Patent ID: 9384314
Filing Date: 2016-07-05
CPC Classification: G06F,Y02P

Claim Text:
1. A computer implemented method of performing a calculation associated with controlling warpage in a multilayered substrate, the method comprising the steps of: (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.