Response surface methodology for matrix PBGA warpage prediction

The manufacturing process of chip-scale plastic ball grid arrays (PBGAs) can cause appreciable warpage. The simultaneous manufacture of PBGAs can be accomplished by attaching a matrix of silicon dies onto a bottom layer of substrate. The resulting structure is termed a matrix PBGA. Because the matrix PBGA has too complex a structure for a simple mechanistic model, response surface methodology (RSM) is used to construct an empirical model of the warpage. The response surface model is created by regression analysis between the design parameters and data obtained through 3D finite element simulations. Another method, the dual-curvature approach, which is based on classical mechanics, is also used to predict matrix PBGA warpage. The prediction quality of the two models, is compared using three different error metrics, and the prediction variance of the response surface model is discussed. Comparison of the dual-curvature and response surface models shows the response surface estimates to conform more closely with simulation results