Surface acoustic wave amplification by drifting electrons in semiconducting epitaxial graphene on silicon carbide

Abstract A theory is presented for the amplification of a surface acoustic wave (SAW) due to its interaction with conduction electrons in gate-controlled epitaxial graphene (epigraphene) on a SiC substrate. It is assumed that the SAW is launched onto the substrate in the direction of an external dc electric field applied to the graphene sample and causing the conduction electrons to drift at a speed greater than the speed of the SAW. The wavelength of the SAW is assumed to be shorter than the mean free path of the electrons, so that the quantum regime of interaction of those electrons with the SAW is realized. The Green’s function method is used to calculate the SAW gain as a function of the electron concentration in epigraphene and the external dc electric field strength. It is shown that the substrate-induced band gap in the electronic spectrum of epigraphene leads to a significant (at least an order of magnitude) increase in the SAW gain as compared to the case of gapless graphene. In addition, the opening of the band gap results in a non-monotonic dependence of the SAW gain on the electron concentration, controlled by the gate voltage applied to the graphene sample. This dependence is characterized by the presence of a distinct maximum at a certain value of electron concentration (of about <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> cm −2 for typical values of the other parameters involved), which distinguishes it from the monotonic concentration dependence of the SAW gain in gapless graphene.