Patent ID: 9672323
Date: 2017-06-06
CPC Classifications: G06F,Y02P

Claim:
1. A computer readable non-transitory article of manufacture tangibly embodying computer readable instructions which, when executed, cause a computer to control a warpage of a multilayered substrate, the computer readable instructions comprising: first instructions to discretize 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; second instructions to calculate 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; third instructions to calculate the warpage of the multilayered substrate based on the calculated composite properties of the two-dimensional surface according to a finite element method; fourth instructions to calculate a maximum length scale that corresponds to an allowable warpage; fifth instructions to extract 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; sixth instructions to reduce 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; seventh instructions to calculate the warpage of the multilayered substrate based on the adjusted mixing ratio of the two different occupancies according to the finite element method; and eighth instructions for repeating steps of said fifth, sixth and seventh instructions until the calculated warpage falls below a required warpage.