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First-Principles Study of p‑n-Doped Silicon Quantum Dots: Charge Transfer, Energy Dissipation, and Time-Resolved Emission Jiangchao Chen,† Andrew Schmitz,† Talgat Inerbaev,‡ Qingguo Meng,† Svetlana Kilina,§ Sergei Tretiak,∥

and Dmitri S. Kilin*,†

†Department of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States ‡L.N.Gumilyov Eurasian National University, Munaitpasov str. 5, Astana 010008, Kazakhstan §Department of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108, United States ∥Theoretical Division and Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87454, United States

*S Supporting Information

ABSTRACT: Electron−phonon coupling controls nonradiative relaxation dynamics of the photoexcited electron−hole pair in semiconductor nanostructures. Here the optoelectronic properties for Al- and P-codoped silicon quantum dots (QDs) are calculated by combining time-dependent density matrix methodology and ab initio electronic structure methods. The energy-band landscape of the codoped Si QD is elucidated via time evolution of population density distributions in energy and in coordinate space. Multiple nonradiative relaxation pathways result in a specific charge-separated state, where a hole and an electron are localized on Al and P dopants, respectively. Analysis of the simulated nonradiative decay shows that high-energy photoexcitation relaxes to the band gap edge within 10 ps, forming the final charge-transfer state. We also simulate time-resolved emission spectra of the codoped Si QD that reveals optical and IR emissions below the optical band gap. These emission features are attributed to the intraband transitions introduced by doping.

SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis

Being one of the most abundant elements on the Earth,silicon remains the main focus of intense engineering and synthetic efforts in developing new, cheaper-processing nano- sized materials for future technological applications. Thus, crys- talline silicon quantum dots have well-studied electronic and optical properties1−4 and exhibit technological potentials for photovoltaic devices.5−7 Silicon nanowires (SiNWs)8,9 have recently found many promising applications in electronic devices, waveguides, and solar cells.10−12 Most of the photophysical pro- perties important for these applications can be tuned by p- and n-doping of silicon nanostructures. In such doped systems, the p-n junction governs conditions for electron transfer, the effi- ciency of which is the key factor in energy-conversion materials. As such, elucidating electron-transfer pathways together with energy losses due to lattice-induced charge-carrier relaxation and their dependence on doping is critical for optimizing an efficiency of Si-based optoelectronic and photovoltaic devices. For example, excited-state energy relaxation of SiNW with axial arrangement of p-n junctions13 determines the carrier lifetime,14−16 and photo- luminescence efficiency.17−20 Femtosecond pump−probe imaging has been recently applied to get insights into charge-carrier recombination in SiNW;19,20 however, interpretation of time- resolved emission spectra is challenging because of the “dark” character of electronic states of indirect-bandgap semiconductors, such as silicon. As such, theoretical insights into pathways and mechanisms of relaxation dynamics and photoemission in silicon

nanostructures could elucidate ways for controlling these pro- cesses and help in rational design of Si-derived materials. Various first-principle approaches beyond Born−Oppenheimer

approximations have been developed to describe such hot carrier relaxation dynamics in different molecules,21−24 solids,25,26 and nanostructures,27−29 including surface-hopping technique30

combined with methods ranging from density functional theory (DFT)27−29 to semiempirical configurationally interaction (CI) approaches31−34 and the multilevel Redfield theory.35−43 Our previous computational modeling of various silicon nanostruc- tures (including elongated codoped silicon QDs) based on DFT electronic structure calculations and linear response time- dependent DFT (TDDFT) simulations of excited states allowed for a detailed analysis of their optical properties,44−47 while relaxation rates in these systems have been investigated based on the phenomenological Redfield theory.48

In the present work, we extend our simulations of the relaxa- tion rates of photoexcited electrons and holes in Si QDs with Al and P dopants by applying an ab initio treatment of the elec- tronic states, when the underlying nonadiabatic transitions are accompanied by the respective vibrational dynamics. Such calculated

Received: April 10, 2013 Accepted: June 2, 2013 Published: August 15, 2013

Letter

pubs.acs.org/JPCL

© 2013 American Chemical Society 2906 dx.doi.org/10.1021/jz400760h | J. Phys. Chem. Lett. 2013, 4, 2906−2913

pubs.acs.org/JPCL

on-the-fly nonadiabatic couplings are then used as parameters to the Redfield theory, providing dynamics of carriers and allow- ing for analysis of multiple nonradiative relaxation pathways in codoped Si QDs. The observed ultrafast electron−phonon dynamics following photoexcitation is found to be controlled by doping concentration and location. In addition, we simulate, for the first time, the time-resolved emission spectra of the codoped Si QD: the observable that can be directly compared with experimental data. Our simulations provide information on the nature and lifetime of emission states in doped nano- materials. Because interpretation of time-resolved data is a chal- lenging experimental task, our calculations could be valuable in the analysis of pump−probe spectroscopy measurements. We focus our modeling on Al- and P-codoped silicon quantum

dot (QD) with a composition formula Si36Al1P1H42. The codoped QDs are elliptical and elongated in the ⟨111⟩ direction, along which the dopant atoms are spread. The undoped Si QD of the composition Si38H42 is used for a reference. An electronic struc- ture of these clusters has been calculated using DFT49,50 with the Perdew−Burke−Ernzerhof (PBE) functional,51 as imple- mented in the VASP software package.52 In this software, the valence electrons are treated explicitly, while the core electrons are described with PAW pseudopotentials.53 All calculations are done in the plane-wave basis. Several electronic properties have been extracted from these calculations, including the energy gap between the respective Kohn−Sham highest occupied (HO) and lowest occupied (LU) molecular orbitals, the electronic density of states (DOS), the excitation lifetime, and the absorption spectrum. The absorption spectra are calculated as

∑α ω δ ω ω= ℏ − ℏ ≡

f( ) ( ) I ij

I I (1)

where the double index I = ij runs over all possible transitions between occupied i and valence j Kohn−Sham energy levels with transition frequency ℏωI. Each Dirac delta function δ is weighted by the oscillator strength f I corresponding to the transition. (See the details in the Supporting Information.) Each resonance has been further broadened by 0.05 eV to model the finite spectral width of the peaks. The question of validity of a single-particle approach to the

excited state in QDs has been addressed in several investigations.54 The studies of CdSe QDs show that excitonic effects lead to a systematic red shift of transition energies (of ∼0.3 eV), while not changing the shape and profile of the spectra. The reason for such behavior is that the quantum confinement effect in QD ensures that the electron and hole kinetic energies (T ≈ 1/R2) dominate their electrostatic interaction (Eex ≈ 1/R), as can be derived from the effective mass theory.55 As a result, the optical spectra of QDs are qualitatively represented by the independent electron and hole picture.56 To confirm the validity of this approach in the case of Si QD, we have compared optical transitions obtained from a single-particle approach used in our work with those calculated by linear response TD-DFT, which incorporates electron−hole corrections. (See the details in the Supporting Information.) As shown in Figure S1 in the Supporting Information, TD-DFT and DFT spectra of doped and pristine Si38H42 exhibit the same features shifted by a constant energy offset of ∼0.6 eV independent of transition energy, while the spectral shape stays unchanged. Thus, similar to reported results for CdSe QDs,56 a single-particle approach is appropriate for qualitative descrip- tion of the optical spectra of Si quantum dots.57

By analogy to the absorption spectra, we further evaluated the spectral density of emission from the density matrix ρij(t) corresponding to excited, nonequilibrium states as

∑ω δ ω ω ρ ρ= ℏ − ℏ − >

E t f t t( , ) ( ){ ( ) ( )} j i

ij ij jj ii (2)

∫ω ω= ∞

E t E t( ) d ( , )int 0

Here f ij, ℏωij, and ω stand for an oscillator strength, Kohn− Sham orbital energy difference, and emission frequency, respectively, and i(j) labels virtual (occupied) orbitals. The information about time evolution of density matrix elements is a critical component for computing time-resolved spectral probes, charge density distribution, as well as rates of energy dissipation and charge transfer. To simulate time-dependent electronic properties, we further

performed molecular dynamics modeling using the VASP package for up to 1 ps trajectory at ambient temperature. In our approach, we neglect the vibrational reorganization of the excited state, assuming that the geometry o

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