Computational Lithography

Chapter 7

Computational Lithography with Partially Coherent Illumination

In Chapter 5, a set of gradient-based OPC and PSM optimization methods have been developed to solve the inverse lithography problem under coherent illumination. Most practical illumination sources, however, have a nonzero line width and their radiation is more generally described as partially coherent [75]. While the inverse lithography methods derived in Chapter 5 are effective in coherent illumination, these algorithms fail to account for the nonlinearities of partially coherent illumination (PCI), and produce inadequate results when applied to a partially coherent illumination system. PCI is desired, since it can improve the theoretical resolution limit. PCI is thus introduced in practice through modified illumination sources having large coherent factors or through off-axis illuminations. In partially coherent imaging, the mask is illuminated by light traveling in various directions. The source points giving rise to these incident rays are incoherent with one another, such that there is no interference that could lead to nonuniform light intensity impinging on the mask [92, 93]. According to the Hopkins diffraction model, the light intensity distribution exposed on the wafer in PCI is bilinear and described by [74]

(7.1)

where , , and . is the mask pattern, is the complex degree of coherence, and represents ...