Doped silicon quantum dots as sources of coherent surface plasmons

In the present work, we propose using a doped silicon quantum dot (Si-QD) as a source of coherent surface plasmons (SPASER). The possibility of spasing in single Si-QD is investigated theoretically utilizing full quantum mechanical treatment. We show that spasing can take place in doped Si-QDs whenever the quality factor of a plasmon mode exceeds some minimum value. The minimum value depends on the size and doping concentration of Si-QDs. It can be used to design an optimum structure as SPASER in silicon technologies. The condition on the quality factor is translated to a condition for radius and it is shown that for a given localized surface plasmon (LSP) mode, the radius should be less than the critical value. This value only depends on the mode index. The required relations for design purposes are derived and, as an example of feasibility of the approach, a SPASER is designed for mid infrared. Moreover, we propose a more applicable device by arranging an array of doped Si-QDs on top of a graphene layer. Interaction between the surface plasmon polariton (SPP) modes of graphene and LSP modes of Si-QDs causes outcoupling of an intense ultra narrow beam of coherent SPPs to be used in real probable applications.