Alternating phase-shifting mask design for low aberration sensitivity

Mak, Giuseppe Y.; Wong, Alfred K. K.; Lam, Edmund Y.

doi:10.1117/12.534686

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…These parameters are wrapped inside the functions and in (5), because both functions contain the information about the photomask. The optimal parameter set is found by solving subject to (6) where 7The randomness of image placement error is due to the random normalized aberration function . Since random variables are usually denoted by capital letters, we write for image placement error hereafter.…”

Section: Optimization Processmentioning

confidence: 99%

“…It is assumed that the mean of the root mean square (rms) aberrations of those exposure systems is a known constant, which is the only constraint of this optimization problem. In our previous paper [6], we already considered the optimization of alternating phase-shifting mask (PSM) with symmetric 0 and 180 phase regions under coherent imaging. We extend the generality of the theory by considering a general mask pattern with one-dimensional (1-D) spatial variation under a general illumination.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of Photomask Design for Reducing Aberration-Induced Placement Error

Mak¹,

Wong²,

Lam

2006

IEEE Trans. Semicond. Manufact.

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In semiconductor manufacturing, the accurate placement of circuit components ensures the proper functioning of microelectronic circuits. This is often subject to photolithography, an optical technique that transfers circuit patterns from photomasks to silicon wafers. Sources of placement error include aberration and misalignment between different levels, and we focus on the former. Aberration is an optical phenomenon that often degrades imaging system performance. Since aberration differs from one imaging system to another, a photomask design that minimizes the aberration-induced placement error is desired. In this paper, we discuss the optimization process of a general one-dimensional mask pattern under a general illumination condition. The constraint is a known population mean of the root mean square aberrations for the imaging systems under consideration. To apply the theory, we search for the optimal parameters for two common mask designs: alternating phase-shifting masks (PSMs) and attenuated PSMs. The theoretical results are compared with those from a Monte Carlo analysis on a large set of imaging systems. These results are indicative to mask manufacturers and circuit designers of increasing manufacturability of circuits.

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Section: Optimization Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization of Photomask Design for Reducing Aberration-Induced Placement Error

Mak¹,

Wong²,

Lam

2006

IEEE Trans. Semicond. Manufact.

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“…There has been an extensive study on the relationship between aberration and PSM [4][5][6]. For example, the spherical aberration is found to tilt the isolated pattern printed by alternating PSM.…”

Section: Introductionmentioning

confidence: 98%

The analysis of the criteria of phase error by evaluating the influence of lens aberration on the lithographic performance

Jeong

Ahn

Park

et al. 2005

Optical Microlithography XVIII

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We investigated the influence of lens aberration on the lithographic performance according to the phase error and topography effects of phase-shift mask (PSM). Twin-bar and isolated pattern showing high sensitivity to lens aberration were used for this study. The simulation of aberrated images was carried out using the Solid-CTM simulator. Specially, we quantified the relationship between patterning behaviors such as the isofocal tilt, the left-right (L-R) CD difference and the Z7 and Z9 individual Zernike coefficients. Isofocal tilt aberration sensitivity for Z9 was 0.4nm/nm, which resulted in 2nm CD variation using lens with 5nm Z9 value. When using the lens with 5nm Z7 value, the L-R CD difference and its sensitivity are 10nm and 2nm/nm, respectively. Finally, we evaluated the patterning performance by phase error effect, and determined the phase error criteria for PSM. The pattern placement error was increased by increasing phase error as well as Z7 value, while its slope to the defocus was similar regardless of lens aberration. However, it was found that the aberration sensitivity was not affected by phase error. The simulation predicted that the sensitivity of lens aberration could be increased due to mask topography effect. The nominal shift of phase edge attributed to mask topography was measured.

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Alternating phase-shifting mask design for low aberration sensitivity

Mak

Wong²,

Lam

2005

J. Micro/Nanolith. MEMS MOEMS

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The aberration present in the lenses of exposure systems can cause placement errors to the images produced by alternating phaseshifting masks (PSMs). In reality, when the aberration signature varies from one lens to another, the magnitude of placement error also varies. It remains a question of how the alternating PSM should be designed, so that the image placement error, on average, can be minimized. To achieve this goal, we are interested in optimizing the phase width of an alternating PSM with a fixed critical dimension (CD). The constraint of the optimization is the mean of root mean square (rms) aberrations for a set of interest of exposure systems. To begin the analysis, the image placement error is expressed as a function of illumination, mask spectrum, and wave aberration. A Monte Carlo technique is then applied to produce random samples of wave aberration and image placement error. This analysis shows that a global minimum of mean image placement error is likely to occur at phase widths between 0.2[/numerical aperture (NA)] and 0.4(/NA). This is further confirmed by analytically considering the expected value of the square of the image placement error. The methodology of finding the optimal phase width is applicable to the design of all alternating PSMs. © 2005 Society of Photo-Optical Instrumentation Engineers.

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Alternating phase-shifting mask design for low aberration sensitivity

Cited by 3 publications

References 10 publications

Optimization of Photomask Design for Reducing Aberration-Induced Placement Error

Optimization of Photomask Design for Reducing Aberration-Induced Placement Error

The analysis of the criteria of phase error by evaluating the influence of lens aberration on the lithographic performance

Alternating phase-shifting mask design for low aberration sensitivity

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