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Saturation of two-photon absorption in layered transition metal dichalcogenides: experiment and theory Ningning Dong, Yuanxin Li, Saifeng Zhang, Niall McEvoy, Riley Gatensby, Georg S. Duesberg, and Jun Wang ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00010 • Publication Date (Web): 21 Feb 2018 Downloaded from http://pubs.acs.org on February 23, 2018
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Saturation of two-photon absorption in layered transition metal dichalcogenides: experiment and theory Ningning Dong,†,‡ Yuanxin Li,†,‡ Saifeng Zhang,†,‡ Niall McEvoy,*,§ Riley Gatensby,§ Georg S. Duesberg,§ Jun Wang*,†,‡,ǁ
† Key Laboratory of Materials for High-Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. ‡ §
ǁ
University of Chinese Academy of Sciences, Beijing 100049, China.
Advanced Materials and BioEngineering Research (AMBER) Centre and School of Chemistry, Trinity College Dublin, Dublin 2, Ireland
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
*Corresponding Authors:
[email protected] and
[email protected] Abstract The saturation of two-photon absorption (TPA) in four types of layered transition metal dichalcogenides (TMDCs) (MoS2, WS2, MoSe2, WSe2) was systemically studied both experimentally and theoretically. It was demonstrated that the TPA coefficient is decreased when either the incident pulse intensity or the thickness of the TMDCs nanofilms increasing, while TPA saturation intensity has the opposite performance, under the excitation of 1.2 eV photons with pulse width of 350 fs. A three-level excitonic dynamics simulation indicates that the fast relaxation of the excitonic dark states, the exciton-exciton annihilation and the depletion of electrons in the ground state contribute significantly to TPA saturation in TMDCs nanofilms. Large third order nonlinear optical responses make these layered 2D semiconductors strong candidate materials for optical modulation and other photonic applications. KEYWORDS: two-photon absorption, saturable absorption, transition metal dichalcogenides, 2D semiconductor, optical modulation, nonlinear optics
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Two-dimensional (2D) layered transition metal dichalcogenides (TMDCs) exhibit unique nonlinear optical (NLO) features including layer-dependent second/third harmonic generation,1-3 ultrafast saturable absorption,4-6 optical limiting,7 etc., which have led to these nanomaterials being touted for intriguing and promising applications in the 2D photonic and photoelectric fields.8 Recently, two-photon effects9 in MoS2 and WS2 have also attracted considerable research interest. Ye et al. used two-photon absorption (TPA) induced luminescence spectroscopy to reveal the excitonic dark states in monolayer WS2.10 Our previous studies have demonstrated the large degenerate TPA coefficient both in monolayer and few-layer MoS2 and WS2.11,12 In addition, the saturation of the TPA process has been experimentally observed,11 which is one of the fundamental, yet most important, NLO mechanisms in TMDCs if these 2D semiconductors are to be considered as candidate materials for next-generation photonic and optoelectronic devices. However, TPA saturation in TMDCs is not yet fully understood, and the characteristics and magnitudes of this third order NLO response in various TMDCs with different thicknesses have not been studied in detail. On the other hand, few-layer TMDCs can act as saturable absorber for Q-switched or mode-locked laser pulses generation above 1 µm that is below the bandgap of the TMDCs, the physical mechanism of which is still vague and the TPA saturation could be a rational explanation. In this work, we present an experimental and theoretical investigation of frequency-degenerate TPA in four TMDCs nanofilms (MX2 = MoS2, WS2, MoSe2, WSe2). Our findings show that the TPA saturation process in these 2D semiconductors is similar, but depends significantly on the thickness of the TMDCs. The saturation of photon excited carriers and depletion of the electron population in the ground state of these 2D semiconductors contributes to the saturation of the TPA. Additionally, it is theoretically demonstrated that TMDCs can be promising candidates for optical modulation if the device is appropriately designed.
Results and discussion
Experimental In this study, MX2 samples of high quality were prepared by a vapor-phase growth method,12-15 whereby transition metal films were first sputtered onto quartz substrates followed by the sulfurization (or selenization) in a custom-built tube furnace. In this way MX2 films of different thickness can be produced, e.g., 1.5 ± 0.75, 5.5 ± 0.75, 18.7 ± 0.70, 50.0 ± 0.75 nm for MoS2. The thickness was determined by cross-sectional transmittance electron microscopy for thin (< 10 nm) samples and X-ray reflectivity measurements for thicker ones.12,14 In the case of the 1.5 ± 0.75 nm MoS2 sample, it consists mostly of a thickness of 1.5 nm, and a small part of 0.75 nm and 2.25 nm coexist in this sample. The values of thickness with error bars for other samples have similar meaning. The detailed parameters for the other samples are summarized in Table 1. In addition, Raman spectroscopy characterization (Fig. S1 in SI) was also carried out to confirm the high quality and uniformity of the samples. Transmission electron microscopy and electron diffraction pattern characterization (Fig. S2 in SI) confirmed the 2H crystal structure of the samples. Single-beam nonlinear transmittance measurements were carried out on the MX2 nanofilms using a modified intensity-scan system.11,16-19 Optical pulses with duration ( ) of 350 fs at 1030 nm (ℏω = 1.2 eV), generated from a mode-locked fiber laser, were used to excite the MX2 at a repetition rate of 100 Hz. The beam was focused down to a waist radius of ~ 8.5 µm on the surface of MX2 by an f/10 cm lens. The pulse energy was tuned by a Glan-Taylor prism, allowing focused intensities changing from a few GW/cm2 to ~ 200 GW/cm2. The reference beam from the fiber laser and the transmitted signal through the MX2 were detected by two high-precision 2 / 15
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photodetectors. The variation of the transmittance versus the incident intensities was recorded, which reflects the NLO response of the MX2. The NLO measurements were carried out on random spots of the samples, and repeated at least three times for each spot to confirm that this point was not damaged (Fig. S2 in SI). In addition, we carried out the NLO experiments at 10 Hz, 100 Hz and 1 kHz pulse repetition, and found the NLO responses had little difference among three excitation conditions (see Fig. S4), which demonstrated the possible femtosecond laser heating has little effect on the nonlinear absorption.
Figure 1. Nonlinear transmittance versus incident pulse peak irradiance for MX2 nanofilms. The solid lines are the fitting results obtained by numerically solving Eq. 6. Figure 1 shows the normalized nonlinear transmittance (NLT) for four types of MX2 with different thickness. The solid circles with error bars show the experimental data and the solid lines are the fitting curves obtained using the method discussed in the following text. All of the samples, except for 1.40 ± 0.70 and 5.8 ± 0.64 nm MoSe2, show very interesting NLT variation that it firstly decreases in the low intensity region (the first half) and then increases after a certain intensity (the second half). This phenomenon can be explained using TPA saturation theory, as discussed later in this article. It should be pointed out that TPA saturation in semiconductors (GdS),17 nanomaterials (GdS nanocrystals)20 or organic molecules18 has been reported, however, few previous studies have observed the second half. We attribute this unique phenomenon in TMDCs to: 1) large TPA coefficient ( ) and small TPA saturation intensity ( ), 2) the depletion of the electron population in the ground state (E0, Fig.2), and 3) fast relaxation of excitons in the high energy level (E2 E1) followed by an exciton-exciton annihilation (EEA) effect and a slow recombination process of the 1s excitons (E1 E0). As for 1.40 ± 0.70 nm and 5.8 ± 0.64 nm MoSe2, only the first half could be observed under our experimental conditions because their TPA saturation 3 / 15
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intensities are larger compared with the other samples, as discussed in the following text.
TPA saturation fitting Firstly, we use the TPA saturation theory to fit the experimental data in Fig. 1 to obtain and . Our theory is aimed at such layered MX2 as illustrated by Fig. 2 (a). Under the excitation conditions mentioned above, all of the samples can experience degenerate TPA processes when a laser beam interacts with the MX2 films. It is known that TMDCs have a layer-dependent band structure, which usually involves a direct energy bandgap (Eg) for monolayer and an indirect bandgap for few-layer and bulk.21-24 However, the direct excitonic transition at the K point of the Brillouin zone dominates the optical properties of TMDCs, even for few-layer and bulk, e.g., almost constant A and B exciton absorption peaks can be observed in all the monolayer, few-layer and bulk TMDCs22,25 in spite of the distinction of the energy bandgap and the excitonic binding energy. The characteristic photoluminescence (PL) peaks also originate from the direct transition of A and B excitons in monolayer and few-layer TMDCs.21,24 In addition, it has been demonstrated that rich dark excitonic states exist in the region between 1s excitons and quasiparticle band edge, which contains many two-photon active states.10,26-29 Therefore, TPA in monolayer and few-layer TMDCs nanofilms in this work is attributed to the direct excitonic absorption of these states. As shown in Fig. 2 (b), two exciting photons (2.4 eV) can be absorbed by the two-photon active excitonic dark states at E2 energy level, which then relax to 1s excitonic state followed by the exciton-exciton annihilation (EEA)30-32 and the recombination of the ground excitons. For example, MoS2 has the 1s excitonic state at 1.88 eV, and dark excitons near 2.35 eV,29 which is close to two-photon energy in our experiments. A similar excitonic picture can be found in previous works on WS2,10,27 MoSe226 and WSe2.28
Figure 2. (a) The schematic of light interacting with an MX2 nanofilm on quartz. The solid arrows show the propagation of the light beam and the dashed arrows show the linear reflected light. I0: incident pulse intensity; IL: transmitted pulse intensity. N0, N1, N2 are the complex refractive indices of air, MX2 nanofilm and quartz, respectively. (b) The three-level system and the degenerate TPA process in MX2 nanofilm. The blue line, green line and orange lines show the valence band maximum, 1s excitonic state and dark exciton states, respectively. In a simple model, the attenuation of the transmitted intensity through MX2 as a function of the incident intensity is given by the following differential equation:17,19 ⁄ = ,
(1)
where is the linear absorption coefficient, is the intensity dependent TPA coefficient. The TPA coefficient is supposed to be dependent on the intensity, but different equations have been used to model the variation for 4 / 15
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semiconductors or organic molecules. Here, we will discuss four models:17,33-35 _ !": = . _$%& '(: = +,-
)*
_$3 ∶ =
_6 $3: =
* /-/01
)*
,
+,-* /-/01 5 )*
8* 5 /01
7+,8
(2)
,
,
(3) (4) (5)
These four models were proposed for the nonsaturable TPA cases, the hyperbolic approach in bulk semiconductors, the homogeneously and inhomogeneously broadened systems, respectively. Isat is the TPA saturation intensity and is the low intensity response of the material. Equation 1 can be numerically solved through the four Models to fit the experimental data.
Figure 3. (a) Comparison of the four TPA saturation models. The blue spheres are the experimental data. (b) The normalized transmittance of MoS2 with thickness of 1.5 ± 0.75, 5.5 ± 0.75, 18.7 ± 0.70 and 50.0 ± 0.75 nm. Inset: depth ratio of four samples. (c)TPA coefficient versus incident pulse intensity for MoS2 of different thickness. (d) Nonsaturation TPA coefficient and TPA saturation intensity for MoS2 nanofilms with different thickness. As shown in Fig. 3 (a), only the homogeneously broadened model fits well with the experimental data, which reveals that MoS2 should be homogeneously broadened system during the TPA saturation process. It is known that the MX2 nanofilm prepared using the vapor-phase growth method is polycrystalline in nature. However, the NLO measurements on different spots of a same sample have little difference as shown in Fig. S2 (c) (see SI), which is consistent with the homogeneously broadened nature. That is to say, different crystalline in the range of laser spot contributes equally to the TPA saturation process. Other three models can fit well with the first half, but depart differently with the experimental data at the second half. If the saturation effect is not taken into consideration, the 5 / 15
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reciprocal transmittance will vary linearly with input pulse intensities as described by the nonsaturation model, where the TPA coefficient is considered as a constant. If the saturation effect is taken into account as the hyperbolic approach for bulk semiconductors, the transmittance will vary as calculated by Eq. 3. In both approximations, the calculated results strongly depart from the experimental data. That is to say, the TPA process in MX2 is definitely saturated, and the homogeneously broadened model is a better form allowing one to obtain a set of parameters that account for the experimental results. In addition, Model_inhomo for the inhomogeneously broadened systems also cannot fit the experimental results well as depicted by the green line in Fig. 3 (a), which confirms that the MX2 nanofilm belongs to the homogeneously broadened system in the TPA process. From the homogeneously broadened model, the normalized transmittance (9:;
