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Proceedings Paper

Modeling within-field gate length spatial variation for process-design co-optimization
Author(s): Paul Friedberg; Yu Cao; Jason Cain; Ruth Wang; Jan Rabaey; Costas Spanos
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Paper Abstract

Pelgrom's model suggests that a spatial correlation structure is inherent in the physical properties of semiconductor devices; specifically, devices situated closely together will be subject to a higher degree of correlation than devices separated by larger distances. Since correlation of device gate length values caused by systematic variations in microlithographic processing is known to carry a significant impact on the variability of circuit performance, we attempt to extract and understand the nature of spatial correlation across an entire die. Based on exhaustive, full-wafer critical dimension measurements collected using electrical linewidth metrology for wafers processed in a standard 130nm lithography cell, we calculate a spatial correlation metric of gate length over a full-field range in both horizontal and vertical orientations. Using a rudimentary model fit to these results, we investigate the impact of correlation in the spatial distribution on the variability of circuit performance using a series of Monte Carlo analyses in HSPICE; it is confirmed that this correlation does indeed present a significant influence on performance variability. From the same dataset, we also extract both the across-wafer (AW) and within-field (WIF) contributions to systematic variation. We find that the spatial correlation model’s shape is strongly related to these two components of variation (both in magnitude as well as by spatial fingerprint). By artificially reducing each of these components of systematic variation-thereby simulating the effects of active, across-field process compensation-we show that spatial correlation is significantly reduced, nearly to zero. This implies that Pelgrom's model may not apply to die-scale separation distances, and that a more accurate correlation theory would combine Pelgrom's model over very short separation distances with a systematic variation model that captures variability over longer distances by means of non-stationary distributions.

Paper Details

Date Published: 5 May 2005
PDF: 11 pages
Proc. SPIE 5756, Design and Process Integration for Microelectronic Manufacturing III, (5 May 2005); doi: 10.1117/12.600028
Show Author Affiliations
Paul Friedberg, Univ. of California/Berkeley (United States)
Yu Cao, Univ. of California/Berkeley (United States)
Jason Cain, Univ. of California/Berkeley (United States)
Ruth Wang, Univ. of California/Berkeley (United States)
Jan Rabaey, Univ. of California/Berkeley (United States)
Costas Spanos, Univ. of California/Berkeley (United States)

Published in SPIE Proceedings Vol. 5756:
Design and Process Integration for Microelectronic Manufacturing III
Lars W. Liebmann, Editor(s)

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