The dynamical dielectric function of a silicon slab, in the region from near IR to UV light frequencies, is expected to vary with its thickness, and it is important to know whether its optical properties are similar to those of bulk silicon. Slabs of varying thickness are modeled starting from their atomic structure. Modeled Si(111) surfaces are terminated by hydrogen atoms to compensate the dangling bonds, and optical properties have been obtained for Si slabs with 4, 8, and 12 layers. Real and imaginary parts of the dielectric function are obtained from the polarization of the slab, expressed in terms of a delayed response function constructed from a reduced density matrix (RDM) which includes electronic dissipative effects due to coupling of photoexcited electrons to the substrate lattice and to electronic excitations. The related index of refraction and absorption coefficient have also been calculated from the above treatment. These optical properties are obtained using density functional theory (DFT) and plane wave basis sets to construct the equation of motion of a RDM, solved for steady light absorption. Both GGA (PBE) and hybrid (HSE) DFT exchange-correlation density functionals are employed to calculate the optical properties from the RDM. The imaginary part of the dielectric function is related to the light absorbance, and has been compared to measurements showing that better agreement is obtained with the HSE hybrid functional containing part of the exact short-range electronic exchange energy. We present a procedure by which one can reproduce the HSE results for the dielectric function from the computationally less expensive GGA PBE functional calculations, using a single photon energy shift parameter and results from PBE calculations. Our treatment shows that the onset of light absorption and strong diffraction are similar for thin slabs and bulk silicon, and that they have similar peak structure as functions of photon energy. Both properties increase with slab thickness at most photon energies. This makes silicon slabs reliable structures for photovoltaic applications.

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.

The optical properties of silicon surfaces are affected by their atomic structure and in particular by whether their lattice is crystalline or amorphous. Silver atoms adsorbed on the Si surface enhance the absorption of light and electronic charge transfer at the surface, and the size and shape of the adsorbed Ag clusters play a big role in the photovoltaic properties of Si. We have modeled the photoabsorbance and photovoltage of a nanostructured Si(111) surface with a slab terminated with hydrogen (H) atoms on both surfaces to compensate for dangling bonds, without and with a periodic lattice of adsorbed Ag cluster. Similar structures were also constructed with amorphous lattices to compare the properties of the structures. The optical properties of these structures are investigated using density functional theory to generate a basis set of orbitals and to construct equations of motion for a reduced density matrix from which properties have been obtained in a unified way. Density of electronic states, band gap, and intensity of light absorption with and without silver adsorbates are presented. Light absorbance and surface photovoltages have been calculated in terms of the reduced density matrix. The absorbance in the region around visible light and surface photovoltage (SPV) created by steady light absorption and charge redistribution are calculated for Si slabs containing one, three, or four adsorbed Ag atoms. The ratio of averaged values of absorption flux densities over photon energies in the IR and visible region generally show an increase in absorption with increasing size of a Ag cluster. The changes of absorbance due to silver adsorbates were not large but should be observable. Crystalline Si slabs absorb light mainly at high photon energies, while amorphous Si structures show broader absorption with less intensity. In the case of SPVs, we found that addition of silver adsorbates enhances the SPV of both c-Si and a-Si slabs with a very large increase for c-Si and smaller ones for a-Si. The a-Si structures also show broader SPV spectra compared to the corresponding c-Si structures.

Doped Si(111) surfaces have been modeled with a Si slab, and their photovoltage has been calculated with a combination of ab initio electronic structure and density matrix treatments from the steady state solution of the electronic density matrix (DM) for electrons interacting with thermalized lattice vibrations. Densities of electronic states and photovoltage spectra of the silicon surfaces are drastically affected by the presence of p or n doping. We report results on the effect of surface doping by group III (B, Al, and Ga) and group V (N, P, and As) elements, of interest in the study of surface optical properties, for concentrations of doping atoms in the host lattice in the range of 0.5−1.5%, obtained from slab atomic models with several hundred atoms. Analysis of the results provides insight on trends relevant to the absorption of near IR, visible, and near UV light and to measurements of photovoltages and shows some of the trends found for doped bulk Si in experiments at lower dopant densities.

The interaction of silicon quantum dots with light is remarkable, as electronic transitions are influenced by the interplay of their atomic structure and by electronic quantum confinement in three dimensions. In this study, the optical properties of 4 undoped and 16 doped silicon quantum dots were calculated using time-dependent density functional theory. The HOMO–LUMO gap, maximum absorption wavelength, and oscillator strength at that wavelength were calculated for two crystalline structures, c-Si29H36 and c-Si35H36, and two amorphous structures, a-Si29H36 and a-Si35H36; in addition, optical properties were calculated for each of the structures doped with either phosphorus or aluminum in one of two different positions: in the center of the cluster or at the surface of the cluster. The calculated optical properties reveal that the absorbance spectrum of the amorphous structures is red shifted compared to that of the crystalline structures, and doping causes the spectrum to shift even further toward the red. Additionally, absorption of light at the maximum wavelength in doped structures caused charge density to transfer from the center of the quantum dot to the surface. The combination of strong absorptions in the visible region of the electromagnetic spectrum and the observed charge transfer make doped silicon quantum dots promising candidates as materials for solar energy applications.

Relaxation pathways of photoinduced electronic redistribution at nanostructured semiconductor surfaces are obtained from time-dependent density matrix and ab initio electronic structure methods, giving electronic changes in energy and space over time. They are applied to a Ag cluster on a Si(111) surface, initially photoexcited by a short pulse, and show that the Ag cluster adds surface-localized states that enhance electron transfer. Results on the time evolution of population density distributions in energy and in space, for valence and conduction bands, explore the energy band landscape of a Si slab, with various relaxation pathways ending up in a charge-separated state, with a hole in the Si slab and an electron in the adsorbed Ag cluster. Calculated electronic relaxation times for Si(111)/H are of the same order as experimental values for similar semiconductor systems.Keywords (keywords): charge transfer; density matrix; energy materials; excited states; femtosecond dynamics; nanoparticles; photovoltaics; quantum chemistry; quantum confinement; spectral dynamics; surface science; thin films; time-resolved;

Charge transfer photoinduced by steady light absorption on a silicon surface leads to formation of a surface photovoltage (SPV). The dependence of this voltage on the structure of surface adsorbates and on the wavelength of light is studied with a combination of ab initio electronic structure calculations and the reduced density matrix for the open excited system. Our derivations provide time averages of surface electric dipoles, which follow from a time-dependent density matrix (TDDM) treatment using a steady state solution for the TDDM equations of motion. Ab initio calculations have been carried out in a basis set of Kohn−Sham orbitals obtained by a density functional treatment using atomic pseudopotentials. Applications have been done to a H-terminated Si(111) surface and for adsorbed Ag, with surface coverage ranging from 0 to 3/24 of a monolayer. Calculations done also for amorphous Si agree with measured values of the SPV versus incident photon frequency for H-terminated a-Si. Surface adsorbates are found to enhance light absorption and facilitate electronic charge transfer at the surface. Specifically, Ag clusters add electronic states in the energy gap area, provide stronger absorption in the IR and visible spectral regions, and open up additional pathways for surface charge transfer. Our treatment can be implemented for a wide class of photoelectronic materials relevant to solar energy capture.