# Optoelectronic Devices Based on Atomically Thin Transition Metal Dichalcogenides
## 3 Photodetectors
The trapped charge can influence the conductance of the TMD transistor (i) by shifting the threshold voltage from \(V_{th}\) in the dark to \(V_{th}-\Delta V_{th}\) under optical illumination (photogating effect), and (ii) by increasing the channel conductivity \(\Delta\sigma\) due to photo-induced excess carriers (photoconductive effect) [41; 53]. The photogating effect gives rise to a photocurrent \(I_{ph}=g_{m}\Delta V_{th}\), where \(g_{m}\) is the transistor's transconductance. The photocurrent produced by the photoconductive effect is simply given by \(I_{ph}=(W/L)\,V_{D}\Delta\sigma\), where \(W\) and \(L\) denote the channel width and length, respectively, and \(V_{D}\) is the applied voltage. In general, the photoresponse is a combination of both mechanisms with the photogating effect being dominant in the transistor ON-state and the photoconductive contribution being more prominent in the OFF-state. Responsivities and response times are typically in the range \(\sim\)10\({}^{-1}\)-10\({}^{4}\) A/W and \(\sim\)10\({}^{-4}\)-10 s, respectively, depending on the light intensity, the operation conditions, and the type of trap. The trap  
Figure 2: (a) Inset: Transition metal dichalcogenides TMD field-effect transistor as a photodetector. Main panel: typical gating characteristics with and without illumination. Reproduced with permission from [40], Copyright Nature Publishing Group, 2013. (b) Left: density-of-states (DOS) in MoS\({}_{2}\). Band tail states exist underneath and above the conduction and valence band edges, respectively, that act as charge traps. Right: simplified energy band diagram that approximates the valence band tail by a discrete distribution of trap states. Reproduced with permission from [41], Copyright American Chemical Society, 2014.  
states get filled with increasing illumination intensity, resulting in saturation of the photoresponse. It has been demonstrated that TMD encapsulation can enhance the detector performance under ambient conditions by increasing the mobility, reducing the degradation by environmental effects and preventing current fluctuations due to charge transfer into physisorbed gas molecules [54]. Photogain can also be achieved by integration of 2D materials with other materials, such as e.g., quantum dots, to realize a hybrid photodetector (see Figure 3a). This was demonstrated by sensitizing graphene with lead sulfide quantum dots [55]. Light absorption in the dots results in a charge transfer to the underlying graphene channel, which modifies the channel conductance. A related work employed the charge transfer from MoS\({}_{2}\) into graphene for photodetection [56]. Both devices, however, suffered from high dark current and large power consumption because of graphene's semi-metallic behavior. The dark current can be reduced by replacement of the graphene channel with MoS\({}_{2}\) and transistor operation in the OFF-state [57]. Light is then absorbed in the dots and the photoexcited carriers are separated at the quantum dot/MoS\({}_{2}\) interface, as shown in Figure 3b. While the holes remain trapped in the dots, electrons circulate through the MoS\({}_{2}\) channel driven by the applied voltage. The device in [57] showed a photoresponsivity of 10\({}^{6}\) A/W and a low dark current, which resulted in a detectivity of almost 10\({}^{15}\) Jones. Two-dimensional materials can be assembled layer by layer to form a van der Waals heterostructure [58]. The surfaces of 2D materials do not have any dangling bonds and the absence of lattice matching conditions in van der Waals heterostructures permits to combine any arbitrary sequence of 2D materials. Heterostructures, comprised of vertical stacks of graphene-TMD-graphene layers, can act as photodetectors [59; 60]. In these devices (see Figure 4a), graphene is employed as work function tunable electrode, whereas a TMD semiconductor is utilized as photoactive material, showing strong photon absorption.