Klein tunneling through the trapezoidal potential barrier in graphene: conductance and shot noise

When a single-layer graphene sheet is contacted with metallic electrodes, tunnel barriers are formed as result of the doping by metal in contact region. If Fermi energy level modulated gate voltage, phenomenon Klein tunneling results specific features conductance and noise. Here we obtain analytically exact solutions for transmission reflection probability amplitudes using trapezoidal potential barrier, allowing us to calculate differential Fano factor ballistic regime. We put evidence an unexpected global symmetry - same energies symmetric respect half barrier height. outline proposal experimental verification these ideas realistic sample parameters.