Device Characteristics with Potential Fluctuation Induced by Nonuniformity at Gate Oxide Interface with Multifractal Analysis

Nonuniformity at the gate oxide interface is considered to be one of the serious fluctuation issues, which is induced by polysilicon grain boundary, impurity segregation, silicide and high-k stack. We introduce a mosaic layer at the gate oxide interface and relate the degree of the nonuniformity with device characteristics through multifractal analysis. There is an analogy between the degree of randomness and thermodynamics. More entropy increase in the mixture gives less variation in device characteristics. Finally, we discuss the allowable nonuniformity which is caused by unintended process variation in the view of pattern