Photon emission induced by elastic exciton-carrier scattering in semiconductor quantum wells

Abstract

We present a study of the elastic exciton-electron (X − e − ) and exciton-hole (X − h) scattering processes in semiconductor quantum wells, including fermion exchange effects. The balance between the exciton and the free carrier populations within the electron-hole plasma is discussed in terms of ionization degree in the nondegenerate regime. Assuming a two-dimensional Coulomb potential statically screened by the free carrier gas, we apply the variable phase method to obtain the excitonic wavefunctions, which we use to calculate the 1s exciton-free carrier matrix elements that describe the scattering of excitons into the light cone where they can radiatively recombine. The photon emission rates due to the carrier-assisted exciton recombination in semiconductor quantum-wells (QWs) at room temperature and in a low density regime are obtained from Fermi's golden rule, and studied for mid-gap and wide-gap materials. The quantitative comparison of the direct and exchange terms of the scattering matrix elements shows that fermion exchange is the dominant mechanism of the exciton-carrier scattering process. This is confirmed by our analysis of the rates of photon emission induced by electron-assisted and hole-assisted exciton recombinations.

Searching for confined modes in graphene channels: The variable phase method

“…There is also a fundamental mathematical difference between the two confinement potentials under consideration; namely, the different behavior of the logarithmic derivative of the potential, which features in Eq. (9). In general the logarithmic derivative term will reach zero asymptotically for a power-law decay, whereas it will tend to a constant value for any exponential damping.…”

“…[3][4][5][6] The method has proven to be robust in the nonrelativistic case and has been applied to various physical problems, including an analysis of the statically screened Coulomb potential 7 and the ionization of the electron-hole plasma 8,9 in conventional semiconductors. The method has also been used to find scattering lengths of colliding atoms 10 and has been extended for use with nonlocal potentials.…”

Phase diagram of electron–hole systems: Interplay between exciton Mott transition and quantum pair condensation

“…The e-h Hubbard model (1) is one of the lattice fermion models, which have been often used for strongly correlated electron physics in terms of the tight-binding picture. On the other hand, the nearly free electron picture leads to the continuum-space fermion models (written often in the momentum space), which have been usually employed for conventional semiconductor physics to study the excitons and free-carrier plasma [26][27][28][29][30]. In such continuum models, the range and strength of the Coulomb interaction depend on the r s parameter, the inverse density.…”

Superconductivity with excitons and polaritons: review and extension

“…In the microcavity, an electron (from the 2DEG) interacts with a polariton (from the condensate) through its excitonic component, so this is really the electron-exciton interaction that is to be computed, 44 weighted by the Hopfield coefficient (the excitonic fraction) X. Let us consider, therefore, the scattering of an electron in one of the parallel QW, separated by a distance L from the QW with excitons.…”