Energy levels of erbium and silicon nanoclusters (Si-nc) used for this work. Si-ncs are modeled as a two level system and the as a three level system, where the ground state transition, , emits at . is the transfer coefficient between Si-ncs and . Values for the lifetimes and cross sections are given in Table I.
Radiative rate enhancement, , in a slot waveguide as a function of position, at 1535 nm (red curve), and 750 nm (black dotted curve). The large average value of in the slot leads to a large increase in the radiative rates of both the Si-ncs and ions.
Pulsed electrical excitation of an Er:Si-nc slot. (a) Pulsed excitation (blue dotted curve) allows steady state inversion of the (red dotted curve), while after each pulse the nanocluster excited fraction quickly approaches zero (green curve). (b) The ratio of gain to absorption, , is greater than one for a large part of each pulse. Gain from overcomes carrier absorption loss as excited carriers in the nanoclusters recombine. (c) Modal gain in the slot waveguide reaches 0.9 dB/cm after each pulse.
Maximum gain for Er:Si-nc in a slot waveguide. As the slot thickness increases, more of the mode overlaps the active region, resulting in increased modal gain.
Rate equation parameters.
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