考虑量子效应的双栅MOSFET的阈电压解析建模

推导了双栅MOSFET器件在深度方向上薛定谔方程的解析解以求得电子密度和阈电压.该解析解考虑了任意深度情况下沟道中深度方向上电势的不均匀分布,结果与数值模拟吻合.给出了电子密度的隐式表达式和阈电压的显式表达式,它们都充分考虑了量子力学效应.模型显示,在亚阈值区或者弱反型区,电子密度随深度增加而增加;然而,在强反型区,它与深度无关,这与数值模拟的结果吻合.结果进一步显示,只考虑方形势阱的量子力学结果,略高估计了阈电压,且低估了电子密度.误差随着深度的增加或者栅氧厚度的减少而增加.

Analytical Modeling of Threshold Voltage for Double-Gate MOSFET Fully Comprising Quantum Mechanical Effects

The analytical solutions to 1D Schr(o)dinger equation (in depth direction) in double-gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non-uniform potential in the channel is concerned with an arbitrary depth so that the analytical solutions agree well with numerical ones.Then,an implicit expression for electron density and a closed form of threshold voltage are presented fully comprising quantum mechanical (QM) effects.This model predicts an increased electron density with an increasing channel depth in subthreshold region or mild inversion region.However,it becomes independent on channel depth in strong inversion region,which is in accordance with numerical analysis.It is also concluded that the QM model,which barely considers a box-like potential in the channel,slightly over-predicts threshold voltage and underestimates electron density,and the error increases with an increasing channel depth or a decreasing gate-oxide thickness.