In this article, we study the dispersion properties of bulk and surface electrostatic oscillations of a spherical quantum electron-hole semiconductor plasma as a simple model of a semiconductor nanoparticle. We derive general dispersion relation for both bulk and surface modes, using quantum hydrodynamic theory (including the electrons and holes quantum recoil effects, quantum statistical pressures of the plasma species, as well as exchange and correlation effects) in conjunction with Poisson’s equation and appropriate boundary conditions. We show that for the arbitrary value of angular quantum number ? ? 1 there are only two surface plasmon modes, but two infinite series of bulk modes for ? ? 0 that owe their existence to the curvature of the interface. We use the typical values of GaAs semiconductor to compute the bulk and surface mode frequencies for different value of ?.
