In the step of developing lithography devices, VTRM (Variable Threshold Resist Model), aerial image based simulation, is useful to get feedback for a resist process margin. VTRM is also used to compensate for the mask pattern's OPE (Optical Proximity Effect) and to optimize the optical system rather than the full simulation method that requires all the process parameters. However, VTRM has shown some problems that the exposure dose and focus should be fixed in one special condition to improve the prediction accuracy and cannot be combined together in one equation for pattern's size and type variation. In this paper, a new simulation method that has more accuracy and wider applicability than the VTRM method was suggested. The new simulation method can represent the photolithography process with simple formula. The parameters of this formula are composed of exposure dose and defocus as input components, CD as output component, and all the resist processes are kept constant to keep consistency for other resist processes. The first technical improvement of this equation is to use process-matched aerial image derived from the fact that the aerial images at the top resist surface cannot represent the bulk resist energy distribution. The second one is to introduce a new concept TERM (Threshold Energy Resist Model). The energy threshold level is used instead of the aerial image's intensity threshold level in order to predict CDs. Energy threshold level can be simply found by the simple equation and an experiment. The simple equation consists of a mask edge opening energy, the mask edge image intensity, and a process factor.

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To obtain the spun-on resist surface profile around a topographical feature, the analytical solution of an equation derived from mass continuity and the Navier-Stokes equation using the lubrication approximation was used. The final resist thickness profile was obtained by applying our previous experimental result of resist thickness reduction due to the soft bake process. We found that the difference in resist thickness could induce severe critical dimension variation. Since the resist height differences between above and far from the feature could be greater than the focus margin, a 180 nm line and space pattern could not be obtained for the entire area within the process latitude. To overcome this problem, we applied mask bias and an edge phase-shift mask. As a result, the desired line and space pattern was obtained for the entire global topographical area.

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