Photoluminescence Enhancement by Band Alignment Engineering in MoS2/FePS3 van der Waals Heterostructures

Single-layer semiconducting transition metal dichalcogenides (2H-TMDs) display robust excitonic photoluminescence emission, which can be improved by controlled changes to the environment and the chemical potential of the material. However, a drastic emission quench has been generally observed when TMDs are stacked in van der Waals heterostructures, which often favor the nonradiative recombination of photocarriers. Herein, we achieve an enhancement of the photoluminescence of single-layer MoS2 on top of van der Waals FePS3. The optimal energy band alignment of this heterostructure preserves light emission of MoS2 against nonradiative interlayer recombination processes and favors the charge transfer from MoS2, an n-type semiconductor, to FePS3, a p-type narrow-gap semiconductor. The strong depletion of carriers in the MoS2 layer is evidenced by a dramatic increase in the spectral weight of neutral excitons, which is strongly modulated by the thickness of the FePS3 underneath, leading to the increase of photoluminescence intensity. The present results demonstrate the potential for the rational design of van der Waals heterostructures with advanced optoelectronic properties.


Raman spectroscopy of single-layer MoS 2 / multi-layer FePS 3 van der Waals heterostacks
Raman spectroscopy with a 532 nm excitation line has been employed to characterize the samples ( Figure S1). The non-resonant Raman spectrum of a control sample (1L MoS 2 flake deposited onto 300-nm SiO 2 /Si substrate) is dominated by two vibrational modes: !" # , due to in-plane vibrations of two S atoms with respect to the Mo atom, and #" , due to the out-of-plane vibrations of S atoms in opposite directions. It is well-known that the frequency difference between these two peaks diminishes with lowering the number of material layers due to a reduced dielectric screening. The location of these two modes, 384 cm -1 and 403 cm -1 , respectively, yields a difference in Raman shift of ~19 cm -1 which is a distinctive signature of a single layer MoS 2 flake 1 . For a ML FePS 3 flake, six prominent vibrational modes are observed, which are in good agreement with previously reported works [2][3][4][5] S-4 Specifically, the differential reflectance spectra shown in Figure S2 correspond to: (R-R 0 )/R 0 , being R the reflectance of the FePS 3 flake and R 0 the reflectance of the SiO 2 /Si substrate. The simulations are based on the transfer-matrix method for Fresnel equations, as in reference 6 , accounting for a layer of Si with infinite thickness, a layer of SiO 2 with 295 nm thickness (previously adjusted under a similar optical reflectance simulation), and a layer of FePS 3 flake with variable thickness followed by an ultimate layer of air with infinite thickness (see Figure S3 for clarification).

Thickness estimation of FePS
In the simulations, an approximately constant refractive index value of n = 2.45 +i0.15 has been used for FePS 3 7 , whereas the refractive indices of SiO 2 and Si were taken from the database provided in 8 . The approximate value for FePS 3 refractive index has been obtained from our previous work 7 , where we find this approximation to be enough to be   Table S1. Fitting parameters obtained from photoluminescence spectra shown in Figure 1.

Sample
Peak Xarea The photoluminescence spectrum has been fitted to three Lorentzian peaks, corresponding with the negatively charged trion associated to exciton A (X -), the neutral exciton associated to exciton A (X 0 ) and the exciton B (B) as follows: where the peak area is given by , ' denotes the position of the peak and ' is the full width at half maximum (FWHM) for i = 1, 2, 3. The mass action law associated with trions is used to evaluate the electron density in 1L

Estimation of the electron density in one-layer MoS
MoS 2 as part of the van der Waals heterostructure or as a control sample (equation 1 in the main article). Here, the effective mass values are ( " = 1.15 ) , ( # = 0.8 ) and is the mass of a free electron. The temperature is T = 300 K and the trion binding energy is E b ~30 meV.
Considering a three-level energy system (inset of Figure S4), the PL intensity of the trion and exciton can be written as 9 + " ≈ ,-+ " , (S2) where ,-and *./ are the radiative decay rates of trions and excitons, respectively.
Substituting expressions S2 and S3, the trion spectral weight is then related to the population of trions and excitons as where ,-*./ ⁄ is equal to ~0.15 9 . From the mass action model (equation 1 in the main article), the population of trions and excitons is directly related to the electron density as Thus, the trion spectral weight varies with the electron density as (plotted in Figure S4) ,0,12 ≈ 3.14 × 10 5#6 *2 1 + 3.14 × 10 5#6 *2 . (S6) S-9

Analysis of the photoluminescence of 1L MoS 2 /FePS 3 heterostructures with different FePS 3 thickness
The photoluminescence spectra at room temperature of all the samples have been fitted to three Lorentzian peaks, corresponding with the negatively charged trion associated to exciton A (X -), the neutral exciton associated to exciton A (X 0 ) and the exciton B (B) as follows: where the peak area is given by , ' denotes the position of the peak and ' is the full width at half maximum (FWHM) for i = 1, 2, 3. S-10 Control (1) 2.9489 Control (2) 4.5580 Control (3) 2.3306 Figure S6. Photoluminescence enhancement in single-layer MoS2/FePS3 heterostructures with thicknesses of FePS3 larger than 100 nm. S-11

Valence band UPS spectrum of bulk FePS3
From a linear fit to the data in the valence band region of the UPS spectrum of bulk FePS3, we obtain an energy cut-off of ~0.56 eV. Considering an error in the determination of the UPS slope of ±0.2 eV, and taking into account the activation energy obtained in section S8, the difference between both energies falls within the permitted uncertainty range.
Considering minor calculation error in the low-temperature photocurrent measurements,  The activation energy of a multi-layer FePS 3 flake, in contact with prepatterned Ti/Au electrodes, has been obtained through temperature-dependent transport measurements.
Conductivity in p-type semiconductors, as for the case of FePS 3 , is mediated by holes that are available in the valence band due the promotion of electrons to higher acceptor energy levels. These acceptor levels are generated by the 3d levels of Fe +2 ions that are partially filled 10 . Here, the extrinsic behavior 11 of FePS 3 has been studied as a function of the applied source-drain voltage for a temperature range between 220 to 285 K. In this range, the conductivity is a thermally activated process of Arrhenius-type 12 where thermal energy favors the formation of electron-hole pairs, promoting conductivity through holes in the material. We found that below 220 K the current is so small that this one is masked by the noise of the measurement itself. Above 285 K, there is a saturation range where all the valence band electrons have been promoted to the acceptor energy levels and the conductivity exhibit a different behavior as pointed out by Kuzminskii et al 13 . The Arrhenius-type equation for conductivity as a function of temperature is given by where is the conductivity, E a is an activation energy, E V is the valence band edge energy, K B is the Boltzmann's constant and T is the temperature. A linear fit to the data falling within the extrinsic thermal range (from 220 K to 285 K) reveals an energy difference of (E a -E V ) ~ 0.37 eV ± 0.02 eV. We found that a slab of 4 layers isolated by vacuum provides essentially the same results that considering higher number of layers. Both the work functions and the energy levels are represented in Figure S10.

S-15
Band alignment: The work function was first determined for MoS2 and FePS3 monolayers and bulk FePS3, which was simulated with slabs formed by 4 and 6 layers, being already converged in the 4-layers slab calculation. Our DFT results yield work functions of 5.22 eV and 5.11 eV for FePS3 and MoS2, respectively, with the Fermi energy of MoS2 lying slightly above the Fermi energy of FePS3 ( Figure S10). We also determine the work function of singlelayer FePS3 ( = 5.25 eV), which indicates that the same type I of band alignment would be preserved at the 2D limit ( Figure S11).

Theoretical analysis of S vacancy in MoS 2
To give an explanation to the unusual charge transfer observed in the experiment, the existence of sulfur vacancies was proposed. A 4x4 supercell was constructed to ensure the absence of interaction between different defects originated in the periodical boundary conditions generated in the DFT simulation. In this conditions, one atom of sulfur was removed to simulate the vacancy. The electronic structure of this system is presented in Figure S12.

S-18
Band alignment: To analyze the effect of this vacancy in the band alignment we calculated the work function and scaled the energy levels to the vacuum. The Fermi level lies on the energy level of the defect ( Figure S13). S-19

Photoluminescence in heterostructures prepared in air
To discern the effects of sample preparation under a controlled atmosphere and in air conditions, new heterostructures were fabricated in air. Figure S14 shows the photoluminescence spectra of control and heterostructure samples prepared in air and fitted to three Lorentzian peaks (negatively charged exciton X -, neutral exciton X 0 and exciton B). Time-resolved photoluminescence. TRPL measurements were carried out using a home-made optical setup operating at room temperature. As an excitation source, we used a 1034-nm Flint FL1 laser with 80 MHz repetition rate and a pulse duration of <120 fs connected to a free-standing harmonic generator, which converts the initial beam to 517 nm wavelength. The laser power is filtered by using a variable metallic neutral density filter, and then is reflected on a dichroic mirror that directs light to a high numerical aperture lens. In this manner, the final laser power reaching the sample is adjusted to a variable power below 100 µW to rule out any possibility of laser-induced damage. The detection of the PL signal was performed by means of a silicon CCD attached to a doubleexit spectrometer. A photomultiplier detector is connected at the second exit of the spectrometer and monitored by means of a Time Correlated Single Photon Counting electronics. S-21

Four Lorentzian peak fitting of photoluminescence spectrum at low temperature
The photoluminescence spectra as a function of temperature have been fitted to four Lorentzian peaks, accounting for the bands D (associated to defects), negative trion (X -), neutral exciton A (X0) and exciton B (B) following the expression below: where the peak area is given by , ' denotes the position of the peak and ' is the full width at half maximum (FWHM) for i = 1, 2, 3. Figure S16. Photoluminescence spectrum of a 1L MoS2/FePS3 heterostructure at 10 K, fitted to four Lorentzian peaks.
Although we do perform the fitting including band B, in the variable temperature measurements, we unfortunately had to ignore the quantitative analysis of this peak because in this experimental setup the pump laser tails at this position, and thus the fittings of the B band are disturbed by this signal. S-22

Semiconductor bandgap model
To quantify the blue shifting of the PL emission in the heterostructure and control samples when decreasing temperature, a standard semiconducting bandgap model has been used 14 : where Eg(0) is the bandgap at 0 K, S is a parameter related to the electron-phonon coupling strength and ℏ is the average phonon energy involving the electron-phonon interaction.
This model perfectly fits the temperature dependence of the three peaks labeled as D, Xand X 0 in Figure 3c (heterostructure) and 3f (control sample). Table S4. Summary of the parameters used to fit the PL spectra of Figure 4a-b into the model described in Equation 4. S-23 Figure S17. Temperature dependence of the defect peaks relative spectral weight for MoS2 on SiO2 and on top of FePS3. The red continuous lines represent the fit of the data to an Arrhenius model. From its slope, activation energies of 11 meV and 9 meV are obtained for MoS2 on SiO2 and on FePS3, respectively.