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

•A compact charge model for Si gate-all-around nMOSCAPs with cylindrical cross-sections is proposed.•The density-gradient equation is integrated to consider the quantum confinement effect.•Terms related to quantum correction are modeled with empirical expressions. 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.