Optical absorption of semiconducting and metallic nanospheres with the confined electron-phonon coupling

We study the optical absorption, especially the (far-) infrared absorption by phonons, of semiconducting and metallic nanospheres. In the nanoscopic sphere, phonons as well as states of electronic excitations are quantized by confinement. It is also known that in the nanoscopic geometry, the confined electron-phonon interaction has a different form from the usual one in the bulk. First, we analyze the phonon and electron contributions to the dielectric response of nanospheres like ε(q,ω)=ε_<ph>(q,ω)+ε_<el>(q,ω) or 1/ε(q,ω)=1/ε_<sc-ph>(q,ω)+1/ε_<el>(q,ω) from the confined electron-phonon interaction for three cases: the intrinsic semiconductor, the doped semiconductor, and the metal. From the dielectric response, the optical absorption spectra are calculated within the semiclassical framework concentrating on the (far-) infrared region and compared to the spectra without imposing confinement. Nontrivial differences of the spectra with confined phonons stem from two features: the electron-phonon coupling matrix has a different form and the phase space q of the confined phonon is reduced because of its quantization to q_n. Finally, size distribution effects in an ensemble of isolated nanospheres are briefly discussed. Those effects are found to be important in metallic spheres with rapid sweepings of resonances by a small change of the sphere size.