Encapsulation Narrows Excitonic Homogeneous Linewidth of Exfoliated MoSe$_2$ Monolayer

The excitonic homogeneous linewidth of an exfoliated monolayer MoSe$_2$ encapsulated in hexagonal boron nitride is directly measured using multidimensional coherent spectroscopy with micron spatial resolution. The linewidth is 0.26 $\pm$ 0.02 meV, corresponding to a dephasing time $T_2 \approx$ 2.5 ps, which is almost half the narrowest reported values for non-encapsulated MoSe$_2$ flakes. We attribute the narrowed linewidth to Coulomb screening by the encapsulated material and suppression of non-radiative processes. Through direct measurements of encapsulated and non-encapsulated monolayers, we confirm that encapsulation reduces the sample inhomogeneity. However, linewidths measured using photoluminescence and linear absorption remain dominated by inhomogeneity, and these linewidths are roughly 5 times larger than the homogeneous linewidth in even the highest-quality encapsulated materials. The homogeneous linewidth of non-encapsulated monolayers is very sensitive to temperature cycling, whereas encapsulated samples are not modified by temperature cycling. The nonlinear signal intensity of non-encapsulated monolayers is degraded by high-power optical excitation, whereas encapsulated samples are very resilient to optical excitation with optical powers up to the point of completely bleaching the exciton.

excitation, whereas encapsulated samples are very resilient to optical excitation with optical powers up to the point of completely bleaching the exciton.

Keywords
Transition metal dichalcogenides, encapsulated monolayer, homogeneous linewidth, radiative lifetime, multidimensional coherent spectroscopy Monolayer van der Waals crystals are a class of materials with widely varying properties and the potential to transform future electronics and optoelectronics. [1][2][3] These atomically thin layered materials can be stacked into heterostructures with new functionalities. 4 A subset of these materials are the semiconducting monolayer transition metal dichalcogenides (TMDCs), which have a direct band gap that makes their electronic transitions optically accessible and thus useful for optoelectronic applications. [5][6][7][8] The low dimensionality resulting from confinement to a monolayer also means monolayer TMDCs have very strong many-body interactions that result in ∼100x larger binding energy of excitons than more conventional III-V semiconductors, such as gallium arsenide. Excitons thus dominate the optical response of semiconductor TMDCs and remain strongly bound at room temperature. The low dimensionality also means excitations in these materials are very sensitive to the external dielectric environment through both screening and introduction of defects.
Encapsulation of monolayer van der Waals crystals in hexagonal boron nitride (hBN) enhances carrier mobility 9,10 and significantly improves the monolayer resistance to photodegradation. 11 Most notably hBN encapsulation has been shown to greatly reduce the photoluminescence linewidth of MoSe 2 , MoS 2 , WSe 2 , and WS 2 . [12][13][14] Narrowing of the photoluminescence linewidth of a TMDC monolayer has been taken as an indicator that encapsulation passivates the monolayer and minimizes inhomogeneity resulting from trapped states and defects. However, narrowing of the photoluminescence linewidth can also result from a change in the radiative linewidth of the exciton, which scales with the substrate index. The substrate can further affect the linewidth through its effect on pure dephasing resulting from interactions of the exciton with photons, phonons, and other collective modes. So while it is impressive that encapsulated TMDC photoluminescence linewidths approach the homogeneous limits measured in similar monolayers on different substrates, linear techniques cannot disentangle the linewidth contributions from inhomogeneous broadening, non-radiative processes, and radiative decay. Here we show that encapsulation narrows both the homogeneous and inhomogeneous linewidths such that the inhomogeneous linewidth still dominates. We discuss how our results imply that hBNencapsulation of monolayer TMDC samples minimizes defects and static doping that result in both long-and short-range disorder. Along with the static lineshape differences, we measure significant permanent modification of the homogeneous linewidth of non-encapsulated samples resulting from temperature cycling and exposure to weak radiation. In contrast, encapsulated samples are very robust to numerous temperature cycles and high radiation exposure.
To directly measure homogeneous linewidths and distinguish the dephasing and decay processes, it is necessary to use nonlinear spectroscopy techniques. of light by the encapsulated sample is an additional indicator that encapsulation decreases the non-radiative decay processes that contribute to incoherent absorption. We also see that the transition energies of excitons in the two samples differ by about 20 meV. This difference is primarily due to the significant decrease of both the band gap and partially compensating exciton binding energy by encapsulating the monolayer in a high index material. 27, 28 We depict these changes in the inset of Fig. 1(b). With measure the effects of encapsulation on both the inhomogeneous and homogeneous exciton linewidths using MDCS.
In Fig. 2(a) we plot characteristic multidimensional coherent spectra at low temperature using a rephasing pulse sequence. To generate these plots we measure the phase-resolved evolution of an induced nonlinear response as a function of the evolution of a phase-resolved linear response. We measure these responses using a sequence of four pulses in the time domain having relative delays (τ between the first two pulses, T between the second and third pulse, and t between the last two pulses) that are referenced to a co-propagating continuous-wave laser. Fourier transforming the response with respect to two of the pulse delays yields spectra with two dimensions that correlates absorption (ω τ ) and emission (ω t ) energies of the sample coherences. In these plots absorption energy (ω τ ) is correlated with emission energy (ω t ). (b) Slices along the diagonal (left) of the multidimensional spectrum roughly correspond to the inhomogeneous distribution of exciton resonances. Slices along the cross-diagonal (right) roughly correspond to the homogeneous lineshape. We plot these slices for low temperature, low power measurements of four samples: two non-encapsulated samples in blue and two encapsulated samples in red. Since the diagonal and cross-diagonal slices are correlated, it is essential to fit them simultaneously to determine the homogeneous and inhomogeneous linewidths. 29 (c) We plot extrapolated zero power linewidths of each sample as a function of temperature. Grouped in the legend, circle data points correspond to a first measurement set of the sample and square data points correspond to a measurement set made after temperature cycling the same sample.
is the square root of a Lorentzian. 30 Ignoring inhomogeneous broadening and using the wrong fit function when determining a sample's homogeneous linewidth (or dephasing times in photon echo FWM experiments) can thus significantly skew the measurement, up to a factor of √ 3. For inhomogeneous linewidths that are comparable to the homogeneous linewidth, as is the case in these samples, it is essential to simultaneously fit the codependent diagonal and cross-diagonal slices. Here we fit the entire two-dimensional spectrum using an analytical solution to the optical Bloch equations (OBEs) derived by Bell et al. 29 We measure the homogeneous linewidth as a function of beam power and sample temperature. Exciton-exciton interactions are density dependent, and so we measure the density dependence of the linewidth to determine their contribution. We increase the power of all three excitation beams equally, and determine the linewidth scaling as a function of the excitation density of a single beam. We estimate that the linewidth linearly broadens with a slope of 4 × 10 −13 meV cm 2 , shown in the Supporting Information. We measure this linear dependence up to an excitation density of 10 12 cm −2 . For each sample temperature, measured between 5 and 80 K, we extrapolate the power dependence of the linewidth to zero power and plot that as γ. Exciton-phonon scattering can be suppressed by lowering the sample temperature to nearly 0 K. At low temperatures the phonon broadening is due to acoustic phonons, which has a linear dependence on temperature. In Fig. 2(c) we plot γ as a function of temperature for the four different samples. The non-encapsulated samples are indicated in blue. The circle data points correspond to a first set of measurements on a sample, where the linewidths are first measured at 5.3 K and the temperature is increased.
The square data points correspond to measurements made after a temperature cycle defined by warming the sample up to room temperature and cooling it back down to again start the measurement set at 5.3 K. It is evident from this data that the linewidth of the nonencapsulated monolayer is very sample dependent, which confirms results by Jakubczyk et al. 16,17 We further find significant broadening of the exciton linewidth of non-encapsulated samples with a single temperature cycle. By measuring many points on the sample, we con-firm that the broadening effect is not the result of a positioning error. We rather suggest that the broadening is likely due to deposition of molecules such as water on the sample surface.
Whether the change results from surface molecules or substrate strain, we demonstrate that the homogeneous linewidth is a sensitive indicator of a change in the sample environment.
The hBN-encapsulated monolayer samples are indicated in red. The sample variance is very small, and there is no measurable broadening due to temperature cycling in these samples.
This consistency is evidence that defect scattering is minimal in encapsulated samples. The durability of the monolayer with temperature cycling is an important confirmation that experiments on encapsulated samples will be consistent and reproducible.
From the temperature dependence we measure a linewidth broadening of 0.010 ± 0. Finally we compare photodegradation of low temperature samples resulting from excitation by resonant pulses. We treat samples by irradiating them with laser light for one minute at the given treatment beam power. The pulsed light is focused to a 2 μm spot and has a repetition frequency of 76 MHz. After each treatment we turn off the treatment beam and measure a multidimensional spectrum with low power, 1 μW/beam, pulses. In Fig. 3 we plot the MDCS signal strength as a function of treatment pulse power. We find that the non-encapsulated samples exhibit lasting damage by beams having powers greater than 45 μW. Measured homogeneous linewidths vary significantly between treatments and scans.
The encapsulated samples, however, are resilient up to powers that fully saturate the exciton and have a consistent homogeneous linewidth. We demonstrate saturation of the exciton in an encapsulated sample with single pulse reflectance, similar to an experiment recently presented on non-encapsulated samples. 26 We plot reflectance measured with beams having powers between 2 and 640 μW, a range over which the sample is not damaged. Reflectance at the exciton resonance of the encapsulated sample with a beam having a power of 640 μW is saturated. This type of measurement would not be reliable in non-encapsulated MoSe 2 .
In summary, we have measured a significant improvement in sample consistency and stability by encapsulating monolayer MoSe 2 in hBN. In agreement with previous studies, we find that encapsulated samples have narrower inhomogeneous linewidths than non-encapsulated samples. However, we also find that the excitonic homogeneous linewidth is still significantly narrower than the total linewidth. The measurements indicates that inhomogeneity

Supporting Information Available
The following files are available free of charge.
Detailed schematic and description of the MDCS experiment and experimental procedures can be found in the Supporting Information: