Adherence of fine wires: Solution by energy minimum principle and nano adhesional bonding

Abstract

Surface activated adhesional elastic contact solution between cylindrical bodies (wires) is deduced by energy minimum principle. The energy difference of Delta-gamma = 2gamma(sub s) - gamma(sub i) makes the contact width greater than Hertz's solution, where gamma(sub s) is the surface energy and gamma(sub i) is the interface energy at the contact area. The adhesional contact width a(sub j) is given by f = (R x a(sub j)(exp 2))/(4R(sub 1)R(sub 2)k) - sq root of (Delta-gamma x a(sub j)/k), where k is expressed by k = (k(sub 1) + k(sub 2))/2. Here, k(sub 1) and k(sub 2) are the elastic constants of two cylindrical bodies (or fine wires), R(sub 1) and R(sub 2) are the radii of two cylinders, R = (R(sub 1) + R(sub 2)/2, and f is the applied force per unit length of cylinders. The adhesional elastic contact width a(sub j) without load (f = 0) is given by a(sub j) = alpha x R(exp 2/3) x (k x Delta-gamma)(exp 1/3), where alpha is the constant and alpha = 4(exp 2/3) for wire-wire contact with a same radius, alpha = 4 for wire-plane contact and alpha = 4(exp 5/6) for wire rigid plane contact. The contact ratio a(sub j)/R increases as R decreases because a(sub j)/R is proportional to R(exp -1/3). It is suggested that heatless and pressureless nano-order interconnection is possible. Also, the possibility of nano adhesional bonding of very fine Au wire is discussed, taking into account some calculated results. Further, an experimental evidence of Au wire adnesional bonding is shown.