Optical projection lithography has been the key technology for the ongoing miniaturization in semiconductor devices over the past 40 years. Shorter wavelengths, larger numerical apertures, and various resolution enhancement techniques, including phase shift masks, application-specific illumination techniques, rule- and model-based mask layout corrections, and computational lithography have enabled the reduction of minimum feature sizes from micrometers for early generations to less than 30 nm nowadays. Although many nonoptical lithography approaches have been introduced, none of them have been proven ready to replace projection optical lithography. Further advancements of optical lithography have become increasingly difficult, especially considering the stringent economic requirements of semiconductor fabrication. The reduction of the exposure wavelength from DUV (193) nm to EUV (13.5) nm introduces potential improvement in imaging performance, but still faces several large technical challenges, including the availability of sufficiently bright and stable light sources, a defect-free mask infrastructure, and solutions to high-NA issues. Advances in semiconductor fabrication and other areas of nanotechnology require novel patterning approaches as well, introducing 3D patterning to the current challenges of optical lithography. Innovation is necessary as existing methods may prove insufficient to meet the needs of these new technologies. This issue from the Journal of the Optical Society A and Applied Optics features original research covering mask and image modeling methods and computational techniques for various inverse problems in advanced lithography, including source and mask optimization, wavefront retrieval, and design of Fresnel lenses.

The paper by Xinjiang Zhou and his colleagues from Huazhong University of Science and Technology proposes a mask and imaging simulation method for the efficient computation of mask diffraction effects for different illumination directions. Predictive modeling of the lithographic imaging performance requires a correct modeling of light diffraction from small mask features by rigorous electromagnetic methods, such as rigorous coupled wave analysis (RCWA) or finite-difference time-domain (FDTD). The required rigorous simulations for many incidence direction of the light are time consuming and become a severe bottleneck for many applications of computational lithography. The paper proposes a new method, which enables fast and rigorous mask simulations for varying incidence directions and illumination conditions. The model represents the mask transmittance function by a series expansion of a set of predetermined basic functions. The accuracy of this modeling approach is verified for typical lines and spaces patterns with different duty ratios.

Wen Lv and co-authors propose new techniques for the optimization of the illumination source for optical lithography. The illumination shape for lithographic applications has to fulfill several, sometimes contradictory criteria: the source should create bright images with a high fidelity of the features and a high image contrast. To avoid local lens heating or other problems, the source distribution should be reasonably smooth. To achieve this, the authors combine a Zernike-representation of the source geometry with appropriately weighted merit functions and a derivative-free optimization technique, which has not been applied for source optimization problems in lithography before. Although the examples in the manuscript cover some basic problems only, the application of this method to design relevant layouts can provide interesting solutions for advanced lithographic imaging.

The article “Robust and efficient inverse mask synthesis with basis function representation,” by X. Wu and co-authors concerns the inverse lithography program. This article formulates the mask design as an optimization problem. The optimization problem maximizes a combination of image fidelity and mask manufacturability. The mask pattern is represented by its discrete cosine transform; more generally by a linear combination of basis functions. This is distinct from pixelated and level-set representations of the mask pattern in previous studies.

The article “Gradient descent algorithm applied to wavefront retrieval from through-focus images by an extreme ultraviolet microscope with partially coherent source,” by K. Yamazoe and co-authors describes the retrieval of the wavefront error of an EUV imaging system from intensity images of a pinhole at different focus settings. The wavefront is estimated by minimizing a norm of the difference of computed images and optically acquired images. The norm is minimized with respect to the wavefront map. The novel contribution of this article is a method of calculating the Frechet derivative of the norm with respect to the pupil wavefront map in a time that is comparable to computing the set of through-focus images once. This method significantly speeds up the recovery of wavefront from intensity images.

Xiaowen Wan and co-authors from the University of Utah describe design approaches for Fresnel lenses to focus the light in the near field. A genetic algorithm is employed to identify the best parameters of binary zone plates to generate focal spots below the classical resolution limit. Analysis of the obtained best solutions using scalar diffraction theory and rigorous finite-difference time-domain simulations verify the sufficient performance of the zone plates for fabrication errors. The designed zone plates can provide interesting applications in lithography and microscopy.

In “Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks,” Waller et al. report on theoretical and experimental results for imaging of electromagnetic phase edge effects in lithography photomasks using the transport of intensity equation, which solves for phase from through-focus intensity images.

And Johnson, in “Nodal line-scanning method for maskless optical lithography,” provides a conceptual overview of the basic principles of scanned-spot-array lithography and nodal line printing that builds on technology development and know-how in optical lithography, using state-of-the-art microfabrication methods to simplify and improve upon the technology.