Probing Critical Point Energies of Transition Metal Dichalcogenides: Surprising Indirect Gap of Single Layer WSe₂

Abstract

Experimental determinations of the electronic band structures in TMDs are quite non-trivial.Optical spectroscopies [1][2][3][4][5] are unsuitable to measure the quasi-particle band structures due to the existence of large exciton binding energies. Using angle resolved photoemission (ARPES), it is difficult to probe the conduction band structures 6,7 . In principle, scanning tunneling spectroscopy (STS) would be an ideal probe to determine both the valence and conduction band structures.However, the reported results have been controversial thus far, even for the determination of the quasi-particle band gaps [8][9][10] . As we will show, this is due primarily to the intriguing influence of the lateral momentum in the tunneling process, making certain critical points difficult to access in the conventional scanning tunneling spectroscopy acquired at a constant tip-to-sampledistance (Z). By using a comprehensive approach combining the constant Z and variable Z spectroscopies, as well as state-resolved tunneling decay constant measurements, we have shown 3 that detailed electronic structures, including quasi-particle gaps, critical point energy locations and their origins in the BZs in TMDs can be revealed.The TMD samples are grown using chemical vapor deposition (CVD) for WSe 2 11 or molecular beam epitaxy (MBE) for MoSe 2 on highly-oriented-pyrolytic-graphite (HOPG)substrates. In addition, MoSe 2 has also been grown on epitaxial bi-layer graphene to investigate the environmental influences on the quasi-particle band structures. Figures 1a and b show scanning tunneling microscopy (STM) images of MoSe 2 and WSe 2 , respectively. Due to a nearly 4:3 lattice match with the graphite, the TMD samples also show Moiré patterns with a periodicity of ~ 1nm. An example is shown as an inset in Fig. 1b, similar to those reported earlier 9 . In Fig. 1c we show a generic electronic structure for SL-TMD materials. We first discuss the result of MoSe 2 due to the availability of experimentally determined E vs. k dispersion in the valence band which can be used to cross-check with our results. 4Such a large difference in the decay constant is responsible for the difficulty in detecting the states near the VBM. The lack of the sensitivity in the constant-Z STS can be overcome by acquiring spectra at variable Z as described before 14 . Here we adopt a form of variable Z spectroscopy by performing STS at constant current. In this mode, as the sample bias is scanned across different thresholds, Z (the dependent variable) will respond automatically in order to keep the current constant. The differential conductivity (I/V) I is measured by using a lock-in amplifier (Fig. 2b). In the meantime, the acquired Z-value is used to deduce (Z/V) I which can be used to identify individual thresholds (Fig. 2c).For the valence band (left panel), the state at the  point also appears as a prominent peak in the (I/V) I spectrum. Moreover, spectroscopic features above  are observed due to the significant enhancement of the sensitivity. A shoul...

Band Alignment in MoS2/WS2 Transition Metal Dichalcogenide Heterostructures Probed by Scanning Tunneling Microscopy and Spectroscopy

“…22, this CB onset must not arise from the K point of MoS 2 . As previously stated, the ability to probe a point in the band with high in-plane momentum is not very likely given the distance away from the tip.And as shown in Ref 45,. the Q point is a stronger contributor of current than the K point.…”

“…A further demonstration of this dependence can be seen in equation(2)by noticing how the lack of a parallel momentum term, representative of current flowing from the Γ point, can decrease the value of the term within the square root by about 30%. Our treatment of parallel momentum in the tunneling probability term is also implemented in another recent work 45. The effective mass of the electron (m*) are given the values of 0.35m 0 and 0.3m 0 for MoS 2 and WS 2 , respectively 48.…”

Excitons in atomically thin transition-metal dichalcogenides

“…3a). The reported values, as summarized in the Table II, range from 0.22 eV for MoS 2 to 0.55 eV for MoSe 2 (Ugeda et al, 2014); further reports include (Bradley et al, 2015;Chiu et al, 2015;Rigosi et al, 2016;Zhang et al, 2015a). The differences can be related to (i) the overall precision in extracting the onsets of the tunneling current and (ii) to the use of different conducting substrates required for the STS, i.e., the influence of different dielectric environments and related proximity effects.…”

Excitonic effects in the optical properties of 2D materials:an equation of motion approach

“…Finally, the numerical procedure to calculate the optical conductivity is the following: we solve the integral equation (45) to determine the eigenfunctions ψ sτ λ (k), calculate the polarization from the integral in equation (46), and lastly the optical conductivity is calculated from relation (37). The absorbance for a MoS 2 suspended sheet for a TEM wave with normal incidence can be obtained from the optical conductivity as [42]:…”