Compact charge model for Si gate-all-around nMOSCAPs with cylindrical cross-sections considering the density-gradient equation

Abstract

A compact charge model for Si gate-all-around n-type metal-oxide-semiconductor capacitors (nMOSCAPs) with cylindrical cross-sections including the quantum confinement effect is presented. The density-gradient equation with a penetrating boundary condition is integrated to consider the quantum confinement effect. From the integrated equation, an expression for the surface potential is derived, and a compact charge model is presented. To calculate the charge-voltage characteristics, parameter modeling for terms related to quantum correction is done. The results from the model for various radii show excellent agreement with numerical simulations.