Statistical Analysis of Threshold Voltage Variation Using MOSFETs With Asymmetric Source and Drain

Abstract

Threshold voltage variation is considered to be caused by various factors, such as random dopant fluctuation, surface roughness, metal gate granularity, and so on. Its magnitude ( $\sigma {V}_{\mathrm {th}}$ ) is proportional to the reciprocal of the square root of the gate area in conventional rectangular transistors. In this letter, the statistical analysis of the threshold voltage variation of trapezoidal and octagonal transistors that have asymmetric gate widths at source and drain side was discussed, in addition to the rectangular transistors. From the statistical analysis, it is experimentally demonstrated that $\sigma {V}_{\mathrm {th}}$ is correlated with the gate width at source side ( ${W} _{S}$ ), not average gate width ( ${W} _{\mathrm {ave}}$ ) which determines the gate area. Therefore, it is considered that $\sigma {V}_{\mathrm {th}}$ is characterized by the common parameter of ${W} _{S}$ even if the main factor of the threshold voltage variation would be changed.