▎ 摘　　要

We present a Boltzmann equation analysis of microwave second-harmonic generation (SHG) due to mobile carriers in the doped graphene layer grown epitaxially on a SiC substrate (or, alternatively, deposited on a h-BN substrate) and lost its space inversion symmetry owing to the graphene-substrate interaction. The latter also induces a finite gap between the conduction and the valence band at the corners of the graphene's Brillouin zone. Within such a gapped band model, which includes, as a key necessary ingredient, the trigonal warping of the graphene conduction band involved, we derive an explicit analytical expression for the SHG response function of the graphene's mobile carriers at room temperature, when the effect of electron-momentum relaxation is primarily due to acoustic phonon scattering. The results obtained show that the possibility to tune the doping level of graphene by an external gate voltage allows one to maximize the output power of the microwave SHG, which may be of practical interest for the designs of graphene-based nonlinear devices operating in the millimeter-wave range.