A Nanosized-Metal-Grain Pattern-Dependent Threshold Voltage Model for the Work Function Fluctuation of GAA Si NW MOSFETs

To estimate characteristic fluctuation of emerging devices, three-dimensional device simulation has been performed intensively for various random cases; however, it strongly relies on huge computational resources. In this paper, we report a nanosized-metal-grain pattern-dependent model by using the method of multi-variable non-linear regression (MVNLR) for the threshold voltage fluctuation (
$\sigma \text{V}_{\mathrm {th}}$
) of gate-all-around silicon nanowire metal-oxide-semiconductor field-effect transistors. The model is developed by perturbing the local metal grains of specific patterns and summing up each metal grain of various grain patterns. The method of MVNLR is applied to build equations for nominal devices, and devices with high work-function (WK) and low WK with respect to process parameters (radius of channel, gate length, channel doping, and oxide thickness), which are generated by the design of experiments. The proposed model can estimate the magnitude of
$\sigma \text{V}_{\mathrm {th}}$
accurately (error rate < 1%) for all parameters, where an error-correction process is further adopted by using a simplified one-perceptron method.