Charge transfer across monolayer/bilayer MoS₂ lateral interface and its influence on exciton and trion characteristics

Atomically thin two-dimensional (2D) transition metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS₂), exhibit a noticeable change in the electronic band structure from an indirect bandgap in bulk to a direct bandgap in monolayer (1L) [1, 2]. Owing to the modifications in the electronic structures as a function of the layer number (N), a few-layer MoS₂ (1  ⩽  N  ⩽  4) has a great potential for optoelectronic devices such as phototransistors [3–6], solar cells [7], and light emitting sources [8]. In a few-layer MoS₂, two distinct optical transitions are observed at ~1.85 eV (A exciton) and ~2 eV (B exciton) [1], which originate from the valence band splitting at the K point of the Brillouin zone due to the spin–orbit coupling and the interlayer interaction [2, 9]. In MoS₂, unintentional n-type doping can be caused by sulfur vacancies [10], PMMA or acetone used in a transfer process [11], and charge traps at the interface between MoS₂ and SiO₂ substrate [12]. As a result, an excess electron can be tightly bound to a neutral exciton (X), forming a negatively charged exciton (X⁻) [13, 14]. As both the neutral excitons and the negatively charged excitons (also known as negative trions) are closely related to the optical transitions of MoS₂, understanding their characteristics is one of the important issues not only for optoelectronic applications but also for fundamental research works.

Optical responses of excitons and negative trions in 1L MoS₂ are strongly influenced by the carrier density. For example, spectral weights of the absorption and photoluminescence (PL) responses of the excitons can be systematically increased with decreasing electron doping density via back-gate voltage, whereas those of the negative trions are nearly unchanged [13]. When the excess electrons of unintentionally n-doped 1L MoS₂ are extracted by the adsorption of chemical p -type dopants, trion formation rate from excitons decreases, resulting in the enhancement in the PL spectral weight of the X peak [15]. In contrast, the PL spectral weight of the X peak is reduced by the adsorption of chemical n-type dopants [15]. Without the external extraction or injection of electrons, charge transfer can also occur in the 'vertically stacked' TMD heterostructures, resulting in the variations of the PL intensities of the X and X⁻ peaks in the constituent TMD layers [16, 17]. For example, in the vertically stacked MoS₂/WS₂ bilayers, charge transfer occurs from WS₂ to MoS₂ owing to the type-II band alignment, resulting in an increase of the PL intensity of the X⁻ peak in MoS₂ [16]. The difference in work functions of constituent TMD materials also leads to charge transfer. For example, a work function difference across the 'lateral' WS₂/MoS₂ heterojunction induces the electrical potential distribution and, in turn, initiates the charge transfer between WS₂ and MoS₂ [18, 19]. The work functions are influenced by several factors: layer thickness, surface chemistry, underlying substrate, and edge termination type [20, 21]. The charge transfer can occur even at the lateral homojunction of monolayer and multilayer MoS₂, resulting in an enhancement of the photoresponse [22]. The space charge region induced by the charge transfer at the 2D lateral junction extends to a much longer distance than that in a bulk junction [18, 19, 23, 24]. Because the PL responses of layered TMDs are sensitive to the variation of the electron density and the number of atomic layers, PL mapping images of the X and X⁻ peaks can provide useful information on the charge transfer across the lateral interface and the space charge region over the area around the lateral interface of the layered TMDs.

In this paper, we report simultaneous studies of spatially resolved Raman scattering and PL from a few-layer MoS₂ in which 1L/2L lateral interface is formed. In particular, PL mapping images revealed that spectral intensities of the excitons were greatly enhanced in the 1L region near the lateral interface between 1L and 2L MoS₂, whereas those of the negative trions were nearly unchanged. To understand the exciton and trion emission behaviors near the 1L/2L lateral interface, we used density functional theory (DFT) to calculate work functions for 1L and 2L MoS₂ on a SiO₂ substrate. Furthermore, we calculated work functions for different types of edge terminations of 1L and 2L MoS₂ and compared the DFT calculations with the experimental PL results.

The morphology of the multilayer-stacked MoS₂ was identified by optical microscopy, atomic force microscopy (AFM), and Raman spectroscopy. Figure 1(b) shows an optical microscope image of the deformed triangular-shaped MoS₂ flakes on the SiO₂ substrate. The multilayer-stacked MoS₂ exhibits a change in brightness contrast due to the thickness variation. The AFM height image in figure 1(c) reveals that the co-centered triangular-shaped MoS₂ is stacked layer by layer on the large 1L MoS₂. The lateral size of each co-centered MoS₂ becomes smaller and smaller with an increase of the number of layers. Note that the 1L/2L lateral interface exhibits a deformed triangular shape boundary composed of the skewed edges. AFM line scan profiles show that the thickness of the 1L MoS₂ on the SiO₂ substrate and that on the MoS₂ are ~12 Å and ~9 Å, respectively. These values are in good agreement with previously reported ones [25, 26]. The bright center in the AFM image corresponds to bulk MoS₂ with a thickness of ~50 nm.

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Optical phonon energies in MoS₂ vary as a function of N. Figure 1(d) shows a series of the Raman spectra along the dashed arrow in the optical microscope image. Two distinctive Raman peaks are observed: $E_{2g}^{1}$ and ${{A}_{1g}}$ phonon modes, corresponding to the in-plane and out-of-plane vibrational modes, respectively [25]. As the number of layers increases, the $E_{2g}^{1}$ phonon energy shifts downward from 385 cm⁻¹ for N  =  1 to 383 cm⁻¹ for bulk, while the ${{A}_{1g}}$ phonon energy shifts upward from 404 cm⁻¹ for N  =  1 to 409 cm⁻¹ for bulk. These shifts in their phonon energies are mainly due to the changes in the short-range interlayer and the long-range Coulomb interactions with an increase in the number of layers [27]. The difference in the peak energies $\Delta \omega =\omega \left( {{A}_{1g}} \right)-\omega (E_{2g}^{1})$ identifies the number of layers (figure 1(f)): 19.36  ±  0.08, 22.20  ±  0.14, 23.33  ±  0.57, and 24.53  ±  0.21 cm⁻¹ for N  =  1, 2, 3, and 4, respectively. For bulk MoS₂ at the center region, $\Delta \omega =$ 25.79  ±  0.09 cm⁻¹. The $\Delta \omega$ image in figure 1(g) clearly visualizes the vertically stacked MoS₂ layer by layer and is comparable to the AFM data. The values of $\Delta \omega$ are in excellent agreement with previously reported ones for mechanically exfoliated MoS₂ [25, 26] and chemical vapor deposition (CVD)-grown MoS₂ [28, 29].

To explore the exciton and trion emission properties related to the changes in the band structures of 1L, 2L, and a few layers of MoS₂, spatially resolved PL measurements were performed over the same area where the AFM and Raman images were obtained. Figure 2(a) shows an image of the spectral weight of the A exciton (I_A) obtained over the area shown in figure 1(c). Emission efficiency of I_A decreases when the layer thickness increases from 1L to a few layers. The PL response is finally quenched in thick MoS₂ for N  >  5. A remarkable feature observed in the PL mapping image is that I_A is significantly enhanced in the 1L MoS₂ region near the 1L/2L lateral interface, identifying a sharp spectroscopic contrast between 1L and 2L MoS₂. Furthermore, the enhancement in I_A strongly oscillates in its intensity around the 1L/2L boundary.

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The PL spectrum obtained from 1L MoS₂ consists of the A exciton and the B exciton that originate from the direct gap transitions at the K point [1]. The A–B splitting comes from the valence band splitting mainly due to the spin–orbit coupling [2, 9]. For 2L MoS₂, the interlayer interaction also contributes to the valence band splitting [2, 9]. In the case of the unintentional n-doping in MoS₂, excess electrons can contribute to the formation of negative trions consisting of two electrons and one hole [13]. Because of the large trion binding energy of ~40 meV in 1L MoS₂ [14, 15, 30, 31], the trions are present in 1L MoS₂ at room temperature. In contrast, in 2L MoS₂, as the conduction band minimum occurs at the Λ point lying between the K and Γ points, the photo-excited electrons can be easily relaxed to the Λ valley via thermal escape from the K-point valley at room temperature, leading to a significant decrease of the trion emission [32]. As a result, in 2L MoS₂, only the exciton emission becomes a dominant process in the K–K transition, whereas the trion emission at the K point is considerably suppressed [14]. Figure 2(b) shows the representative PL spectra obtained from 1L MoS₂ remote from the 1L/2L interface (marked by 1L-1), 1L MoS₂ near the interface (marked by 1L-2), and 2L MoS₂ (marked by 2L). In the 1L MoS₂, the spectral region of the A peak is decomposed into two Lorentzian peaks, consisting of the X and the X⁻ peaks. The PL spectra obtained from 1L MoS₂ are well reproduced with the sum of these two peaks and the B exciton peak, while the PL spectra in 2L MoS₂ consist of only the X and the B components. The spectrally integrated intensity, peak energy, and linewidth maps of the X⁻ and the X peaks are shown in figures 2(c)–(h). Note that the band-to-band PL transition of the trions at the K point occurs only in 1L MoS₂ at room temperature. Thus, the trion emission is negligible in the other MoS₂ region for N  ⩾  2, designated by black colors in figures 2(c)–(e). Interestingly, figures 2(c) and (f) show that ${{I}_{X}}$ is spatially inhomogeneous and strongly enhanced near the 1L/2L lateral interface in the 1L region, whereas ${{I}_{{{X}^{-}}}}$ is relatively uniform. Therefore, the strong enhancement in I_A in the 1L MoS₂ region is mainly attributed to the enhancement in ${{I}_{X}}$. For N  ⩾  2, there is no appreciable change in ${{I}_{X}}$. Finally, the exciton emission is quenched for N  >  5.

The average peak energies of the negative trions (${{\bar{\omega }}_{{{X}^{-}}}}$) and neutral excitons (${{\bar{\omega }}_{X}}$) obtained from the region enclosed by the dashed squares in the peak energy maps in figures 2(d) and (g) are 1.808  ±  0.002 eV and 1.843  ±  0.003 eV, respectively, giving rise to the trion binding energy of ~35 meV, which is consistent with the previously reported values of mechanically exfoliated [14, 15] and CVD-grown 1L MoS₂ [30, 31]. Distinctive difference in ${{\bar{\omega }}_{X}}$ is clearly observed in the exciton transitions at the K point of the Brillouin zone as the number of layers are increased: ${{\bar{\omega }}_{X}}$ decreases to 1.837  ±  0.005 eV and 1.824  ±  0.001 eV for N  =  2 and 3, respectively. The decrease in ${{\bar{\omega }}_{X}}$ with an increase of the layer thickness is partly due to the relaxation of size confinement [33, 34]. In addition to the changes in the peak energies of the excitons, the average spectral widths of the excitons (${{\bar{\Gamma }}_{X}}$) are also affected by layer numbers: ${{\bar{\Gamma }}_{X}}$ decreases systematically from 99.3  ±  2.5 meV to 95.2  ±  3.4 meV and to 82.4  ±  2.2 meV for N  =  1, 2, and 3, respectively.

The MoS₂ sample shown in figure 1(b) consists of multi-stacked layers. Therefore, the electronic correlation between the 1L and 2L MoS₂ might be altered in the presence of MoS₂ for N  ⩾  3. To understand the exciton and trion characteristics related only to the 1L/2L lateral interface more precisely, PL mapping measurement was performed on the other sample consisting of only 1L and 2L MoS₂ (figure 2(i)). Figures 2(j)–(l) show the intensity, energy, and linewidth maps of the X peaks for the 1L and 2L MoS₂ with a deformed triangular shaped 1L/2L lateral interface. Similarly to the previous result, the X peak intensity is substantially enhanced in the 1L MoS₂ region near the 1L/2L interface, whereas ${{I}_{X}}$ in the 2L region does not exhibit any noticeable changes. Besides, the energy and the linewidth of the X peak are decreased in 2L MoS₂. The average values of the X peak energies are 1.844  ±  0.009 eV and 1.817  ±  0.004 eV for 1L and 2L MoS₂, respectively. The variations in the X peak energies between two different MoS₂ samples for N  =  2 are presumably due to the differences in interlayer twist angles, shapes, and/or stacking configurations between 1L and 2L MoS₂ [35, 36].

Figures 2(f) and (j) show that the PL signals exhibit some distinct features such as strong enhancement and oscillation of ${{I}_{X}}$ in the vicinity of the skewed/deformed outer edge of 2L MoS₂. The spatial variation in ${{I}_{X}}$ seems to be attributed to the electrostatic potential difference because it affects the sensitivity of PL response. For example, electrochemical control of PL was reported in the case of a MoS₂ flake, suggesting that the electrostatic potential can influence the overall strength of PL of MoS₂ [37]. According to the surface potential study of MoS₂/SiO₂ using Kelvin probe force microscope, the work function ($\Phi$) of 1L MoS₂ is smaller than that of 2L MoS₂ by 0.05 eV [38]. Therefore, to explain the spatial variation in ${{I}_{X}}$, we may consider the electron transfer from 1L to 2L MoS₂ across the 1L/2L lateral interface owing to the work function difference. The decrease in the number of excess electrons in 1L MoS₂ suppresses the trion formation rate, resulting in the enhancement of the exciton PL intensity. Our experimental observation is consistent with the results of the changes in ${{I}_{X}}$ and ${{I}_{{{X}^{-}}}}$ in 1L MoS₂ when the number of excess electrons are decreased via back-gate voltage in the field-effect transistor structure and when p -type dopants are adsorbed onto 1L MoS₂ [13, 15, 39]. The strongly enhanced ${{I}_{X}}$ and the relatively unchanged ${{I}_{{{X}^{-}}}}$ with the decrease of the excess electrons can be theoretically explained by solving the rate equations within the framework of a three-level model in a steady-state condition [15]. Based on the three-level model consisting of an exciton, a trion, and the ground state, the exciton PL intensity is strongly enhanced with a decrease of the electron density, whereas the trion intensity is relatively insensitive to the change in the electron density [15]. The 1L MoS₂ region near the 1L/2L boundary might be strained due to the presence of the 2L MoS₂, resulting in the changes in the neutral exciton peak position and intensity. The in-plane $E_{2g}^{1}$ phonon mode is sensitive to strain and shifts in energy linearly at a rate of  −5.2 cm⁻¹/% for biaxial strain [40]. The average $E_{2g}^{1}$ phonon energies are 384.1  ±  0.1 cm⁻¹ and 384.3  ±  0.2 cm⁻¹ in the 1L MoS₂ region near and away from the 2L boundary edge, respectively. The peak energy difference of 0.2 cm⁻¹ corresponds to a strain of ~0.038%. The exciton PL peak position and intensity changes are negligible under such a small strain [40].

Considering the charge transfer across the 1L/2L lateral interface due to the work function difference, the strong oscillation of ${{I}_{X}}$ in the vicinity of the 'skewed' or 'deformed' triangular-shaped 1L/2L lateral interface is not observed in other types of MoS₂ homostructures with a CVD-grown 'equilateral' triangular-shaped 1L/2L lateral interface and a mechanically exfoliated 'flat' 1L/2L interface [41, 42]. Figure 2(f) shows that the oscillation of electrostatic potential in the vicinity of the skewed edge is evident. The work function depends appreciably on a straight edge that comprises the oblique edge boundaries. Furthermore, the work function in MoS₂ depends on the edge termination atoms [21]. Indeed, Wei et al has reported that the work functions of TMD edges with different edge terminations should be taken into account in order to understand charge transfer behaviors in the lateral heterostructure of TMDs [21].

To understand charge transfer characteristics in more detail, we performed theoretical calculations of work functions of 1L and 2L MoS₂ based on the DFT. The work functions are calculated to be 5.34 eV and 4.97 eV for the 1L and 2L MoS₂, respectively (figure 3(a)). However, our experiments were performed on the MoS₂ layers on the SiO₂ substrate with possible exposure to H₂O during the transfer process. In order to include the effect of the substrate, we calculated work functions and charge density isosurfaces for two MoS₂ 1Ls, with an atomically thin SiO₂ layer (thickness ~6 Å) and H atoms inserted between the 1Ls. Similarly, we also calculated work functions and charge density isosurfaces for two MoS₂ 2Ls, with the SiO₂ layer and H atoms inserted between the MoS₂ 2Ls. From the charge density isosurfaces in figures 3(b) and (c) we infer there are more S-Si interactions in 2L MoS₂/SiO₂ than in 1L MoS₂/SiO₂. Interestingly, the order of the calculated work functions is reversed: Φ  =  4.52 eV and 4.67 eV for the 1L and the 2L MoS₂ with the SiO₂ layer and H atoms, respectively. The difference in the work functions allows us to interpret the overall features of the PL maps in the 1L MoS₂ region around the 1L/2L lateral interface. To equilibrate the Fermi energies, transfer of electrons from the 1L to the 2L MoS₂ should take place across the step boundary. The transfer of electrons from the 1L to the 2L MoS₂ leads to an enhancement in ${{I}_{X}}$ in the 1L MoS₂ region near the 2L MoS₂ flake. However, the transfer of electrons will not affect ${{I}_{X}}$ in the 2L MoS₂ region because the conduction states near the K points are mostly empty.

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The PL characteristics are also influenced by a termination atom of the 1L MoS₂ flake on the basal 1L MoS₂. S terminal atoms tend to gain electrons and Mo terminal atoms tend to lose them because the electronegativity of the S atom is larger than that of the Mo atom. The negatively charged S-termination exerts Coulomb force away from the termination on the electrons in the vicinity. Likewise, the positively charged Mo-termination exerts the force towards the termination on the electrons. Therefore, the S-termination weakens the enhancement effect of ${{I}_{X}}$ in the 1L MoS₂ region near the 1L/2L lateral interface, whereas the Mo-termination strengthens the effect.

To assess the enhancement effect of ${{I}_{X}}$ in terms of electronic energies, we calculated work functions for various edge terminations of MoS₂. Experimentally, Mo-terminated zigzag edges and S-terminated antenna edges have been observed in 2L MoS₂ boundary edges on 1L MoS₂, indicating that various edge structures can be formed via CVD growth [43]. In general, four different types of edge terminations can be considered for the 1L MoS₂, as shown in figure 4(a): a zigzag edge with S termination (z-S), a zigzag edge with Mo termination (z-Mo), an antenna edge with S termination (a-S), and an antenna edge with Mo termination (a-Mo) [44]. We included a pair of symmetric MoS₂ strips in a supercell to accurately calculate work functions of different terminations of MoS₂. The zigzag (antenna) terminations have edge atoms forming zigzag-shaped (antenna-shaped) arrays. S-termination and Mo-termination indicating outer edge atoms correspond to S and Mo, respectively. In the cases of 2L MoS₂, we additionally considered the mixed terminations whose outer edge atoms are both S and Mo (figure 4(b)).

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The computed work functions are summarized in figures 4(a) and (b) for 1L and 2L MoS₂, respectively. The work functions of S-terminations of 1L MoS₂ are 6.19 eV (6.21 eV) for the zigzag edge (the antenna edge), and those of 2L MoS₂ are 6.11 eV (6.36 eV) for the zigzag edge (the antenna edge). Similarly, the work functions of Mo-terminations of 1L MoS₂ are 4.46 eV (4.38 eV) for the zigzag edge (the antenna edge), and those of 2L MoS₂ are 4.40 eV (4.31 eV) for the zigzag edge (the antenna edge). Interestingly, the work functions of mixed terminations of 2L MoS₂ are 5.12 eV (5.00 eV) for the zigzag edge (the antenna edge), which are in between the work functions of S-terminations and those of Mo-terminations. Our calculated work functions indicate that the electronic potential away from the edge depends strongly on the types of the outer edge atoms (S or Mo atoms), but weakly on the zigzag and the antenna types of the same species. The calculated work functions of the 1L and 2L MoS₂ are larger for the S-terminations and smaller for the Mo-terminations as expected in terms of the electronegativity of the S and Mo atoms. The calculated work functions confirm our claim that the S-termination weakens the enhancement effect of ${{I}_{X}}$ in the 1L MoS₂ region near the 1L/2L lateral interface, whereas the Mo-termination strengthens the effect.

In the case of a MoS₂ flake with a skewed/deformed triangular shape, outer atom configurations and edge types may vary, and the electron density at the boundary of the skewed/deformed triangle (i.e. the 1L/2L interface) is expected to be highly non-uniform. The non-uniform electron density at the 1L/2L interface and the corresponding transfer of electrons from the 1L MoS₂ to the 2L MoS₂ lead to the varying effect of ${{I}_{X}}$ in the 1L MoS₂ region near the MoS₂ flake (i.e. 2L MoS₂). The irregular shape and large change of PL around the 1L/2L lateral interface is consistent with our calculated work functions. The enhanced area of ${{I}_{X}}$ in the 1L MoS₂ region extends more than 10 µm (figures 2(f) and (j)). Theoretical studies show that the depletion width of the 2D lateral junction extends much longer than that of the bulk counterpart [23, 24]. For example, Kelvin probe force microscopy of MoS₂/WS₂ heterojunction has revealed the depletion width of several micrometers [19]. Furthermore, the space charge region extends even longer beyond the depletion width [23]. Therefore, our experimental PL results clearly demonstrate that the space charge region spreads over the large area around the 2D lateral junction.

We performed Raman and PL mapping measurements simultaneously on the multi-stacked MoS₂ to study optical phonons and exciton properties. The Raman mapping images helped identify the number of MoS₂ layers, which was confirmed by the AFM measurement. Interestingly, a strong enhancement and an oscillatory behavior of the neutral exciton emission were observed in the 1L MoS₂ region near the 1L/2L lateral interface. DFT calculations showed that the work function was significantly influenced by the underlying SiO₂ substrate: it was lower in 1L MoS₂ than in 2L MoS₂, resulting in the electron transfer from 1L to 2L MoS₂. Furthermore, the work function strongly depended on the terminal atoms of the MoS₂ edge, leading to the non-uniform electrical potential distribution at the 1L/2L lateral interface. As a result, highly inhomogeneous exciton emission was observed in the 1L MoS₂ region. Finally, our experimental and theoretical analysis of a TMD material demonstrates that the exciton and trion properties can be modulated by the type of the edge termination, providing diverse design strategies for 2D optoelectronic nanodevices.

Synthesis of layered MoS₂ film on SiO₂

PL and Raman measurements

Theoretical calculations

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Nos. 2016R1D1A1B03935270 and 2016R1D1A1B04931384). SMK acknowledges support by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. 2018R1A2B2002859).