Energy Storage and Reuse in Negative Capacitance

Abstract

In this article, we analyze how a ferroelectric (FE) acts as a rechargeable energy storage medium which stores, releases, and retrieves energy, and helps the gate achieve a desired charge density with reduced energy (voltage) from the external gate drive. During transistor turn-on, the FE releases energy, while the whole system is absorbing energy, and during turn-off, the FE retrieves energy, while the whole system is releasing energy. Capacitor energy is analyzed using two different approaches: static material free energy integrals and transient circuit power integrals. The two results agree within 1%. Energy analysis is also performed for a metal–oxide–semiconductor field-effect transistor structure for two gate lengths, 20 nm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2~\mu \text{m}$ </tex-math></inline-formula> , in an inverter circuit. At 2- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> gate length, the values of energy match under these two different approaches with less than a 6% difference. The difference is larger in the 20-nm gate length case due to larger parasitic capacitances, such as gate-to-drain and gate-to-source capacitance, affecting the transient circuit analysis. Even so, most of the energy storage and retrieval benefit is retained even in small size negative capacitance transistors.