Influence of statistical spatial-nonuniformity of dopant atoms on threshold voltage in a system of many MOSFETs

We have experimentally and analytically studied the influence of the statistical spatial-nonuniformity of dopant atoms on the threshold voltage V-th in a system of many metal-oxide-semiconductor field-effect-transistors (MOSFETs). According to experimental results and our analytical model, it is found that the nonuniformity of dopant atoms along the channel (the lateral nonuniformity) causes the unstable drain bias V-d dependence of V-th, whereas the standard deviation of V-th has weak dependence of V-d. Moreover, the substrate bias dependence of V-th fluctuates due to the vertical nonuniformity of dopant atoms which is perpendicular to the channel. Consequently, V-th fluctuation is caused by the statistical spatial-nonuniformity of dopant atoms as well as their total-number variation in the channel depletion volume.