Electron-hole Interaction Energy Research Articles

Real Space-Real Time Evolution of Excitonic States Based on the Bethe-Salpeter Equation Method.

We introduce a method for constructing localized excitations and simulating the real time dynamics of excitons at the Many-Body Perturbation Theory Bethe-Salpeter Equation level. We track, on the femto-seconds scale, electron injection from a photoexcited dye into a semiconducting slab. From the time-dependent many-body wave function we compute the spatial evolution of the electron and of the hole; full electron injection is attained within 5 fs. Time-resolved analysis of the electron density and electron-hole interaction energy hints at a two-step charge transfer mechanism through an intermediary partially injected state. We adopt the Von-Neumann entropy for analyzing how the electron and hole entangle. We find that the excitation of the dye-semiconductor model may be represented by a four-level system and register a decrease in entanglement upon electron injection. At full injection, the electron and the hole exhibit only a small degree of entanglement indicative of pure electron and hole states.

The dominant molecular orbitals contributing into absorption peaks of an organic light-emitting molecule

The dominant molecular orbitals (MO) making roles in electronic transitions responsible for optical processes in an OLED molecule are investigated. Whole molecule transition during absorption of stimulus light in such devices are commonly described first-principally as a summation of electronic transitions between several MOs. Time dependent density functional theory (TDDFT) can determine the percent of each electronic transition contributing into a specific molecular transition between ground and excited states. This scheme, however, ignores electronic correlation during the transitions, which of crucial importance for correcting the difference energies between MO levels. This electron-hole interaction energy can be recovered considering every peak of absorption spectrum of the molecule to one single electronic transition between two specific MOs. The corresponding single-excited molecular orbitals (SEMO) are employed to calculate the intensities of absorption peaks of a well-known OLED molecule Alq3. First, TDDFT is used to simulate the molecule and to obtain its MOs and it is shown that TDDFT is capable to track the dominant electronic transitions and their specific MOs responsible for the optical process, and so, it provides a reliable basis for calculations of SEMO. The SEMO is then applied on MOs contributing dominantly in each absorption peak of the molecule. The calculations, performed within this scheme, move the computational curve excellently closer to experimental measurement of the absorption peaks.

Optical properties of colloidal semiconductor quantum dots in dielectric media: A natural potential well approach

Colloidal quantum dots exhibit size-dependent optical properties due to quantum and dielectric confinements at the semiconductor/solvent boundary. To consider both confinement effects, we take a natural potential well approach that assumes separate potential wells for electron and hole which are surrounded by dielectric media. The potential well depths for electron and hole are set by the band offsets at the semiconductor/solvent heterojunction. The kinetic energy is calculated using an effective mass approximation and the electron-hole interaction energy is obtained by taking image charges into account. For cadmium chalcogenides, resulting transition energies agree well with size-dependent optical bandgaps from experiments.

The behaviour of charge distributions in dielectric media

Screened Coulomb interaction in dielectrics is often used as an argument for a lower exciton binding energy and easier exciton dissociation in a high dielectric material. In this paper, we show that at length scales of excitons (10–20Å), the screened Coulomb law is invalid and a microscopic (quantum chemical) description is necessary to describe the medium effect on exciton dissociation. The exciton dissociation energy decreases with increasing dielectric constant, albeit deviating from the inversely proportional relationship. The electron–hole interaction energy, approximated with a point charge model, is apparently not affected by the dielectric constant of the environment.

Optoelectronic Properties of Carbon Nanorings: Excitonic Effects from Time-Dependent Density Functional Theory.

The electronic structure and size-scaling of optoelectronic properties in cycloparaphenylene carbon nanorings are investigated using time-dependent density functional theory (TDDFT). The TDDFT calculations on these molecular nanostructures indicate that the lowest excitation energy surprisingly becomes larger as the carbon nanoring size is increased, in contradiction with typical quantum confinement effects. In order to understand their unusual electronic properties, I performed an extensive investigation of excitonic effects by analyzing electron-hole transition density matrices and exciton binding energies as a function of size in these nanoring systems. The transition density matrices allow a global view of electronic coherence during an electronic excitation, and the exciton binding energies give a quantitative measure of electron-hole interaction energies in the nanorings. Based on overall trends in exciton binding energies and their spatial delocalization, I find that excitonic effects play a vital role in understanding the unique photoinduced dynamics in these carbon nanoring systems.

Electron and hole addition energies in PbSe quantum dots

We calculate electron and hole addition energies of PbSe quantum dots using a pseudopotential configuration-interaction approach. We find that (i) the addition energies are nearly constant for the first eight carriers occupying the $S$-like shell. (ii) The charging sequence of the first eight carriers is non-Aufbau, but filling of the $P$-like single-particle states takes place only after the $S$-like states are filled. (iii) The charging spectrum shows bunching-up of all lines as the dielectric constant ${\ensuremath{\epsilon}}_{\text{out}}$ of the material surrounding the dot increases. At the same time, the addition energies are significantly reduced. (iv) The calculated optical gap shows a rather weak dependence on ${\ensuremath{\epsilon}}_{\text{out}}$, reflecting a cancellation between electron-hole interaction energies and surface polarization self-energies.

Electron-hole interaction energy in the organic molecular semiconductor PTCDA

We have used photoemission, inverse photoemission and electron energy loss spectroscopies to determine the on-site attractive electron-hole interaction energy E e−h in the organic molecular semiconductor 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA). E e−h is found to be 1.0 ± 0.2 eV, larger than the PTCDA band width estimated to be smaller than 0.4 eV. Correlation effects in PTCDA are therefore important, consistent with the molecular nature of the solid. They are smaller than in purely molecular solids like C 60 due to the strong π-electron coupling between overlapping molecules in the molecular stacks.

Doping Dependent Bandgap Narrowing in Silicon and Germanium

AbstractA simple model for bandgap narrowing in doped silicon and germanium is developed. The model assumes that bandgap narrowing in doped semiconductors results primarily from electron—electron, electron—hole, electron—donor, and hole—donor interactions. Based on the suggestion of Hermanson and Phillips that in an impure crystal spatially dependent dielectric screening represents a measure of electron—hole, electron—donor, and hole—donor interactions, the model attempts to determine electron—donor, hole—donor, and electron—hole interactions by making use of the DYP (Dingle/Yakawa potential) modified by including spatially variable dielectric constant. The electron—hole interaction energy is estimated on the basis of many‐body techniques of Mahan and Abram et al. Physics justifying the use of modified DYP for calculating bandgap narrowing is discussed in some details. It is noted that the use of the DYP is valid for doping concentrations up to about 4 × 1020 cm−3. Calculated results are displayed in figures, which show good agreements with available experiments.

Effect of crystallite shape on exciton energy: Quantum Monte Carlo calculations

We have applied the quantum Monte Carlo (random walk) method to calculate the energies of electron-hole pairs (Wannier excitons) in crystallites of varying shapes and sizes. The Schrödinger equation was solved for a model of Brus using effective masses for the electron and the hole, an interaction potential based on the dielectric constant for the bulk, and zero charge density at boundaries. Results are reported for spheres, cubes, and rectangular parallelopipeds of semiconductor materials CdS and ZnO. The exciton energy is given approximately by the sum of the independent localization energies for electron and hole if any dimension of the crystallite is small, and by the electron-hole interaction energy if all dimensions are large. For fixed independent localization energy the energy lowering due to confinement of electron and hole in the same region decreases with crystallite shape in the order: sphere, cube, rectangular parallelopiped of high length-to-width ratio.

Core Exciton and Band Structure in LiF

By applying yield spectroscopy we could confirm recent absorption measurements locating the onset of ${\mathrm{Li}}^{+}$ ${\mathrm{Li}}^{+} 1s$ transitions at 54 eV. From energy-distribution-curve measurements using 120-eV photons, the ${\mathrm{Li}}^{+}$ ${\mathrm{Li}}^{+} 1s$ separation from the top of the valence band is found to be 50.2 eV. Combining these numbers with the band gap (13.6 eV), we find an electron-hole interaction energy of 10 eV. This is discussed in the context of two the-oretical calculations of ${\ensuremath{\epsilon}}_{2}$ spectra.