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3.1.3 Test Structure Design for Electrically-Based Calibration of Optical Overlay Measurement Instruments

Will Guthrie

Statistical Engineering Division, ITL

Mike Cresswell,
Richard Allen

Semiconductor Electronics Division, EEEL

Misalignment of circuitry layers on IC chips often results in defects or degraded chip performance. Thus when selecting chip manufacturing methods or monitoring output, the ability to determine the amount of misalignment (called overlay) is important.

Overlay is typically measured using high-volume optical instruments. These instruments, however, are susceptible to systematic errors called tool-induced shifts (TIS). TIS can be minimized with `shift management techniques', but cannot be eliminated. However, development of a test structure allowing comparison of optical measurements with more accurate overlay determinations would allow reliable correction for TIS. Not coincidentally, electrically-based methods are good candidates for this application. They are relatively precise and are insensitive to many sources of error affecting optical instruments.

Simulated data and analysis results from the electrical portion of a new test structure design are shown in the accompanying figure. The data from this structure (upper left) is discrete, indicating electrical contact between vias (wires connecting circuit layers) and one of two underlying bars separated by a space. The vias have built-in offsets (o) which, with the unknown overlay (OL) and noise, control whether or not contact will be made.

To extract an estimate of OL, replicate substructures are embedded in each test structure. This allows the proportion of vias with each built-in offset that contact the first bar to be estimated (upper right, lower plot). The proportion of vias contacting the second bar is computed similarly (upper right, upper plot). The contact/noncontact transition points between the vias and each bar equal $OL \pm C$ respectively, where C is a constant related to the difference in size between the vias and the space between the bars.

The transition points are estimated by fitting generalized linear models

\begin{displaymath}p = \frac{\mbox{exp}(\beta_0 + \beta_1o)}{1+\mbox{exp}(\beta_0 + \beta_1o)} + \varepsilon \end{displaymath}

to the data by maximum likelihood with (scaled) binomial errors. These models are then linearized using the logistic transformation, $\mbox{log}(p/(1-p))$, to allow computation of approximate uncertainties for the transition point estimates. Under the linearized models the transition points are given by the x-axis offset values associated with y-axis values of zero (lower left plots). Finally the estimated transition points are averaged to estimate OL. Their uncertainties, along with a rough estimate of their correlation, are combined into an overall uncertainty which is an approximate 95% confidence interval for OL.


Figure 3: Simulated data from a prototype test structure with accompanying data analysis and results. The dashed lines on the final plot indicate transition points and the solid lines indicate the estimated overlay (center line) and uncertainty. The uncertainty is an approximate 95% confidence interval. The estimated overlay in this example is $-12.001 \pm 1.255$ nm. The true overlay, from the simulation input, is -12 nm.

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Date created: 7/20/2001
Last updated: 7/20/2001
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