Calculation of transition matrix element, |MAB|, in a triboelectric nanogenerator (TENG) system

The aim of this paper is to calculate the transition matrix element (MAB), which is one of the parameters related to quantum mechanical charge exchange to describe the microscopic transition process on the contact interface in a triboelectric nanogenerator (TENG) system. It is well known that |MAB| squared (|MAB|2) is correlated to the transition probability of electrons through the barrier between two materials. In particular, the potential barrier between the metal and the polymer is reflected by the electric field resulting from the tribocharges via triboelectrification. Based on the derived formula for |MAB|, a numerical analysis is performed to understand the electron transfer pattern. As a result, it is determined that |MAB| is reduced exponentially at a fixed distance, d, as the electronic energy state, E, is farther away from the Fermi-energy level (EF). In contrast, |MAB| slowly increases as the triboelectric charge density, σ, increases. That is, electrons near EF can influence |MAB| during the charge transfer process. As |MAB| differs among tribomaterials, further study into material selection could enhance TENG performance.