Non-Radiative Electron-Hole Recombination in Silicon Clusters: Ab Initio Non-Adiabatic Molecular Dynamics Jin Liu, † Amanda J. Neukirch, ‡ and Oleg V. Prezhdo* ,§ † Departments of Chemical Engineering, ‡ Physics and Astronomy, and § Chemistry, University of Rochester, Rochester, New York 14627, United States ABSTRACT: Silicon clusters hold exciting potential for optoelectronic and solar energy applications by yielding strong and tunable visible absorption and luminescence. Nonradiative relaxation of excitons induced by electron- phonon interactions is detrimental to these applications. We combine nonadiabatic molecular dynamics (NAMD) with time-domain density functional theory to study electron-hole recombination in Si n clusters (n = 5-10, 15). The recombination is much faster in clusters than in bulk Si due to enhanced electron-phonon coupling and transition from indirect to direct bandgap. By applying quantum-classical NAMD, we investigated the importance of the decoherence correction in determining the nonradiative lifetime. The recombination rates decrease by an order of magnitude due to decoherence, bringing the calculations in close agreement with experiment. We interpreted the results of the atomistic simulations analytically using Fermi’s golden rule, rationalizing the dependence of the relaxation rate on the electron-phonon coupling and temperature. The electron-hole recombination time is roughly independent of the size of these small clusters, with Si 5 and Si 7 exhibiting longer lifetimes due to enhanced stability to thermal fluctuations. 1. INTRODUCTION Quantum confinement in nanocrystals imparts novel electronic properties and leads to a variety of applications, including solar cells, 1-3 light-emitting diodes, 4,5 field-effect transistors, 6 and biosensors. 7 Tunable bandgaps, enhanced exciton lifetimes and multiple exciton generation in quantum dots (QDs) are favorable for photovoltaics and photocatalysis, as the research on CdTe, 8 CdSe, 9 PbSe, 10,11 PbS, 12 and InAs 13 QDs has shown. Strong and tunable radiative emission motivates development of light-emitting diodes and related devices. 4,5 A thorough experimental and theoretical understanding of the charge pathways and optical properties of QDs is essential for realizing their full potential. QDs differ from the parent bulk materials due to both quantum confinement and surface effects. Quantum confinement allows one to vary continuously QD properties by changes in size. Surface regions deviate from bulk in structure and composition, containing ligands and defects. As the electronic energy levels become sparse with decreasing QD size, the electron-phonon relaxation slows down, leading to the expectation of a phonon bottleneck. 14,15 The phonon bottleneck is not as common as expected initially, 14,16 because of a large density of electronic states, especially at high energies, 15,17,18 stronger electron-phonon coupling in QDs compared to bulk, and a broad spectrum of phonon modes participating in the nonradiative relaxation. QDs deviate from the ideal behavior due to symmetry breaking, defects, 19,20 ligands, 21,22 and anharmonicities. 16,23 Auger-type exchange of energy between electrons and holes 24,25 accelerate the relaxation further. The nonradiative relaxation represents inelastic electron-phonon scattering. Elastic scattering deter- mines homogeneous line widths of optical signals and lifetimes of electronic state superpositions encountered during multiple exciton generation, fission and other excited state processes. 26 Silicon is the most common material in electronics and solar energy applications. Bulk Si is not suitable for optoelectronics owing to its indirect bandgap (∼1.1 eV). As the size of Si crystals decreases below the exciton Bohr radius, around 5 nm, 27 novel effects emerge. The bandgap becomes direct, 28 stimulating development of silicon-based optoelectronic components. In contrast to crystalline silicon, porous silicon produces highly efficient, visible luminescence. 29-31 The Franck-Condon shift increases abruptly around 1 nm, manifesting transition from crystals to molecules. 32 Si luminescence lifetime depends strongly on material size and generally decreases in smaller systems. The excited state lifetime of bulk Si is extremely long, around a millisecond, 33 since radiative relaxation is forbidden by the indirect bandgap, and the electron-phonon coupling causing nonradiative energy losses is weak. The exciton lifetime reduces to 0.1 ms in 50 nm Si crystals. 34 When the size decreases further to several nanometers, the photoluminescence lifetime reduces to micro- seconds. 31,35,36 Mason et al. 30,37 spatially isolated and detected luminescence from individual Si nanoparticles in the 5-20 nm range, suggesting a 1 μs lifetime. Bechstedt 38 investigated electron-hole relaxation using first-principles simulations and found the radiative lifetime to be proportional to the Si cluster diameter. When the Si cluster size decreased to 5 Å, which is comparable to the size investigated in our work, the calculated lifetime was around 4 ns. Recently, Wei Yu et al. 39 created a Si- Received: July 6, 2014 Revised: August 15, 2014 Published: August 15, 2014 Article pubs.acs.org/JPCC © 2014 American Chemical Society 20702 dx.doi.org/10.1021/jp5067296 | J. Phys. Chem. C 2014, 118, 20702-20709 Downloaded via UNIV OF SOUTHERN CALIFORNIA on November 7, 2019 at 19:59:31 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.