Transition metal dichalcogenides (TMDCs), and MoS2 in particular, belong to an extended family of atomic layered materials brought to life by the isolation of graphene [1,2]. A single layer of MoS2 turns out to be a new direct-gap semiconductor [3] that was used in the creation of a viable transistor [4]. It was shown that gating of electronic properties of several-layer MoS2 is possible [5]. In addition, it was found that optical properties of excitons in a monolayer of MoS2 can be controlled by electrical gating due to the optical Pauli blocking [6,7] and trion formation, while no influence of gating on the optical properties was observed for a bilayer MoS2 due to the fact that the exciton electrons and conduction electrons occupy different regions of phase space [6]. Tunable optical properties of atomic layered MoS2 were recently reviewed [8] while high optical anisotropy of MoS2 was discussed as a foundation for next-generation photonics [9,10].

To realize the full potential of a material in photonics, one should be able to perform its nanostructuring without the loss of important optical properties. Nanostructuring is necessary for fabrication of nano-optical devices, and it often brings about new exciting applications. For example, graphene nanoribbons opened the field of graphene plasmonics [11] that delivered novel selective optical sensors [12], while nanostructured hexagonal boron nitride nanoribbons yielded unusual phonon-polaritons [13]; see review [14]. However, the physics and technology of monolayer and bilayer MoS2 nanostructures for optoelectronic applications are still at its infancy. The experimental works are scarce [15,16], even though there is a large body of works devoted to a theoretical description of MoS2 nanoribbons. For example, using first-principles calculations, Li et al. discussed high stability and unusual electronic and optical properties of MoS2 nanoribbons [17]; Ataca et al. calculated their mechanical and electronic properties [18]; Dolui et al. discussed electric field effects on electronic properties of MoS2 nanoribbons [19]; tuning of electrostatic and magnetic properties of MoS2 nanoribbons by strain was discussed in Ref. [20]; and a promising thermoelectric effect in MoS2 nanoribbons was introduced in Ref. [21]. Many other theoretical works debated properties of MoS2 nanoribbons. At the same time, the number of experimental works on MoS2 nanoribbons is well below that dedicated to the theory.

The purpose of this paper is to address the lack of experimental works that measure the standard optical properties of MoS2 nanoribbons and to investigate the properties of excitons in these nanoribbons. To this end, we have fabricated sufficiently large arrays of bilayer MoS2 nanoribbons with different periodicities and measured their optical spectra in the standard reflection setup provided by a Brucker FTIR microscope. We also measured photoluminescence spectra of the nanoribbon samples in a confocal Raman installation. The main conclusion of our optical measurements is the existence of optically inactive “exciton-free” regions of very large sizes of ∼10nm (most probably near the edges of the ribbons) which significantly alters the optical properties of the studied bilayer MoS2 nanoribbons. Throughout the paper, by an “exciton-free” region we will imply a place where excitons do not provide a sizable contribution to an optical response for whatever reason. We also found that the “exciton-free” region can be electrically controlled by external gating. To the best of our knowledge, this is the first work where optical reflection was measured from sufficiently large MoS2 nanoribbon samples and changes of optical properties of several-layer MoS2 due to nanostructuring and gating voltage were elucidated.

In 1963, by analyzing excitons near the crystal boundary, Hopfield and Thomas came to the conclusion that there should be a layer near the boundary of a semiconductor where excitons cannot exist due to basic quantum mechanics arguments connected to the boundary conditions [22]. More accurately, they showed that there exists a repulsive potential for excitons near the boundary, which is difficult to calculate but easy to replace (for all practical purposes) with an infinite potential barrier of a finite distance inside the crystal [22]. They also suggested that the size of the exciton-free layer should be about twice the exciton Bohr radius for all semiconductors [22]. This layer in bulk crystals was referred to as a “dead” exciton layer [23].

The properties of a “dead” exciton layer in anisotropic semiconductors are more complicated. We recently studied a “dead” exciton layer near the surface boundary in bulk anisotropic MoS2 crystals [24]. By measuring and fitting the polarized optical reflections of MoS2 crystals polished parallel to the c-axis, we found that bulk MoS2 crystals near the edges perpendicular to the a- and b-axes have “exciton-free” regions of sizes of ∼10nm while the exciton-free regions near the edges perpendicular to the c-axis had sizes of ∼1nm [24]. This disparity was assigned to exciton anisotropy. The presence of “exciton-free” layers studied in Ref. [24] bulk MoS2 was supposed to be provided by Hopfield and Thomas theory [22]. At the same time the measured sizes of the “exciton-free” layers near the edges perpendicular to the a- and b-axes appeared to be significantly larger than the ones predicted by Hopfield and Thomas theory (which is supposed to be governed by the exciton Bohr radius [24]).

In monolayer or bilayer MoS2 samples, the in-plane optical anisotropy should be negligible as the properties of excitons in a- and b-directions should be the same. So, we can ask a question: what is the size of an “exciton-free” region (which is an analog of a “dead” exciton layer for bulk semiconductors) for atomically thin MoS2 samples? To address this question, we fabricated a set of reasonably large samples of MoS2 nanoribbons using exfoliated flakes of MoS2 that could be measured by standard optical microscopy (with an overall area of ∼50μm2) with different sizes of the ribbons (50 nm, 100 nm, 150 nm, and 200 nm) and the same filling factor of 50% (which implies that the size of the nanoribbons is equal to the nanoribbon spacing); see Section 6. One would assume that contributions of A and B excitons [7] to the optical response of these samples should be the same as the case that there are no plasmonic resonances of MoS2 nanoribbons in visible light. However, we found that this is completely opposite to what we observed in the experiments. Figure 1(a) depicts a typical studied bilayer MoS2 nanoribbon with width d in which the regions near the edges of width δ are optically “exciton-free” (shown by the red color). The presence of “exciton-free” edge regions in accordance with Hopfield and Thomas theory (which assumes that no excitons are possible near the boundary at some distance close to the boundary due to quantum mechanical arguments) implies that only the area of d−2δ of a MoS2 nanoribbon will contribute to the excitonic transitions. Hence, the smaller the size of nanoribbons, d, the smaller the contribution of overall excitonic transitions to the overall optical response will be. In simple terms, due to the presence of “exciton-free” edge regions of size δ the filling ratio for excitons will change from 0.5 to d−2δ2d. Using simple geometrical optic arguments (taking the ratio of the filling ratios), we conclude that for two different widths of nanoribbons, d1 and d2, produced with the same filling factor 50%, the ratio of the optical response near excitonic transitions should be r=1−2δd11−2δd2.(1)

It is worth stressing that this is an extremely rough estimate (in which many things were simplified considerably!). At the same time, if the “exciton-free” regions in nanoribbons are absent (δ=0), the ratio should be r=1 and we should see no change of the nanoribbon response as we change the size of the nanoribbons.

Figure 1(b) shows the experimental geometry in which the reflections from the samples were measured. MoS2 nanoribbons were fabricated on Si/SiO2 substrates that, in principle, allow electric gating of the samples (see Section 6). Figure 1(c) shows the optical image of the samples investigated in this study (d=50nm, 100 nm, 150 nm, and 200 nm) and provides scanning electron microscopy (SEM) images of the corresponding nanoribbons.

We measured the optical reflection and photoluminescence intensity near the excitonic transitions for the nanoribbon MoS2 samples with different d. For the sake of simplicity, we provide data for two samples with d=50nm and d=150nm. Figure 2(a) shows the ratio of the optical reflection of d=50nm nanoribbons over the optical reflection of d=150nm nanoribbons. We can see that, outside the excitonic A and B transitions in the 600–750 nm band, the reflections of nanoribbons with d=50nm and d=150nm are mostly the same (as the reflection ratio goes to 1 outside the exciton band). In the spectral band of excitonic A and B transitions, the sample with d=50nm produced much smaller optical reflection than that of the sample with d=150nm. The ratio of measured normal reflections r=R(MoS2_d=50nm)R(MoS2_d=150nm) reaches the minimum value of 0.55±0.05 at the position of the B exciton transition (wavelength of ∼610nm in a bilayer MoS2 placed on a SiO2/Si substrate) and 0.67±0.2 for the A exciton transition (wavelength of ∼665nm). This large difference of exciton contribution to optical response of d=50nm and d=150nm did not depend on the light polarization; see Fig. 2(a).

Using Eq. (1), we can evaluate the size of the optically inactive “exciton-free” region in bilayer MoS2 as δ=13.7±2nm for the B exciton and δ=10.5±0.5nm for the A exciton. These sizes are much larger than the “dead” regions expected for excitons in several-layer MoS2 which are supposed to be around ∼1nm (see Ref. [7]) and agree well with the sizes of “exciton-free” layers observed for the bulk MoS2 as discussed in Ref. [24]. The presence of optically inactive exciton regions should also affect the photoluminescence (PL) of the samples. Indeed, the smaller the size of the nanoribbons the smaller the intensity of the PL one would expect to observe due to the presence of exciton-free regions. Figure 2(b) shows that this is indeed the case: PL from nanoribbons with d=50nm is much smaller than that from nanoribbons with d=150nm of the same filling factor of 50%. Using Eq. (1) again, we find that the size of an exciton-free region evaluated from PL measurements for B excitons is ∼15nm and for A excitons is ∼17nm. Combining the optical reflection and PL data, we conclude that the “exciton-free” regions in bilayer MoS2 have sizes above 10 nm, which is a completely unexpected result. (The discrepancy between the size of “exciton-free” regions evaluated from PL and FTIR reflection measurements could be explained by much tighter focusing of a laser beam by a high aperture objective on the nanoribbons during an acquisition of PL as well as by exciton properties as explained below.)

Another unexpected result was observed in gating of the nanoribbons. It is well known that an optical response of excitons in a monolayer MoS2 can be changed by electrostatic gating due to Pauli blocking [7]. However, previous works found no change of optical response of excitons induced by gating voltage in large bilayer MoS2 flakes due to the fact that the exciton electrons and conduction electrons occupy different regions of phase space [6]. Hence, a bilayer MoS2 represents an excellent platform for studying the effect of electrostatic gating on the properties of excitons confined in nanoribbons as non-structured bilayer MoS2 flakes should show no changes of optical exciton response due to electrostatic gating. To investigate the effect of gating on the optical properties of the fabricated bilayer MoS2 nanoribbons, we made two gold contacts—the source and the drain—to the underlying MoS2 flake on which patterning was performed. Two contacts were necessary to bias Schottky barriers formed at gold–MoS2 interfaces. The overall electrical gating scheme is shown in Fig. 3(a); the optical scheme is provided in Fig. 3(b). As expected, we saw no gating for both nanoribbon samples (d=50nm and d=150nm) when both the source and the drain contacts were grounded (Vs=Vd=0); see Figs. 3(c) and 3(d). When we apply small bias to the source-drain contacts (Vs=−2V and Vd=0) we observed sizable gating (∼10%) for the sample with d=50nm bilayer MoS2 nanoribbons and virtually no gating for the sample with d=150nm nanoribbons; see Figs. 3(e) and 3(f), respectively. Remarkably, the gating of the bilayer MoS2 sample with d=50nm nanoribbons resulted in quadratic nature of gating shown in the inset of Fig. 3(e). This implies that the Pauli optical blocking is not responsible for this gating effect.

The fact that there exist “dead” exciton regions of sizes of ∼10nm in bilayer MoS2 nanoribbons (as it follows from reflection and PL measurements; see Fig. 2) is surprising. Indeed, anisotropy of excitons observed in bulk MoS2 [24] and the Hopfield–Thomas model [22] cannot explain the results obtained on bilayer MoS2 nanoribbons as the sizes of excitons in atomic MoS2 are just around 1 nm [7], which is much smaller than the observed “exciton-free” regions. Hence, there should be some other reasons why the optical response of excitons is suppressed for small size nanoribbons. There are several possible explanations for our results. One explanation suggests that excitons are created by light illumination near the edges of nanoribbons but the surface of MoS2 nanoribbons can introduce alternative, non-radiative mechanisms for excitons to recombine. The size of the dead region will then depend on the characteristic diffusion length and lifetime of the excitons. While this explanation provides a firm basis for PL results, it still requires some physical mechanism of suppressing exciton creation near the surface in order to explain the reflection results. Alternatively, one can assume that there exist “exciton-free” regions near the edges of the MoS2 nanoribbons conditioned by surface-state-induced band bending [25]. Even on a clean semiconductor surface, surface states may exist due to the termination of lattice at the surface. As a result, near the surface, the unpaired electrons in the dangling bonds of surface atoms will produce a narrow band in the bandgap [25]. For an n-type semiconductor (which MoS2 is), Fermi energy EF is closer to the conduction band (CB) while the surface states have Fermi energy EFsurface somewhere in the middle of the forbidden zone. In equilibrium between surface and bulk states, the Fermi energy of bulk and surface should be equal to each other, which leads to the band bending as shown in Fig. 4. There are two important consequences of the band bending produced by the surface states in our studied system. First, depletion regions (with small electron concentrations) arise near the edges of the nanoribbons. The sizes of these regions in typical bulk semiconductors (calculated using the Poisson equation) would be around 10 nm according to Ref. [25]. In a 2D case, the screening of the fields is less potent, and the size of the depletion regions could be much larger reaching ∼100nm. These depletion regions are important for an explanation of gating experiments; see below. Second, and more important, surface electric field Es appears near the edges of nanoribbons due to charge separation near the surface; see Fig. 4. This field suppresses the formation of excitons (as the exciton electron and hole will be dragged by the field in the opposite directions) and suggests non-radiative decay pathways of excitons near the edges of the nanoribbons. Suppression of exciton formation happens only in the field of large enough intensity. We recently discussed exactly this situation for p-n junctions induced in graphene by electrical doping with electron/hole densities of ∼1013cm−2 and found that the size of the area that can effectively break electron–hole pairs is around 10–20 nm [26], which is close to the sizes of exciton-free regions estimated from the optical measurements above.

Hence, we suggest the following picture of the “exciton-free” area near the edges in bilayer MoS2. The surface electric field (produced by band bending near the edges of the nanoribbons) separates electrons and holes produced by light. As a result, excitons near the edges become unstable or “dead” in a region of ∼10nm near the edges of a nanoribbon where the surface electric field is large enough to separate the electrons and holes [26]. This explains why we see much stronger light absorption at the excitonic wavelengths for the nanoribbons with larger sizes (150 nm) as compared to that of nanoribbons of smaller sizes (50 nm) despite the same filling ratio; see Fig. 2 and Eq. (1). It is clear that the surface field produced by band bending should affect photoluminescence more than reflection measurements. Indeed, transient excitons [27] (which are not yet separated by the surface fields) can still contribute to reflection but cannot contribute to PL (which requires stable excitons). Hence the contrast for PL is larger than that for reflection when we compare the 50 and 150 nm nanoribbons, as can be seen in Fig. 2.

Finally, we discuss gating of excitons observed in bilayer MoS2 nanoribbons. Gating of excitons in a MoS2 monolayer is connected to the Pauli blocking effect [6,7,27]. Figure 5(a) shows the bandgap structure of a monolayer MoS2 which is a direct bandgap semiconductor. A and B excitons appear due to the direct transitions near the K-point. A gating voltage applied to a monolayer of MoS2 affects the electron density at the K-point by reducing the phase space available for exciton formation [the yellow area corresponds to the electrons induced by gating, Fig. 5(a)]. This leads to sizable changes of optical reflection of a MoS2 monolayer under electrical gating [6,7]. In contrast to a MoS2 monolayer, a MoS2 bilayer is an indirect gap semiconductor whose bandgap structure is shown in Fig. 5(b). For a MoS2 bilayer, a gating voltage induces electron density far from K-point, as shown by the yellow area of Fig. 5(b). As a result, the optical properties of excitons in a MoS2 bilayer do not significantly change under the applied gating voltage [6]. At the same time, one can observe exotic interlayer excitons in a bilayer MoS2 (they are more pronounced at very low temperatures, T=4K) whose properties can be affected by electric gating in a quadratic nature [28].

The presence of depletion regions near the edges of the nanoribbons makes Pauli blocking problematic (as the number of electrons in these regions is small). Hence, the observed in Fig. 3 gating of optical properties of 50 nm nanoribbons is not connected to the Pauli blocking effect. Another argument against Pauli blocking is the fact that it would lead to optical changes which would be linear in field. Therefore, we suggest that the observed gating of 50 nm nanoribbons is connected to the changes of electrostatics of the depletion regions. In addition, the presence of perpendicular electric field induced by a gating voltage facilitates formation of interlayer excitons [28] which in turn contributes to reflection in a quadratic manner.

In conclusion, we have fabricated large arrays of nanoribbons of a bilayer MoS2 and measured their optical properties using light reflection and photoluminescence. We found that there exist optically inactive “exciton-free” regions with the sizes of >10nm near the edges of the MoS2 nanoribbons. These regions can significantly impede the development of nano-optical devices based on MoS2 excitons. We attributed the “exciton-free” regions to the band bending and surface electric fields that suppress formation of excitons near the nanoribbon edges. (Another discussed possibility for optically inactive excitons could be some non-radiative way for excitons to recombine near the edges of the ribbons.) We also found that the “exciton-free” regions can be gateable by external electric field for the nanoribbons of 50 nm pitch and non-gateable for nanoribbons of >150nm pitch. Our results are important for the development of nano-optical devices based on TMDCs.

The MoS2 crystal was purchased from HQ graphene. Thin MoS2 flakes were exfoliated on PDMS substrates and subsequently characterized via their optical contrast under an optical microscope. Then the selected bilayer flakes were transferred onto a Si/SiO2 substrate at room temperature with the assistance of a transfer stage. After that, flakes were patterned into nanoribbons with different nanoribbon sizes (50, 100, 150, and 200 nm) using electron‐beam lithography (JEOL, JBX-6300FS) followed by deep reactive ion etching. Finally, 5-nm‐Ti/60-nm‐Au layer electrodes were contacted to the nanoribbons by standard lithography, metal E-beam evaporation, and lift-off processes.

Reflection measurements were performed with the help of a Bruker Vertex 80 FTIR spectrometer and a Hyperion 3000 microscope. The recording of the visible and near-IR reflection spectra was done at the normal incidence at room temperature in the frequency range from 500 to 1000 nm by performing 1024 scans with a resolution of 4cm−1 using a Si detector. The standard 15× vis-IR (aperture number, NA=0.4) Schwarzschild objective was used for focusing incident light on the surface of sample. The measurements of polarized vis/near-IR spectra were performed with a polarizer (A 675-P), and as the reference we used the reflection from the silver thick mirror. Electric-field-dependent ratios of the reflection spectra as a function of applied gate voltage also were determined: R(Vg)/R(Vg=0V).

PL spectra of the bilayer MoS2 nanoribbons were recorded with a Witec confocal Raman spectrometer at the excitation wavelength of 514 nm and focusing objective of 100×. Due to using a high aperture number objective (NA∼0.9), the focusing spot was about 1 μm in dimeter and the laser power was less than 1 mW for prevention of sample destroying.

Acknowledgment. A. N. G. and V. G. K. acknowledge the support of Royce ICP.