  In the present work, we propose using doped Silicon Quantum Dot (SiQD) as a
source of coherent surface plasmons (SPASER). The possibility of spasing in
single SiQD is investigated theoretically utilizing full quantum mechanical
treatment. We show that spasing can take place in doped SiQDs whenever Quality
factor of a plasmon mode exceeds some minimum value. The minimum value depends
on size and doping concentration of SiQDs. It can be used to design an optimum
structure as SPASER in silicon technologies. The condition on 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 some critical value.
This value only depends on 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 SiQDs on top of a graphene layer.
Coupling the Surface Plasmon Polariton (SPP) modes of graphene with LSP modes
of SiQDs causes outcoupling of an intense ultra narrow beam of coherent SPPs to
be used in real probable applications.
