The use of an alternating phase shift mask is an effective method of improving resolution compared with binary and embedded attenuated phase shift mask technologies, but the intensity imbalance between the light propagating through the zero- and π-shifted spaces is the main obstacle to be overcome. Several technical methods are proposed to compensate for such an imbalance in the mask manufacturing process. The known general solutions for the intensity imbalance are applying a space bias and/or an undercut of the space region of the alternating phase shift mask. We evaluated the uniformity of the resist profile after the application of a space bias or an undercut of the mask space region in order to minimize the pattern position displacement and the critical dimension difference between the phase-shifted and unshifted regions for the 90 and 65 nm nodes. Additionally, we found that the imperfect side wall angle of an undercut or a space bias obviously affected the quality of pattern fidelity and hence investigated how the side wall angle affects pattern printability.

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We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.

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Resolution enhancement technology (RET) refer to techniques that extend the usable resolution of an imaging system without decreasing the wavelength of light or increasing the numerical aperture (NA) of the imaging tool. Off-axis illumination (OAI) and phase shift mask (PSM) are essentially accompanied with optical proximity correction (OPC) for most devices nowadays. In general, these three techniques do not work in isolation and the most aggressive mainstream lithography approaches use combinations of all RETs. In fact, OAI and PSM are essentially useless for typical chip-manufacturing applications unless accompanied by OPC. For low k 1 imaging, strong OAI such as Quasar or dipole illumination types is the best. We used dipole illumination in this study. By using strong OAI, the amplitude of the 0 th order is decreased and the amplitude of the 1 st order is increased. Chromeless phase lithography (CPL) is one of PSM technologies and CPL mask is the possible solution for small geometry with low mask error enhancement factor (MEEF). CPL uses only 180 degrees phase-shifter on transparent glass without chromium film to define light-shielding region, destructive interference between light transmitted through the 0 degree and 180 degrees regions produces dark images. To obtain the best resolution, proper OPC is required with CPL. While the most common and straightforward application of OPC is to simply move absorber edges on the mask by giving simple mask bias, the interesting and important additional technique is the use of scattering bars. Also, we can use zebra patterns for the transmission control. Mask intensity transmission changes can impact the image quality. Zebra patterns are formed by adding chromium transverse features. The transmission will be controlled by the zebra pattern density. Technology node with ArF source is studied and the mask optimization is found to be a critical. And the linewidth of scattering bars, transmission (using zebra feature) are varied at line and space (L/S) patterns. We used 65 nm node 5 L/S and 45 nm node isolated line pattern. In order to optimize the zebra pattern density, we need to control the line width and pitch of the zebra patterns. For dense line and isolated line, the use of scattering bars and zebra patterns affected target critical dimension. We found out the better process window at dense 65 nm node by comparing the use of scattering bars with zebra patterns. Likewise, we optimized the isolated 45 nm node.