Highly Efficient and Anomalous Charge Transfer in van der Waals Trilayer Semiconductors Frank Ceballos 1, Ming-Gang Ju 2 Samuel D. Lane 1, Xiao Cheng Zeng 2 & Hui Zhao 1 1 Department of Physics and Astronomy, The University of Kansas, Lawrence, KS 66045, United States 2 Department of Chemistry, University of Nebraska - Lincoln and Nebraska Center for Materials and Nanoscience, Lincoln, NE 68588, United States These authors contributed equally to this work. This file includes: Sample Fabrication Pump-Probe Measurements Estimation of Pump-Injected Carrier Density Supporting Figures S1 - S9 1
Sample Fabrication The monolayers in the heterostructure were fabricated by mechanically exfoliating TMD bulk crystals using adhesive tape. A small fraction of the flakes were then transferred onto a transparent polydimethylsiloxane (PDMS) substrate by placing the adhesive tape on it and peeling it off. The PDMS substrate, already placed on top of a glass slide, is then inspected under a microscope and monolayers are then identified by optical contrast and PL spectrum. Each TMD monolayer was then manually transferred, using a micromanipulator and microscope, from the PDMS substrate onto a silicon wafer covered with 90 nm of silicon dioxide. By comparing the known optical contrast for MoSe 2, WS 2, and MoS 2 monolayers, we further confirmed the thickness of the transferred flakes. The first TMD monolayer transferred onto the wafer was MoSe 2 and immediately after the WS 2 monolayer was place on top of it. The bilayer heterostructure was then thermally annealed at 200 C for 2 h under a H 2 /Ar (20 sccm/100 sccm) environment at a pressure of about 3 Torr. Finally, the MoS 2 monolayer was place on top, and the sample was thermally annealed again under the same conditions. Pump-Probe Measurements In the transient absorption setup, a continuous laser with a center wavelength at 532 nm and a power of 8.5 W is used to pump a Ti-sapphire laser. The generated pulses centered at 790 nm have a 100 fs pulse duration, a 80 MHz repetition rate, and an average power of 2.0 W. Part of this beam was then sent into a photonic crystal fiber for supercontinuum generation, which output has 2
a broad spectral range. The desired spectral component was then selected with bandpass filters that have 10 nm bandwidth. For any given configuration of laser beams, both the pump and probe beams were linearly polarized along perpendicular directions, combined by beam splitters, and focused on the sample with a microscope objective lens to spot sizes of 2.0-2.6 µm in full width at half maximum. The pump beam intensity was modulated at about 2 KHz by a mechanical chopper. The collimated reflected probe beam is sent to a biased silicon photodiode connected to a lock-in amplifier that reads its output. The pump beam is prevented from reaching the detector by using a set of filters. To measure the differential reflection as a function of probe delay, the pump beam or the probe beam (depending on the configuration) path length is changed by using a linear motor stage. Estimation of Pump-Injected Carrier Density To calculate the injected carriers in each layer, the laser fluence, the energy per unit area each pulse delivers, must first be known. In these experiments, the Ti-sapphire laser generates Gaussian laser pulses at a frequency f rep (Hz) known as the repetition rate of the laser. By measuring the time averaged power P and the repetition rate f rep, the energy each pulse contains can be estimated by : E pulse = P f rep. (1) Before conducting the pump-probe experiments, the laser spot size was measured by precisely scanning the pump beam across the probe with the use of calibrated picomotors. By doing so, the convolution between the pump and probe beam spatial profiles was obtained. By nothing that the 3
convolution between two Gaussian profiles, f and g, is also Gaussian with a variance equal to the sum of the original variances, the convoluted spatial profile is then fitted to a Gaussian curve from which we obtained the full width at half maximum, w RT. Since both beams have similar laser spots and Gaussian profiles, we can assume that the full width at half maximum (FWHM) of the pump, w pump, to be w pump = w RT 2 (2) as: The fluence is position dependent. For laser beams with Gaussian profiles, it can be described F (r) = F peak e 2r2 /w 2, (3) where F peak is the peak fluence, r is the radial distance from the center of the beam, w is the Gaussian beam radius at which the fluence drops to 1/e 2 of its peak value. By integrating the fluence, F (r), over all space, the energy delivered by each pulse is found to be: and therefore E pulse = F peak πw 2 2, (4) F peak = 2E pulse πw 2. (5) It can be shown that the FWHM, w 0, is related the width, w, of the Gaussian profile by w = w 0. (6) 2ln 2 By using equation 6 and the measured quantities P, f rep, and w pump, equation 5 can be rewritten as F peak = 8ln2 π 4 P. (7) f rep wrt 2
The peak fluence can be converted to the incident number of photons per unit area by diving it by hν, where h is Planck s constant and ν the frequency of the laser. From the incident photons, only a fraction of them will be absorbed. By assuming that each photon absorbed creates an excited electron-hole pair, the injected carrier density can be modeled as n = F peak hν b a e αz dz = F peak hν (e αa e αb ). (8) Here, α is the absorption coefficient of the sample, z is the direction the beam is propagating, a the position where the layer begins, and b the end of the layer. For each ML, we used the α values reported 1 for the corresponding incident pump photon energy. For a certain pump flence incident to a multilayer structure, it is necessary to consider the multiple reflections from all the interfaces in order to obtain the actual pump fluence in each layer. For this purpose, we used Rouard s method, where the reflection of light from k different thin films on a substrate is calculated using an iterative approach 2. This method yields the reflection coefficient R which is define as the ratio between the reflected intensity I r by the whole structure and the incident intensity I 0. With the known R, we can then calculate the fraction of incident intensity that enters the first layer, according to energy conservation. By knowing the fraction of transmitted intensity into the first layer, we can then apply Rouard s method again, but this time using k 1 films by removing the top film, in order to calculate the amount of light reflected from the k 1 thin films. This allows us to obtain the fraction of light transmitted into the second layer. By using this approach again, We finally obtain the fraction of light transmitted into the last layer. The actual intensity in each layer is used calculate F peak, which is used in Eq. 8 to obtain the injected carrier density. 5
Supporting Figures 6
Figure S1: Electronic structures of configuration at t = 1000 fs. The total density of states (DOS) (top) and projected density of states (PDOS) and the charge density distribution (bottom) of the bands around the gap edge of the configuration. 7
Figure S2: Electronic structures of configuration at t = 2000 fs. The total DOS (top) and PDOS and the charge density distribution (bottom) of the bands around gap edge of configuration. 8
Figure S3: Electronic structures of configuration at t = 3000 fs. The total DOS (top) and PDOS and the charge density distribution (bottom) of the bands around gap edge of configuration. 9
Figure S4: Electronic structures of configuration at t = 4900 fs The total DOS (top) and PDOS and the charge density distribution (bottom) of the bands around gap edge of configuration. 10
Figure S5: Electronic coherence between LUMO+4 and LUMO+2. Pure-dephasing functions for the charge transfer between LUMO+4 and LUMO+2. The decay time scale represents the elastic electron-phonon scattering time, fitted by a Gaussian (left). Fourier transformation of the energy gaps between the LUMO+4 and LUMO+2 for electron transfer (right). 11
Figure S6: Electronic coherence between LUMO+3 and LUMO+2. Pure-dephasing functions for the charge transfer between LUMO+3 and LUMO+2. The decay time scale represents the elastic electron-phonon scattering time, fitted by a Gaussian (left). Fourier transformation of the energy gaps between the LUMO+3 and LUMO+2 for electron transfer (right). 12
10 8 ProbeMoSe 2 ML ProbeWS 2 MLscaled ProbeWS 2 ML R/R 0 (10-3 ) 6 4 2 0 0 100 200 300 400 500 Probe Delay(ps) Figure S7: Origin of signal from the WS 2 layer. The differential reflection signal of the 2.00-eV probe, shown as the gray squares, after a 1.57-eV pump excites the multilayer structure displays a relatively low magnitude, lacks a transient temporal region, and has an unexpected long lifetime. In fact, the dynamics displayed closely resembles the long lived signal obtained from monitoring the holes in the multilayer structure, blue squares. For this reason, we conclude that the signal in the middle layer arises due to screening effects and closely monitors the holes in the MoSe 2 layer that change the probe reflection. 13
Normalized R/R 0 1.0 Data FWHM=0.24ps FWHM=0.35ps 0.8 FWHM=0.45ps 0.6 0.4 0.2 0.0-0.6-0.4-0.2 0.0 0.2 0.4 0.6 Probe Delay(ps) Figure S8: Calculation of the pump-probe cross correlation function. To determine the instrumental response time, we utilize the the rising part from a differential reflection, R/R 0, signal obtained from monitoring the hole population in the trilayer structure after a 1.88 ev pump pulse injected carriers into it, black squares. We assume that the response time of the sample is instantaneous. In the case that the pump and probe are infinitely narrow, the instrumental response would be a step function that jumps to its maximum value at zero delay. As the pump and probe pulses acquire a finite width, the response function evolves to one that quickly rises to its maximum value within the pulse width. To demonstrate this effect, the integral of a Gaussian function with different FWHMs are shown as the solid curves. From this its clear that the pump-probe cross correlation width is 0.35 ps, blue curve. That translates to pulse widths of 0.25 ps for each pulse, using 0.35/1.414. The sample response cannot be instantaneous, therefore, this is actually the upper limit of the pulse width. 14
Normalized R/R 0 1.0 0.8 0.6 0.4 MoS 2 ML WS 2 ML MoSe 2 ML Trilayer 0.2 0.0 0 100 200 300 400 Probe Delay(ps) Figure S9: Excitons lifetimes in constituent monolayers. As controlled measurements, the lifetime of excitons in mechanically exfoliated monolayers of MoS 2, WS 2, and MoSe 2 was measured by monitoring the transient absorption of a probe pulse in reflection geometry (see Methods). The probe pulse for each of these measurements was tuned to the A exciton resonance of MoS 2 (blue squares, 1.88 ev), WS 2 (red squares, 2.00 ev), and MoSe 2 (pink squares, 1.57 ev). For a more clear comparison, the signal obtained from the MoS 2 -WS 2 -MoSe 2 is also shown, green squares. Is evident that the lifetime of excitons in isolated monolayers is considerably shorter than those in the multi-layer structure. 15
Reference 1. Liu, H.-L. et al. Optical properties of monolayer transition metal dichalcogenides probed by spectroscopic ellipsometry. Appl. Phys. Lett. 105, 201905 (2014). 2. Vašíček, A. & Watney-Kaczér, H. Optics of Thin Films (Amsterdam, 1960). 16