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Pixel-based optical proximity correction (PBOPC) methods have been developed as a leading-edge resolution enhancement technique (RET) for integrated circuit fabrication. PBOPC independently modulates each pixel on the reticle, which tremendously increases the mask's complexity and, at the same time, deteriorates its manufacturability. Most current PBOPC algorithms recur to regularization methods or a mask manufacturing rule check (MRC) to improve the mask manufacturability. Typically, these approaches either fail to satisfy manufacturing constraints on the practical product line, or lead to suboptimal mask patterns that may degrade the lithographic performance. This paper develops a block-based optical proximity correction (BBOPC) algorithm to pursue the optimal masks with manufacturability compliance, where the mask is shaped by a set of overlapped basis blocks rather than pixels. BBOPC optimization is formulated based on a vector imaging model, which is adequate for both dry lithography with lower numerical aperture (NA), and immersion lithography with hyper-NA. The BBOPC algorithm successively optimizes the main features (MF) and subresolution assist features (SRAF) based on a modified conjugate gradient method. It is effective at smoothing any unmanufacturable jogs along edges. A weight matrix is introduced in the cost function to preserve the edge fidelity of the printed images. Simulations show that the BBOPC algorithm can improve lithographic imaging performance while maintaining mask manufacturing constraints.
Pixel-based optical proximity correction (PBOPC) methods have been developed as a leading-edge resolution enhancement technique (RET) for integrated circuit fabrication. PBOPC independently modulates each pixel on the reticle, which tremendously increases the mask's complexity and, at the same time, deteriorates its manufacturability. Most current PBOPC algorithms recur to regularization methods or a mask manufacturing rule check (MRC) to improve the mask manufacturability. Typically, these approaches either fail to satisfy manufacturing constraints on the practical product line, or lead to suboptimal mask patterns that may degrade the lithographic performance. This paper develops a block-based optical proximity correction (BBOPC) algorithm to pursue the optimal masks with manufacturability compliance, where the mask is shaped by a set of overlapped basis blocks rather than pixels. BBOPC optimization is formulated based on a vector imaging model, which is adequate for both dry lithography with lower numerical aperture (NA), and immersion lithography with hyper-NA. The BBOPC algorithm successively optimizes the main features (MF) and subresolution assist features (SRAF) based on a modified conjugate gradient method. It is effective at smoothing any unmanufacturable jogs along edges. A weight matrix is introduced in the cost function to preserve the edge fidelity of the printed images. Simulations show that the BBOPC algorithm can improve lithographic imaging performance while maintaining mask manufacturing constraints.
Recently, a set of gradient-based optical proximity correction (OPC) and phase-shifting mask (PSM) optimization methods has been developed to solve for the inverse lithography problem under scalar imaging models, which are only accurate for numerical apertures (NAs) of less than approximately 0.4. However, as lithography technology enters the 45 nm realm, immersion lithography systems with hyper-NA (NA>1) are now extensively used in the semiconductor industry. For the hyper-NA lithography systems, the vector nature of the electromagnetic field must be taken into account, leading to the vector imaging models. Thus, the OPC and PSM optimization approaches developed under the scalar imaging models are inadequate to enhance the resolution in immersion lithography systems. This paper focuses on developing pixelated gradient-based OPC and PSM optimization algorithms under a vector imaging model. We first formulate the mask optimization framework, in which the imaging process of the optical lithography system is represented by an integrative and analytic vector imaging model. A gradient-based algorithm is then used to optimize the mask iteratively. Subsequently, a generalized wavelet penalty is proposed to keep a balance between the mask complexity and convergence errors. Finally, a set of methods is exploited to speed up the proposed algorithms.
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