Raman scattering with infrared excitation resonant with the ${\mathrm{MoSe}}_{2}$ indirect band gap

Raman scattering with infrared excitation resonant with the ${MoSe}_{2}$ indirect band gap

Simone Sotgiu, Tommaso Venanzi, Francesco Macheda, Elena Stellino, Michele Ortolani, Paolo Postorino, and Leonetta Baldassarre

Phys. Rev. B 106, 085204 – Published 16 August 2022

Abstract

Resonance Raman scattering, which probes electrons, phonons, and their interplay in crystals, is extensively used in two-dimensional materials. Here we investigate Raman modes in ${MoSe}_{2}$ at different laser excitation energies from 2.33 eV down to the near infrared 1.16 eV. The Raman spectrum at 1.16 eV excitation energy shows that the intensity of high-order modes is strongly enhanced if compared to the first-order phonon modes' intensity due to resonance effects with the ${MoSe}_{2}$ indirect band gap. By comparing the experimental results with the two-phonon density of states calculated with density functional theory, we show that the high-order modes originate mostly from two-phonon modes with opposite momenta. In particular, we identify the momenta of the phonon modes that couple strongly with the electrons to produce the resonance process at 1.16 eV, while we verify that at 2.33 eV the two-phonon modes' line shape compares well with the two-phonon density of states calculated over the entire Brillouin zone. We also show that by lowering the crystal temperature, we actively suppress the intensity of the resonant two-phonon modes and we interpret this as the result of the increase of the indirect band gap at low temperature that moves our excitation energy out of the resonance condition.

Received 27 April 2022
Revised 12 July 2022
Accepted 27 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.085204

Physics Subject Headings (PhySH)

Phonons

Transition metal dichalcogenides

Density functional theory Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Simone Sotgiu ^1,*, Tommaso Venanzi ¹, Francesco Macheda ², Elena Stellino ³, Michele Ortolani ¹, Paolo Postorino ¹, and Leonetta Baldassarre ^1,†

¹Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185, Roma, Italy
²Istituto Italiano di Tecnologia, Graphene Laboratories, Via Morego 30, I-16163 Genova, Italy
³Department of Physics and Geology, University of Perugia, Via Alessandro Pascoli, 06123 Perugia, Italy

^*Corresponding author: simone.sotgiu@uniroma1.it
^†Corresponding author: leonetta.baldassarre@uniroma1.it

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Vol. 106, Iss. 8 — 15 August 2022

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Figure 1
Room temperature PL (red curve) obtained fitting the background of Raman spectrum ${MoSe}_{2}$ crystal (dotted red curve). The extrapolated gap is $E_{gap}^{PL} = 1.137 \pm 0.001$ eV. Tauc procedure (blue curve) from absorption experiment (dotted blue curve). The extrapolated gap is $E_{gap}^{Tauc} = 1.16 \pm 0.02$ eV. We have highlighted our 1.16 eV laser energy $E_{laser}$ .
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Figure 2
(a) Spectra of ${MoSe}_{2}$ bulk taken at infrared (1.16 eV) and visible (1.96 and 2.33 eV) energies. We can observe the presence of the first-order Raman peaks (labeled in black) and high-order modes due to difference (labeled in blue) or summation (labeled in red) processes (see main text for their definition). The high-order Raman peaks in the spectrum taken at 1.16 eV are strongly enhanced. The $E_{1 g}$ peak becomes visible as the excitation energy approaches the energy of the $C$ exciton (2.6 eV). All the spectra are normalized at the intensity of the $A_{1 g}$ mode and vertically shifted for the sake of clarity. (b) Integrated area of the $S$ Raman features, normalized to the area of the $A_{1 g}$ peak for the different laser energies used. One can clearly see the intensity enhancement of the $S$ modes with respect to first-order Raman peaks.
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Figure 3
(a) Raman spectra of $S_{3}$ modes compared with the 2ph-DOS. Besides the enhancement of the Raman scattering by using near-infrared excitation, the line shape of the peaks varies by changing the excitation laser energy revealing a resonant process. The spectra are normalized to the intensity of the $A_{1 g}$ mode. (b) Phonon dispersion of bulk ${MoSe}_{2}$ restricted to the FBZ along the $Γ - M - K - Γ$ line. The $T$ point, i.e., the minimum of the conduction band, is highlighted, together with the phonon wave vector which allows the indirect electronic transition. The $S_{3}$ feature is then obtained as the direct sum of phonon branches highlighted in black, its energy being hence the sum of the energy of the two branches restricted to a neighborhood of $T$ . In red are denoted the IR-active modes, in blue those Raman active. (c) Scheme of the resonant process described in this work: two phonons with opposite momenta can allow the indirect transition making the Raman process resonant. Note that the value of the energy gap is slightly underestimated by our DFT results, which is a typical feature of these calculations [17].
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Figure 4
(a), (b) Comparison between the spectrum taken at 2.33 eV and the 2ph-DOS integrated over all the FBZ for different Raman shift ranges. (c), (d) Comparison in the same spectral ranges for the spectrum taken at 1.16 eV and the 2ph-DOS restricted at q*.
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Figure 5
(a) Temperature-dependent Raman spectra of ${MoSe}_{2}$ taken at 1.16 eV plotted between 100–700 ${cm}^{- 1}$ and a zoom of the $S_{3}$ modes. The PL background has been subtracted from the spectra that are then normalized to the $A_{1 g}$ peak. Spectra have been offset for the sake of clarity. (b) PL peak as extracted from Raman measurements for several temperatures indicated in figure. We observe a PL emission between 200 K and 450 K suggesting that in this temperature range we are able to reach the conduction band minimum through an indirect electronic transition; hence the resonance condition is fulfilled for the second-order Raman process described above. The vertical line represents the laser energy. (c) Comparison between the thermal occupancy given by the BE statistics and the ratio of the $S_{3}$ modes and the $A_{1 g}$ peak. We used the values $ℏ ω_{1} = 310$ ${cm}^{- 1}$ and $ℏ ω_{2} = 286 {cm}^{- 1}$ , as explained in the main text. The BE curve has been multiplied for a constant so to match the values of the experimental points at low temperature (i.e., to the average of the $I_{S 3} / I_{A 1 g}$ value of the three points below 100 K where there is no PL peak, hence no resonance condition).
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Physical Review B

covering condensed matter and materials physics

Raman scattering with infrared excitation resonant with the ${MoSe}_{2}$ indirect band gap

Simone Sotgiu, Tommaso Venanzi, Francesco Macheda, Elena Stellino, Michele Ortolani, Paolo Postorino, and Leonetta Baldassarre

Phys. Rev. B 106, 085204 – Published 16 August 2022

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Physical Review B

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Raman scattering with infrared excitation resonant with the MoSe2 indirect band gap

Simone Sotgiu, Tommaso Venanzi, Francesco Macheda, Elena Stellino, Michele Ortolani, Paolo Postorino, and Leonetta Baldassarre

Phys. Rev. B 106, 085204 – Published 16 August 2022

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Raman scattering with infrared excitation resonant with the ${MoSe}_{2}$ indirect band gap