Theoretical study of amplification of the tunnel current in the redox-mediated tunneling junctions for the symmetric and asymmetric electron-molecular coupling in the case of the adiabatic transport regime

Abstract

Dependence of amplification A of the tunnel current in the electrochemical bridged tunneling junction on the bias voltage Vb, reorganization free energy Er, the broadening Δ of the electronic level of the redox molecule (RM) and intensity of the Debye screening in the tunneling gap is studied for the cases of the fully adiabatic and partially adiabatic electron transitions. We consider a one–level single RM within the spin-less model and assume the wide-band approximation for the electronic structure of the working electrodes. It is shown that amplification in the fully and partially adiabatic limits is appreciably smaller than that in the diabatic limit studied earlier [I.G. Medvedev, Electrochim. Acta 186 (2015) 613–623] due to the sufficiently large values of the broadening Δ. It is also shown that, in contrast to the diabatic limit, amplification depends weekly on the asymmetry of the coupling of the RM to the working electrodes. On the other hand, similar to the diabatic limit, amplification as a function of the bias voltage Vb approaches to relatively large values at large values of Vb in the case of the full Debye screening while, in the realistic case of the intermediate Debye screening, amplification increases at first with the increase of Vb, then reaches a maximum value Amax at some value Vb max and, when Vb farther increases, decreases to A = 1. The functions A(Vb) are calculated for different values of the parameters of the tunneling junction and it is shown that Amax increases with the increase of Er and the intensity of Debye screening and decrease with the increase of Δ. The approximate analytical expression which shows in the explicit form the dependence of A on the parameters of the system is presented.