Modulation of carrier lifetime in MoS₂ monolayer by uniaxial strain^*

Reduced dimension brings two-dimensional (2D) transit ion metal dichalcogenides (TMDCs) many stimulating advantages, such as enhanced light–matter interaction,^[1,2] unique physical properties,^[3–7] and facile integration of hybrid structures.^[8–10] With these features, TMDCs have led a revolutionary breakthrough in photodetectors,^[11–13] optical modulators,^[14] light-emitting diodes,^[15,16] valleytronic devices,^[17] etc. To realize and optimize those applications, understanding and engineering the photoexcited carrier dynamic processes are of paramount importance.^[18–20] In TMDCs materials, the nonradiative rather than radiative relaxation pathways dominate the carrier dynamics.^[21–23] Due to the large specific surface area and high density of defects, ∼ 43% excitons will be trapped by surface defect states and only 2.8% excitons can exhibit radiative recombination.^[24] This defect trapping process is ultrafast with time scale of a few picoseconds, which is comparable with the interlayer charge transfer (∼ 1 ps)^[25] and much faster than radiative recombination process (about hundreds of picoseconds).^[23] Therefore, the defect trapping process rather than radiative recombination dominates the performances of TMDCs-based devices, such as charge collection efficiency, photoconductive gain, and response time. Many efforts have been devoted against the trap states. For example, the defect-mediated nonradiative recombination can be efficiently eliminated by decorating an organic superacid;^[26] stacking graphene layer on TMDCs can selectively filter out the radiative recombination and enable pristine PL.^[27] While it is still a challenge to directly prolong the lifetime of defect trapping process.

Benefiting from the high flexibility and toughness, strain has been regarded as a powerful route to effectively and continuously engineering the physical properties of TMDCs recently. The band structure,^[28–32] phonon modes,^[33,34] and the optical nonlinearity^[35] can be significantly tuned. Under in-plane tensile strain, the strain-dependent carrier–phonon interaction in TMDCs has been fully studied and the corresponding nanosecond-scale lifetime is demonstrated to decrease slightly.^[36,37] While a more comprehensive understanding of the modulation of carrier lifetime through the engineering of in-plane uniaxial strain is still lacking so far. Here, for the first time, we directly studied the modulation of the carrier dynamics in MoS₂ monolayer by uniaxial tensile strain. We found that the carrier dynamic process in MoS₂ has four channels (i.e., Auger scattering, trap states scattering, carrier–phonon scattering, and radiative recombination process) with different time scales. Strain can significantly prolong the carrier lifetime associated with defect trapping by 440% per percent strain, while the other three carrier dynamic channels remain largely unchanged.

MoS₂ monolayer samples were grown on 300-nm SiO₂/Si substrate by CVD method using MoO₃ and S powders as precursors. 10.0-mg MoO₃ powder was placed at the center of a tube furnace and 20-mg S powder at the upstream side 14 cm away from the MoO₃ powder. The CVD process was carried out in ultrahigh-purity Argon gas atmosphere under ambient pressure.

The CVD-synthesized MoS₂ monolayer was transferred onto flexible Acrylic substrate by the wet transfer method. PMMA (polymethyl methacrylate, 4%) in ethyl lactate solution was spin-coated onto MoS₂ and baked at 120 °C for 2 min. Then the sample was placed into KOH (1 M) aqueous solution at 80 °C for 5 min to lift off the PMMA/MoS₂ from the substrate. After thoroughly washing with deionized water for three times, the PMMA/MoS₂ film was transferred to the target acrylic substrate. At last, the PMMA/MoS₂/acrylic sample was dried naturally for several hours and baked at 80 °C for 10 min to enhance the interaction between MoS₂ and acrylic.

PL and Raman spectra were measured using self-built equipment with 532-nm CW laser. The integral time was set as 1 s for the PL measurements and 30 s for the Raman measurements with laser power of 1 mW.

We performed the pump–probe measurements with femtosecond pulses (∼ 100 fs, 80 MHz) generated by a Ti:sapphire oscillator (Spectra-Physics Mai Tai laser) and an optical parametric amplifier (OPO). In our pump–probe experiments, we pumped at 410 nm and probed at 670 nm. Those two pulses are separated in the time-domain by a controllable delay-time and focused onto the sample. After collection of the reflected pulses, 460-nm long-pass filter was used to filter out the pump pulse. The transient absorption signal, defined as ΔR/R = (R_{with pump} − R_{without pump})/R_{without pump}, was recorded by a PMT and a lock-in amplifier with reflective geometry. The diameters of focused pump and probe pulse are ∼ 2 μm and ∼ 1 μm, respectively.

The time-resolved PL was excited by pulses from Ti:sapphire oscillator at 410 nm. We selected the PL signal of target wavelength by a 460-long-pass filter and a spectrometer (with resolution of ± 2 nm) after photoexcitation and collection. Then, we acquired the time-resolved PL signal using single-photon APD (PicoQuant Company, TDA 200) combining with a TCSPC module (TimeHarp 260 PICO Single).

In our experiments, uniaxial tensile strain was applied through bending the flexible acrylic substrate. The sample which is at the upper surface is stretched and the uniaxial tensile strain is applied by the friction force between the sample and substrate (Fig. 1(a)). Since acrylic has relatively large Young's modulus parameter and the interaction between acrylic and sample is large enough, the tensile strain can be efficiently transferred from substrate to the target sample. The strain amplitude can be simply estimated from the bending geometry of the acrylic by using the formula ε = d/2r, where d is the thickness of the acrylic and r is the curvature radius. Triangle-shaped MoS₂ flakes were grown by chemical vapor deposition methods on SiO₂/Si and then transferred on acrylic with the assistance of polymethyl methacrylate (PMMA) (Fig. 1(b)). Raman spectroscopy of MoS₂ flake shows two characteristic peaks around 400 cm⁻¹, which correspond to in-plane ${{\rm{E}}}_{2{\rm{g}}}^{1}$ and out-of -plane A_1g phonon modes, respectively (Fig. 1(c)). The 18-cm⁻¹ separation between these two peaks (ω_A–ω_E) indicates that our MoS₂ samples are monolayer in nature.^[38]

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The PL spectrum of MoS₂ monolayer features a prominent peak at ∼ 670 nm that corresponds to the A exciton radiative recombination at the K-valley in the Brillouin zone. Under imposition of tensile strain by bending the flexible acrylic substrate, the A exciton PL peak red shifts correspondingly (Fig. 1(d)). The shift slope is determined to be 16.9 nm/% strain and the relative change slope (λ_ε − λ₀)/λ₀ (where λ_ε and λ₀ stand for the PL peak wavelength with and without strain, respectively) is 0.023/% strain (Fig. 1(e)). Meanwhile, the PL spectrum also slightly broadens with strain. To quantify the broadening, we acquired the full width at half maximum (FWHM) of PL spectra and found that FWHM increases ∼ 1.3 nm/% strain.

To investigate the origin of PL broadening in MoS₂ under tensile stain, we applied time-resolved experiments to track the carrier dynamic processes in the following. The dynamics of photoexcited carriers in MoS₂ could be described by four processes as illustrated in Fig. 2(a): the first process with lifetime τ₁ of hundreds of femtoseconds is via Auger scattering; the second process with lifetime τ₂ of several picoseconds is attributed to the trapping by defect states; the third process is related with carrier-phonon scattering with lifetime τ₃ of tens of picoseconds; and the last process is electron–hole radiative recombination with lifetime τ₄ of hundreds of picoseconds. In order to characterize the carrier lifetimes of these four processes with different time scales, we performed pump-probe measurements with high accuracy and time-resolved PL technique with large detection range. Figure 2(b) shows our experimental setup. One path of femtosecond pulses from Ti:sapphire oscillator at 820 nm was guided into an optical parametric oscillator (OPO) to generate wavelength-tunable probe laser, and another path with controlled time-delay was used as pump laser. The transient absorption signal of MoS₂ was recorded by photomultiplier (PMT) combining with a lock-in amplifier with reflective geometry, and the time-resolved PL signal was monitored by single-photon avalanche photodiode detector (APD) combining with time-correlated single photon counting (TCSPC) module.

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In the pump–probe experiment, we pumped MoS₂ by 410 nm pulse (width of ∼ 100 fs, fluence of 3 μJ/cm²) and probed the carrier population around the band gap with tunable wavelength of 590 nm–710 nm. The transient absorption signal of MoS₂ at different probe wavelengths and different pump–probe delay time is shown in the 2D mapping (Fig. 2(c)). Under horizontal cut of the 2D mapping, wavelength-dependent transient absorption presents a peak around 670 nm, which is consistent with the A exciton PL peak position shown in Fig. 1(d) (Fig. A1 in Appendix A). The vertical cut of the 2D mapping at 670 nm reveals the A exciton dynamics process (Fig. 2(d)). Transient absorption signal scales linearly with pump fluence, suggesting that nonlinear process such as exciton–exciton annihilation can be negligible under our experimental conditions (Fig. A2). From the logarithm plot of the transient absorption spectrum, we can observe that the A exciton dynamics performs two decay channels with two different slopes within the first 10 ps after photoexcitation. After fitting by Gaussian response function convoluted with a biexponential decay function, we can get the lifetime τ₁ = 0.38 ps and τ₂ = 2.2 ps. These two lifetimes are corresponding to the Auger scattering and defect trapping process, respectively.^[24] For comparison, no obvious time-resolved signal could be observed for acrylic substrate (Fig. A3).

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To obtain the slower carrier dynamic processes, we applied time-resolved PL and recorded the A exciton PL intensity under 410-nm pulse laser excitation. The A exciton PL dynamic process in the range of 0 ps–500 ps is shown in Fig. 2(e). Similarly, a biexponential decay trend can be observed and the lifetimes are fitted as τ₃ = 25 ps and τ₄ = 150 ps. These two lifetimes are determined as electron-phonon scattering and radiative recombination processes, respectively.^[23]

After characterizing the carrier dynamic channels in MoS₂, we then investigated the modulation of carrier lifetimes by uniaxial strain. As the A exciton peak position varies with strain, the wavelength of probe pulse and the time-resolved PL were tuned correspondingly during strain to ensure that we were always detecting the A exciton dynamics. Strain-dependent transient absorption spectra are shown in Fig. 3(a). From the spectra, we can find the carrier dynamics evolve significantly with strain. While no significant change can be observed in the time-resolved PL spectra, which were recorded at the same time (Fig. 3(b)).

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To quantitatively analyze the strain engineering carrier dynamic processes, the measured transient absorption curves and time-resolved PL curves are fitted correspondingly. The strain-dependent fitting lifetimes are shown in Figs. 4(a)–4(d), from which we found quite different behaviors of lifetime variations: τ₂ significantly increases with strain, while the other three lifetimes remain largely unchanged within our resolution. For the defect trapping lifetime, the lifetime increases from ∼ 3 ps to ∼ 8 ps under 0.6% tensile strain, corresponding to 440% enhancement per percent strain. The relative change slope, defined as Δ τ_ε/τ₀ = (τ_ε − τ₀)/τ₀, is determined to be 2.8/% strain. Where τ_ε and τ₀ stand for the defect trapping lifetime with and without strain, respectively. Compared with the relative change of slope of the SHG intensity (−0.49/% strain),^[35] PL (−0.025/% strain), and Raman (−0.012/% strain) peak positions,^[28] this value is a few orders higher, indicating that defect trapping process is much more sensitive with uniaxial tensile strain. While the Auger effect, electron–phonon coupling and radiative combination are independent of strain in MoS₂.

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The rise of defect trapping lifetime is expected to enhance the PL intensity under strain. While from our experiment results, the PL intensity reduced slightly with strain increasing (Supplementary information in Fig. A4). That is because the tensile strain will lead a direct to indirect bandgap transition in MoS₂ at the same time.^[28] Also, since only one of four lifetimes vary with strain, the radiative recombination with only proportion of 2.8% is hardly influenced. Even though, the prolongation of defect trapping process is very important for TMDCs-based devices. As the photoconductive gain is proportional to the defect trapping lifetime,^[39] tensile strain will dramatically enhance the responsivity in a photoconductive detector. In a graphene/TMDCs/graphene heterostructure photodetector, where TMDCs serve as absorber and transfer the photoexcited carriers to graphene electrode, the charge transfer process with time scale of ∼ 1 ps is comparable to the defect trapping process in TMDCs themselves, therefore significantly limiting the charge collection efficiency. With prolonging the defect trapping process to ∼ 10 ps, the charge collection efficiency will be enhanced by a few times.

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Currently we do not have a quantitative understanding on the strain-dependent defect trapping lifetime in MoS₂, and we believe more theoretical exploration on the strain modulation of carrier dynamics will be carried out and might provide more in-depth information in the near future. Strain-dependent lifetime under cryogenic temperature can be also very helpful, but it is quite technically challenging now and waiting for future investigations.

In conclusion, we have investigated the engineering of carrier lifetimes under uniaxial tensile strain in 2D MoS₂. We found that, in contrast to the carrier dynamics through Auger scattering, carrier–phonon scattering, and radiative recombination which are insensitive to applied strain, the defect trapping lifetime can be enlarged by 440% per percent strain. As the carrier dynamics processes are similar for different TMDCs, in-plane uniaxial strain is believed to be a universal approach for carrier lifetime engineering. Since the defect states dominate many physical processes in TMDCs, the prolongation of defect trapping lifetime can be very useful for optimizing the performances of TMDCs-based devices.

Some experiment results and figures for better understanding the present article are given below.