Theory of Tribovoltaics: Direct Current Generation at a $p$-$n$ Semiconductor Interface

A simple theory of tribovoltaics is proposed by using a quantum mechanical model of energy release due to sliding-induced bonding between the surfaces of a $p$-doped semiconductor and a $n$-doped semiconductor. The energy release in forming a bond may lead to the excitation of electron-hole pairs at the $p$-$n$ semiconductor interface if the released energy is higher than the effective band gap at the semiconductor interface. An expression for the generated current as a function of the relative sliding speed between the $p$ and $n$ sides is suggested and used to model current transport by solving the complete set of drift-diffusion equations with appropriate boundary and initial conditions. Analytical results are obtained and verified numerically using the comsol finite-element-method software. It is shown that since the typical time period associated with periodic sliding is many orders of magnitude higher than the carrier lifetimes, the time-dependent variations in the electron and hole concentrations and the current density follow the time variation of the sliding speed. Since the electron-hole pair generation occurs near the semiconductor interface only, the current density is shown to be constant as a function of position even if the sliding speed changes in time.