Higher Dimensional Theory of Contact Resistance and Experimental Validation

Electrical contact is an important issue to Z-pinches, pulsed power systems, field emitters, and wafer evaluation, etc. Because of the surface roughness on a microscopic scale, true contact between two pieces of metal occurs only on the asperities of the two contacting surfaces, resulting in contact resistance [1]. We recently developed a higher dimensional theory of contact resistance for an asperity of transverse dimension (a) and finite axial length (h) connecting two metal blocks [2]. For asperity of rectangular, cylindrical or funnel shape, the contact resistance is found to be of the form R[1+p(h/a)] where R is the corresponding h=0 ``a-spot'' theory limit of Holm and Timsit [1], p has a simple form which is geometry-dependent. This scaling law is verified against electrostatic code results [2]. It is also recently validated in a series of controlled experiments [3]. This work is supported by Sandia, AFOSR, AFRL, L-3, and Northrop-Grumman. \\[4pt] [1] R. Holm, \textit{Electric Contact} (Springer-Verlag, 1967); R. S. Timsit, \textit{IEEE Trans. Components Packaging Tech}. \textbf{22}, 85 (1999). \\[0pt] [2] Y. Y. Lau and W. Tang, \textit{J. Appl. Phys.} \textbf{105}, 124902 (2009). \\[0pt] [3] M. R. Gomez et al., \textit{Appl. Phys. Lett}. (submitted).