Hyperbolic Cooling of a Graphene on BN Transistor in the Zener-Klein Regime

Engineering of cooling mechanisms is a bottleneck in nanoelectronics. Whereas thermal exchanges in diffusive graphene are driven by defect assisted acoustic phonon scattering (the so-called supercollisions), the case of highmobility graphene on hexagonal Boron Nitride (hBN) is radically different with a prominent contribution of remote phonons from the substrate. Here, we show that a bi-layer graphene on hBN transistor with local gate can be driven in a very original regime where almost perfect current saturation is achieved by compensation of the decrease of the carrier density and Zener-Klein tunneling (ZKT) at high bias, leading to unprecedented figures for the voltage gain. Using noise thermometry, we show that this Zener-Klein tunneling triggers a new cooling pathway due to the emission of hyperbolic phonons (HPP) in hBN by out-of-equilibrium electron-hole pairs beyond the super-Planckian regime. The combination of ZKT-transport and HPP-cooling promotes graphene on BN transistors as a valuable nanotechnology for power devices and RF electronics.