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 $64000 thoughts. Alfred Wong deals rigorous underpinning, readability in systematic formula, actual perception into rising rules, in addition to a process point view of the parameter tolerances required in production. Readers with a superb operating wisdom of calculus can persist with the step by step improvement, and technologists can assemble normal strategies and the foremost equations that end result. Even the informal reader will achieve a viewpoint at the key suggestions, so as to most likely aid facilitate conversation between technologists.Contents - Foreword - Preface - record of Symbols - simple Electromagnetism - parts of Geometrical Optics - components of Diffraction concept - Imaging of prolonged items with Finite resources - answer and picture 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 checks - Appendix E: decide on Refractive Indexes - Appendix F: diversified Theorems and Identities - Bibliography - ideas to workouts - Index
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U(Z , 0), ' Compared with Eq. 45. org/terms Quasi-monochromatic light 17 Although we can identify the group velocity as the speed at which the electromagnetic energy associated with a wave travels, the waveform smears as the wave propagates because the various frequency components of the wave undergoes different amounts of phase changes. To demonstrate mathematically this phenomenon known as dispersion, let us rewrite Eq. 46) 0 e +i(kz —vit) f A ( (o ) e +i [(a^—w) ( —)] den 0 where dk 1 d(n w=w Vg The symbol k is the wave number corresponding to the peak angular frequency w, namely, k = n(w)w/co.
H(kx ,ky )e + ^ (k xx +kyy +kzz ) dkx dky . 14) The quantity H(kx , ky ) in Eq. 14) denotes the amplitude of the constituent har -monicwaveth or k= For an aperture lying on the z = 0 plane, the field on the diffracting screen is given by Eq. 14) with z = 0: +00 U (x, y, 0) = /ky)e+'(kxx+kyy)dkxdky. In the realm of geometrical optics, the field at P is zero if it lies in the shadow of the wavefront W (as it is drawn in Fig. 4), but its actual field is nonzero because of diffraction. iii The exposition in this section was suggested by Gregg Gallatin and Anthony Yen.
V If a lens is placed behind the aperture [Fig. 6(b)], the waves propagating in the (mo, no) direction are focused at a point Pg on the focal plane of the lens. This point is the geometrical image of the object point Po. The diffracted rays in the (mp , n p ) direction are focused to a different point Pd on the focal plane. Since the optical paths from the diffracted beam to Pd are the same for all the rays, the field at Pd in Fig. 6(b) is the same as that at Pd in Fig. 6(a). The Fraunhofer diffraction `'The waves propagating in the (mp , fl p ) direction can be regarded as the diffracted waves, with the normals to the diffracted wavefronts being the diffracted rays.
