Triboelectric nanogenerators (TENGs) allow generation of electricity based on charge transfer during repeated contact of suitably chosen surfaces. Recently, rapid advances have been made in boosting their performance, but advancement in fundamental understanding has progressed more slowly. Currently, the most popular TENG models assume idealised flat surfaces that guarantee complete contact and a contact force (or load)-independent response. However, all real surfaces possess some level of surface roughness which is known to produce a load-dependent contact area. We develop a new unified model (for dielectric-to-dielectric TENGs) which adds consideration of surface roughness to the established distance-dependent electric field model. We account for surface roughness by applying Persson’s contact theory to determine the load-dependent contact area. The model is applicable from first touch to nearly complete contact provided deformation remains elastic. Compared to load-independent approaches, the presented model is a better predictor of TENG performance. It captures the load-dependent nature of TENG performance apparent in recent tests. It predicts that the electrical output can be expected to be tiny at low contact loads, but should converge to an upper-bound at higher loads as the contact area approaches complete contact. Comparison with test results reveal substantially better prediction of open circuit voltage compared to load-independent models which tend to overestimate considerably. By assisting the designers with better predictions of TENG output, the developed unified theory has huge potential for advancing the use of TENGs in applications such as wearables (i.e. low loads) to tidal or wave energy (i.e. large loads).
