A Physics-Based Three-Dimensional Analytical Model for RDF-Induced Threshold Voltage Variations

In this paper, a 3-D analytical model is proposed to capture the threshold voltage, surface potential, and electric field variations induced by random dopant fluctuations in the channel region of metal-oxide-semiconductor field-effect transistors. The 3-D model treats the effect of each dopant separately and is based on fundamental laws of physics. The proposed approach enables determination of transistor threshold voltage variations with both very low computational cost and high accuracy. Using the developed model, we performed statistical analysis, simulating more than 100 000 transistor samples. Interestingly, the results showed that, although the distribution of the threshold voltage for large-channel transistors is Gaussian, for scaled transistors, it is non-Gaussian. Furthermore, the proposed model predicts known formulas, which are proven for 1-D analysis and large transistors, simply by setting the appropriate transistor size. As a consequence, this model is a logical extension of the theory of large transistors to nanoscaled devices.