Nonlinear Optical Effects in Pure and N-Doped Semiconductors
von Nias Sven Donlagic
Datum der mündl. Prüfung:2000-11-02
Betreuer:Prof. Dr. Kurt Schönhammer
Gutachter:Prof. Dr. Reiner Kree
EnglischOver the last decades, the nonlinear optical properties of condensed matter systems have been an attractive and fruitful field of research. While the linear response functions of solids provide information about the elementary excitations of the systems, nonlinear optical experiments give insight into the dynamics of the fundamental many-body processes which are initiated by the external excitations. Stimulated by the experimental results, new theoretical concepts and methods have been developed in order to relate the observed phenomena to the microscopic properties of the investigated materials. The present work deals with the study of the nonlinear dynamics of the optical interband polarization in pure and n-doped semiconductors.In the first part of the thesis, the relaxation behavior of optically excited electron-hole pairs in a one-dimensional semiconductor, which are coupled to longitudinal optical phonons with an initial lattice temperature T>0, is studied with the help of quantum kinetic equations. Apart from Hartree-Fock-like Coulomb contributions, these equations contain additional Coulomb terms, the so-called vertex corrections, by which the influence of the electron-electron interaction on the electron-phonon scattering processes is taken into account. The numerical studies indicate that the vertex corrections are essential for a correct description of the excitonic dynamics.In the second part of the thesis, the attention is shifted to the characteristics of the optical response of a one-dimensional n-doped two-band semiconductor whose conduction band has been linearized with respect to the two Fermi points. Due to the linearization it is possible to calculate the linear and nonlinear response functions of the interacting electron system exactly. These response functions are then used in order to determine the linear absorption spectrum and the time-integrated signal of a degenerated four-wave-mixing experiment. It is shown that the well-known features of the linear response can directly be related to features of the nonlinear experiments. For example, the exponent which describes the algebraic decay of the time-integrated four-wave-mixing signal is functionally dependent on the exponent of the algebraic singularity in the linear absorption spectrum reflecting the common origin of the different phenomena.
Keywords: quantum kinetic equations; phonons; excitons; Fermi-edge singularity; Tomonaga-Luttinger model; four-wave-mixing