Dielectric function, critical points, and Rydberg exciton series of WSe₂ monolayer

Abstract

The complex dielectric function ([Formula: see text]) of WSe monolayer grown by atomic layer deposition is investigated using spectroscopic ellipsometry. Band structure parameters are obtained by standard line-shape analysis of the second-energy-derivative of [Formula: see text] spectra. The fundamental band gap is observed at 2.26 eV, corresponds to transition between valence band (VB) maximum at the K point and conduction band (CB) minimum at Q point in the Brillouin zone (BZ). Two strong so-called A and B excitonic peaks in [Formula: see text] spectra originate from vertical transitions from spin-orbit split (0.43 eV) VB to CB at K point of the BZ. Binding energies of A and B exactions are 0.71 and 0.28 eV, respectively. Well resolved five excited excitons states has been detected within the spectral region between A and B. Energy profile of the Rydberg series shows significant deviation from the hydrogenic behavior, discussed in connection with the 2D hydrogen model. Results presented here will improve our understanding about the optical response of 2D materials and will help to design better optoelectronic applications and validate theoretical considerations.

Temperature-dependent optical constants of monolayer $${\text {MoS}}_2$$, $${\text {MoSe}}_2$$, $${\text {WS}}_2$$, and $${\text {WSe}}_2$$: spectroscopic ellipsometry and first-principles calculations

“…The band gap decreases linearly with an increase in temperature, which is explained by the vibronic model 23 . Diware et al 24 studied the complex dielectric function of monolayer using spectroscopic ellipsometry. They found that monolayer has an indirect band gap of 2.26 eV and direct band gap of 2.35 eV.…”

Layer-dependent dielectric and optical properties of centimeter-scale 2D WSe2: evolution from a single layer to few layers

“…Commonly used techniques to determine the dielectric function and complex refractive index of 2D WSe 2 include the reflection (or absorption) spectrum method, 15 differential reflection (or transmission) spectrum method, 16 scattering-type scanning near-field optical microscopy (s-SNOM), [17][18][19][20] and ellipsometry. [21][22][23][24] With the reflection (or absorption) spectrum method, Li et al obtained the dielectric function of the monolayer WSe 2 over an energy range of 1.5-3.0 eV by combining a Kramers-Kronig (K-K) constrained variational analysis. 15 This method depends on the absolute detected light intensity, which can be easily affected by the experimental environment.…”

“…21 Similarly, Diware et al extracted the dielectric functions and thicknesses of 1L and 3L WSe 2 from the measured ellipsometric spectra by using multilayer optical calculations with appropriate optical models. 23,24 However, the existing ellipsometric studies on 2D WSe 2 failed to reveal the evolution of layer-dependent dielectric and optical properties due to the lack of high-quality materials with continuous layers. Moreover, the physical mechanisms behind these properties of 2D WSe 2 have not been understood yet.…”

Two-dimensional excitons in monolayer transition metal dichalcogenides from radial equation and variational calculations

“…This prediction has been experimentally confirmed by several experimental studies, with optical spectroscopy measurements performed on ML WS 2 on a SiO 2 substrate [6,14] and also for ML WSe 2 on a SiO 2 substrate [15]. Ground state exciton binding energies have been measured for a freely suspended ML of MoS 2 [12] and TMD monolayers in a variety of dielectric environments, such as MoS 2 on substrate SiO 2 [18,19] or encapsulated in hBN [20], as well as MoSe 2 [21], WS 2 [6,14,18,19,22,23] and WSe 2 [15,21,[24][25][26][27], all on a SiO 2 substrate.…”

“…We note however that these calculated binding energies necessarily depend on the reduced mass, the 2D polarizability and the exact form of the electron-hole interaction potential. Experimentally, ground state exciton binding energies have been measured for isolated MoS 2 monolayers and TMD monolayers on a substrate, most on SiO 2 or fused silica [6,14,15,18,19,[21][22][23][24][25][26][27], which are also listed in Table II (the last two columns) for a quantitative comparison. We have found no measurement on WSe 2 monolayers on a hBN substrate and instead put an experimental value of monolayer WSe 2 on diamond which has a similar dielectric constant to hBN.…”