Surface-polarization instabilities of electron-hole pairs in semiconductor quantum dots

The surface polarization instabilities of a Coulomb-interacting electron-hole pair in a spherical semiconductor quantum dot inside a dielectric medium are studied. Two independent numerical solutions for the ground state are presented which are based on a direct integration of the pair Schr\"odinger equation or on a diagonalization of the Hamiltonian matrix. For decreasing confinement potential at fixed dot radius, and for decreasing dot radius at fixed confinement potential, it is found that the electron-hole-pair state changes from a volume state, in which both particles are mostly inside the dot, to a surface trapped state, in which the surface polarization causes the carriers to be self-trapped at the surface of the dot. The transition from volume to surface trapped states occurs for parameters which are very close to those of II-VI semiconductors in a glass matrix or in a liquid.