Article pubs.acs.org/JPCC
Light Absorption by Crystalline and Amorphous Silicon Quantum Dots with Silver Adsorbates and Dopants David M. Stewart,† Michael G. Mavros,‡ and David A. Micha*,† †
Quantum Theory Project, University of Florida, Gainesville, Florida, United States Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States
‡
ABSTRACT: Recent work on light absorption by model surfaces of Si has shown that Ag adsorbates increase the intensity of photoinduced electronic transitions at lower photon energies. Furthermore, another set of recent results for Si quantum dots (QDs) has shown that P and Al dopants shift the light absorbance toward lower photon energies. In this report, the optical absorbance of Si QDs with P and Al dopants and either one or three Ag adsorbed atoms has been calculated with TD-DFT using the PW91/PW91 density functionals to compare with our previous results. In general, the presence of Ag adsorbates shows both a decrease in the HOMO-LUMO gap and a drastic increase in the absorbance below 4 eV. The addition of dopants leads to a combined effect where the energy gap is further decreased to values below 2 eV. The molecular orbitals for the initial and final states involved in transitions with large oscillator strengths were also calculated, which qualitatively show the excited electrons moving toward the Ag during excitation. This study indicates that stronger absorption in the visible, near-UV, and near-IR parts of the spectrum can be achieved with a combination of Ag adsorbate clusters and doping.
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INTRODUCTION The optical properties of nanometer-sized particles (often called quantum dots or QDs) are affected by confinement of electronically excited quantum states and by the presence of dopants or of adsorbates. These effects can be understood starting from the atomic structures of the QDs and modeling their light absorption with treatments of photoinduced electronic excitations in terms of electronic states and derived quantities such as transition electric dipoles. Several reviews have recently appeared covering structure, properties, and confinement effects in QDs,1−5 some of which relate in particular to silicon QDs. Theoretical and computational aspects based on density functional theories, many-electron perturbation theory, quantum Monte Carlo calculations, and ab initio dynamics of Si QDs have also appeared,6−9 although relating to compounds different from the ones in the present article. As the properties of nanometer-sized particles are investigated, they have been used in a wide range of technological applications including photodetectors,10 light-emitting devices,11 bioimaging,12 and quantum computing.13 Because of their highly tunable electronic structures and phenomena such as multiple exciton generation,14 their use as photovoltaic materials is especially interesting because of the potential to raise the maximum theoretical efficiency of these materials from their theoretical limit of ∼30%15 to perhaps 60%.16 Much work has been done over the last year in both techniques for producing QDs and the issue of charge carrier transport. Although the end goal is a photovoltaic panel that utilizes QDs for photoabsoption, methods of leveraging the properties of QDs © 2012 American Chemical Society
to enhance existing photovoltaic materials have been developed.17 Furthermore, to develop a QD-based photovoltaic material, one would need to build layers of QDs of different sizes.18 For this, and many other applications, precise control over the size of the QDs and their placement in a solid matrix has been developed.19 Silicon quantum dots (Si QDs) show promise in solar energy applications due to silicon’s stability and well-studied band structure. Optical excitations in bulk silicon are phononmediated to allow for indirect band transitions, which weakens light absorption, but in confined structures they need not be.20 The k-conservation rule for indirect band gap semiconductors normally requires the production of such phonons to accompany optical excitations to conserve momentum, but the spatial confinement of electron carriers in QDs increases the spread of their momentum, allowing excitations without involving phonons. Because electronic excitations may occur in QDs without coupling to vibrational modes, exciton recombination occurs slowly, a property that is ideal for charge extraction in photovoltaic devices. Informed by previous success in improving the photoabsorption characteristics of bulk Si using Ag adsorbates,21−24 more recent work on doped Si QDs,25 and work on plasmonic light trapping,26,27 we set out to calculate the effects of adding Ag adsorbates directly to the surface of a Si QD. The optical Received: July 31, 2012 Revised: October 5, 2012 Published: October 5, 2012 23107
dx.doi.org/10.1021/jp3075805 | J. Phys. Chem. C 2012, 116, 23107−23112
The Journal of Physical Chemistry C
Article
and finally cooled back to 0 K over 0.1 ps. The atoms were rebonded until all bonds were saturated and the original number of H atoms passivated the surface. The amorphous geometry was then optimized with DFT. From these four pure Si structures, eight adsorbate structures were created by replacing either a single hydrogen atom or a cluster of three hydrogen atoms with silver. In the latter case, the silver atoms formed a planar structure at the silicon surface. Finally, a silicon atom was replaced with either phosphorus or aluminum in one of two locations: either at the geometric center or at the surface opposite the silver cluster. As in Figure 1, the dopant placement is labeled in the formula of the structure with either an “i” for inner, central doping, or an “o” for outer, surface doping (e.g., “iP” stands for inner phosphorus doping, “oAl” for outer aluminum). The complete set studied included 4 pure Si QDs, 8 undoped adsorbate QDs, and 32 doped adsorbate QDs. The electronic and optical properties of the QDs were calculated using DFT and linear response TD-DFT, respectively, within the Gaussian 03 software using the LANL2DZ basis set31 and the PW91/PW91 exchange/correlation functionals.32 Investigations into the effects of using other functionals, specficially hybrid functionals with partial electronic selfinteraction corrections, have been conducted within our group.33 In this work, it was found by comparing results from the PW91 and HSE34 functionals that the latter gives somewhat larger HOMO-LUMO gaps but that trends in the shifts of absorbances due to dopings are similar in both sets of calculations. Calculations were done with unrestricted electron orbital occupation so that α and β spin-orbitals and their energy levels could be different. Each calculation provided several important properties such as the excitation energy, the oscillator strength of each excitation, and combination coefficients of single-excited determinants making the total excited states. With these data, we were able to calculate the spectral density of light absorbance and excitation lifetimes for each system studied and could gain insight into photoinduced electronic excitation. We define a change in total energy upon doping as follows using the total ground state energy of each species
properties of 44 model QD systems were calculated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) applied in the Gaussian 0328 software package. In total, five independent changes were made to obtain a more complete understanding of these QD systems: • QD size: 29 versus 35 atom clusters. • Geometry: amorphous versus crystalline Si • Ag cluster size: one or three Ag atoms or none • Dopant addition: P or Al doping, or none • Dopant placement: center or surface of QD (labeled below as “i” and “o”, respectively) A comparison of the absorbance and electronic structure of these systems should prove to be useful for identifying the most beneficial effects for Si photovoltaic applications and provide direction for further experimental study.
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METHODOLOGY Following our previous work,25 we have chosen DFT and TDDFT as best suited to the study of our systems. Our goal is to provide numerically results of useful accuracy to discuss trends over a range of different systems. We began with two structures, crystalline Si29H36 and Si35H36, from which we made two amorphous structures. These four QDs formed the basis for all subsequent structures. (See Figure 1.)
Edoping = Eundoped − ESi + Edopant − Edoped
(1)
where Eundoped and Edoped are the energies of the undoped and doped structures, ESi is the energy of a silicon atom in a vacuum, and Edopant is the energy of either an aluminum or phosphorus atom depending on the system. This provides a way to compare the stability of each system after doping. To calculate the spectral density of absorbance, the following equation was used Figure 1. Images of structures illustrative of the calculated set of quantum dots. Crystalline structures are of the Td point group. Orange and pink atoms are P and Al, respectively. The light-blue atoms are Ag.
α(ℏω) =
∑ fI δσ(ℏω − ℏωI ) I
(2)
where the photon energy is ε = ℏω, f is the oscillator strength, and the transition index I ≡ ij ranges over all transitions i → j. In this calculation, the oscillator strength gives weight to a line shape function, which for sharp transitions equals the Dirac delta function within the sum so that the sum over transitions provides an absorbance per unit energy. The broadening of transition lines due to interactions in the medium was described using a Lorentzian to approximate the Dirac delta function as
The crystalline structures were cut from a model A4 crystal of bulk Si by selecting a central atom and enough nearest neighbors to create a roughly spherical shape of the desired diameter. Once isolated, any unsaturated bonds were hydrogenated, and a ground-state geometry optimization was performed using DFT within the Vienna ab initio simulation package (VASP).29 The amorphous QDs were created from the crystalline pair by simulated annealing in the HyperChem software package.30 After all bonds were broken and hydrogens removed, each crystalline structure was placed in a periodic bounding box and a molecular dynamics simulation was performed, during which the Si atoms were heated to 3000 K over 0.1 ps, allowed to diffuse for 10 ps,
δσ(x) = 23108
σ 1 π σ 2 + x2
(3)
dx.doi.org/10.1021/jp3075805 | J. Phys. Chem. C 2012, 116, 23107−23112
The Journal of Physical Chemistry C
Article
Table 1. Summary of structural and optical properties for a-Si29 and c-Si29 QD systemsa excitation data adsorbate a-Si29
pure Ag
Ag3
c-Si29
pure Ag
Ag3
doping undoped inner P outer P inner Al outer Al undoped inner P outer P inner Al outer Al undoped inner P outer P inner Al outer Al undoped inner P outer P inner Al outer Al
Edoping (eV)
energy gap (eV)
energy (eV)
strength
lifetime (μs)
2.2677967 2.1227601 0.4639541 1.6299619 1.0258692 1.3260107 1.5007078 0.2963320 1.1945798 0.5319826 0.4952472 4.3959991 2.5864420 0.2100719 0.6035485 0.5257239 0.7420544 1.3526779 1.3001599 0.6103513 0.6819173 0.2625899
3.8972 3.1952 2.8185 2.7029 2.6958 2.7325 3.0476 1.9535* 2.5936 2.4472 2.4899 5.1221 3.0875 3.2660 3.2021 3.2033 3.1965 3.1208 2.5927 2.6524 2.4939 2.0589
0.0192 0.0925 0.0308 0.0957 0.0237 0.0471 0.0934 0.0219 0.0358 0.0874 0.0389 0.0163 0.3188 0.2181 0.1725 0.2100 0.1042 0.1266 0.0284 0.0186 0.0392 0.0727
0.4966 0.1533 0.5918 0.2071 0.8407 0.4118 0.1669 1.7325 0.6013 0.2766 0.6004 0.3386 0.0476 0.0622 0.0819 0.0672 0.1360 0.1174 0.7585 1.1065 0.5939 0.4699
−1.579972 −0.995624 −3.520102 −2.733114 −1.460718 −1.127727 −3.695063 −2.842974
−2.507658 −2.391290 −4.320841 −4.107431 −1.224402 −1.954479 −3.807726 −4.353988
All excitations listed have the highest oscillator strength for that system with one exception: * denotes the second strongest (but in the energy interval of interest), although the difference was
