Exciton Continuum Research Articles

Optical Emission of Exciton-phonon Quasiparticles in InP

New optical emission structure is observed at a photon energy about one-LO-phonon above the gap of InP at low temperatures. It is suggested that this new structure arises from the emission of a resonant quasiparticle involving the interaction of the exciton continuum with discrete 1s-exciton states plus an LO-phonon. A Green's function formalism is used to calculate the energy spectrum of this quasiparticle and to explain the dependence of the emission rate on temperature and light frequency. Also, an analysis of the feasibility of observating this structure in GaAs is presented.

Experimental evidence for the transition from two- to three-dimensional behavior of excitons in quantum-well structures.

The transition from two- to three-dimensional behavior of excitonic recombination was investigated by optical-absorption and photoluminescence (PL) spectroscopy. By molecular-beam epitaxy, we have grown pseudomorphic ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/Ga(Al)As multiple- and single-quantum-well structures with and without Al in the barriers and with an In content between 13% and 22%. The well width was varied from 25 nm to less than 1 nm. From absorption spectra, we have directly determined the exciton binding energy for the first heavy-hole-to-electron transition and unambiguously for the light-hole-to-electron transition in a sample with a well width of 3 nm. The exciton binding energy nearly reaches the bulk values of the barrier material for very small well widths, e.g., 4.2 \ifmmode\pm\else\textpm\fi{}0.5 meV for a 1-nm well width with a GaAs barrier. The dependence of the PL linewidth on the well width in single-quantum-well structures shows behavior similar to the exciton binding energy. We also reach the narrowest linewidths (0.6 meV) for the thinnest quantum well (0.75 nm) and a maximum (3 meV) at around a 5-nm well width. Samples with Al in the barriers (14%) show similar behavior, but the linewidths increase by about 30% at larger well widths and more than 100% at narrower wells in comparison to samples with a binary barrier material. These experimental results demonstrate very clearly the transition from an exciton with three-dimensional properties of the well material (at larger well widths) to an intermediate state with a maximum two-dimensional character (at around 5 nm) and once again to a three-dimensional behavior of the exciton with the properties of the barrier material (at well widths less than 4--5 nm). All PL peaks show a fine structure, which can be very accurately fitted by only two Gaussian curves. A comparison between absorption and PL spectra shows that an additional higher-energy PL peak, which can be resolved in the spectra of high-quality samples with narrow linewidths, corresponds to the onset of the exciton continuum.

Accurate theory of excitons in GaAs-Ga1−xAlxAs quantum wells

Binding energies of excitons in quantum wells are calculated including valence-band mixing and also other important effects, namely Coulomb coupling between excitons belonging to different subbands (which is predominantly with the exciton continuum), nonparabolicity of the bulk conduction band, and the difference in dielectric constants between well and barrier materials. All these effects are found to be of a comparable size, tend to increase the binding energies, and taken together result in very high binding energies, particularly in narrow GaAs/AlAs quantum wells. Binding energies can be even higher than the two-dimensional limit of four times the bulk Rydberg. Theoretical results agree within a few tenths of a milli-electron-volt with available photoluminescence excitation experiments. Valence-band mixing gives a finite oscillator strength to some excitons not in s states, but does not change the selection rules based on parity. Calculated oscillator strengths of the ground-state heavy- and light-hole excitons are found to be in good agreement with absorption and reflectivity experiments.

Absolute absorption coefficient of Cd1-xMnxTe (x=0.09, 0.16, 0.34) near the E0 gap in external magnetic fields

The optical absorption coefficient of Cd1-xMnxTe (x=0.09, 0.16, 0.34) is determined near the E0 gap at T=1 K in external magnetic fields up to 5 T. Single-crystal Cd1-xMnxTe layers with thicknesses 1-2 mu m were grown on a (001) GaAs substrate by MBE. The substrate was removed by mechanical polishing and chemical etching. In Cd1-xMnxTe a large splitting of the twofold degenerate Gamma 6 conduction band and the fourfold degenerate Gamma 8 valence band occurs at low temperatures in external magnetic fields. As a consequence the free exciton ground state splits into six components. In the Faraday configuration two allowed optical transitions for both right-and left-circular polarized light can be observed in the absorption spectrum. The measured splitting of the exciton ground-state energy as a function of the magnetic field is in good agreement with an existing theoretical band model for diluted magnetic semiconductors. Without an external magnetic field the authors obtain for the absorption coefficient a value of 4.0*104 cm-1 for the continuum exciton states near E0.

Resonant Raman scattering by optical phonons in ZnSe and Zn 0.97Mn 0.03Se near the E0 gap

The efficiency of resonant one-LO-phonon Raman scattering in oriented cubic ZnSe and Zn 0.97Mn 0.03Se single crystals is studied near the E 0 gap at 115 and 80 K, respectively, and compared with theoretical calculations. Absolute values of the Raman scattering efficiency (RSE) were determined for scattering by the deformation-potential and Fröhlich electron-phonon interaction. A quantitative comparison of the experimental data with existing model calculations for the RSE, where bound and continuum exciton states are considered as intermediate electronic states in the scattering process, shows good agreement. No significant differences between constructive and destructive interference of the two scattering mechanisms were found. Near resonance strong Raman intensities were observed in backscattering configurations, where scattering via the deformation-potential and Frölich interaction is forbidden according to calculated Raman selection rules.

Analysis of direct exciton transitions in CuGa(S xSe 1−x) 2 alloys

The absorption coefficient spectra of the chalcopyrite alloys system CuOa(S x Se 1− x ) 2 were measured near the fundamental band edge at 77 K. From the analysis of the data, taking into account both the discrete and continuum exciton contributions, the exciton binding energy and the broadening were determined. It is shown that the exciton-phonon coupling is weak and that the absorption line shape is given by a symmetrical Lorentzian function. Also, it was found that the dependence of the oscillator strength on the energy gap can be explained by the dipole approximation.

Excitonic relaxation processes in quantum well structures

Excitonic relaxation processes in quantum well structures are reviewed, focusing attention on the localized and the weakly delocalized regimes. In the localized regime, the acoustic phonon-assisted exciton transfer among the localized sites due to the interface roughness plays an important role in determining the energy and phase coherence relaxation at low temperatures. The effect of magnetic field on the exciton localization is also discussed. In the weakly delocalized regime the possible mechanisms of the dephasing relaxation are the acoustic phonon-mediated intra- and inter-subband scattering, the Fano-type resonance between the light hole exciton and the heavy hole exciton continuum and the elastic scattering by the interface roughness. Under the high intensity excitation, the interactions between excitons and free carriers become increasingly important in determining the dephasing relaxation.

Theory of line shapes of exciton resonances in semiconductor superlattices.

Realistic model calculations on the absorption spectra of semiconductor superlattices are presented. Emphasis is put on the analysis of line shapes of various peak structures arising from discrete excitonic states of one pair of subbands coupled with the excitonic (discrete and continuum) states associated with other pairs of subbands. The angle-dependent valence-band mixing and the final-state interaction effects are properly taken into account via the k-space sampling technique. Our results are in excellent agreement with recent high-resolution photoluminescence excitation spectra for a number of GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum wells and superlattices.

Optical investigation of the exciton transfer between growth islands of different well widths in GaAs/AlxGa1-xAs quantum wells.

The exciton population and the transfer of excitons was investigated for growth islands in quantum wells (QW's) by cw-photoluminescence (PL), time-resolved PL, and photoluminescence excitation spectroscopy (PLE). For high-quality GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As QW's with 13 nm QW thickness we found a strong dependence of the exciton population of three observed different island regions on excitation wavelength and excitation intensity. In a wide range of excitation wavelengths, the intensity ratios of the corresponding exciton transitions vary strongly with excitation intensity and, in general, do not reflect the area ratios of these islands. This behavior is caused by the different relaxation processes at the different excitation wavelengths when the lowest-energy states of the island regions are populated. By resonantly exciting the subbands in the QW, the created excitons remain localized and relax within the island regions. By nonresonantly exciting the exciton continuum of the confined subbands, the islands with the lowest energy are effectively populated within a time smaller than the luminescence decay-time constant. We determined the area ratios of the islands and the normalized exciton-transfer rates. A quantitative analysis of the intensity ratios of the cw measurements and time-resolved PL measurements revealed a surprisingly long exciton-transfer--time constant in the order of 2 ns, which is dependent on the potential-energy difference between neighboring islands.

On the Dynamical Stark Effect of Excitons. The Low‐Field Limit

AbstractThe dynamical Stark effect of excitons in semiconductors is treated in three and two dimensions (bulk material and MQW structures, respectively). Within the low‐field limit, theoretical results are presented for the gap function, the excitonic enhancement of the Stark shift, and the induced density. Higher bound states and the excitonic continuum are fully taken into account using the Coulomb Green's function.

Resonance Raman scattering by optical phonons in GaAs near the E0 band gap.

We report the resonance of the first-order Raman scattering by longitudinal and transverse optical phonons in GaAs very near to the E 0 band gap at 100 K. The resonance enhancement observed at E 0 for deformation-potential (TO,LO) and Frohlich-interaction-induced (LO) scattering is about 100 times larger than calculated for uncorrelated electron-hole pairs. The effect is attributed to the Coulomb correlation of discrete and continuum excitons and agrees with Martin's calculation of these effects. The Faust-Henry coefficient is found to be nearly independent of frequency in the region of our measurements (C=-0.6±0.2).

Exciton effects in the index of refraction of multiple quantum wells and superlattices

We present theoretical calculations of the index of refraction of multiple quantum wells and superlattices. The model incorporate both the bound and continuum exciton contributions for the Γ region transitions. In addition, the electronic band structure model has both superlattice and bulk alloy properties. Our results indicate that large light-hole masses, i.e., mlh∼0.23, produced by band mixing effects, are required to account for the experimental data. Furthermore, it is shown that superlattice effects rapidly decrease for energies greater than the confining potential barriers. Overall, the theoretical results are in very good agreement with the experimental data and show the importance of including exciton effects in the index of refraction.

Optical and structural properties of molecular-beam epitaxially grown Ga0.47In0.53As/Al0.48In0.52As superlattices, emitting at 1.55 ?m at room temperature

We have combined photoluminescence and absorption measurements with double crystal x-ray diffraction in order to study the influence of growth conditions on optical and structural properties of Ga0.47In0.53As/Al0.48In0.52As superlattices of 10.5 nm well width grown by molecular beam epitaxy on InP∶Sn substrates. Superlattices with excellent structural properties can be grown even at low substrate temperatures of 500 °C, as indicated by narrow linewidths of the satellite peaks of the x-ray diffraction pattern of 20 to 25 s of arc (FWHM). However, elevated substrate temperatures are required to increase the intensity of the intrinsic luminescent subband transition at 77 K, to reduce the luminescence linewidth to 12 meV (FWHM), and to sharpen the absorption spectra. In addition to the absorption due to the steplike variation of the two-dimensional density of states, we observe excitonic transitions to the excitonic continuum at the subband edges.

Self-localized states in chain molecules of finite lengths

Chain molecules such as aggregates of pseudoisocyanine dye have long been known to develop a very high and narrow peak at the low energy end of the absorption spectrum commonly regarded as a typical indicator for aggregation of long polymers. Contrary to the usual interpretation of this so-called J band by an in-phase excitation of transition dipoles along the chain (giant dipole), the present publication puts forward the thesis that, in chains of finite length, the J band rather originates from bound states due to strong exciton–phonon interaction. These polaronic states (which bear a close relationship to Holstein’s and Davydov’s solitons) are situated immediately below the excitonic continuum. They are visible in light scattering experiments above a chain length threshold L>L0, where L0 is determined by electronic and elastic energies and the magnitude of the exciton–phonon coupling. These length-dependent effects are smeared out in solutions on account of the presence of polymers with variable lengths with distributions which depend on concentration and temperature and have been derived in a prior publication.

Direct absorption inside the electron‐hole liquid in Ge: Warping effects and final state interactions

AbstractEarlier absorption experiments in highly excited Ge are successfully explained and quantitatively fitted by a theory including Moss‐Burstein shift in warped hole bands, self‐energy effects, and multiple electron‐hole scattering via screened Coulomb potential. The corresponding Bethe‐Salpeter equation is solved numerically in momentum space. At frequencies above Moss‐Burstein influence, calculated absorption spectra are close to the exciton continuum independent of excited carrier concentration in agreement with experiment, which disqualifies a one‐particle description of direct absorption in the electron‐hole liquid of Ge.

On the Experimental Determination of Many‐Particle Effects at Interband Transitions

AbstractThe energy‐derivative spectra of the real and imaginary part of the dielectric function ε(ω) = ε1 + iε2 in the range of critical interband transitions can be used to determine a parameter which describes the influence of many‐particle effects. Afterwards the computation of the one‐electron spectra becomes possible from experimental spectra, which are modified by many‐particle interactions. The application of this procedure to ellipsometrically determined spectra of GaP and GaAs for the E1 transition results in the predominant influence of the continuum—exciton effect in accordance with theoretical predictions of Hanke and Sham.

Brillouin scattering, piezobirefringence, and dispersion of photoelastic coefficients of CdS and ZnO

We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position of the isotropic point of the stress-induced birefringence. From these spectra it is concluded that the Brillouin scattering in CdS and ZnO is determined by elasto-optic effects alone. The spectra of some of the photoelastic coefficients have been determined. A model dielectric constant is derived where both ground-state excitons and unbound continuum exciton states contribute. From this dielectric constant and the quasicubic model we calculate all the six independent photoelastic coefficents. By comparison with the experimental results the shear deformation potentials of the valence bands are obtained. It is found that the exchange interaction between the excitons may change the values of the photoelastic coefficients in ZnO about 10%.

Thermoabsorption in SnO2

The thermoabsorption spectra of Sn${\mathrm{O}}_{2}$ crystals have been measured near the fundamental absorption edge at 25, 80, and 115\ifmmode^\circ\else\textdegree\fi{}K with polarized light. New fine structure above the exciton continuum is observed with light polarized $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ which appears to be associated with exciton-phonon quasi-bound-states. For $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ the onset of a direct-allowed transition is indicated at about 4.0 eV.

Resonance Raman Scattering in Cuprous Halides

Resonant behavior of Raman cross-section is studied in CuCl, CuBr and CuI by using an argon ion laser and a tunable dye laser as the excitation light source. The results are in good agreement with existing theory demonstrating the significance of the discrete and continuum levels of excitons as the intermediate state of the transition. It is concluded that the 1 L O scattering cross-section near the resonance region is governed by the n =1 exciton level, while the exciton continuum contributes predominantly in the off resonance region. contrary to the cases of CuBr and CuI, higher exciton series ( Z 12 ) also plays an important role in CuCl, which fact is ascribed to the characteristic band structure of this material. As in CdS and ZnO previously reported, the observed frequency dependence of the 2 L O Raman intensity in CuCl is consistently interpreted in terms of the consecutive scattering of virtually created excitons by two phonons.

Electro-optical effects at the discrete and continuum exciton states in GaAs

We report electroreflectance spectra from a GaAs-Au Schottky barrier interface, in the region of the fundamental energy gap, at a temperature of ∼ 1.8 K. Both the ground exciton level and the continuum of states are investigated separately, by operating in the small modulation and in the on-off field limit, respectively. The field profile is monitored by I– V, C- V, and photovoltage measurements. It is found that, even at ∼ 1.8K, a high surface field is generally present. This moves the actual reflecting boundary of the exciton-polariton away from the surface and affects the ER lineshape through field-induced inhomogeneity effects and interference across the high field layer below the surface. The spectra corresponding to the states of the continuum are discussed in terms of the recent calculations of photon-assisted tunneling with coulomb interaction.