A three-parameter Weibull-like fitting function for flip-chip die strength data

Abstract

Die cracking in the assembly and reliability testing of flip-chip (FC) packages is often a major concern. A widely used die strength test is the so-called the four-point bending (4PB) test. In the 4PB test, the die is under pure bending and the strength of the die is determined by its breaking tensile stress. Although the 4PB test has been widely used, a well-established relation between the 4PB result and the die breaking in FC package has not been reported. This paper discusses the relation from a probabilistic mechanics point of view. The theory considers the following issues in the material strength test and the application loading conditions: (1) the die top in the 4PB test is under uniaxial tensile stress and the die in FC package is under multi-axial stress; (2) the 4PB test only puts part of the die top under tension and the die top in FC plastic package has almost 100% of the die top area under tension; (3) the die stress in the 4PB and in the package has a different distributions which contribute differently to die cracking. Weibull distribution will be used to analysis the 4PB test data. A three-parameter Weibull distribution fitting procedure will be presented. The function form of the cumulative density function of Weibull distribution is specially modified to take the above three issues into consideration and reflect the stress distribution difference between the test and application. The three-parameter Weibull fitting is compared to a two-parameter fitting. It turns out that some systems need three-parameter fitting and some other systems only need the two-parameter fitting. For systems need three-parameter fitting, a two-parameter fitting will be too conservative in design.