Electrical switching between exciton dissociation to exciton funneling in MoSe2/WS2 heterostructure

The heterostructure of monolayer transition metal dichalcogenides (TMDCs) provides a unique platform to manipulate exciton dynamics. The ultrafast carrier transfer across the van der Waals interface of the TMDC hetero-bilayer can efficiently separate electrons and holes in the intralayer excitons with a type II alignment, but it will funnel excitons into one layer with a type I alignment. In this work, we demonstrate the reversible switch from exciton dissociation to exciton funneling in a MoSe2/WS2 heterostructure, which manifests itself as the photoluminescence (PL) quenching to PL enhancement transition. This transition was realized through effectively controlling the quantum capacitance of both MoSe2 and WS2 layers with gating. PL excitation spectroscopy study unveils that PL enhancement arises from the blockage of the optically excited electron transfer from MoSe2 to WS2. Our work demonstrates electrical control of photoexcited carrier transfer across the van der Waals interface, the understanding of which promises applications in quantum optoelectronics. The ultrafast carrier dynamics across the van der Waals interface of transition metal dichalcogenide heterostructures govern the formation and funnelling of excitons. Here, the authors demonstrate a reversible switch from exciton dissociation to exciton funnelling in a MoSe2/WS2 heterostructure, which manifests itself as a photoluminescence quenching-to-enhancement transition.

For the device configuration shown as Fig. 1b, we have established the equivalent circuit model for our heterojunction as shown in Supplementary Fig. 3, where 1 is the geometrical capacitance between the back gate and MoSe2, and 2 is the geometrical capacitance between the MoSe2 and WS2.
1 , 2 are the quantum capacitance of MoSe2 and WS2 monolayers, respectively. The PL from MoSe2 A exciton in the heterojunction is determined by the MoSe2 A exciton density. When the electron and holes density are no equal, either due to initial doping or charge transfer, the MoSe2 A exciton density in the heterojunction is determined by the minor carrier (electron or hole, whichever has the smaller density). We study three different regions, controlled by the gate voltage, for the different EF response from the heterojunction: (I) both the MoSe2 and WS2 monolayers are intrinsic; (II) the MoSe2 layer is intrinsic while the WS2 layer is n-doped, (III) both the MoSe2 and WS2 layers are n-doped.
First, for the region (I), both MoSe2 and WS2 are charge-neutral, and the Fermi level lies within their bandgap. In this case, the quantum capacitances from both layers are small (0 at 0 K). From the circuit model ( Supplementary Fig. 3), all voltages will drop on the quantum capacitances, and there will be no free carriers induced by the gating. Therefore, all free carriers (i.e., both electrons and holes) in the system are generated by optical excitation. For the photoexcitation centered at 1.797 eV (690 nm), there is no optical excitation of the WS2, and we only need to consider electron transfer from MoSe2 to WS2. As a result, the optically generated electron will have less density than the optically excited hole, and the PL intensity will be determined by the remaining electron density in the MoSe2 after the carrier transfer. This electron transfer is not affected by the gate voltage until the Fermi level is raised to the conduction band of WS2. Therefore, we would expect a largely constant EF with a value less than 1 in this region.
Secondly, in the region (II), the Fermi level is raised above the Fermi level of WS2 to introduce electron doping in the WS2 layer, while the MoSe2 is still intrinsic. After the optical excitation, MoSe2 will have more electrons than the case in the region (I) because there will be less optically excited electrons transferred to WS2. Therefore, the EF will increase. This regime ends when the electron density in MoSe2 exceeds the hole density in MoSe2, controlled by the increase of the gate voltage (holes are all optically excited and do not depend much on gate voltage).
Third, for the region (III), when the electron density in MoSe2 exceeds the optically excited hole density, the PL intensity will be limited by the hole density, which is almost a constant for both off-resonance and on-resonance excitation. For the on-resonance excitation, the hole transfer from WS2 to MoSe2 can be viewed as nearly 100% and not sensitive to the gate voltage, considering the large band offset between the VBM of WS2 and MoSe2 Therefore, the EF will again be a constant, which should be 1 for the off-resonance excitation centered at 1.797 eV excitation in the ideal scenario and larger than 1 for the on-resonance excitation at 2.0 eV. There will be more holes in the MoSe2 layer in the latter case, considering the hole transfer from WS2 to MoSe2. As a result, the MoSe2 A exciton density will be larger in the hetero-junction compared with the MoSe2 monolayer.
Next, we will quantitatively determine the proportion of the electrons transferred to WS2, when the optical excitation generates electron and hole in the MoSe2 at a given band alignment and chemical potential. The answer can be easily generalized to hole transfer or to charge transfer from WS2 to MoSe2.
Define the following "number capacitance." n1, n2 are the electron density in MoSe2 and WS2, 1 and 2 are the chemical potential counting from the conduction band edge of each material, S is the area of the device, and e is the electron charge. These "number capacitance" basically tells how much electron density is changed from the change of chemical potential or electrical potential.
The charge transfer process can be understood in the following, taking the excitation centered at 1.797 eV as an example. Prior to the optical excitation, the two layers are in equilibrium so that their chemical potential is aligned. Optically injected electrons raise the chemical potential in MoSe2, breaking the equilibrium. After the electrons transfer from MoSe2 to WS2, the chemical potential for electrons becomes aligned again. Considering the electron transfer, the final equilibrium condition is described by: where is the optically excited electron density, Δ is the electron transferred from MoSe2 to WS2. The second term on the right-hand side corresponds to the fact that the charge imbalance between the two layers, arising from the charge transfer, induces an electrical potential difference (or band alignment change).
For the on-resonance excitation centered at 2.0 eV, the hole transferred from WS2 to MoSe2 needs to be considered, which we assume to be 100%. The Equation (2) needs to be modified as follows: However, the qualitative behavior of EF will not change. Without loss of generality, we restrict our discussion to the off-resonance excitation centered at 1.797 eV. We thus have: In the region where the PL is dominated by the density of electrons, we have ∝ 1 − Δ .
At equilibrium, we have is the conduction band offset between MoSe2 and WS2, Δ 0 is the initial conduction band offset (MoSe2 minus WS2), and is the chemical potential of the system counting from the conduction band of WS2.
We can now be more quantitative and obtain the expression for all the capacitance at the finite temperature T. The geometrical number capacitance between WS2 and MoSe2 is given by: where d = 1.3 nm is the distance between the MoSe2 and WS2. We use 2 2 = 6.85 as the average dielectric constant for the monolayer MoSe2 and WS2. Numerically we have = 1.67 × 10 14 2 / 2 = 2.91 × 10 13 2 / Considering the EF is ~0.4 for the region (I) for off-resonance excitation at 1.797 eV (Fig. 2e in the main text) and EF is ~0.8 for the region (III), we expect the quantum efficiency for the MoSe2 A exciton the heterojunction is 80% of that in monolayer MoSe2. As a result, the true EF for the heterojunction in the region (I) should be ~0.5. With = 0, we combine Equations (3), (7) and (8) to obtain the initial band alignment Δ 0 = 49 , for the EF~ 0.5. This result is consistent with the calculation result of 60 meV 3 .
With the quantitative analysis, we can also estimate at which voltage the type II to type I alignment transition will occur. We first formulate the relation between the gate voltage and chemical poetical: To get the transition point of the band alignment, we set Δ 0 = 49 and Δ = 0. By solving equation (10) and (4), the transition gate voltage can be calculated. It has been that the geometry capacitance 1 can be as high as 4 µF based on a reported value of double of 0.885 nm 4 , in the heavily doped regime. Even considering possible lack of optimization of the device structure, with an effective double layer as thick as ~ 8.85 nm, we would have an underestimated geometry capacitance 1 = 3.98 × 10 12 2 / , which determines the transition voltage of ~1.4 V. As a result, at the heavily doped region as shown in the main text, corresponding to the gate voltage as high as ~ 4 V, should already be in the regime that the type II configuration has been switched to the type I configuration.

Supplementary Note 3. Derivation of the effective capacitance circuit model for the heterostructure device.
It has been shown by Luryi 5 that for a circuit shown in Supplementary Fig. 4a, the equivalent capacitance circuit is as shown in Supplementary Fig. 4b. In Supplementary  Fig. 4a, the top and bottom plates are ideal metal plate, and the middle plate, Q, is a two-dimensional metal which does not screen the field completely. It could be 2D electron gas (2DEG) of a quantum well (QW), or in our case, a monolayer TMDC. As the quantum capacitance, C Q = g me 2 πħ 2 , is comparable to geometry capacitance C1 and C2, the energy to fill electron in the TMDC is not negligible and has to be taken into account. By minimizing the total energy of the system, including the energy to charge the two geometry capacitors (C1 and C2) and quantum capacitor (C Q ), it can be shown that the charge density in electrode 1 (σ1) and electrode 2 (σ2) follows the relation, , and the charge neutrality condition gives σ Q = −σ 1 − σ 2 . It is evident then that the equivalent circuit of Supplementary Fig. 4a should be Supplementary Fig.  4b.   Supplementary Figure 4. Schematic of the capacitance model for a two-dimensional material sandwiched by two plates (a) and the equivalent circuit (b) 5 . Now, if we only have one monolayer TMDC device shown as schematically in Supplementary Fig. 5a, it will be equivalent to have the bottom plate (the grounded C2) in Supplementary Fig. 5a to be placed at infinity, which gives a C2 =0, and the effective capacitance will be C1 and CQ in series. For the heterostructure device schematically shown in Supplementary Fig. 5c (also Fig. 1b of the main text), the bottom plate is not an ideal metal anymore and does not completely screen the electrical field. Instead, it is a quantum plate, just like the middle plate Q. In this case, we name the middle plate Q1, and following our equivalent circuit of the monolayer device ( Supplementary Fig.  5b), now the C2 in Supplementary Fig. 5b should be replaced with geometry capacitance (C2) and quantum capacitance (CQ2) in series, and the resulting equivalent circuit will be as shown in Supplementary Fig. 5d (also the inset of Fig. 4 of the main text). Another way to understand is that, the extra voltage drop on the quantum capacitance 1 (CQ1) has to be the same as the total voltage drop on the geometry capacitance (C2) and quantum capacitance (CQ2), as both the quantum plate 1 (the original middle plate Q in Supplementary Fig. 5a) and quantum plate 2 (the original bottom plate in Supplementary Fig. 5a) are both grounded, same as our experimental setup.

Supplementary Note 4. The low energy PL in the heterojunction originating from intralayer excitons in MoSe2.
The fabrication of the hetero-bilayer of MoSe2/WS2 was through random stacking, which means that the K (K') valleys of the MoSe2 and WS2 are not aligned. This makes the charge transfer excitons (interlayer excitons) indirect bandgap in nature with momentum-mismatched electrons and holes. As a result, their radiative recombination rate and PL intensity should be strongly reduced. We have also performed systematic study to show that the low energy PL peak from the heterojunction is from the MoSe2 A exciton.
We have performed the TRPL measurements at the MoSe2 A exciton resonance for the monolayer MoSe2 and MoSe2/WS2 heterojunction, as shown in Supplementary Fig.  6. It is evident that the PL lifetime from the MoSe2 monolayer and the MoSe2/WS2 hetero-bilayer are almost the same (the one from the heterojunction is actually slightly shorter), contradicting the expected longer lifetime from the interlayer exciton due to spatial separation of electrons and holes. In addition, the fitting shows a fast decay component of ~ 5 ps ( Supplementary Fig. 6), consistent with the previously reported lifetime of intralayer exciton but much shorter than the reported interlayer exciton lifetime in MoSe2/WS2 heterojunction (~ 80 ps) extracted from the transient absorption measurement 6 . Figure 6. The time-resolved PL of the monolayer MoSe2 and MoSe2/WS2 junction at room temperature. (a) TRPL spectra from the heterojunction (red dots), monolayer MoSe2 (blue dots), and response from the laser (black). (b) and (c) and convolution fittings to the experimental TRPL using the laser response as the kernel for the heterojunction and monolayer MoSe2, respectively.

Supplementary
We have fabricated seven heterostructure devices on LaF3 and three devices on SiO2/Si in total. The data from devices on the LaF3 substrate are shown in Supplementary Fig. 7, and all the heterojunction showed PL quenching with no gate voltage applied, and the enhancement factor (EF) varying from 0.5 to 0.9. This systematic quenching behavior is different from the PL enhancement observed in previous work reporting the interlayer exciton in MoSe2/WS2 heterojunction 6 , in which the PL enhancement was observed (EF>1) as the signature of the CT exciton (interlayer exciton). Due to the frozen ion effect in the LaF3, we cannot tune the doping easily through gate voltage at low temperature and did not do extensive low-temperature study. However, we did fix the gate voltage at 0 V and measure PL from the heterojunction at room temperature and 77 K under the same excitation condition. The results are shown in Supplementary Fig. 8. It is obvious that the PL at 77 K is much stronger than that at room temperature, opposite to the observation in the previous work of indirect bandgap interlayer exciton 7 and contradicts the expected behavior of indirect bandgap interlayer exciton. Figure 8. PL spectra from the MoSe2/WSe2 junction on LaF3 substrate at room temperature (red) and 77 K (blue).

Supplementary Note 5. Discussion of the trion effects in the doped region.
Charged exciton (trion) will emerge when WS2 is sufficiently n doped. However, in the current model, the charged exciton (trion) plays the same role as the neutral exciton. For example, whether exciting an exciton or a trion in WS2 would lead to the same amount of additional electron and hole density, and therefore the same amount of charge transfer between layers. As a result, the only relevant parameter here is the absorption of WS2 at the excitation light energy, regardless of the nature of the excited state. The introduction of charged exciton does not change our theoretical understanding or our model.