Nicolas B. Cobb

Fast sparse aerial-image calculation for OPC

Fast sparse aerial image simulation and its use in optical proximity correction (OPC) is the topic of this paper. The primary result is a new lookup table formulation of aerial image calculation for a partially coherent optical system. As a generalization of our previous work for Manhattan geometry, the new technique extends the fast lookup technique to arbitrary polygonal mask geometry. Using the new method, the computation required for a sample point of the image intensity is proportional to the number of polygon edges in the local mask region. Moreover, the method is particularly well suited for perturbations to the mask such as those OPC might produce. Our implementation of the new technique achieves intensity calculation speeds of 6 msec/point and perturbational update speeds of 26 microsecond(s) ec/point on a Sun SPARC 10.

Fast, low-complexity mask design

In previous work, Cobb and Zakhor developed an automated mask design algorithm using optimization to produce masks which can print at smaller feature sizes. In this work, we build upon our previous approach with special regard to computational efficiency and mask manufacturability to produce an Optical Proximity Correction (OPC) algorithm which operates orders of magnitude faster and produces simpler optimized masks. The algorithm can be used for OPC of Manhattan geometry masks for which phase assignment has been previously completed. Therefore, the OPC problem is divorced from phase-mask design and the two tasks are performed independently. Our algorithm decomposes the mask features into edges and corners which can be moved from their original placements to improve the image characteristics. The resulting optimization algorithm inherently requires computation of O((rho) o3) where (rho) o is the density of edges and corners on the mask. A major feature of the algorithm is a new fast intensity computation technique which uses lookup tables to achieve single point intensity computation on the order of O(Na (DOT) Mr) where Na is the order of approximation to the optical system and Mr is the number of rectangles in the mask region description. The single point intensity computation time is typically around 300 microsecond(s) ec for fairly complicated masks on a HP 700 series workstation. The resulting algorithm optimized a 36 X 36 micrometers 2 test mask in 6 iterations at 11 seconds per iteration pass on the same machine. The new techniques make the described algorithm viable for a production environment with k1 as low as k1 equals 0.4.

Large-area phase-shift mask design

In previous work, Liu and Zakhor developed an algorithm for automated design of diffraction compensated phase-shift masks (PSM) in isolated small areas. In our current work we focus on devising an algorithm that performs optimization for larger mask areas up to 100 X 100 micrometers 2. We model Manhattan geometry masks using polygons composed of floating objects -- deformable edge segments and corner serifs. The model accommodates binary masks, alternating phase shift masks, and attenuated phase shift masks. With this underlying model, the positions of mask objects are optimized. Because of the simulation intensive nature of the optimization, we need an efficient intensity calculation method. To this end we employ mask function windowing approximation. We also use the fast Fourier transform (FFT) in changing to and from Fourier representations as necessary in the Hopkins image intensity equations. We demonstrate the effectiveness of our algorithm in improving image intensity characteristics at the focus plane and at defocus for various examples of binary and phase-shift masks.