Analytic Model of Threshold Voltage Variation Induced by Plasma Charging Damage in High-$k$ Metal--Oxide--Semiconductor Field-Effect Transistor

We discuss plasma charging damage (PCD) to high-$k$ gate dielectrics and the resultant threshold voltage shift ($\Delta V_{\text{th}}$) in n-channel metal--oxide--semiconductor field-effect transistors (n-ch MOSFETs). The PCD induced by the antenna effect is focused on, and $\Delta V_{\text{th}}$ and its variation are estimated for MOSFETs treated by various plasma processes. We propose a $\Delta V_{\text{th}}$ variation model based on both the power-law dependence of $\Delta V_{\text{th}}$ on the antenna ratio $r$ (= exposed metal interconnect area/gate area) and the $r$ distribution deduced from an interconnect-length distribution function (ILDF) in a large-scale integrated (LSI) circuit. Then, we simulate the variations in $\Delta V_{\text{th}}$ [$\sigma(\Delta V_{\text{th}})$] and the subthreshold leakage current $I_{\text{off}}$ [$\sigma(I_{\text{off}})$], in accordance with the employed $r$ distribution. The model prediction quantitatively shows the effects of PCD on $\sigma(\Delta V_{\text{th}})$ and $\sigma(I_{\text{off}})$: The antenna effect is found to increase $\sigma(\Delta V_{\text{th}})$ and $\sigma(I_{\text{off}})$.