Theoretical and Experimental Study of Self-Powered Piezoelectric Sensors Response to Applied Force

Nanogenerators are devices that can effectively convert mechanical energy into electricity. Thus, nanogenerators can be implemented in self-powered sensors for many applications such as internet of things, environmental monitoring, health and medical monitoring and security. In this emerging context, providing a theoretical model and a mathematical representation that links the electrical output signal with the applied mechanical stimulus is a key point to understand and optimize this type of self-powered sensors.<br/>In this communication, we present a theoretical description about the derivation of the output signal of a piezoelectric self-powered sensor. Our work is based on the constitutive differential equation derived from Maxwell’s equations [1], in which a change in the effective surface charge σ(t) due to a certain stimulus (σ_p(t)) produces a displacement current through the dielectric layers in the nanogenerator. Unfortunately, the closed analytic expression of the solution under an arbitrary time dependent function σ_p(t) cannot be integrated. Thus, we propose it as an expansion series of the successive time derivatives or antiderivatives of the stimulus, in our case the applied force. This theoretical approximation allows us to distinguish and analyze two different regimes depending on the device and measurement configurations. In the first regime, the output signal is proportional to the force, and is observed for high impedance loads and top-bottom device configurations (lower impedance matching). In the second regime, the output signal is proportional to the time derivative of the force, and occurs for low impedance loads and laterally connected devices (higher impedance matching). For intermediate conditions, more terms of the function series need to be considered.<br/>Our theoretical considerations were corroborated for real devices [2,3], which were manufactured and measured under these regimes and the results were compared with numerical simulations. Thus, the presented models provide an effective theoretical foundation for understanding and predicting the sensitivity regions of nanogenerators and self-powered sensors for practical applications.<br/> <br/>References:<br/>[1] Z.L. Wang, <i>Nano Energy</i>, 68 (2020), Article 104272<br/>[2] A. Filippin, A. Borras et al., <i>Nano Energy</i>, 58 (2019), Pages 476 – 483.<br/>[3] X. Garcia-Casas, A. Borras et al., <i>Nano Energy</i>, 91 (2022), Article 106673