Directed Energy Transfer from Monolayer WS2 to Near-Infrared Emitting PbS–CdS Quantum Dots

Heterostructures of two-dimensional (2D) transition metal dichalcogenides (TMDs) and inorganic semiconducting zero-dimensional (0D) quantum dots (QDs) offer useful charge and energy transfer pathways, which could form the basis of future optoelectronic devices. To date, most have focused on charge transfer and energy transfer from QDs to TMDs, that is, from 0D to 2D. Here, we present a study of the energy transfer process from a 2D to 0D material, specifically exploring energy transfer from monolayer tungsten disulfide (WS2) to near-infrared emitting lead sulfide–cadmium sulfide (PbS–CdS) QDs. The high absorption cross section of WS2 in the visible region combined with the potentially high photoluminescence (PL) efficiency of PbS QD systems makes this an interesting donor–acceptor system that can effectively use the WS2 as an antenna and the QD as a tunable emitter, in this case, downshifting the emission energy over hundreds of millielectron volts. We study the energy transfer process using photoluminescence excitation and PL microscopy and show that 58% of the QD PL arises due to energy transfer from the WS2. Time-resolved photoluminescence microscopy studies show that the energy transfer process is faster than the intrinsic PL quenching by trap states in the WS2, thus allowing for efficient energy transfer. Our results establish that QDs could be used as tunable and high PL efficiency emitters to modify the emission properties of TMDs. Such TMD-QD heterostructures could have applications in light-emitting technologies or artificial light-harvesting systems or be used to read out the state of TMD devices optically in various logic and computing applications.


Section 2: Photoluminecence contribution (PLctr) derivation
The photoluminescence contribution (PLctr) by the transition metal dichalcogenide (TMD) monolayer to the quantum dot (QD) emitter is derived. Vavilov's rule, 1 which states that PLQE is independent of excitation wavelength, forms the key assumption in this derivation. Given the range of wavelengths presented in PLE measurements (560 nm -680 nm) this assumption is regarded as reasonable. We consider the photoluminescence excitation (PLE) of the QD at excitation resonant and non-resonant to the underlying WS2 monolayer i.e. PLEλ* and PLEλ respectively. In each case the PLE from the QD emission detection is given by equations 1 and 2: * = * * = * × (1) Where n and Abs are the number of photons per second injected and absorption of the QDs. By dividing equation 1 by equation 2 we obtain: * = ( * Hence the absorption ratio is equivalent to the ratio of WS2 resonant PLE to non-resonant PLE. This is ratio is given by R: By comparing the R values on the heterostructure and the QD control, we can identify an additional contribution to the QD absorption i.e. ΔR from the underlying WS2. Expressing equation (6) as a proportion of the heterostructure R value (RHet), we obtain the contribution of PL by the WS2 to the QDs.

Section 3: Corroborating Förster resonance energy transfer (FRET)
Section 3.1: PLE study on heterostructures with alternative quantum dot to two dimensional material (QD-2D) surface attachment ligands of increasing length SI figure 2 shows the wide field PLE spectra of tungsten disulphide/ lead sulphide-cadmium sulphide (WS2/PbS-CdS) heterostructures with varying QD-2D surface attachment thiol ligands. Table 1 lists the ligands used and their corresponding lengths. The difference in prominence of the WS2 resonant peak is due to the variation in size of the WS2 monolayers used. The 1,3 Benzene dithiol (BDT) sample has the largest monolayer and hence the most prominent WS2 `A' exciton signal with less contribution of the QD emission shoulder blue of the WS2 peak as seen in other samples. All signals were obtained by scanning about WS2 `A' exciton and detecting and PbS-CdS emission (~ 900 nm). All signals show the WS2 `A' exciton peak in the expected spectral region (614 -620 nm).  Considering the 2D TMD as an array of point-like emitters and the QD film as an array of point-like absorbers, the FRET radius, R0, is defined in equation 7. 4 This system is also well approximated by a 2D quantum well donor and nanoparticle acceptors, which follows a d -6 distance dependence for nonradiative energy transfer. 6 0 6 = 9 10 128 5 2 4 (7) NA is Avogadro's number, n is the refractive index of the medium surrounding the FRET pair, PLQED is the donor's intrinsic photoluminescence quantum efficiency and κ 2 is the dipole orientation factor, which is equal to 2/3 for randomly oriented dipoles. 7 J is the overlap integral between the area normalised emission spectrum, 4 FD and acceptor absorption spectrum given by the acceptor molar extinction coefficient, εA.
We then calculate the QD volume assuming a spherical shape. This is followed by multiplying the volume by the density of PbS by assuming a vacuum between the emitter and absorber, i.e. n = 1 and orientation factor κ 2 = 2/3. For the ideal system, we assume the TMD donor to have unity PLQE. This approximation is however considered reasonable as we subsequently find that the energy transfer rate from WS2 band edge to QD band edge outcompetes the intrinsic exciton quenching in WS2, which is the known cause of low PLQE in newly prepared TMDs. (11) From equation 11, we obtain R0 ≈ 6.5 nm, which exceeds the ligand separation distances between donor TMD and acceptor QD listed in table 1. This highlights the significance of the oscillator strength of the constituent heterostructure materials over their physical separation distance. This strongly implies FRET as the dominant ET process observed. Figure 5.a WS2 PL scatter data presented in Figure 5.a were measured from the 64 µm x 48 µm rectangular region (orange dashed lines) shown in the optical images of the monolayer below.  Following the RHS of SI Figure 5. WS2 donor PL kinetics in the heterostructure can be described via the following set of related ordinary differential equations (ODEs): * = −( + + ) * (12)

Section 4: WS2 PL map region for PL scatter data shown in
Where D* and Tr represent the WS2 donor and trap state exciton populations respectively. The constants kD, kTR, kET and k2 represent the donor's intrinsic recombination rate; intrinsic trapping rate; donor-acceptor energy transfer (ET) rate; and trap-ground state recombination rate respectively. By integration we arrive at the solutions to equations 12 and 13. * ( ) = 0 * −( + + ) Where D*0 represents the initial donor population. As such, the PL dynamics in the heterostructure can be defined as the sum of donor and trap population decay terms given by equations 14 and 15: i.e.
In the absence of the QD acceptor the pristine WS2 kinetics can be modelled by setting the transfer term kET = 0 so that: The PL dynamics described by equations 17 and 18 consist of fast and slow decay components. In the pristine case (equation 18), at short time, i.e. t  0, the fast decay time is given by: Similarly, in the heterostructure case (equation 17): At long time i.e. t  ∞, given that the slow decay component (τ2) remains unchanged for a given fluence (see Table 2), the slow decay time in both pristine and heterostructure cases is given as:

2~2 ′~1
( 2 ) ⁄ From equations 19 and 20, we can deduce the ET rate, kET, as: The ET efficiency can then be determined in terms of rate constants.