A detailed geometric analysis of spherical triboelectric nanogenerators is presented. In comparison with earlier works on spherical triboelectric generators, the general case where the moving dielectric rolls on the inside surface of the larger sphere of the TENG is discussed in terms of maximum energy harvesting. An optimization analysis of geometrical parameters allows various cases of electrode geometry, either in the form of a spherical circle, spherical ellipse, spherical rectangle, or spherical isosceles trapezium, to be solved. The analytical insight and computational effective models provided by differential geometry make the mathematical model superior compared to standard three-dimensional (3D) numerical methods.

Photon emission during contact electrification (CE) has recently been observed, which is called as CE-induced interface photon emission spectroscopy (CEIIPES). Physical mechanisms of CEIIPES are essential for interpreting the structure and electronic interactions of a contacted interface. Using the methods of density functional theory (DFT) and time-dependent DFT (TDDFT), it is confirmed theoretically that the spectrum of emitted photons is contributed from electron transfer and transition during CE. Specifically, the excited electrons from higher energy state in one material may transfer to a lower energy state of another material followed by a transition; and/or some unstable excited electrons at a higher energy level of one material may transit to a lower energy state of itself, both of which result in CEIIPES. Furthermore, the CE-induced interface absorption spectrum (CEIIAS) has been demonstrated, due to the intermolecular electron transfer excitation.