Triboelectric nanogenerators (TENGs) have rapidly risen to the forefront of mechanical energy harvesting technologies in the last five years, showing the potential to generate high power outputs at high efficiency and low cost. The maximum instantaneous power density of these devices has been reported to exceed 500 W/m2.  TENGs have been demonstrated for their use as energy harvesters and self-powered active sensors which operate on ambient energy sources such as wind, machine vibrations and human movement, hence providing the pathway for sustainable energy generation.  However, the lack of knowledge in the fundamental working principles of TENGs has impeded the progress in this field. 
The classical theoretical models explaining TENGs are based on parallel plate capacitors, which makes it challenging to comprehensively describe the working principles of these devices. Furthermore, numerous circuit element based models are derived for different TENG types. These explanations are limited to planar geometries with parallel TENG layer arrangements, and some of the output predictions show significant deviations from experimental observations. 
Herein, we present the first analytical model to fully describe the working principles of different TENG types using Maxwell’s equations.  The new model is based on the distance-dependent electric field (DDEF) concept, derived using the spatial field variations of charged TENG layers. The DDEF model is capable of accurately predicting the output behaviour of vertical charge polarization TENGs including vertical contact and separation mode, single electrode mode and free standing TENG layer mode, hence encompassing the majority of existing TENG structures. The current, voltage, charge and power output of different TENG types are predicted using the DDEF model which show an excellent agreement with the experimental TENGs, indicating significant improvements over the existing models. Unlike the previous models, this model is not constrained to a planar geometry, and can be universally applied to complex geometries and surface topographies found in practical TENGs. Furthermore, a number of unique relationships between the TENG device parameters and power output is revealed using the DDEF model and verified experimentally, enabling the design of more efficient TENG structures for different applications.
In conclusion, this work, for the first time, presents a unified theoretical framework for different TENG working modes along with a systematic study on the device optimization, providing critical guidance for the design and construction of efficient TENG structures.
1. Wang et. al., Energy Environ. Sci. 8 (2015), 2250-2282.
2. Dharmasena et. al., Energy Environ. Sci. 10 (2017), 1801-1811.