Phonon-Polaritons In Ternary Mixed Crystals And Their Low-Dimensional Systems Of Polar Semiconductors

Ternary mixed crystals (TMCs) of polar semiconductors are considered to be very important materials for many new electronic and photoelectronic devices due to their unique physical properties as well as their comprehensive application in artifical layered structures and low-dimensional semiconductor structures such as heterostructures, quantum wells, superlattices, quantum well wires, and quantum dots. The studies of elementary excitations in TMCs have received persistent and extensive attention and become one of the frontier research fields in condensed matter in recent years. In this thesis, we have systematically investigated the dispersion properties of phonon-polaritons and related problems in bulk and semi-infinite materials, slabs, bilayer systems, quantum wells, and free-standing quantum wires consisting of polar TMC materials. Phonon-polaritons in these systems are investigated with the modified random-element-isodispalcement (MREI) model and the Born-Huang approximation, base on the Maxwell's equations with the boundary conditions. Moreover, the effects of the "two-mode" and "one-mode" behaviors of the TMCs on the phonon-polaritons are also discussed. Some main results obtained in the thesis are generalized as follows:[1] Within the MREI model and the Born-Huang approximation, the dispersion relations and corresponding oscillator strengths of bulk phonon-polaritons in polar TMCs are investigated. The numerical results of the polariton frequencies as functions of the wave-vector and the composition, and the dependences of their oscillator strengths on the compositions for ternary mixed crystals Al_xGa_1-xAs, Zn_xCd_1-xS, and Ga_xIn_1-xN are obtained and discussed. It is shown that there are three propagated bands separated by two forbidden bands for the phonon-polaritons in bulk materials, and the dependence of the energies of two branches of bulk phonon-polaritons, which have phonon-like characteristics, on the compositions of ternary mixed crystals is nonlinear. The "two-mode" and "one-mode" behaviors of phonon-polaritons are also shown in the dispersion curves of bulk phonon-polaritons.[2] By employing the MREI model and the Born-Huang approximation based on the Maxwell's equations with the boundary conditions, we have investigated theoretically the surface phonon-polaritons in semi-infinite polar TMCs. The energies of the surface phonon-polaritons have been calculated. The numerical calculations for several III-V and II-VI compound systems are performed and the polariton and surface phonon frequencies as functions of the wave-vector and the compositions for ternary mixed crystals Al_xGa_1-xAs, Zn_xCd_1-xS, and Ga_xIn_1-xN as examples are given and discussed. The results show that there are two branches of surface phonon-polaritons in semi-infinite systems. The dependence of the two branches of polaritons on the compositions of TMCs is found nonlinear. The "two-mode" and "one-mode" behaviors of surface phonon-polaritons are also shown in their dispersion curves.[3] Surface phonon-polaritons in slabs of polar ternary mixed crystals are investigated. The numerical results of the surface phonon-polariton frequencies as functions of the wave-vector and thickness for slabs of ternary mixed crystals Al_xGa_1-xAs, Zn_xCd_1-xS, and Ga_xIn_1-xN are obtained and discussed. It is shown that there are four branches of surface phonon-polaritons in slab systems. The "two-mode" and "one-mode" behaviors of surface phonon-polaritons are also shown in their dispersion curves.[4] We have investigated the surface and interface phonon-polaritons in bilayer systems consisting of polar ternary mixed crystals. The numerical results of the surface and interface phonon-polariton frequencies as functions of the wave-vector, thickness, and the compositions of the ternary mixed crystals in GaAs/Al_xGa_1-xAs, ZnS/ZnS_xSe_1-x, and ZnSe/Zn_xCd_1-xSe bilayer systems are obtained and discussed. It is shown that there are six branches of surface and interface phonon-polaritons in binary/ternary systems. The effects of the "two-mode" and "one-mode" behaviors of the ternary mixed crystals on the surface and interface phonon-polariton modes are shown in the dispersion curves. The electric fields of surface and interface phonon-polaritons are also presented for various cases. Some special cases are also discussed in the end.[5] The interface phonon-polaritons in quantum well systems consisting of polar ternary mixed crystal are studied. The numerical results of the interface phonon-polariton frequencies as functions of the wave-vector, thickness, and the compositions of the ternary mixed crystals in GaAs/Al_xGa_1-xAs, ZnS_xSe_1-x/ZnS , and Zn_xCd_1-xSe/ZnSe quantum well systems are obtained and discussed. It is shown that there are six branches of interface phonon-polaritons in quantum well structures. The effects of the "two-mode" and "one-mode" behaviors of the ternary mixed crystals on the interface phonon-polaritons are shown in the dispersion curves. The effects of the "two-mode" and "one-mode" behaviors of the ternary mixed crystals on the interface phonon-polariton modes are shown in their dispersion curves. The electric fields of the interface phonon-polaritons are also presented for different conditions.[6] The surface phonon-polaritons in freestanding rectangular quantum wires are derived and analyzed based on the Maxwell's equations with the boundary conditions. Numerical calculation on several freestanding Al_xGa_1-xAs quantum wires is performed. The results reveal that the dispersion frequencies of surface phonon-polaritons modes sensitively depend on the geometric structure of the rectangular quantum wires, the free wave-vector k_z in z-direction and the compositions of the TMC material.