Abstract

As todays' semiconductor fabrication industry tries to keep up with Moore's Law, which predicts the downscaling of integrated circuit size and the doubling of transistor counts every two years, resolution enhancement techniques (RET) play a much more important role than anytime in the past. Optical proximity correction (OPC), phase shifting mask (PSM), and off-axis illumination (OAI) are RETs used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. Preserving the fidelity of the circuit patterns is important for preserving the performance predicted in the design stage of the integrated circuit (IC). Typical circuit patterns exhibit regular geometries, such as lines, L-joint, U-joint and so on. These regular geometries reduce the resistances between nodes and simplify the process of routing. In the past decades, a variety of OPC, PSM and illumination design approaches have been proposed in the literature. In general, these approaches are divided into two subsets: rule-based and model-based approaches. This dissertation focuses on the study and development of model-based OPC, PSM and illumination optimization approaches for both coherent imaging systems and partially coherent imaging systems.

For coherent imaging systems, we develop generalized gradient-based RET optimization methods to solve for the inverse lithography problem, where the search space is not constrained to a finite phase tessellation but where arbitrary search trajectories in the complex space are allowed. Subsequent mask quantization leads to efficient design of PSMs having an arbitrary number of discrete phases. In order to influence the solution patterns to have more desirable manufacturability properties, a wavelet regularization framework is introduced offering more localized flexibility than total-variation regularization methods traditionally employed in inverse problems. The algorithms provide highly effective four-phase PSMs capable of generating mask patterns with arbitrary Manhattan geometries. Furthermore, a double-patterning optimization method for generalized inverse lithography is developed where each patterning uses an optimized two-phase mask.

These algorithms are computationally efficient, however, they focused on coherent illumination systems. Most practical illumination sources have a nonzero line width and their radiation is more generally described as partially coherent. Partially coherent illumination (PCI) is desired, since it can improve the theoretical resolution limit. PCI is thus introduced in practice through modified illumination sources having large coherent factors or through off-axis illumination. In partially coherent imaging, the mask is illuminated by light travelling in various directions. The source points giving rise to these incident rays are incoherent with one another, such that there is no interference that could lead to nonuniform light intensity impinging on the mask. The gradient-based inverse lithography optimization methods derived under the coherent illumination assumption fail to account for the nonlinearities of partially coherent illumination and thus perform poorly in the partially coherent scenario.

For partially coherent imaging systems with inherent nonlinearities, the sum of coherent systems (SOCS) model and the average coherent approximation model are applied to develop effective and computationally efficient OPC optimization algorithms for inverse lithography. Wavelet regularization is added to the optimization framework to reduce the complexity of the optimized masks. Subsequently, a Singular Value Decomposition (SVD) model is used to develop computationally efficient PSM optimization algorithms for inverse lithography. A novel DCT post-processing is proposed to cut off the high frequency components in the optimized PSMs and keep the fabricating simplicity. Furthermore, a photoresist tone reversing technique is exploited in the design of PSMs to project extremely sparse patterns.

As traditional RETs, the above mentioned gradient-based inverse OPC and PSM optimization methods fix the source thus limiting the degrees of freedom during the optimization of the mask patterns. To overcome this restriction, computationally efficient, pixel-based, simultaneous source mask optimization (SMO) methods for both OPC and PSM designs are developed in this dissertation. The synergy is exploited in the joint optimization of source and mask patterns. The resulting source and mask patterns fall well outside the realm of known design forms. In these SMO algorithms, the Fourier series expansion model is applied to approximate the partially coherent system as a sum of coherent systems. Cost sensitivity is used to drive the output pattern error in the descent direction. In order to influence the solution patterns to have more desirable manufacturability properties, topological constraints are added to the optimization framework. Several illustrative simulations are presented to demonstrate the effectiveness of the proposed algorithms.

The above gradient-based inverse lithography optimization approaches are effective and computationally efficient under the thin-mask assumption, where the mask is considered as a 2-D object. As the critical dimension (CD) printed on the wafer shrinks into the subwavelength regime, the thick-mask effects become prevalent and thus these effects must be taken into account. Thus, OPC and PSM methods derived under the thin-mask assumption have the inherent limitations and perform poorly in the subwavelength scenario. In order to overcome this limitation, the final contribution of this dissertation focuses on developing OPC and PSM optimization methods based on the boundary layer (BL) model to take into account the thick-mask effects. Attributed to the nonlinear properties of the BL model, model-based forward lithography methods are exploited to obtain the optimized binary and phase-shifting masks. The advantages and limitations of the proposed algorithm are discussed and several illustrative simulations are presented.