Optical rule checking for detecting at risk structures for overlay issues

摘要

A method and system is provided for detecting at risk structures due to mask overlay that occur during lithography processes. The method can be implemented in a computer infrastructure having computer executable code tangibly embodied on a computer readable storage medium having programming instructions. The programming instructions are 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.

主权项

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:Pin⁡(via⁢⁢covers⁡[x,y])=⁢1-P⁡(Ox≤-x&⁢Oy≤-y)=⁢1-P⁡(Ox≤-x)⁢P⁢⁢(Oy≤-y)=⁢1-14⁢P⁡(Ox≥x)⁢P⁡(Oy≥y)(equation⁢⁢1) wherein:
Pin 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:Pout⁡(via⁢⁢covers⁡[x,y])=⁢P⁡(Ox≥(Rv-x)&⁢Oy≥(Rv-y))=⁢P⁡(Ox≥(Rv-x))⁢P⁡(Oy≥(Rv-y))(equation⁢⁢2) wherein:
Pout is representative of the probability that the via covers the metal layer, at the arbitrary point outside the nominal via shape; andOx and Oy follows Gaussian distributions to calculate for the Pin and Pout;Rv 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:dAP=⁢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 Co, C1. . . Cn; andcalculating a total probabilistic area of contact made by the via by integrating over r∞ by:Ap=∫r=0∞⁢ⅆAp=∫r=0∞⁢P⁡(via⁢⁢covers⁡[r,r])⁢Mr⁢⁢2⁢π⁢⁢r⁢ⅆr;(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 Ox and Oy 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).