Theory of multi-exciton states in semiconductor nanocrystals

In this article, the fundamental physics of multi-exciton states in semiconductor nano-crystals is reviewed focusing on the mesoscopic enhancement of the excitonic radiative decay rate and the excitonic optical nonlinearity and the mechanism of their saturation with increase of the nanocrystal size. In the case of the radiative decay rate the thermal excitation of excited exciton states having small oscillator strength within the homogeneous linewidth of the exciton ground state is essential in determining the saturation behavior. The weakly correlated exciton pair states are found to cause a cancellation effect in the third-order nonlinear optical susceptibility at the exciton resonance, providing the first consistent understanding of the experimentally observed saturation of the mesoscopic enhancement of the excitonic optical nonlinearity. The presence of the weakly correlated exciton pair states is confirmed convincingly from the good correspondence between theory and experiments on the induced absorption spectra from the exciton state in CuCl nanocrystals. Furthermore, ultrafast relaxation processes of biexcitons are discussed in conjunction with the observed very fast rise of the biexciton gain in nanocrystals. In prospect of future progress in research, the theoretical formulation to calculate the triexciton states as one of the multi-exciton states beyond the biexciton is presented for the first time including the electron-hole exchange interaction.     

Multiple exciton generation in silicon quantum dot arrays: density functional perturbation theory computation

We use the density functional theory (DFT) combined with the many-body perturbation theory to derive expressions for the rates of the optical photon→exciton and photon→bi-exciton processes in nanoparticles, and for quantum efficiency, all to the leading order in the screened Coulomb interaction between Kohn–Sham quasiparticles. Also, we calculate exciton→bi-exciton rates due to the impact ionisation (II) mechanism in Si₂₉H₃₆ quantum dots (QDs) with both crystalline and amorphous core structures, and in quasi-one dimensional (1-D) arrays constructed from these QDs. We observe significant dependence of the carrier multiplication rates on the structure’s morphology and structural disorder. Amorphous silicon QD arrays are predicted to have more efficient bi-exciton generation rates as a function of exciton energy compared to their crystalline counterparts, and the isolated QDs of both kinds.     

Excitons in tubular molecular aggregates

We present a brief overview of recent work on the optical properties of molecular aggregates with a tubular (cylindrical) shape. The exciton states responsible for these properties can be distinguished with regard to a transverse wave number, which directly relates to optical selection rules and polarization direction of the associated absorption line. We discuss two types of analytical solutions for the exciton wave functions and the associated absorption and dichroism spectra.     

Specific features of the hybridization of Frenkel and Wannier–Mott excitons in a microcavity

Polariton states have been investigated in a microcavity, where the energy of the Frenkel exciton in an organic quantum well and the energy of the semiconductor Wannier–Mott exciton in an inorganic quantum well are close to the microcavity optical mode. It has been shown that the interaction of each of these excitons with the microcavity optical mode leads to their interaction with each other and to the formation of mutually coupled hybrid excitations. The influence of the location of the quantum wells in a microcavity on the spectra of hybrid states with different polarizations has been analyzed.     

Octaethylporphin films. II absorption and emission of amorphous films

Amorphous thin films octaethylporphin have been prepared and are observed to crystallize over time if thicker than about 100 nm. Transmission spectra of amorphous films have a sharper Soret band than transmission spectra of crystalline films and lack the exciton band seen in crystalline films. The exciton band can be resolved in amorphous films by taking a difference spectrum between two amorphous films of different thickness. Fluorescence is observed from one impurity in amorphous films as compared to two impurities in crystalline films. This indicates a smaller exciton diffusion length in amorphous films as compared to crystalline films, consistent with the differences in the transmission spectra of the two kinds of film.     

Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

We have investigated stress effects on yellow exciton states in a Cu₂O thin film sandwiched by MgO plates by measuring wavelength modulated (WM) absorption spectra and their thermal variations. In the WM absorption spectra, dispersive spectral structures owing to 2P~4P states in the yellow excitons are clearly resolved in the thin film sample. A stress due to the lattice mismatch between Cu₂O and MgO provides a large red shift of the band gap in the green excitonic system. However, in the yellow excitonic transitions, it is found that a red-shift of the 2P excitonic state is much smaller than that in the green excitonic system. This result suggests that a shallow potential minimum for the yellow excitons is built up in the Cu₂O thin film sandwiched by MgO plates.     

Excitons in ZnP2 crystals in the electric field of a Schottky barrier

A study is made of the effect of electric fields on the exciton states of β-ZnP₂ crystals (T=77 K) in structures with Schottky barriers formed by depositing semitransparent electrically-conducting InSnO₂ films on the crystal surface. The observed changes in the exciton optical reflection spectra when an electrical potential is applied to a barrier are explained by the shift and broadening of the exciton level caused by the Stark effect. The experimental data are compared with calculations based on a theory of exciton optical reflection from planar spatially nonuniform structures. Fiz. Tverd. Tela (St. Petersburg) 40, 884–886 (May 1998)     

Charged excitons in quantum dots: novel magnetic behavior and Auger processes

We describe theoretically multiply-charged excitons interacting with a continuum of delocalized states. Such excitons exist in relatively shallow quantum dots and have been observed in recent optical experiments on InAs self-assembled dots. The interaction of an exciton and delocalized states occurs via Auger-like processes. To describe the optical spectra, we employ the Anderson-like Hamiltonian by including the interaction between the localized exciton and delocalized states of the wetting layer. In the absence of a magnetic field, the photoluminescence line shapes exhibit interference effects. When a magnetic field is applied, the photoluminescence spectrum demonstrates anticrossings with the Landau levels of the extended states. We show that the magnetic-field behavior of charged excitons is very different to that of diamagnetic excitons in three and two-dimensional systems.     

Optical studies of ZnSe/ZnMgSSe-based quantum-well semiconductor heterostructures

Results of an optical study of heterostructures based on new compounds, ZnSe/ZnMgSSe, are presented. The possibility of using these compounds to produce high-quality quantum-well structures having strong exciton features in optical spectra is demonstrated. An analysis of reflectance spectra has yielded the exciton parameters: the resonant frequency, oscillator strength, and exciton line damping. The exciton binding energies have been determined from magneto-optical spectra. The samples studied have a high structural perfection and small inhomogeneous width of the excitonic resonances. Fiz. Tverd. Tela (St. Petersburg) 40, 811–812 (May 1998)     

Quasiparticle spectrum and optical excitations of semiconductor surfaces

I investigated the spectra of well-ordered semiconductor surfaces within an ab-initio framework. Both the quasi-particle spectrum of electron and hole states and the optical differential reflectivity spectrum were addressed. As examples, I discuss the spectra of three surfaces: Si(111)-(2×1), hydrogenated H:Si(111)-(1×1), and Si adatom-terminated 6H-SiC(0001)-(×). I studied a number of physical features beyond the single-particle band-structure picture. In the case of Si(111)-(2×1), the dangling-bond surface states give rise to a surface exciton which dominates the differential reflectivity spectrum. In the case of 6H-SiC(0001)-(×), a Mott-Hubbard metal-insulator transition is observed. All calculations were performed within many-body perturbation theory, employing single- and two-particle Green functions. The solutions of the corresponding equations of motion yielded the observable excitations, i.e., single-particle electron and hole excitations, as well as bound and resonant electron-hole pair excitations. Received: 28 April 2000 / Accepted: 19 June 2000 / Published online: 7 March 2001     

Ionic displacement caused by electronic excitations

Electronic excitations are often accompanied by displacement of the ions from their ground-state equilibrium positions. This leads to line broadening of optical spectra, Stokes shifts, conformational changes, and photoinduced reactions. Here we discuss approaches to these features within ab-initio methods, in particular within many-body perturbation theory. A number of various systems, including molecules, point defects, polymers, and surfaces, are discussed to illustrate issues like localization and self-trapping that are relevant for a detailed understanding of the interrelation between excited states and geometrical structure. To cite this article: M. Rohlfing, C. R. Physique 10 (2009).     

Proposal of structures possessing high exciton concentration

The possibility of achievement of high exciton concentrations is analyzed. It is shown that high concentrations can be achieved in a three-layer thin molecular film due to the autoreduction processes taking place in it. Shortly, the appearance of high concentrations is the consequence of boundary conditions in film and of the magnitude of matrix elements of dipol-dipol interactions. The autoreduction takes place in the cases when matrix elements characterizing exciton transfer are less than statistical matrix elements. Based on numerical analysis, it was found that optical quanta concentrations of a three-layer film can achieve values of about 5×10⁻². The structures possessing so high concentration do not exist in nature, thus they have to be synthesised. For the current state of nanotechnology, it is not a problem. Fortunately achieving high concentrations requires only certain ratios of relevant characteristics of the film with a two-level exciton scheme, but not their single values.     

Size-dependent photo-induced shift of the first exciton band in CdTe quantum dots in glass prepared by a two-stage heat-treatment process

CdTe nanocrystals were grown from commercially available RG850 Schott filter glass by two-step heat-treatment process which almost doubles the particle to matrix volume fraction. A calculation shows that a quantized-state effective mass model in the strong confinement regime might be used to deduce the average radius for the nanocrystals larger than 2 nm in radius from the energetic position of the first exciton peak in optical absorption spectrum. Size-induced shift of ∼360 meV in the first exciton peak position was observed. The steady state photoluminescence spectra exhibit a broad band red shifted relative to the first exciton band, which indicates the existence of shallow trap states. The non-linear optical properties of CdTe nanocrystals were studied by room temperature resonant photoabsorption spectroscopy. The differential absorption spectra had three-lobed structure whose size-dependent evolution was explained by bleaching of the absorption, red shift and broadening in the Gaussian absorption band used to fit the first exciton peak. A maximum red shift of 2.32 meV for the average nanocrystal radius of 4.65 nm was estimated by fitting the photomodulation spectra with a combination of first and second derivative Gaussian absorption bands. We presume that the red shift is induced by the electric field of trapped charges in surface states. Internal electric field strengths of 23 and 65 kV/cm were predicted for the average nanocrystal radii of 3.95 and 4.65 nm, respectively, with the help of second-order perturbation theory in the strong confinement limit.     

Synthesis of zinc oxide microrods and nano-fibers with dominant exciton emission at room temperature

Employing a simple chemical synthesis method, hexagonal-shaped zinc oxide microrods and zinc oxide nano-fibers were deposited on pyrex-glass and aluminum substrates, respectively. Both kinds of deposits showed zincite crystalline phase with lattice parameters: a=3.2498 Å and c=5.2066 Å. Microrods showed very uniform wide and large sizes of around 1 and 10 μm, respectively. Both deposits were homogeneous over all substrate surfaces. Microrods and nano-fibers resulted with good optical quality and with preferential crystalline growth in [1 0 1 0] and [0 0 0 1] directions. The principal optical characteristics for both microrods and nano-fibers were: a) room-temperature photo and cathodo-luminescent spectra with strong exciton emission centered around 390 nm and with FWHMs around 125 and 160 meV, respectively, b) poor photo and cathode-luminescent emissions in the visible region of the electromagnetic spectrum, c) energy band gap of 3.32 eV, d) good emission efficiency supported by the not-required high energy densities to obtain strong exciton emission and e) good ZnO stoichiometry endorsed by photoluminescent results. These characteristics make of these microrods and nano-fibers good for potential photonic applications.     

Exciton and multi-exciton structures in GaAs quantum dots studied by single-photon correlation spectroscopy

Single-photon emitters and detectors are key devices for realizing secure communications by single-photon-based cryptography and single-photon-based quantum computing. For the establishment of these technologies, we need to understand the electronic structures of single and multiple excitons. Therefore, we have studied their emissions via the micro-photoluminescence (μ-PL) spectra of strain-free GaAs/AlGaAs single quantum dots, using excitation power dependence, time-resolved, and single-photon correlation measurements. Under pulsed excitation, we observed clear photon antibunching and bunching by auto- and cross-correlation measurements. From these results, we found that the emission peaks observed in the μ-PL spectra originated from exciton, charged exciton, and biexciton states.     

Assessment of the coherent potential approximation for the absorption spectra of a one-dimensional Frenkel exciton system with a Gaussian distribution of fluctuations in the optical transition frequency

We investigate the accuracy of the coherent potential approximation (CPA) for the optical absorption spectra of a one-dimensional Frenkel exciton system with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the optical transition frequency (diagonal Gaussian disorder). Our earlier studies have established that the CPA gives highly accurate results for the integral of the density of states of this system. In this paper we compare the CPA results for the normalized optical absorption with the finite-array calculations of Schreiber and Toyozawa and Schreiber for the same model. It is found that the CPA results for the absorption are in good agreement with their findings. It is pointed out that an expansion of the density of states in terms of the eigenstates of the ideal (no disorder) array contains a term proportional to the normalized absorption. Since the density of states is accurately approximated by the CPA, the presence of this term explains the success of the CPA in reproducing the absorption spectra. Our findings support the use of the Gaussian disorder model to interpret the absorption spectra of one and quasi-one dimensional exciton systems.     

Exciton dynamics in ZnCdSe/ZnSe quantum-well structures

Exciton dynamics in ZnCdSe/ZnSe quantum-well structures have been studied from luminescence spectra obtained at T=2 K. The energy and phase relaxation times of localized exciton states have been determined from a study of the destruction of exciton optical alignment by an external magnetic field and direct measurements of the polarized-radiation decay kinetics in the picosecond range. The exciton polarization lifetimes measured by two independent techniques are found to be in a good agreement. Fiz. Tverd. Tela (St. Petersburg) 40, 809–810 (May 1998)     

Exciton band structure of crystalline anthracene

The density of states in the first exciton band of crystalline anthracene has been obtained at room, dry-ice-alcohol, and liquid nitrogen temperatures by applying a thermal modulation technique to observe the hot band-first exciton band optical transition (1-0 transition). The density of states function obtained has been interpreted in terms of the exciton band structure and the Davydov splitting. The K dependent selection rule for the 1-0 transition is discussed. The bandwidth of the first exciton band is 0.09 eV.