Ultrafast Charge Transfer Cascade in a Mixed-Dimensionality Nanoscale Trilayer

Innovation in optoelectronic semiconductor devices is driven by a fundamental understanding of how to move charges and/or excitons (electron–hole pairs) in specified directions for doing useful work, e.g., for making fuels or electricity. The diverse and tunable electronic and optical properties of two-dimensional (2D) transition metal dichalcogenides (TMDCs) and one-dimensional (1D) semiconducting single-walled carbon nanotubes (s-SWCNTs) make them good quantum confined model systems for fundamental studies of charge and exciton transfer across heterointerfaces. Here we demonstrate a mixed-dimensionality 2D/1D/2D MoS2/SWCNT/WSe2 heterotrilayer that enables ultrafast photoinduced exciton dissociation, followed by charge diffusion and slow recombination. Importantly, the heterotrilayer serves to double charge carrier yield relative to a MoS2/SWCNT heterobilayer and also demonstrates the ability of the separated charges to overcome interlayer exciton binding energies to diffuse from one TMDC/SWCNT interface to the other 2D/1D interface, resulting in Coulombically unbound charges. Interestingly, the heterotrilayer also appears to enable efficient hole transfer from SWCNTs to WSe2, which is not observed in the identically prepared WSe2/SWCNT heterobilayer, suggesting that increasing the complexity of nanoscale trilayers may modify dynamic pathways. Our work suggests ”mixed-dimensionality” TMDC/SWCNT based heterotrilayers as both interesting model systems for mechanistic studies of carrier dynamics at nanoscale heterointerfaces and for potential applications in advanced optoelectronic systems.


Beam Size Measurements
The beam size for different pump excitation wavelengths was performed using a CCD camera beam profiler BC106N-VIS(/M) from Thorlabs.To account for the difference in pulse energy between the trilayer and the other materials (see Table SS1), the TA absorption and kinetic data are normalized to peak intensity.Table S1: Pulse energies associated with the TA spectral data for each material.

Additional Transient Absorption Spectra
Figure S1 shows the TA spectra of a WSe 2 bilayer using WSe 2 purchased from 2D semiconductors and WSe 2 grown via chemical vapor deposition at NREL.Upon selective excitation of WSe 2 , electron or hole transfer do not occur, indicated by the absence of the WSe 2 ground state bleach (750 nm) and SWCNT trion induced absorption (1175 nm). Figure S2 shows the transient spectra of neat WSe 2 after 750 nm excitation at 200 fs, 100 ps and 5 ns delay.The A, B and C exciton GSB can be osberved at 750 nm, 600 nm and 510 nm, respectively.Figure S2: Transient absorption spectra of neat WSe 2 after 750 nm excitation.The A exciton GSB can be observed around 750 nm, B exciton at 600 nm and C exciton at 510 nm.
In the main text we speculate that releasing WSe 2 from its original substrate may modify the valence band energy in such a way that hole transfer is now spontaneous in the trilayer, but not in the bilayer.Figure S3 shows no presence of hole transfer in the "reverse" SWCNT/WSe 2 bilayer (SWCNTs spray coated onto monolayer WSe 2 grown via CVD directly on a sapphire substrate), refuting this hypothesis.Figure S5A shows the kinetic traces corresponding to the trion wavelength (1175 nm) for the MoS 2 /SWCNT bilayer, MoS 2 /SWCNT/WSe 2 trilayer and the simulation obtained from the curve fitting procedure.The initial decay comes from the initially populated singlet SWCNT state that gives rise to the charge separated states.The 200 fs delay spectra for the corresponding bilayer, trilayer and neat SWCNT are also present in panel B showing the initial contribution at 1175 nm that corresponds to singlet SWCNTs photoinduced absorption (PIA).Due to the use of the air free holder to prevent sample damage/degradation, there is reflection due to the air free holder walls.Figure S6 shows the presence of the second pulse in all our samples marked by the rectangle, and it shows the effect it has on the trion kinetics.Important to notice panel c where we show the "rise" of the trion signal due to presence of the second pulse, the "rise" is also present in the MoS 2 A exciton kinetics but not the artifact around 10 ps.From our fitting model for the trilayer (black curve in Figure S5A) you can observe that we do not model a rise of the trion feature because this is an artifact and not real kinetics present on the system of interest.after 1000 nm and 750 nm excitation.Panel a shows the kinetics of the trion feature at 1175 nm, where we see a long time rise of the trion feature after 750 nm excitation while we observe only a decay after 1000 nm excitation.This hints to a different mechanism between electron transfer (750 nm, direct WSe 2 excitation) vs hole transfer (1000 nm, direct SWCNT excitation).For future work, the difference in mechanism should be better studied.While in this work we focus only in direct SWCNT excitation to avoid multiple active pathways that make kinetic analysis more difficult.Figure S8: A) Kinetic traces corresponding to the SWCNT trion (X + ) induced absorption for the WSe 2 /SWCNT bilayer after 1000 nm excitation (red) and 750 nm excitation (green).Transient absorption spectra for the WSe 2 /SWCNT bilayer after 1000 nm excitation (red) and 750 nm excitation (green) B) averaged over 2-5 ns delay C) at 1 ps delay and D) at 100 ps delay.

Kinetic analysis
Multivariate curve resolution using Alternating Least Squares.A MATLAB package developed by Jaumot, et al, was used to perform initial singular value decomposition (SVD) and extract associated concentration profiles. 1,2Visible and NIR regions were analyzed separately.The visible region was analyzed using four independent components based on initial TA information.The components correspond to the initial SWCNT excited state (S65 * ), electron transfer from SWCNT to MoS 2 (S65 + MoS − 2 ), hole transfer from SWCNT to WSe 2 (S65 − WSe + 2 ), and the charge separated state where SWCNT charges diffuse away from the initial SWCNT/TMDC generation site while the oppositely charged carriers remain in the respective TMDCs (MoS − 2 or WSe + 2 ).Spectra for each component were fed to the MATLAB package as an initial guess from experimental TA.The kinetic scheme presented in Figure 5b is then proposed and the following rate equations specified: Solving these rate equations led to the following concentration equations, where the different rates are also shown in Figure 5a in the main text for reference: Concentration profiles obtained from the MATLAB package are then fitted to the solved equations (5-8) until convergence is achieved, also done through the MATLAB package.Upon convergence, one of the outputs of the software is the associated spectrum to each component, shown below in Figure S1.The SWCNT initial excited state (S65 * , black) only presents the GSB for the S 22 excitonic transition around 575 nm, the electron transfer from SWCNT to MoS 2 (S65 + MoS − 2 , blue) presents the A and B exciton GSB for MoS 2 around 660 and 620 nm respectively, and the GSB of the SWCNT.The hole transfer from SWCNT to WSe 2 (S65 − WSe + 2 , red) presents the A exciton GSB of WSe 2 around 740 nm and the SWCNT GSB, the B exciton GSB of WSe 2 is observed as a slight dip in the photo induced absorption around 600 nm.Lastly, the charge separated state generated by SWCNT charges diffusing away from the initial TMDC/SWCNT generation into the opposite TMDC layer (MoS − 2 WSe + 2 , green) presents all previously mentioned GSB features.The concentration profiles are also an output from the MATLAB software shown in Figure 5c in the main text.From the fitted concentration profiles important kinetic information is obtained such as the rates for the different pathways presented in Table SS2 with the corresponding standard deviation.The decay for the last state (charges diffusing within the SWCNT layer) is not probed in ultrafast TA, as the limit of the stage is 5 ns.From a separate nanosecond-microsecond TA measurement, the longest decay of MoS 2 A exciton GSB was fitted to be around 7 µs (amplitudeaveraged lifetime of 1.3 µs).A surface plot of the experimental TA data presented in Figure S10a is compared to the simulated TA data (Figure S10b) obtained from the fitted concentration equations and spectra are shown.The kinetic scheme and derived equations explain 95% of the experimental data.
The NIR region was analyzed with the same MATLAB package, based on the rate equations and solved concentration profiles for the visible region.Instead of four independent components, three components were specified because the electron transfer from SWCNT to MoS 2 (S65 + MoS − 2 ), and hole transfer from SWCNT to WSe 2 (S65 − WSe + 2 ) do not have different spectral signature in the NIR.These two components were included as one, resulting in a combined concentration profile.The solved concentration profiles, initially obtained from the visible region analysis were fed to the software resulting in the final output presented in Figure S11a, and the associated spectra shown in Figure S11b.The SWCNT initial excited state (S65 * , black) only presents the GSB for the S 11 excitonic transition around 1010 nm.The electron transfer from SWCNT to MoS 2 (S65 + MoS − 2 ) combined with the hole transfer from SWCNT to WSe 2 (S65 − WSe + 2 ) presents the trion (X + ) feature around 1180 nm and the SWCNT GSB (purple).Lastly, the charge separated state formed by charge diffusion within the SWCNT layer to the opposite TMDC (MoS − 2 WSe + 2 , green) presents remaining SWCNT GSB because the charges have left the SWCNTs to inject (via diffusion-limited CT) into the opposite TMDC.
From the concentration profiles and associated spectra, the quantum yields for electron and hole transfer were calculated.The associated spectrum for electron transfer from SWCNT to MoS 2 (S65 + MoS − 2 ), and hole transfer from SWCNT to WSe 2 (S65 − WSe + 2 ) cannot be indistinguishable in the NIR but from the visible region independent concentration profiles have been obtained, allowing independent calculation of carrier density for each state.The hole transfer quantum yield is 0.29, and electron transfer quantum yield is 0.12, accounting for a total charge transfer yield of 0.41.This derivation and calculation is further explained in section 3 below.A surface plot of the experimental TA data presented in Figure S12a is compared to the simulated TA data (Figure S12b) obtained from the fitted concentration equations and spectra are shown.The kinetic scheme and derived equations explain 95% of the experimental data.The Gibbs free energy change for electron and hole transfer between WSe 2 -SWCNT and SWCNT -MoS 2 was calculated using the equation: The electron affinity (EA) and ionization potential (IP) for (6,5) SWCNTs are taken as -3.86 eV and -5.40 eV respectively. 3The EA and IA for MoS 2 in Table S3 are an average of two calculated band energies and one experimental value for MoS 2 on sapphire. 4The optical band gap of WSe 2 and MoS 2 are calculated from the A exciton in their respective absorption spectra (see Figure 1).The electronic band gap (E el ) can be calculated from the sum of the optical band gap (E opt ) and the binding energy of the exciton (E b,exc ). 4 Using the calculated optical band gap and exciton binding energy the electronic band gap for WSe 2 and MoS 2 are 1.89 ev and 1.9 eV respectively.

Charge Transfer Yield
The S 11 optical density (OD S 11 ) is the maximum of the S 11 absorption peak in the trilayer (see Figure 1e).The trion (OD X +/− ) optical density is from the TA spectra associated with the concentration profiles where both the WSe 2 and MoS 2 charge concentration are at their max.The relative trion optical density (OD X + /OD S 11 ) is used to find the hole or electron concentration according to Dowgiallo et al.: where N h/e is the hole or electron density/nm of tube length.We then determine the charge yield as N h/e /N exc , where N exc is the initial exciton concentration from the number of absorbed photons in the pump area.][8] beam area 2.022x10 −3 cm 2 energy fluence 1.5x10 −8 J incident energy fluence 7.41x10 −6 J/cm 2 excitation wavelength 1000 nm energy of singlet photon 1.98x10 −19 J/photon incident Photon fluence 3.74x10 13 photons/cm 2 S 11 trilayer absorbance 0.029 absorbed photon fluence 2.43x10 12 photons/cm 2 areal density of C atoms 6.76x10 15 C atoms/cm 2 nm tube/cm 2 7.46x10 13 nm tube/cm 2 excitons/nm tube 0.032 exciton/nm tube OD(X + ) M oS 2 3.43x10

Figure
FigureS4ashows the transient absorption spectra of the MoS 2 /SWCNT bilayer and trilayer upon selective excitation of WSe 2 at 750 nm.When tracking the MoS 2 GSB, selective excitation of WSe 2 in the trilayer results in a slow rise of MoS 2 charges (FigureS4b).
Figure S5: A)Trion kinetics for the MoS 2 /SWCNT bilayer (purple), MoS 2 /SWCNT/WSe 2 trilayer (gold) and the simulation obtained from our curve fitting procedure (black), highlighting that early time dynamics correspond to singlet contributions from direct SWCNT excitation and longer time dynamics are governed by the trion feature.B) Early time (200 fs) spectra for the neat SWCNT, MoS 2 /SWCNT bilayer and MoS 2 /SWCNT/WSe 2 trilayer showing the photoinduced absorption band is present due to singlet state contribution from direct SWCNT excitation.

Figure
Figure S6: A) Trion kinetics for the MoS 2 /SWCNT/WSe 2 trilayer (yellow) and neat SWCNT (black) showing the second pulse inside the marked area.A) Trion kinetics for the WSe 2 /SWCNT bilayer (red) and neat SWCNT (black) showing the second pulse inside the marked area.C) Trion kinetics for the MoS 2 /SWCNT bilayer (solid purple) and neat SWCNT (black) and Mo 2 A exciton kinetcs showing the second pulse inside the marked area.

Figure
FigureS7highlights a faster decay of trions in the nanosecond time frame for the trilayer, relative to the bilayer, continuing to make a case for charges diffusing away from SWCNTs.

Figure
Figure S8 compares the WSe 2 /SWCNT bilayer transient spectroscopy results after 1000 nm and 750 nm excitation.Panel a shows the kinetics of the trion feature at 1175 nm, where we see a long time rise of the trion feature after 750 nm excitation while we observe only a decay after 1000 nm excitation.This hints to a different mechanism between electron transfer (750 nm, direct WSe 2 excitation) vs

Figure S9 :
Figure S9: Associated spectra for the four different components obtained from the solved equations fitted to the concentration profiles obtained from the MATLAB package.SWCNT initial excited state (S65 * , black), electron transfer from SWCNT to MoS 2 (S65 + MoS − 2 , blue), hole transfer from SWCNT to WSe 2 (S65 − WSe + 2 , red), and charge separated state generated by SWCNT charges diffusing away from the initial TMDC/SWCNT generation into the opposite TMDC layer (MoS − 2 WSe + 2 , green).

Figure
Figure S10: A) Experimental TA surface plot for the visible region of the trilayer excited at 1000 nm.B) Simulated TA surface plot from the concentration equations and associated spectra.Vertical axis is wavelength (nm): GSB for S 22 at 575 nm, MoS 2 A exciton at 660 nm and WSe 2 at 740 nm can be identified.Horizontal axis is time (ps), showing the behavior along time.Color-bar to the right specifies intensities of the different signals

Figure
Figure S12: A) Experimental TA surface plot for the NIR region of the trilayer excited at 1000 nm.B) Simulated TA surface plot from the concentration equations and associated spectra.Vertical axis is wavelength (nm): GSB for S 11 at 1010 nm can be identified.Horizontal axis is time (ps), showing the behavior along time.Colorbar to the right specifies intensities of the different signals

Table S2 :
Rate constants associated with the kinetic scheme

Table S5 :
Summary of values used to calculate excitons/nm of tube, relative trion optical density and charge transfer yield for the WSe 2 /SWCNT bilayer excited at 1000 nm at 20 nJ fluence and 750 nm at 15 nJ fluence