Process Watch: Breaking parametric correlation

When you’re designing a geometrically complex structure like a high-k metal gate, FinFET, or vertical DRAM, you will probably use SEM/TEM cross-sectional imaging to work out the bugs. Maybe even a touch of AFM. However, in production, optical scatterometry-based technology is used, chosen for its speed, non-destructive nature and ability to monitor the 3D shape of a feature. This group of metrology techniques is commonly called OCD (Optical Critical Dimension) or SCD (Scatterometry Critical Dimension).

SCD tools commonly employ either reflectometry, ellipsometry, or a combination of the two methods.  In both approaches, the tool focuses a beam of light onto the structure and collects the light that bounces back. By varying the wavelength, a spectrum is constructed that can be sensitive to the shape of the structure, to the optical properties of the materials that comprise the structure, and to previous-layer features buried within materials transparent at the measurement wavelength.

For a given structure and SCD measurement setup, a set of modeled spectra are generated (either on the fly, or offline and stored as a library of curves) that characterize how the spectrum would change if a parameter of interest were varied—for example, the depth of a trench in a vertical DRAM. The measured spectrum is then compared to the modeled spectra to determine which of the models fits best. The result should correspond to a precise, repeatable value for the parameter of interest.

Of course, seldom is anything that simple in real life. Sometimes more than one parametric change (e.g. trench depth and top CD) results in about the same change in the spectrum. The SCD community calls this phenomenon “parametric correlation.”

Let’s say SCD is being used to monitor the shape of a high-k metal gate structure in production

(Figure 1). Suppose the metal undercut, metal and silicon layer bottom CDs and the silicon sidewall angle are the parameters of interest; various failure analysis techniques have shown that small variations in these parameters can correspond to significant degradation in device performance or yield. Let’s also say that small variations in the undercut length are evident in the SCD spectrum—but in a way that’s indistinguishable from what happens when the metal bottom CD changes. A similar issue was reported by GLOBALFOUNDRIES and IBM, in a paper published in a recent SPIE Proceedings on Advanced Lithography.1 


How can you unravel which structural or material variation is causing the change in the spectrum in the presence of parametric correlation? It’s easy if you are certain that one of the two correlated parameters is well controlled—and therefore you can assume that the other parameter is changing. Unfortunately, this is not always the case.

A related way to reduce the variables in the problem is by carrying data forward from previous layers.  If the results for a given layer on a given wafer have already been determined, that information can be used to “fix” the values of some parameters in new layers.  This capability is available today if the wafer has been consistently measured on the same SCD tool. In the future it will be possible to extend this capability to wafers measured on different SCD tools within a fab—as long as those tools are well matched.

When it’s not possible to remove variables by fixing their values, parametric correlation can often be broken by changing the type of SCD measurement: using a different wavelength range; sending the light in at a different azimuth or altitude angle; changing the polarization; or using ellipsometry instead of reflectometry or vice versa. If you have enough different technologies to throw at the problem, you may find one setup that allows the SCD tool to respond sensitively to one of the correlated parameters and not the other.  Sometimes it’s necessary to combine spectra from multiple technologies (angles, polarizations, etc.) or from measuring multiple structures (vertical and horizontal lines, or isolated and dense lines) to come up with a unique solution.

In the example cited earlier, GLOBALFOUNDRIES and IBM found that the use of multiple azimuth angles (parallel and perpendicular to the direction of the dominant lines and spaces) allowed SCD to monitor variations in the metal undercut with high precision and repeatability—and low parametric correlation.

Rebecca Howland, Ph.D., is a senior director in the corporate group and Lanny Mihardja is a product marketing manager in the Films and Scattering Technology (FaST) Division at KLA-Tencor.

Check out other Process Watch articles: “The Dangerous Disappearing Defect,” “Skewing the Defect Pareto,” “Bigger and Better Wafers,” “Taming the Overlay Beast,” “A Clean, Well-Lighted Reticle,” “Breaking Parametric Correlation,” “Cycle Time’s Paradoxical Relationship to Yield,” and “The Gleam of Well-Polished Sapphire.”


1.       Matthew Sendelbach, Alok Vaid, Pedro Herrera, Ted Dziura, Michelle Zhang and Arun Srivatsa, “Use of multiple azimuthal angles to enable advanced scatterometry applications,“ Metrology, Inspection, and Process Control for Microlithography XXIV, ed. Christopher J. Raymond, Proc. of SPIE Vol. 7638, 76381G, 2010.


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