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.

中文翻译：

---

考虑密度梯度方程的圆柱截面Si栅nMOSCAP的紧凑电荷模型

提出了一种具有圆柱形横截面的包括量子约束效应的Si栅全能n型金属氧化物半导体电容器（nMOSCAPs）的紧凑电荷模型。结合具有穿透边界条件的密度梯度方程，以考虑量子约束效应。从积分方程中，导出表面电势的表达式，并提出了紧凑的电荷模型。为了计算电荷-电压特性，对与量子校正有关的项进行了参数建模。该模型对于各种半径的结果与数值模拟显示出极好的一致性。