Statistical Modeling of Gate Capacitance Variations Induced by Random Dopants in Nanometer MOSFETs Reserving Correlations

We consider intrinsic gate capacitance variations due to random dopants in the nanometer metal oxide semiconductor field effect transistor (MOSFET) channel. The variations of total gate capacitance and gate trans?capacitances are investigated and the strong correlations between the trans?capacitance variations are discovered. A simple statistical model is proposed for accurately capturing total gate capacitance variability based on the correlations. The model fits very well with the Monte Carlo simulations and the average errors are -0.033% for n-type metal-oxide semiconductor and -0.012% for p-type metal-oxide semiconductor, respectively. Our simulation studies also indicate that, owing to these correlations, the total gate capacitance variability will not dominate in gate capacitance variations.