# Optoelectronic Devices Based on Atomically Thin Transition Metal Dichalcogenides
## 2 Basic Optical Properties  
TMDs have the chemical formula \(MX_{2}\), where \(M\) is a transition metal (e.g., Mo, W, _etc._) and \(X\) is a chalcogen atom (S, Se, or Te) [5; 6; 7; 8; 9]. The atoms in 2D TMDs are arranged in an \(X\)-\(M\)-\(X\) sandwich, with a monolayer thickness of 0.6-0.7 nm. For optoelectronic devices, mainly Mo and W-based dichalcogenides have been studied. These are semiconductors with optical properties that depend on the material thickness. Bulk TMD semiconductors possess an indirect gap, which becomes a direct one in monolayers [5; 10]. Figure 1a depicts band structure calculations for MoS\({}_{2}\) with various thicknesses [10]. Bulk MoS\({}_{2}\) has a bandgap of 1.3 eV, with the valence band maximum at the \(\Gamma\)-point in the Brillouin zone and the conduction band minimum along the \(\Gamma\)-K direction. As the number of layers decreases, the valence band maxima and conduction band minima shift due to quantum confinement and a direct semiconductor is obtained in the monolayer limit. The indirect-to-direct semiconductor transition is manifested as enhanced photoluminescence (PL) in monolayers. For example, in MoS\({}_{2}\), the monolayer quantum yield is more than four orders of magnitude larger than that in bulk (see Figure 1b) [5]. Similar observations have been made for other TMDs [11]. Mo- and W-based TMDs exhibit optical bandgaps in the range \(E_{X}\) = 1.1-2.0 eV (see Table 1), _i.e._, energies corresponding to the technologically important visible and near-infrared spectral regimes. However, despite being direct gap semiconductors, the reported photoluminescence quantum yields of as-exfoliated (or synthetically grown) TMD monolayers are poor. The room-temperature photoluminescence quantum yield of exfoliated MoS\({}_{2}\), for example, was found to be 4 \(\times\) 10\({}^{-3}\) only [5]. It is believed that unintentional doping and crystal defects play a major role in suppressing the luminescence. Very recently, however, solution-based chemical treatment of MoS\({}_{2}\) by an organic superacid [12] has resulted in a quantum yield of more than 95%. Similar improvements were reported by chemical treatments of other TMDs [13]. These studies open the door for the development of more efficient TMD-based light emitters and other optoelectronic devices. Excitons are strongly bound in 2D materials with binding energies of up to \(\sim\)0.6 eV. This is due to the enhanced electron-hole interaction in 2D systems and the reduced dielectric screening [18]. As a result, the optical spectra of TMDs are dominated by excitonic rather than band-to-band transitions even at room temperature and exhibit pronounced peaks. This is in contrast to traditional three-dimensional (3D) semiconductors, in which exciton binding energies are smaller than the thermal energy at room temperature. In TMDs, several excitonic transitions can be observed, where the two lowest-energy peaks, the A and B-excitons, arise from optical transitions between the spin-orbit split valence and conduction bands [5; 10; 21]. The spin-orbit splitting \(\Delta E_{SO,p}\) in the valence band varies between 0.16 and 0.4 eV (see Table 1), whereas calculations suggest a splitting \(\Delta E_{SO,e}\) in the range of tens of mV for the conductions band. \begin{table}
\begin{tabular}{c c c c} \hline
**TMD** & \(E_{X}\) **(eV)** & \(\Delta E_{SO,p}\) **(eV)** & \(\Delta E_{b}\) **(eV)** \\ \hline MoS\({}_{2}\) & 1.85 [10] & 0.16 [10] & 0.57 [14] \\ MoSe\({}_{2}\) & 1.55 [11] & 0.2 [15] & 0.55 [16] \\ WS\({}_{2}\) & 2.0 [17] & 0.4 [17] & 0.32 [18] \\ WSe\({}_{2}\) & 1.65 [11] & 0.4 [17] & 0.37 [19] \\ MoTe\({}_{2}\) & 1.1 [20] & 0.25 [20] & - \\ \hline \end{tabular}
\end{table} 
Table 1: Optical bandgap, spin orbit splitting and exciton binding energy for monolayer transition metal dichalcogenides (TMDs). Figure 1: **(a)** Band structure calculations of bulk, four-layer, bilayer and monolayer MoS\({}_{2}\) (from left to right). Arrows indicate the lowest energy transitions.