Through-focus pattern matching applied to double patterning

ABSTRACT A fast-CAD method for evaluating through-focus interaction among features is developed based on dual layout convolution kernels derived and tested for accuracy in predicting intensity changes. The model is derived by extending the Taylor series expansion for OPD to include a quadratic term, resulting in not only the usual pattern match factor Z 3 for defocus, but also match factors for Z 0 and Z 8 . The model is tested through-focus on a logic layout and the predicted intensity change versus the actual intensity change through-focus is graphed. Results for basic case near coherent illumination show an R 2 of 0.92. Generalization to use only two patterns instead of three is shown to work well for line ends, with an R 2 of 0.96. Keywords: Pattern matching, double patterning, defocus. 1. INTRODUCTION The through-focus behavior of various feature types and feature-to-feature layout interactions in dense patterns fundamentally limit the process window for optical projection printing. Two-dimensional features such as contacts and line ends suffer the most severe effects a nd the higher sensitivity of the critical dimension of isolated lines compared to line arrays is well known. Design rule restrictions can help filter out the use of highly fo cus sensitive scenarios such as forbidden pitches but identifying interactions among 2-D features is challenging in DRC. Once a layout is generated, OPC can help extend through-focus performance generally by increasing image quality and specifically by adding non-printing features such as SRAFs. There remains, however, a need for physically based through-focus models to anticipate problematic issues during the initial circuit design and to improve the efficiency with which post layout OPC computes multiple focus behavior for pre-compensation. Additionally, the ability to provide through-focus feedback during double patterning decomposition would allow the identification among optional split locations of those splits which yield the lowest through-focus variability. Historically, through-focus effects have been well characterized, considered in design rules, mitigated in OPC, and examined with approximate fast-CAD Pattern Matching techniques. The focus dose latitude such as the E-D trees of Bern Lin 10[1] are often used to determine the starting set points for biases and expected process window. The relative quality of features versus pitch are commonly used to identif y and set placement constraints in design rules. The image simulation engines of OPC are often used to consider severa l additional out-of-focus points and simulation of the laser bandwidth on focus is also recommended [1]. Perturbation based fast-CAD techniques called Pattern Matching considered focus among other aberration terms [3][4], and later illumination, high-NA, and polarization [5][6]. These approximate methods employ continuous layout convolution kernels in contrast to the discrete on-off rectangle overlaps that have become associated with Pattern Matching today. The upside potential for these fast-CAD approximate methods is enormous for finding edge placement errors [7], Ring Osc illator variations [8] and interconnect delay variation [9]. The bottleneck, however, has been that while most aberrations are small (Strehl > 0.97), defocus is not a small aberration (Strehl ~ 0.9) and the perturbation based formulation must be revisited. This paper derives and evaluates the accuracy of dual convolution kernels for algebraically modeling intensity change through-focus. The paper begins with background information on the severity of through-focus effects, convolving with transforms of Zernike aberration terms, and the tendency for proximity and focus to affect different locations within a feature. Section 3 then makes a formal derivation of the spill over of electric fields among features and incorporates this field into approximate models for the intensity change. Section 4 first shows how match factor terms in the model correlate with rigorous simulation of intensity changes through-focus and then discusses the level of these effects for various feature types. Section 5 discusses applications for the through-focus model, including double patterning decomposition. Section 6 concludes the paper.