By Alfred Kwok-Kit Wong
Right here for the 1st time is an built-in mathematical view of the physics and numerical modeling of optical projection lithography that successfully covers the entire spectrum of the real innovations. Alfred Wong deals rigorous underpinning, readability in systematic formula, actual perception into rising rules, in addition to a approach point view of the parameter tolerances required in production. Readers with a superb operating wisdom of calculus can keep on with the step by step improvement, and technologists can assemble common strategies and the most important equations that outcome. Even the informal reader will achieve a standpoint at the key ideas, with the intention to most likely support facilitate conversation between technologists.Contents - Foreword - Preface - checklist of Symbols - easy Electromagnetism - components of Geometrical Optics - components of Diffraction conception - Imaging of prolonged items with Finite assets - solution and photograph Enhancement - indirect Rays - Aberrations - Numerical Computation - Variabilities - Appendix A: Birefringence - Appendix B: Stationarity and Ergodicity - Appendix C: a few Zernike Polynomials - Appendix D: Simulator Accuracy assessments - Appendix E: decide upon Refractive Indexes - Appendix F: different Theorems and Identities - Bibliography - options to routines - Index
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Extra info for Optical Imaging in Projection Microlithography
The problem of determining the field at P becomes an evaluation of the integral in Eq. 20). 19)] implies that R0, RP » max(11 2 + 42 ) This requirement is rather stringent. For example, a circular opening 1 mm in radius under 193 -nm illumination requires that Ro,R p » 5m. In practice, Fraunhofer diffraction can be observed with a more compact setup by a suitable arrangement of lenses. If we place a converging lens behind the aperture, the field across the focal plane of the lens is the Fraunhofer diffraction pattern of the opening.
7 Fraunhofer diffraction patterns Before calculating the Fraunhofer diffraction patterns of some commonly encountered pupil shapes, let us rewrite Eq. 20) as U(p, q) = C rrr e J ik(prl+q^) lA e+ik(Ro+Rp) where did C = — pupil R0Rp Denoting the area of the pupil by D, the field at the center of the diffraction pattern is U(0,0) = C • D. 1 Rectangular pupil Consider a rectangular aperture centered at the origin with a width a parallel to the 1-direction and a height b parallel to the a-direction, as shown in Fig.
Illustrated in Fig. 3, a light ray AB traveling in a medium with refractive index ni ne impinges onto a dielectric interface at an angle 9i nc . In general, a reflected ray and a refracted ray result, with both secondary rays having linear trajectories by virtue of Eq. 6). 3. Sufficient for the present is the relationship between the angles 8inc and O, where °tra„ is the angle between the refracted ray and the normal to the interface. Suppose the optical path is zero at B, namely, cp(B) = 0, the optical path at C is (p(C) = ntrando.