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Excited Electron Dynamics at Semiconductor-Molecule TypeII Heterojunction Interface: First-Principles Dynamics Simulation Lesheng Li, and Yosuke Kanai J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00436 • Publication Date (Web): 02 Apr 2016 Downloaded from http://pubs.acs.org on April 7, 2016

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The Journal of Physical Chemistry Letters

Excited Electron Dynamics at Semiconductor-Molecule Type-II Heterojunction Interface: First-Principles Dynamics Simulation Lesheng Li and Yosuke Kanai Department of Chemistry, University of North Carolina at Chapel Hill, NC 27599-3290

ABSTRACT: Excited electron dynamics at semiconductor-molecule interfaces is ubiquitous in various energy conversion technologies. However, a quantitative understanding of how molecular details influence the quantum dynamics of excited electrons remains a great scientific challenge because of the complex interplay of different processes with various time scales. Here, we employ first-principles electron dynamics simulations to investigate how molecular features govern the dynamics in a representative interface between the hydrogen-terminated Si(111) surface and a cyanidin molecule. Hot electron transfer to the chemisorbed molecule was observed, but was short-lived on the molecule. Interfacial electron transfer to the chemisorbed molecule was found to be largely decoupled from hot electron relaxation within the semiconductor surface. While the hot electron relaxation was found to take place on a time scale of several hundred femtoseconds, the subsequent interfacial electron transfer was slower by an order of magnitude. At the same time, this secondary process of picosecond electron transfer is comparable in time scale to typical electron trapping into defect states in the energy gap.

TOC Graphic

Understanding excited electron dynamics at a heterogeneous interface is central to various optical and electronic device applications.1-9 For instance, dynamics of highly excited electrons/holes (hot carriers) at such interfaces play an essential role in achieving high conversion efficiency in solar cells.7, 1011 In addition to the solar energy conversion application, hot carrier dynamics at a heterointerface is of great interest also for optoelectronic applications such as light emitting diodes.1214 For instance, tailoring the coverage and type of the molecular passivation on nanoparticle surfaces enables control over the fluorescence efficiency of the nanoparticles.15-16 Dynamics of excited electrons at the interface between a semiconductor material and adsorbed molecule is particularly important for photovoltaic (PV) and photo-electrochemical (PEC) devices that are based on the dye-sensitized solar cell

(DSSC) concept.1, 17-18 Within DSSCs, the electrons injected from the electronically excited adsorbate undergo several distinct processes in the semiconductor,19-20 including a rapid relaxation to the semiconductor conduction band minimum (CBM) and drift under the internal electric field. The excited electrons can also be trapped by localized electronic states below the CBM, which are often associated with surface defects. This could be further followed by a number of additional processes such as electron-hole recombination, interfacial electron transfer, and de-trapping. No matter the order of these dynamical processes, transfer of the injected electron back to the oxidized molecule (or to the electrolyte molecule) is of great concern in DSSCs, negatively impacting device performance.19, 21-22 This so-called back electron transfer (BET) is often described using an effective two-state model, symbolically denoted as Semiconductor(e-)-Molecule+→Semiconductor-Molecule. With TiO2 as the semiconductor material, BET is generally rate-limited by the intra-oxide hopping transport, and a very long time scale of microseconds has been reported.23-25 In some other cases, such as Sn-doped In2O3 nanoparticles (nanoITO), the electron transfer itself dominates the BET kinetics,25 exhibiting a rather slow time scale of nanoseconds.26 The interplay among various competing mechanisms involved in the BET remains poorly understood. At the same time, there are a number of ultrafast spectroscopy experiments on related interfaces. Lian and co-workers have demonstrated that interfacial electron transfer to the adsorbed molecules could be very fast for small PbS quantum dots (QDs) with diameters of ~3.6 nm (with the time scale of ~370 fs)27 and CdSe QDs with diameters of ~3 nm (with the time scale of ~60 fs)28. More recently, Okano et al. have inves-

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Figure 1. Interface structures of the H-Si(111):cyanidin interface in (a) monodentate and (b) bidentate adosrption modes, isosurface of the single-particle Kohn-Sham electronic wavefunction for the molecule’s LUMO is also shown at top. The spatial-resolved density of states (DOS) for the conduction band states of the (c) monodentate and (d) bidentate adsorption modes. The spatialresolved DOS is calculated by averaging electron density in the surface plane, and the silicon surface CBM is set to 0 eV as the reference energy.

tigated the excited electron dynamics at a CdS/CdTe Type-II heterojunction within individual nano-rods, which were synthesized by anion exchange in CdS nano-rods.29 Upon electronic excitation in the CdTe side, a majority of the hot electrons were found to relax to the CBM within several hundred femtoseconds. Essentially no hot electron transfer to the CdS side was observed. The interfacial electron transfer was found to take place after the hot electron relaxation on a time scale of 450 fs. These recent experimental observations pose the question of how fast the “intrinsic” interfacial electron transfer from the semiconductor to the adsorbed molecule is at a typical semiconductor-molecule interface. While significant advancements have been made for simulating hot carrier dynamics from firstprinciples theory in the last several years,20, 30-36 detail studies on elucidating hot carrier dynamics at semiconductormolecule interfaces remain scarce, partly due to the difficulties in describing their electronic structure accurately for such large systems.37 In this letter, using first-principles electron dynamics simulations, we show that the intrinsic electron transfer to the adsorbed molecule can be quite fast when no defects are present to trap the hot electron at the semiconductor surface. A representative semiconductor-molecule interface between a hydrogen-terminated Si(111) surface38 and a natural dye molecule cyanidin is considered in this work because the H-Si(111) semiconductor surface can be controllably synthesized with minimal defects.38 We considered a low surface coverage of approximately 11% in terms of the Si-H units (see Figure 1). To study the adsorption dependence, monodentate and bidentate adsorption modes were considered as shown in Figure 1(a, b). We employed a quantum dynamics simulation approach based on accurate electronic energy levels at the heterogeneous interface,39 by synergistically combining fewest switches surface hopping algorithm,40-41 G0W0 many-body perturbation theory calculation,42-44 and first-principles molecular dynamics45 (see Computational Methods section). Figure 1(c, d) shows the spatial-resolved density of states (DOS) for conduction band states in the surface normal direction (Z axis). The surface’s CBM is set to 0 eV as the reference energy, and the LUMO refers to the lowest unoccupied

Figure 2. Population change for the excited electron in (a) monodentate and (b) bidentate H-Si(111):cyanidin interface. Cyanidin’s LUMO is located energetically below the surface CBM (E=0 eV) for both adsorption modes.

Figure 3. Top: isosurface of the single-particle Kohn-Sham electronic wavefunction for the molecular state 87 (monodentate) and 88 (bidentate). Bottom: population change in the molecular state 87 (monodentate), state 88 (bidentate), and cyanidin LUMO.

electronic state with its spatial character only within the adsorbed cyanidin, which is assumed to be in the oxidized state. The oxidized state here represents the situation after an excited electron is injected from the adsorbed molecule. The LUMO state is located energetically lower than the CBM by 0.37 eV and 0.13 eV for the monodentate and bidentate adsorptions, respectively. We initiate the first-principles simulation by placing the excited electron in a high-lying silicon state (~3.6 eV above the CBM). The excited electron population change for an ensemble of atomic trajectories at room temperature is shown in Figure 2 as a function of time and average energy of electronic states for the H-Si(111):cyanidin interfaces. As can be seen in Figure 2, a non-negligible magnitude of hot electron transfer into a molecular state was observed. The accepting molecular states are quite high in energy at 2.3 eV and 2.4 eV above the CBM for mondentate and bidentate adsorptions, respectively. The states are indexed as 87 (mondentate) and 88 (bidentate) in Figure 2. We note here that, except for the


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Figure 4. Time-averaged non-adiabatic couplings (NACs) matrix of the unoccupied states (in atomic units) for (a) monodentate and (b) bidentate adsorption modes. The NACs for the cyanidin LUMO and molecular state 87/88 are shown for comparison in (c) monodentate and (d) bidentate. The state index of the cyanidin LUMO is set to 1 as the reference. NACs are particularly large close to the diagonal line.

LUMO, the state 87/88 is the only electronic state that is solely localized on the adsorbed cyanidin molecule. The transfer rate into these molecular states is quite fast even though they are spatially well localized within the molecule as shown in Figure 3. For these two molecular states, non-adiabatic couplings (NACs, which are often referred to also as vibronic couplings in literature) indicate significant coupling to some semiconductor states as shown in Figure 4. Despite the very fast transfer rate into the molecule, the resident time of the hot electron within the molecule is quite short, and fitting the population of the electronic states 87 and 88 to Gaussian curves gives full widths at half maximum of 80.64 fs and 58.08 fs for the monodentate and bidentate adsorptions, respectively (see Figure 3). The hot electron transfers back to the semiconductor without remaining in the molecule for an extended time. Consequently, the hot electron relaxation takes place almost entirely within the semiconductor. Appreciable transfer of the excited electron from the silicon surface to the chemisorbed cyanidin occurs only after the electron has relaxed near the bottom of the conduction band.

Figure 5. Population change in the cyanidin LUMO (blue), silicon states within 10 kBT above the surface CBM (red), and their subtotal (black) in the (a) monodentate and (b) bidentate adsorption modes.

As can be seen in Figure 4, the molecular LUMO does not show strong NACs to semiconductor states, and the electron transfer to the LUMO is rather gradual when compared to the hot electron transfer to states 87/88 as discussed above (see Figure 3). Beyond ~0.8 ps, the entire population can be accounted for in the semiconductor states within 10 kBT (~0.25 eV) above the CBM and the molecular LUMO as shown in the left panel of Figure 5. This allows us to employ an effective two-state kinetic model between the semiconductor and the chemisorbed molecule to efficiently describe the dynamics at longer time scales. This is convenient especially since firstprinciples simulation of the electron dynamics is computationally very demanding and currently not practical for more than several picoseconds. The right panel of Figure 5 shows the population change according to the two-state kinetic model for time beyond 1 ps. The shaded regions indicate an uncertainty that stems from fitting the model to the first-principles simulation data for obtaining the rate constant. The time constants for the interfacial electron transfer were found to be 5.56 ps and 2.44 ps for the monodentate and bidentate adsorptions, respectively. For the electron population in the cyanidin LUMO to reach the equilibrium Boltzmann distribution for the monodentate and bidentate cases, it takes approximately 37.7 ps and 16.7 ps, respectively. Our simulation predicts a typical intra-band relaxation time of several hundred femtoseconds, and the interfacial electron transfer to the adsorbed molecule’s LUMO is largely decoupled from the relaxation process. A similar finding was also reported by Okano et al. for “ideal” CdS/CdTe Type-II heterojunction interfaces that are formed within individual nanomaterials.29 In their study, the interfacial electron transfer was observed to take place subsequently after the hot carrier relaxation of several hundred femtoseconds, and the interfacial electron transfer itself was characterized with a time scale of 450 fs. In the present work on the H-Si(111):cyanidin semiconductor-molecule interface, the interfacial electron transfer rate is found to be a few picoseconds. This transfer rate is approximately an order of magnitude slower than the rates observed experimentally at PbS QD-methylene blue (~370 fs) and CdSe QD-methyl viologen (~60 fs) interfaces by Lian and co-workers.27-28 At the same time, the picoseconds transfer rate in the present work is much faster than the nano- to microseconds time scales that are typically reported experimentally for oxide-molecule interfaces.23-25 Such an enormous difference is



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indicative of additional processes in those experiments at oxide-molecule interfaces that are outside of the two-state model description. Given the defective nature of typical oxide materials, defect-induced electronic states might trap the excited electron rapidly below the conduction band. We indeed observe that trapping of the excited electron by a defect state can be very fast when we include a missing hydrogen danglingbond defect at the H-Si(111) surface in our simulation. Our simulation shows that this process takes place on the time scale of a few picoseconds (see Figure S8 in Supporting Information). In conclusion, our work shows that, the interfacial electron transfer from semiconductor to the adsorbed molecule is largely decoupled from the fast hot electron relaxation process at a representative semiconductor-molecule Type-II interface between H-Si(111) surface and cyanidin molecule. Similar to QD-molecule interfaces,27-28 we found that the interfacial electron transfer is quite fast with a time constant of a few picoseconds. However, the corresponding time scale is much shorter than the typical time scales reported for back electron transfer (BET) between a semiconductor and a molecule in the case of oxide materials.23-25 These findings point to the importance of excited electron trapping by defect-induced states below the conduction band for understanding the overall BET mechanism for oxide materials. Our future work will focus on how different types of defects play an important role in oxide materials. How electron transfer among adsorbed molecules might influence the resident time of hot electron transfer in the molecule is another interesting question for a future study.

COMPUTATIONAL METHODS Fewest-switches surface hopping (FSSH) simulation21, 40-41, was perfomed in the single-particle description within the so-called classical path approximation (CPA) as formualted by Prezhdo and co-workers.20-21 The CPA assumes a classical equilibrium path that is representative of the system’s nuclei at all times and surface hops do not significantly influence the nuclear dynamics. The validity of CPA in the context of this work is discuused in Section S6 in Supporting Information. In the single-particle FSSH approach, the instantaneous probability for transition from state to state in time Δ is governed by 2 = − 2 Δ/ ℏ where is the density matrix for the excited electron and is the non-adiabatic coupling (NAC) matrix. is the effective single-particle Hamiltonian matrix for the excited electron. The probability for a stochastic hop from state to state is given by → = max 0, "→ 46

and

&' %&( $% +

) * ,- . > . "→ = # 1 ,- . ≤ .

where εk,j are the quasi-particle energies for satisfying the details balance. Time evolution of the density matrix for excited electron, 2 = |4 564 |, is given by Liouville-von Neumann equation

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7 = 8, 9 − ,ℏ8, 9 7 The second term on the right hand side arises because the electronic state depends on the (time-dependent) positions of classical nuclei. In the adiabatic basis, the time evolution of the density matrix elements are ,ℏ

,ℏ: ; = ;= − ,ℏ;= = − ;= .= >= − ,ℏ= 9 ;

where .= is the single-particle energies of state l, and ;= is the NAC matrix element between state i and l. The single-particle energies and NACs are the two essential ingredients in this apporach, and they are obtained from first-principles quantummechanical calculations as follows. (1). NAC matrix is calculated using 7 ; = ?@; A∇C A@ D ∙ 7 = F@; G

H

HI

G@ J

We implemented the numerical calculation of NACs using the time derivative by enforcing the phase continuity as in Ref. 47-48. NACs can be calculated efficiently on-the-fly within first-principles molecular dynamics (FPMD) simulation. We follow the prescription by Hammes-Schiffer and Tully for calculating the NACs numerically, from the Kohn-Sham (KS) adiabatic wavefunctions at adjacent time steps.49 We found that the time step of 0.48 fs in the FPMD is sufficient to accurately compute the NACs as discussed in Section S2 in Supporting Information. Generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE)50 was used for the exchange-correlation potential, and the KS states were expanded in a plane wave basis using norm-conserving pseudopotentials51 with kinetic energy cutoff of 50 Ry. The FPMD simulations were performed with the Qbox code52 for 2 ps at 295 K. (2). Single-particle energy level alignment at the semiconductor-molecule interfaces was modeled using quasiparticle (QP) energies within G0W0 approximation. QP energies were obtained from .; = .;KL + N1 − F@; O

HPQ HQ

G

QR&S

O@; JT

%U

∙

6@; |ΣW, W X ; .; − Z[\ W >W − W′ |@; 5

where .;KL is the KS energies from FPMD simulations and Σ is the self-energy, the second term represents the many-body correction using the KS wavefunctions, ψi, at the equilibirum geometry (details see Section S4 in Supporting Information). Quantum Espresso code53 was used to obtain the KS wavefunctions. The many-body corrections were calculated using many-body perturbation theory within the “one-shot” G0W0 approximation,44 starting from PBE KS wavefunctions and eigenvalues within random phase approximation. The G0W0 calculations were performed using Yambo code,54 where Godby-Needs plasmon-pole model55-56 was used in calculating the dielectric function. Convergence tests on various parameters were performed and discussed in Section S3 in Supporting Information. Because of the very high computational cost associated, the many-body corrections were calculated for all electronic states only once at the equilibrium structure. The same (time-independent) many-body corrections were used to correct individual time-dependent KS energies from the


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FPMD simulation as discussed above. We verified the validity of this strategy by calculating the many-body corrections using a random structure from the FPMD trajectory to compare with the ones for the equilibrium structure as discussed in Section S4 in Supporting information. In order to take into account the ordering changes of the electronic states due to the nuclear motions, the state index is updated throughout the FPMD trajectory. The FSSH simulation was then performed within the CPA approximation as discussed above. This allows us to use a large number of nuclear trajectories for converging the ensemble-averaged quantities because the nuclear trajectories do not depend on the hops within the CPA. 2116 nuclear trajectories were generated from the FPMD simulation, and each of these 1 ps-long trajectories start with different positions/momenta of the FPMD simulaiton. 500 FSSH simulations were then performed for each nuclear trajectory, converging the sampling of hopping probability distribution using the Monte Carlo method (see Section S5 in Supporting Information).

ASSOCIATED CONTENT Supporting Information Available: Surface slab models, FPMD simulations, convergence tests of G0W0 calculations, convergence of nuclear trajectory ensemble, assessment of classical path approximation.

AUTHOR INFORMATION Corresponding Author * Author to whom correspondence should be addressed: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The work was wholly funded by the UNC Energy Frontier Research Center (EFRC) “Center for Solar Fuels”, an EFRC funded by the U.S. Department of Energy, Office of Science, Office of Basis Energy Sciences, under Award DE-SC0001011. We thank National Energy Research Computing Center, which is supported by the Office of Science of the U.S. Department Energy under Contract No. DEAC02-05CH11231 for computational resources.

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Figure 1. Interface structures of the H-Si(111):cyanidin interface in (a) monodentate and (b) bidentate adosrption modes, isosurface of the single-particle Kohn-Sham electronic wavefunction for the molecule’s LUMO is also shown at top. The spatial-resolved density of states (DOS) for the conduction band states of the (c) monodentate and (d) bidentate adsorption modes. The spatial-resolved DOS is calculated by averaging electron density in the surface plane, and the silicon surface CBM is set to 0 eV as the reference energy.


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Figure 2. Population change for the excited electron in (a) mono-dentate and (b) bidentate HSi(111):cyanidin interface. Cyanidin’s LUMO is located energetically below the surface CBM (E=0 eV) for both adsorption modes.



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Figure 3. Top: isosurface of the single-particle Kohn-Sham electronic wavefunction for the molecular state 87 (monodentate) and 88 (bidentate). Bottom: population change in the molecular state 87 (monodentate), state 88 (bidentate), and cyanidin LUMO.


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Figure 4. Time-averaged non-adiabatic couplings (NACs) matrix of the unoccupied states (in atomic units) for (a) monodentate and (b) bidentate adsorption modes. The NACs for the cyanidin LUMO and molecular state 87/88 are shown for comparison in (c) monodentate and (d) bidentate. The state index of the cyanidin LUMO is set to 1 as the reference. NACs are particularly large close to the diagonal line.



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Figure 5. Population change in the cyanidin LUMO (blue), silicon states within 10 kBT above the surface CBM (red), and their sub-total (black) in the (a) monodentate and (b) bidentate adsorption modes.


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