Two-Channel Indirect-Gap Photoluminescence and Competition between the Conduction Band Valleys in Few-Layer MoS2

MoS2 is a two-dimensional layered transition metal dichalcogenide with unique electronic and optical properties. The fabrication of ultrathin MoS2 is vitally important, since interlayer interactions in its ultrathin varieties will become thickness-dependent, providing thickness-governed tunability and diverse applications of those properties. Unlike with a number of studies that have reported detailed information on direct bandgap emission from MoS2 monolayers, reliable experimental evidence for thickness-induced evolution or transformation of the indirect bandgap remains scarce. Here, the sulfurization of MoO3 thin films with nominal thicknesses of 30 nm, 5 nm and 3 nm was performed. All sulfurized samples were examined at room temperature with spectroscopic ellipsometry and photoluminescence spectroscopy to obtain information about their dielectric function and edge emission spectra. This investigation unveiled an indirect-to-indirect crossover between the transitions, associated with two different Λ and K valleys of the MoS2 conduction band, by thinning its thickness down to a few layers.


Introduction
Group-VI layered two-dimensional (2D) transition metal dichalcogenides (TMDs) (e.g., MoS 2 , WS 2 , MoSe 2 and WSe 2 ) exhibit very interesting semiconducting properties and are attracting a lot of attention that has been increasingly growing after the discovery of metallic two-dimensional graphene.As graphene, TMD monolayers have hexagonal symmetry and show a direct bandgap in the range of 1-2 eV [1].Bi-or multilayers of TMDs are indirect bandgap semiconductors [1].The remarkable versatility of monolayer and multilayer TMDs as a viable alternative to graphene [2] arises from their unique crystal structure.Their bandgaps and chemical properties [3] can be effectively tuned using different approaches (varying the number of layers, intercalation, alloying, mechanical stress, doping, etc.) [4,5].
As far as MoS 2 is concerned, numerous studies have revealed its intricate electronic spectrum and optical properties, surpassing the limitations of the conventional one-electron band structure [6].The substantial influence of multiexcitonic effects has highlighted the importance of thorough experimental studies on electronic excitations [7][8][9][10][11], placing them at the forefront of the current scientific research concerning MoS 2 .According to a series of theoretical works [1][2][3][4][5]12], the reported tunability of the direct bandgap due to indirect-todirect crossover [13,14] in atomically thin MoS 2 is directly related to the variable orbital composition of the involved electronic states.For the same reason, the indirect bandgap of few-layer MoS 2 will also vary with the thinning of its thickness, and even an indirectto-indirect crossover between the transitions associated with two different valleys of the conduction band may occur.While few-layer MoS 2 exhibits two valleys along the Γ-K line with similar energy, as highlighted by Zhao et al. [15], the particular valley responsible for forming the conduction band minimum remains poorly understood.Fundamental questions persist regarding the circumstances under which the indirect Λ−Γ transition will shift to indirect K−Γ band alignment and whether this shift will occur at all, because the valley responsible for forming the conduction band minimum is yet to be specified.
In this work, we report the preparation of MoS 2 ultrathin films by sulfurization of few-layer MoO 3 films that were preliminary obtained on a SiO 2 /Si substrate by plasmaenhanced atomic layer deposition (PE-ALD).All sulfurized samples were examined at room temperature with spectroscopic ellipsometry and photoluminescence spectroscopy to obtain information about their dielectric functions (DF) and emission spectra.The latter unveiled the competition of two indirect transitions from the Λ and K valleys of the conduction band by thinning the MoS 2 thickness down to a few layers.

MoO 3 Thin Films
The MoO 3 films were deposited in a PE-ALD system (SI ALD LL, SENTECH Instruments, Berlin, Germany), as described in detail in [28,29].The films were grown on thermal oxidized (SiO 2 with a nominal thickness of 105 nm) p-type Si (100) wafers (thickness 650-700 µm) with a resistance of <0.005 Ohm × cm (high-doped substrates).X-ray diffraction (XRD) patterns were recorded on a Malvern PANalytical X'Pert Pro MRD diffractometer(Malvern Panalytical Ltd., Bristol, UK) equipped with a fast PIXcel detector, using CuK α radiation generated at 40 kV and 40 mA.Grazing incidence XRD (GIXRD) patterns were recorded at an incident angle of 0.5 • , with a step size of 0.01 • 2θ and a counting time of 0.5 s, over a 5-55 • 2θ interval.Typical GIXRD patterns and dielectric functions (DFs) retrieved using spectroscopic ellipsometry (SE), performed with the aid of a rotating-compensator M 2000DI (J.A. Woollam, Lincoln, NE, USA) ellipsometer at different incident angles over the photon energy range of 0.7-6.5 eV, are given in Figure S1a and Figure S1b, respectively.All the obtained MoO 3 films, subjected to further sulfurization, were crystalline, and their DFs were indicative of the absence of the oxygen deficiency, as discussed in the supplementary information S1 Section.Their thicknesses, found in an X-ray reflectometry (XRR) examination were 3, 5 and 30 nm.

MoS 2 Thin Films
The sulfurization of the MoO 3 films was carried out in a 2-inch single-zone tube furnace (OTF-1200X-S, MTI Corporation, Richmond, CA, USA).For this purpose, the MoO 3 films were placed at the center of the furnace.The furnace and samples were purged multiple times under Ar flow (250 sccm 99.999% Ar).The temperature of the furnace was ramped up from room temperature to 700 • C over 15-20 min and maintained at that temperature for 60 min under atmospheric pressure.During heating, H 2 S (10 sccm 99.5% H 2 S) was introduced at 300 • C; it was removed at the end of the 60 min thermal treatment.Afterward, the furnace was purged with Ar (250 sccm) during the cool-down process.After cooling to ~400 • C, the furnace was opened for rapid cooling at ~100 • C over ~10 min.
The topographies of the prepared 30, 5 and 3 nm-thick MoS 2 films (plan view) were examined using a Zeiss UltraPlus scanning electron microscope (Carl Zeiss, Oberkochen, Germany).The corresponding scanning electron microscopy (SEM) images are given in Figure S2b-d.
Examinations using X-ray reflectivity and SE revealed that sulfurization induces changes in film thickness.Specifically, the thickness of 30 nm-thick film was reduced by nearly 30% after sulfurization.On the other hand, the films with nominal thicknesses of 3 and 5 nm each experienced less than a 15% change in thickness after sulfurization.To simplify the references in this text, each of the MoS 2 films studied will be identified based on its nominal thickness, which corresponds to the thickness of the source MoO 3 film before sulfurization.The variation in thickness among the resulting MoS 2 films is distinctly evident in their Raman spectra (Figure S2a).These were recorded using backscattering geometry on a Nanofinder-30 confocal Raman system (Tokyo Instrument Inc., Tokyo, Japan) equipped with a Juno 3050 GS-11 (Kyocera Soc Corporation, Yokohama, Japan) Nd:yttrium-aluminum-garnet laser (second harmonic, 532 nm).The maximum output power of the excitation source was 10 mW.The cross-sectional beam diameter was 4 µm.Diffraction grating with 1800 grooves per mm provided a spectral resolution of 0.5 cm −1 .The spectral signal was detected using a photon-counting charge-coupled device (CCD) camera "Andor" (Andor Technology, Belfast, Ireland) cooled down to −100 • C.
As shown in Supplementary S2, the observed decreases in intensity and disappearance of the 521 cm −1 Raman line of the Si substrate with increasing thickness of the MoS 2 film (Figure S2a) corroborates the value of the absorption coefficient (Figure S3) extracted from the DFs of the 3, 5 and 30 nm MoS 2 films.
Despite the large number of theoretical works on ultrathin MoS 2 , only a few address its DFs.So far, as the thicknesses of the obtained 3 and 5 nm MoS 2 samples exceeded one layer (L) and approximately corresponded to 4 L and 8 L MoS 2 (Supplementary S2), respectively, they were of primary importance in the context of the present work.Nevertheless, along with the latter two, bulk and 2 L MoS 2 were also included in the band structure calculations to obtain a more complete picture and unravel the main trends that band structure and DF show upon thinning of the MoS 2 thickness.
We used the full-potential linearized augmented plane wave (FP LAPW) method implemented in the scheme reported in [30].The exchange-correlation interactions were described as within the generalized gradient approximation (GGA), using the strategy reported in [31].The convergence parameter R mt K max , where R mt is the smallest atomic sphere radius and K max is the largest K-vector of the plane wave expansion of the wave function, was set to 7.0.Within the atomic spheres, the partial waves were expanded up to l max = 10, where l max is the highest value of the orbital angular-momentum quantum number used for partial waves inside atomic spheres.Integrations over the first Brillouin zone (BZ) were performed using the tetrahedron method, with 60 points in the irreducible part of the BZ.The R mt values for Mo and S were set to 2.34 and 2.08 a. u. (atomic unit), respectively.The value of −6.0 Ry of cut-off energy was used for the separation of the core and valence states.The imaginary part of the DF was calculated using the joint density of the states for optical transitions between the valence and conduction bands, using the Monkhorst-Pack technique for integration over the Brillouin zone [32].The real part of the dielectric function was calculated from the imaginary part using the Kramers-Kronig relation.
While SE is a powerful tool for studying direct optical transitions, photoluminescence (PL) is a well-endorsed technique for studying indirect-gap emissions in MoS 2.
In the present work, PL studies were performed on an Infrared PL/PLE/Raman spectrometer (Tokyo Instrument Inc., Tokyo, Japan) using lasers with two excitation wavelengths, 785 nm (NovaPro 785-250) and 532 nm (NovaPro PB 532-200 DPss), to embrace a possibly wider range of intrinsic electronic excitations that may decay radiatively and contribute to the PL of MoS 2 .The obtained PL spectra are given and discussed together with the other main results in the next section.

Results and Discussion
Among the significant parameters in the resulting electronic energy spectrum of MoS 2 (Figure 1a-d) is the splitting between adjacent bands at the K-point of the BZ.As highlighted in Figure 1, for each MoS 2 layer count, it arises from interlayer interactions and spin-orbit coupling (SOC).The splitting magnitude was reduced in the 8, 4 and 2 L MoS 2 compared to the bulk material, primarily due to the finite number of layers in ultrathin MoS 2 .In a 1 L MoS 2 limit, the splitting solely originates from SOC [3].
dielectric function was calculated from the imaginary part using the Kramers-Kronig relation.
While SE is a powerful tool for studying direct optical transitions, photoluminescence (PL) is a well-endorsed technique for studying indirect-gap emissions in MoS2.
In the present work, PL studies were performed on an Infrared PL/PLE/Raman spectrometer (Tokyo Instrument Inc., Tokyo, Japan) using lasers with two excitation wavelengths, 785 nm (NovaPro 785-250) and 532 nm (NovaPro PB 532-200 DPss), to embrace a possibly wider range of intrinsic electronic excitations that may decay radiatively and contribute to the PL of MoS2.The obtained PL spectra are given and discussed together with the other main results in the next section.

Results and Discussion
Among the significant parameters in the resulting electronic energy spectrum of MoS2 (Figure 1a-d) is the splitting between adjacent bands at the K-point of the BZ.As highlighted in Figure 1, for each MoS2 layer count, it arises from interlayer interactions and spin-orbit coupling (SOC).The splitting magnitude was reduced in the 8, 4 and 2 L MoS2 compared to the bulk material, primarily due to the finite number of layers in ultrathin MoS2.In a 1 L MoS2 limit, the splitting solely originates from SOC [3].
As shown in Figure 1e (shaded area), this splitting manifests itself through the irregular behavior of the ellipsometric parameter Ψ within the narrow photon energy gap spanning from 1.8 to 2 eV.As shown in Figure 1e (shaded area), this splitting manifests itself through the irregular behavior of the ellipsometric parameter Ψ within the narrow photon energy gap spanning from 1.8 to 2 eV.Such peculiar behavior was observed across all MoS 2 /SiO 2 /Si stacks studied in this work and for all incident angles accessed during the SE measurements.Note that the mean square error (MSE) given in Figure 1e for each studied MoS 2 /SiO 2 /Si structure is related to the model that was fitted to the ellipsometric parameters not only within the 1.4 to 2.1 eV range shown in Figure 1 but also for the entire accessible photon energy range spanning from 0.7 to 6.5 eV.The obtained MSE values fell below eight, indicating that the fit was acceptable and the retrieved DF was accurate enough.
The DF across the entire range of photon energies is displayed in Figure 2, with separate representation for the real (a) and imaginary (b) parts.The data for the MoS 2 films with thicknesses of 30, 5, and 3 nm are indicated by the blue, green and red lines, respectively.
Nanomaterials 2024, 14, x FOR PEER REVIEW 5 of 12 Such peculiar behavior was observed across all MoS2/SiO2/Si stacks studied in this work and for all incident angles accessed during the SE measurements.Note that the mean square error (MSE) given in Figure 1e for each studied MoS2/SiO2/Si structure is related to the model that was fitted to the ellipsometric parameters not only within the 1.4 to 2.1 eV range shown in Figure 1 but also for the entire accessible photon energy range spanning from 0.7 to 6.5 eV.The obtained MSE values fell below eight, indicating that the fit was acceptable and the retrieved DF was accurate enough.
The DF across the entire range of photon energies is displayed in Figure 2, with separate representation for the real (a) and imaginary (b) parts.The data for the MoS2 films with thicknesses of 30, 5, and 3 nm are indicated by the blue, green and red lines, respectively.Based on its crystal structure and symmetry [33], MoS 2 is a uniaxial crystal, and its optic axis is normal to the layer plane (LP).As reported in Figures S4 and S5, the calculated DF indeed shows different dispersions for light polarized parallel and perpendicular to the layer plane.Comparison between the SE-based (Figure 2) and calculated (Figure S4) data drove us to the conclusion that the obtained SE-based DF is overwhelmingly determined by dielectric response to the light polarized in the LP for all MoS 2 films studied in this work.The descending trend in the intensity of the main features of the SE-based DFs of the 30, 5 and 3 nm MoS 2 was reproduced using the calculated DFs obtained before and after rescaling (Figure S6).The latter mitigated the vacuum dilution effect, since the band structure calculations for MoS 2 with a finite number of layers were conducted using supercells that included vacuum space.
The A, B and C transitions depicted in Figure 1 and reproduced by SE-based DFs in Figure 2 are commonly observed in the majority of the related studies.The exciton peaks (Figure 2) related to these transitions clearly exhibit blue shifts with the thinning of the MoS 2 samples.The E-exciton, which is also frequently observed in optical studies [34] does not show noticeable shift.The most significant shift was observed for the C-excitons, which are not originating from transitions between parabolic bands with opposite concavities, like A-and B-excitons, but resulting from transitions between the valence and conduction band regions with similar concavities, known as the nested band regions.The comparison of the C-exciton position in 30 nm MoS 2 with those in 5 and 3 nm MoS 2 indicated a considerable blue shift upon thinning, exceeding 100 meV (Figure 2b).As illustrated in the inset of Figure 2b, the A-and B-excitons also exhibited shifts toward higher photon energies as the thickness of the obtained MoS 2 was reduced to 5 or 3 nm.In comparison to the Cexcitons, the B-and A-excitons experienced smaller shifts (approximately 50 and 20 meV, respectively).
Overall, as stated before, the above analysis confirms that the obtained 30 nm MoS 2 is a good counterpart to bulk MoS 2 .Along with the already mentioned Raman spectra (Supplementary S2 Section), this assertion was corroborated by the PL spectra taken for the studied MoS 2 thin films and shown in Figure S7.
The exciton landscape in MoS 2 is highly intricate, embracing neutral, charged and dark excitons, all of which directly or indirectly contribute to the DFs.This landscape is dynamic, with various components influenced by numerous factors, including the fabrication process [20].Therefore, when the retrieved DFs are evaluated, they should be analyzed in conjunction with PL data, comparing the absorption coefficient derived from the DFs to the PL spectra within the same spectral range.Since our primary focus was on few-layer MoS 2 , we initially concentrated on MoS 2 /SiO 2 /Si structures featuring 3 and 5 nm-thick MoS 2 layers.
Figure 3 displays the photon energy dependencies of the absorption coefficients (α) and PLs of the few-layer MoS 2 films.The PLs under the excitation wavelength of 532 nm (2.33 eV) are given for various levels of excitation power.The normalized PL spectrum (shape function) for each excitation level underwent little change, with increasing excitation power in the range of 2-10 mW (Figure S8), and the positions of the emission lines remained unchanged.
A-and B-excitons, which are positioned above 1.8 eV in MoS 2 [13,[33][34][35][36], clearly manifested themselves in the spectral features of the α and PL values of the studied films.Comparison with the reported energy positions of A exc. (1L MoS 2 ) and B exc. (1L MoS 2 ) for a single layer showed that the energy gap between the A-and B-excitons in our case did not exceed approximately 150 meV.This value is noticeably smaller than 200 meV that is the value of the splitting between A-and B-excitons in bulk MoS 2 [3].This observation is directly related to a few layers' thickness of the prepared films.In the case of the 5 nm MoS 2 , the energy position of the emission line ascribed to the B-excitons was red-shifted by nearly 20 meV from its energy position in the MoS 2 monolayer and from its absorption peak as reported in Figure 2b.For the 3 nm MoS 2 , the shift was definitely less pronounced (see Figure 2a).The energy difference between absorption and emission, known as the Stokes shift, is inherent to all materials and varies widely depending on the material type (semiconductor, molecular crystal) and internal electrical fields.For typical semiconductors like GaAs, this shift is only 4 meV [39].There are no reports on the intrinsic Stokes shift value in MoS 2 .However, as the shift is decreased in 3 nm MoS 2 compared to 5 nm MoS 2 , the Stokes shift in the latter is non-intrinsic and is likely caused by some strain or inhomogeneity in 5 nm MoS 2 .[13,[34][35][36][37] and the reported value of the indirect gap for bulk MoS2 [38].
A-and B-excitons, which are positioned above 1.8 eV in MoS2 [13,[33][34][35][36], clearly manifested themselves in the spectral features of the α and PL values of the studied films.Comparison with the reported energy positions of Aexc.(1L MoS2) and Bexc.(1L MoS2) for a single layer showed that the energy gap between the Aand B-excitons in our case did not exceed approximately 150 meV.This value is noticeably smaller than 200 meV that is the value of the splitting between A-and B-excitons in bulk MoS2 [3].This observation is directly related to a few layers thickness of the prepared films.In the case of the 5 nm MoS2, the energy position of the emission line ascribed to the B-excitons was red-shifted by nearly 20 meV from its energy position in the MoS2 monolayer and from its absorption peak as reported in Figure 2b.For the 3 nm MoS2, the shift was definitely less pronounced (see Figure 2a).The energy difference between absorption and emission, known as the Stokes shift, is inherent to all materials and varies widely depending on the material type (semiconductor, molecular crystal) and internal electrical fields.For typical semiconductors like GaAs, this shift is only 4 meV [39].There are no reports on the intrinsic Stokes shift value in MoS2.However, as the shift is decreased in 3 nm MoS2 compared to 5 nm MoS2, the Stokes shift in the latter is non-intrinsic and is likely caused by some strain or inhomogeneity in 5 nm MoS2.
Strong enhancement in PL intensity related to the direct exciton radiative transitions in MoS2 when MoS2 thickness goes down to a few nanometers is a well-known and solid fact.According to the PL spectra in Figure 3, some enhancement also takes place at the nanoscale when MoS2 thickness is changed from 5 to 3 nm.It can be clearly seen that under  [13,[34][35][36][37] and the reported value of the indirect gap for bulk MoS 2 [38].
Strong enhancement in PL intensity related to the direct exciton radiative transitions in MoS 2 when MoS 2 thickness goes down to a few nanometers is a well-known and solid fact.According to the PL spectra in Figure 3, some enhancement also takes place at the nanoscale when MoS 2 thickness is changed from 5 to 3 nm.It can be clearly seen that under the same excitation levels, the PL intensity in 3 nm MoS 2 was noticeably stronger than in the 5 nm MoS 2 .
While α is structureless and, for both the 3 and 5 nm MoS 2 , showed only absorption tails descending toward lower photon energies, the PL spectrum showed an indirect-gap emission band centered around 1.25 eV (Figure 3).
It has been established in many experimental and theoretical works [2,5,14,15,18,38,40,41] that MoS 2 remains an indirect semiconductor even when reduced to bilayers.Observation of the indirect-gap emission around 1.25 eV on 3 nm-thick MoS 2 (Figure 3) has revealed that MoS 2 retains its indirect characteristics even when its thickness is reduced to just four layers.This agrees well with the already-quoted works.

Figure 1 .
Figure 1.Electronic band structures of 2 L (a), 4 L (b), 8 L (c) and bulk (d) MoS 2 .Valence band splitting is encircled; possible indirect radiative transitions are indicated by arrows; and bold and dashed vertical lines show direct transitions A, B and C, respectively.(e) Ellipsometric parameter Ψ as a function of photon energy for the obtained MoS 2 /SiO 2 /Si structures with 3 (top plot), 5 (middle

Figure 1 .
Figure 1.Electronic band structures of 2 L (a), 4 L (b), 8 L (c) and bulk (d) MoS2.Valence band splitting is encircled; possible indirect radiative transitions are indicated by arrows; and bold and dashed vertical lines show direct transitions A, B and C, respectively.(e) Ellipsometric parameter Ψ as a function of photon energy for the obtained MoS2/SiO2/Si structures with 3 (top plot), 5 (middle plot) and 30 nm (bottom plot) MoS2.On the top, colored open circles and solid lines represent experimental data and the fits to these data, respectively; each color corresponds to one of the four accessed angles of incidence.

Figure 2 .
Figure 2. Real (a) and imaginary (b) parts of the experimental DFs retrieved for 30 (blue lines), 5 (green lines) and 5 nm (red lines)-thick MoS2 in a wide photon energy range.The splitting-related features of the spectra are encircled.Notations A, B, C and E, commonly used for MoS2, are related to the particular peaking structures in the spectrum of each of the considered MoS2 thin films.The vertical dashed lines and small horizontal arrows are given for convenience to show how A, B, and C exciton peak positions shift with changing the thickness of MoS2.As illustrated in the inset in (b), A-and B-excitons also exhibited shifts toward higher photon energies as the thickness of the obtained MoS2 was reduced to 5 or 3 nm.

Figure 2 .
Figure 2. Real (a) and imaginary (b) parts of the experimental DFs retrieved for 30 (blue lines), 5 (green lines) and 5 nm (red lines)-thick MoS 2 in a wide photon energy range.The splitting-related features of the spectra are encircled.Notations A, B, C and E, commonly used for MoS 2 , are related to the particular peaking structures in the spectrum of each of the considered MoS 2 thin films.The vertical dashed lines and small horizontal arrows are given for convenience to show how A, B, and C exciton peak positions shift with changing the thickness of MoS 2 .As illustrated in the inset in (b), Aand B-excitons also exhibited shifts toward higher photon energies as the thickness of the obtained MoS 2 was reduced to 5 or 3 nm.

Nanomaterials 2024 , 12 Figure 3 .
Figure 3. Top part: SE-based absorption coefficients of the 3 (a) and 5 nm (b) MoS2, respectively; bottom part: PL spectra at various excitation densities under the excitation wavelength of 532 nm (2.33 eV) for MoS2/SiO2/Si thin film structures with 3 (a) and 5 nm (b) MoS2 on the top.Vertical dashed lines, given for eye guidance, show the reported positions of the A-and B-excitons in a single layer of MoS2[13,[34][35][36][37] and the reported value of the indirect gap for bulk MoS2[38].

Figure 3 .
Figure 3. Top part: SE-based absorption coefficients of the 3 (a) and 5 nm (b) MoS 2 , respectively; bottom part: PL spectra at various excitation densities under the excitation wavelength of 532 nm (2.33 eV) for MoS 2 /SiO 2 /Si thin film structures with 3 (a) and 5 nm (b) MoS 2 on the top.Vertical dashed lines, given for eye guidance, show the reported positions of the A-and B-excitons in a single layer of MoS 2[13,[34][35][36][37] and the reported value of the indirect gap for bulk MoS 2[38].