Using the Normalized Image Log-Slope, part 4

The slope or gradient of an image near the edge of a feature to be printed in photoresist is a good representation of the information contained in the image as to where the edge should be. A large slope gives a clear indication as to where the photoresist line edge belongs. In particular, the normalized image log-slope (NILS) and the latent image gradient were found to be good metrics for the aerial image and latent image respectively. The information contained in each image propagates through the lithography process, from the formation of an aerial image I(x), to the exposure of a photoresist by that image to form a latent image of chemical species m(x), to post-exposure bake where diffusion and possibly reactions create a new latent image m*(x), and finally to development where the latent image produces a development rate gradient R(x) that results in the definition of the feature edge. In the last edition of this column would looked at the transfer of information during exposure and how the resulting latent image gradient depends on the NILS. Continuing with the resist processing, post-exposure bake (PEB) will change this latent image, and thus change the latent image gradient. Diffusion during PEB will spread out the latent image, degrading the information present in the image and decreasing the gradient near the line edge. The change in the latent image gradient due to diffusion can be describe approximately by 2 2 2 2