Toward Realistic CD Specifications

Syed Rizvi, Photronics, Inc., Milpitas, CA


  • CD measurement and feature-edge position

  • Uncertainty in feature edge

  • Challenges ahead

  • References
  • The 1997 edition of the National Technology Roadmap for Semiconductors, an update of the earlier 1994 edition, is not only more aggressive but also more comprehensive. The target dates for all nodes are earlier by a year or two, while such requirements as minimum feature size are spelled out in greater detail. For example, the 1997 Roadmap includes specifications for isolated lines on MPU gates, dense lines on DRAMs, and contacts.

    Industry has kept up with the NTRS timeline for minimum feature size and is likely to continue to do so. Even post-optical lithography offers a number of promising candidates. Although making smaller features is a challenge that industry is ready to meet, making small features within a given tolerance increases the difficulty by orders of magnitude. Tight tolerances put heavy constraints on machine tune-ups and process stability. Furthermore, measuring instruments must be able to ascertain that the feature size meets its tolerance. A third area of difficulty relates to the lack of clarity in the tolerance specification prescribed in the Roadmap.

    The industry has followed a "10%, 10%" rule of thumb for feature size and instrument tolerances, setting feature tolerance at 10 % of feature width and instrument tolerance (or 3-sigma precision) at 10 % of feature tolerance, or 1.0 % of feature width. The Roadmap follows this "10%, 10%" rule to some degree.

    CD Measurement and precision (back to top)
    It is important to note that the Roadmap is only a set of guidelines for industry to follow. A "one hundred percent" adherence to the Roadmap should never be recommended. Fabrication technology is dynamic while the Roadmap is a "chart" or an "outline" that by its very nature is static. Industry must react promptly to changes in the marketplace even if it means deviating from the Roadmap.

    The Roadmap's most significant contribution is in its balanced support for all facets of manufacturing. Progress in all disciplines must be fully synchronized and compatible. Accelerated progress in one area is of little value if complementary technologies lag behind. CD is one such crucial area: the ability to make smaller features must be complemented by the ability to measure them.

    Measuring features below 180 nm is going to be increasingly difficult for two reasons. One reason, of course, is the availability of high precision and highly accurate instruments. This issue cannot be over emphasized and needs serious attention. Another, more subtle, reason often goes unnoticed: the lack of sound methodology for CD measurement. As the industry moves toward the sub-180 nm regime, factors such as edge-fuzziness, line slope, and instrument/artifact interactions come into play and need to be addressed. High density poly and metal lines are not only getting thinner but their aspect ratios (height: width) are getting larger. The cross-sections of these lines, due to process limitations, tend to be trapezoidal rather than rectangular. This departure from the perfect rectangular cross section can decrease the distance between the bases of the two adjacent features, increasing crosstalk between the lines and degrading circuit performance.

    Characteristics of such trapezoidal lines can best be examined by an atomic force microscope (AFM) since a scanning electron microscope (SEM) cannot give true quantitative measurements of the slope of the feature walls. This fact also illustrates the need to correlate different types of instruments. Artifacts arising from edge-shapes and materials can respond differently to different measuring systems. Relating these responses to the true CD values requires a well thought out CD definition that considers the uncertainties in locating the edge positions.

    CD measurement and feature-edge position (back to top)
    The required precision of an instrument is conventionally specified as 10% of the CD tolerance. The distance between two edges determines feature width, so an instrument's precision in measuring feature width depends on the precision with which it can locate feature edges. Feature-edge precision is the fundamental building block that ultimately defines the precision of a CD measurement.

    The relationship between the two can be expressed as:

    where scd and se are the standard deviations relating to the feature-width and feature-edge measurements, and g is the coefficient of correlation between the positions of the two edges [1,2]. In most cases g is considered to be zero, but there can be situations where g is not zero.

    Table 1 lists the required precision for edge location measurements, based upon the specifications for feature measurement in the Roadmap [3]. Depending upon the correlation between the two edges the precision of edge-position measurements can vary considerably. The author in his own observation has seen the correlation number vary from 0 to 6. More investigation is definitely needed.

    Table 1: 3-Sigma precision for locating feature-edge positions [3]. (All measurements in nanometers)
    Year for technology nodes 2001 2001 2003 2003 2006 2006 2009 2009
    Technology node 150 150 130 130 100 100 70 70

    Iso Dev Iso Dev Iso Dev Iso Iso
    Target line width or CD 120 100 100 70 70 50 50 35
    3-s tolerance CD 12 10 10 7 7 5 5 3.5
    3-s tolerance on measuring CD 1.2 1.0 1.0 0.7 0.7 0.5 0.5 0.35
    3-s tolerance on locating edges
    for g = 0 0.86 0.71 0.71 0.50 0.50 0.36 0.36 0.25
    for g = 0.3 1.02 0.85 0.85 0.59 0.59 0.42 0.42 0.30
    for g = 0.5 1.20 1.00 1.00 0.70 0.70 0.50 0.50 0.35
    for g = 0.7 1.55 1.29 1.29 0.90 0.90 0.65 0.65 0.45
    for g = 0.9 2.69 2.24 2.24 1.57 1.57 1.12 1.12 0.78

    To a great extent the correlation numbers depend upon the nature of the artifact and the type of measuring instrument. When there is no correlation between the two edges, which is likely to be the case under most measurement conditions, the required precision of the edge measurement can be 30% more stringent than the required precision of the CD measurement.

    Uncertainty in feature edge (back to top)
    The above discussion shows that in order to improve the precision in CD measurement the focus should be on improving the precision in edge-position measurement.

    Feature edges are not "clearly defined lines" but are fuzzy bands that run parallel to the two edges. AFMs, SEMs and optical microscopes interact differently with different types of artifacts, making it difficult to correlate the output from different systems. The degrees of uncertainty associated with each measuring system are also going to be difficult to correlate as higher precision is demanded.

    Challenges ahead (back to top)
    Since measuring the edge position is the determining factor in CD measurement, but uncertainty seems to be an integral part of edge position measurement, the question amounts to, "What can be done to improve the precision in CD measurement?"

    Before a precision specification is assigned, it is important to reality check the numbers. A preliminary evaluation of the correlation coefficients for the given case will establish theoretical limits for the specifications. Next, the industry must adopt a culture that recognizes uncertainty as an integral part of a measuring system, and begin to quantify the uncertainty values. Many books and literature are available to address this issue [4]. Once uncertainty begins to be accepted as a quantifiable entity, then the next step would be to search for techniques and methodology to minimize the uncertainty. Edge detection using neural net is one possible technique [5].

    The physical reality of the situation can best be described by a quote from one of the NIST publications [4]: The result of a measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, that is the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.

    References (back to top)
    1. S. Rizvi, "Analyzing Tolerance and Controls on CD's and Overlay as prescribed by the NTRS," SPIE Symposium on Microlithographic Techniques in IC Fabrication (Singapore) Invited paper, June 25-26, 1997. (back to article)

    2. H. Arkin, R. Colton, Statistical Methods, pp 33-47 Barnes & Noble, New York, 1971. (back to article)

    3. National Technology Roadmap for Semiconductors 1997, Semiconductor Industry Association. (back to article)

    4. B.N. Taylor, Chris Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results." NIAT Technical Note 1297, 1994 Edition. (back to article)

    5. Ye Dai, "Neural Network for Edge Detection" Master's Thesis, Department of Physics, Indiana State University, Terre Haute, Indiana. 1995. (back to article)

    Author Information: Syed Rizvi, Photronics, Inc.1982 Tarob Ct. Milpitas, CA 95035. Tel: 408-262-8800, fax: 408-263-3228. Email:
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