Optical Imaging in Projection Microlithography

Abstract

From the corpuscular theory in which light propagates in the form of minute particles, to the wave theory that elucidates diffraction phenomena, to the quantum theory in which both the wave and corpuscular theories are simultaneously valid, humankind's concept of light has evolved much over the last two hundred years. The principles of optical projection lithography with which we are concerned were substantially formulated before the twentieth century, prior to the general theory of relativity, which stipulates the bending of light rays by gravitational fields. By that time, Augustin Jean Fresnel (1788-1827) had laid the wave theory of light on a firm foundation, and James Clerk Maxwell's (1831-1879) conjecture that light waves are electromagnetic had been verified by Heinrich Hertz (1857-1894). In the first three chapters of this text, we review properties of light that are relevant for analysis of image formation in photolithography. Starting with Maxwell's equations, we deduce the characteristics of light in this chapter. We shall learn 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.