Researches On Phonon Polaritons And Excitons In Semiconductor Superlattice Structures

The study of low-dimensional semiconductor structures such as superlat-tices(SLs) and quantum wells, etc., have promoted the development of the re-search in semiconductor and high technology since 1970's. Due to their novelphysical properties and potential applications in opto-electron devices, the low-dimensional semiconductor structures have become one of the frontier researchtopics in condensed matter physics in recent years. In this thesis, we systemat-ically investigate the characteristics of the phonon polaritons and Wannier exci-tons in SLs with structural defect layer (or surface layer), it is expected that ourresults are very useful for designing revelant opto-electron devices and experi-ments. Some main results achived in this thesis are summarized as follows:Using transfer matrix method, we derive the dispersion equation for inter-face phonon polariton modes (IPPMs) in two semi-infinite coupling SLs with astructural defect layer. The characteristics of the localized IPPMs in such struc-ture are investigated. We find that the dielectric constant of the defect layer in?u-ences the number, distribution of the localized IPPMs in Reststrahlen regions andthe characteristic of the odd IPPMs. The nature and width of the defect layer arecrucial factors for determing the coupling strength between two semi-infinite SLsand in?uence the charactristcs of the localized IPPMs. In addition, the charac-teristics of the localized IPPMs depend on the stack sequence, relative thicknessof the constituent layers and transverse wavenumbers. For the SLs with struc-tual defects consisting of ternary mixed crystal Al_xGa_1-xAs, the GaAs-like andAlAs-like localized IPPMs, respectively, shift toward higher and lower frequencyregions in Reststrahlen regions with increase of the concentration x.We investigate the evolution of the IPPMs in finite SLs with a structural de-fect layer. The numerical results show that there exist localized IPPMs inside oroutside the Reststrahlen regions. In nonradiative regime, the localized IPPMsin the Reststrahlen regions may lie in bulk bands, the minigaps or below andabove the bulk bands. Those IPPMs inside band correspond to extended state,and those IPPMs below and above the bulk bands are localized in the vicinityof the defect layer, while those IPPMs in the minigaps are located in the vicinityof the defect layer or surface layers. The evolution of the IPPMs localized in the vicinity of a different interface can clearly be tracked by changing the thicknessesof the defect and constituent layers. For the SLs with structual defects consistingof ternary mixed crystal Al_xGa_1-xAs, we can also observe the evolution of theIPPMs between different states by changing the composition x. In addition, itcan be found that there exists a one-to-one correspondence between the radiativeand nonradiative IPPMs, the evolution between the radiative and nonradiativeIPPMs can be tracked.We study the existence and characteristics of the surface phonon polaritonmodes (SPPMs) in a semi-infinite SL with a cap layer consisting of ternary crystalAl_xGa_1-xAs. Our numerical results show that Reststrahlen regions are dividedinto two parts due to the two-mode behavior of the ternary mixed crystal andsome new and very interesting features are found in such structure. It is foundthat the new GaAs-like SPPMs arise in the vicinity of the transverse optical fre-quencies of the GaAs-like mode, while no new AlAs-like SPPMs exsit in the vicin-ity of the transverse optical frequencies of the AlAs-like mode. In the GaAs Rest-strahlen region, some GaAs-like SPPMs shift toward higher frenquency regions.While in the AlAs Reststrahlen region, some AlAs-like SPPMs shift toward lowerfrenquency regions. When two SPPMs anticross, there is a transfer between thelocalization characters of these two modes at anticrossing joint. Our results alsoshow that some SPPMs are fairly sensitive to the variation of the thickness of thecap layer, the thicknesses of the constituent layers and the transverse wavenum-ber. Moreover, we find that the characteristics of the new SPPMs originated fromthe two-mode behavior of the ternary mixed crystal are weakly dependent onthe thickness of the cap layer, the thicknesses of the constituent layers and thetransverse wavenumber.Under the effective mass approximation, we study theoretically the charac-teristics of the localized Wannier exciton in defect layer (GaAs) embedded be-tween two semi-infinite SLs (GaAs/Al_xGa_1-xAs) by using variational approachand transfer matrix method. It can be clearly seen the exciton changes in charac-ter between three- and quasi-two-dimensional states from the variation of excitonbinding energy, in-plane radius and probablity in the SLs growth direction. Wefind that the extensions of exciton in directions both parallel and perpendicularto the interface of SLs almost approach their minimums as the exciton bindingenergy reaches peak value at a certain defect width. The binding energies of exci-ton are sensitive to Al concentrations x in SLs insitituent layers and decrease with the decrease of the x. The values of the exciton binding energy decrease with theincrease of thickness of the GaAs, while they increase with the increase of thick-ness of the Al_xGa_1-xAs. Comparing excitonic behavior in structure consideredhere with that in single quantum well, we find some differences between thembecause of different coupling strength.