Data processing: measuring – calibrating – or testing – Measurement system – Statistical measurement
Reexamination Certificate
2001-08-10
2004-07-27
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Statistical measurement
C702S023000, C702S032000, C702S033000, C702S040000, C702S034000, C702S035000
Reexamination Certificate
active
06768967
ABSTRACT:
TECHNICAL FIELD
The present invention relates to optical measurement of parameters of interest on samples having diffractive structures thereon, and in particular relates to improvements in real-time analysis of the measured optical signal characteristics from a sample to determine parameter values for that sample.
BACKGROUND ART
(This specification occasionally makes reference to prior published documents. A numbered list of these references can be found at the end of this section, under the sub-heading “References”.)
In integrated circuit manufacture, the accurate measurement of the microstructures being patterned onto semiconductor wafers is highly desirable. Optical measurement methods are typically used for high-speed, non-destructive measurement of such structures. With such methods, a small spot on a measurement sample is illuminated with optical radiation comprising one or more wavelengths, and the sample properties over the measurement spot are determined by measuring characteristics of radiation reflected or diffracted by the sample (e.g., reflection intensity, polarization state, or angular distribution).
This disclosure relates to the measurement of a sample comprising a diffractive structure formed on or in a substrate, wherein lateral material inhomogeneities in the structure give rise to optical diffraction effects. If the lateral inhomogeneities are periodic with a period significantly smaller than the illuminating wavelengths, then diffracted orders other than the zeroth order may all be evanescent and not directly observable, or may be scattered outside the detection instrument's field of view. But the lateral structure geometry can nevertheless significantly affect the zeroth-order reflectivity, making it possible to measure structure features much smaller than the illuminating wavelengths.
A variety of measurement methods applicable to diffractive structures are known in the prior art. Reference 7 reviews a number of these methods. The most straightforward approach is to use a rigorous, theoretical model based on Maxwell's equations to calculate a predicted optical signal characteristic of the sample (e.g. reflectivity) as a function of sample measurement parameters (e.g., film thickness, linewidth, etc.), and adjust the measurement parameters in the model to minimize the discrepancy between the theoretical and measured optical signal (Ref's 10, 14). (Note: In this context the singular term “characteristic” may denote a composite entity such as a vector or matrix. The components of the characteristic might, for example, represent reflectivities at different wavelengths or collection angles.) The measurement process comprises the following steps: First, a set of trial values of the measurement parameters is selected. Then, based on these values a computer-representable model of the measurement sample structure (including its optical materials and geometry) is constructed. The electromagnetic interaction between the sample structure and illuminating radiation is numerically simulated to calculate a predicted optical signal characteristic, which is compared to the measured signal characteristic. An automated fitting optimization algorithm iteratively adjusts the trial parameter values and repeats the above process to minimize the discrepancy between the measured and predicted signal characteristic. (The optimization algorithm might typically minimize the mean-square error of the signal characteristic components.)
The above process can provide very accurate measurement capability, but the computational burden of computing the structure geometry and applying electromagnetic simulation within the measurement optimization loop makes this method impractical for many real-time measurement applications. A variety of alternative approaches have been developed to avoid the computational bottleneck, but usually at the expense of compromised measurement performance.
One alternative approach is to replace the exact theoretical model with an approximate model that represents the optical signal characteristic as a linear function of measurement parameters over some limited parameter range. There are several variants of this approach, including Inverse Least Squares (ILS), Principal Component Regression (PCR), and Partial Least Squares (PLS) (Ref's 1-5, 7, 11, 15). The linear coefficients of the approximate model are determined by a multivariate statistical analysis technique that minimizes the mean-square error between exact and approximate data points in a “calibration” data set. (The calibration data may be generated either from empirical measurements or from exact theoretical modeling simulations. This is done prior to measurement, so the calibration process does not impact measurement time.) The various linear models (ILS, PCR, PLS) differ in the type of statistical analysis method employed.
There are two fundamental limitations of the linear models: First, the linear approximation can only be applied over a limited range of measurement parameter values; and second, within this range the approximate model does not generally provide an exact fit to the calibration data points. (If the calibration data is empirically determined, one may not want the model to exactly fit the data, because the data could be corrupted by experimental noise. But if the data is determined from a theoretical model it would be preferable to use an approximation model that at least fits the calibration data points.) These deficiencies can be partially remedied by using a non-linear (e.g., quadratic) functional approximation (Ref. 7). This approach mitigates, but does not eliminate, the limitations of linear models.
The parameter range limit of functional (linear or non-linear) approximation models can be extended by the method of “range splitting”, wherein the full parameter range is split into a number of subranges, and a different approximate model is used for each subrange (Ref. 7). The method is illustrated conceptually in
FIG. 1
(cf.
FIG. 2
in Ref. 7), which represents the relationship between a measurement parameter x, such as a linewidth parameter, and an optical signal characteristic y, such as the zeroth-order sample reflectivity at a particular collection angle and wavelength. (In practice one is interested in modeling the relationship between multiple measurement parameters, such as linewidths, film thicknesses, etc., and multiple signal components, such as reflectivities at different wavelengths or collection angles. However, the concepts illustrated in
FIG. 1
are equally applicable to the more general case.) A set of calibration data points (e.g., point
101
) is generated, either empirically or by theoretical modeling. The x parameter range is split into two (or more) subranges
102
and
103
, and the set of calibration points is separated into corresponding subsets
104
and
105
, depending on which subrange each point is in. A statistical analysis technique is applied to each subset to generate a separate approximation model (e.g., a linear model) for each subrange, such as linear model
106
for subrange
102
and model
107
for subrange
103
.
Aside from the limitations inherent in the functional approximation models, the range-splitting method has additional deficiencies. Although the functional approximation is continuous and smooth within each subrange, it may exhibit discontinuities between subranges (such as discontinuity
108
in FIG.
1
). These discontinuities can create numerical instabilities in optimization algorithms that estimate measurement parameters from optical signal data. The discontinuities can also be problematic for process monitoring and control because small changes in process conditions could result in large, discontinuous jumps in measurements.
Another drawback of the range-splitting model is the large number of required calibration points and the large amount of data that must be stored in the model. In the
FIG. 1
illustration, each subrange uses a simple linear approximation model of the form
y≅ax+b
&ems
Johnson Kenneth C.
Stanke Fred E.
Hoff Marc S.
Stallman & Pollock LLP
Therma-Wave, Inc.
Tsai Carol S. W.
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