Thermosonic ball bonding model based on ultrasonic friction power

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 γ 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 A₀, the vertical clamping force F_N, the surface area of the interface S, the compliance of the bonding system c, the initial friction coefficient μ, the bond time t_US, and the shear yield stress of the ball/pad interface, σ. In this paper, the theory is extended by the bond growth coefficient β, which is used for the formulation of a differential equation, the solution of which connects the main process parameters with the process response γ. The formula for the ultrasonic friction power P(t) now includes the degree of bond growth γ and is found to be P(t) = 4 f [1-γ(t)] μ F_N [A₀-c F_T(t)], where F_T(t) = γ(t)σ S + [1-γ(t)] μ F_N. Using the ansatz dγ/dt=βP(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.