<title>Mask error enhancement factor</title>

Abstract

Optical lithography at the limit of resolution is a highly non-linear pattern transfer process. One consequence of this is an apparent magnification of mask errors. The paper first demonstrates early experimental evidence of this effect. Then it assesses the influence of pattern geometry, of the lithography tool setup, and of different optical enhancement techniques on the MEEF using primarily simulation data. The correspondence of MEEF as an effect of mask linewidth variations to the increased printability of mask defects is illustrated. Strategies to minimize the MEEF -like alternating phase shift masks -are presented. Because the MEEF describes conveniently the concerted action of all components on the whole lithographic pattern transfer process, it is proposed to use the MEEF as a new yardstick to characterize the degree of difficulty of a given lithographic process.

Yield- and cost-driven fracturing for variable shaped-beam mask writing

“…The pairs of rays reaching each other's origin are v1 = ((1, 9), (9, 1)), h1 = ((1, 4), (4, 1)), v2 = ( (2, 8), (8, 2)), h3 = ((6, 9), (9, 6)). There are two cases of two rays being copies of each other: a ray h1 = (1, 4) sent horizontally from the concave point 1 and its copy h2 = (1, 4) sent from the endpoint 1 of the slant edge (1,2) and, similarly, a ray h3 = (9, 6) sent horizontally from the concave point 9 and its copy h4 = (9, 6) sent from the endpoint 9 of the slant edge (8,9). (b) The corresponding bipartite graph B, in which the vertices h1 − h4 form the maximum independent set.…”

“…a) A polygon with three concave points 1, 4, and 9 and three slants (1, 2), (6, 7) and (8,9). The pairs of rays reaching each other's origin are v1 = ((1, 9), (9, 1)), h1 = ((1, 4), (4, 1)), v2 = ( (2, 8), (8, 2)), h3 = ((6, 9), (9, 6)).…”