The ionization equilibrium of an electron-hole plasma in a highly excited semiconductor is investigated. Special attention is directed to the influence of many-particle effects such as screening and lowering of the ionization energy causing, in particular, the Mott effect ͑density ionization͒. This effect limits the region of existence of excitons and, therefore, of a possible Bose-Einstein condensate at low temperatures. Results for the chemical potential and the degree of ionization are presented for zinc selenide ͑ZnSe͒. A possible window for the occurrence of a Bose-Einstein condensate of excitons is shown, taking into account the Mott effect.

We investigate both experimentally and theoretically the excitonic absorption in ZnSe in a temperature range between 2 and 60 K with increasing densities of carriers. For higher temperatures a weak redshift of the exciton resonance is found which turns into a blueshift for lower temperatures. While the widely used simplified treatment of the scattering processes within a static screening approximation fails completely to describe this thermally induced crossover, it can be explained by the interplay between Coulomb-Hartree-Fock renormalizations and carrier-carrier and carrier-polarization scattering including the dynamical screening. [S0031-9007 (98)06251-6] PACS numbers: 71.35.CcThe nonlinear behavior of the excitonic absorption is one of the most investigated manifestations of many-particle effects in a highly excited narrow-gap semiconductor. For instance the Mott transition observed for increasing excitation densities is well understood as a consequence of screening of the Coulomb interaction between charge carriers. While the absolute energy of the 1s exciton stays nearly unchanged in bulk samples over a wide range of carrier densities its oscillator strength disappears due to band gap shrinkage. This was proved in many experiments [1-3] and explained qualitatively by strong compensation of gap shrinkage and weakening of the Coulomb interaction due to screening inspecting the effective Wannier equation of an exciton embedded in a thermal plasma [4][5][6][7]. The situation is rather different in quantum wells, where a blueshift of the exciton with increasing density was observed [8,9]. Qualitatively, this behavior is caused by the reduced dimensionality, which leads to a reduction of the Coulomb interaction between carriers [10] as was confirmed by more elaborated calculations for a dense exciton gas model [11]. In GaAs͞Ga 12x Al x As quantum wells the transition from quasi-2D to 3D behavior was found to occur at well widths of 19 nm, i.e., already at less than two exciton Bohr radii [9,12].The present situation is characterized by two aspects. At first, recent experimental results shed new light on the commonly accepted view that the excitonic resonance stays nearly constant in a large density region. In GaAs͞Ga 12x Al x As quantum wells of 21 nm width the exciton shift was found to change from a weak blueshift under resonant excitation to a weak redshift under nonresonant excitation [13]. Also in bulk ZnSe, where the influence of many-particle effects on the exciton can be observed much more pronounced than in the III-V semiconductors (GaAs) due to the larger exciton binding energy, a weak blueshift of the exciton [14] at resonant excitation and low temperatures has been found recently. Second, substantial progress has been achieved during the last few years to find out which many-particle effects have to be included into the semiconductor-Bloch equations (SBE) in order to describe the nonlinear absorption features of laser pulses. In particular, inclusion of carrier-polarization scattering processes was sh...

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We investigate the breakup of bound electron-hole pairs, known as Mott transition of excitons, in GaAs-GaAlAs quantum wells with increasing excitation, comparing two different theoretical approaches. Firstly, a thermodynamic approach is used to investigate the ionization equilibrium between electrons, holes and excitons, where the abrupt jump of the degree of ionization from 0 to 1 indicates the Mott density. It is extended to a self-consistent quasi-particle approximation (QPA) for the carrier properties, including dynamical screening of the Coulomb interaction between carriers. Secondly, a spectral approach based on the semiconductor Bloch equations within linear optical response is used, considering the quasi-particle (QP) properties of carriers and the dynamical screening between electron-hole pairs. While the first is effectively a one-particle approach, in the second the whole twoparticle spectrum is analyzed. Within the thermodynamic approach, a simple criterion for the Mott transition can be given: namely, if the sum of chemical potentials of carriers, reflecting the effective shrinkage of the band edge, crosses the exciton energy with increasing excitation. We demonstrate that this simple picture cannot be maintained in the two-particle approach. Here, a compact quantity, which describes the behavior of the band edge, does not exist. In fact, the behavior of the single states in the spectrum is generated by the interplay of dynamical screening in the interband self-energy and the effective interaction of the electron-hole pairs. Moreover, the band edge cannot be clearly resolved, 2 since it is merged with excited exciton states (e.g. 2s state), which show up only for densities far below the Mott density. Instead of a Mott density, only a density range can be given, where the Mott transition appears. We demonstrate that a small damping as a prerequisite for the validation of the extended QPA in the thermodynamic approach breaks down, analyzing (i) the dephasing processes with increasing excitation, (ii) the strong increase of the excitonic linewidth and (iii) comparing with the lifetime of carriers in the QP description. Contents

The many-exciton theory of highly excited semiconductors is reformulated in order to apply it to the case of a quasi two-dimensional confinement of electrons and holes in a multiple quantumwell structure. Using simple variational ansatzes for the exciton wave function in the low excitation limit density dependent exciton parameters are calculated for a GaAs-GaAlAs multiple quantum-well system. I n contrast to bulk material but in agreement with experimental findings a blue shift of the excitonic resonance with increasing excitation intensity is obtained. The results are used to demonstrate nonlinear optical behaviour, especially bistabilities, for such systems.Die Vielexzitonen-Theorie hochangeregter Halbleiter wird fur den Fall der quasizweidimensionalen Begrenzung von Elektronen und Lochern in Vielquantentopfstrukturen umformuliert. Unter Benutzung eines einfachen Variationsansatzes fur die Exzitonwellenfunktion im Grenzfall niedriger Anregungsdichte werden fur ein GaAs-GaAlAs-Vielquantentopf-System dichteabhangige Exziton-Parameter berechnet. I n tfbereinstimmung mit experimentellen Ergebnissen und im Gegensatz zum Volumenmaterial wird eine Blauverschiebung der Exzitonenresonanz mit wachsender AnregungsintensitLt erhalten. Die Ergebnisse werden zur Demonstration nichtlinearen optischen Verhaltens solcher Systemeinsbesondere von Bistabilitatenbenutzt.