  The underlying mechanisms responsible for triboelectricity have yet to be
completely understood. We have previously proposed a model which explains
charge transfer in non-metals via band bending due to electromechanical,
especially flexoelectric, effects at deformed asperities coupled with work
function differences. Here, we investigate whether the shape of asperities is
important for triboelectricity. The results indicate that the shape is
important in general, since how the electromechanical response scales with
force and asperity size depends on the shape. This is qualitatively in
agreement with experimental results. Further, we discuss how the impact of the
shape depends on material, geometric, and electronic transport details.
Additionally, gradient elasticity is incorporated into the model. As asperity
contact is a nanoscale phenomenon, size-dependent mechanics can become
significant and give more physically reasonable results. In some cases, the
impact of gradient elasticity terms on the electromechanical potentials is very
large, indicating that standard elasticity theory is not enough to cover some
relevant cases in modelling triboelectricity.
