Analytical Release Voltage Model of Monolithic 3-D Integrated Nanoelectromechanical Memory Switches

Determining the accurate release voltage ( <tex-math notation="LaTeX">Vᵣ) </tex-math> of nanoelectromechanical (NEM) memory switches is essential for the operation of monolithic 3-D (M3D) CMOS-NEM circuits. In this article, we propose a physics-based analytical S-arc-transition model to accurately predict <tex-math notation="LaTeX">Vᵣ </tex-math> by applying the S-shaped cantilever beam in contact derived from the Euler–Bernoulli beam equation. The proposed model reflects the beam deformation from arc-shape to S-shape. Its accuracy is validated in comparison with finite element analysis (FEA) results, which shows a < 1% error over the low voltage (0.8–1.3 V) range. The NEM memory switches optimized by the proposed model show ~97% and ~21% lower program power consumption and cell area, respectively, than those designed by the previous model. Finally, when applied to various technology nodes, our proposed model achieves high accuracy.