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Excitonic Molecule. III. Electronic Structure
Abstract
The electronic structure of excitonic molecule is discussed by taking into account the detailed band structure of CuCl, CuBr, CdS, CdSe and ZnO. Especially the excitonic molecule in CuBr is interesting due to the less simple valence band. The fine structure of the excitonic molecule is clarified under the effective electron-hole exchange effect and the interband hole-hole scattering beyond the effective mass approximation.
... Similar results can be observed in Fig. 6(b,d) for Au and Ag NCs, respectively. A fingerprint of biexciton emission can be obtained by using right (σ+) and left (σ−) circularly polarized beam laser excitation 55,61,64 . However, when using circularly polarized light, the samples studied in this work did not exhibit any significant change in spectral PL emission, as shown in Fig. 7. Then the superlinear behavior cannot been unambigously adscribed to biexciton emissions, and instead the carrier dynamic is probably dominated by uncorrelated electrons and holes pairs. ...
An intense photoluminescence emission was observed from noble metal nanoclusters (Pt, Ag or Au) embedded in sapphire plates, nucleated by MeV ion-implantation and assisted by an annealing process. In particular, the spectral photoluminescence characteristics, such as range and peak emission, were compared to the behavior observed from Pt nanoclusters embedded in a silica matrix and excited by UV irradiation. Correlation between emission energy, nanoclusters size and metal composition were analyzed by using the scaling energy relation EFermi/N1/3 from the spherical Jellium model. The metal nanocluster luminescent spectra were numerically simulated and correctly fitted using the bulk Fermi energy for each metal and a Gaussian nanoclusters size distribution for the samples. Our results suggest protoplasmonics photoluminescence from metal nanoclusters free of surface state or strain effects at the nanoclusters-matrix interface that can influence over their optical properties. These metal nanoclusters present very promising optical features such as bright visible photoluminescence and photostability under strong picosecond laser excitations. Besides superlinear photoluminescence from metal nanoclusters were also observed under UV high power excitation showing a quadratic dependence on the pump power fluence.
We have studied the nonstationary transmission of two ultrashort laser pulses incident on a thin film. The radiation frequency of one of these pulses is in resonance with the two-photon transition from the ground state of the crystal to the biexciton state, while the other pulse coherently mixes the exciton and biexciton states, leading to strong renormalization of the energy spectrum of the crystal. We have obtained a system of nonlinear equations describing the time evolution of the exciton and biexciton amplitudes and the fields of three pulses transmitted through the film. We have analyzed the effect of amplitudes and widths of incident pulsed and of the time delay between them on the peculiarities of film transmission of these pulses. We have predicted the effect of a substantial time delay in the generation of the pulse transmitted through the film relative to the incident pulse, which is in resonance with the exciton–biexciton transition frequency. The possibility of generation of a precursor, viz., a pulse transmitted through the film sooner than the peak of the incident pulse reaches the film, as well as possibility of generation of a reflected pulse in the absence of the incident pulse, has been proven.
Splittings of spontaneous emission lines in laser excited wurtzitetype CdS and ZnO are observed under a uniaxial stress at 1.8 K. The relative intensity of the split components of the excitonic molecule emission line is accounted for by using Hanamura's wave function for the excitonic molecule.
An exciton in a pure crystal interacts with other excitons or/and lattice vibrations. The exciton is not always the most stable elementary excitation in solids and when excitons are created at such a high density that they enter each other’s range of interaction before their decay, they condense into the more stable states of elementary excitations, i.e., excitonic molecules (EM) or electron-hole (e-h) metallic droplets. The type of condensation depends on the electronic band structure of the material. For example, it depends on whether the lowest band-to-band transition is direct or indirect (in many-valley structure) in the wave-vector space and whether the direct transition is dipole-allowed or -forbidden and the indirect one is phonon-allowed or -forbidden.
The transmission and reflection of ultrashort laser pulses by a thin semiconductor film are studied theoretically under the conditions corresponding to two-photon, two-pulse creation of biexcitons from the ground state. Specific examples are given to demonstrate various possibilities of controlling the transmission of both incident pulses by changing the amplitude of one of them
In CuBr the polariton dispersion E(Q-->,H-->) in the presence of a
magnetic field H--> is dissymmetric with respect to Q--> and
H-->, Q--> denoting the polariton wave vector. We study this
dissymmetry using hyper-Raman scattering techniques in the presence of a
static magnetic field which is varied between - 70 and 70 kG in a given
configuration. The experimental results are quantitatively explained,
considering Q--> and H-->-linear terms in the exciton Hamiltonian.
The effective g values and the CQ-linear interaction term are
determined with a good accuracy and an upper limit of the anisotropic
exciton-mass parameters is established. Since biexcitons are involved in
the scattering process, the influence of the magnetic field on their
different states and on the selection rules of hyper-Raman scattering
are studied. In agreement with our theoretical considerations, no
decomposition of the biexciton ground state has been observed.
A study was made of the induced absorption in amorphous selenium particles (average radius ~20 nm) embedded in a polymer. A picosecond pump and probe technique was used. The change in the absorption was measured in the spectral range 550–750 nm when the pump radiation was in the form of pulses of 15 ps duration and 2.3 eV photon energy. The induced-absorption spectra were attributed to optical exciton—biexciton transitions. The exciton lifetime was estimated to be 424 ± 32 ps.
This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.
Two-photon forward Raman scattering in CuCl is the four polariton process; two incident polaritons ħωo(ko) are scattered into a pair of lower branch polaritons having different energies via excitonic molecule state at k=2ko. Scattering into lower and upper branch polaritons can take place via excitonic molecule with small k<ko. At resonant excitation, the secondary emission consists of Raman and luminescence components. From the line shapes of luminescence bands, the relaxation of resonantly created excitonic molecules is discussed.
The biexciton states in CuBr have been studied at K ≅ 0 by two-photon absorption, using two different laser sources. The energy and the symmetry of these states have been unambiguously assigned: EB(Γ1) = 5.9061 eV, EB(Γ5) = 5.9103 eV, EB(Γ3) = 5.9128 eV.
Using a two-beam “pump and probe” technique, we investigate the gain/absorption spectra of CuBr samples as a function of the photon energy and the intensity of the pump beam. We find contributions from optical transitions between exciton and biexciton states, and from transitions involving excitons bound to impurities as well as intraband exciton scattering. The detailed spectral shape depends on the exciton and biexciton population distribution, governed by the excitation conditions.
Specific features of two-photon nutation in a system of coherent biexcitons in CuCl-type semiconductors are studied. It is shown that, depending on the parameters of the system, nutation represents a process of periodic conversion of photon pairs into biexcitons and vice versa. The possibility of phase control of optical nutation is predicted.
A new lasing mechanism for semiconductors like CuCl, CuBr is proposed based on the two-photon pumping of biexcitons from the ground state of the crystal and generation or amplification of light in the region of M-band of luminescence due to the optical exciton-biexciton conversion. It was shown that the net gain essentially depends on the level of two-photon pumping and rapidly decreases deep into the crystal due to the spatial depletion of pump radiation. Estimations for CuCl give the values of lasing photons with the energy about 3,2 eV and the maximum small signal gain about the value of the exciton absorption coefficient.
This paper considers the effects on the symmetries and binding energies of biexcitons of 1) the short-range interaction (Coulomb and exchange), 2) a multi-valley conduction band and 3) the mass anisotropy of the valleys. It demonstrates that the ground state of the biexciton in a multi-valley semiconductor should be a spin triplet with an antisymmetric valley function and that poly-excitons Xx
,x>2, should be stable in a material like Si.
We present an experimental set-up which allows us to perform two-photon spectroscopy to biexciton states. By changing the geometry of the experiment, these biexcitons may be created with different wave-vectors. In this way, evidence of a biexciton dispersion is obtained.
We present a model for lasing oscillation due to bi-excitons and localized bi-excitons in wide-gap II-VI semi-conductor quantum wells. We introduce the condition for population inversion in bi-exciton-exciton optical transition, and show the importance of studying the thermodynamic equilibrium between bi-exciton and exciton states. The Saha equation shows that bi-excitons decompose into two free excitons at fairly low temperatures due to the small binding energy (10 to 30 meV) in II-VI quantum wells, making the population inversion possible only at low temperatures. We point out that bi-excitons localized at certain potential minima in the quantum-well plane will achieve the population inversion even at room temperature if the local potential is deep enough to prevent thermal activation (about 100 meV). By simple theoretical calculation, we show that the localized bi-exciton-exciton optical transition will produce sufficient optical gain for lasing oscillation and has potential application in low-threshold-current blue-light emitting lasers.
Time-dependence of the excitonic molecule luminescence in CuBr is measured at 4.2 K under the one-photon band-to-band excitation and the two-photon resonant excitation of excitonic molecules by using a picosecond tunable laser. The lifetimes of excitonic molecules and single excitons are determined to be 60 ps and 150 ps, respectively, by analyzing the results for the two cases of excitation. With these values of the lifetimes, the time-dependence of the luminescence under two types of excitation is explained self-consistently. The lifetime of molecules almost agrees with the radiative lifetime calculated by using existing theories. It is found that the probability of the formation of excitonic molecules per one collison of two single excitons is quite low, and that in the case of the resonant excitation the re-formation process of molecules is negligible.
By the use of two dye lasers, the spatial dispersion of the excitonic molecule has been studied by the excitation into states of large wave vectors. With the first laser beam omega1(k1) an excitonic polariton is created at a large wave vector and an excitonic molecule is formed with the second laser beam omega2(k2). The relation between omega1 and omega2 is expressed by a straight line of slope 0.57, and the mass of the excitonic molecule is determined to be 2.3 times as much as that of the transverse exciton. In the two different configurations in which the two laser beams are in the same and opposite directions, excitonic molecules are created at k1± k2. From the analysis of the relation between omega1 and omega2 in the two configurations, the excitonic mass is deduced to be (2.5˜3.0)m0.
Dynamical behavior of population of excitonic molecules in the kinetic energy space is investigated by taking into account the mutual interaction of molecules and the interaction with the heat bath of acoustic phonons. The potential energy between molecules is assumed to be constant for momentum transfer q0, where K is the momentum of the excitonic molecules, the number density in the energy space is described exactly by a Fokker Planck equation. The integral differential equation for the number density is solved numerically and some characteristics of this equation are clarified.
Giant two-photon absorption for the direct generation of excitonic molecule is found at 2.5507 eV in CdS. Two-photon resonance Raman scattering is found which has an excitonic molecule and a transverse exciton as the intermediate and final states, respectively.
In CuBr, biexcitons are excited resonantly by the absorption of two photons which are provided by two different laser sources. By a change in the geometrical configuration of the experiment, the wave vector K--> of these biexcitons can be tuned. Thus, for the first time, a momentum spectroscopy of biexciton states is achieved. The biexciton dispersion E(K-->) is established and a splitting of biexciton states, degenerate at K-->=0, is observed. This dispersion is fully explained by the band parameters known from the exciton case.
Analytic solutions are used to describe a transient interaction of resonant laser radiation with a thin semiconductor film under the conditions of two-photon excitation of biexcitons from the ground state of a crystal. Several nonlinear effects are predicted for the transmission of ultrashort pulses by a thin film: intensity discrimination, compression and transformation of the profile of a pulse incident on a film, and the possibility of 'superradiative' amplification of a short pulse traversing a previously excited crystal.
A theoretical calculation which fully takes into account the electron-hole exchange effect is performed for the ground state energy of the excitonic molecule in thallous halides. It is found that the previous variational calculations are insufficient to obtain a stable formation of the excitonic molecule in these materials.
Excited states of excitonic molecules are found in the study of the two-photon-resonant Raman scattering. These states consist of four levels and have binding energies of 1.0–1.8 meV, which are very small compared with those of the ground states. They are considered to be the rotational and vibrational states of excitonic molecules.
Excitons are the energetically lowest excitations of the electronic system in an ideal semiconductor at zero temperature. If the excitons couple to the electromagnetic field, a mixed state is formed, the quanta of which are called excitonic polaritons. Associates of two excitons, so-called biexcitons, have been observed in many semiconductors. Excitons are known for about forty years. During the first three decades, they have been investigated mainly by the classical spectroscopic methods, i.e., reflection, transmission and luminescence spectroscopy. In the last decade, several new techniques have been developed, which allow for a direct spectroscopy in momentum space. In this contribution, we review these novel techniques, both linear and nonlinear ones, and present results obtained for excitons, polaritons and biexcitons. The review is restricted to semiconductors which have their conduction band minimum and their valence band maximum at the same point of the Brillouin zone (direct-gap materials) and which have a band to band transition which is dipole allowed.
Bose-condensation of the excitonic molecule gas is expected from the large quantum effect and the boson character of the particles. It is discussed how to accumulate the Bose-condensed system of excitonic molecules directly and how to observe evidence of the Bose-condensation of excitonic molecules in the luminescence spectrum.
The peculiarities of two-photon nutation in a system of coherent biexcitons in CuCl semiconductors are considered taking into account the elastic biexciton - biexciton interaction. It is shown that depending on the system parameters, optical nutation represents a process of periodic transformation of photon pairs into biexcitons and vice versa. The possibility of exercising the phase control of the optical nutation process is predicted. (nonlinear optical phenomena)
The theory of regular and chaotic self-pulsations in a CuCl crystal with the participation of coherent excitons and biexcitons is elaborated. The method of chaotic self-pulsation suppression in the system of coherent excitons and biexcitons is proposed. This method consists in action of external periodical turbulence upon a stochastic system. The range of amplitude values and frequencies of external harmonic pump were found at which the chaotic oscillation regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. The feasibility of observing the predicted effects in experiment is discussed.
We study the influence of the short-range electron-hole exchange interaction (EHEI) on the (A°, X)-bound exciton ground state, for direct gap semiconductors with positive spin-orbit coupling at k = 0. The envelope contribution to the EHEI is computed using our previously obtained 35-term Page and Fraser-type wave function, showing that the EHEI are comparable in the cases of excitons and bound excitons. The crystalline part of the EHEI lifts the degeneracy between the states J = 5 2, (Γ7 + Γ8) and J = 3 2 (Γ8), the former being lower in energy. In the case of GaAs, the EHEI is smaller than the j-j coupling of the two holes, so that the states J = 1 2 (Γ6) are the highest in energy in agreement with the experimental data, relative to shallow impurities.
We consider two gain theories which take into account the Coulomb interaction, i.e., the semiconductor Bloch equation and the three-level model including bi-exciton states. Based on the three-level model, we derive a formula for a linear bi-exciton gain. Using rate equations including excitons, bi-excitons, and cavity photons, we show possibilities and performance of blue-light bi-exciton lasing in quantum-well and quantum-dot lasers.
Line shapes of the luminescence, coexisting with the Raman scattering, of excitonic molecules (EM) have been studied in the case of the resonant excitation. The EM's are resonantly created with wave vectors, such as k{=}0, \mbi{k}{=}2\mbi{k}0 and \mbi{k}{=}2.3˜12.2\mbi{k}0 (k0{=}4.44× 105 cm-1), by the two-photon excitation technique. By the use of model calculations based on the Gaussian distribution in the k-space, the EM's are inferred to re-distribute anisotropically in the range |\mbi{k}-2\mbi{k}0|
Specific features of two-photon nutation in a system of coherent biexcitons in CuCl-type semiconductors are studied. It is
shown that, depending on the parameters of the system, nutation represents a process of periodic conversion of photon pairs
into biexcitons and vice versa. The possibility of phase control of optical nutation is predicted.
Direct creation of bi-exciton states by two-photon absorption in direct gap semiconductors is investigated theoretically. A numerical application to the case of CuCl shows that the two-photon absorption coefficient for bi-excitonic transitions is larger than that for two-photon interband transitions by three orders of magnitude. It becomes comparable to that for one-photon excitonic transitions for available laser intensities. The main contribution to this enhancement of the absorption coefficient for the transitions to the bi-exciton states is found to be from the resonance effect.
Biexcitons in CuCl decay into Z3 excitons (longitudinal or transverse) and photons (ML or MT luminescence). Here an intense, tunable-laser pulse is used to study this luminescence in thin CuCl films. As a function of laser frequency (3.209-3.219 eV) the luminescence line shapes in the ML and MT bands show absorption which we interpret as a resonant two-photon (laser plus luminescence) transition from the ground to biexciton state. The polariton nature of the intermediate state is explicitly considered and shown to bring about a resonant condition, greatly enhancing the absorption process. Reabsorption involving the upper and lower transverse polariton branches has been reported previously. Here we report a new transition which uses the longitudinal exciton as an intermediate state. From laser frequencies and these three reabsorption dip positions we determine a portion of the Z3 exciton-polariton dispersion curve.
The dispersion of excitons and hence of excitonic polaritons in zinc-blende-type semiconductors reflects the complexity of the band structure of these materials. We calculate the dispersion of the exciton branches Ei(Q⃗) of the eightfold ground state from an invariant expansion of the center-of-mass Hamiltonian, including exchange interaction, up to second order in the exciton total wave vector Q⃗. The excitonic polaritons are then constructed according to Hopfield's polariton theory, which is extended to the case of more than one oscillator. The polariton dispersion is experimentally studied for CuBr by hyper-Raman scattering via biexcitons. The selection rules for this process are calculated for different scattering configurations, whereby the symmetry of the biexciton ground state, having components of Γ1, Γ3, and Γ5 symmetry, is considered. A self-consistent analysis of the observed hyper-Raman emission lines yields the dispersion of the multicomponent excitonic polaritons in CuBr.
The dynamics of biexciton radiative decay in semiconductor quantum wells is treated within the excitonic-molecule mode including super-radiance, exciton recoil, and nonzero photon momentum. For parameters describing GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{$-${}}\mathit{x}}$As quantum wells, we find that the rate for the decay of the excitonic molecule (in the ground state of the relative motion between excitons) into an exciton and a photon is less than the decay rate characteristic of radiative free one-excitons.
Starting from the two-electron and two-hole representation of the biexciton Hamiltonian in the degenerate-band case, we formulate the secular equation of the interacting biexciton ground state by an invariant expansion. We include various biexciton exchange interactions and the symmetry-breaking effect due to the finite biexciton wave vector. Solving the resulting Schrödinger equation numerically, we then compare it to experimental results for the biexciton dispersion and give an estimate of the biexciton energy for vanishing exchange interactions.
We have observed the lasing of submicron-sized ZnO particle in a Fabry-Perot cavity at low temperatures. A thin alkali-halide crystal including a small amount of ZnO particles are sandwiched between two quartz plates arranged as a pair of opposite mirrors, that is, a Fabry-Perot cavity. Under low excitation due to a He–Cd laser, emissions of free and bound excitons and their phonon replicas are recognized markedly, while a biexciton emission band appears under high-dense excitation by a pulsed N2 laser. Biexciton lasing is demonstrated as a narrowed emission by focusing the excitation light beam on an appropriate position being a ZnO particle in the cavity. When a cavity length satisfies the resonant condition, the lasing occurs in the spectral region of the biexciton emission band and with the very small divergence angle. The obtained threshold of excitation-power density is about 0.50 MW/cm2. We discuss lasing in terms of stimulated emission caused by population inversion between biexciton and exciton states.
Renormalization and damping of excitonic molecules due to their coupling to the radiation field is theoretically investigated within a picture of interacting polaritons and excitonic molecules. Numerical results are given for some cubic and wurtzite-type materials. For CdS the renormalization reaches nearly 20% of the binding energy of the excitonic molecule.
Es werden Renormierung und Dämpfung von Exzitonenmolekülen infolge ihrer Ankopplung an das Strahlungsfeld im Rahmen eines Bildes wechselwirkender Polaritonen und Exzitonenmoleküle theoretisch untersucht. Für einige kubische und Wurtzitmaterialien werden numerische Resultate angegeben. Im Falle von CdS erreicht die Renormierung nahezu 20% der Bindungsenergie des Exzitonenmoleküls.
The probabilities of the two-photon absorption by a biexciton in the ground and the first vibrational states in CuBr and the probability of the two-photon Raman scattering with the participation of the ground and the first vibrational states of the biexciton as intermediate states are calculated by perturbation theory method. Supposing that a Lorentzian distribution of frequencies ωi of the exciting light and a Lorentzian shape of the emission lines of the excition occur, the shape of the emission line at different values of the biexciton half-width Γm is calculated. The dependence of the Raman scattering maximum position on ωi is obtained. At the condition 2Γ ≧ Γm; Γ Γm ≦ Γf the experimentally observed deviation of the Raman scattering maximum shifting from 2Δωi, is explained. The polarizational properties of the Raman scattering probability are obtained including the case when the intermediate states are the biexcitons Γ1, Γ5, Γ3.Die Wahrscheinlichkeiten der Zwei-Photon-Absorption durch ein Biexziton im Grundzustand und im ersten Schwingungszustand für CuBr und die Wahrscheinlichkeit der Zwei-Photon-Raman-Streuung unter Teilnahme des Grundzustandes und des ersten Schwingungszustandes des Biexzitons als Zwischenzustände werden mit der Methode der Störungstheorie berechnet. Unter der Annahme einer Lorentzverteilung der Frequenzen ωi des anregenden Lichts und einer Lorentzform der Emissionslinien des Exzitions wird die Form der Emissionslinie für verschiedene Werte der Biexzitonenhalbwertsbreite Γm berechnet. Eine Abhängigkeit des Raman-Streumaximums von ωi wird gefunden. Unter der Bedingung 2Γ ≦ Γm, Γ; Γm ≧ Γf wird die experimentell beobachtete Abweichung der Maximumverschiebung der Ramanstreuung von 2Δωi erklärt. Die Polarizationseigenschaften der Ramanstreuwahrscheinlichkeit, einschließlich des Falles, wo die Zwischenzutände die Biexzitonen Γ1, Γ5, Γ3 sind, werden erhalten.
A many-particle system of composite particles consisting of two different fermions each and interacting by the Coulomb potential is considered. For the case that the composites are present in bound states only the constituent self-energy is calculated to linear order in the densitytaking all symmetries of the many-body wavefunctions into account. The correlational part (screening part) of the selfenergy is calculated in the Born collision approximation. Numerical values for the shift of the continuum-edge of the spectrum of excitons in GaAs are presented.
Es wird ein Vielteilchensystem untersucht, dessen Teilchen je aus zwei verschiedenen Fermionen mit Coulomb-Wechselwirkung zusammengesetzt sind. Für den Fall, daß die Teilchen nur in Bindungszuständen vorliegen, wird ihre Selbstenergie linear in der Dichte unter Berücksichtigung aller Symmetrien der Wellenfunktionen berechnet. Der Korrelations-(Abschirmungs-) beitrag zur Selbstenergie wird in Bornscher Näherung untersucht. Numerische Werte für die Absenkung der Kontinuumskante der Exzitonen in GaAs werden angegeben.
Splitting of spontaneous emission lines in laser excited wurtzite-type CdS and ZnO are observed under an uniaxial stress at 1.8 K. Energy shifts and polarization characteristics of these lines are successfully accounted for by an energy scheme of the excitonic molecule using a group theoretical classifications.
The excitonic polariton dispersion in wide k-space for k∥[111] is measured through the two-photon-resonant Raman scattering with the use of the double beam excitation technique. The k-linear effect, the heavy and light masses and the polariton effect of the Z1,2 exciton are clarified.
The polarization properties of biexciton luminescence and resonant two-photon Raman emission are studied. For the first time, direct evidence on the biexciton distribution function in momentum space is obtained. Raman lines are found to be due to a four-particle process where all momenta are well defined. The origin of the biexciton luminescence lines is, on the contrary, a cold gas of biexcitons, which is subjected to elastic and inelastic collisions. Its distribution function is wide spread but not yet isotropic in the momentum space.
Les propriétés de polarisation de la luminescence du biexciton et de l'émission Raman à deux photons résonnante ont été étudiés. Pour la première fois, des informations sur la distribution des biexcitons dans l'espace des moments sont obtenues. Les raies Raman sont dues à un processus à quatre particules dans lequel tous les moments sont bien définis. Les raies de luminescence du biexciton sont dues, au contraire, à la recombinaison d'un gaz froid de biexcitons, qui a été soumis à des collisions élastiques et inélastiques. La distribution de ces biexcitons dans l'espace des moments est étendue mais n'est pas complètement isotrope.
The behavior of the semiconductor dielectric susceptibility under the action of a strong laser pulse in the range of the luminescent
M band and two-photon probe of a biexciton level is investigated. It is shown that the pronounced Autler-Towns effect occurs
at the two-photon transition. The position of the absorption peaks is essentially determined by the amplitude and frequency
of the pump field.
We report on symmetry-based calculations of the spin structure of excitons and biexcitons in quantum wells. Depending on the point-group symmetry of the material and the growth directions of the quantum wells, we derive Hamiltonians appropriate for the description of excitons and biexcitons. We show possible paths of coherent spin-flip processes of a particle and their consequences for experimental observations.
The theory of the electronic excitations in a highly excited semiconductor is presented. The relaxation processes, the formation of excitons and excitonic molecules, the interaction among the various forms of electronic excitations, as well as their optical and thermodynamical properties are analyzed. At low temperatures one expects condensations into the quantum statistically degenerate phases of the excitonic molecules and of the electron-hole plasma. The physical properties of these low temperature phases are investigated. Possibilities and previous attempts to observe the Bose-Einstein condensation in excitonic systems are discussed critically. The experimental observations of the electron-hole liquid phase transition are reviewed.
The binding energy of the excitonic molecule, a complex consisting of two electrons and two positive holes, is calculated as a function of the mass ratio me/mh by avariational method. It is shown that the excitonic molecule is stable for any value of the mass ratio. For me{=}mh, the binding energy is estimated to be 0.00684 mee4/\varepsilon{0}2\hslash2. Some results about the wave function are also presented.
New emission bands called the M, N1, N2 and N3 bands have been found near the band edge in CuCl single crystal with excitation by the two-photon absorption of a Q-switched ruby laser. All emission intensities show nonlinear dependences upon the excitation intensity. One of them, the M band located at lambda3919 A at 4.2°K, is concluded as the radiative decay of a free excitonic molecule. The shape variation and peak shift to the low energy side of the M emission band with respect to the increase of the laser power are similar to those due to the raising of temperature. The line shape is an inverted replica of the Maxwell distribution. The system of the excitonic molecule has been concluded to have the effective temperature which is higher than the lattice temperature in the high density state of excitonic molecule. The mechanism of the radiative decomposition of the excitonic molecule has been discussed.
The binding energy of the excitonic molecule is calculated as a function of the mass ratio . It is found that the excitonic molecule should be stable for any value of the mass ratio.ZusammenfassungDie Bindungsenergie des Exzitonenmoleküls wird als Funktion vom Verhältnis der Elektronenmasse zur Lochmasse berechnet. Es zeigt sich, dass das Exzitonenmolekül füf jeden Wert vom Masseverhältnis stabil sein sollte.
If a band edge has N equivalent minima in the Brillouin zone, it is possible consistent with the exclusion principle to place 2N identical electrons in the same molecular orbital. This theorem suggest the possible stability of exciton molecular complexes, (exc)8 in Ge and (exc)12 in Si. Supported by National Science Foundation GH 35688.
Transverse magnetoreflection measurements give evidence for a longitudinal and a triplet state near the first exciton band in CuCl.
The two-photon absorption spectrum due to excitonic molecules is measured in CuCl at 77 and 4.2°K. We measured values of the two-photon transition cross section of the order of 10-44 cm4 sec and estimated a peak value of 10-42. The binding energy of the molecule is found to be 255 cm-1.
In this paper the energetics of the formation of electron-hole metallic liquids in semiconductors is examined. The ground-state energies of electron-hole metals are calculated using Hubbard's approximate treatment of the electron gas for the following cases: (a) germanium, (b) germanium with a large (111) strain, (c) silicon, and (d) GaAs. The simple case of a single isotropic maximum for the valence band and a single minimum for the conduction band is also treated. It is shown that for both Si and Ge, the binding energy of the metallic state relative to free excitons is 5.7 and 1.7 meV, respectively. These values and the values of the equilibrium density are in good agreement with experiment. In the isotropic model the metallic state is not bound while for GaAs and strained Ge the metallic-state energy per electron is essentially equal to that for a gas of free excitons. The low-density limit of the isotropic band model is examined and the ground state for this system is predicted to be a dilute gas of molecules. It is argued that the forces between molecules are repulsive and will cause this state to break up at relatively low densities. If the density is increased, the system will undergo a first-order transition to the metallic state. The relevance of these calculations to the metal-insulator transition problem is discussed. It is pointed out that the fact that anisotropic and many-valleyed bands favor the metallic state means that the metal-insulator transition must ultimately be first order.
The states of the biexciton molecule are related to the band structure of the crystal and effects due to spin–orbit interaction and to electron–hole exchange are taken into account. The cases of CuCl and CdS are explicitly studied and the possible bound states are given. Optical luminescence decay processes and two-photon excitation processes are discussed and related selection rules are given. In the case of CdS all decay processes are shown to produce polarized photons. Experimental results are analyzed and are compared with theoretical calculations of the biexciton ground state energy.Les états de la molécule biexcitonique sont reliés à la structure de bande du cristal en tenant compte des effets dǔs à l'interaction spin–orbite et à l'échange électron-trou. Les cas de CuCl et de CdS sont étudiés en détail et on donne les états liés possibles. On discute les processus de recombinaison luminescente et d'excitation optique à deux photons, avec leurs règles de sélection. Dans le cas du CdS, on montre que toutes les recombinaisons radiatives produisent des photons polarisés. Les résultats expérimentaux sont discutés et comparés aux calculs théoriques de l'énergie de l'état fondamental du biexciton.
The interaction of excitons in Ge and Si was recently investigated in a large number of experimental studies. All these results may be explained if one assumes that after reaching the threshold temperature and excitation level the condensed phase of non-equilibrium carriers appears. There is a direct confirmation of the existence of collective substances, which consist of a large number of non-equilibrium carriers.
The exciton spectra of CuCl have been investigated in the presence of high transient magnetic fields up to 180 kG.The Zeeman splitting of the broad orthoexciton line ν1f (25,865 cm−1 at 4.2°K) is unresolved because of a too small effective g factor (g = 0.9). The paraexciton line ν1 (25,814 cm−1 at 4.2°K) is detected in magnetic field. The mixing of the ortho and paraexciton states T15 and T2 in magnetic fields is discussed.The bound exciton line ν2 (25,654 cm−1 at 4.2°K) splits in four components in magnetic field, both in absorption and in emission. The sharp line ν21 (25,665 cm−1 at 4.2°K) behaves similarly. The g factors of both the ground and excited states are obtained from the temperature variation between 1.9° and 20°K of the intensities of the absorption lines. This allows us to ascribe the above lines to excitonneutral acceptor complexes.