REDUCTION OF WARPAGE OF MULTILAYERED SUBSTRATE OR PACKAGE

摘要

A method that minimizes adjustment of a wiring layer in reducing a warpage of a multilayered substrate and enables location of a part of a wiring layer that needs correction in order to reduce the warpage. The difference in average coefficient of thermal expansion, Δα, varies in a substrate. The method focuses in on the difference in Δα with a great length scale (low frequency) having a relatively significant effect on the warpage compared to the difference in Δα with a smaller length scale (high frequency) and corrects only the difference in Δα with a greater length scale. The distribution of the difference in Δα in a plane of substrate is determined. Then digital filtering is performed to extract only the difference in Δα with a low frequency and the difference in Δα between before and after correction, thereby revealing a part that requires correction.

主权项

1. A computer readable non-transitory article of manufacture tangibly embodying computer readable instructions which, when executed, cause a computer to carry out a method for controlling a warpage of a multilayered substrate by:
(1) discretizing a two-dimensional surface of the multilayered substrate into finite planar elements, wherein the multilayered substrate has an upper wiring layer and a lower wiring layer, wherein the upper and lower wiring layers are made of at least two different materials having different elastic moduli, and wherein the materials are distributed two-dimensionally with different occupancies; (2) calculating a difference in coefficient of thermal expansion of the two-dimensional surface based on composite properties determined from two elastic moduli, two occupancies, and difference between the two occupancies obtained for each finite planar element; (3) calculating the warpage of the multilayered substrate based on the calculated composite properties of the two-dimensional surface according to a finite element method; (4) calculating a maximum length scale that corresponds to an allowable warpage; (5) extracting an element involved with a pattern having a length scale greater than a maximum length scale by digital filtering of the difference in coefficient of thermal expansion to produce an extracted element; (6) reducing the difference in coefficient of thermal expansion by adjusting a mixing ratio of the two different occupancies for the extracted element involved with a pattern having a length scale greater than the maximum length scale to produce an adjusted mixing ratio; (7) calculating the warpage of the multilayered substrate based on the adjusted mixing ratio of the two different occupancies according to the finite element method; and (8) repeating steps (5), (6) and (7) until the calculated warpage falls below a required warpage.