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Role of Surface Termination on Hot Electron Relaxation in Silicon Quantum Dots: A First Principles Dynamics Simulation Study Kyle Gregory Reeves, Andre Schleife, Alfredo Correa, and Yosuke Kanai Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b01707 • Publication Date (Web): 02 Sep 2015 Downloaded from http://pubs.acs.org on September 3, 2015
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Nano Letters
Role of Surface Termination on Hot Electron Relaxation in Silicon Quantum Dots: A First Principles Dynamics Simulation Study
Kyle G. Reeves1, Andre Schleife2, Alfredo A. Correa3, and Yosuke Kanai1,* 1. Department of Chemistry, University of North Carolina at Chapel Hill 2. Department of Materials Science and Engineering, University of Illinois at Urbana Champaign 3. Condensed Matter and Materials Division, Lawrence Livermore National Laboratory
Abstract: The role of surface termination on phonon-mediated relaxation of an excited electron in quantum dots was investigated using first-principles simulations. The surface terminations of a silicon quantum dot with hydrogen and fluorine atoms lead to distinctively different relaxation behaviors, and the fluorine termination shows a non-trivial relaxation process. The quantum confined electronic states are significantly affected by the surface of the quantum dot, and we find that a particular electronic state dictates the relaxation behavior through its infrequent coupling to neighboring electronic states. Dynamical fluctuation of this electronic state results in a slow shuttling behavior within the manifold of unoccupied electronic states, controlling the overall dynamics of the excited electron with its characteristic frequency of this shuttling behavior. The present work revealed a unique role of surface termination, dictating the hot electron relaxation process in quantum-confined systems in the way that has not been considered previously. Keywords: fewest switches surface hopping, quantum dots, electron relaxation, silicon, surface passivation
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Controlling phonon-mediated relaxation process of hot carriers (i.e. excited electrons and holes) in low dimensional materials is of great interest for realizing various advanced future technologies. For example, hot-carrier relaxation must be slow in hot carrier solar cells in order to extract the carriers into the electrode before they have time to relax to the band edge. The carrier relaxation rate is the dominant factor leading to the thermodynamic efficiency limit of ~32% in a single junction solar cells as calculated by Shockley-Queisser,1 and any practical demonstration of hot carrier solar cells will represent a truly game-changing advancement. On the other hand, fast relaxation of hot electrons and holes is important for quantum-dot light emitting diodes. In these systems, carriers must relax quickly to the band edges in order to generate narrower emission peaks centered around the energy gap, a property that can be controlled by the quantum dot size2-4. Unlike for conventional bulk materials, the use of nano-materials is particularly promising because various optical and electronic properties can be tuned through controlling structural features such as the size, surface termination, etc. In the context of the phonon bottleneck in nano-material, various physical phenomena such as quantum Zeno effects5, inverse Auger processes6, 7 as well as structural factors such as ligand traps8-10 have been discussed in the literature as being responsible for the slow hot carrier relaxation. Although large numbers of experiments have investigated the hot carrier relaxation processes using ultrafast pump-probe spectroscopy, a quantitative understanding of the extent to which the relaxation process depends on these various factors is still absent. One challenge associated with studying lowdimensional materials comes from the sensitivity of their properties to minor structural modifications (i.e. modifying one structural detail often changes more than one specific physical property). For instance, changing surface ligands of a quantum dot would not only change surface electronic states, but could influence the electronic structure of the entire quantum dot.11 A systematic computational investigation based on first-principles theory would be of great use in developing a predictive understanding of how changes at the atomistic level influence a system’s carrier relaxation dynamics. In recent years, Prezhdo and co-workers have made important progress by employing a surface hopping stochastic simulation method in the context of single-particle KohnSham electronic states of density functional theory.12-17 In order to investigate the role of the surface termination on the
Figure 1. The optimized geometry of the silicon quantum dots. Both Si66H40 and Si66F40 have a diameter of approximately 1.5 nm.
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Figure 2. Population change with an excited electron initially occupying a state that is located ~1 eV above th LUMO (18 state above LUMO), shown in (a) energyrepresentation and (b) state-representation for hydrogenpassivated and fluorine-passsivated SiQDs. Energy axis shows the eigenvalues that are averaged for a specific state over the length of the first-principles molecular dynamics simulations.
phonon-induced hot electron relaxation, we implemented and employed this computational approach (see Theoretical Methodology section), and we consider here a small, welldefined silicon quantum dot with two different surface passivating layers: one exclusively hydrogen atoms and the other exclusively fluorine atoms. We observe that the electronic structure is significantly altered by the surface termination in small quantum dots. We uncovered that a unique, hot-electron relaxation mechanism is operative in the case of the fluorine terminated quantum dot because there exists a particular electronic state that shuttles hot electrons between two electronic state manifolds of higher and lower energies. The silicon quantum dots (QD) we investigated in this work are shown in Figure 1. Both Si66H40 and Si66F40 QDs have a diameter of approximately 1.5 nm. These sizes are representative of the smallest silicon quantum dots that are well characterized in experiments.18,19 All silicon dangling bonds are terminated with either H or F atoms, and no localized electronic states are present at surface in these QDs. Using the first-principles surface hopping simulation approach described in Theoretical Methodology section, we investigated how an excited electron relaxes in the manifold of the singleparticle electronic states above the LUMO for a thermal ensemble of the quantum dots. Each of these electronic states corresponds to a particular Kohn-Sham (KS) single-particle state. The hot-electron relaxation can therefore be analyzed either in terms of the electronic state’s average energy or its index. The energy representation allows us to follow the dynamics of the hot electron as it relaxes through the manifold of unoccupied states to the LUMO. At a specific energy, the total population may come predominantly from a single electronic state or from several electronic states due to the quasi-degeneracy. Alternatively, quantifying the hot electron relaxation process in terms of the electronic state index is convenient for analyzing the relaxation mechanism. Figure 2 shows a hot-electron relaxation process in these two representations; the relaxation starts from a selected electronic
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H-SiQD
F-SiQD
Figure 3. Population change for hydrogen and fluorine-passivated SiQDs, starting from different initial states between ~0.5 eV and ~1.3 eV above the LUMO. The white horizontal line indicates the initial state.
Figure 4. Distributions of non-adiabatic couplings (NAC) for different electronic states and with adjacent electronic states in F-SiQD (state index of ± 1 change).
Figure 5. Distribution of non-adiabatic coupling (NAC) for electronic states with other electronic states that fall within four states above or below, for F-SiQD. The NAC for ES11 are shown as red dots. An inverse relationship fit to Equation 1 is shown in blue.
illustrative cases in Figure 3. For H-SiQD, the relaxation behavior is consistent for all initial states studied, and each simulation exhibits a characteristic, continuous relaxation within the conduction band. In the F-SiQD case, however, the population change is similar to the H-SiQD only in cases when the initially occupied electronic state fall within ~0.5 eV above the LUMO. The distinctively unique population decay behavior appears when the hot electron initially occupies any electronic state that is higher in energy than the 11th unoccupied electronic state above the LUMO (ES11), which lies roughly 0.75 eV above the LUMO. The important observation here is that these two QDs exhibit drastically different hot electron relaxation behaviors despite there being no surface states or molecular states from the ligands. To better understand this unique behavior, we investigate the non-adiabatic coupling (NAC) between different electronic states, a quantity that describes how well the motion of the nuclei mediates the coupling between the electronic states. This is the key ingredient that dictates the relaxation of a hot electron when there are no crossings of the electronic states as in this work. The non-adiabatic coupling between two electronic states j and k can be expressed in terms of the energy difference as
state (ES18) that is located approximately 1 eV above the LUMO for both the hydrogen- and fluorine-terminated silicon QDs. The population with the hot electron at specific energies (or in a specific electronic state) is plotted as a function of time. In spite of their structural similarity between the two QDs, the relaxation behaviors of the hot electron differ considerably between the fluorine-terminated silicon QD (FSiQD) and the hydrogen-terminated silicon QD (H-SiQD). While the population decay appears rather monotonic for the H-SiQD, the decay behavior for the F-SiQD deviates significantly from that of a simple electron relaxation through the conduction band manifold. Figure 2 shows that in the case of H-SiQD the entire hot electron population relaxes close to LUMO within approximately 400 fs whereas in the F-SiQD, a significant population remains as a hot electron for an extended period (~700 fs). The hot electron relaxation appears bottlenecked by a particular transition between some select electronic states. The dependence of this unique relaxation behavior on the initial state of the hot electron is shown in Figure 3, where the state index representation is used for analyzing this non-intuitive result. We considered all electronic states that are within 2.0 eV above LUMO as the initially-populated electronic state, and include several ACS Paragon Plus Environment
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Figure 8. Two perspectives of the same isosurface plot for ES11 in the F-SiQD system showing high tetrahedral symmetry. Here we plot only the isosurface for the initial geometry of F-SiQD. Figure 6. The energy differences between adjacent states for the F-SiQD during the simulation (left), and it is also expressed as histograms (right). The top plots show the behavior of nearby electronic states of ES11 while the bottom plots show behavior of ES11 itself.
j ∇ R Hˆ k & d jk = j ∇ R k ⋅ R& = ⋅R εk − ε j
(1)
where H is the Kohn-Sham Hamiltonian, εk is the eigenvalue for electronic state k, and ܴሶ is the time derivative of the nuclei positions. Thus, NACs are usually of significant magnitude for the states that are energetically close. We found that the distribution of NACs for ES11 state with its energetically adjacent states (ES10 and ES12) is more tightly distributed around zero as compared to other electronic states (Figure 4). A comparison to the more homogeneous distribution of NACs in the case of H-SiQD can be found in the Supporting Information. Figure 5 shows the distribution of NAC as a function of the energy difference. The observed distribution follows roughly an inverse function, and it indicates that the energy differences play the central role in determining the magnitude of the coupling and the numerator in Eq. (1) plays a rather minor role. This observation allows us to discuss the unique hot electron relaxation behavior in the F-SiQD in terms of the physically intuitive electronic energy differences. Figure 6 shows the dynamical fluctuation of energy
Figure 7. Fourier transforms of the energy differences (Figure 6) between adjacent electronic states for F-SiQD (left) and H-SiQD (right) systems.
differences for ES11 state with its energetically adjacent states in comparison to other nearby electronic states. Unlike for the other electronic states, the energy differences fluctuate much more significantly for ES11 state, and the distribution results in a large variance. We note, however, that ES11 is not energetically isolated from other electronic states in the static density of states of the equilibrium structure (see Figure S1 in Supporting Information). Fourier transform of these dynamical energy differences shows strong peaks at 48 THz (Figure 7), corresponding to the infrequent narrowing of the energy differences for ES11 state with ES12 and ES10. Such strong peaks are not observed for the H-SiQD. In the first-principles molecular dynamics simulations, the fluctuating geometry of the F-SiQD shows that the ES11 wave function frequently becomes highly tetrahedral in symmetry as shown in Figure 8. We do not observe any such highly-symmetric state in HSiQD for the electronic states considered in this work. Comparison of the Fourier transform of the energy fluctuation of the ES11 state to phonon spectrum21 reveals that the ES11 state is coupled to several phonon modes in addition to the prominent peak around 800cm-1 for F-SiQD.. The 800cm-1 is associated with the Si-F bond motion, and as such no corresponding peaks are observed for H-SiQD (see Figure S2 and S3 in Supporting Information). These observations lead to the following qualitative picture of the unique hot electron relaxation behavior in the FSiQD. Initially, the hot electron relaxes though the conduction band states until it reaches ES12 state. The energy differences for ES12-ES11 and ES11-ES10 show a significant dependence on the nuclei dynamics, and they remain quite large throughout most of the simulation (Fig. 6). As ES11 state oscillates between the adjacent electronic states (ES12 and
Figure 9. Population decay with different initially-occupied electronic states. The rate was obtained by fitting to a single exponential function.
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ES10), the non-adiabatic coupling infrequently becomes large enough to allow for the electron to efficiently hop between the electronic states. This occurs with a frequency of approximately 4~8THz, which corresponds to a shuttling rate of 125~250 fs. Indeed, a much greater lifetime was observed for the initial state population when the excited electron occupies either ES12 or ES11 states (Figure 9) because ES11 energy must dynamically fluctuate for the hot electron to hop to the lower state with significant probability. The electronic structure of a quantum dot varies greatly with its size, and its surface often dictates important optical and electronic properties of nano-materials. In this work we investigated how the hot electron relaxation through the conduction band states is influenced by the surface termination in silicon quantum dots with hydrogen and fluorine atoms using first principles theory. We show that the surface termination plays an important role in the relaxation process but not because the hot electron is trapped by the electronic states in the molecular ligands or by localized surface states as is often discussed in the literature. Weiss and co-workers have stressed importance of “strong coupling” regime where the opto-electronic properties are significantly modified, based on their experimental measurements.8, 11, 22, 23 Our first-principles theory work shows that such a paradigm significantly effects the hot electron relaxation in quantum dots. A detailed analysis revealed that the fluorine termination causes a particular electronic state to act as a bottleneck in the continuous electron relaxation through the conduction band manifold. The dynamical fluctuation of this particular electronic state is coupled to a specific phonon mode at the surface of the quantum dot. The characteristic frequency at which this electronic state approaches its adjacent electronic states ultimately controls the hot electron relaxation behavior. The present work revealed a unique role of surface termination, dictating the hot electron relaxation process in the way that has not previously been considered in quantumconfined systems.
Theoretical Methodology
dynamics (FPMD) simulation. We follow the prescription by Hammes-Schiffer and Tully in calculating the NAC numerically from the KS wavefunctions at adjacent time steps.28 We tested and found the time step of 0.5 fs in the FPMD is sufficient to accurately compute the NACs (See Figure S8 in Supporting Information). The generalized gradient approximation of Perdew-Burke-Ernzerhof29 was used for exchange-correlation potential, and KS wavefunctions are expanded in a planewave basis with kinetic energy cutoff of 50 Ry. The FPMD simulations were performed with the Qbox code30 at 295 K for 1.25 ps for the two silicon quantum dots of ~1.5 nm with hydrogen and fluorine surface termination as shown in Figure 1. Using a 1 ps window of the NAC generated in the FPMD simulations, the surface hopping dynamics simulations were performed. From this FPMD, a set of 500 trajectories with different initial conditions was sampled and 500 FSSH calculations were performed for each trajectory, generating an ensemble of 250,000 unique surface hopping dynamics runs used to obtain the converged results (see Figure S7 in Supporting Information). Each surface hopping simulation starts with a single KS state populated by the excited electron. A total of 80 unoccupied KS states, covering approximately 3 eV above LUMO, is considered in this work. While trivial and avoided crossings may both exist between electronic states over time,20 we do not observe trivial crossings in our simulations of SiQDs, which are rather homogeneous (see Figures S4 and S5 in Supporting Information).
Associated Content Supporting Information Density of states, power spectra, electronic structure isosurfaces, eigenvalue fluctuations, distribution of NAC, and atomic coordinates. This material is available free of charge via the Internet at http://pubs.acs.org.
Author Information
In order to investigate the hot electron relaxation in the silicon Corresponding Author quantum dots, we follow the computational approach *E-mail:
[email protected] proposed by Prezhdo and co-workers in combining fewestNotes switch surface hopping (FSSH) algorithm by Tully24, 25 and The authors declare no competing financial interest. Kohn-Sham (KS) single-particle description within the socalled classical path approximation (CPA). The CPA assumes Acknowledgements a classical equilibrium path that is representative of the system’s nuclei at all times and surface hops do not We would like to thank Oleg V. Prezhdo and Amanda J. significantly influence the nuclear dynamics.26 The use of the Neukirch for insightful discussions on the surface hopping FSSH algorithm was motivated in part by its ability to satisfy methodology. This material is based upon work supported by detailed balance.25 Time-independent, adiabatic KS singlethe National Science Foundation under Grant No. DGEparticle states are used as the basis in describing the time1144081. dependent dynamics of an excited electron for an ensemble of the system. A probabilistic description for the ensemble is References necessary because the electron dynamics is coupled to the nuclei movement. This approach allows us to describe the relaxation of a single excited electron within the conduction 1. Shockley, W.; Queisser, H. J. J. Appl. Phys. 1961, 32, band manifold as we are interested in this work. Non-adiabatic 510-519. couplings (NAC) calculation is an essential ingredient in the 2. Soloviev, V. N.; Eichhofer, A.; Fenske, D.; Banin, U. single-particle FSSH approach. We implemented the J. Am. Chem. Soc. 2000, 122, 2673-2674. numerical calculation of NAC by enforcing the phase 3. Banin, U.; Cao, Y. W.; Katz, D.; Millo, O. Nature continuity as in Ref. 27 so that NAC can be calculated 1999, 400, 542-544. efficiently on-the-fly using first-principles molecular 4. Alivisatos, A. P. Science 1996, 271, 933-937. ACS Paragon Plus Environment
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5. Kilina, S. V.; Neukirch, A. J.; Habenicht, B. F.; Kilin, D. S.; Prezhdo, O. V. Phys. Rev. Lett. 2013, 110, 180404180411. 6. Chen, Y.; Vela, J.; Htoon, H.; Casson, J. L.; Werder, D. J.; Bussian, D. A.; Klimov, V. I.; Hollingsworth, J. A. J. Am. Chem. Soc. 2008, 130, 5026-5027. 7. Califano, M.; Zunger, A.; Franceschetti, A. Nano Lett. 2004, 4, 525-531. 8. Malicki, M.; Knowles, K. E.; Weiss, E. A. Chem. Commun. 2013, 49, 4400-4402. 9. Kilina, S.; Velizhanin, K. A.; Ivanov, S.; Prezhdo, O. V.; Tretiak, S. ACS nano 2012, 6, 6515-6524. 10. Guyot-Sionnest, P.; Wehrenberg, B.; Yu, D. J. Chem. Phys. 2005, 123, 074709. 11. Frederick, M. T.; Amin, V. A.; Weiss, E. A. J. Phys. Chem. Lett. 2013, 4, 634-640. 12. Fischer, S. A.; Habenicht, B. F.; Madrid, A. B.; Duncan, W. R.; Prezhdo, O. V. J. Chem. Phys. 2011, 134, 024102. 13. Neukirch, A. J.; Guo, Z. Y.; Prezhdo, O. V. J. Phys. Chem. C 2012, 116, 15034-15040. 14. Fischer, S. A.; Duncan, W. R.; Prezhdo, O. V. J. Am. Chem. Soc. 2009, 131, 15483-15491. 15. Long, R.; Prezhdo, O. V. J. Am. Chem. Soc. 2011, 133, 19240-19249. 16. Nelson, T. R.; Prezhdo, O. V. J. Am. Chem. Soc. 2013, 135, 3702-3710. 17. Craig, C. F.; Duncan, W. R.; Prezhdo, O. V. Phys. Rev. Lett. 2005, 95, 163001. 18. Cheng, C.-H.; Lien, Y.-C.; Wu, C.-L.; Lin, G.-R. Opt. Express 2013, 21, 391-403. 19. Wolkin, M. V.; Jorne, J.; Fauchet, P. M.; Allan, G.; Delerue, C. Phys. Rev. Lett. 1999, 82, 197-200. 20. Wang, L.; Prezhdo, O. V. J. Phys. Chem. Lett. 2014, 5, 713-719. 21. Habenicht, B. F.; Kilina, S. V.; Prezhdo, O. V. Pure Appl. Chem. 2008, 80, 1433-1448. 22. Jin, S. Y.; Harris, R. D.; Lau, B.; Aruda, K. O.; Amin, V. A.; Weiss, E. A. Nano Lett. 2014, 14, 5323-5328. 23. Peterson, M. D.; Cass, L. C.; Harris, R. D.; Edme, K.; Sung, K.; Weiss, E. A. Annu. Rev. Phys. Chem. 2014, 65, 317339. 24. Tully, J. C. J. Chem. Phys. 1990, 93, 1061-1071. 25. Parandekar, P. V.; Tully, J. C. J. Chem. Phys. 2005, 122, 094102. 26. Prezhdo, O. V.; Duncan, W. R.; Prezhdo, V. V. Prog. Surf. Sci. 2009, 84, 30-68. 27. Hu, C. P.; Sugino, O.; Hirai, H.; Tateyama, Y. Phys. Rev. A: At., Mol., Opt. Phys. 2010, 82, 062508-062516. 28. Hammes-Schiffer, S.; Tully, J. C. J. Chem. Phys. 1994, 101, 4657-4667. 29. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865-3868. 30. Gygi, F. IBM J. Res. Dev. 2008, 52, 137-144.
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