Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation

Abstract

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.

Transition from excitonic to plasma emission from localized electron‐hole pair states in GaAs‐AlGaAs quantum wells

“…This approximative treatment is valid for low excitations, where the influence of many-body effects on the chemical potentials is small. In [6] we have demonstrated for a bulk semiconductor (ZnSe), that there is a pronounced influence of many-body effects on the chemical potentials even at higher excitation around the Mott transition. In this paper we extend the earlier treatments for quantum wells [11,12] and include the renormalized carrier energies in the distributions f a,0 (e…”

“…The density of excited carriers was well below the Mott transition and for the distribution of carriers Fermi functions for non-interacting carriers were used. This approximation fails (see [6] for bulk ZnSe) for excitations around the Mott transition of excitons, rather the influence of many-body effects has to be considered, which change both the dispersion and the chemical potentials of carriers for fixed density and temperature. In this paper we present a detailed theoretical explanation of experimental results for the emission of localized ex- citons in GaAs-GaAlAs quantum wells [4,5], investigating the influence of dynamical screening both on the oneparticle properties of carriers and on the whole spectrum of electron-hole (eh) pair states, ranging from 1s-and 2s-excitonic states up to the band edge.…”

On the phase diagram of a two-dimensional electron–hole system

“…There are several options for choosing the mean field. Very common is to use a Hartree-Fock like approximation that couples to the fermion densities c † k,σ c k,σ [25]. Then the mean field is a self-energy iΣ a damping of the quantum dynamics.…”

“…[25] with special attention to the influence of many-particle effects such as screening and lowering of the ionization energy. The dissociation of excitons in GaAs-GaAlAs quantum wells with increasing excitation was studied within two different theoretical approaches [26].…”

On the condensation of polaritons

“…One of the difficulties of experiments on excitons lies in the fact that excitons should undergo a Mott transition [20] from an insulating state (bosonic) to a metallic plasma (fermionic) above some critical density [21,22]. Also, it appeared that two-body recombinations (Auger recombination, see, for example, the works of Manzke and coworkers [23], Portnoi et al [24], and Snoke [25]) between excitons occur as soon as the exciton gas reaches a high density, therefore limiting the maximum achievable density and also giving rise to a large heating the exciton cloud. Last, but not least, excitons in three-dimensional (3D) crystals should be viewed as polaritons (see Hopfield [26]) and, upon cooling of the exciton gas, should transform continuously into photons as there is no energy minimum on the polariton dispersion.…”