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 complete spectrum of the real ideas. Alfred Wong deals rigorous underpinning, readability in systematic formula, actual perception into rising principles, in addition to a method point view of the parameter tolerances required in production. Readers with an exceptional operating wisdom of calculus can stick with the step by step improvement, and technologists can assemble normal suggestions and the major equations that outcome. Even the informal reader will achieve a standpoint at the key suggestions, with a purpose to most likely support facilitate conversation between technologists.Contents - Foreword - Preface - record of Symbols - simple Electromagnetism - parts of Geometrical Optics - parts of Diffraction conception - Imaging of prolonged gadgets with Finite resources - solution and photo 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: pick out Refractive Indexes - Appendix F: various Theorems and Identities - Bibliography - recommendations to workouts - Index
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Extra resources for Optical Imaging in Projection Microlithography
Example text
For another plane wave impinging onto the screen at an angle 0, as shown in Fig. 1(b), the rays AIY, BJY, and CKY have different path lengths. For example, the path AIY is shorter than BJY by BB'. If BB' is an integral number of wavelengths, rays AIY and BJY will reinforce each other at Y. Cancellation occurs if the difference is an odd multiple of half wavelengths. The field at Y is the sum of all aperture ray contributions with proper consideration of their relative phases. When CC' is a nonzero integer multiple of the wavelength, the field at Y is 0.
The diffraction pattern of a rectangular aperture with a = ? and b = 2% is shown in Fig. 8(b). 2 Circular and annular pupils An annular pupil with radius vp and obscuration ratio r (0 < £ < 1) centered at the origin is shown in Fig. 10(a). 45.
For paraxial rays, namely, light rays that travel sufficiently close to the axis (x, y « R1), we can approximate the radical in Eq. 45. 5: Separation of a thin lens into two parts for analysis. such that x2 + y2 di(x,y) =dog— 2R1 Similarly, the thickness function for L2 is x2 + y 2 d2 (x, y) = do, + 2R2 where d0 2 is the thickness of L2 at (x, y) = (0, 0), and R2 < 0 for L2 depicted in Fig. 5. The total thickness function is 2 1 d(x,y)=dl(x,y)+d2(x,y)=d0—2 +y 1 R l R2J where do = ( do, + d0 2 is the thickness of the lens at (x, y) = (0, 0).