In particular, the surface plasmon polariton (SPP) is attractive to enhance the spontaneous emission (SE) from active
materials due to the larger density of state (DOS) and smaller mode volume comparing with optical wave, namely
Purcell effect. Usually, the Purcell factor (PF) is calculated from the reduced form of Fermi’s golden rule, where only the
DOS and mode volume of photon (or SPP mode) are involved. Obviously, the PFs calculated with reduced form exclude
the influence of active material and only evaluate the effect of cavity or SPP waveguide. However, for a practical
emitter, the linewidth could not always be ignored. For example, the ensemble emission linewidth of mass Si- quantum
dots (QD) is about 220meV~400meV (90~160nm), which are much wider than the linewidth of the SPP DOS
In this work, the PF of SPP mode on Au-Si3N4 grating is calculated with full integration formula of Fermi’s golden rule by taking account of the spontaneous emission linewidth from single Si-QD. The calculated PF is about 1.7~1.4 within the emission range of †hω0 =1.9~1.6eV. Comparing with the PF value of 266.9~30.1, which is calculated without including the emission linewidth of Si-QD, it could be easily concluded that the impact of rather wide emission linewidth is fatal for applying plasmonic enhancement. To obtain some useful guidelines, we also discuss the necessary linewidth for effective plasmonic enhancement on Si-QDs. It is found that if the emission linewidth could be decreased to several tens of μeV, plasmonic enhancement would be helpful.