Data processing: measuring – calibrating – or testing – Measurement system – Dimensional determination
Reexamination Certificate
2003-02-07
2004-11-30
Bui, Bryan (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system
Dimensional determination
C702S159000, C702S170000, C356S504000
Reexamination Certificate
active
06826511
ABSTRACT:
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims priority of the German Patent Application No. 102 04 943.2, filed Feb. 7, 2002, which is incorporated by reference herein.
FIELD OF THE INVENTION
The invention concerns a method for the determination of layer thicknesses and optical parameters of a number of layers of a specimen, in which the reflectance spectrum of the specimen is measured and subsequently smoothed, and a modeled reflectance spectrum is adapted to the measured one so as thereby to determine the layer thicknesses; and refers to the problem of determining the thicknesses of multiple-layer systems.
BACKGROUND OF THE INVENTION
Reflection spectrometry is a method, widely used and known for some time, for the examination of layered systems, in particular wafers, and for the determination of layer thicknesses and other optical parameters. The principle of the method is very simple: a specimen that has multiple layers is irradiated with light of a defined wavelength. If the layers are transparent, the light penetrates into the media and is partially reflected in the transition regions between two layers, including the transition between the topmost layer and the ambient atmosphere. The superimposition of incident and reflected light results in interferences, thus influencing the intensity of the reflected light. The ratio between the intensities of the incident and the reflected light determines the so-called absolute reflectance; both intensities must therefore be measured. If the wavelength is then varied continuously within a defined range, this yields a reflectance spectrum that, as a function of the wavelength, has maxima and minima that are produced by the interferences. The locations of these extremes depend on the material properties of the specimen, which determine the optical behavior. These optical parameters include, for example, the refractive index and absorption coefficient. The layer thickness additionally influences the location of the extremes in the reflectance spectrum.
It is possible, in principle, to deduce these parameters from the measured reflectance spectrum; in an ideal model, the limits in terms of the thickness and number of layers are very wide. The basic formulae can be derived from Fresnel refraction theory, as described in detail in the article “Polycrystalline silicon film thickness measurement from analysis of visible reflectance spectra” by P. S. Hauge in J. Opt. Soc. Am., Vol. 69 (8), 1979, pp. 1143-1152. As is evident from the book by O. Stenzel, “Das Dünnschichtspektrum” [The thin-layer spectrum], Akademieverlag 1996, pp. 77-80, the determination of optical constants and layer thicknesses by back-calculation in reality turns out to be very difficult and laborious, however, since the number of unknowns is very large.
One must therefore resort to approximations, or apply limitations. Thickness determination is simplest if the number of layers is limited to one layer whose thickness is to be determined. In this case a correlation can be created between the layer thickness d and the refractive indices n(&lgr;
i
) for the wavelengths &lgr;
i
that belong to the extremes in the reflectance spectrum, where the index i indicates the extremes. If the reflectance spectrum contains a total number m of extremes between two arbitrarily selected extremes &lgr;
i
and &lgr;
j
, the layer thickness can then be determined using the equation
d
=
1
4
·
m
-
1
n
(
λ
i
)
λ
i
-
n
(
λ
j
)
λ
j
(
1
)
To arrive at this expression, however, the limiting assumption of only one weakly dispersive layer must be applied; this formula fails with strong dispersion and with absorbent layers. This limits the class of materials that can be investigated. A further prerequisite is that the wavelength-dependent refractive index n(&lgr;) be known. This principle, hereinafter called the “extremes method,” is the basis of, for example, the method described in U.S. Pat. No. 4,984,894 for determining the layer thickness of a layer.
U.S. Pat. No. 5,440,141 describes a method for determining the thicknesses of three layers. In this, an approximate thickness of the first layer is determined using the aforementioned “extremes method.” The exact thickness of the first layer is then determined by calculating, in a region approximately ±100 nm around this value and for various thicknesses, firstly a modeled reflectance spectrum and secondly the deviations of the respective modeled reflectance spectrum from the measured spectrum. These deviations are combined into an error function E min which the deviations are squared:
E
∼
∑
λ
i
w
λ
i
(
R
ex
(
λ
i
)
-
R
th
(
λ
i
)
)
2
.
(
2
)
where w
&lgr;
is a weighting factor, R
ex
the experimentally determined reflectance spectrum, and R
th
the modeled reflectance spectrum for a layer thickness. This layer-thickness-dependent function E is then minimized by looking for the modeled reflectance spectrum at which the deviations are smallest. The layer thickness at which the function E is minimal is identified as the actual layer thickness. With multiple layers, however, this method can be implemented only if the first layer reflects in a first wavelength region in which the lower layers absorb light, so that they can be left out of consideration when determining the thickness of the first layer. In the document cited, reflection measurements are therefore performed in two different wavelength regions.
To determine an approximate thickness of the second layer, a frequency analysis of the reflectance spectrum in the second wavelength region is performed, based on the fact that maxima and minima repeat periodically in the reflectance spectrum; this is expressed in the converted spectrum by the presence of more or less pronounced peaks. These peaks allow an initial approximate conclusion as to the thickness of the second layer. An approximate thickness of the third layer is obtained by lowpass filtration, the differing material properties of the layer stack once again being exploited here. Similarly to the procedure for the first layer, an error function dependent on the thicknesses of the second and third layers is minimized, by looking for those thicknesses at which the deviations between the experimental and modeled spectra are smallest.
It is thus clearly evident from U.S. Pat. No. 5,440,141 that the thicknesses of multiple layers can be determined, but that this works only for layer combinations of specific materials.
Lastly, U.S. Pat. No. 5,493,401 describes a method for determination of the thicknesses of—in principle—an arbitrarily large number of layers. This is done by first determining the total number of extremes as well as the smallest and largest wavelength that corresponds to one extreme. From these magnitudes, conclusions can be drawn as to the total thickness of the layer stack, i.e. the summed thicknesses of the individual layers. For each of the various combinations of individual thicknesses that together yield the total thickness, a modeled reflectance spectrum is then calculated and an error function E, containing the deviations between the modeled and the experimental reflectance spectrum, is determined as described above. That combination of thicknesses for which those deviations are smallest is then found.
The applicability of the method described in U.S. Pat. No. 5,493,401 is also limited, however. As soon as the experimental spectrum is more greatly modified by influences that the model does not, or does not adequately, account for, the results are no longer reliable, and what is obtained is very probably an incorrect set of layer thicknesses for which the function E assumes a local minimum. Light scattering, such as occurs e.g. in polysilicon, and specimen surface roughness influence e.g. the expression of the extremes: at high levels of roughness and diffusion, certain extremes will be less pronounced, i.e. will have lower reflectance, than actually predicted in the model
Engel Horst
Mikkelsen Hakon
Wienecke Joachim
Bui Bryan
Leica Microsystems Jena GmbH
Simpson & Simpson PLLC
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