As discussed in Chapter 1, the goal of lithography is to place the edges of a given mask pattern on the wafer within a specified tolerance. Doing so with effective controls requires a good understanding of the image formation process-from the mask image to the final transferred image. The aerial image is formed from the light that illuminates the mask and carries the information of the mask pattern through the lens to focus on the image plane. The aerial image becomes reflected and refracted as it propagates into the resist and is reflected and refracted numerous times by the resist, as well as by the multiple film layers on the wafer substrate. The superposition of reflected and refracted images in the resist exposes this medium, producing chemical and physical changes. The distribution of these changes is the latent image. The exposed resist has a distribution of dissolution rate according to the latent image. The developer removes the resist according to the dissolution rate distribution and the topography of the resist surface. The developed resist is now the resist image. The transferred image is dictated by the resist image and the characteristics of the transfer process. These images are discussed below.
3.1 The Aerial Image
We define the aerial image as light distribution at the vicinity of the image plane without any resist or multiple-reflecting surface. The image must be treated as light waves in physical optics as opposed to light rays in geometric optics. When the light wave has a perfect wavefront to form the image, there is no aberration to deteriorate the image. The only limit on resolution comes from the finite extent of the wavefront dictated by the aperture of the imaging lens. A larger extent produces a better diffracted image. Such an imaging system is called a diffraction-limited system. We start our investigation using a perfect spherical wavefront with a finite lens aperture to form a point image, which leads to the relationship of diffraction-limited resolution to wavelength and aperture size, followed by the relationship of depth of focus to the same set of parameters. Deviation from the spherical wavefront is treated in Sec. 3.1.4 below.