Transport Dynamics of Neutral Excitons and Trions in Monolayer WS2

Publication Date (Web): September 24, 2016. Copyright © 2016 American Chemical Society. *E-mail: [email protected]. Cite this:ACS Nano 10, 10,...
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Transport Dynamics of Neutral Excitons and Trions in Monolayer WS2 Toshiaki Kato* and Toshiro Kaneko Department of Electronic Engineering, Tohoku University, 980-8579 Sendai, Japan S Supporting Information *

ABSTRACT: Understanding the spatial motion of excitons is of both fundamental interest and central importance for optoelectrical applications. Here, we have investigated the temperature (T) dependence of the transport dynamics of neutral excitons and charged excitons (trions) in atomically thin two-dimensional crystals of the transition-metal dichalcogenide WS2. The transport dynamics of neutral excitons can be divided into three temperature ranges, where the diffusion of neutral excitons is governed by thermal activation (≤∼75 K), ionized impurity scattering (∼75 K ≤ T ≤∼200 K), and LO phonon scattering (≥∼200 K). The trions have a diffusion length that is over 20 times longer than that of neutral excitons at very low temperatures (≤∼10 K), which may be related to theoretically predicted Pauli-blocking effects during the excitation process. KEYWORDS: excitons, transport dynamics, WS2, photoluminescence, temperature dependence

E

xcitons, i.e., electron−hole pairs coupled via Coulomb attraction, are bosonic quasiparticles that play a crucial role in various optoelectrical sciences and applications.1−3 Because the behavior of excitons is sensitive to the ratio of the exciton Bohr radius (typically a few nanometers) to the crystal thickness, low-dimensional materials (smaller than the exciton Bohr radius) can be expected to exhibit various outstanding optoelectrical features. From a historical point of view, these quantum confined effects were first investigated with quasi-two-dimensional (quasi-2D) (GaAs/GaAlAs) and one-dimensional (1D) (GaAs wire) systems.4,5 Then, the trend of study gradually shifted to a “true” low-dimensional system. Thus, a carbon nanotube (diameter ∼1 nm) was utilized as a true 1D system, and several novel 1D optical properties were reported, such as excitons with broken time-reversal symmetry,6 the Aharonov−Bohm effect,7 long exciton diffusion,8 and stable trion states.9 Recently, atomically thin (thickness ∼1 nm) transition-metal dichalcogenides (TMDs) have also attracted considerable attention as ideal true 2D systems.10−12 Many interesting optical features have been reported for TMDs, such as a lack of inversion symmetry, resulting in the strong coupling of the spin and valley degrees of freedom,13−15 and a stable trion (charged exciton) state due to its strong binding energy (∼30 meV).16−18 Recent progress in time-resolved studies has uncovered important physics related to exciton relaxation, such as exciton−exciton annihilation,19 an exciton relaxation pathway,20 and the valley lifetime of excitons.21 In spite of these pioneering works with time-resolved studies, the spatial motion of excitons (both neutral excitons and trions), another © 2016 American Chemical Society

important subject for understanding the behavior of excitons, is still unclear. Zhao et al. reported the exciton diffusion of TMDs with transient absorption microscopy at room temperature,22,23 but the diffusion dynamics of the excitons over a wide temperature (T) range have not been clarified. Understanding the transport dynamics of electrical (electron and hole) and optically generated (excitons) carriers is very important to fully utilize the potential of TMDs in optoelectrical applications. The transport dynamics of electrical carriers such as electrons and holes have been thoroughly studied by many researchers and are understood in detail.24,25 However, the elucidation of the transport dynamics of optically generated carriers such as neutral excitons, trions, and biexcitons still remains a challenge. Knowledge of the transport dynamics for both electrical and optically generated carriers is important to develop TMD-based optoelectrical devices with high performance. Here, we demonstrate the T-dependent transport dynamics of excitons in TMDs. This was measured by two different methods: (1) size-dependent photoluminescence (PL) intensity (IPL) measurements combined with numerical calculations and (2) the direct charge-coupled device (CCD) imaging method. On the basis of a systematic analysis of the Tdependent exciton diffusion length, it has been revealed that the three critical dynamics govern the transport of neutral excitons. Received: August 18, 2016 Accepted: September 24, 2016 Published: September 24, 2016 9687

DOI: 10.1021/acsnano.6b05580 ACS Nano 2016, 10, 9687−9694

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Figure 1. (a) Exciton density profile in WS2 for different LWS2 (LWS2 = 3, 4, 5, 6, and 7 μm with fixed Ldif = 2000 nm). (b) Plot of IPL as a function of LWS2 with Ldif varying from 100 to 5000 nm (Ldif = 100, 300, 500, 700, 1000, 2000, 3000, 4000, and 5000 nm). (c) Ldif dependence of α given by fitting (b).

Further, the anomalously long diffusion of trions is revealed at very low T conditions (≤∼10 K). These findings related to the diffusion dynamics of excitons in TMDs should be useful to fully utilize the potential of TMDs in various optoelectrical applications.

Ldif 2

Estimation of the Diffusion Length of Excitons from the Size Dependence of the PL Intensity. We first estimated the diffusion length of excitons from the size dependence of the PL intensity (IPL). A numerical calculation was carried out to obtain the correlation between IPL and the size of WS2; then, the diffusion length of excitons was experimentally obtained through a comparison of the numerical calculation and experimental results. This approach is based on a well-known method for estimating the exciton diffusion length in other materials.8,26,27 We used a 2D diffusion model to describe the exciton density profile in WS2. The steady-state 2D diffusion equation is given by d 2n(x , y) dx

2

+D

d 2n(x , y) dy

2

−

+ Ldif 2

d 2n(x , y)

dy 2 ⎛ x2 + y2 ⎞ ⎟=0 + N exp⎜ − σ2 ⎠ ⎝ dx

2

− n(x , y)

(2)

where Ldif (= (Dτ)1/2) and N (= Γ0τ) are the exciton diffusion length and constant, respectively. Equation 2 was solved numerically by assuming that the origin was at the center of the WS2 crystal and by imposing the boundary condition n(x, y) = 0 at the edge of the electrodes (see the Methods for more detailed information). Figure 1a shows the spatial distribution of the normalized exciton density for different WS2 sizes with fixed Ldif (2 μm). For longer Ldif, the edge quenching becomes significant, and the density profile of excitons clearly varies from that in the short Ldif case. We assumed that IPL is directly proportional to the accumulated number of excitons in the crystal.8 Figure 1b shows IPL on a logarithmic scale as a function of the WS2 size (LWS2) for different values of Ldif (0.1 ≤ Ldif ≤ 5 μm). These curves can be fitted well by the function LWS2α, where α is a fitting parameter. Obviously, α and Ldif are correlated as shown in Figure 1c. This occurs because exciton quenching is dominant at the edge of the crystal because the diffusion length is similar to or longer than the WS2 size. This α−Ldif plot is used in the discussion below to estimate Ldif from the experimental measurements. Next, we attempted to measure the size dependence of IPL for WS2 experimentally. We used a suspended WS2 device prepared by the mechanical transfer of a monolayer of WS2 to Au electrodes without any post processes, obtaining very clean suspended monolayer WS2, which enables the investigation of the intrinsic features of WS2 without unknown effects such as localized impurity doping and carrier scattering (see the Methods and Figure S1 for the fabrication process). Parts a and b of Figure 2 show optical microscope images and IPL maps obtained for the same region on the substrate, respectively. In order to avoid exciton−exciton annihilation, we used a very low

RESULTS

D

d 2n(x , y)

n(x , y) + Γ(x , y) = 0 τ (1)

where D, n(x, y), τ, and Γ(x, y) are the diffusion constant, the exciton density at the position (x, y), the exciton radiative lifetime, and the exciton generation rate, respectively. Being a first-order approximation, this equation does not explicitly contain the exciton−exciton annihilation term. Because the exciton generation rate is proportional to the laser intensity profile, we let Γ(x, y) = Γ0 exp[−(x2 + y2)/σ2], where Γ0 and σ are the proportionality constant and the radius of the laser spot (∼1.6 μm) (see the Methods), respectively. Equation 1 can be written as follows 9688

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arrow in Figure 2f). The diffusion length increases with T, and there are two clearly distinguishable peaks around 125 and 200 K (red arrows in Figure 2f). The relatively longer NLdifN at very low temperatures (≤∼30 K) may be an overestimate due to anomalous trion motion (discussed later). Direct Observation of the Exciton Diffusion Length. To crosscheck the accuracy of the T dependence of NLdifN estimated from the size dependence of IPLN, NLdifN was measured by another method, CCD imaging, which can be used to measure NLdifN directly under different T conditions.28,29 Figure 3a shows a typical result from a CCD

Figure 2. (a) Optical microscope and (b) IPL mapping image of WS2 taken at the square region in (a). Dotted lines in (a) and (b) provide a guide for the eye to identify the WS2 crystal and electrodes, respectively. (c) Typical raw PL spectra of WS2 taken from different LWS2. IPL plot as a function of LWS2 measured at (d) 75 K and (e) 175 K. The black line shows the LWS2α fitting curve. (f) Temperature dependence of NLdif estimated with the α-Ldif plot of Figure 1c. (The value of α was provided experimentally through fitting the IPL−LWS2 plot.)

laser power for exciton generation, where the PL intensity and laser power maintain a linear correlation (Figure S2). Lineshaped dark areas with periodic structures were obtained in the PL map, which were caused by exciton quenching through the contact of WS2 with the Au electrodes (Figure 2b). Figure 2c shows typical raw PL spectra of suspended WS2 for different electrode widths (= WS2 size: LWS2). IPL decreases with LWS2, which is consistent with the numerical results for a relatively longer Ldif. The temperature dependence of the PL map was measured to estimate the diffusion length of the neutral excitons (LdifN). Note that because estimation of the absolute value of LdifN with this method is difficult owing to its short scale (approximately on the order of a micrometer), we only discuss the T dependence of the normalized diffusion length (NLdifN) in this paper. Parts d and e of Figure 2 show the integrated intensity of neutral excitons (IPLN) as a function of LWS2. The value of IPLN was obtained by decomposing the raw PL spectra into neutral exciton and trion peaks with a Lorentzian fitting. The experimentally obtained IPLN−LWS2 plot can be described with a power law (LWS2α), indicating that the exciton diffusion model in monolayer WS2 can be considered with the simple model described in Figure 1, as for other materials.6,26,27 Then, NLdifN was estimated through a comparison of the experimental result for α obtained by fitting (Figure 2d,e) and the numerically simulated α−Ldif correlation (Figure 1c). A clear T dependence of the diffusion length can be obtained, as shown in Figure 2f. In the low T region, the minimum diffusion length was obtained around 50 K (blue

Figure 3. (a) Typical CCD image, (b) raw PL spectrum, and (c) special profile of the neutral exciton density measured from a suspended monolayer WS2 crystal. (d) Typical spatial profile of the neutral exciton density measured at different temperatures (○, 4.5 K; □, 100 K; and ◊, 225 K). (e) Temperature dependence of NLdif (○) estimated from fitting the spatial distribution of the neutral exciton density (◊) with a numerically calculated profile (see the Supporting Information).

image. The color scale indicates the PL emission intensity. The horizontal axis includes the information on the photon energy (Figure 3b), whereas the vertical axis shows the spatial length (“zero” corresponds to the center of the laser spot used for the excitation) (Figure 3c), indicating that the 1D spatial distribution of IPLN can be extracted by CCD imaging. We confirm that the excitation laser radius is clearly smaller than the distribution scale of IPLN (Figure 3c). This is a well-known powerful tool for estimating the exciton diffusion length in other semiconductor materials.28,29 The T dependence of NLdifN was systematically investigated with this direct imaging technique (see the Methods and Figure S3 for more details). Figure 3d shows the typical exciton density profile measured at three different temperatures (4.5, 100, and 225 K). The IPLN profile clearly broadens with increasing T, showing that NLdifN is sensitive to T. Figure 3e 9689

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Figure 4. (a) Raw PL spectra of a suspended monolayer WS2 crystal at various temperatures (4.5−275 K). The blue and red areas show the neutral exciton and trion components (obtained from the spectra fitting), respectively. (b) Temperature dependence of normalized D calculated from NLdif in Figure 2(f) (pink triangle) and Figure 3(e) (black circle). The two dotted curves are T and T5/2 curves. (c, d) Temperature dependence of (c) ΓPL and (d) IPLN, IPLT, and IPLT/IPLN obtained through fitting (a). The black and colored curves in (c) show the fitting curve of Γ0 + Γi + ΓLO and each of its components, i.e., Γ0 (blue), Γi (green), and ΓLO (red).

shows NLdifN estimated from the spatial distribution of IPLN as a function of T from 4.5 to 275 K. At low T, NLdifN attains the minimum value and increases with T, with two peaks appearing around 125 and 200 K. An increase in T beyond 200 K shortens the diffusion length. The overall tendencies of the T dependence of NLdifN, as measured by the two different methods (Figures 2f and 3e), are similar, including the double peak shape at ∼125 K and ∼200 K. The random fluctuation level indicated by the error bars is much smaller than the change in NLdifN with T. This indicates that the overall trend should be influenced by the intrinsic transport dynamics of the neutral excitons in WS2.

1/τm = γtot

(3)

γtot = γo + γi + γac + γLO

(4)

where γtot, γo, γi, γac, and γLO are the total scattering rate of neutral excitons and the rates of scattering caused by the Tindependent intrinsic broadening term, ionized impurities, acoustic phonons, and LO phonons, respectively.32 The scattering effects determining τm can be estimated experimentally from the T dependence of the PL width (ΓPL). The T dependence of ΓPL can be described by the following equation33 ⎡ ⟨E ⟩ ⎤ ΓPL = Γ0 + ΓaT + Γi exp⎢ − b ⎥ + ⎣ kBT ⎦ exp

DISCUSSION Transport Dynamics of Neutral Excitons. The diffusion length can be described by L = (Dτ)1/2, where D and τ are the diffusion coefficient and exciton radiation lifetime, respectively. Then, the T dependence of D (normalized by the maximum value) was replotted with the results for NLdifN in Figures 2f and Figure 3e (we used the theoretical value of the T dependence, i.e., τ = 3.81T (ps)30) (Figure 4b). A plot of normalized D vs T obtained from different two methods ((1) IPL in Figure 2f and (2) the CCD imaging in Figure 3e) shows a very similar trend. In a classical approach, D can be estimated from the product of the thermal activation and momentum relaxation terms, D = (kBT/m*)τm, where m* = me + mh and m*, me, and mh are the total exciton, electron, and hole effective masses, respectively.31 Here, τm is the momentum relaxation time of a neutral exciton, which can be expressed by

ΓLO

( )−1 ℏ ϖLO kBT

(5)

where Γ0, Γa, Γi, ⟨Eb⟩, kB, ΓLO, and ℏωLO are the T-independent intrinsic broadening term, the acoustic phonon-coupling coefficient, the bandwidth due to ionized impurity scattering, the binding energy averaged over all possible impurity locations, the Boltzmann constant, the optical phonon-coupling coefficient, and the optical phonon energy of WS2 (∼44 meV),34 respectively. In order to identify the scattering effects with eq 5, we measured the T dependence of PL, given IPL for neutral excitons (IPLN) and trions (IPLT) and the PL width for a neutral exciton (ΓPLN) (Figure 4a). The T dependence of ΓPLN is fitted well by eq 5 (we ignored the Γa term because of its very small slope in the low T region), revealing that Γ0, Γi, ⟨Eb⟩, and ΓLO are ∼12, 15.4, 19.8, and 61.3 meV, respectively (Figure 4c). Through this fitting, it is found that the dominant scattering 9690

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depression of the trion formation rate when T increases. This is known as ionized impurity scattering, which satisfies the relation γi ∝ T3/2, i.e., D ∝ T5/2.32 The experimental results in region ii follow the T5/2 curve well (Figure 4b), which also shows that ionized impurity scattering mainly governs the diffusion dynamics of a neutral exciton in region ii. The estimated value of the activation energy for the charged impurity (19.8−22 meV) in this study is almost similar to the trion binding energy (∼20 meV) reported by another group,9 indicating that the charged impurity scattering of neutral excitons can be strongly related to trion formation. The depression of D between 75 and 150 K can be also explained as follows (Figure 4b). In this T range, there are two possible processes causing neutral exciton emission. One originates from the non- or weakly diffusive neutral excitons, including the larger D discussed for region i. The other is the neutral excitons scattered by ionized impurities, where D is small in this T range, as shown in Figure 4b. At 75 K, the former process should be dominant owing to weak ionized impurity scattering. The later process becomes dominant when T increases owing to the thermal activation of neutral excitons, resulting in a depression of D as T increases from 75 to 150 K. In region iii (≥∼200 K), the PL width fitting shows that LO phonon scattering is dominant (Figure 4c). This significant scattering increases the nonradiative recombination of neutral excitons and results in the depression of IPLN. Then, D can also decrease with T in region iii (Figure 4b). Anomalous Diffusion of Trions at Low-Temperature Conditions. As mentioned above, trion emission becomes significant in the low T region (∼4.5 K). The transport dynamics of trions was also measured by the direct CCD imaging method. Parts a and b of Figure 5 show a CCD image and raw PL spectrum of the suspended WS2 taken at 4.5 K. It is

mechanism is clearly different in each T range (i, ii, and iii) (Figure 4c). Based on these results regarding the T dependence of ΓPL and IPL, the following explanation is possible for the diffusion dynamics of neutral excitons in each T range. In region i (≤∼75 K), because the intensity of neutral excitons is over five times weaker than that of the trions (Figure 4d), the trion density should be higher than that of the neutral excitons, indicating that the trion formation rate (the probability of electron attachment to neutral excitons) should be very high in this T range. Thus, once the neutral excitons collide with electrons during the diffusion process, almost all of the neutral excitons can form trions. If we assume that the emission of neutral excitons originates only from the recombination of neutral excitons (for simplicity, we ignore the emission of neutral excitons through the deformation of trions), the emission of a neutral exciton can be obtained only from neutral excitons that do not collide with electrons during the diffusion process. This explanation is consistent with the T dependence of ΓPL in this T range (region i). As shown in Figure 4c, ΓPLN is almost constant in this T range, showing that only the T-independent broadening term γ0 is dominant, without any other significant scattering process. Because γ0 is a T-independent term, the following relation should be satisfied: D = (kBT/m*)/γ0 ∝ T. This is also consistent with the experimental results for D in region i. We find a good linear correlation between D and T, indicating that non- or weakly diffusive transport with thermal activation is the main effect explaining the diffusion dynamics of neutral excitons in region i (Figure 4b). In general, acoustic phonon scattering is dominant in this low T range (≤75 K). As shown in Figure 3e, NLdifN(75 K)/NLdifN(275 K) and τ at 75 K are 1.6 and 285.75 ps, respectively. If we assume LdifN at 275 K is about 1−1.8 μm according to a previous report,35 it can be estimated that the speed of the neutral excitons is about 5.6−10 μm/ns. This speed is much faster than that of a longitudinal acoustic phonon in TMDs (∼1.1 μm/ns).36 This indicates that neutral excitons can be transported in WS2 without causing acoustic phonon scattering, which is also consistent with the weak (negligible) acoustic phonon scattering coefficient observed from the T dependence of ΓPLN in this T range (Figure 4c). This weak acoustic phonon scattering may be explained by the relatively larger Bohr radius (∼2 nm) of excitons in TMDs.37 Acoustic phonon scattering originates from the combination of the deformation potential and piezoelectric potential, which are known as short- and long-range scattering, respectively. Since the neutral excitons do not have charge, the effects of the deformation potential can be greater than those of the piezoelectric potential.38 Because the deformation potential originates from the local changes in the crystal potential caused by the atomic displacements due to an acoustic phonon, the relatively larger Bohr radius of excitons in TMDs can screen the short-range deformation potential, resulting in the weak acoustic phonon scattering coefficient. In region ii (∼75 K ≤ T ≤∼200 K), IPLT decreases and IPLN increases with increasing T (Figure 4d). As revealed through the PL width fitting, ionized impurity scattering should be dominant in this region. When we plot log(IPLN) as a function of 1/T, i.e., an Arrhenius-type plot, it is found that the activation energy is about 22 meV (Figure S4). This value is almost consistent with the average energy for ionized impurity scattering obtained from the peak width fitting (⟨Eb⟩ = 19.8 meV) (Figure 4c), indicating that the kinetic energy of the neutral exciton increases by thermal activation and results in the

Figure 5. (a) Typical CCD image and (b) raw PL spectrum of a suspended monolayer WS2 crystal measured at 4.5 K. The raw PL spectrum can be decomposed into five different peaks (N, P1(T), P2, P3, and P4). (c, d) Temperature dependence of (c) NLdifN and NLdifT and (d) ΓPL for trions (red) and neutral excitons (blue). Inset in (c) shows typical raw integrated intensity profile for neutral excitons and trions at 4.5 K. 9691

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ACS Nano found that various fine structures (P1, P2, P3, and P4) can be observed in addition to the neutral exciton. On the basis of the literature, we assigned P1 in Figure 5b to the trion peak,9 and we do not focus on the other fine structures because the origins of those peaks are still not clarified. Figure 5c shows the normalized trion diffusion length (NLdifT) as a function of T. For comparison, NLdifN is also shown in the same figure. In general, trions have a larger mass than neutral excitons, showing a shorter diffusion length than NLdifN. Surprisingly, however, much longer diffusion lengths were observed for trions than for neutral excitons in the low T range (below 10 K). This type of anomalous diffusion of trions can be observed only for the suspended sample (Figure S5a). Moreover, NLdifT > NLdifN can also be obtained from an indirect estimate of NLdifT from the size dependence of IPL (Figure S6). Although the reasons for this anomalous diffusion of trions are still not clear, a possible explanation can be provided by considering the theoretical prediction of the radiative lifetime of trions at low T. A recent theoretical calculation reports that the radiation lifetime of trions decreases monotonically with decreasing T up to around 10 K and then suddenly increases with decreasing T below 10 K.30 This longer radiative lifetime of trions at low T is explained by Wang et al. by considering that the phase space for the electron that remained in the conduction band when the trion recombined is either not available or is greatly reduced near the conduction band edge because of Pauli blocking.30 Then, D was plotted from the experimental data of NLdifT and the theoretical value of the T dependence of τ with the relation L = (Dτ)1/2.30 We find that the trion D follows the T−1/2 law, indicating that acoustic phonon scattering should be significant (Figure S5b).32 The dominance of acoustic phonon scattering can be also found in the T dependence of the PL width. The width of neutral excitons and trions was plotted as a function of T (Figure 5d). The width−T plot shows a linear correlation with a different slope, indicating that the width can be fitted by the first and second terms of eq 5, i.e., Γo + ΓaT. The fitting reveals that Γa is very low for neutral excitons (∼29.3 μeV), indicating nondiffusive transport, which is consistent with the results shown in Figure 4. On the other hand, a higher Γa can be observed for trions (∼104.5 μeV). This indicates that acoustic phonon scattering governs the diffusion dynamics of trions in this T range, which is consistent with the results in Figure S5b. These results show that the anomalous diffusion of trions is mainly caused by the theoretically predicted longer radiative lifetime of trions at low T. In this T range, acoustic phonon scattering determines the transport dynamics of the trions. The momentum relaxation time is extended owing to the relatively weak acoustic phonon scattering, resulting in a relatively longer diffusion length for trions than that of neutral excitons at very low T (4.5 K). It should be mentioned that the transport dynamics of neutral excitons and trions were discussed on the basis of several assumptions and approximations. First, we used the steady-state model to describe the exciton-transport dynamics in this study. The exciton diffusion process contains various nonequilibrium reactions. Thus, it is difficult to express the complete dynamics of exciton diffusion with this steady-state equation. Since the exciton transport dynamics in TMD is a new topic and lacks a basic model, we used the steady-state model in this study as a first-order approximation as similar to previous studies in other materials.8,26,27 Second, the normalized D was estimated with the T-dependent radiative

lifetime given by the theoretical calculations.30 Because it is known that there is a sample-to-sample variation for the radiative lifetime of excitons, further accurate dynamics of exciton diffusion can be obtained with the experimentally obtained T-dependent PL lifetime for a wide range of temperatures, which should be varied from a very shortrange, around a few picoseconds or less to several nanoseconds. However, the linear correlation between the radiative lifetime and T has also been assumed in another theoretical study,39 indicating that the qualitative discussion presented in this paper should be reasonable. Third, we did not take into account PL quenching through a bright-to-dark state transition, which may influence the PL yield and carrier lifetime.40,41 Zhang et al. reported that the PL intensity decreases with the temperature through the transition from a bright state to a dark state. Since the T dependence of IPL in this study is opposite to their results (the summation of the PL intensities from neutral excitons and trions increase as T decreases), we think that PL quenching through a dark-state transition is not very significant, at least within our sample. Third, the influence of background electrons in the low density of excitons may change the transport of excitons from ambipolar to minority transport. The other components in the PL spectra (P2, P3, and P4 in Figure 5b), which may be correlated with biexcitons and localized impurity states, may affect the transport dynamics of neutral excitons and trions. These effects should also be taken into account for further understanding of the exciton transport dynamics in TMDs.

CONCLUSIONS We have investigated the T-dependent transport dynamics of excitons in monolayer WS2 using two different methods. The T-dependent transport dynamics of neutral excitons and trions can be clarified on the basis of systematic measurements of the T-dependent diffusion length, PL width, and integrated intensity. For neutral excitons, the transport dynamics are divided into three different regions, where the main transport dynamics are governed by thermal activation (≤∼75 K), ionized impurity scattering (∼75 K ≤ T ≤ ∼200 K), and LO phonon scattering (≥∼200 K). Unlike for the neutral excitons, anomalous diffusion can be observed for trions only in a very limited low T range (4.5−10 K) and is explained by the extended radiative lifetime and the increase in the momentum relaxation time due to weak acoustic phonon scattering. These findings for the transport dynamics of excitons in TMDs should be useful for the future development of high-performance exciton-based optoelectrical devises. METHODS Preparation of WS2. A monolayer WS2 was prepared by conventional mechanical exfoliation from the bulk crystal (2D semiconductor). The monolayer WS2 was transferred on to Au electrodes with different channel lengths using a homemade micro aligner, resulting in suspended WS2 structures (see the Supporting Information for details). Optical Measurement. The PL measurements and CCD imaging were carried out with a confocal micro-optical measurement system with Ar laser (488 nm wavelength) excitation (HR-800, Horiba). The substrate temperature was controlled between 4.5 and 300 K using a temperature control unit with liquid helium (Oxford instruments). We used 100× objective, whose laser radius should be originally around 500 nm. Since the laser goes through the quartz window of the vacuum chamber, the laser spot size was slightly broadened up to 1.6 μm, confirmed by CCD imaging. 9692

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ACS Nano Numerical Solution. The numerical solution was carried out with the Partial Differential Equation Toolbox of Matlab (Mathworks). The Curve Fitting Tool of Matlab was also utilized for the fitting of experimental data. Estimate of NLdifN with Direct CCD Imaging. At first, the CCD images were taken for the suspended WS2 (the electrode distance was 7 μm), which is the same sample used for the indirect measurement of NLdifN shown in Figure 2. Then, the CCD image was decomposed into raw PL spectra for different spatial positions. Spectral fitting was carried out for each raw spectrum, decomposing it into neutral exciton and trion components. Then, the integrated intensity of the neutral excitons provided by the fitting was plotted as a function of the distance from the excitation center, thus obtaining the spatial distribution of IPLN (note that we assumed that the integrated intensity of the neutral excitons is proportional to the density of neutral excitons). Then, NLdifN was obtained through fitting the experimentally obtained spatial distribution of IPLN to the theoretically calculated profile (see Figure S3 for more detailed information).

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ASSOCIATED CONTENT S Supporting Information *

This material is available free of charge at The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b05580. Fabrication process of suspended TMD device; effects of excitation power on the PL measurement; measurement of exciton diffusion length with CCD imaging; activation energy for ionized impurity scattering; trion diffusion length measured by size-dependent PL intensity (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported in part by JSPS KAKENHI (Grant Nos. JP 25706028, JP 26107502, JP 16H03892, and JP 16K13707) and the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University. REFERENCES (1) Najafov, H.; Lee, B.; Zhou, Q.; Feldman, L. C.; Podzorov, V. Observation of Long-Range Exciton Diffusion in Highly Ordered Organic Semiconductors. Nat. Mater. 2010, 9, 938−943. (2) Sun, Y.; Giebink, N. C.; Kanno, H.; Ma, B.; Thompson, M. E.; Forrest, S. R. Management of Singlet and Triplet Excitons for Efficient White Organic Light-Emitting Devices. Nature 2006, 440, 908−912. (3) Awschalom, D. D.; Flatté, M. E. Challenges for Semiconductor Spintronics. Nat. Phys. 2007, 3, 153−159. (4) Eytan, G.; Yayon, Y.; Rappaport, M.; Shtrikman, H.; Bar-Joseph, I. Near-Field Spectroscopy of a Gated Electron Gas: A Direct Evidence for Electron Localization. Phys. Rev. Lett. 1998, 81, 1666−1669. (5) Wegscheider, W.; Pfeiffer, L. N.; Dignam, M. M.; Pinczuk, A.; West, K. W.; McCall, S. L.; Hull, R. Lasing from Excitons in Quantum Wires. Phys. Rev. Lett. 1993, 71, 4071−4074. (6) Zaric, S.; Ostojic, G. N.; Shaver, J.; Kono, J.; Portugall, O.; Frings, P. H.; Rikken, G. L. J. A.; Furis, M.; Crooker, S. A.; Wei, X.; Moore, V. C.; Hauge, R. H.; Smalley, R. E. Excitons in Carbon Nanotubes with Broken Time-Reversal Symmetry. Phys. Rev. Lett. 2006, 96, 016406. (7) Zaric, S.; Ostojic, G. N.; Kono, J.; Shaver, J.; Moore, V. C.; Strano, M. S.; Hauge, R. H.; Smalley, R. E.; Wei, X. Optical Signatures 9693

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DOI: 10.1021/acsnano.6b05580 ACS Nano 2016, 10, 9687−9694