Liang
Guo
abc,
Chun-An
Chen
d,
Zhuquan
Zhang
e,
Daniele M.
Monahan
ab,
Yi-Hsien
Lee
d and
Graham R.
Fleming
*abf
aDepartment of Chemistry, University of California, Berkeley, California 94720, USA. E-mail: grfleming@lbl.gov
bKavli Energy Nanoscience Institute at Berkeley, Berkeley, California 94720, USA
cMechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China
dMaterials Sciences and Engineering, National Tsing-Hua University, Hsinchu 30013, Taiwan
eSchool of Physics and Technology, Wuhan University, Wuhan 430072, China
fMolecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
First published on 21st April 2020
The optical properties of monolayer transition metal dichalcogenides (TMDCs), an important family of two-dimensional (2D) semiconductors for optoelectronic applications, are dominated by two excitons A (XA) and B (XB) located at K/K's valleys. The lineshape of the excitons is an indicator of the interaction of the excitons with other particles and also largely determines the performance of TMDC-based optoelectronic devices. In this work, we apply 2D electronic spectroscopy (2DES), which enables separation of the intrinsic homogeneous linewidth and the extrinsic inhomogeneous linewidth, to dissect the lineshape of XA in monolayer WS2. With a home-built broadband optical parametric amplifier, the 2D spectra give the exciton linewidth values for extensive ranges of excitation densities and temperatures, reflecting inter-exciton and exciton–phonon interactions. Meanwhile, the time-domain evolution of the lineshape reveals a similar rate of spectral diffusion to that in quantum wells (QWs) based on III–V semiconductors.
Two-dimensional electronic spectroscopy (2DES) provides a clearer method of determination of various contributions to the lineshape than absorption and photoluminescence measurements. 2DES has proved to be a powerful technique for analysing the exciton lineshape in a variety of materials such as GaAs quantum wells,11 CdSe quantum dots,12 and CdSe nanoplatelets.13 The amplitude of the photon echo signal is presented as a 2D function of the excitation and the emission photon energies. In such a diagram, homogeneous (intrinsic) and inhomogeneous (caused by defects, local strain, etc.) broadening are projected onto perpendicular directions, i.e., the anti-diagonal and the diagonal directions, thus providing a readout of the two contributions.14 In addition, evolution of the lineshape versus the waiting time between excitation and emission indicates spectral diffusion caused by dynamic mechanisms such as phonon-assisted migration of excitons.15 During this process, the system loses memory of the excitation photon energy so that the correlation between the excitation and the emission photon energies gradually diminishes as the waiting time increases.
In particular, 2DES and also its time-domain version, photon echo spectroscopy, have been utilized to study the exciton linewidth of monolayer TMDCs.7,16–18 However, the laser sources used in most of the previous studies were Ti:sapphire laser oscillators, limiting the studied materials mainly to WSe2 and MoSe2 since their exciton resonance energies are covered by the laser spectrum. In ref. 17, an optical parametric oscillator (OPO) driven by an oscillator served as the laser source to access exciton A of monolayer MoS2. However, an OPO generally has a narrow bandwidth (long transform-limited pulse width) so that characterization of the exciton linewidth has been limited to temperatures below 40 K, above which the homogeneous linewidth becomes too wide to be well resolved (equivalently, the dephasing is too fast). A previous study applied time-domain four-wave mixing with an OPO (with a bandwidth of about 25 meV) to study the impact of the environment on exciton and trion dynamics.19 So far, detailed experimental analysis of the exciton lineshape with information in the frequency domain including the phenomenon of spectral diffusion for monolayer WS2 has been rare. As we will demonstrate later, the homogeneous and inhomogeneous widths are similar requiring accurate 2D spectra to determine these quantities by fitting to more complex functions than simple Lorentzian or Gaussian forms.
In this work, we used a Ti:sapphire laser amplifier to drive a home-built noncollinear optical parametric amplifier (NOPA), realizing broadband output covering the exciton resonance energies of monolayer WS2 over a wide temperature range. With this NOPA, we applied 2DES to measure the exciton linewidth of monolayer WS2 up to 100 K. In addition, we studied the spectral diffusion of the exciton by tracking the lineshape over the waiting time. A similar strategy could be applied for comprehensive investigation of exciton properties of the promising TMDC family, especially for MoS2 and WS2.
A home-built NOPA was used to perform the 2DES measurements and was driven by a Ti:sapphire femtosecond laser amplifier (Astrella, Coherent Inc., 800 nm, 1 kHz). The design of the NOPA involves proper selection of the nonlinear crystal, alignment of the white light (seed) versus the 400 nm pump, and compensation of the pulse-front tilt between the seed and the pump.21–23 These considerations together enable a broadband output in the visible range fully covering the resonance energy of exciton A in monolayer WS2 for an extensive temperature range, which is the key for successful characterization of the exciton linewidth. The pulse was compressed using a prism pair and measured to be about 33 fs (full width at half maximum, FWHM) at the sample position. All the four beams were co-circularly polarized.
2DES was conducted in the phase-stabilized boxcar geometry involving three beams for generating the photon echo and one beam for heterodyne detection as illustrated in Fig. 1(c). The pulse sequence for rephasing 2DES, in which the photon echo is induced, is illustrated in Fig. 1(d). The photon echo signal is acquired as a function of the coherence time τ and the waiting time T. The signal is frequency-resolved in the emission photon energy domain using a spectrometer (equivalently, Fourier transformed with respect to the emission time t) while the resolution in the excitation photon energy domain is realized by Fourier transform with respect to τ, thus generating the 2D spectrum. The sample was mounted in a liquid helium cryostat for temperature-tunable measurements. A signal processing system based on two choppers and one microcontroller was described in detail in our previous work,24,25 and is important for ensuring the signal-to-noise ratio given the relatively low repetition rate of the laser amplifier, a tradeoff for achieving the capability of driving a broadband NOPA.
Fig. 2 (a) A representative 2D spectrum showing the lineshape of exciton A in monolayer WS2 (the dot dashed lines serve as a visual guide). The temperature was 10 K and the laser fluence was 2.42 μJ cm−2; (b) the broadband spectrum of the NOPA output. The red dot dashed lines in (a) and (b) indicate the same spectral range: 2.1 eV to 2.15 eV; (c) extraction of the homogeneous linewidth (gray arrows) and the inhomogeneous linewidth (red arrows) by fitting using eqns (1) and (2). |
From Fig. 2(a), it can be inferred that the homogeneous and the inhomogeneous linewidths have comparable magnitudes. Therefore, it is not accurate to assume that the inhomogeneous broadening dominates and that the two linewidths can be directly read. Instead, the expressions derived in ref. 14 for arbitrary inhomogeneity are applied for linewidth extraction. Briefly, the signal amplitude is related to the homogeneous linewidth γ and the inhomogeneous linewidth σ through
(1) |
(2) |
Due to the many-body interaction among excitons, the exciton linewidth is sensitive to the density of excitons. Fig. 3(a) and (b) illustrate the effect of the excited exciton density on the linewidth measured at 10 K. As more excitons are excited by increasing the laser fluence, the interaction among excitons is intensified, which accelerates the dephasing process and broadens the homogeneous linewidth, consistent with the picture of excitation-induced dephasing (EID).7,27 The extracted homogeneous linewidth is plotted as a function of the exciton density in Fig. 3(c). Extrapolation to zero exciton density gives a homogeneous linewidth of 5.96 meV at 10 K without external perturbation.
There is also a notable blueshift of the exciton resonance energy in the order of 10 meV when the exciton density reaches the order of 1012 cm−2, which agrees with a previous study and is due to an attraction-repulsion crossover of the inter-exciton interaction.28 Spectral shift of exciton resonance (either red or blue) upon excitation is universal among monolayer TMDCs resulting from this crossover mechanism, band gap renormalization, and/or exciton binding energy reduction.28–31 Therefore, frequency-domain analysis of the exciton lineshape is necessary to indicate whether the exciton resonance is well covered by the laser spectrum. In this work, the 140 meV FWHM of the NOPA output ensures coverage of exciton resonance.
The temperature-dependence of the homogeneous linewidth without external perturbation was studied from 10 K to 100 K. Over this temperature range, the resonance energy of exciton A redshifted by about 14 meV as shown in Fig. 4 (right axis). The homogeneous linewidth is constant within uncertainty over this temperature range. This agrees with the experimental results in a previous study32 employing PL measurements and numerical deconvolution to extract the homogeneous linewidth. Since acoustic phonons dominate the phonon population at such low temperatures, the results indicate that the interaction between excitons and acoustic phonons contributes little to the homogeneous broadening and the role of optical phonons is only manifested in the linewidth above 100 K.
Fig. 4 Variation of the homogeneous linewidth (left axis) and the exciton resonance energy (right axis) versus temperature. The black dashed line serves as a visual guide. |
As the waiting time T between the excitation and the emission increases, the system loses memory of the excitation photon energy so that the correlation between excitation energy and emission energy becomes weaker. This process is reflected by the evolution of the lineshape from being elongated along the diagonal direction to being symmetric, which indicates a complete loss of the memory about the excitation. Spectral diffusion for excitons in monolayer WS2 was tested at 20 K with an exciton density of 6.79 × 1011 cm−2. As shown in Fig. 5, the lineshape of exciton A changes negligibly within 0.500 ps (Fig. 5(a)–(c)) and changes noticeably at later waiting times in terms of shape symmetry (Fig. 5(d)–(h)). The timescale of spectral diffusion is close to that of a GaAs quantum well at similar temperatures.8 However, the lineshape at longer waiting times, such as 3.00 ps, does not follow the shape predicted by free and random spectral diffusion. The intensity is concentrated more below the diagonal line than above it. This could arise from two possible causes. The first is intrinsic exciton dynamics including exciton cooling and recombination, which places more excitons in the low-energy levels. The second is the existence of traps due to defects on the sample. Such traps localize excitons and prevent spectral diffusion so that the lineshape features a combination of static disorder due to trapping and dynamic disorder due to migration. Further study is necessary to clarify the mechanism of this effect. For example, hBN-sandwiched9,10 or chemical-treated samples33 with deactivated defects could be used in control experiments to evaluate the influence of static disorder.
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