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Defects Slow Down Non-radiative Electron-Hole Recombination in TiS3 Nanoribbons: A Time-Domain Ab Initio Study Yaqing Wei, Zhaohui Zhou, and Run Long J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02099 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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The Journal of Physical Chemistry Letters

Defects Slow Down Non-radiative Electron-Hole Recombination in TiS3 Nanoribbons: A Time-Domain Ab Initio Study Yaqing Wei,1 Zhaohui Zhou,2 Run Long1* 1

College of Chemistry, Key Laboratory of Theoretical & Computational

Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, P. R. China 2

International Research Center for Renewable Energy, State Key Laboratory of

Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, P. R. China

ABSTRACT: Layered TiS3 materials hold appealing potential in photovoltaics and optoelectronics due to their excellent electronic and optical properties. Using time-domain density functional theory combined nonadiabatic (NA) molecular dynamics, we show that the electron-hole recombination in pristine TiS3 nanoribbons (NRs) occurs on tens of picoseconds and is over 10-fold faster than the experimental value. By performing an atomistic ab initio simulation with a sulfur vacancy, we demonstrate that sulfur vacancy greatly reduces electron-hole recombination, achieving good agreement with experiment. Introduction of sulfur vacancy increases the bandgap slightly because the NRs highest occupied molecular orbital is lowered in *

Corresponding Author Email: [email protected] 1

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energy. More importantly, sulfur vacancy diminishes partially electron and hole wave functions overlap and reduces NA electron-phonon coupling, which competes successfully with the longer decoherence time, slowing down recombination. Our study suggests that rational choice of defects can control nonradiative electron-hole recombination in TiS3 NRs and provides mechanistic principles for photovoltaic and optoelectronic devices design.

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Since the first discovery of graphene in 2004,1 research efforts dedicated towards low dimensional materials, particularly on itself, two-dimensional transition metal dichalcogenides (TMDs), and black phosphorus, have attracted tremendous attention because these materials show excellent electronic and optical properties, and have enabled promising advances in photovoltaic and photocatalytic applications.2-10 The lack of bandgap in graphene, however, restricts significantly its applications in electronic and optoelectronic devices due to rapid electron-hole annihilation leading to very short-lived excited-state electron lifetime.11 Monolayers of TMDs hold great appeal for solar cells (SCs) applications due to the direct bandgap behavior and strong light-matter interactions.12,13 For instance, direct bandgaps about ~2 eV14,15 of monolayers of MoS2 and WSe2 make them active under visible-light irradiation and potentially enhance their photocatalytic activity and photovoltaic power conversion efficiency with certain incident light flux. Unfortunately, MoS2 and WSe2 themselves have negligible photon-to-electron conversion efficiencies due to inefficient photoinduced charge separation arising from large electron-hole binding energy.16 Such bound electron-hole pair, known as exciton, is detrimental to photovoltaic

SCs

because only free electrons and holes can take part in either generating photocurrent or driving chemical reaction. Even worse, low carrier mobility, around 15 cm2V-1s-1 of MoS2, inevitably reduces photo-to-electron conversion efficiencies because major charges recombine before they arrive at material surface.17 Another disadvantage of TMDs that their bandgaps are thickness dependent and occur direct-to-indirect transition, as the number of layers increases. The indirect bandgap weakens light 4


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harvesting. Furthermore, the un-avoided intrinsic defects in MoS2, such as sulfur vacancy,18 accelerate significantly excited state energy losses to heat and degrade photovoltaic SCs performance.19 Sensitizing MoS2 with organic molecules remarkably enhances the luminescence efficiency due to passivating sulfur vacancy defects and suppressing electron-hole recombination.20 As a rising and appealing material, 2D black phosphorus, also known as phosphorene, has been attracting great attention because of its tunable direct band gap, a high photoresponse,21 broadband response,22 and high carrier mobility (104 cm2V-1s-1) at room temperature,23 making them suitable for fabrication of filed-effect transistor and other optoelectronic devices. However, phosphorene suffers from oxidation under ambient atmosphere to degrade its stability and electronic properties and restrict their realistic applications.

Transition metal trichalcogenides (MX3, M = Ti, Zr, Hf, Nb, Ta; X = S, Se, Te), as a newly emerged member of 2D material family, have been attracting intense research efforts due to their complementary properties to TMDs.24-26 The crystal MX3 consists of MX3 sheets bound together by van de Waals forces.27,28 A single MX3 sheet is also called quasi-1D material, because it can be easily broken into nanoribbons (NRs) along a certain direction. The existing studies on MX3 have mainly focused on TiS3 because the composed elements are earth abundant and low cost. First-principles calculations have illustrated that TiS3 has a robust direct bandgap about 1.02 eV regardless of layer thickness, strain, and stacking order,29,30 showing slight underestimation to the experimental value of 1.2 eV due to the well-known density

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funcitonal theory problem.31 The suitable bandgap allows TiS3 to be active in the solar spectrum ranging from visible-light to infrared regime and suggests promising SCs applications that can beat other 2D materials mentioned above. In addition, the predicted electron mobility of TiS332 is as high as phosphorene33 and graphene,34 which trigger other applications of TiS3, such as photoanodes in photocatalysis for hydrogen generation35,36 and electrodes in lithium battery37. Among all of the applications, charge carriers dynamics play a central role because they affect power conversion efficiency in SCs, and determine the photocatalytic activity and so on. Recently, Hui Zhao and co-workers reported the photoinduced charge recombination dynamics in TiS3 NRs by time-resolved transient absorption measurement.38 They show that the electron-hole recombination occurs on 140 ps, following ultrafast electron excitation, thermalization and energy relaxation. Although the experiment provides important information on the excited electron dynamics, the mechanism responsible for charge recombination remains largely unclear and necessitates a comprehensive understanding by first-principles atomistic simulations, in order to generate valuable guidelines for materials design and further optimization. Many ab initio ground state density functional theory (DFT) calculations have been carried out in the past few years to study the electronic properties of TiS3 nanomaterials.30,39-41 Kang and coauthors showed that only b-TiS3 NRs has bandgap whose periodicity is along the b axis.30 Importantly, the direct bandgap is width-independent and such advantage does not strictly requires the shape and size of samples for devices fabrication because the most important and fundamental 6


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electronic structure of the materials remains. This favorable property is in contrast to graphene NRs whose bandgap shows strong dependence on the NRs widths.42,43 Iyikanat et al. have investigated the formation energy for several possible types of vacancies as well as their influence on the electronic structures of monolayer TiS3.41 The calculated results demonstrated that sulfur vacancy (S_v) is the most likely defect due to the lowest formation energy. Other types of vacancies induce metallic behavior of the material to different extent and should accelerate charge recombination. However, there are lack of quantum dynamics studies of nonradiative electron-hole recombination in TiS3 NRs despite such electron-phonon relaxation process is important of both fundamental science and realistic applications.

The substantial promise of the TiS3 NRs for SCs and optoelectronic applications, combined with the recent theoretical and experimental work,38,41 simulates us to study the fundamental mechanism of the electron-hole recombination in this material. To interpret the experimental data, provide a detailed understanding of the charge recombination in pristine TiS3 NRs and S_v systems, and eventually generate practical guidelines for enhancing SCs and optoelectronic performance, we perform ab initio time domain simulations to characterize the time scales and participating phonon modes for the electron-hole recombination.

Our simulations show that the nonradiative electron-hole recombination in pristine TiS3 NRs occurs on the time scale of tens of picoseconds which is over 10-fold slower than experimental data.38 By performing an atomistic simulation with a 7



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sulfur vacancy, which is a common defect in TiS3, demonstrates that the vacancy defect retards the charge recombination and achieves excellent agreement with the experiment. The nearest surface S atom to the vacancy binds with two Ti atoms and forms reconstructed bonds that remove unsaturated chemical bonds and create no deep trap states, which form the TiS3 valence band. As a result, the NRs highest occupied molecular orbital (HOMO) is lowered in energy, and the bandgap increases slightly. More importantly, sulfur vacancy decouples electron and hole wave functions overlap and decreases nonadiabatic (NA) coupling. The reduced NA electron-phonon coupling competes successfully to the long-lived quantum coherence time, suppressing electron-hole recombination. The simulated results suggest that one can control electron-hole recombination via surface chemistry engineering to realize high performance TiS3 SCs.

The NA molecular dynamics (NAMD) simulations employ the quantum-classical decoherence induced surface hopping (DISH)44 and implemented within the framework of time-dependent Kohn-Sham formulation.45 DISH is associated with the fewest switching surface hopping (FSSH) approach.46 The lighter and faster electrons are treated differently from heavier and slower nuclei. The former particles are described quantum mechanically and the latter particles are treated classically. DISH considers quantum decoherence into the quantum-classical approximation, capturing the physical mechanism of nuclei wave function branching for surface hops.44,47 Transitions of classical trajectories between electronic states take place in DISH at

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decoherence events. Decoherence is included in the calculation because it is significantly faster than the electron-hole recombination.38 To save the computational cost, the classical path approximation (CPA) is used. CPA is valid because the changes in the nuclear geometry upon photo-excitation are smaller than the amplitude of the thermally induced fluctuations in the nuclear coordinates, which is the case in the present study because TiS3 NRs are rigid and large. Promotion of a single electron to an excited state by absorption of light induces minor changes in the electronic density, and very minor changes in the nuclear geometry. The state-of-the-art real-time NAMD approach has been applied to study photoindued charge dynamics in a broad range of systems,5,48-54 including black phosphorus,49 black phosphorus/MoS2 interface,5 a polymer interfaced with a carbon nanotube50, and a metallic54 and semiconducting53 quantum dot, as well as water/perovskite,52 TiO2/quantum dot hybrids,48 and high-temperature cuprate superconductors.51 A detailed description of the theoretical approach can be found elsewhere.55,56

The structure of TiS3 bulk is a stack of layered sheets connected by van der Waals force. The one dimensional TiS3 NRs was constructed based on a (1×4×1) supercell and the periodicity is along b axis, which contains 48 atoms, Figure 1. The dangling bonds are saturated by hydrogen atoms to remove unphysical gap states. Subsequently, S_v cell is created via removal of the single sulfur atom labelled by purple color on the NRs, Figure 1, corresponding to 4.17% sulfur vacancy concentration. A 15 Å vacuum depth is added in the other two directions perpendicular to the periodic

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direction to eliminate spurious interactions. The Vienna ab initio simulation package (VASP)57 is used for geometry optimization, electronic structure calculations, and adiabatic MD. The simulations are performed with the Perdew-Burke-Ernzerhof (PBE) functional31 for electron exchange and correlation interactions, projector-augmented wave58 pseudopotentials for electron and ion cores interaction, and 400 eV plane-wave basis energy cutoff. A 1 × 11 × 1 Γ-centered k-point Monkhorst-Pack mesh is employed for geometry optimization and MD.59 To obtain accurate density of states, a much denser 1 × 50 × 1 Γ-centered k-point Monkhorst-Pack is used.59 After relaxing the geometry at 0 K, repeated velocity rescaling was used to bring the two systems temperatures to 300 K. Then, a 6 ps adiabatic MD trajectories are generated in the microcanonical ensemble with a 1 fs atomic time-step. To simulate the electron-hole recombination, 1000 initial conditions are selected randomly from the adiabatic MD trajectories for NAMD simulations.

Figure 1 shows the optimized pristine TiS3 NRs geometry at 0 K with (left panel of Figure 1a) and without (left panel of Figure 1b) sulfur vacancy and two corresponding snapshots taken from the adiabatic MD run (right panels of Figure 1a and 1b). The calculated formation energy of 0.86 eV for sulfur vacancy at 0 K suggests that such defect easily appears during sample synthesis, agreeing with previous DFT calculations in which sulfur vacancy is the most possible defect among other intrinsic common defects.41 A comparison of these four panels indicates that thermal fluctuations have a little influence on the system geometry because the TiS3

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NRs are rigid. The largest-scale motion is associated with tilt of the S-S bonds perpendicular to NRs periodic direction in the pristine TiS3 NRs, top and side views of Figure 1a. In the case of S_v system, the tilt motion becomes insignificant and negligible at both 0 K and room temperature, top and side views of Figure 1b. Importantly, the remaining S atom occurs reconstruction with the two binding Ti atoms that removes the unsaturated bonds. This situation has a significant impact on the electronic properties of TiS3 NRs and will be discussed below. The averaged bond lengths of the TiS3 NRs backbone in the pristine system are 2.279 Å at 0 k to 2.302Å at room temperature respectively, they become 2.277Å at 0 K and 2.293Å at ambient temperature in the S_v system. The observations are interesting because sulfur vacancy stabilizes the geometry and makes NRs more rigid compared to the pristine case.

Figure 1. Top and side views of H-saturated TiS3 nanoribbons (NRs) geometry at 0 K and 300 K. a) pristine TiS3 NRs; b) TiS3 NRs with S vacancy created by removing the sulfur atom colored in purple. 11



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In order to explore the physical origin of this observation, we compute the average magnitude of atomic fluctuations in pristine TiS3 NRs and S_v systems at 300 〉. Here, K, that is, the standard deviation of the position of atom i, = 〈 −〈 〉

means the location of atom i at time t, the angular bracket characterizes ensemble averaging. The standard deviation is positively correlated to the fluctuation. In the S_v system, the atoms are divided into two types: those around the S vacancy whose neighboring atoms contain five sulfur atoms and three titanium atoms and the rest of them. The computed data listed in Table 1 suggest that the S vacancy decreases the mobility of overall atoms by half compared to pristine system. In particular, the motions of the atoms around the S vacancy decrease more than half and the rest of other atoms follows. This quantitative analysis provides compelling evidence that the sulfur vacancy makes the TiS3 NRs more rigid and suppresses atomic vibrations at room temperature, decreasing electron-phonon coupling.

Table 1. Standard deviations of the atomic position in the pristine TiS3 NRs and S_v systems. Overall pristine

0.282

S_v

0.143

Atoms around the vacancy/rest

0.121/0.147

Figure 2 presents the projected density of states (PDOS) of the pristine TiS3 NRs and S_v systems, calculated using the optimized geometry at 0 K. The PDOS is 12


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separated into the contributions from Ti (black line), S (red line) and H (blue line). Figure 2 shows that the hydrogen atoms have no contribution to the highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) and they contribute to the DOS in higher energy, rationalizing that the use of hydrogen saturating dangling bonds in those systems is reasonable. LUMO and HOMO of the pristine TiS3 NRs are separated by an energy gap of 0.94 eV by canonical averaging over the 6 ps MD trajectory, Figure 2a. The calculated value is smaller than the experimental bandgap of 1.2 eV due to well-known DFT problem.60 Figure 2a shows that the HOMO is composed of titanium and sulfur orbitals, while the LUMO primarily originates from titanium orbitals. The LUMO and HOMO orbitals are important because they constitute the initial and final states for electron-hole recombination, whose charge densities are displayed in the inset of Figure 2a. The charge densities further provide a complementary clue that Ti/S hybridization orbitals contribute to the HOMO and the Ti orbitals primarily contribute to the LUMO. Both electron and hole wave functions are delocalized over the whole NRs. The more mixing of wave functions, the stronger NA electron-phonon coupling.

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Figure 2. The projected density of states (PDOS) of a) the pristine TiS3 NRs and b) S_v system. The Fermi level is set to zero. The insets show the corresponding charge density of the HOMO and LUMO.

Introduction of sulfur vacancy increases slightly the canonically averaged bandgap to 1.01 eV, Figure 2b, because removal of sulfur atom weakens the hybridization between Ti and S orbitals, pushing the HOMO downward. Importantly, sulfur vacancy does not generate deep trap states and the states mix well with the valence band manifold. This is because the reconstruction of the S atom and its binding with two Ti atoms create no unsaturated bonds. The inset of Figure 2b demonstrates that charge density of LUMO remains largely unchanged relative to pristine case. While it depletes on whole column of Ti atoms on the remaining sulfur atom side that decreases the interaction between initial and final states due to diminishing the electron and hole wave functions overlap. The situation favors a 14


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decrease in the NA coupling. The increased bandgap and decreased NA coupling of TiS3 NRs containing sulfur vacancy should suppress electron-hole recombination.

Thermal motions not only modulate the geometry, Figure 1, but also lead to the atomic vibration at their equilibrium positions. The magnitude of the energy fluctuations characterizes the strength of electron-vibrational interaction. Figure 3a shows the time evolution of the HOMO and LUMO energy levels for pristine TiS3 NRs and S_v systems. Both the HOMO and LUMO of the pristine TiS3 NRs show more notable fluctuations compared to S_v system, agreeing well the analysis of the averaged atomic motions (Table 1) and reflecting stronger electron-phonon coupling in the former case than the latter case. Contrary to the general cognition that defects increase electron-phonon coupling due to a more localized nature and generate high-frequency vibrations, such as defects in carbon nanotube,61 and hematite,62 sulfur vacancy in the TiS3 NRs decreases electron-phonon coupling because the defect maintains the HOMO and LUMO delocalized behavior largely unchanged. At the same time, defect increases the bandgap, resulting in the electronic and vibrational quanta far away from resonance. This behavior has been previously reported in phosphorene,49 graphane63 and graphene nanoribbons.64

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Figure 3. (a) Time evolution of the energy fluctuations of HOMO and LUMO for pristine TiS3 NRs (red line) and S_v (black line) systems at room temperature. (b) Fourier transforms of the autocorrelation functions of the fluctuations of HOMO-LUMO energy gap shown in the left panel. More strain in the S_v system makes the NRs more rigid and reduces energy levels fluctuations.

Fourier transforms of the autocorrelation function of the fluctuations of HOMO-LUMO energy gap characterizes the phonon modes that couple to electronic subsystem.

Electron-vibrational

interaction

leads

to

elastic

and

inelastic

electron-phonon scattering. Elastic scattering destroys the quantum coherence formed between

the

initial

and

final

states.

Inelastic

electron-phonon

scattering

accommodates the excess energy lost during nonradiative electron-hole recombination. Figure 3b shows the spectral density for the pristine TiS3 NRs and S_v systems. To be clear, the intensity of the phonon modes for pristine TiS3 NRs is scaled by half its original value. The dominant peak at 350 cm-1 in the pristine TiS3 NRs can be assigned to the out-of-plane S-Ti stretching mode at 370 cm-1.65 This mode modulates the NRs geometry, creates the strongest NA coupling, and causes fast dephasing. The side peaks at 150 cm-1 and 300 cm-1 can be attributed to the Raman-active A1g modes at ~176 and 298 cm-1, corresponding to the in-plane and out-of-plane vibrations

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respectively.66,67 The very high-frequency at 718 cm-1 can be seen as the second-order overtone of S-Ti stretching modes at 370 cm-1. This mode contributes to create the part of NA coupling due to reflecting fast nuclei motions. Introduction of sulfur vacancy does not create new vibrational modes, suggesting the system symmetry remains largely unchanged. The prominent mode shifts to 366 cm-1 and the magnitude of such peak reduces more than half compared to pristine system, leading to a weaker electron-phonon coupling and slower dephasing. The other frequencies seen in the spectral density of pristine system can be also found in the S_v system. These vibrations together with the major mode coupled to the electronic subsystem result in nonradiative electron-hole recombination. The decoherence known as pure-dephasing in the optical theory,68 can be calculated by the second order cumulant approximation. The pure-dephasing functions are shown in Figure 4. The time scales of pure-dephasing,, are obtained by fitting the data with a combination of a Gaussian and an exponent: =

−/ + 1 − −0.5/ % . Considering the strong

oscillations in the pure-dephasing function of the S_v system, the normalized cosine term was added. B and 1-B represent the magnitude of the exponential decay component and Gaussian component respectively. The pure-dephasing times defined by + 1 − are summarized in Table 2. The pure-dephasing time is equal to 5.2 and 45 fs for pristine TiS3 NRs and S_v systems. The factor of 9 increase in the pure-dephasing time for the S_v system arises from the reduction of intensity of the

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major phonon modes (Figure 3b) as well as slower atomic motions (Table 1). The elastic electron-phonon scattering is much faster than the inelastic quantum transition process that occurs over one hundred picoseconds.38 Therefore, a decoherence correction is necessitated using the employed NAMD algorithm to model the electron-hole recombination in the present two systems under investigation.

The unnormalized autocorrelation functions (un-ACF), inset of Figure 4, computed from the fluctuations of the HOMO–LUMO energy gap directly characterize pure-dephasing rate. The dephasing is fast if the electron-phonon coupling is strong, and if it arises from a broad range of phonon modes. The rate of ACF decays on similar time scales, because similar modes participate in both cases, Figure 3b. Therefore, the differences in the pure-dephasing times originate from the electron-phonon coupling strength. The strength of coupling to individual modes is reflected in the FT peak amplitudes and nuclei motions, Figure 3b and Table 1. Under the cumulant approximation, the pure-dephasing function is computed by integrating un-ACF. A smaller initial value of un-ACF leads to slower dephasing. As a result, S_v system shows longer-lived quantum coherent motion.

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Figure 4. Pure-dephasing function computed using the autocorrelation function of the fluctuations of the HOMO-LUMO energy gap. The inset shows the unnormalized autocorrelation function (Un-ACF). A smaller initial value leads to slower dephasing.

The electron-hole recombination occurs in pristine TiS3 NRs and S_v systems via nonradiative quantum transition from the LUMO to the HOMO and reflects inelastic electron-phonon scattering. To improve the SCs and optoelectronic devices performance, the nonradiative electron-hole recombination should be minimized to reduce electronic energy losses to heat during recombination process.

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Figure 5. Electron-hole recombination dynamics in pristine TSi3 NRs and S_v systems.

In the calculation, the canonically averaged bandgap of pristine TiS3 NRs is scaled to the experimental value of 1.20 eV60 via adding a constant. The same value is added to the bandgap of the S_v system assuming that DFT has an identical error for both systems. The time-evolution of the lowest excited state population is displayed in Figure 5. The recombination time scales, summarized in Table 2, are obtained by fitting the data with an exponent: & = exp−/ . They show that, on the one hand, electron-hole recombination occurs on tens of picoseconds and is over 10-fold faster than experimental data of 140 ps,38 and that, on the other hand, introduction of sulfur vacancy greatly extends excited state lifetime to 151 ps, achieving excellent agreement with experimental measured ones.

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The observed changes in the electron-hole recombination upon introduction of sulfur vacancy are rationalized by the magnitude of HOMO-LUMO energy gap, NA coupling, and pure-dephasing time, Table 2. The recombination rate is approximately linear in the energy gap based on energy gap law,69 is proportional to the NA coupling squared according to Fermi’s golden rule, depends subtly on the decoherence time which enters the rate expression in the form of the Franck-Condon factor.70 The energy gap difference between pristine TiS3 NRs and S_v systems is very small, around 0.07 eV and its influence on electron-hole recombination rate is insignificant in the present two systems. In turn, the strong NA coupling has major influence on the electron-hole recombination rate which competes successfully to the long-lived quantum coherence time, leading to slower charge recombination in TiS3 NRs containing sulfur vacancy.

Table 2. Average absolute NA coupling, Pure-Dephasing Time, Nonradiative electron-hole recombination Time for pristine TiS3 NRs and S_v system. NA coupling (meV)

Dephasi ng

Bandgap (eV)

Recombination (ps)

(fs) pristine

8.3

5.2

1.2

10.1

S_v

1.7

45

1.27

156

Decreasing the S vacancy concentration is expected to narrow bandgap and to reduce nonadiabatic coupling. The rate of decoherence increases due to increased 21



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atomic motions. In the limit of infinite low vacancy concentration, the recombination rate of TiS3 NRs containing S vacancy approaches to that of pristine system, because the role of vacancy becomes negligible. Increasing the S vacancy concentration forms double S vacancy (S_2v) via removing a second sulfur atom shown in the Figure S1 of the supporting information (SI). The smallest formation energy of double S vacancy is 4.06 eV when two neighboring S atoms are removed, Figure S1 and Table S1. This value agrees well with previous first-principle calculations41 and is fivefold larger than single vacancy, indicating that double S vacancy is very rare in the experimental samples. Once such double S vacancy forms, TiS3 NR exhibits metallic behavior and narrows its bandgap, shown by the calculated PDOS in the Figure S2 of the SI. At the same time, the rate of quantum decoherence decreases. Consequently, electron-hole recombination accelerates in TiS3 NR. Interestingly, theoretical calculations indicated that the bandgap of TiS3 NRs is independence of its width.30 Varying the NRs width does not change decoherence time because the kinds of atoms remain unchanged. In turn, NA coupling determines the overall the rate of electron-hole recombination. Particularly, widening the NRs width will reduce NA coupling due to wave function delocalize over a large simulation cell, the recombination slows down. On the contrary, narrowing the NRs width accelerates electron-hole recombination. In addition, the edge of TiS3 NRs is another factor to affect the rate of recombination because it significantly influences the electronic properties. NRs along b-direction is semiconductor that is under investigation in the present work. In contrast, NRs along a-direction show metallic behavior and 22


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accelerate recombination.

Similar to a single S vacancy in the TiS3 NRs, a single sulfur vacancy increases the bandgap of two-dimensional TiS3 nanosheet without creating deep gap state.41 The situation diminishes partially overlap between electron and hole wavefunctions, thus reducing NA electron-phonon coupling. The atomic vibrations are expected to be suppressed due to S vacancy stabilizing the system. The interplay of the three factors delays electron-hole recombination in pristine TiS3 nanosheet relative to the system containing S vacancy.

By performing ab initio time-domain simulations, we investigated the electron-hole recombination in the TiS3 NRs with and without sulfur vacancy at atomistic level and established the factors responsible for the slow recombination time reported experimentally. Because sulfur vacancies are common defects on the TiS3 NRs surface, we repeated the NAMD simulation with a sulfur vacancy defect. The obtained time scale achieves excellent agreement with experiment. Removing a sulfur atom lowers the NRs HOMO energy and decouples the electron and hole wave functions. As a result, the energy gap increased slightly and the NA coupling decreased significantly. The small reduction of bandgap has little influence on the electron-hole recombination rate. In turn, the reduced NA coupling competes successfully to the long-lived quantum coherence, slowing down electron-hole recombination. The study demonstrates the importance of sulfur vacancy in electron-hole recombination in TiS3 nanoribbons and advances our understanding that 23



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rational choice of defects is an effective way of control over charge recombination.

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website.

Possible two-atom-vacancy geometry and formation energy as well as the PDOS of the smallest formation energy TiS3 NRs containing double sulfur vacancy.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGEMENTS R. L. is grateful to the National Science Foundation of China, grant No. 21573022, the Recruitment Program of Global Youth Experts of China, the Beijing Normal University Startup Package, and the Fundamental Research Funds for the Central Universities. Z.H.Z acknowledges support of the China Postdoctoral Science Foundation (No. 2013M542343).

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