Analytical approach to temperature evaluation in bonding wires and calculation of allowable current

Wirebonding is still the most common technique being applied to device assembly. Since the entire electrical power for the chip has to be delivered through the wires, considerable current densities may occur. As a result, bond wires are heated up and in case of too excessive current wires or surrounding materials might suffer and subsequently fail. In order to increase reliability of semiconductor devices it is important to know the resultant temperature due to a given current and deduced from this, the allowable loading so that a maximum temperature will not be exceeded. In this paper universally valid formulas for steady state, single pulse and periodic loading are introduced. They are derived from the heat diffusion equation resulting from a mathematical model which is proposed for simplification. In case of ceramic packages radiation and convection effects are considered whereas conduction through the molding compound is taken into account if the wire is encapsulated in plastic. The formulas also enable comparison between the effects of heat conduction through the wire and through the molding compound. Besides, the system of differential equations considers the temperature dependence of the specific resistance and the thermal conductivity of the wire material. Corrections for very thin plastic packages and multiple bonding are suggested. The formulas have been checked by both experimental data and numerical computation by means of Finite Element Analysis