Defect-Mediated Charge-Carrier Trapping and Nonradiative

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Article Cite This: J. Am. Chem. Soc. 2019, 141, 10451−10461

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Defect-Mediated Charge-Carrier Trapping and Nonradiative Recombination in WSe2 Monolayers Lesheng Li† and Emily A. Carter*,‡ †

Department of Mechanical and Aerospace Engineering and ‡School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544-5263, United States

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S Supporting Information *

ABSTRACT: Nonradiative charge-carrier recombination in transition-metal dichalcogenide (TMD) monolayers severely limits their use in solar energy conversion technologies. Because defects serve as recombination sites, developing a quantitative description of charge-carrier dynamics in defective TMD monolayers can shed light on recombination mechanisms. Herein we report a first-principles investigation of charge-carrier dynamics in pristine and defective WSe2 monolayers with three of the most probable defects, namely, Se vacancies, W vacancies, and SeW antisites. We predict that Se vacancies slow down recombination by nearly an order of magnitude relative to defect-free samples by breaking the monolayer’s symmetry and thereby reducing the spectral intensity of the A1g phonon mode that promotes recombination in the pristine monolayer. By contrast, we find W vacancies accelerate recombination by more than an order of magnitude, with half of the recombination events bypassing charge traps. The subsequent dynamics feature both charge trapping and charge-trap-assisted recombination. Although SeW antisites also slightly accelerate recombination, the predicted mechanism is different from the W vacancy case. First, a shallow energy level traps a photoexcited electron. Then, both shallow- and deep-trap-assisted recombination can occur simultaneously. Accelerated recombination arises for W vacancies and SeW antisites because they introduce new phonon modes that strongly couple to electron and hole dynamics. This work thus provides a detailed understanding of the mechanisms behind charge-carrier recombination in WSe2 monolayers with distinct defects. Thus, materials engineering, particularly to avoid W vacancies, could advance this technology. The insights derived are important for future design of high-performance photoactive devices based on WSe2 monolayers.

1. INTRODUCTION Direct-band-gap transition-metal dichalcogenide (TMD) monolayers of the general formula MX2 (M = Mo, W; X = S, Se, Te) are garnering attention particularly in materials science and solid-state physics communities because of their great potential for electronics and optoelectronics applications.1−3 Their desirable properties include having band gaps in the visible range4,5 and intrinsic chemical and physical robustness.6,7 These make them candidates for photovoltaics and other promising solar energy applications, such as the direct conversion of light energy to hydrogen fuel via photoelectrochemical water spitting.8 Although TMDs have been used successfully in highperformance solar cells as interfacial charge-carrier transport layers,9−11 to date the performance of TMDs as primary lightharvesting materials has been far below expectations.8,12,13 In addition, their photoluminescence quantum yields are unexpectedly low for direct-gap semiconductors.14 Moreover, typical TMD-based devices exhibit intrinsic n-type or p-type behavior without intentional doping,15,16 which is not what one would expect from a perfect crystal. These studies © 2019 American Chemical Society

altogether suggest that structural defects in TMD monolayers play significant roles in determining their electronic and optical properties.17,18 The relatively large and highly variable concentrations of defects in TMD monolayers probably provide a multitude of recombination sites for charge carriers, resulting in low photoluminescence quantum yields. Among the family of TMD monolayers, defects in tungsten diselenide (WSe2) monolayer exhibit the most interesting behavior. Chalcogen vacancies are often regarded as the most common intrinsic defect in TMD materials,19−21 making most TMD monolayers n-doped.15,22 However, mechanical exfoliation and chemical vapor deposition experiments indicate that WSe2 monolayers also can exhibit p-type doping.16,23 Very recently, by combining low-temperature scanning tunneling microscopy, scanning tunneling spectroscopy, and firstprinciples calculations, W vacancies were found responsible for the p-type doping of the WSe2 monolayer, dominating the excitonic emission of the WSe2 monolayer at low temperReceived: April 30, 2019 Published: June 5, 2019 10451

DOI: 10.1021/jacs.9b04663 J. Am. Chem. Soc. 2019, 141, 10451−10461

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Journal of the American Chemical Society

directions, was used to compare directly with 5 × 5 supercell models of defective WSe2 monolayers containing one Se vacancy (VSe), one W vacancy (VW), and one antisite defect where a neutral Se atom substitutes for a W atom (SeW). These defects were chosen because of their predicted low formation enthalpies.24 These individual point defects in the 5 × 5 supercell correspond to a defect concentration of 4.3 × 1013 defects/cm2, which is higher than found in experiments20,46 but is inevitable due to the cost associated with modeling large simulation cells. To verify that the point defects introduced here are well isolated in the 5 × 5 supercell, we also simulated WSe2 monolayers containing a VSe with supercell sizes of 3 × 3, 4 × 4, and 6 × 6. Densities of states (DOS) and bond length deviations introduced by the point defect in these supercells (Figure S2) indicate that the point defects in the 5 × 5 supercell do not interact. Therefore, we expect that a supercell size of 5 × 5 would be able to mimic a much lower defect concentration. We used a vacuum region of at least 15 Å in the direction perpendicular to the monolayer to avoid spurious interactions between periodic images. Geometry optimization of the defective WSe2 monolayers utilized a converged 3 × 3 × 1 Γ-point-centered Monkhorst−Pack k-point grid (Figure S1b displays convergence of the k-point grid for the 5 × 5 supercell containing a defective monolayer with a VSe as an example). We performed Born−Oppenheimer molecular dynamics (BOMD) simulations with the Nosé−Hoover thermostat47,48 to mimic the canonical ensemble (constant number of atoms N, volume V, and temperature T) within the Vienna ab initio Simulation Package (VASP)49,50 at 300 K with a time step of 1.0 femtosecond (fs). In these simulations, we used the allelectron, frozen-core projector-augmented-wave (PAW)51 method to handle the electron−ion interactions, the PBEGGA functional for electron XC, a plane-wave basis kineticenergy cutoff of 500 eV, and only the Γ-point in the Brillouin zone to accelerate the simulations. The Nosé mass corresponded to a period of 40 time steps for the frequency of temperature oscillations in the BOMD simulation. We examined the validity of the time step in the pristine WSe2 monolayer, as shown in the Supporting Information. The time step of 1.0 fs is short enough to conserve the Nosé−Hoover Hamiltonian (Figure S7). The total trajectory length of the BOMD simulation depends on the system under investigation. To obtain a converged trajectory representative of the positions of the system’s nuclei at all times, BOMD simulations were performed with durations of 8, 24, 36, and 40 picoseconds (ps) for pristine and defective WSe2 monolayers with VSe, VW, and SeW defects, respectively. The Supporting Information provides details of how we determined the required total trajectory length. Electronic state energies and nonadiabatic couplings (NACs) were calculated using BOMD-generated geometries. The Supporting Information also provides details of the numerical calculation of NAC matrix. To simulate charge-carrier trapping and recombination dynamics in the WSe2 monolayers, we employ the decoherence-corrected surface-hopping algorithm.52,53 Charge-carrier recombination exhibits a time constant of several hundred ps in TMD monolayers,31,54 a time scale far beyond the capability of current quantum dynamics simulations. Due to the high computational cost, instead we intercept the last 5 ps of each original BOMD trajectory and replicate it 201 times. Essentially, we are assuming that the last part of the trajectory is fully equilibrated and that 5 ps is longer than any

atures.24 Later, Silverman and co-workers25 demonstrated that electron-beam irradiation can be used to selectively introduce defect-bound excitonic states associated with Se vacancies in the WSe2 monolayer. Their first-principles calculations and time-resolved spectroscopy measurements further revealed that these Se-vacancy-bound excitons exhibit exceptional optical properties, including an ultralong recombination lifetime of 200 nanoseconds (ns). The functionality of a material depends on its quality and morphology. By altering the mechanical and chemical properties of TMD monolayers and creating defects within the material, the introduced charge-carrier trap states can undermine the material’s stability and lead to charge-carrier losses. In recent experiments,8 Sivula and co-workers showed that point defects in WSe2 monolayers act as charge-carrier recombination sites and significantly limit device performance. Defect treatments improved quantum efficiency significantly, producing a new benchmark for the performance of solutionprocessed WSe2. However, the mechanistic origin of these improvements is unclear. Recognizing the critical role of defects in determining device performance,26−30 a quantitative description of charge-carrier dynamics in defective WSe2 monolayers would advance understanding and ultimately materials design for photoactive devices. Defects frequently introduce charge-trap energy levels in the band gap and can accelerate nonradiative electron−hole recombination.31−33 However, the mechanisms of these processes in defective WSe2 monolayers are unclear, since charge-carrier dynamics in this material have yet to be investigated. It therefore is not known whether all defects are equally detrimental to or whether certain defects are particularly consequential for the performance of WSe2 monolayers. To this end, here we apply first-principles-derived, mixed classical-quantum dynamics techniques to elucidate how different point defects affect charge trapping and electron− hole recombination in WSe2 monolayers.

2. COMPUTATIONAL DETAILS Electronic structure calculations and geometry optimizations were done within spin-restricted density-functional theory (DFT) using the Quantum Espresso software package.34 We employed spin-restricted DFT because pristine TMD materials are nonmagnetic35,36 and because the ground states of all of the defective WSe2 monolayers considered here were as well (Table S1). The Kohn−Sham one-electron wave functions for the valence electrons of W (5s25p65d46s2) and Se (4s24p4) were expanded in a plane-wave basis set and electron−ion (screened nuclei) interactions were represented by optimized norm-conserving pseudopotentials.37−39 We used the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE)40 for the DFT exchange-correlation (XC) functional. We study only the 2H phase WSe2 because it is the air-stable phase under ambient conditions.41−43 We optimized all geometries until the Hellmann−Feynman forces were smaller than 0.001 a.u. (∼0.0257 eV/Å). We first structurally relaxed the monolayer WSe2 primitive cell of three atoms using a 27 × 27 × 1 Γ-point-centered Monkhorst−Pack44 k-point grid with a plane-wave basis kinetic-energy cutoff of 50 Ry (680 eV; a convergence test for this cutoff appears in Figure S1a of the Supporting Information), where the Brillouin zone was integrated using the tetrahedron method.45 A 5 × 5 supercell of a pristine WSe2 monolayer, generated by repeating the 3-atom primitive cell five times in the a and b 10452

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Supporting Information). Although yielding different band gaps, PBE, HSE06, and PBE0 all predict the same band edge character (mainly W states) for the VBM and the conduction band minimum (CBM) (Figure S4). The results presented hereafter therefore use the more efficient PBE functional. As seen in Figure 2a, the VSe introduces an empty peak in the band gap about 0.5 eV below the CBM. The presence of the VSe also produces an occupied state at 0.65 eV below the VBM (Figure S5 in the Supporting Information). All of these electronic states introduced by the VSe localize near the point defect site (Figure S5), consistent with recent work by Silverman et al.25 and Neaton et al.67 Here, we only focus on the midgap unoccupied states because our goal is to investigate how such defect levels affect electron−hole recombination. In contrast to a VSe, a VW in the WSe2 monolayer exhibits one filled peak (0.5 eV above the VBM) and two empty peaks in the band gap. The two empty peaks are located 0.9 and 1.1 eV below the CBM. Introducing a SeW antisite also produces one filled peak (0.37 eV above the VBM) and two empty peaks at quite different energies in the band gap. The deep empty peak is located 1.05 eV below the CBM, while the shallow empty peak is only 0.16 eV below the CBM. The electronic states introduced by these point defects in the WSe2 monolayer all localize around the defect sites, while the VBM and CBM maintain their delocalized character within the monolayer for all four cases (Figure S6 in the Supporting Information). 3.2. Possible Mechanisms Involved in Charge-Carrier Trapping and Recombination. Figure 2b illustrates the bulk and defect states and possible mechanisms that could be involved in charge-carrier trapping and recombination dynamics based on the distinct electronic structures discussed above. The far left depicts the mechanism in the pristine material, in which an electron in the conduction band directly recombines with a hole in the valence band. The point defects introduce occupied and unoccupied electronic states in the band gap that can serve as hole traps (HTs) and electron traps (ETs), respectively. The trap states open up the possibility of several distinct dynamical processes that could take place simultaneously, complicating the entire quantum dynamics of charge-carrier recombination.31,32 For instance, because the WSe2 monolayer with a VSe has an ET below the CBM (Figure 2a), ET-assisted recombination could occur (Figure 2b). With a VW or a SeW in the WSe2 monolayer, the charge-carrier dynamics may become even more complicated due to the presence of HTs above the VBM (Figure 2a). Specifically, in addition to direct and ET-assisted recombination mechanisms, electron−hole recombination could also occur via hole trapping (HT-assisted) and simultaneous electron and hole trapping (ET- and HT-assisted), as shown in Figure 2b. In fact, the mechanisms for charge-carrier trapping and recombination could be different in each of these three types of defective WSe2 monolayers because they exhibit distinct energy level alignments for the trap states (Figure 2a). 3.3. Charge-Carrier Trapping and Recombination in WSe2 Monolayers. Figure 3 displays predicted populations of the key electronic states involved in the charge-carrier trapping and recombination dynamics in the pristine and defective WSe2 monolayers. Electron−hole recombination (population change in the ground state), electron trapping and ET-assisted recombination (population change in ET states), hole trapping and HT-assisted recombination (population change in HT states), and recombination through simultaneous electron and hole trapping (population change in those HT states that

characteristic correlation time. Such a strategy was employed successfully to investigate closely related materials.31,55 We used these artificially created trajectories with total durations of 1005 ps each to generate the nonadiabatic Hamiltonian over a ns time scale. We then performed decoherence-corrected surface-hopping simulations within the classical-path approximation (CPA).56,57 This approach enables use of a large number of nuclear trajectories to converge ensemble-averaged quantities (the nuclear trajectories do not depend on the hops within the CPA). First, 1000 initial conditions were chosen evenly from the first 5 ps of the artificially generated trajectory to sample the canonical distribution of the atomic positions. We then performed 500 surface-hopping simulations for each initial condition, converging the sampling of hopping probabilities using Metropolis Monte Carlo.58 Further details of the theoretical methodology, validation of the CPA in the context of pristine and defective WSe2 monolayers, and discussion of decoherence effects are provided in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. Geometric and Electronic Structures. The optimized lattice constants of the structurally relaxed WSe2 primitive cell are a = b = 3.297 Å, α = β = 90°, and γ = 120°, consistent with the measured values of a = b = 3.28 Å, α = β = 90°, and γ = 120°.59 Top views of the fully optimized geometries of the pristine and defective WSe2 monolayers with VSe, VW, and SeW defects appear in Figure 1, where we denote

Figure 1. Top views of the fully optimized geometries of the pristine and defective WSe2 monolayers with a Se vacancy, W vacancy, and SeW antisite defect.

the defects by green circles, and the first and second layers of Se atoms by green and pink balls, respectively. Figure 2a displays the predicted DOS of pristine and defective WSe2. We align the energy levels to the vacuum level obtained from electrostatic potential calculations (Figure S3a in the Supporting Information). For the VSe case, we employ a dipole correction because of the intrinsic dipole introduced by the point defect (Figure S3b). In Figure 2a, filled and empty curves represent occupied and unoccupied bands, respectively, where the valence band maximum (VBM) of the pristine WSe2 monolayer is set as the zero of energy. DFT-PBE predicts the band gap of the pristine WSe2 monolayer to be 1.64 eV, which is in fortuitous agreement with measured values of 1.63−1.65 eV.4,23,60−63 Use of hybrid XC functionals within DFT, such as HSE0664 and PBE0,65,66 significantly overestimates the band gap at 2.12 and 2.74 eV, respectively (Figure S4 in the 10453

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Figure 2. (a) Densities of states (DOS) of pristine and defective WSe2 monolayers. Energy levels of different systems aligned based on vacuum levels from electrostatic potential calculations. The valence band maximum (VBM) in the pristine WSe2 monolayer is set as the reference energy at 0 eV. Filled and empty curves represent occupied and unoccupied bands, respectively. Positions of band edges (VBM and conduction band minimum, CBM) and defect-induced trap states are labeled; ET and HT represent the electron and hole traps, respectively. Gaussian broadening with σ2 = 0.055 eV is used to plot the DOS. (b) Schematic of energy level alignments and possible mechanisms involved in carrier trapping and recombination in pristine and defective WSe2 monolayers.

fitting the simulation data to different functions relevant for the appropriate dynamical process. For instance, in the WSe2 monolayer with a VW (Figure 3c), the overall recombination time constant was obtained by fitting the black curve to a sigmoid function (details of the fitting procedure are provided in the Supporting Information). We fit the rising and decaying parts of the red curve respectively to a sigmoid function and a single exponential, in order to obtain separately the time constants for electron trapping and ET-assisted recombination. The recombination time indicates how long the nonradiative electron−hole recombination takes, while the time constants for charge-carrier trapping and trap-assisted recombination correspond to the lifetimes of the charge carrier within the trap states, i.e., how long the carriers remain trapped. Nonradiative electron−hole recombination generally is the major loss mechanism for charge carriers, with the excess energy of the charge carriers wasted as phonons (heat) instead of photons, leading to low photoluminescence quantum yields.14 Nonradiative electron−hole recombination therefore severely limits the efficiencies of materials in various optoelectronic applications. In the pristine WSe2 monolayer, fitting the simulation data in Figure 3a to a single exponential function gives an electron− hole recombination time constant of 405.4 ps. Such a time scale is consistent with measured values of several hundred ps in a WSe2 monolayer63 and in other TMD materials such as a MoS2 monolayer,68,69 and other theoretical work.31 As seen in Figure 3b, the VSe significantly slows down the recombination (by a factor of 7.6) compared to the pristine WSe2 monolayer, with a recombination time constant of 3.1 ns. By contrast, the VW notably accelerates recombination (by a factor of 25.1), with a time constant of 16.1 ps (Figure 3c; note time axis scale change). Although the SeW also accelerates electron−hole recombination (time constant of 151.2 ps; Figure 3d), it is 9.4 times slower than predicted for the VW case. Most importantly, the mechanistic origins of the acceleration must be different for the VW and the SeW because the population evolution of the trap states is substantially different (Figure 3c and 3d). Note

Figure 3. Charge-carrier trapping and recombination in (a) pristine and defective WSe2 monolayers with (b) Se vacancies, (c) W vacancies, and (d) SeW antisite defects. Nonradiative electron−hole recombination is shown in black, electron trapping and ET-assisted recombination in red, hole trapping and HT-assisted recombination in green, and electron−hole recombination through simultaneous electron and hole trapping (ET and HT-assisted) in orange. For the VSe case in panel b, unlike all other panels, the black curve can be interpreted as ET-assisted recombination rather than direct electron− hole recombination, because the entire electron population first traps in the electron trap.

recombined with ET states) are illustrated in black, red, green, and orange curves, respectively. Table 1 lists time constants predicted for all possible dynamical processes, obtained by 10454

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Table 1. Time Constants for Nonradiative Electron−Hole (CBM e− and VBM h+) Recombination, Hole Trapping and HoleTrap-Assisted (HT-assisted) Recombination, Electron Trapping and Electron-Trap-Assisted (ET-assisted) Recombination, and Recombination through Simultaneous Electron and Hole Trappinga time constants for charge-carrier trapping and recombinationb WSe2 monolayers

recomb. of CBM e− and VBM h+

hole trapping and HT-assisted recomb.

electron trapping and ET-assisted recomb.

recomb. through electron and hole trapping

pristine Se vacancy W vacancy SeW antisite

405.4 ps − 16.1 ps 151.2 ps

− − 40.6 and 17.3 ps 506.6 psc

− 2.7 ps and 3.1 ns 6.9 and 12.1 ps 0.3 and 207.1 ps (47.5 and 213.6 ps)d

− − 6.7 and 9.2 pse 57.3 ps and 1.31 nse

a

For cases with more than one time listed, each time corresponds to the process listed in the column heading in that order. bWhen two values are listed, they correspond respectively to the events listed in the column heading. cFor the SeW antisite defect, only the hole trapping time constant is listed because the HT population does not decay. dFor SeW ET mechanisms, the time constants outside and inside the parentheses characterize electron trapping and ET-assisted recombination by the shallow and deep ETs, respectively. eThese two values correspond to the time constants of the rising and decaying parts of the recombination through simultaneous electron and hole trapping.

Table 2. Average Nonadiabatic Couplings between Key States Involved in Charge-Carrier Trapping and Recombination in the Defective WSe2 Monolayers average nonadiabatic couplings (meV) defects

recomb. CBM/VBM

hole trapping HTs/VBM

HT-assisted recomb. CBM/HTs

elec. trapping CBM/ETs

ET-assisted recomb. ETs/VBM

ET- and HT-assist. recomb. ETs/HTs

VSe VW SeW

8.0 8.7 7.7

− 53.6 93.3

− 11.8 11.9

65.9 22.3 269.2(19.7)a

10.2 26.1 10.1(22.4)a

− 98.8 17.3(34.6)a

a

For the SeW antisite defect, values outside and inside parentheses characterize the average nonadiabatic coupling associated with the shallow and deep electron traps, respectively.

they were found to play key roles in charge-carrier dynamics, e.g., in interfacial electron transfer72−74 and electron−hole recombination.31,32,54,75−77 Table 2 displays the predicted average NACs between key electronic states involved in distinct dynamical processes. For instance, electron trapping typically involves NACs between the CBM and ET states. Therefore, NACCBM/ETs represents how well the CBM couples to the ET states and one can use it to characterize qualitatively the electron trapping process. In the WSe2 monolayer with a VSe, the NAC for electron trapping (65.9 meV) is significantly larger than for recombination (8.0 meV). Thus, fast electron trapping takes place first and electron−hole recombination occurs only thereafter. In addition, the NAC between ET states (302.1 meV; see Figure S11a of the Supporting Information) is considerably larger than that of the one involved in ET-assisted recombination (10.2 meV; see table in Figure S11). Consequently, once the electron transfers to the ET, it mostly hops between the trap states. This assertion is corroborated by the significant population predicted for the individual ET states even after 1 ns (Figure S10b). Therefore, unconventionally slower recombination (3.1 ns) occurs when VSe are present compared to the pristine WSe2 monolayer (405.4 ps), as shown in Figure 3b. The accelerated charge-carrier recombination by a VW occurs via a traditional mechanism in which traps serve as intermediate states that facilitate recombination. First, the ET is populated, red curve in Figure 3c. Second, the HT is populated, orange curve in Figure 3c. The physical meaning of the orange curves is different from that of the green curves in Figure 3. The former refers to recombination assisted simultaneously by an ET and a HT, whereas the latter represents recombination assisted solely by HTs. Figure 3c shows HTs populate during secondary events in which the hole can recombine only with the electron from the ET but not

that the radiative lifetimes in WSe2 monolayers at room temperature were estimated to be 3.5−4 ns in previous theoretical70 and experimental71 work. Such time scales for the radiative decay are significantly longer than the nonradiative electron−hole recombination times predicted here, indicating that nonradiative recombination is the dominant mechanism for charge-carrier loss in WSe2 monolayers. In the WSe2 monolayer with the VSe, the defect-induced ET populates very quickly (red curve in Figure 3b). The entire electron population can be accounted for in the ET after 5 ps, while relaxation into the VBM does not occur at all within this time frame (Figure S10a in the Supporting Information). Fitting the ET population in the first 5 ps to a sigmoid function yields an electron trapping time constant of 2.7 ps. Once the ET is fully populated, the electron relaxes to the VBM and recombines with the hole on a longer time scale. Chargecarrier dynamics in the WSe2 monolayer with VSe therefore involves a two-step process: electron trapping and subsequent ET-assisted recombination. Trap states introduced by defect levels in the band gap typically are assumed to accelerate electron−hole recombination.31−33 This is because they serve as intermediate states that provide smaller energy gaps for which stronger coupling to the ground state is expected. However, such a traditional acceleration does not apply in the case of the VSe. Although all recombination events involve the ET because electron trapping is fast, the subsequent ET-assisted recombination is quite slow. The electron is long lived in the ET states. Fitting the recombination (black curve in Figure 3b) to a growing exponential function yields an ET-assisted recombination time constant of 3.1 ns, about 7.6 times slower than in the pristine WSe2 monolayer. To understand these results, we examine nonadiabatic couplings (NACs) and time-averaged energy gaps because 10455

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Journal of the American Chemical Society with the electron at the CBM, since the green curve does not populate significantly. Finally, electron−hole recombination takes place, black curve in Figure 3c. The electron trapping and ET-assisted recombination exhibits a similar time constant (19.0 ps; sum of entries in Table 1) as direct electron−hole recombination (16.1 ps; Table 1), indicating that there are nearly equal probabilities for the electron and hole to recombine directly or via the ET. On the other hand, hole trapping exhibits a relatively large time constant of 57.9 ps (sum of entries in Table 1). Moreover, the HT never populates significantly, with a peak population of only 0.06 (green curve of Figure 3c). Consequently, HT-assisted recombination is rare. Furthermore, recombination through simultaneous electron and hole trapping (orange curve in Figure 3c) exhibits a time constant of 15.9 ps (sum of entries in Table 1) that is very similar to the ET-assisted recombination. Thus, ET-assisted recombination and recombination through simultaneous electron and hole trapping contribute nearly equally. The predicted NAC for electron trapping by a VW (22.3 meV; Table 2) is smaller than for a VSe (65.9 meV; Table 2). The former also exhibits a larger time-averaged energy gap between CBM and ET (0.73 eV; Table S2) than the latter (0.24 eV; Table S2). It therefore makes sense that a VW exhibits slower electron trapping (6.9 ps) than a VSe (2.7 ps) (Table 1 and Figure 3). Additionally, we can explain the starkly different recombination time constants for a VW (16.1 ps) and a VSe (3.1 ns) as follows. First, in the VW case, roughly half of the electron−hole recombination events bypass the ET, occurring directly from the band edges. Second, the lifetime of an electron within the ET is considerably shorter in a VW (19.0 ps) than in a VSe (3.1 ns). In the VW case, electron trapping exhibits a larger coupling (22.3 meV) than HTassisted recombination (11.8 meV) (Table 2). Thus, it is easier for electrons to move from CBM to the ET than to recombine with a hole in the HT. HT-assisted recombination therefore is unlikely to occur, consistent with Figure 3c, green curve. In the WSe2 monolayer with a SeW, Figure 3d shows that the ET populates rapidly, quite similar to the case of a VSe. The entire electron population can be accounted for in the ET after 3 ps, whereas relaxation into the VBM does not occur at all within this time period (Figure S12 in the Supporting Information). Fitting the population of the ET in the first 3 ps to a single growing exponential function gives an electron trapping time constant of 0.3 ps (Table 1). As the SeW introduces both deep and shallow electron traps in the band gap (Figure 2a), we must characterize the charge-carrier trapping among these ETs. The deep and shallow ET populations displayed as a function of time in Figure 4 reveals that the shallow ET fully populates by 3 ps (see inset) and only then does the deep ET start to take off. Therefore, the fast electron trapping seen in Figure 3d with the time constant of 0.3 ps is trapping by the shallow ET. The deep ET, on the other hand, populates much more slowly. By fitting the population of the deep ET (red curve in Figure 4) to a sigmoid function and a decaying exponential respectively for the rising and decaying parts, we extract a time constant for the deep electron trapping and deep-ET-assisted recombination to be 261.1 ps (sum in parentheses in Table 1). The time constants for recombination (151.2 ps) and deep electron trapping (261.1 ps) for a SeW (Table 1) suggest that a substantial fraction of the electron−hole recombination events bypass the deep ET. Moreover, electron−hole recombination through simultaneous electron and hole trapping is quite slow

Figure 4. Population evolution of the shallow and deep electron traps in the WSe2 monolayer with a SeW antisite defect.

(orange curve in Figure 3d). Fitting the curve’s rise to a sigmoid function and the decay to an exponential yields a time constant of 1.37 ns (sum of entries in Table 1). The time constant difference between deep electron trapping and deepET-assisted recombination (261.1 ps) and recombination through simultaneous electron and hole trapping (1.37 ns) indicates that most of the deep-ET-assisted recombination events take place through the deep ET only, and the contribution through simultaneous electron and hole trapping is negligible. The population of the HT grows slowly and does not decay, with a maximum value of 0.09 after 1 ns (green curve in Figure 3d). Fitting the population of the HT to a single growing exponential gives a time constant for hole trapping of 506.6 ps (Table 1). Therefore, HT-assisted recombination is unlikely to occur. As shown in Table 2, the SeW case exhibits a considerably larger NAC (269.2 meV) for shallow electron trapping than does the VSe (65.9 meV). Moreover, the former has a smaller time-averaged energy gap between the CBM and the shallow ET (0.08 eV; Table S2) than the latter (0.24 eV; Table S2). These data are consistent with the SeW defect exhibiting faster electron trapping by the shallow ET (0.3 ps) than for the VSe (2.7 ps) (Table 1). The different recombination time constants observed in the SeW (151.2 ps) versus the VSe (3.1 ns) can be understood as follows. Roughly half of the electron−hole recombination events bypass the deep ET, occurring directly between the shallow ET and the VBM for the SeW, consistent with the considerably shorter lifetime of the electron within the shallow ET in the SeW (207.4 ps; sum of entries in Table 1) versus the V Se (3.1 ns). By contrast, the different recombination time constants for the SeW (151.2 ps) versus the VW (16.1 ps) are attributable mainly to the following. First, roughly half of the electron−hole recombination events bypass the ET in the latter, whereas the electron is trapped first in the shallow ET states in the former. Second, the lifetime of the electron within the shallow ET is considerably longer in the SeW (207.4 ps) than the VW (19.0 ps) (sum of entries in Table 1). Furthermore, in the WSe2 monolayer with the SeW, both the shallow and the deep ETs exhibit larger NACs (269.2 and 19.7 meV; Table 2) than that for HT-assisted recombination (11.9 meV; Table 2). In other words, it is much easier for an electron to transfer from the CBM to an ET rather than to recombine with a hole in the HT. Therefore, once again, HTassisted recombination is unlikely to occur. Moreover, the 10456

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point defects more significantly perturb the WSe2 monolayer and introduce new phonon modes at both high and low frequencies. These modes strongly couple to the charge-carrier dynamics involving both electrons and holes (Figure S13 in the Supporting Information), inducing the fast recombination predicted in WSe2 monolayers with the VW and the SeW (Figure 3). Similar findings were predicted recently for another TMD material, MoS2.31 3.5. Mechanisms of Charge-Carrier Dynamics in WSe2 Monolayers. Figure 6 schematically summarizes all of these

couplings involved in recombination through simultaneous electron and hole trapping (17.3 and 34.6 meV for shallow and deep ETs, respectively; Table 2) for the SeW are considerably smaller than for the VW (98.8 meV; Table 2). Consequently, recombination through simultaneous electron and hole trapping in the SeW case (time constant 1.37 ns; sum of entries in Table 1) is significantly slower than the rate predicted for the VW (time constant 15.9 ps; sum of entries in Table 1). 3.4. Phonon Modes Participating in Charge-Carrier Recombination. To provide insight into charge-carrier recombination in the pristine and defective WSe2 monolayers, we calculated Fourier transforms (FTs) of the normalized autocorrelation function (ACF) of the energy gaps between relevant electronic states. One can use the resulting FT spectrum, also known as the phonon influence spectrum or spectral density,78 to identify the phonon modes directly involved in specific dynamical processes. By examining the FT spectrum, we can learn which vibrational motions promote nonradiative charge-carrier recombination and are responsible for energy loss as heat (via phonons). Figure 5 displays the FT

Figure 6. Mechanisms of charge-carrier trapping and nonradiative electron−hole recombination in the (a) pristine and defective WSe2 monolayers with (b) Se vacancies, (c) W vacancies, and (d) SeW antisite defects.

mechanisms of charge-carrier trapping and nonradiative electron−hole recombination in pristine and defective WSe2 monolayers. Figure 6a shows an electron in the conduction band directly recombining with a hole in the valence band; the pristine WSe2 monolayer has a predicted time constant of 405.4 ps for this process, qualitatively consistent with experiment.63 Figure 6b displays the salient charge-carrier dynamics predicted for the WSe2 monolayer with an isolated Se vacancy. Here, the charge carriers evolve first via electron trapping and then ET-assisted recombination. The midgap trap states first rapidly trap all excited electrons, with a time constant of 2.7 ps. The subsequent electron−hole recombination exhibits a time constant of 3.1 ns due to the long-lived electrons in the trap states. When a W vacancy exists in the WSe2 monolayer, Figure 6c, about half of the electron−hole recombination events bypass the ET and directly involve the CBM and VBM charge carriers, on a faster time scale than the pristine material (16.1 ps). On the basis of their time constants, ET-assisted recombination (19.0 ps) and recombination through simultaneous electron and hole trapping (15.9 ps) are competitive with direct recombination from the band edges, whereas HT-assisted recombination (57.9 ps) is rare. In the case of the SeW, Figure 6d, all excited electrons first trap in shallow ETs, with an ultrafast time constant of 0.3 ps. Then,

Figure 5. Phonon modes involved in charge-carrier recombination in the pristine (black and gray-filled curves) and defective WSe2 monolayers with a Se vacancy (magenta), a W vacancy (red), and a SeW antisite defect (blue).

spectrum corresponding to charge-carrier recombination in the pristine (black and gray-filled curves) and defective WSe2 monolayers with a VSe (magenta), a VW (red), and a SeW (blue). Two strong lattice modes exist in the pristine WSe2 monolayer, one with a peak frequency at 220 cm−1 and the other near 160 cm−1. The phonon mode at 220 cm−1 corresponds to the out-of-plane A1g mode, with a measured frequency of 248.3 cm−1.79−81 As seen in Figure 5, the VSe breaks the symmetry of the WSe2 monolayer and reduces the spectral intensity of the phonon mode at 220 cm−1 but retains the phonon mode at 160 cm−1. Because the VSe significantly slows down chargecarrier recombination (Figure 3), the reduced intensity at 220 cm−1essentially the only change in the spectrum compared to the pristine casesuggests that the out-of-plane A1g mode promotes charge-carrier recombination in the pristine WSe2 monolayer. For the VW and the SeW, although the spectral intensity of the phonon mode at 220 cm−1 decreases, these two 10457

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presence of a Se vacancy significantly inhibits recombination, with a much longer time constant of 3.1 ns, because of longlived electrons in trap states. The deceleration occurs because the Se vacancy breaks the symmetry of the monolayer and considerably reduces the spectral intensity of the A1g mode. By contrast, the W vacancy greatly accelerates recombination, with a time constant of 16.1 ps. Our analysis suggests in this case that roughly half of the recombination events bypass the electron trap and take place directly between the band edges. Competing events include electron-trap-assisted recombination and recombination through simultaneous electron and hole trapping. Although SeW antisite defects also accelerate recombination somewhat, with a time constant of 151.2 ps, the mechanism behind such acceleration is different from the W vacancy case. First, the photoexcited electrons readily trap in shallow electron levels due to large nonadiabatic couplings. Then, roughly half of the recombination events bypass the deep electron trap and occur directly between the shallow electron trap and the VBM. Competing events involve deepelectron-trap-assisted recombination and recombination through simultaneous deep electron trapping and hole trapping. Surprisingly, hole-trap-assisted recombination is rare for both W vacancies and SeW antisite defects. This is because it is easier for electrons to transfer to electron traps than to recombine with a hole in a hole trap. Acceleration of charge-carrier recombination by W vacancies and SeW antisite defects also can be attributed to the presence of new phonon modes that strongly couple to dynamical processes involving both an electron and a hole. Thus, a detailed description of charge-carrier trapping and recombination rates and mechanisms in the pristine and defective WSe2 monolayers is now available. Lastly, the insights gleaned offer design suggestions to improve high-performance photoactive devices based on WSe2 monolayers. Namely, modifying synthesis conditions to suppress W vacancies and encourage Se vacancies should improve performance.

about half of the electron−hole recombination events bypass the deep ET, occurring directly between the shallow ET and the VBM on a much slower time scale with a time constant of 207.4 ps. On the basis of their time constants, deep ET-assisted recombination (261.1 ps) will be more competitive than recombination via simultaneous deep electron trapping and hole trapping (1.37 ns). Likewise, HT-assisted recombination is even more unlikely to occur in the SeW case (506.6 ps) than in the VW case (57.9 ps). If the shallow traps fill up completely in the WSe2 monolayer with the SeW, then direct electron− hole recombination from the band edges will compete with other processes, given its time constant of 151.2 ps. We predict that the Se vacancy in the WSe2 monolayer exhibits unusual behavior in terms of charge-carrier trapping and recombination. As discussed above, electron−hole recombination only occurs between the electron trap and the VBM, after electron trapping. Although the electron trapping is fast, the charge-carrier recombination exhibits a characteristic time scale of 3.1 ns. By contrast, Prezhdo and co-workers31 recently predicted that sulfur (S) vacancies in an MoS2 monolayer accelerate charge-carrier recombination with a time constant of 225 ps, where the trap states introduced by the S vacancy serve as intermediate states. Not only is the effect of a chalcogen vacancy on charge-carrier dynamics different for distinct TMDs, but the mechanisms behind these dynamical processes are also different. Chalcogen vacancies in TMDs are regarded to be the most common intrinsic point defect.19−21 Normally, the mechanisms found in one material are considered transferable to other family members. Our work, indicates that changes in charge-carrier dynamics induced by chalcogen vacancies in the TMD family and the associated mechanisms found in one TMD material may not be generalizable to other members. Individual investigations of each TMD with chalcogen vacancies therefore will remain important. More importantly, our simulations suggest that W vacancies are the defects most detrimental to the performance of WSe2 monolayers among the three most probable point defects. Although the SeW antisite defect accelerates nonradiative recombination, it does so only by a factor of 2.7. The W vacancy accelerates recombination by a factor of 25.1, with a time constant of 16.1 ps. Such a fast time scale for nonradiative recombination is much faster than any recombination time constant ever reported for MoS2.31 The ps time scale of the nonradiative electron−hole recombination will produce rapid loss of the charge carriers to heat and will result in a low photoluminescence quantum yield. Methods to suppress formation of W vacancies therefore will be critical to manufacturing high-performance optoelectronic devices based on WSe2 monolayers.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.9b04663. Theoretical methodology, spin state of defective WSe2 monolayers, convergence tests of kinetic energy cutoff and k-point grid, convergence of the supercell size, calculation of the electrostatic potential and corresponding vacuum level, dependence of the electronic structure on the exchange-correlation (XC) functional, defect states introduced by the Se vacancy, localization of the trap states introduced by point defects, validation of time step and the total trajectory length in the Born− Oppenheimer molecular dynamics (BOMD) simulations, validation of the classical-path approximation (CPA), details of population evolution of the electron trap (ET) states introduced by the Se vacancy, nonadiabatic coupling (NAC) matrices and average energy gap, population evolution of the ET states introduced by the SeW antisite defect, phonon spectra of defective WSe2 monolayers, decoherence effects, and details of fitting procedure (PDF)

4. CONCLUSIONS In this work, we investigated how the three favorable point defects, Se vacancies, W vacancies, and SeW antisite defects, influence charge-carrier trapping and nonradiative electron− hole recombination in WSe2 monolayers with DFT-MD-based quantum dynamics simulations. The pristine WSe2 monolayer exhibits direct charge-carrier recombination between the band edges with a characteristic time constant of 405.4 ps, which is qualitatively consistent with measurements and thus lends credence to our simulation protocol. Phonon spectrum analysis indicates that the out-of-plane A1g mode facilitates electron− hole recombination in the pristine WSe2 monolayer. The 10458

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AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Lesheng Li: 0000-0002-1601-8868 Emily A. Carter: 0000-0001-7330-7554 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the U.S. Department of Energy, Office of Science, Basic Energy Sciences (Grant No. DE-SC0002120) for support of this work. We also thank Dr. J. Mark P. Martirez and Ms. Nari L. Baughman for a critical reading of an early draft of this paper.

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DOI: 10.1021/jacs.9b04663 J. Am. Chem. Soc. 2019, 141, 10451−10461

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DOI: 10.1021/jacs.9b04663 J. Am. Chem. Soc. 2019, 141, 10451−10461