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By R. Newman

ISBN-10: 0444853510

ISBN-13: 9780444853516

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8 D is better. Although this limitation is fundamental, it is not a major obstacle since a few test exposures are usually all that are required to pick the value of D that is best for any given problem. The second disadvantage relates to the problem of pattern edge control. As shown in fig. 28, there is n o average dose that yields both correct line widths and length: to achieve this requires more finesse. The solution is to subdivide each primitive figure into smaller figures, and to keep subdividing until the l9 2 N itj c C C 48 Ν.

One on the pattern edge. Therefore, pattern shape control, adjusting the dose on the pattern edge until it equals D , requires other methods. The simplest methods are those that retain one adjustable parameter a n d one quantifier per primitive figure. Ν repre­ sentative points are chosen a n d the calculated dose is compared with the specified dose at each point, a set of Ν linear equations results: c £ ι Μ * ι > ) Ί ) + 2k (*vyi) + ··· + E k (x ,y ) = D £ i M * 2 > : V 2 ) + E k (x ,y ) + ··· + E k {x y ) = E 2 2 2 2 2 y ) + E k (x y ) N 2 2 N9 N N N + ··· + N l N l 29 1 2 D 2 E k (x N N N9 where E is the incident exposure t o the ith box, Ε^(χ,γ) is the component of the dose at the point (x y) due t o this exposure (this product is identical to D in eq.

O n e common method is to include in the calculation only those primitive figures inside or on the boundary of an imaginary circle of radius ~ 3 / J , recognizing that figures outside this circle can have only a miniscule contribution to the dose. ) can be used to move dose isocontours. These capabilities form the basis of methods for predicting and controlling proximity effects. Predicting proximity effects is relatively easy. Using the methods outlined above, one can trace the outline of the isocontour along which the dose equals D and obtain a simulation of the developed pattern; or, one can calculate the deviation of that isocontour from the desired pattern shape and obtain a measure of pattern distortions.

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Fine Line Lithography by R. Newman

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