Patent Document ID: 9330223
Application ID: 13630098
Patent Status: 1

Claim One:
1. A method implemented in a computer infrastructure having computer executable code tangibly embodied on a computer readable storage medium having programming instructions operable to: obtain a simulation of a metal layer and a via; and determine a probability that an arbitrary point (x, y) on the metal layer is covered by the via by calculating a statistical coverage area metric followed by mathematical approximations of a summing function; detecting at risk structures of a semiconductor device during lithography based on the determined probability, wherein determining the probability that the arbitrary point (x, y) on the metal layer is covered by the via comprises: determining that the metal layer is inside the via by calculating: P in ⁡ ( via ⁢ ⁢ covers ⁡ [ x , y ] ) = ⁢ 1 - P ⁡ ( O x ≤ - x & ⁢ O y ≤ - y ) = ⁢ 1 - P ⁡ ( O x ≤ - x ) ⁢ P ⁢ ⁢ ( O y ≤ - y ) = ⁢ 1 - 1 4 ⁢ P ⁡ (  O x  ≥ x ) ⁢ P ⁡ (  O y  ≥ y ) ( equation ⁢ ⁢ 1 ) wherein: P in is representative of a probability that the via covers the metal layer, at the arbitrary point; determining that the metal layer is outside the via by calculating: P out ⁡ ( via ⁢ ⁢ covers ⁡ [ x , y ] ) = ⁢ P ⁡ ( O x ≥ ( R v - x ) & ⁢ O y ≥ ( R v - y ) ) = ⁢ P ⁡ ( O x ≥ ( R v - x ) ) ⁢ P ⁡ ( O y ≥ ( R v - y ) ) ( equation ⁢ ⁢ 2 ) wherein: P out is representative of the probability that the via covers the metal layer, at the arbitrary point outside the nominal via shape; and O x and O y follows Gaussian distributions to calculate for the P in and P out ; R v represents the radius of the nominal via shape; computing a probabilistic area of contact made by a ring having radius “dr” at a distance “r” from a center of the via, wherein: dA P = ⁢ P ⁡ ( via ⁢ ⁢ covers ⁡ [ r , r ] ) · M ⁡ ( r ) · A ⁡ ( r ) = ⁢ P ⁡ ( via ⁢ ⁢ covers ⁡ [ r , r ] ) · M ⁡ ( r ) · 2 ⁢ π ⁢ ⁢ rdr ( equation ⁢ ⁢ 3 ) wherein: M(r) is a fraction of the ring on which metal exists ε(0,1), where “0” represents no metal on the ring and “1” represents metal existing on an entire portion of the ring; providing equi-probability regions generated by sizing the via by a maximum overlay amount, wherein the equi-probability regions are represented by C o , C 1. .. C n ; and calculating a total probabilistic area of contact made by the via by integrating over r ∞ by: A p = ∫ r = 0 ∞ ⁢ ⅆ A p = ∫ r = 0 ∞ ⁢ P ⁡ ( via ⁢ ⁢ covers ⁡ [ r , r ] ) ⁢ Mr ⁢ ⁢ 2 ⁢ π ⁢ ⁢ r ⁢ ⅆ r ; ( equation ⁢ ⁢ 4 ) and wherein the mathematical approximations of the summing function is provided by discretizing equation (4), wherein the arbitrary point (x, y) is defined by an x coordinate and a y coordinate in a cartesian coordinate system, wherein P is a probability, and O x and O y is an overlay in an x direction and a y direction, respectively, and wherein [r, r] is a point, Mr2πrdr is an area of the ring covered by the metal, and ε is a member of a set of (0, 1).