Statistical Model for the Inherent Tilt of Flip-Chips

Abstract

The tilt of flip-chips is becoming increasingly important in optical and high-power electronic applications. This paper outlines the principal sources of tilt, and presents a mathematical algorithm for the statistical variation in inherent tilt, the component related to variability of solder pad dimensions. With the assistance of a Monte Carlo simulation, closed form equations are developed for several common families of symmetric pad footprints. Possible extension of the analytical tools to other important cases is discussed.