Thermosonic ball bonding model based on ultrasonic friction power

Abstract

Prior work addressed a theory about the ultrasonic friction aspect of the microelectronic ball bonding process and introduced a parameter named degree of bond growth /spl gamma/ which by definition varies from 0, unbonded, to 1, completely bonded. This degree is a process response correlating with a standard measure for bond quality, the shear force per area. The main process parameters were identified to be the ultrasonic frequency f, the ultrasonic free-vibration amplitude at the capillary tip A/sub 0/, the vertical clamping force F/sub N/, the surface area of the interface S, the compliance of the bonding system c, the initial friction coefficient /spl mu/, the bond time t/sub US/, and the shear yield stress of the ball/pad interface, /spl sigma/. In this paper, the theory is extended by the bond growth coefficient /spl beta/, which is used for the formulation of a differential equation, the solution of which connects the main process parameters with the process response /spl gamma/. The formula for the ultrasonic friction power P(t) now includes the degree of bond growth /spl gamma/ and is found to be P(t) = 4 f [1-/spl gamma/(t)] /spl mu/ F/sub N/ [A/sub 0/-c F/sub T/(t)], where F/sub T/(t) = /spl gamma/(t)/spl sigma/ S + [1-/spl gamma/(t)] /spl mu/ F/sub N/. Using the ansatz d/spl gamma//dt=/spl beta/P(t)/S, the model for this process is established and is applied for several numerical example simulations. From the comparison with experimental values, it is found that P decreases with FN.