can optimize reflectivity curves of MoS2 flakes to investigate their exciton properties by selecting proper SiO2 thickness.
2. Materials and methods
MoS2 flakes were prepared from monolayer to multilayer on SiO2/Si substrate with different SiO2 thickness by micromechanical cleavage of a bulk MoS2 crystal (2D semiconductors Inc.). We selected 3 types of most commonly used SiO2/Si substrates with SiO2 thickness of 89, 100 and 302nm. The thicknesses of the SiO2 capping layer were measured by a spectroscopic ellipsometer (J A Woollam, M-2000DI) with repeatability of 0.5 nm. MoS2 flakes were easily seen by naked eyes via microscope. Their layer number were pre-estimated by the ultralow-frequency Raman measurements of S and B modes, as previously done for MoS2 flakes . Due to the micron-sized samples, reflection spectrum measurements were performed in a backscattering geometry using a Jobin-Yvon HR800 micro-Raman system, which was equipped with liquid nitrogen cooled charge coupled device and the objective of 50X (NA = 0.45). The size of samples was above 5 μm to ensure the accuracy of subsequent tests. Tungsten halogen lamp was used as a light source, with the spot size below 2 μm. A Semrock mirror with a high reflectivity up to 99% in the range from 350 to 1100 nm was used as a reference to the light intensity from lamp source. The reflection spectra were measured from the samples, the bare substrates and the Semrock mirror in the broad wavelength range of 400-800 nm. The 600 lines per mm grating was used, which enables one to have each CCD pixel to cover 1nm. The best reflected light signal was achieved by focusing the microscope to get maximum peak intensity. The reflectivity of MoS2 flakes on SiO2/Si substrate were obtained by dividing the reflection spectra from the samples by that from the Semrock mirror.
We first measured reflection spectra of MoS2 flakes on SiO2/Si substrate with 100nm SiO2 thickness. Figure 1(a) shows the reflectivity curves of 1L-5L, 9L and 10L MoS2 on 100nm SiO2/Si substrate and of bare substrate in the range of 400-800 nm. (The optical images and Raman spectra of samples are presented in the Appendix.) The outlines of these reflectivity curves of MoS2 flakes are similar on which there are many dips by contrast of the smooth reflectivity curve of bare substrate. Because both MoS2 flakes and SiO2 layer are penetrable by incident and reflected lights in reflection spectrum measurements, the incident lights passed through them and finally were absorbed by the Si layer, but the reflected lights were collected from interfaces of Air/NL-MoS2, NL-MoS2/SiO2 and SiO2/Si. The dips in the reflectivity curves of MoS2 flakes provide an effective measure of absorbance of MoS2 flakes, which are the reciprocal of absorption peaks of gap transitions.
3. Results and discussion
A and B excitons arise from direct gap transitions at the K point due to a spin–orbit split valence band and degenerate conduction band at the K point, with the energy difference as an indication of the strength of spin-orbit interaction [5,15,16]. According to previous reports about band structure and exciton transitions in MoS2 flakes [5,15,16], the dips of our reflectivity curves in the range of 550-700nm derive from the absorption of A and B excitons. The energy of B exciton is higher than A exciton with the energy difference approximate to 0.15 eV  or 50 nm , and their energy depend on the layer number of MoS2 flakes , all of which can be easily shown in our reflectivity curves with wavelength as horizontal axis. In order to obtain the more detailed emission wavelength of A and B excitons for different N of NL MoS2, we showed reflectivity curves of bare substrate and MoS2 flakes in the range of 550-700nm in Fig. 1(b). The curves were offset for clarity. The A and B excitons in 1L MoS2 locate at 652 nm and 603 nm respectively. Both of them show blueshift as N increases. Because the dips due to excitons are not so sharp, we didn’t read directly the position of A and B excitons. We inverted reflectivity curves by the calculation of 1/x. In the inverted curve, the data of vertical axis were multiplied a lot, and A and B excitonic peaks became a lot sharper. We obtained the position of A and B excitons by using the “peak searching” function in the Labspec 6 software and the error bar for that is ± 1nm. The emission wavelength of A and B excitons from 1L-5L, 9L and 10L MoS2 were summarized by red and blue circles respectively in Fig. 1(c). There is a big shift in the wavelength of A exciton from ~652 nm for N = 1 to ~662 nm for N = 2. The wavelength spacing is 10 nm between 1L and 2L. However, the shift of A exciton becomes smaller with N increases, which is gradual from ~662 nm for N = 2 to ~665 nm for N = 10. The B exciton shifts more slowly from 1L to 2L than the A exciton. It shifts from ~603 nm for N = 1 to ~605 nm for N = 2, and then it gradually shifts from ~605 nm for N = 2 to ~606 nm for N = 10. Because the energy difference between A and B direct excitonic transitions is due to the spin-orbital splitting of the valence band at the Brillouin zone K point, the position change of A and B excitons as a function of layer number is derived from the change of direct excitonic states with layer thicknesses. Based on the photoluminescence spectra of 1-6L MoS2 and WS2 samples in the reference , frequency shifts of A and B excitonic peaks are relatively easy to be seen from 1L to 2L. Especially, A exciton movement is more obvious from 1L to 2L maybe due to the influence of the emerging indirect emission peak on the side of it in 2L.
Due to the SiO2 thickness of SiO2/Si substrate as one of the important influence factors in reflection spectra, we further studied the reflectivity curves of MoS2 flakes on SiO2/Si substrate with 89nm SiO2 thickness and 302nm SiO2 thickness. (The optical images of samples are presented in Appendix in Fig. 7.) Fig. 2(a) shows A and B excitons of 1L-3L MoS2 on 89nm SiO2/Si substrate in the range of 550-700nm. The curves were offset for clarity. These reflectivity curves are similar with those of 1L-3L MoS2 on 100nm SiO2/Si substrate. Both A and B excitons shift toward longer wavelengths with increasing N. The position of A and B excitons from 1L-3L MoS2 on 89nm SiO2/Si substrate were summarized in Fig. 2(b) by red and blue dotted circles respectively, compared with those on 100nm SiO2/Si substrate plotted by red and blue circles respectively. The wavelength difference in two cases is smaller than 2nm, which is close to our test error limit. However, the reflectivity curves of MoS2 flakes with 302nm SiO2 thickness changed dramatically as shown in Fig. 3(a), compared with the former reflectivity curves with 89nm and 100nm SiO2 thickness. There are three dips in 3L MoS2 on 302nm SiO2/Si substrate in the range of 550-700nm, which means new interference effects occur related with SiO2 thickness.
In order to manifest the above phenomena, we used the multiple reflection interference method [10,11] to calculate the reflectivity curves of 3L MoS2 on 89nm, 100nm and 302nm SiO2/Si substrates in the range of 550-700nm, as shown in Fig. 3(b). In the Air/3L-MoS2/SiO2/Si structure, the incident light and the emergent light undergoes multiple reflection at the interfaces of Air/3L-MoS2, 3L-MoS2/SiO2 and SiO2/Si, and optical interference within each medium. We assume normal incidence perpendicular to the MoS2 atom plane, the reflectivity curves were calculated by using transfer matrix formalism based on classical electrodynamics and Fresnel’s law. Details of calculations are described in Appendix. In Fig. 3(b), there are two dips in 3L MoS2 on 89nm and 100nm SiO2/Si substrate but three dips in 3L MoS2 on 302nm SiO2/Si substrate, which is consistent with the experimental results.
We further calculated the reflectivity of MoS2 flakes for different N. Figures 4(a)–4(d) are the color contour plots of the reflectivity of bare substrate and 1L, 3L, 10L MoS2, respectively, as function of both SiO2 thickness of 0-500nm and reflection wavelength of 500-750nm. We can see bright areas and dark areas appear alternately in the reflectivity of bare substrate, as shown in Fig. 4(a). Due to the SiO2 layer tuned as an antireflection coating [11,12], MoS2 flakes become visible in these dark areas. The first dark area is around dSiO2 = 50~120 nm. The contained 89nm and 100nm is used in our experiment. The second dark area is around dSiO2 = 200~300 nm. The contained 300 nm is used in our experiment. The pink dotted lines were marked to show these three used SiO2 thickness.
In Fig. 4(b)-(d), the shapes of bright areas and dark areas change a lot compared with bare substrate due to the absorption of excitons. The shape changes are more noticeable as N increases, which is consistent with the experimental results shown in Fig. 1(a). The green dotted lines were marked to show the emission wavelength of A and B excitons in Fig. 4(b)-(d). Due to the first dark area nearly parallel to the wavelength axis, we can easily identify A and B excitons for the fixed 89nm and 100nm SiO2 thickness. However, other dark areas have non-negligible angles with the wavelength axis due to the phase changes in different wavelengths caused by thicker SiO2 thickness in the interference process [11,12]. The higher the order of dark area is, the larger the angle is. Thus, for the fixed 302nm SiO2 thickness, we fail to identify A and B excitons. The optimized SiO2 thickness is 50-100 nm to investigate the exciton properties of MoS2 flakes by reflectivity curves. Using the similar method, we have showed the optimized optical matching between 1L to 5L graphene flakes and SiO2 layer in terms of interference effect , which opens the possibility to exploit the enhancement of anti-reflection coating with the nanoscale thickness. In addition, we have found similar results in the research of N dependent excitons properties in other TMDs  and related research can be extended to N dependent optical properties of anisotropic 2D flakes , all of which prove optical reflectance techniques to be very powerful techniques to study 2D materials.
We demonstrated a simple and fast technique to probe reflectivity of MoS2 flakes as a function of layer number and studied the emission wavelength of A and B excitons dependent on layer number. However, the substrate-related interference effect was very likely to hamper the detection of excitonic features collected from MoS2 flakes. Based on our results, the optimized SiO2 thickness is 50-100 nm to investigate the exciton properties of MoS2 flakes by reflectivity curves.
5.1 The optical images and Raman spectra of MoS2 flakes on a SiO2/Si substrate with 100nm SiO2 thickness
We prepared two sets of 1L-5L, 9L, 10L MoS2 flakes on 100nm SiO2/Si substrate by micromechanical cleavage of a bulk MoS2 crystal. Samples of different layers are stacked in the same position to avoid measurement errors as much as possible in the reflection spectra measurements, as presented in Fig. 5. Figure 6 shows Raman spectra of MoS2 flakes. Fig. 6(a) shows S and LB modes located below 60cm−1 in MoS2. The S and LB modes do not exist in 1L MoS2. With increasing N, the frequency of the LB mode decreases and that of the S mode increases, as shown in Fig. 6(c). The S and LB vibrations are an intrinsic property of NL MoS2. The frequencies of these modes are linked with N by a linear chain model (LCM) in which each atom layer is considered as a single ball and there is mutual coupling between them. Therefore, the S and LB modes can be utilized to identify N of NL MoS2 flakes. The layer number of samples in this paper were pre-estimated by the Raman measurements of S and B modes. Fig. 6(b) shows that E12g and A1g modes are respectively located at ∼ 380cm−1 and ∼ 402cm−1 in MoS2. With increasing N, the frequency of the A1g mode decreases and that of the E12g mode increases, as shown in Fig. 6(d).
5.2 The optical images of MoS2 flakes on SiO2/Si substrate with 89nm and 302nm SiO2 thickness
5.3 The reflectivity calculation in an Air/NL-MoS2/SiO2/Si structure
In the paper, we used the multiple reflection interference method to calculate the reflectivity curves of MoS2 on SiO2/Si substrates in the range of 500-750nm and studied substrate-related interference effect. The Air/NL-MoS2/SiO2/Si structure contains air (), NL-MoS2 ( , ), SiO2( , ), Si( , ), where and (i=0,1,2,3) are the complex refractive index and the thickness of each medium. The light in this four-layer structure undergoes multiple reflection at the interfaces and , and optical interference within the medium , as shown in Fig. 8(a). The calculation is based on classical electrodynamics and on the transfer matrix formalism. We assume normal incidence in the z direction. The transmission and reflection of total electric and magnetic fields in the four-layer structure can be described by characteristic matrices and , where describes the propagation across the interface from to layer applying the boundary conditions, and denotes the propagation through the layer at depth . The transverse electric field component and transverse magnetic field component are all perpendicular to the graphene c-axis, and they are associated by . and can be expressed as follows:
The incident electric field component passes through interfaces of Air/NL-MoS2, NL-MoS2/SiO2 and SiO2/Si, and finally is absorbed by the Si layer. Meanwhile, the reflective electric field component is collected from each interface and finally transmits into the Air. Schematic diagram of the electric field component transfer process is shown in Fig. 8(b). The total transfer matrix equation in this four-layer structure is:
The reflectivity can be expressed as: , where . and are incident and reflected electric field component into or out of the NL-MoS2 flakes. The calculated values of the bare 100nm SiO2/Si substrate (with N=0, denoted as black curve) and 1L-5L, 9L, 10L MoS2 flakes on 100nm SiO2/Si substrate (denoted as colorized curves) with dSiO2=100 nm and λ=500-750 nm are showed in Fig. 9 to compare with the measured values. The calculation results are basically consistent with the experiment. In fact, it was limited when we take as the complex refractive index of bulk MoS2. Some articles have reported that the complex refractive index of bulk MoS2 is different from that of 1L MoS2 . However, quantitative analysis of the calculated emission wavelength of A and B excitons of ultrathin NL-MoS2 flakes on SiO2/Si substrate was difficult because there exist abundant features in the λ dependent for MoS2 flakes and of MoS2 flakes itself significantly depends on N due to the indirect-to-direct transition from multilayer to 1L. We can only give a qualitative explanation about the energy difference between A and B direct excitonic transitions. Due to the spin-orbital splitting of the valence band at the Brillouin zone K point, the emission wavelength of A and B excitons as a function of layer number was derived from the change of direct excitonic states with layer thicknesses.
On the other hand, the calculations revealed that there is an optimized SiO2 thickness to avoid substrate-related interference effect influencing the investigation of exciton properties. The optimized SiO2 thickness is 50-100 nm.
Youth Project of the National Natural Science Foundation of China (11504077); National Natural Science Foundation of China (61774053); Youth Project of Hebei Province Natural Science Foundation (A2017201012); Key Project of Hebei Province Department of Education Fund (ZD2017007).
The authors are grateful to P.H.Tan for the Raman spectra measurements.
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