First-principles calculations on the electronic, vibrational, and optical properties of semiconductor nanowires

The semiconductor nanowire (NW) has attracted significant attention as a new one-dimensional structure for fundamental studies and also as a potential building block for nanodevices. When the size of NWs becomes close to the order of the de Broglie wavelength of electrons, the quantum confinement effect significantly affects the electronic behaviors of NWs and raises expectations for many novel applications in microelectronics. As the technology advances, more and more fine semiconductor NWs are fabricated in the laboratories, which provide good platforms to study the special properties of low-dimensional systems. From these new nanostructures, we choose to study the single crystal silicon nanowire (SiNW). One advantage of this choice of SiNWs is that we have the solid and complete knowledge about the electronic structure of bulk silicon, which provides valuable information for us to understand the quantum confinement effect in SiNWs. The other reason for this choice is that the silicon-based technology is so highly developed that scientists prefer silicon as the elementary material for the cost consideration, even it may not be the highest performance candidate. Therefore, our calculations on SiNWs should be useful for the industrial development of today's nanotechnology.; As a starting point, we begin by studying the ground electronic state of SiNWs and performing calculations on the following three physical properties. Based on thorough knowledge about the ground state of electrons, the first part of our work is to calculate the properties of lattice vibrations of SiNWs. The density functional theory (DFT) based linear-response method is used to obtain lattice vibrational modes. We plot the density of vibrational modes at the Gamma point of the Brillouin zone and show a clear evolutionary from bulk silicon to the narrow SiNW. Two kinds of frequency shifts of lattice vibrational modes are found: One is the red shift of the optical modes, the other is the blue shift of the radial breathing modes (RBMs). We discover that the size dependence of the frequency shifts of RBMs can be described well by the elastic model with the cylindrical boundary confinement. In order to characterize these confined modes in SiNWs, we calculate the first-order Raman activities of the smallest SiNW, and find that the RBM is strongly active in the scattering spectrum. Therefore, our calculated result about the size dependence of the frequency of RBM provides an easy way to estimate the size of the nanowires from the corresponding Raman spectrum.; The excited-state properties of nanostructures are of critical importance in the design of functional optical devices. The low dimensionality and reduced size tend to strengthen the effective Coulomb interaction in nanostructures. Quantitative evaluations of physical properties manifesting this effect are therefore timely and valuable to the nanotechnology research. In the second part of my work, we focus on the correlated electron-hole states in semiconductor NWs and their influence on the optical absorption spectrum. First-principles calculations are performed for an isolated hydrogen-passivated SiNW with a diameter of 1.2 nm. By using plane waves and pseudopotentials, the quasiparticle states are calculated within the many-body perturbation theory with the so-called GW approximation, and the electron-hole interaction is evaluated with the Bethe-Salpeter equation (BSE). The enhanced Coulomb interaction in this confined system results in an unusually large shift (1-2 eV) of the optical spectrum as well as a significant increase in certain absorption peak intensity. The current results predict anomalous excited-state properties in semiconductor NWs that may impact future applications of these nanostructures.; In the third part of my work, the electronic band structures of Si/Ge core-shell NWs are studied with first-principles calculations. The electronic states close to the band gap of NWs along the [110] d...