Many-body Interactions Among Carriers And Their Effects On Optical Spectra Of Semiconductor Quantum Wires

Semiconductor nanostructures have become a frontier and hot research area in theworld in recent years. Comparing with the bulk semiconductor materials, as a result ofthe quantum confinement in multi dimensions, the density of states of thesemiconductor nanostructures is dramatically different. Ideal quantum wires are typicalone-dimensional semiconductor nanostructures, in which carriers are confined in twodimensions. Their density of states is divergent by E-1/2near the band edge.It is predicted by free carrier theory that absorption and gain of quantum wires wouldbe dramatically enhanced when compared with bulk materials. Thus, they could beapplied to semiconductor light emitting devices with high gain and low thresholds. Sinceit is not difficult to change and control the carrier density in semiconductor quantumwires by changing external conditions, they become the ideal research platforms forfundamental physics, such as quantum phase transformation.Optical spectra are important research approaches for semiconductor materials. Bythe study about the optical spectra of semiconductor quantum wires, on one hand thefundamental process of optical excitation and mechanism of light emission in a quantumconfined many-body system could be revealed, we could deeply understand theinteractions between carriers and quasi-particles such as excitons on the other hand.This could provide theoretical guide to research and develop new light emittingdevices based on quantum wires.There are many theoretical approaches for the study of optical spectra ofsemiconductors. The simplest approach is free carrier theory, where the Coulombinteraction among carriers is neglected. From this theory, the essential properties ofabsorption and gain near the band edge are given. When the Coulomb interaction amongcarriers is considered, based on many-body theories in the frame of semiconductorBloch equations, the exciton peak in zero density is obtained explicitly. It is necessary toadd the effects of screening in finite carrier densities. Therefore, the screenedHartree-Fock approximation is developed. In this theory, exciton peak positions are notin accordance with those in experiments because scattering effects among carriers are only described by a constant related to spectral width. In order to obtain the exacttheoretical calculation results, it is needed to describe the scattering in a moremicroscopic level, i.e., consider the Coulomb correlation effects.Coulomb interactions among carriers in quantum wires are dramatically differentform three-dimensional materials. The effective potential of quantum wires could notbe given by an analytic form. It could only be obtained by approximation of envelopefunction and numerical approaches, in which wave functions of electrons and holescould be obtained by solving the two-dimensional Schr dinger equation in thecross-section.Screening effects of carrier in quantum wires become much complex due to theeffects of phase space blocking and quasi-particles, which will strongly make effects onthe optical properties. As the static approximation is applied, by static dielectricfunctions, only the approximately screened Coulomb potential could be obtained forhigh carrier densities. By the theory of Green’s functions, considering the dependenceon temperature, carrier density and frequency of dielectric functions, more accuratecalculated results of optical spectra could be obtained.Given all those mentioned above, the work of this thesis mainly contains two parts:The first part: Starting from the simplest free carrier theory of no Coulombinteractions to the Semiconductor Bloch Equations and Screened Hartree-Fockapproximation and thereafter to the Coulomb correlation theory of consideringscattering among carriers, we systemically study the properties of absorption spectraand gain spectra in different theories at different level of approximation. By solving thematrix equation about effective Hamiltonian, the absorption spectra of low carrierdensity and gain spectra of high carrier density are obtained. The properties of excitonicpeak position and its width, the gain peak position and maximum peak gain are analyzedwhen the carriers density changes. The transparency density is the threshold carrierdensity in the transformation between absorption and gain, therefore its dependence ontemperature in different level of approximation is studied. From the results oftheoretical calculation, due to the many-body interactions among carriers in quantumwires, there are complex features in the optical spectra. In our current thesis, the theory of correlation effects treated by the second Born approximation is applied to thetheoretical study about absorption and gain of semiconductor quantum wires at the firsttime. From our numerical results, the properties of excitonic absorption peak and gainpeak are improved obviously when compared with those in the lower level ofapproximation. Though the phenomena of peak gain suppression in one-dimensionalwere predicted by screened Hartree-Fock theory, scattering effects are only representedby input parameters. According to the results of higher-order approximation, peak gainsuppression at low temperatures in one-dimensional systems is confirmed. At lowtemperatures, the peak gain increases with the increase of carrier density and thendecreases. This part is the major and core part in this thesis.The second part: In the calculation of the first part, effective Coulomb potentials areobtained by infinite barrier. As dealing with the screened Coulomb potentials, only thestatic screened potential is applied. In order to be more close to real systems, it isnecessary to apply the finite barrier. Therefore, we study the effective Coulombpotentials of finite barrier. Compared with static screening, dynamical screening gives usthe properties of dependence on frequency. We studied the dynamical screening effectsin quantum wires. What we found is that the effective Coulomb potentials ofelectron-electron and hole-hole interactions are dramatically enhanced with thedecrease of size of quantum wires and the self-energy of dynamical screening ofelectrons and holes have different dependence on the size as a result of differenteffective masses.