Exciton-Polaritons In Ternary Mixed Crystals

Ternary mixed crystals (TMCs) are extensively used in artifical layered structures and low-dimensionality systems, e.g.: heterostructure, quantum well, superlattice and quantum dot etc, due to their unique physical properties quite different from binary crystals, such as band-gap energy and the optical phonon frequency, can be controlled directly by the concentration x. Therefore, they are considered to be very important materials for many new electronic and photoelectronic devices. Some important elementary excitations in TMCs, such as phonons, excitons, polarons and phonon-polaritons, have been extensively studied. In this work, we investigate the dispersion properties of exciton-polaritons and related problems in bulk and semi-infinite polar TMC materials.Firstly, within the Born-Huang approximation, the dispersion relations and corresponding energy splitting of bulk exciton-polaritons in polar TMCs are investigated by using the Maxwell's equations. The numerical results of the polariton frequencies as functions of the wave-vector and the compositions, and the dependences of their energy splitting on functions of the compositions for TMCs Al_xGa_1-xAs, Cd_xZn_1-xSe, and Al_xGa_1-xN are obtained and discussed. Theoretical results show that the dispersion curves of TMCs are the same to those of the corresponding binary crystals when x=0 and x=1; when the composition x is neither zero nor one, the new dispersion characteristics for exciton, polaritons in TMC systems are found in comparison with binary crystals. The values of energies are different from quantitatively those of the binary crystals, and change nonlinearly with the variety of the composition x of the TMCs. The dependence of the splitting of two branches of polaritons on the compositions of TMCs is found nonlinear and there exists a minimum of the splitting at the long-wavelength case. The calculated results for some TMC systems, such as Al_xGa_1-xAs as well as GaAs, ZnSe and CdSe are in agree with the reported experimental results.Next, we have investigated theoretically the surface exciton-polaritons of TMCs in the surface impedance method by Fuchs and Kliewer. The energies of the surface exciton-polaritons have been calculated. The numerical calculations for severalâ…¢-â…¤andâ…¡-â…¥compound systems are performed and the polariton frequencies as functions of the wave-vector and the compositions for TMCs Al_xGa_1-xAs, Cd_xZn_1-xSe and Al_xGa_1-xN as examples are given and discussed. The results show that the dispersion characteristics of surface exciton-polaritons of TMCs are the similar to those of the corresponding bulk exciton-polaritons, their energies are different from those of the binary crystals quantitatively, but the nonlinearly with the composition x of the TMCs are weaker than those of bulk modes.