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.