Optical Imaging in Projection Microlithography

Optical Imaging in Projection Microlithography
Author(s):    Alfred Kwok-Kit Wong
Published:   2005
DOI:             10.1117/3.612961
eISBN: 9780819478702  |  Print ISBN13: 9780819458292  |  Print ISBN10: 0819458295

Here for the first time is an integrated mathematical view of the physics and numerical modeling of optical projection lithography that efficiently covers the full spectrum of the important concepts. Alfred Wong offers rigorous underpinning, clarity in systematic formulation, physical insight into emerging ideas, as well as a system-level view of the parameter tolerances required in manufacturing. Readers with a good working knowledge of calculus can follow the step-by-step development, and technologists can gather general concepts and the key equations that result. Even the casual reader will gain a perspective on the key concepts, which will likely help facilitate dialog among technologists.

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Optical projection lithography will remain the predominant microlithography technology in the foreseeable future. With 193-nm radiation and an immersed numerical aperture of 1.38, the k1 factor of a 45-nm feature is 0.32. Fabrication at such low k1 factors requires both image enhancement and tight control of process fluctuations. A prerequisite to successful resolution improvement and variability control is an understanding of optical imaging fundamentals. This book aims to explicate the principles of image formation in projection microlithography, balancing intuitive understanding with mathematical rigor such that the readers can both distill the essence of the physics and form a firm foundation from which imaging techniques can be analyzed and developed.

Chapter 1 derives the properties of light that are relevant for analysis of image formulation in photolithography. From Maxwell's equations we deduce that light is a transverse wave, with the electric and magnetic field vectors vibrating in a plane that is normal to its direction of propagation. When light interacts with objects whose physical dimensions are large compared with its wavelength, we can neglect the field vectors under many circumstances, and approximate Maxwell's equations by laws formulated in the language of geometry. This topic of geometrical optics is treated in Chapter 2. To describe light transmission through apertures whose dimensions are comparable to or smaller than the wavelength, however, we need to resort to diffraction theory, a subject we discuss in Chapter 3.

Photomasks used in optical lithography require illumination by light sources that are physically extended. Despite incoherence between source points making up the extended source, vibrations at different object points are correlated due to diffraction of the illumination optics. Chapter 4 develops the concept of spatial coherence and the associated mutual intensity function that enable mathematical description of partially coherent imaging scenarios. The resulting equations are used in Chapter 5 to examine the theoretical and practical limits of the minimum dimension and the minimum half-pitch.

Based on the foundation of the first five chapters, we further our development to address topics that are becoming crucial as microlithographers push the limits of optical imaging. The use of high-numerical-aperture lenses necessitates consideration of the directional nature of light vibrations. Chapter 6 formulates the vector theory of imaging that is applicable for immersion lithography in the presence of a stratified wafer stack. Simultaneous with increasing numerical aperture are stringent aberration requirements. The impact of lens aberrations is explored through diffraction theory in Chapter 7.

Our abilities to harness the power of affordable computers to predict images of object patterns, and to optimize the photomask and exposure configuration given a desired image are becoming indispensable. Chapter 8 discusses common numerical approaches for imaging simulation. Variability control is also integral for successful low-k1 lithography, as both layout shapes and image tolerance are shrinking rapidly compared with λ0∕NA. Chapter 9 discusses significant causes of patterning nonuniformity arising from optical imaging, and techniques for their measurement.

I am thankful to many friends and colleagues during the course of this project. In the first place, I am grateful to Dr. Anthony Yen for encouraging me to write a text on this topic. I am indebted to Dr. Timothy Brunner, Dr. Gregg Gallatin, Professor Andrew Neureuther, Dr. Alan Rosenbluth, Dr. Frank Schellenberg, and Dr. Yen for their comments and their meticulous review of the manuscript. I am much beholden to my dissertation advisors, Professor Andrew Neureuther and Professor William Oldham, for introducing me to microlithography and for their lessons of wisdom. It is an honor to have the Foreword of this book written by Professor Neureuther.

I am obliged to Dr. Gallatin and Dr. Yen for their suggestions on development of the Rayleigh-Sommerfeld diffraction formula in §3.5, and to Dr. Rosenbluth for his exposition of the obliquity factor in §4.2. I would also like to acknowledge Dr. Wilhelm Ulrich's permission for reproduction of the illustration in Fig. 2.6. Publication of this book is the culmination of years of work by the SPIE Press staff, to whom I owe much thanks.

I have many fond memories in writing this text, as my wife Aida and I often agonize side by side on our respective writings. I hope the readers will also enjoy this book, and privilege me with suggestions for improvement.

Alfred Wong Kwok-Kit


© 2005 Society of Photo-Optical Instrumentation Engineers

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