Influence of OPC features on the profile of 2D mask patterns

Andrew Khoh, Tom Milster, Byoung Il Choi, Ganesh S. Samudra, Yihong Wu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


With increasing use of OPC, there is a need to understand image formation better. The widely used Hopkin's model gives believable results but yields little insight into image formation. We present in this paper a new image formation technique based on the Geometrical Theory of Diffraction (GTD). Using GTD, we obtained a relationship between the edge on the mask and the disturbance in image space. We call this disturbance the Diffraction Edge Response (DER). Heuristically, the strength of the DER must drop nearing the end of an edge. The DER is thus modulated by a certain function. At this point of the development, we could not derive an expression for this function. However, we postulate that the Modulation Function is the square root of the intensity of the edge segment. This postulate is justified by the excellent agreement with results obtained using existing simulation tool. Image formation is thus governed by the DER and the Modulation Function. If the new image formulation is separated into the cross and non-cross terms respectively, it is observed from simulations that the cross terms have values closed to zero at the feature boundary. This unique property, stemming from the nature of the DER, turns a non-linear problem into approximately a linear problem at the feature boundary. A host of problems could then be understood. Using this tool, we show how the behavior of a simple corner varies with NA, PC and its dimension. We also discuss the implications of this tool on current OPC strategy. We have assumed an aberration-free system and an infinitely-thin 2D mask in this development. It is possible to extend it to an aberrated system and to 3D-mask. That will be our work in the future.

Original languageEnglish (US)
Pages (from-to)1127-1138
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4691 II
StatePublished - 2002


  • 2D profile
  • Corner
  • GTD
  • Image formation technique
  • Line-end
  • OPC
  • Simulation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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