Coupling and cooperative up-conversion coefficients in Er-doped Si nanocrystals

In the present work, a quantitative understanding of the Er-doped Si nanocrystals interaction is reported. We present a model based on an energy level scheme taking into account the coupling between each Si nanocrystal and the neighboring Er ions. By fitting the steady state and time resolved luminescence signals at both the 1.54 and 0.98 mum Er lines we were able to determine a value of 3x10(-15) cm(3) s(-1) for the coupling coefficient. Moreover, a strong cooperative up-conversion mechanism, active between two excited Er ions and characterized by a coefficient of 7x10(-17) cm(3) s(-1), will be shown to be active in the system, demonstrating that each Si. nanocrystal can actually excite more than one Er ion.