Supporting Information. Carrier Trapping by Oxygen Impurities in Molybdenum Diselenide

Transcription

1 Supporting Information Carrier Trapping by Oxygen Impurities in Molybdenum Diselenide Ke Chen 1, Anupam Roy 2, Amritesh Rai 2, Amithraj Valsaraj 2, Xianghai Meng 1, Feng He 1,4, Xiaochuan Xu 3, Leonard F. Register 2, Sanjay Banerjee 2, Yaguo Wang 1,4* 1. Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712, USA 2. Microelectronics Research Center and Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78758, USA 3. Omega Optics, Inc., Austin, TX 78757, USA 4. Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA *Corresponding Author: S-1

2 1. Determination of flake thickness with Atomic force microscope (AFM) Figure s1. (a) Microscopic Figure of the sample flake. (b) The height value along bar 1 across the sample boundary shown in (a), from which a thickness around 80nm is obtained. 2. Analysis of the relation between differential reflection and the refractive index change For optical thin films with thickness smaller or comparable to the light penetration depth, the entire reflection from the film is determined by both the real (n) and imaginary (κ) part of the refractive index. The entire reflection is actually the interference of multiple light beams that bounce back and forth between the film/air and the film/substrate interfaces, and transmit through the film/air interface back into air. In this case, the Fresnel equation which is valid for reflection at only one interface is not accurate to describe the entire reflection. To get the entire reflectivity of such thin-film-on-substrate structure, one should adopt the transfer matrix method. 1 Using this method, the entire reflectivity of such thin-film-onsubstrate structure can be calculated. The analytical expression of the reflectivity R of thin film/sio 2 /Si system is presented as Equation (1) in the manuscript: R, (1) where,, are the complex amplitude of reflection coefficients for air/ film, film/sio 2, and SiO 2 /Si interfaces, respectively; is the complex refractive index of each material (note that positive κ stands for absorption), and 2 / is the complex phase shift due to a change in the optical path and the absorption in thin film or Si. Clearly, it can be seen from Equation (1) that the reflectivity is related to both n and κ of the thin film. Theoretically, after a pump pulse generates excited carriers in the thin film, both n and κ of the thin film will change, i.e. n=n 0 + n, κ= κ 0 + κ, which will result in a change of reflectivity, R=R 0 + R. Firstly, we want to show how the differential reflection change, R/ R 0, depends on the refractive index change, n/n 0 and κ/κ 0, according to Equation (1). As shown in Figure s2, when n/n 0 and κ/κ 0 are small, R/R 0 shows an almost linear relation with both n/n 0 and κ/κ 0. The slope of R/R 0 with respect to n/n 0 is around 3.7 times of that of κ/κ 0, indicating the reflection change is more sensitive to the real part of refractive index change. S-2

3 Figure s2. Differential reflection R/R 0 at 1.55eV as a function of the refractive index change, n/n 0 and κ/κ 0. However, in a real physical system, the n/n 0 and κ/κ 0 are not independent parameters, but correlated to each other through the Kramers-Kronig relation. As will be shown below, the relative magnitudes of the excited-carrier-induced changes in refractive index, n/n 0 and κ/κ 0, can differ much at different probing wavelength: in resonant wavelength region (note that here the resonant region refers to photon energies close to the direct band gap, i.e., the PL peak region), κ/κ 0 is typically much larger than n/n 0 ; but at wavelengths far away from resonance, κ/κ 0 is usually negligible while n/n 0 will dominate. The Kramers-Kronig relation, which correlates the response functions of a physical system, is expressed as: 1, (2), (3) Hence, the change of the real and imaginary parts of refractive index are also correlated:, (4), (5) If the magnitude of either n change or κ change is known, we can use Equations (4)~(5) to estimate the change of the other one. In a semiconductor material with a well-defined band structure, such as MoSe 2 in our case, the excited carrier induced absorption change ( ) is typically due to the phase space filling effect. After carrier thermalization and cooling, the excited carriers will mainly occupy the band edge energy states (or the exciton state for 2D cases), giving rise to an absorption change only non-trivial at around band edge (or the exciton energy). 2-5 Since photoluminescence (PL) signal just reflects the distribution of the excited carriers at the band edge, the absorption change - and the PL signal will typically have the same shape. 2,6 Based on this understanding, we can assume the absorption change with the following expression: S-3

4 exp 4ln2, (6) where is the extinction coefficient before excitation, which has been measured in reference, 7 is the angular frequency corresponding to the band gap of the direct transition, and Γ is a line width parameter characterizing the occupied energy range, and is the absorption reduced ratio with a stepfunction like shape (to eliminate the part with energies lower than the direct band gap where little is contributed to the absorption change). The profile of carrier induced absorption change / 0 based on equation (6) is plotted in Figure s3 as the black curve. By substituting Equation (6) into Equation (4), we can calculate the correlated change of real part of refractive index, n/n 0, which is also plotted in Figure s3. It can be seen that, in the resonant region (marked by green dashed rectangle), / is much larger than n/n 0, showing at the band edge states, the excited carriers have much greater influence on the extinction coefficient (absorption) than on the real refractive index. In the non-resonant region (marked by blue dashed rectangles), / is negligible but n/n 0 is non-trivial, showing the excited carriers mainly cause change in the real part of refractive index. Physically, the dominant change in / at the band edge states comes from the phase-space filling (Pauli blocking effect). Because in equation (4) has odd symmetry with respect to and vanishes away from, and the integrand in equation (4) at the band edge is a product of the odd symmetric term with a smooth and gradual change term, hence, in the resonant region, this integrand will have opposite sign with comparable magnitude, which will result in a major cancellation when performing the integration to get the refractive index change. So mathematically it is reasonable to reach a small around the band edge. As shown in Figure s3, the central wavelength of our laser is set to be close to the resonance, but the laser spectrum still spreads over a certain range within which n/n 0 can change sign. If we further consider the sign changing feature of the n/n 0 in the coverage of the laser spectrum, the average value of n/n 0 in the detected region will be further reduced comparing with that of /. Figure s3. The excited-carrier-induced refractive index change calculated from Kramers-Kronig relation. In the resonant region (circled by green dashed rectangle), / is much larger than n/n 0 ; while in the non-resonant region (circled by blue dashed rectangles), / is almost 0 but n/n 0 is non-trivial. S-4

5 According to Figure s3, the ratio of ( / )/( n/n 0 ) within our detection spectrum is 23.8/1. With this ratio, now we can replot the dependence of R/R 0 on the actual / and n/n 0 at the resonant detection region, as shown in Figure s4. As a result of the large ( / )/( n/n 0 ) ratio, the R/R 0 signal due to / is actually much larger than that due to n/n 0. So we can conclude that: even though according to equation (1) R/R 0 is more sensitive to n/n 0 (Figure s2), the actual n/n 0 induced by the excited carriers is very small compared with the actual / in the resonant region (Figure s3). Therefore, even seemingly counterintuitive, the reflection change R/R 0 in fact mainly comes from the change in absorption /, as shown in Figure s4. According to Figure s4, positive (negative) R/R 0 corresponds to positive (negative) /, indicating enhanced (reduced) absorption. In our experiments, we observed negative R/R 0 signals in pristine MoSe 2 sample (and at zero time delay in plasma-treated samples). These signals indicate that the pump excitation leads to a reduced absorption, which is physically reasonable because the Pauli blocking effect induced by excited carriers will just decrease the absorption. Our treatment here is consistent with several previous studies, where the observed differential reflection change was attributed to absorption change induced by the excited carriers, 2, 6, 8-9 and the observed peak R/R 0 signals closely resemble the PL spectrum. 2, 6 (Equation (6)) Figure s4. Differential reflection R/R 0 at 1.55eV as a function of the refractive index change, n/n 0 and κ/κ 0, correlated through K-K relation. 3. Analysis of the relative importance of direct transition and indirect transition in the signal detection The measured R/R 0 signals can only indirectly link to the indirect recombination under our experimental conditions. That is, the R/R 0 signals should only directly reflect the carrier density in the K valleys, but the indirect recombination from the conduction bottom to the Γ valley of valence band can facilitate the decrease of carrier in the K valleys so that the indirect recombination information can be indirectly included in the R/R 0 signals. The main reason of this understanding lies in the very low efficiency of indirect transition at the wavelength of our laser. We chose 800 nm wavelength, which is resonant with energy difference between the conduction and valence bands at K(K ) point. In this case, the direct S-5

6 absorption transition around K point can occur very efficiently, the process can be excited and detected by the pump and probe lasers respectively. However, the indirect absorption transition for 800nm (1.55eV) photons requires assistance of phonons with large wave vector (about 1/10 of the K-K distance or even larger in scale estimated from the band structure) to satisfy the momentum conservation. The efficiency of transition involving multiple particles/processes is originally low, and if the involved particles have small population such as large-wave-vector phonons required here, the efficiency of the transition will be even lower. Typically, the efficiencies of the direct and indirect transitions can differ with several orders of magnitudes. The extremely larger difference in efficiency can be seen in the measured absorption spectrum of MoSe 2 reported in the literatures, 7 as shown in Figure s5, where the extinction coefficients in the indirect transition region is indeed 3 or 4 orders smaller than those in the direct transition region. Therefore, it can be concluded that the absorption due to indirect transition (if there is any) should be negligible compared with the one due to direct transition at our resonant wavelength. And obviously, if the indirect absorption channel at the wavelength is very weak, the detection of the indirect recombination through such channel due to the saturable effect should also be very weak. That is, our probed wavelength is not sensitive to the indirect transition. The information of indirect recombination can only go into the signal indirectly by affecting the population of carriers in the K valleys. Figure s5. Measured extinction coefficient of bulk MoSe 2, 7 showing large difference between indirect and direct transition efficiencies. 4. Normalized R/R 0 signals of the pristine MoSe 2 S-6

7 Figure s6. Normalized R/R 0 signals of the prinstine MoSe 2. Figure s6 shows the R/R 0 signals normalized with respect to the peak values. The relative magnitude of the fast component actually does not change much with pump fluences, but all stops at around 40% of the peak value. For the slow decaying components, the two curve measured at lowest pump fluences overlap with each other, indicating the carrier dynamics are still in the linear region under a pump fluence of 0.8 µj/cm 2. However, at larger pump fluences, the decay rates increase with pump fluences, indicating the carrier recombination at high densities has non-linear feature and many body effect (very likely the Auger process) should dominate the carrier recombination dynamics. 5. Comparison between R/R 0 signals of the pristine MoSe 2 and the plasma-treated MoSe 2 at high carrier densities Figure s7 shows the comparison of R/R 0 signals normalized at a certain late time delay and measured at the highest pump fluence. It can be seen that the normalized signals indeed roughly overlap at long time delays, indicating very similar decay time constants for the later recombination kinetics. We agree with the reviewer that, the similar decay time constants can serve as another proof that carrier traps are saturated at high excitation densities. S-7

8 Figure s7. R/R 0 signals of pristine and plasma-treated MoSe 2 samples measured at the highest pump fluence and normalized at late time delay. 6. Estimation of the excited carrier density We estimate the excited carrier density based on the assumption that each absorbed photon can generate one electron-hole pair. We use the transfer matrix method to calculate the reflectivity at the sample surface R 0, the transmittance into Si substrate T, to get the absorptance inside the sample (A=1-R 0 -T). With the absorptance of the sample known, we can convert the pump fluence to the absorbed energy density, and finally estimate the excited carrier density. This approach requires the absorption to stay in the linear regime with the pump fluence. To check the linearity, we plot the peak value of the R/R 0 signals against the pump fluence, as shown in Figure s8. It can be seen that the peak value of reflection signal is roughly proportional to the pump fluences except for the highest pump fluence (25 µj/cm 2 ). This indicates that the excitation (i.e. the generated carrier density) is indeed roughly in the linear region with pump fluence and our method to estimate the carrier density is valid. The deviation of linearity for the data point at the highest fluence is due to the saturable absorption at the pumped energy states at the arrival of the intense pump pulse, which has also been observed in the literatures. 6 Note that the defect saturation occurs at low pump fluences (0.4 and 0.8 µj/cm 2 for the successive irradiations), so the deviation from linearity at much higher pump fluences actually does not affect our estimation of defect density. S-8

9 Figure s8. Peak value of R/R 0 signals of 2 nd plasma-treated sample as a function of pump fluence. The red dots are the experimental data and the solid line marks the linear trend. 7. Details of DFT calculations for band structure of MoSe2 with O atoms occupying Mo vacancies The DFT calculations were performed using the projector-augmented wave method with a plane-wave basis set as implemented in the Vienna ab initio simulation package (VASP) A kinetic energy cutoff of 400 ev was chosen. The k-mesh grid of 7x7x1 for the sampling of the first Brillouin zone of the supercell was selected according to Monkhorst-Pack type meshes, with the origin being at the Γ point for all computations except the band structure computation. 14 The local density approximation (LDA) was used for the exchange-correlation potential Van der Waals forces were also simulated due to the absence of covalent bonding between the layers. 16 In our computations, we have adopted the DFT-D2 scheme to model the non-local dispersive forces wherein a semi-empirical correction is added to the conventional Kohn-Sham DFT theory. 15 A 2x2 supercell of bulk MoSe 2 was constructed with an O-atom incorporated into Mo-vacancy site. Atomistic relaxations were allowed to converge when the Hellmann- Feynman forces on the atoms were less than ev/ang. In previous studies, Mo-vacancy in TMDs has shown to introduce defect states in the nominal band gap of TMD material In our simulations, the highest occupied state of the system with vacancies serves as the zero- energy reference in these 0 K simulations. References (1) Katsidis, C. C.; Siapkas, D. I. General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference. Appl. Opt. 2002, 41 (19), (2) Sun, D.; Rao, Y.; Reider, G. A.; Chen, G.; You, Y.; Brézin, L.; Harutyunyan, A. R.; Heinz, T. F. Observation of rapid exciton exciton annihilation in monolayer molybdenum disulfide. Nano Lett. 2014, 14 (10), S-9

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