Auger‐Assisted Secondary Hot Carrier Transfer in a Type I MoS2/PtSe2 Heterostructure

Charge transfer is vital in determining the optoelectronic properties of atomically thin materials, yet remains elusive in type I heterostructures. Here, distinct two‐step charge transfer processes in a type I MoS2/PtSe2 heterostructure are reported. By exclusively exciting the smaller bandgap PtSe2, strong exciton photobleaching peaks of the larger bandgap MoS2 are observed, indicating primary hot carrier transfer from PtSe2 to MoS2 within 70 fs. More importantly, the amplitude of the exciton peaks shows a secondary increase after the initial rapid decay. These dynamics are distinctly different from the monotonic decrease in monolayer MoS2 and indicate a secondary charge transfer process that is attributed to hot carriers re‐generated in PtSe2 by intralayer Auger recombination. Concurrently, the exciton energy blue shifts within 100 ps, probing the dynamic buildup of a charge‐transfer induced electric field across the heterostructure interface, which displaces electron and hole wavefunctions of MoS2 excitons and reduces the exciton binding energy. The results are corroborated by carrier dynamics and transient absorption spectra simulations by considering the two‐step charge transfer processes. The work reveals Auger‐assisted hot carrier transfer processes in type I heterostructures and suggests the possibility for optoelectronic and photocatalytic applications by optical sub‐bandgap excitation.


Introduction
Atomically thin 2D layered materials possess many intriguing properties such as high carrier mobility, [1,2] large exciton binding energy, [3,4] and strong light-matter interaction, [4,5] thus attracting intensive research interest for potential applications in flexible and ultrathin electronic and optoelectronic devices. [1,2,6][21] The vast choices of materials make van der Waals heterostructure an ideal platform for exploring fundamental physical and chemical properties.According to the band alignment, the heterostructure can be classified into type Ι and II.In type I heterostructures, the lowest conduction band (CB) and the highest valence band (VB) are within the same layer, so electrons and holes can be transferred from the layer with a larger bandgap to the smaller bandgap layer. [13,16,22]For type II heterostructures, the lowest CB and highest VB are located in different molecular layers, so the electrons and holes can be separated in different layers after charge transfer and form interlayer excitons. [13,19,23]o date, our understanding of the charge transfer process in type II heterostructure has been much improved thanks to the extensive research efforts on this type of heterostructure. [10,13,19,24,25]he consensus is that carriers in one layer will be immediately and efficiently transferred to another layer on a sub-picosecond time scale, before the occurring of intraband processes, such as cooling and exciton formation. [13,23,26,27]In contrast, charge transfer in type I heterostructures is less studied.Several studies reported that energy can be effectively transferred from a material with a large bandgap to that of a small bandgap. [28,29]A transfer of charge from the small to the large bandgap material (reversed transfer), which is energetically not favorable, has been much less observed.Such abnormal charge transfer from graphene to 2D transition metal dichalcogenides (TMD) has been reported in the type I graphene/TMD heterostructure, thanks to the effective hot carrier generation in graphene. [16,21,30]The quantum yield reached 50% for the hot electron injection from graphene to WS 2 under sub-bandgap excitation. [30]The charge-separated state persisted for 1 ns after hot electrons injection from graphene to WS 2 by photo-thermionic emission for sub-A-exciton excitation. [21]hese studies show that charge transfer from low to high energy states can be realized by exploiting the energy characteristics of hot carriers, which provides an interesting opportunity for the development of photoelectric devices based on hot carrier effects.So far, however, such abnormal hot charge transfer processes have only been reported for graphene/TMD heterostructure.This raises the question whether such hot carrier transfer from small to large bandgap layers can also be realized in a type I TMD/TMD heterostructure.If so, how fast will this process be and what are the underlying microscopic transfer mechanisms?Addressing these fundamental questions related to the reversed charge transfer will be highly beneficial for the design of novel optoelectronic devices with new functionality.
In this work, we report evidence for charge transfer in a type I heterostructure, constructed by stacking monolayer MoS 2 and bilayer PtSe 2 , via an ultrafast transient absorption (TA) spectroscopic study.By exclusively exciting the smaller bandgap PtSe 2 , we observe obvious photobleaching of the MoS 2 exciton, indicating efficient charge transfer from PtSe 2 to MoS 2 within 70 fs.This is attributed to hot carrier generation in PtSe 2 with electronic temperatures of up to 3000 K by fitting the TA spectra to the Maxwell-Boltzmann function.Surprisingly, unlike the monotonic exciton relaxation dynamics of bare MoS 2 , the corresponding dynamics of the MoS 2 exciton peak in the MoS 2 /PtSe 2 heterostructure show a delayed growth, several 10 ps after pump excitation, indicating a secondary charge transfer process.Comparative studies show that this secondary charge transfer results from the re-generated hot carriers in PtSe 2 assisted by Auger recombination.Concurrently, a continuous blue shift of the exci-ton energy of MoS 2 is observed due to the internal electric fields that are created by the charge separation across the interface.The finding is supported by carrier dynamics calculations using a coupled rate equation model and TA spectra simulations assuming both primary and secondary charge transfer processes in the MoS 2 /PtSe 2 heterostructure.Our work uncovers the mechanism of the two-step charge transfer processes in type I TMD/TMD heterostructure and is valuable for designing new optoelectronic and photocatalytic devices based on this.

Heterostructure and its Optical Properties
MoS 2 is a representative TMD material exhibiting an indirectdirect bandgap transition when reducing the thickness from bulk to monolayer. [31]Instead, PtSe 2 is an indirect bandgap TMD material.Its bandgap increases from zero in the bulk to 1.2 eV in the monolayer, i.e., a transition from semi-metal to semiconductor due to the reduction of interlayer interaction. [32]oS 2 /PtSe 2 heterostructure was constructed by transferring monolayer MoS 2 to the surface of a bilayer PtSe 2 (Figure 1e), both synthesized by chemical vapor deposition on sapphire substrates (Experimental Section).An optical image of the heterostructure shows good surface uniformity within 800 × 800 μm 2 area as shown in Figure 1e.The Raman spectrum of the heterostructure in Figure 1a shows vibrational peaks from both PtSe 2 and MoS 2 .The peaks located at 178 cm −1 , 205.2 cm −1 , and 236 cm −1 can be assigned to E g , A 1g , and LO modes of PtSe 2 , respectively.[33] The 383 cm −1 (E 1 1g ) and 403.8 cm −1 (A 1g ) peaks are from MoS 2 , with a spacing of 20.8 cm −1 , characteristic of monolayer thickness.[34] A weak peak at ≈225 cm −1 can be attributed to disorder-induced Raman scattering, [35] indicating that the MoS 2 sample has a low defect density.An analysis of the width of the Raman peaks of PtSe 2 suggests that the sample may also contain a finite amount of defects (see details in Figure S1, Supporting Information).The absorption spectrum of monolayer MoS 2 (red line in Figure 1b) shows typical A, B, and C exciton (AX, BX, and CX) resonance peaks at 1.87 eV, 2.01 eV, and 2.90 eV, respectively.The MoS 2 sample is transparent below 1.7 eV.Bilayer PtSe 2 has a broad absorption band at 1.0 -3.1 eV.The spectrum of the heterostructure shows absorption features from both materials.A detailed analysis shows that the bandgap of 2L PtSe 2 is decreased from 0.77 eV in the bare material to 0.7 eV in the heterostructure (Figure S2, Supporting Information).This suggests a strong interaction between PtSe 2 and MoS 2 that alters the bandgap of PtSe 2 .These bandgap energies match those obtained for samples prepared by similar methods, [36] while considerably lower bandgap energies are found for single crystalline material.[37] The inter-layer interaction is further evidenced by photoluminescence (PL) measurements with 400 nm laser excitation. Te results in Figure 1c show that the A exciton emission intensity of the heterostructure is decreased by more than 90 percent compared to that of bare MoS 2 .0,13,23] These spectroscopic To reveal the type of MoS 2 /PtSe 2 heterostructure, density function theory (DFT) was used to calculate the band structure of 1L MoS 2 and 2L PtSe 2 , the results of which are shown by red and blue lines in Figure 1d, indicating the direct and indirect bandgap features of MoS 2 and PtSe 2 , respectively.Importantly, both valence band maximum (VBM) and conduction band minimum (CBM) locate in the PtSe 2 layer, indicating a type Ι heterostructure.Therefore, photoexcited electrons and holes in MoS 2 with a larger bandgap will be spontaneously transferred to PtSe 2 , in agreement with the PL results.The reversed charge transfer from PtSe 2 to MoS 2 is, however, energetically forbidden.

Primary Hot Carrier Transfer
We use ultrafast femtosecond TA spectroscopy to study the carrier dynamics of the heterostructure (Figure 1e).The sample is excited by a narrow band pump pulse and the change of absorption (ΔA) is monitored by a broadband probe pulse.The positive and negative ΔA signals indicate the enhanced and weakened absorption of the sample to the probe light, respectively.First, 800 nm pump pulses with 9.6 μJ cm −2 fluence were employed to excite MoS 2 , 2L PtSe 2 , and the MoS 2 /PtSe 2 heterostructure.TA spectra of PtSe 2 , recorded within the first ps after excitation, exhibit a negative signal in the full probe energy range of 1.65 -2.7 eV (Figure 2a), followed by a fast decay on a few ps time scale.Figure 2c plots representative TA spectra of PtSe 2 at selected delay times (dashed lines), indicating a broadband bleaching signal (ΔA < 0) immediately after pump excitation.This photo-bleaching (PB) feature can be attributed to the state filling and Pauli-blocking of photoexcited carriers in the CB of PtSe 2 . [38]For the heterostructure (Figure 2b), a similar broadband bleaching signal is also seen, contributed by the excited carriers in PtSe 2 layer.In addition, two strong absorption peaks are also detected at 1.86 eV and 2.01 eV, corresponding well to the A and B exciton peaks of MoS 2 , respectively.This can be seen more clearly by comparing the spectra of the heterostructure (solid lines in Figure 2c) to that of PtSe 2 (dashed lines).To highlight the difference, we shift the PtSe 2 spectra downwards (i.e., increasing its amplitude, dotted lines).The spectra thus show that the nonlinear signal of the heterostructure has contributions from both the slowly varying PtSe 2 response and the MoS 2 exciton response.The latter can be traced already at 90 fs.The amplitude of broadband bleaching nonlinearity in the heterolayer is larger than in the bare PtSe 2 , likely due to an increased pump absorption in heterolayer because of the change in dielectric environment of PtSe 2 and/or state filling in the CB of MoS 2 .
Since the pump energy of 1.55 eV is much lower than the A exciton resonance (1.86 eV), it exclusively excites PtSe 2 .Indeed, pure MoS 2 monolayer under 1.55 eV excitation shows no signal in the TA spectra (Figure S4, Supporting Information).Therefore, it is unambiguous that the A and B exciton bleaching peaks in the heterostructure are caused by carriers transferred from PtSe 2 to MoS 2 .To isolate the pure MoS 2 exciton contribution from the signal of the heterostructure, we remove the broadband bleaching signal contributed by PtSe 2 (see details in Figure S5, Supporting Information).The obtained pure exciton signal of MoS 2 /PtSe 2 is shown in Figure 2d.Consistent with the original data, the exciton peak is already present at 90 fs (Figure S5, Supporting Information).Since the pure exciton signal is induced by a charge transfer process, its dynamics can be used to determine the charge transfer time.By convoluting the instrument response function (Gaussian pulse with 180 fs width) with an exponential function, we can estimate the charge transfer time in our MoS 2 /PtSe 2 heterostructure to be 70 ± 15 fs (Figure 2e).Moreover, the quantum efficiency of the primary charge transfer can be roughly estimated to be 34%, according to the linear relationship between ΔA and the carrier density N (see details in Supporting Information Section 3).
According to the band alignment of the type Ι MoS 2 /PtSe 2 heterostructure (Figure 1d), neither electrons nor holes in PtSe 2 can be transferred from their respective band edges to MoS 2 .[41] This is attributed to hot carriers generated after carrier-carrier scattering in graphene, which have sufficient energy to be transferred to the CB of TMDs.We believe that the same mechanism can account for our experimental observation, i.e., the hot electrons in the CB of PtSe 2 are transferred to the CB of MoS 2 immediately after optical excitation.[44][45] The amplitude of the signal also decreases with increasing probe energy and generally follows the expected Fermi-Dirac distribution of the hot carriers (Figure S6a, Supporting Information).
We fit the high-energy tail of the TA spectra by a Maxwell-Boltzmann distribution, [42] and obtain the transient electron temperature T c in 2L PtSe 2 (Figure S6a,b, Supporting Information).T c increases up to 3000 K at 0.5 ps and decays to about 600 K after ≈40 ps.This indicates the existence of high energy hot electrons resulting from carrier-carrier scattering.The electron temperature drops quickly with a time constant  1 = 1.8 ps, which reflects its cooling via electron-phonon scattering. [42]The slow decay process with  2 = 49 ps can be generally attributed to lattice cooling.As discussed later, Auger recombination can account for this slow decay. [45]In a heterostructure, the main driving force for charge transfer is the band offset between the CB and VB of the two components.Therefore, electrons (holes) occupying higher (lower) energy states will be spontaneously transferred to a lower (higher) energy one.Such charge transfer usually occurs on a sub-ps time scale, even faster than the intralayer carrier dynamics such as hot electron cooling and exciton formation. [10,13]hus, the observation of distinct MoS 2 exciton peaks in TA spectra indicates that a portion of high-energy carriers with sufficient energy in PtSe 2 are transferred to MoS 2 .Since the hot carriers are generally formed via carrier-carrier scattering, one expects that the hot carrier temperature will depend on the pump fluence.Indeed, as shown in Figure S6c (Supporting Information), a lower excitation fluence of 5.5 μJ cm −2 (and thus a lower carrier density) leads to a relatively lower hot carrier temperature of ≈2000 K directly after excitation.

Secondary Charge Transfer Mediated by Auger Recombination
To further analyze the underlying mechanism of the observed charge transfer process and examine the relaxation of the carriers, we measured TA spectra of the MoS 2 /PtSe 2 heterostructure for a longer time delay up to 1 ns (Figure 3a).For comparison, we also recorded TA spectra of 1L MoS 2 excited by 400 nm pump pulses with 9 μJ cm −2 fluence (Figure 3b).We note that MoS 2 can be optically excited in this case since the energy of the pump pulse is now much larger than its bandgap.As shown in Figure 3b, the negative PB signals of A (1.86 eV) and B (2.0 eV) excitons can be clearly seen.Furthermore, at both the high and low energy sides of the exciton energy, positive TA signals are also observed.Similar dispersive spectral features have been observed in TMD materials and extensively discussed in literature.The optical nonlinearity of MoS 2 is largely dominated by many-body effects on the excitonic resonance.Different mechanisms including bandgap or exciton energy renormalization [46,47] and excitation induced dephasing (EID) have been proposed. [48,49]We attribute our results mainly to EID effect because it leads to a transient broadening of the exciton resonance due to exciton-exciton scattering, which leads to positive signal at both sides of the exciton energy as observed in our experiment (Figure S7, Supporting Information).The TA spectra of the MoS 2 /PtSe 2 heterostructure show similar features as those of bare MoS 2 .This suggests that in this spectral range, the optical nonlinearity of the heterostructure is also dominated by the excitonic response of MoS 2 .Note that the heterostructure is excited with 1.55 eV pump pulse that cannot be directly absorbed by MoS 2 .Therefore, these distinct TA spectral features of MoS 2 in the heterostructure are due to charge transfer from PtSe 2 .
One difference of the TA spectra of the two samples is that the positive TA signal around the exciton energy appears already at time zero for bare MoS 2 (Figure 3b) but only shows up after some delay time in the heterostructure (Figure 3a).For further analysis, we plot the dynamics of the A and B exciton bleaching peaks and the corresponding positive peaks at the low energy side of the A and B excitons in Figure 3c-f.To distinguish the carrier relaxation processes, the time-dependent curves are highlighted by four different colors and labeled as stage Ι, II, III, and IV.
We first examine the negative bleaching peak.For bare MoS 2 (black curves in Figure 3c,d), the amplitudes of both A and B exciton peaks quickly increase within ≈300 fs corresponding to initial photo-excitation (stage I).This is followed by a fast decay on a few-ps time scale (stage II) and a slow decay within tens to hundreds of ps (stages III and IV).The fast and slow decay processes can be attributed to defect trapping and exciton recombination, respectively. [50]The A exciton dynamics can be fitted by a rate equation (Figure S9, Supporting Information), considering a defect-assisted Auger recombination process in monolayer MoS 2 consistent with previous reports. [50]For the heterostructure (red curves in Figure 3c,d), the exciton bleaching signal appears on the same time scale as that of bare MoS 2 , but the rising edge is a little bit delayed in time (comparing red and black curves in Figure 3c,d).This is attributed to a finite charge transfer time of 70 ± 15 fs from PtSe 2 to MoS 2 .A fast decay component is also seen in the heterostructure (stage II), but the dynamics are slightly different from that of bare MoS 2 .This is because the negative bleaching signal is contributed by carrier relaxation from both PtSe 2 and MoS 2 due to their spectral overlap.From the transients we also note that there is a minor revival of the peak amplitude at ≈3.5 ps, which is due to the re-excitation of the samples by the fraction of the pump pulse that is reflected from the back side of the sapphire substrate.This is also seen in the TA spectra of PtSe 2 in Figure 2a.
Surprisingly, the A and B exciton signals in the heterostructure show a secondary increase in amplitude between ≈5 to 60 ps (stage III).This is best seen by comparing the signals of bare MoS 2 (black curves) and the heterostructure (red curves) in Figure 3c,d that highlights the difference in stage III.After this, the signal continues to decay from 60 to 1000 ps (stage IV).While the signal on the high-energy side of the exciton resonances becomes more strongly negative, that on the low-energy side shows an increase of similar magnitude.This is a distinct sign of a transient spectral blue shift of the exciton resonance.We will argue below that this blue shift probes the transient electric field across the interface induced by the light-driven charge transfer in the heterostructure.Before that, we analyze the feature of the positive peak at the lower energy side of the excitons (Figure 3e,f).As discussed above, the positive signal results mainly from the EID effect, which is expected to show up and grow at the same time with the negative exciton bleaching peaks. [49]This is indeed the case in our experiment by checking the signal of bare MoS 2 (black curves in Figure 3e,f).The decay dynamics of the positive signal are the same as that of the bleaching, featuring fast and slow processes and originating from the same exciton relaxation processes of MoS 2 .
While the positive signal appears at time zero for bare MoS 2 , it shows up only after 5 ps for the heterostructure (red curves in Figure 3e,f).This can still be attributed to the overlapping of the negative bleaching signal of PtSe 2 and the positive signal from MoS 2 at 1.80 eV and 1.93 eV.Importantly, the negative PtSe 2 signal has contribution from those charge carriers that are transferred to MoS 2 and those that remain in PtSe 2 .The latter relaxes within PtSe 2 which leads to the decrease of the bleaching signal in stage II, as discussed for the bare PtSe 2 sample.Those charges transferred to MoS 2 would, however, still give rise to a bleaching signal, but face a competition with the positive signal of MoS 2 .Therefore, a transition of the signal from negative to positive is seen from stage II to III (red lines in Figure 3e,f), indicating that the EID-induced positive signal from the excitons of MoS 2 dominates the optical response in stage III.Interestingly, the positive signal continues to grow in stage III and then decreases again in stage IV.Both the growing and decay of the positive signals in stages III and IV occur on the same time scale as the negative A and B exciton bleaching peaks shown in Figure 3c,d.Therefore, those interesting peak dynamics are likely to originate from the same physical processes.
In our experiment, the sub-bandgap excitation induces a distinct bleaching of the MoS 2 exciton resonances (Figure 2) that are caused by charges transferred from PtSe 2 .Since, as discussed in more detail below, the indirect inter-layer recombination of the separated electron-hole pairs is too slow compared to the carrier transfer process, the net carrier population in MoS 2 tends to increase, thus enhancing the bleaching effect of excitons.Therefore, the re-grown exciton signals in stage III reflect an increased number of carriers in MoS 2 .This suggests a secondary hot carrier injection from PtSe 2 to MoS 2 .The decay of the exciton signal in the heterostructure is about a few hundreds of ps (stage IV), which is much longer than that in bare MoS 2 (≈148 ps).This can be ascribed to a slow inter-layer recombination of the spatially separated electron and holes in the two materials.
Commonly, the hot carrier cooling in 2D materials can be accomplished through carrier-phonon coupling within a few picoseconds, which matches well with the time scale of hot carrier decay shown in Figure S6 (Supporting Information) (stage II).We see that while the pure MoS 2 signal starts to decay at ≈300-400 fs directly after excitation, the signal in the heterostructure only decays from ≈500-600 fs (comparing black and red curves in Figure 3c-d).This indicates that the population in MoS 2 continues to grow until about 500 fs.Since the heterostructure is a type-I structure, only those hot electrons with sufficient energy can be transferred to MoS 2 .With the cooling of the hot electrons, their energy decreases progressively.The result thus indicates that 500 fs after optical excitation, the electrons still have enough energy to overcome the barrier for charge transfer.After that, their energy is insufficient, and we start to observe the decay of the exciton signal of MoS 2 .
A previous report used ultrafast optical-pump terahertz-probe spectroscopy to show that under high excitation fluence another slower relaxation dynamics attributed to defect-assisted Auger recombination exists in few layers PtSe 2 . [51]Auger recombination is a non-radiative, many-body process, in which electronhole pairs recombine and transfer the excess energy to a third electron or hole.This promotes the third electron or hole to a higher energy state.Since Auger recombination is a many-body process, it only occurs when the excitation density is sufficiently high. [52,53]We therefore recorded excitation fluence dependent TA spectra of PtSe 2 , varying the pump fluence from 4.82 to 8.26 μJ cm −2 (Figure 4b; Figure S8a, Supporting Information).At pump fluence > 6.1 μJ cm −2 , the carrier dynamics curves probed at 750 nm show a bi-exponential decay, containing both fast and slow components, whereas for low pump fluence only the fast decay is observed (Figure 4b; Figure S8b, Supporting Informa-tion).The slow decay process has a decay time of ≈50 ps and can be ascribed to Auger recombination.Moreover, the linear correlation between [ΔA] −1 and time delay provides unambiguous evidence for a defect-assisted Auger recombination in our 2L PtSe 2 sample (Figure S8c, see further discussion in Supporting Information). [51]While Auger scattering processes occur, some electrons can gain energy and can be lifted to a higher energy state in the PtSe 2 layer.Hence, they can again overcome the barrier and be transferred to MoS 2 .Therefore, we propose that the secondary hot carrier charge transfer from PtSe 2 to MoS 2 , mediated by Auger recombination in PtSe 2 , is responsible for the observed re-growth of the exciton signal in MoS 2 in stage III.Since earlier studies showed no significant temperature dependence for the photoexcited carrier dynamics in PtSe 2 , [51] it is likely that this Auger recombination is defect-assisted rather than phononassisted.
Recently, Adhikari et al. reported the generation and capture of secondary hot carriers within ≈25 ps in WS 2 and WSe 2 via Auger recombination, using ultrafast photocurrent spectroscopy. [54]lectron transfer assisted by Auger scattering between adjacent quantum wells has also been observed in 2D perovskites. [55]oreover, first-principle calculations suggested that charge transfer in WS 2 /graphene heterostructures stems primarily from interlayer Auger processes driven by strong electron-hole interaction but not from the directly excited carriers. [56]These works demonstrated the possibility of a charge transfer of re-generated hot carriers from Auger recombination, i.e., a secondary charge transfer.Our observation of such a two-step (primary and Augerassisted) charge transfer process is consistent with the type I band alignment, for which only electrons in the smaller bandgap PtSe 2 with sufficient energy can be transferred to MoS 2 .In principle, both hot electrons and hot holes in PtSe 2 can be transferred to MoS 2 (i.e., energy transfer).However, the slow decay of the exciton signal suggests the spatial separation of electrons and holes in the PtSe 2 and MoS 2 layers.This may be related to the indirect band gap feature of PtSe 2 , in which the dispersions of CB and VB are not symmetric.Thus, only electrons or holes favoring momentum matching with MoS 2 can be transferred.At present, we cannot directly distinguish whether electrons or holes are transferred to MoS 2 , since both cases will give the same TA signals.Time and angle resolved photoemission spectroscopy with momentum information would be necessary to completely distinguish between electron and hole transfer. [57,58]

Carrier Dynamics Simulation by Rate Equation
To further support this conclusion of a two-step charge transfer process, a rate equation model is used to simulate the carrier dynamics in MoS 2 /PtSe 2 heterostructure, which is an effective and common way to quantitatively describe the temporal evolution of carriers in a multi-state system.For physical clarity, we tried to minimize the number of excited states involved in the model.We thus restrict the discussion to four states in the PtSe 2 and two states in the MoS 2 layers (Figure 4a).In PtSe 2 , we considered an initially photoexcited state E 1 , a low-energy state near the band gap energy E 2 , a defect state E 3 , and a highly excited state E 4 , populated by Auger scattering.In MoS 2 , we limit the discussion to a state near the exciton resonance E 5 and a lower-lying defect state E 6 .We denote the light-induced populations in the different states as n i , i = 1,…,6.At this point, we do not explicitly discuss the physical nature of the different states (single particle, exciton, or charge-transfer state).We merely used them to phenomenologically analyze the measured TA spectra and to gain first insight into the light-driven charge transfer processes and their dynamics that are relevant in the MoS 2 /PtSe 2 heterostructure.
Before simulating the dynamics of the heterostructure, we calculate the carrier dynamics in pure PtSe 2 and MoS 2 independently and fit it to the experimental results.We find that the decay in both materials can be fairly good modeled by including Auger-assisted electron-hole recombination, as shown in Figure S9 (Supporting Information).The corresponding Auger recombination rates of PtSe 2 and MoS 2 are k P = 2.8 × 10 10 cm −2 ps −1 and k M = 1.1 × 10 10 cm −2 ps −1 , respectively.Based on this, we establish the coupled rate equation model that is schematically illustrated in Figure 4a.The rate equations are as follows, The time constant t ij is the average scattering, relaxation, or charge transfer times of carriers from state i to state j, the corresponding rate is thus 1 . The optical excitation only leads to ), using a pump pulse with a Gaussian temporal profile with a duration t p = 180 fs and intensity I 0 .Since the energy of pump pulse is 1.55 eV, the energy of E 1 is much larger than the bandgap of PtSe 2 (0.77 eV).For simplicity, we term this the "hot electron" state.Therefore, carriers in E 1 can partly be transferred to the CB of MoS 2 , and concurrently be cooled to E 2 .The cooled carriers in E 2 can be trapped by the defect state E 3 , followed by a defect-assisted Auger recombination to promote carriers from E 2 to E 4 .The carriers in E 4 will now again have enough energy to be transferred to MoS 2 .This is the basis for the secondary charge transfer process.Carriers in MoS 2 can also be trapped by the defect state E 6 and undergo relaxation and inter-layer recombination.
The detailed description of the setting of the rate equation is presented in Supporting Information.We assume that the amplitude of TA spectra (ΔA) is proportional to the total carrier density N in the excited state (ΔA ∝ N) of the individual layers.Therefore, the peak amplitude of PtSe 2 (ΔA P (t)) and MoS 2 (ΔA M (t)) can be written as, N P (t) is used to fit the peak dynamics at 1.65 eV of the heterostructure, since this low-energy signal only comes from the PtSe 2 layer.Instead, N M (t) is used to fit the pure exciton peak dynamics probed at 1.86 eV of the heterostructure after removing the contribution of PtSe 2 .The fitted carrier dynamics are shown as curves in Figure 4b, which reasonably well reproduce the experiment (open circles).The intensity I 0 is adjusted to reach an excitation density that matches the experiment.Other parameters are detailed in Supporting Information.Therefore, we fit the As can be seen, the hot electron cooling time, including t 12 and t 42 , is ≈700 fs, consistent with the values reported for other TMD materials. [59,60]The charge transfer time for both primary and secondary charge transfer processes is 200 fs, larger but close to the value directly determined from TA spectra of 70 ± 15 fs.In addition, the time constant for the Auger recombination in the PtSe 2 layer of the heterostructure is ≈60 ps, which agrees well with the re-growth time of the exciton signal in stage III observed in Figure 3.The inter-layer recombination time t 0 is determined to be 1100 ps, much longer than the relaxation in bare MoS 2 (Figure S9, Supporting Information).In graphene/WS 2 heterostructure, the charge-separated state has also been observed to persist 1 ns after hot electrons injection from graphene to WS 2 . [21]This indicates that also in our heterostructure, the nonlinear signal from MoS 2 is connected to the spatial separation of electrons and holes in the two layers.Importantly, from the simulated carrier dynamics curves (blue lines in Figure 4b,c), we see a fast increase of the exciton population followed by a fast decay and another re-growth of the population, before a slow decay on hundreds of ps.This four-stage dynamics well reproduces the experimental results.The rate equation simulation, therefore, supports the idea that the re-growth of the signal in stage III stems from the Auger-assisted secondary charge transfer process.

Simulation of Transient Absorption Spectra
To further corroborate the experiments and deepen our understanding of the charge transfer processes, we simulate the TA spectra by solving the master equation and obtaining the nonlinear polarization of the system. [61,62]For this, we consider a phenomenological model by taking PtSe 2 and MoS 2 as few-level systems, which is similar to the one shown in Figure 4a but with slight modulation (See Experimental Section and Figure S13, Supporting Information).As in the experiment, we use a narrow band pump pulse at 1.55 eV with 180 fs pulse width.The probe pulse has a 7-fs pulse width and broadband spectrum to cover a wide wavelength range.The A and B exciton resonances of MoS 2 and their linewidths (dephasing rate) are set according to the fitting of the linear absorption spectrum (Figure S3, Supporting Information).The optical transition of PtSe 2 is set to 1.55 eV and the dephasing rate is large (0.12 eV) such that it has a broadband response that has spectral overlap with the A and B excitons.We note that this oversimplifies the optical response of PtSe 2 , yet allows us to capture the main experimental findings.In this way, the pump pulse is resonant with PtSe 2 but does not overlap with the optical transition of MoS 2 .Therefore, any signal of MoS 2 should be caused by a charge transfer process.Indeed, no TA signal of MoS 2 can be observed when we switch off the charge transfer channel (Figure S16, Supporting Information).Charge transfer, intra-and inter-band relaxation, and Auger recombination are modeled as incoherent population transfer between different electronic states (see details in Experimental Section).An EID effect is included by introducing an additional dephasing rate Δ (t) = a m N M (t) to account for the linewidth broadening, [48] which is proportional to the total population of MoS 2 N M (t), and a m is a scaling parameter.Therefore, population in MoS 2 will lead to a time-dependent, broadened exciton transition, which gives TA spectra with positive-negative-positive line shape near the exciton energy.
The simulated TA spectra and peak dynamics of the excitons are shown in Figure 5a and Figure 5b, respectively.We observe dispersive line shapes at the MoS 2 A and B exciton resonance energy resulting from the EID effect, and a negative bleaching peak at 1.55 eV that we set for modeling the optical excitation of PtSe 2 .The amplitudes of all these peaks increase quickly around time zero (Figure 5b).After that, the exciton peak amplitude decreases quickly on a time scale of a few hundreds of femtoseconds due to the trapping of electrons by the defect state in MoS 2 .As in experiment, we observe an additional increase of the signal resulting from the secondary charge transfer mediated by Auger recombination, which is followed by a slow decay attributed to inter-layer recombination.For the bleaching peak of PtSe 2 , we see a fast decay after time zero due to charge transfer and the simultaneous cooling to the CBM.The slow decay can be attributed to Auger recombination.Representative simulated TA spectrum at 2 ps is shown in the inset of Figure 5a (red line), which closely reproduces the experimental spectra (blue line).This agreement confirms that EID is a dominant origin of the optical nonlinearity of MoS 2 .Note that the experimental spectrum is taken at 20 ps when the signal of PtSe 2 has decayed and the line shape of MoS 2 does not change in the whole delay window (Figure S7, Supporting Information).We point out that the time delay window in our simulation of 7 ps is much shorter than that in experiment, which is up to 1 ns.We have chosen a shorter window to minimize the computational cost of the simulations.As such, the time constants we use for Auger and interlayer recombination processes are chosen to be shorter than the values determined experimentally.The simulation, therefore, is aimed to uncover the essential charge transfer processes and reproduce the main experimental findings by reducing the relevant time scales.Simulations including Coulomb interaction and exciton-exciton scattering shall be used for a more quantitative description of carrier dynamics. [49,63,64]Importantly, the signal at the low energy side of the two excitons is also negative at the beginning (red and green curves in Figure 5b), which turns to be positive and grows at the same time as the negative bleaching peaks, followed by a slow decay.Compared to the rate equation simulation, the simulated TA spectra provide detailed spectral information, which, together with the peak dynamics, reproduce well the experimental results.This agreement further confirms that our model captures the essential physical processes after optical excitation in the heterostructure, i.e., the primary charge transfer from hot electrons and the secondary charge transfer mediated by Auger-recombination followed by slow inter-layer recombination.
We note that the negative signal at the lower energy side of the two excitons at early delay time (Figure 3e,f) is from the bleaching of the PtSe 2 due to their spectral overlap.When subtracting this "background" signal from the original experimental result, one can find that the signal is positive at very early delay times (Figure S10, Supporting Information).This is also confirmed in simulation by reducing the linewidth of PtSe 2 , thus reducing its spectral overlap with the MoS 2 A and B exciton responses.In this case, the positive signal appears at the same time as the negative exciton bleaching peak (Figure S17, Supporting Information).

Exciton Energy Shift Induced by Charge Transfer
Lastly, we also note an obvious blue-shift of both A and B exciton bleaching peaks in the TA spectra of the heterostructure (Figure 6a,b).Due to the spectral overlap with the bleaching signal of PtSe 2 , the exciton peak in the heterostructure is slightly distorted at early delay times (Figure 2c; Figure S11, Supporting Information).Therefore, we focus on the exciton peak shift for time delay after 1 ps.Such a blue shift is also observed for the exciton peaks in bare MoS 2 for time delays after 1 ps (Figure 6c).Also, within the first 0.2 ps after pump excitation, the A exciton peak quickly blue shifts.This blue shift behavior can be explained by an increased screening of the Coulomb interaction as the number of excited carriers increases, resulting in a decrease in exciton binding energy E b . [46]We note there is also a quick red-shift (0.2-1 ps) of the exciton peak, the time scale of which is well consistent with the fast decay process of exciton dynamics (Figure S12, Supporting Information).This is due to the sharp decrease of the exciton density by defect trapping.After the blue-shift in the first few ps, the exciton bleaching peaks gradually red-shift.The red shift of exciton is clearly associated with the relaxation of the excited carriers, leading to a decreased Coulomb screen-ing effect. [65]Overall, the amount of energy shift in bare MoS 2 is relatively small, ≈4 and 7 meV for A and B excitons, respectively.
Remarkably, the A and B exciton peaks in the MoS 2 /PtSe 2 heterostructure show a continuous blue shift by ≈12 and 31 meV until 100 ps, respectively (Figure 6b).Therefore, not only the time for the blue shift is much longer in the heterostructure, but also the amount of blue shift is much larger than that in bare MoS 2 (note the same energy range of Figure 6b,c).This exciton blue shift time in the heterostructure is also consistent with the regrowth of the exciton peak amplitude observed in Figure 3.After that, the exciton peak red-shifts on a time scale of hundreds of ps, also much longer than that of the bare MoS 2 but consistent with the slow inter-layer recombination of separated carriers in the heterostructure.The agreement of the exciton peak shift and amplitude change suggests that are originated from the same physical process, that is, Auger-assisted secondary charge transfer process.
Evidently, the exciton blue shift in the heterostructure is much more pronounced than that in bare MoS 2 layer.Hence, it cannot be solely explained by an enhanced Coulomb screening and reduction in exciton binding energy induced by a transient increase in exciton density.In the presence of charge transfer processes in the heterostructure, the separated charges in MoS 2 and PtSe 2 will generate an internal electric field across the interface that is pointing in the direction normal to the interface, i.e., the z-direction. [55,66]Since the electronic transition dipole moment of the MoS 2 excitons lies within the plane of the MoS 2 layer, any optical Stark effects due to the coupling of the electric field to the MoS 2 excitons will be weak (Figure 6d, top).In contrast, the interfacial electric field will lead to a spatial separation of the electron and hole wavefunctions of the A and B excitons in MoS 2 along the z-direction (Figure 6d, bottom). [67,68]Such a spatial displacement will further reduce the attractive interaction of electrons and holes and thus further reduce the exciton binding energy E b , resulting in a larger blue shift of the exciton bleaching peak compared to that in bare MoS 2 . [68]More importantly, the internal field will also cause a (DC) Stark shift of the exciton resonance, leading to an excitonic blue-shift. [66,69]Since the strength of the internal field scales linearly with the number of separated charges, we observe a gradual blue-shift of the A and B exciton resonances in the first 100 ps, consistent with the time scale of the Auger-assisted secondary charge transfer.The following redshift can then be explained by inter-layer recombination, which reduces the strength of the internal fields.Therefore, exciton energy shift probes the dynamic build up and decay of the electric field across the interface, created by the primary and Auger-assisted secondary charge transfer from PtSe 2 to MoS 2 in a type I MoS 2 /PtSe 2 heterostructure under sub bandgap excitation.It is worth mentioning that this two-step charge transfer processes are also present in the heterostructure constructed by 1L MoS 2 and 5L PtSe 2 with a smaller bandgap compared to 2L PtSe 2 , confirming the robustness of the phenomena (Figures S18 and S19, Supporting Information).The existence of such a secondary charge transfer channel may be related to the indirect band structure of PtSe 2 , which makes interband relaxation inefficient compared to that in the direct bandgap materials.Therefore, this two-step charge transfer mechanism shall also be applied to some other type I heterostructures, in which the lower bandgap materials favor Auger scattering at relatively high excitation fluence to reheat the hot carriers.More studies are needed to validate this.The combination of directindirect semiconductor materials thus provides additional platforms to tailor the optoelectronic properties and a valuable means for functional devices.

Conclusions
In conclusion, we have constructed a type I MoS 2 /PtSe 2 heterostructure to explore charge transfer process from the small bandgap PtSe 2 layer to the large bandgap MoS 2 with TA spectroscopy.By exciting PtSe 2 only, we detected distinct exciton signals from MoS 2 in the heterostructure, which unambiguously indicates that the hot electron was transferred from PtSe 2 to MoS 2 on a time scale of 70 fs after photoexcitation.Under our experimental conditions, the electronic temperature is estimated to increase up to ≈3000 K by fitting the high energy tail of the TA spectra, showing efficient hot carrier generation in PtSe 2 .More importantly, we observe a time-delayed increase in the exciton peak amplitude in the heterostructure at delays ≈10 ps after pump excitation.This indicates a secondary charge transfer process, which can be attributed to the re-generated hot carriers in PtSe 2 assisted by Auger recombination.The charge transfer induces an internal electric field across the interface and leads to a spatial displacement of the electron and hole wavefunctions in the MoS 2 layer.This reduces the exciton binding energy and induces a Stark effect that leads to the continuous blue shift of the MoS 2 exciton peaks until 100 ps.The experimental findings are supported by carrier dynamics calculation using coupled rate equation model and TA spectra simulation via density matrix approach.Our work reveals the two-step, primary and secondary, charge transfer processes in the type Ι MoS 2 /PtSe 2 heterostructure.The study offers a route to utilize low-energy photons for optoelectronic and photocatalytic applications of a larger bandgap material, and opens up vast possibilities for exploring type I heterostructures.

Experimental Section
Experiment: Monolayer MoS 2 and bilayer PtSe 2 films were synthesized by chemical vapor deposition on sapphire substrates.The monolayer MoS 2 was then transferred to bilayer PtSe 2 by a dry transfer technique to construct MoS 2 /PtSe 2 heterostructure (6-carbon Technology, Shenzhen).The optical absorption spectra of the samples were collected by a UV-vis-NIR microspectrophotometer (CRAIC technologies Inc.) with the formula of A = − log T, where A and T indicate absorbance and transmittance, respectively.For PL measurements, a 405 nm laser was used for excitation, and a 100× objective with a numerical aperture of 0.8 was used to focus the laser beam onto the sample and collect the emitted PL signals simultaneously.The PL spectra were measured with a microscopy-combined spectrometer (HRS-300, Princeton Instruments) and a high-performance camera (PIXIS, Princeton Instruments).The laser intensity and exposure time were 3 mW cm −2 and 3 s, respectively.A 450 nm long-pass filter was placed before the spectrometer to block the laser.The Raman spectra were detected by the Renishaw inVia Raman spectrometer under 532 nm laser excitation.The TA spectroscopy system is based on the amplified Ti:sapphire laser (Coherent Legend), delivering femtosecond pulses with 800 nm central wavelength at 1 KHz repetition rate and 50 fs pulse duration.A beam splitter is used to divide the pulse into pump and probe pulses.In the pump path, an optical parametric amplifier is equipped to generate tunable pump pulse in the infrared to visible range for exciting the sample.The other portion of the laser is used to excite a sapphire crystal to produce a continuous white light as probe pulse, which is delayed relative to pump with a motorized translation stage.The temporal resolution of the setup is determined to be ≈180 fs.A mechanical chopper is used to modulate the pump light frequency at 500 Hz.TA spectra were recorded in transmission configuration by measuring the transmission of the probe light in the presence (T On ) and absence (T Off ) of the pump as ΔA = −lg( Band Structure Calculation: The DFT calculations were performed by using the Vienna Ab initio Simulation Package. [70]The exchange correlation potential is described by the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation.The Beck-Jonson damping (DFT-D3) method is used in the work to correct the van der Walls interactions, and the spin-orbit coupling (SOC) is taken into all the calculations.The energy cutoff is set as 500 eV.The convergence condition of energy and force are set as 10 −6 eV and 0.001 eV Å −1 , respectively.To simulate the properties of individual layer of MoS 2 and PtSe 2 , the vacuum spaces are set to be 15 Å to wipe out the interaction.The Г-center 12 × 12 × 1 k-point sampling grids are adopted to distribute the geometry optimization.The lattice constants of MoS 2 and PtSe 2 were set to a = b = 3.160 Å, and a = b = 3.724 Å, respectively.The band structure was then obtained from self-consistent calculation using the optimized structure.The energy zero point of the band structure was set at the vacuum level.

Simulation of Transient Absorption Spectra:
To simulate the transient absorption spectra, we consider a phenomenological model by taking PtSe 2 and MoS 2 as few-level systems (Figure S13, Supporting Information) and numerically solve the master equation and obtain the time evolution of the density matrix ‚ (t).The polarization of the system is then calculated as the expectation value of the transition dipole moment P (t) = Tr( μ ‚ (t)).The total polarization P T (t,T) and linear polarization P L (t) were calculated in the presence and absence of the pump pulse, respectively, which lead to the nonlinear polarization P NL (t,T) = P T (t,T) − P L (t) that gives rise to TA spectra.Details of the simulation can be found in supporting information.

Figure 1 .
Figure 1.MoS 2 /PtSe 2 heterostructure and its spectroscopic characterization.a) Raman spectra of 2L PtSe 2 , 1L MoS 2 , and MoS 2 /PtSe 2 heterostructure.The spectra are vertically shifted for clarity.The peak marked by * is from the sapphire substrate; b) UV-visible-infrared absorption spectra of 2L PtSe 2 , 1L MoS 2 , and the MoS 2 /PtSe 2 heterostructure; c) PL spectra of 1L MoS 2 and MoS 2 /PtSe 2 heterostructure, indicating charge transfer induced reduction of PL intensity in the heterostructure; d) Electronic band structure of 1L MoS 2 and 2L PtSe 2 by DFT calculation, the energy is provided relative to vacuum level; e) Schematic illustration of the study of charge transfer process in MoS 2 /PtSe 2 heterostructure by TA spectroscopy.Inset shows an optical microscope image of the thin film of MoS 2 /PtSe 2 heterostructure.results indicate the successful construction of the MoS 2 /PtSe 2 heterostructure with strong inter-layer interaction.To reveal the type of MoS 2 /PtSe 2 heterostructure, density function theory (DFT) was used to calculate the band structure of 1L MoS 2 and 2L PtSe 2 , the results of which are shown by red and blue lines in Figure 1d, indicating the direct and indirect bandgap features of MoS 2 and PtSe 2 , respectively.Importantly, both valence band maximum (VBM) and conduction band minimum (CBM) locate in the PtSe 2 layer, indicating a type Ι heterostructure.Therefore, photoexcited electrons and holes in MoS 2 with

Figure 2 .
Figure 2. Fast charge transfer at early times in the heterostructure for 800 nm pump excitation.a,b) 2D TA maps as a function of probe photon energy and pump-probe delay of 2L PtSe 2 a) and the MoS 2 /PtSe 2 heterostructure b) obtained under identical excitation conditions; c) TA spectra at selected delay times of 2L PtSe 2 (dashed lines) and the MoS 2 /PtSe 2 heterostructure (solid lines).The dotted lines are vertically shifted from the PtSe 2 spectra to show that the heterostructure signal has contributions from both the slowly varying PtSe 2 response and the MoS 2 exciton response.The existence of A and B exciton peaks of MoS 2 indicates charge transfer from PtSe 2 to MoS 2 ; d) 2D TA map of the pure MoS 2 exciton signal of the MoS 2 /PtSe 2 heterostructure, obtained by subtracting the PtSe 2 signal; e) Normalized A exciton dynamics taken from the data in d).By convoluting the instrument response function (gray dashed line) with a single exponential function, the charge transfer (rise) time is determined to be 70 ± 15 fs.

Figure 3 .
Figure 3. Secondary charge transfer in the heterostructure.a,b) Comparison of TA spectra of the MoS 2 /PtSe 2 heterostructure with 800 nm pump excitation a) and of 1L MoS 2 with 400 nm pump excitation b); c,d) Dynamics of negative exciton bleaching peaks in MoS 2 (solid black lines) and the MoS 2 /PtSe 2 heterostructure (solid red lines) probed at 1.86 eV (A exciton) and 2.0 eV (B exciton), respectively; e,f) Dynamics of the peaks at the low energy sides of the A and B exciton resonances in MoS 2 and MoS 2 /PtSe 2 probed at 1.80 eV and 1.93 eV, respectively.All four transients of the heterostructure c-f) displays a secondary increase in signal amplitude in stage III, the signature of an Auger-assisted secondary charge transfer from PtSe 2 to MoS 2 .

Figure 4 .
Figure 4. Coupled rate equation calculation of the carrier dynamics.a) Diagram of the few-level model used to simulate the carrier dynamics in the MoS 2 /PtSe 2 heterostructure for 800 nm excitation; b) Carrier dynamics of PtSe 2 probed at 1.65 eV with different pump fluences, showing a slower Auger recombination process at fluence larger than 6.19 μJ cm −2 ; c) Normalized carrier dynamics of PtSe 2 (1.65 eV, red circles) and pure A exciton dynamics of MoS 2 (1.86 eV, blue circles) in the MoS 2 /PtSe 2 heterostructure and the fitted results obtained from the coupled rate equation calculation (lines).Inset: Zoom-in of the data in the first 60 ps.The pure A exciton signal is obtained by subtracting the PtSe 2 signal from the heterostructure (see Figure S5 for details, Supporting Information).

Figure 5 .
Figure 5. Simulated transient absorption spectra.a) Simulated TA spectra of a MoS 2 /PtSe 2 heterostructure.Inset: the spectrum at a pump-probe delay of 2 ps (red) and the experimental spectrum at 20 ps (blue), the black dashed line marks the position where the intensity of the spectra is zero; b) Dynamics of A and B exciton bleaching (AX, BX) and the corresponding positive peaks at the lower energy side (AX-LES, BX-LES), and the bleaching of PtSe 2 taken from the horizontal lines marked in (a).For better comparison, the amplitude of the AX, BX, and PtSe 2 bleaching signals are reduced by a factor of 10.

Figure 6 .
Figure 6.Charge-transfer induced electric field across the interface blue shifts the exciton energy.a) Typical experimental TA spectra of MoS 2 /PtSe 2 heterostructure under 800 nm pump excitation and the corresponding fits using Lorentzian line-shape; b,c) A and B exciton peak energy as a function of delay time in b) MoS 2 /PtSe 2 heterostructure and c) bare MoS 2 under 400 nm pump excitation.A much larger blue shift can be seen for the exciton peak in the heterostructure; d) Scheme showing excitons in bare MoS 2 (top) and in the heterostructure (bottom).In the heterostructure, the built-in electric field induced by the separated charges between PtSe 2 and MoS 2 results in a spatial separation of the electron and hole wavefunctions (bottom).This reduces the electron-hole interaction and further leads to the blue shift of exciton energy in the heterostructure.

Table 1 .
Fitted time constants from the coupled rate equation model.