  The interaction between graphene plasmons and surface phonons of a
semiconductor substrate is investigated, which can be efficiently controlled by
the carrier injection of the substrate. The energy and lifetime of surface
phonons in a substrate depend a lot on the carrier concentration, which
provides a new machanism to tune plasmon-phonon coupled modes (PPCMs). More
specifically, the dispersion and lifetime of PPCMs can be controlled by the
carrier concentration change of the substrate. The energy of PPCMs for a given
momentum increases as the carrier concentration of a substrate increases. On
the other hand, the momentum of PPCMs for a given energy decreases when the
carrier concentration of the substrate increases. Lifetime of PPCMs is always
larger than the intrinsic lifetime of graphene plasmons without plasmon-phonon
coupling.
