2-2-2 Optical response
Lee et al. [116] presented the Raman-scattering studies of monolayer and few-layer MoS2
films (Fig. 2.27). The spectrum of a bulk MoS2 is composed of two main optical phonon modes at about 382 and 406 cm–1, displaying symmetries of E2g and A1g. The in-plane E2g mode results from opposite vibration of two S atoms with respect to the Mo atom while the A1g mode is associated with the out of plane vibration of only S atoms in opposite directions (Fig. 2.28) [117].
For decreasing layer numbers, the E2g mode increases in frequency whereas the A1g mode decreases (Fig. 2.29) [116]. The origins of the shifts have been identified as the influence of neighbouring layers on the effective restoring forces on atoms and the increase of dielectric screening of long-range Coulomb interactions [117]. Similar evidence has also been observed in the mechanically exfoliated MoS2 flakes [116,118].
In 2012, Larentis et al. [50] shows the Raman-scattering spectra using 442 nm (Fig. 2.30) and 532 nm (Fig. 2.31) excitation wavelength on ultra-thin MoSe2. Fig. 2.30 shows four peaks at 169, 242, 285, and 352 cm-1, corresponding to the E1g, A1g, E2g, and A2u modes, respectively.
Notably, the A2u mode is an infrared active mode, not present in Raman-scattering spectra in bulk samples. The emergence of this mode in Raman-scattering spectra acquired on small flakes
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suggests a breakdown of inversion symmetry, possibly because of the substrate [50]. The Raman-scattering spectra of Fig. 2.31 exhibits similar peaks as Fig. 2.30, but a higher intensity of the A1g (242 cm-1) with respect to other modes. In 2012, Tongay et al. [119] reported the Raman-scattering spectra of single and few-layer mechanical exfoliated MoS2 and MoSe2 flakes onto 90 nm SiO2/Si substrate. Exfoliated few-layer flakes have shown characteristic A1g and E2g Raman modes located at 243.0 and 283.7 cm−1 for MoSe2 and 408.7 and 383.7 cm−1 for MoS2 (Fig. 2.32).
In the single layer limit, the A1g Raman mode softens to 241.2 (406.1) cm−1 as the E2g mode stiffens to 287.3 (384.7) cm−1 for MoSe2 (MoS2). The shifts behavior consistent with earlier studies [116-118]. Very recently, Shaw et al. [120] presented CVD growth of monolayer MoSe2
nanosheets. They observed the most prominent and identifiable peak of the Raman-scattering spectra is the A1g mode, which softening from 243.7 cm-1 for bulk MoSe2 to 241.2 cm-1 for monolayer MoSe2 (Fig. 2.33). In addition, the lower frequency and less noticeably split peaks located at 239 cm-1, 240.1 cm-1 and 240.8 cm-1 for three-, four- and five- layer MoSe2 result from the Davydov splitting [120].
First-principle calculations predict that semiconducting TMDs exhibit indirect to direct band gap transformation with decreasing layer numbers [117,121,122]. The band structures of bulk and monolayer MoS2 calculated from first principles are shown in Fig. 2. 34 [121]. At the Γ point, the band gap transition is indirect for the bulk material, but gradually shifts to be direct for the monolayer. The change in the band structure with layer number is due to quantum confinement and the resulting change in hybridization between pz orbitals on S atoms and d orbitals on Mo atoms [33,45]. The electronic distributions are also spatially correlated to the atomic structure [45]. For MoS2, density functional theory (DFT) calculations show that the conduction band states at the K point are mainly due to localized d orbitals on the Mo atoms,
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located in the middle of the S–Mo–S layer sandwiches and relatively unaffected by interlayer coupling. However, the states near the Γ point are due to combinations of the antibonding pz
orbitals on the S atoms and the d orbitals on Mo atoms, and have a strong interlayer coupling effect [45]. Therefore, as the layer numbers change, the direct excitonic states near the K point are relatively unchanged, but the transition at the Γ point shift significantly from an indirect one to a larger, direct one. The band structures of bulk and monolayer MoSe2 calculated from first principles are shown in Fig. 2. 35 [119]. Bulk MoSe2 displays 0.84 eV (Γ to Γ−K), 1.1 eV (K to Γ−K) indirect bandgap, and a 1.34 eV (K−K) direct band gap. In contrast, for monolayer MoSe2, Γ to Γ−K and K to Γ−K increases, while the K−K direct gap remains nearly unchanged and monolayer MoSe2 shows a direct 1.34 eV band gap at the K symmetry point.
The changes of the electronic band structures in TMDs manifest itself as a strong PL feature.
Mak et al. [33] observed an increase of the photoluminescence (PL) quantum yield by more than a factor of 104 for themechanically exfoliated monolayer MoS2 compared with the bulk crystal.
Furthermore, the main peak of the monolayer MoS2 PL spectrum is the direct gap luminescence feature at 1.9 eV (Fig. 2.36), whereas few-layer MoS2 also has additional peaks corresponding to the indirect gap luminescence, and direct gap hot luminescence [33]. Splendiani et al. [45] also performed PL measurements of mechanically exfoliated monolayer MoS2 films. They observed a strong PL at the direct excitonic transitions in a monolayer MoS2 films, whereas luminescence is absent in the indirect bandgap bulk MoS2 sample (Fig. 2.37). Eda et al. [106] study photoluminescence spectra of chemically exfoliated MoS2 thin films with average thicknesses ranging from 1.3 to 7.6 nm. They observed the thinnest samples exhibiting the strongest photoluminescence while the emission intensity gradually decreases with increasing film thickness, as shown in Fig. 2.38. The emission spectra for the thin films consist of one major
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peak and one minor peak at around 660 and 610 nm, respectively. These peaks labeled as A and B, agree well with the energy of A and B excitons,suggesting that they are from the direct band gap photoluminescence from the K point.
In 2012, Tongay et al. [119] reported the temperature dependence of photoluminescence spectra of single and few-layer mechanical exfoliated MoS2 and MoSe2 flakes onto 90 nm SiO2/Si substrate. At room-temperature, they observed the single-layer MoSe2 exhibits the strongest photoluminescence while the emission intensity gradually decreases with increasing layers, as shown in Fig. 2.39. In addition, Fig. 40a-d show the temperature dependence of PL measured on single- and few-layer samples of MoSe2 and MoS2 [119]. The temperature dependence of PL intensity of the single-layer and few-layer MoSe2 show striking difference.
The PL intensity of MoS2 decrease with increasing temperature regardless of the layer thickness.
In general, the suppression in PL intensity and peak broadening are typically attributed to the exponential enhancement in nonradiative electron−hole recombination processes, reducing the probability of radiative transition [119]. The distinct difference in the temperature behavior of these two materials is due to their intrinsic difference of band structures [119]. The rate of the indirect-to-direct bandgap crossover differs significantly between MoS2 and MoSe2. During this crossover the direct and indirect gaps in the case of single-layer and few-layer MoSe2 becomes nearly degenerate (the indirect bandgap value lies close to the direct bandgap). In contrast to MoSe2, the indirect and direct bandgaps are far from degenerate for MoS2 sample [119]. An increase in temperature slightly expands the interlayer distance. This tends to decouple neighboring MoSe2 layers, pushing the system further toward the bandgap degeneracy. In this case, the contribution from the hot PL across the direct bandgap to the PL intensity becomes much stronger at high temperatures. On the contrary, since the indirect and direct gaps are
well-17
separated in MoS2 sample, band degeneracy cannot be thermally approached. This distinct difference between these two similar materials leads to a drastic difference in the temperature dependence of their PL intensity [119]. In 2014, Shaw et al. [120] reported the PL spectrum on monolayer CVD MoSe2 shows a prominent emission peak at 800 nm ± 5nm (Fig. 2.41). The PL intensity for the bilayer MoSe2 is significant reduced, and the peak position red-shift to 825 nm ± 5nm. In addition, there is no noticeable peak for the tri-layer PL spectrum. The PL spectroscopy demonstrates that the monolayer MoSe2 exhibit strong emission, while bilayer or tri-layer exhibit much weak emission, indicating of the transition to a direct band gap semiconductor as the thickness is reduced to a monolayer.
In 2013, Mak et al. [123] reported the tightly bound trions in monolayer MoS2. They observed the exciton (A) and trion (A－) resonance behave differently under gate voltage from -100 to 80 V (Fig. 2.42). Optical response of monolayer MoS2 is dominated by neutral excitons in undoped sample (gate voltage = -80 V). Trions emerge, accompanied by a reduction of exciton absorption and photoluminescence, when excess electrons are introduced to bind to photoexcited electron-hole pairs. In addition, the trion binding energy estimated to be 18.0 ± 1.5 meV. The existence of tightly bound trions with dynamically controllable hole valley and spin in monolayer MoS2 opens up possibilities of novel many-body phenomena.
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Fig. 2.1: Ambipolar electric field effect in single-layer grapheme. The insets show its low-energy dispersion, indicating the changes in the position of the Fermi energy EF with varying the gate voltage [3].
Fig. 2.2: Optical image of an array of ion gel gated graphene FETs fabricated on a plastic substrate [52].
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Fig. 2.3: Schematic illustration of bottom-gated graphene/GO transistor. The graphene channel which was monolithically patterned with source and drain electrodes is above the GO dielectric [53].
Fig. 2.4: Schematic illustration and photo for electrochemical exfoliation of graphite [60].
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Fig. 2.5: Schematic illustration of CVD growth of graphene and its transfer process [66].
Fig. 2.6: Raman-scattering spectra of graphite and graphene [89].
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Fig. 2.7: Evolution of 2D band as a function of number of layers for 514 nm excitation [89].
Fig. 2.8: Evolution of G band as a function of number of layers for 514 nm excitation [92].
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Fig. 2.9: The real part of the optical sheet conductance of graphite per layer [(a) experiment, (b) calculation)] as well as the calculated conductance of isolated undoped graphene (c). The inset of (c) depicts the optical transitions between hole and electron bands in monolayer graphene [93].
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Fig. 2.10: Absorption spectra for three different samples of graphene over the range of photon energies between 0.5 and 1.2 eV. The left scale gives the absorbance in units of πα, while the right scale gives the corresponding optical sheet conductivity in units of πG0/4.The black horizontal line corresponds to the universal result of an absorbance of πα = 2.293% with a range indicated of ± 0.1 πα or approximately ± 0.2% [94].
Fig. 2.11: Measured graphene absorption spectra of samples 1 and 2 over a range of photon energies between 0.25 and 0.8 eV. Theory fits lines are based on a model of noninteracting massless fermions [94].
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Fig. 2.12: Absorption spectra of single-layer graphene. Dashed curves 1 and 2 are calculations from Yang et al. [96]. Solid curves 3 and 4 are experimental data. The symmetric peak at 5.2 eV (curve 1) is expected by noninteracting theory, whereas interaction effects should result in the asymmetric peak downshifted to 4.6 eV (curve 2). The predicted shift and asymmetry are in qualitative agreement with experimental data (curves 3 and 4) [95].
Fig. 2.13: Optical constants of graphene n (solid line) and k (dashed line) [97].
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Fig. 2.14: Optical functions n and k shown for both a point-by-point fit and an optical dispersion model [98].
Fig. 2.15: Comparison of n and k values between CVD graphene [98] and exfoliated graphene by Kravets et al. [95] and Weber et al. [97].
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Fig. 2.16: Schematic illustration of HfO2-top-gated monolayer MoS2 FET device [36].
Fig. 2.17: A thin-film MoS2 electric double-layer transistors constructed with an ion gel on a plastic substrate [102].
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Fig. 2.18: The dependence of the drain current at a gate voltage, VG, of 1.5 V (red) and the carrier mobility on the curvature radius. The carrier mobility is normalized by the results without bending (blue). The inset schematically illustrates the bending measurements [102].
Fig. 2.19: Schematic illustration and optical images of the MoS2 thin film transistor under stretching [103].
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Fig. 2.20: Top: the strain dependence of the drain current at a reference voltage, VR, of 1.6 V (red) and 0.3 V (blue). Bottom: the strain dependence of the on/off ratio (black) [103].
Fig. 2.21: Top: the electron mobility at various strains (red). Bottom: the specific capacitance of the ion-gel/MoS2 interface at 15 Hz (bottom, black) at various strains. The mobility is normalized by the results obtained in the absence of an applied tension. The blue square in the top panel corresponds to the normalized mobility after stretching at a 5% strain [103].
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Fig. 2.22: G vs.VG–VT at different temperatures, ranging from 298 to 78 K. The data show a noticeable increase of the dG/d(VG–VT) slope with decreasing T. Inset: μ vs. T for three different MoSe2 devices [50].
Fig. 2.23: Schematic illustration of monolayer to few layer MoS2 by sulfurization of Mo thin film [112].
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Fig. 2.24: Schematic of MoS2 layer deposited by two-step thermolysis, and the films obtained on a sapphire and silica substrate [113].
Fig. 2.25: Schematic of CVD of MoS2 from solid S and MoO3 precursors. The red dots indicate the heating elements in the furnace [114].
Fig. 2.26: MoS2 shows great flexibility to surface corrugations [115].
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Fig. 2.27: Thickness-dependence of Raman-scattering spectra for MoS2 [116].
Fig. 2.28: Schematic illustration of in-plane phonon modes E2g and the out-of-plane phonon mode A1g for the MoS2 [117].
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Fig. 2.29: Peak position shifts for the E2g and A1g modes as a function of MoS2 layer thickness for the spectra in Fig. 2.27 [116].
Fig. 2.30: Raman spectra acquired on a MoSe2 flake using excitation wavelengths of 442 nm [50].
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Fig. 2.31: Raman spectra acquired on a MoSe2 flake using excitation wavelengths of 532 nm [50].
Fig. 2.32: Raman spectrum of single (solid red line) and more than 10 layers (dashed blue line) MoX2 (X = S, Se) [119].
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Fig. 2.33: Raman spectra of MoSe2 with various numbers of layers; the bulk spectrum is displayed at a ten fold scale [120].
Fig. 2.34: Band structures calculated from first principles density functional theory (DFT) for bulk and monolayer MoS2 [121].
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Fig. 2.35: Calculated band structure of single-layer and bulk MoSe2 [119].
Fig. 2.36: Normalized PL spectra by the intensity of peak A of thin layers of MoS2 for N = 1-6.
Feature I for N = 4-6 is magnified and the spectra are displaced for clarity [33].
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Fig. 2.37: PL spectra of MoS2 for monolayer, bilayer, hexalauer, and bulk [45].
Fig. 2.38: Photoluminescence spectra of MoS2 thin films with average thickness ranging from 1.3 to 7.6 nm. Inset of Fig. 2.38 shows energy of the A exciton peak as a function of average film thickness [106].
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Fig. 2.39: Measured room-temperature photoluminescence on a single-layer (red), three-layer (blue dashed), and bulk (green dotted dashed) MoSe2. Here the measurement parameters including laser excitation intensity are the same [119].
Fig. 2.40: Temperature dependence of photoluminescence on (a−b) single-layer MoSe2 and MoS2 and (c−d) few-layer MoSe2 and MoS2 [119].
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Fig. 2.41: Photoluminescence spectrum of MoSe2 up to three layers [120].
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Fig. 2.42: Absorption and photoluminescence spectra (red lines) in the range of 1.8–2.0 eV for the indicated back-gate voltages. The exciton (A) and trion (A－) resonances behave differently with gate voltage. Left: Absorption spectra, with the dashed blue lines as a guide to the eye for the threshold energies of A and A－features. The green lines are power-law fits to the experimental results, as described in the main text, with the A and A components shown as the blue lines. Right: The photoluminescence spectra of the A and A－features are fit to Lorentzians (green lines). The dashed blue line indicates the absorption peak of the A－resonance and the arrows show the doping-dependent Stokes shift of the trion photoluminescence [123].
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