Piezoelectric surface acoustical phonon amplification in graphene on a GaAs substrate

We study the interaction of Dirac Fermions in monolayer graphene on a GaAs substrate in an applied electric field by the combined action of the extrinsic potential of piezoelectric surface acoustical phonons of GaAs (piezoelectric acoustical (PA)) and of the intrinsic deformation potential of acoustical phonons in graphene (deformation acoustical (DA)). We find that provided the dc field exceeds a threshold value, emission of piezoelectric (PA) and deformation (DA) acoustical phonons can be obtained in a wide frequency range up to terahertz at low and high temperatures. We found that the phonon amplification rate RPA,DA scales with TBGS−1 (S=PA,DA), TBGS being the Block−Gru¨neisen temperature. In the high-T Block−Gru¨neisen regime, extrinsic PA phonon scattering is suppressed by intrinsic DA phonon scattering, where the ratio RPA/RDA scales with ≈1/√(n), n being the carrier concentration. We found that only for carrier concentration n≤1010cm−2, RPA/RDA>1. In the low-T Block−Gru¨neisen regime, and for n=1010cm−2, the ratio RPA/RDA scales with TBGDA/TBGPA≈7.5 and RPA/RDA>1. In this regime, PA phonon dominates the electron scattering and RPA/RDA<1 otherwise. This study is relevant to the exploration of the acoustic properties of graphene and to the application of graphene as an acoustical phonon amplifier and a frequency-tunable acoustical phonon device.