Figure 6.8 shows the experimental and best-fit calculated data of the monolayer-CVD-MoS2
film. The independently measured experimental data at 60º and 70º incidence angles and the model
curves are in good agreement. The room-temperature optical properties (n, k) of a monolayer-MoS2
film determined from the ellipsometry parameters of Ψ and ∆ are shown in Figure 6.9. We notice that the shapes of the refractive index dispersions of a monolayer-MoS2 film and a MoS2 single crystal in the near-infrared frequency region are quite similar despite a constant 8% lower level difference for the monolayer film. Optical transitions can be identified in the spectrum of resonance features that appear in the extinction coefficient, with detailed analysis shown below.
Figure 6.10 displays the room-temperature absorption spectrum of a monolayer-MoS2 film.
For comparison, the absorption spectrum of a MoS2 single crystal is also shown. The absorption spectrum can reasonably be divided into a region at low energy, which is dominated by excitonic
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transition on an otherwise relatively low absorption background, and a region of strong absorption at higher energies. Notably, the absorption spectrum of the monolayer-MoS2 film is overall blue shifted compared with that of a MoS2 single crystal. Two weak features near 1.88 and 2.03 eV, assigned as A and B excitons [144], are ~ 0.1 – 0.2 eV higher than those of the bulk material [145]. Three strong charge transfer bands centered at 3.0, 3.3, and 4.4 eV shift to higher energies by ~ 0.2 eV compared with those in the bulk counterpart [145]. These blue shifts are a consequence of the reduced dimensionality of the monolayer-MoS2 film.
The discrete states of the exciton observed in a monolayer MoS2 film can be modeled by using a broadened Lorentzian line shape [146]
1 )]
where n is the index number of the valence band, m is the index number of the excited state of the exciton, Rn is the binding energy, ex,m is a broadening parameter of the mth excited exciton state, E0n is the band gap energy, andA0exn is an adjustable fitting parameter. In particular, For common two-dimensional materials, the ground-state exciton binding energy is given by
Ryd D
b E
E2 4 [147]. Our fitting curve is shown in Figure 6.10. A list of fitting parameters is given in Table 6.2. A monolayer MoS2 film has a direct band gap of 1.95 eV. This result is in good agreement with the result observed in mechanically exfoliated MoS2 [33]. Figure 6.11 shows the temperature dependence of the gap. The observed increase in the energy gap with decreasing temperature can be described using the Bose-Einstein model [148]:
Eg(T) = Eg(0) － 2aB / [exp(ΘB/T)－1], (6.2.2)
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where Eg(0) is the band-gap energy at 0 K, aB is the strength of electron-phonon interaction, and ΘB is average phonon temperature. Our fitting results indicate that the band-gap energy toward 0 K is about 2.07 ± 0.05 eV. The strength of the electron-phonon interaction aB and average phonon temperature ΘB are 81 meV and 249 K, respectively. These values are comparable to those of other semiconductor materials; for example, in bulk GaAs, aB = 59.7 meV and ΘB = 241 K [149]. It is also interesting to note that the band-gap narrowing coefficient of the monolayer-MoS2 film obtained using the formula β = dEg/dT is calculated to be about -2 × 10-4 eV / K at 300 K.
Table 6.2. The exciton band-gap energies, exciton binding energies, and exciton broadening parameters of a monolayer MoS2 film.
Monolayer MoS2 300 K
A-exciton energy gap (eV) 1.95 ± 0.01 A-exciton binding energy (eV) 0.28 ± 0.005 A-exciton (eV) Γex,1 (eV) 0.05 ± 0.005 B-exciton energy gap (eV) 2.08 ± 0.01 B-exciton binding energy (eV) 0.16 ± 0.005 B-exciton (eV) Γex,1 (eV) 0.09 ± 0.005
As mentioned above, a monolayer-MoS2 film exhibits an increase in A and B exciton energies compared with that of the bulk material. This blue shift is attributed to carrier confinement in the direction parallel to the c axis (z direction) similar to the quantum size effect
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observed in MS2 (M = W, Mo) nanoparticles [144]. Figure 6.12 shows the temperature-dependent evolution of A and B exciton features. The peak positions of both excitons shift to higher energies by ~ 0.07 eV as the temperature decreases from 300 to 10 K. This is similar to that obtained for excitons in bulk MoS2 [144,150], verifying that the nature of Wannier excitons is preserved; i.e., the excitons are not bound to dislocations or imperfections.
First-principles calculations [117,121,122] predict that bulk MoS2 exhibits an indirect gap transition from the top of the valence band situated at the Γ point to the bottom of the conduction band at a midpoint along the Γ- K symmetry line. When the number of layers reduces to a monolayer, the top of the valence band and bottom of the conduction band move toward the K point; consequently, MoS2 undergoes a transition to a direct-band semiconductor. Moreover, the direct gap transitions at point K between the top of the split valence bands and bottom of the conduction band are called A and B excitons. It is important to point out that the splitting of the top valance band of the monolayer at the K point is purely because of spin-orbit coupling and a lack of inversion symmetry [151]. From the exciton positions, the valence-band spin orbit splitting at point K is estimated to be about 150 and 160 meV for our monolayer CVD-MoS2
film and single crystal, respectively. These results are in good agreement with the results of theoretical calculations [152-154]. The smaller magnitude of spin orbit coupling observed in the monolayer-MoS2 film suggests that structural strain modifies the band curvature at point K [155].
Finally, fitting the optical absorption coefficient spectra of the monolayer- CVD-MoS2 at 10 K, as shown in Figure 6.13. This leads to an exciton binding energy of 0.48 eV for our monolayer-CVD-MoS2 film, which is significantly larger than the bulk value of 0.05 – 0.08 eV [145,156]. Very recently, Zhang et al. [157] reported the exciton binding energy of single layer MoS2 on graphite is 0.22 ± 0.1 eV(or 0.42 eV if the second threshold is use) at 77 K. This value
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is close to our result. Several first-principles calculations have reported that the exciton binding energy in monolayer-MoS2 is clearly higher than our data by about 0.4 – 0.6 eV [152-154,158,159], which is mainly due to their overestimation of the monolayer band gap. On the other hand, the exciton binding energy decreases when the temperature is raised. Such behavior has been theoretically predicted in the effect of temperature on the exciton binding energy in a quantum dot [160]. These results further suggest that many-body interactions play an important role in the excitonic properties of a monolayer MoS2 film. As is also well known, the exciton Rydberg constant is given byERyd 13.6ex/m02, where ex= me m / (h m +e m ) is the effective h exciton mass, m is the electron mass, and0 is the dielectric constant [147]. Using the dielectric constant ( ~ 4.4) obtained from the analysis of the THz spectra, the effective exciton massex is found to be 0.17 me. The exciton radius aex (= a0 m0/ex, where a0 ~ 0.53 Å is the Bohr radius of the hydrogen atom) is estimated to be about 13.7 Å . This radius of the exciton is large enough relative to the in-plane lattice constant, that is, the weakly bonded Mott-Wannier excitons theory should still be at least approximately applicable to our monolayer-CVD-MoS2
film.
6-3 Summary
In summary, the THz absorption and spectroscopic ellipsometry spectra of a monolayer-CVD-MoS2 film provide important insight into the charge dynamics and electronic structures in this system. First, the THz conductivity consists of free carrier absorption at zero frequency. As the temperature is lowered, the Drude plasma frequency (~ 7 THz) decreases, whereas the carrier relaxation time (~ 26 fs) does not show much temperature variation. These scenarios show the
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semiconducting behavior of a monolayer-CVD-MoS2 film. Second, variable temperature absorption spectra of a monolayer-CVD-MoS2 filmshowa direct gap (~ 1.95 eV at 300 K and ~ 2.07 eV at 10 K). Three strong charge transfer bands are overall blue shifted by ~ 0.2 eV compared with those of the bulk material. Most importantly, this study identifies the ground-state exciton binding energy of a monolayer-CVD-MoS2 film at about 0.48 eV. Our results highlight that the distinctive optical properties of a monolayer-CVD-MoS2 film are due to quantum confinement brought about by the nanoscale dimensions of the system.
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Fig. 6.1: Raman-scattering spectra of a monolayer-CVD-MoS2 film and a MoS2 single crystal.
Fig. 6.2: Temperature-dependence Raman-scattering spectra of a monolayer-CVD-MoS2 film.
360 380 400 420 440
Intensity (arb. units)
Raman Shift (cm-1) Mono
Bulk E2g
A1g
360 380 400 420 440
Intensity (arb. units)
Raman Shift (cm-1)
10 K 100 K 200 K 300 K E2g
A1g
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Fig. 6.3(a): Temperature dependence of frequency, damping, oscillator strength, and the asymmetry factor of E2g phonon mode of a monolayer-CVD-MoS2 film. The thin solid lines are results of the fitting taking into account the temperature-induced anharmonicity.
0 100 200 300
-0.8 -0.4
Temperature (K)
1 /q
600 650
p( c m
-1)
9 10 11
( c m
-1)
385 386 387 388 389
( c m
-1)
(a)
E
2gmode
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Fig. 6.3(b): Temperature dependence of frequency, damping, oscillator strength, and the asymmetry factor of A1g phonon mode of a monolayer-CVD-MoS2 film. The thin solid lines are results of the fitting taking into account the temperature-induced anharmonicity.
0 100 200 300
460 480 500
Temperature (K)
p( c m
-1)
7 8 9
( c m
-1)
405 406 407 408 409
( c m
-1)
(b)
A
1gmode
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Fig. 6.4: Room-temperature optical transmission spectra of a bare silicon substrate and monolayer-CVD-MoS2 film.
Fig. 6.5: Real part of room-temperature optical conductivity spectrum of a monolayer-CVD-MoS2 film (solid line). The various terms in the fits are also shown (dashed line): the Drude band and one Lorentz oscillator.
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Fig. 6.6: Temperature dependences of Drude plasma frequency and carrier relaxation time.
Fig. 6.7: Temperature dependence of the Drude conductivity.
0 100 200 300
5 6 7 8 9
Temperature (K)
pD (THz)
22 24 26
Relaxation Time (fs)
0 100 200 300
120 140 160 180
Drude (-1 cm-1 )
Temperature (K)
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Fig. 6.8: Room temperature experimental (symbols) at 60º and 70º incidence angles and fitted (dashed lines) values of ellipsometric parameters of Ψ and ∆ of a monolayer-CVD-MoS2 film.
Fig. 6.9: Refractive index n and extinction coefficient k of a monolayer-CVD-MoS2 film.
0