Large deformation of beam columns - a closed form solution and design guide for vertical buckling probe needles

Higher pin count and reduced pitch along with increased wafer size set new demands to fine pitch wafer probe technology. Vertical buckling probe needles are one of the available concepts. The required elasticity for contacting the pad is achieved by buckling of the needles. The buckling mode guarantees a consistent contact pressure over a large range of overtravel and thus allows for an optimal tolerance even under changing planarity conditions of the wafer. However, the dimensioning of a buckling needle for specified contact forces seems impossible for designers. Therefore, the authors present closed form solutions for large deformation of buckling beam columns. It is an extension of the Euler buckling cases known from textbooks and goes back to a publication of Thimoshenko regarding the first Euler case. This solution will now be discussed and extended to the fourth Euler case. Its applications will be demonstrated for a vertical buckling probe needle with one end built in and the other end guided by a guide plate. A closed form solution of the force-deflection characteristic will be presented and compared with geometrical nonlinear finite element analysis.