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Description  |
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BRIEF DESCRIPTION OF THE INVENTION
This invention relates generally to a method of making submicrometer
dimensional measurements of line structures such as found in semiconductor
devices and the photolithographic method used in making such structures
using confocal and correlation microscopes. More particularly, the
invention relates to a method of processing data representing intensity as
a function of horizontal position x at various z positions of the line
structure by pattern recognition techniques to obtain a line-width
measurement.
BACKGROUND OF THE INVENTION
Submicrometer dimensional measurement is essential for semiconductor
processing. It is necessary to measure the width of a critical line
structure, for example, the gate width of a transistor. More importantly,
critical line-width measurements are often used to characterize VLSI
processing steps. For example, in photolithography, the measured width is
directly related to critical process parameters such as focus distances
and exposure periods.
Traditional techniques based on thresholding of the intensity of an optical
image taken with a standard optical microscope are not accurate enough for
submicrometer measurements. By using a confocal or correlation microscope,
good results for narrow trenches down to widths of 0.4 .mu.m can be
obtained. However, for photoresist lines and arrays of lines and trenches,
the relation between measured line-width and nominal line-width is not
always linear. Furthermore, in the latter case, it is sometimes difficult
to pick out the width of lines less than 0.7 .mu.m wide.
For critical dimensional measurements, one is usually interested in
line-widths. Thus, instead of acquiring a whole two-dimensional image, one
only needs to acquire a line-scan at the same x location on the object
every time its focus position changes. FIG. 1 schematically shows a
microscope objective 11 focused at a spot 12 with respect to an object 13
which includes a line structure 14 to be scanned. The object is placed on
a stage 16 which can be moved in the x-y-z directions so that the focal
spot impinges upon different surfaces and locations on the object. To
obtain a linescan, the object is moved along a line in the x-direction so
there is scanning in the x-directions and then stepped in the z-direction
to scan another line at another elevation. The image acquired by the
microscope is applied to a CCD camera 17 which digitizes the signals which
are stored in a computer 18. The computer controls the positioning stage.
In the preferred embodiment, the focal spot extends over an area to create
an image of a plurality of lines of the line structure and the output of
the CCD camera is lens scanned to give readings for the x-direction. The
stage is only moved to observe a different area. In either embodiment, the
signals can then be processed and displayed on display 19 as a cloud plot.
The cloud plot is a gray scale display of intensity as a function of
horizontal position x and axial focusing position z along a line. FIGS. 2A
and 2B are examples of cloud plots of 0.5 .mu.m wide dense resist
structures recorded by a confocal microscope and a correlation microscope
(the Mirau Correlation Microscope), respectively.
The traditional approach to line-width measurements is to plot the
intensity of the cloud plot as a function of x at various focus planes, z,
of interest. For example, as illustrated in FIGS. 3A and 3B, for a Mirau
correlation microscope and confocal microscope, respectively, L.sub.top is
the top width of the photoresist strips, L.sub.bot is the width at the
trench bottoms and L.sub.resist measures the width of the resist strips at
the substrate interface. We shall call the respective line scans (along x)
at the top of the resist; the bottom of the trench and the bottom of the
resist l.sub.top (X), l.sub.bot (x), and l.sub.resist (x), respectively.
Typically, the width of the actual line is then taken to be the width
between the 1/2 or 1/3 power points of linescans taken in the x direction
at these positions in z. For the confocal microscope, the intensity
linescan is used; while for the correlation microscope, the linescan can
be taken at the transformed intensity image. FIG. 2C is the transformed
intensity image of the cloud plot of FIG. 2B; it is equivalent to the
intensity cloud plot for the confocal microscope. Typically, it is
standard practice to take the width of the line to be the distance between
the 1/2 or 1/3 power points of a linescan in the x direction at a fixed
position z corresponding to either the top or bottom of a trench or line.
It is difficult to determine in the cloud plot the exact axial locations
where the linescans l.sub.top (x), l.sub.bot (x), and l.sub.resist (x)
should be taken, as the absolute locations may shift due to optical
waveguiding or resonance effects inside the line structures. The shapes of
the lines l.sub.top (x), l.sub.bot (x), or l.sub.resist (x) may change as
the true line-widths vary. Typically these regions are picked out by
looking for the position of maximum intensity in a scan in the z
direction, as illustrated in FIGS. 3A and 3B. Consequently, it is not easy
to construct an automatic measurement algorithm which tracks the true
hne-width consistently.
SUMMARY OF THE INVENTION
Accordingly, it is an objective of this invention to provide a method of
measuring based upon pattern recognition-data clustering.
It is another objective of this invention to provide a method of measuring
which provides reproducible measurements from sample to sample without
operator interpretation.
It is yet another objective of this invention to provide a measurement
method which is applicable to both correlation microscopes and confocal
microscopes.
This and other objects of the invention are achieved by obtaining signals
from a microscope from at least a plurality of locations on surfaces along
a line, clustering the signals in the z direction into groups representing
lines and trenches of the surface along the line, and creating a
similarity curve which is a function of the position on the line wherein
the minimum value represents lines or trenches and the maximum value
represents trenches or lines, and measuring the distance between adjacent
points on the curve along a selected line parallel to the maximum or
minimum.
BRIEF DESCRIPTION OF THE DRAWINGS
The purpose and advantages of this invention will be apparent to those
skilled in the art from the following detailed description in conjunction
with the appended drawings, in which:
FIG. 1 is a schematic diagram of a microscope system for carrying out the
method of the present invention.
FIG. 2A shows a cloud plot of a 0.5 .mu.m wide dense resist structure
obtained by a confocal microscope.
FIG. 2B shows a cloud plot of a 0.5 .mu.m wide dense resist structure
obtained by a correlation microscope.
FIG. 2C is a transformed cloud plot of the cloud plot of FIG. 2B.
FIGS. 3A and 3B show the contributions from top of a resist line, silicon
under resist line and trenches to the signals at location x as a function
of z.
FIG. 3C shows the normalized cluster representation of the resist and
trenches of FIGS. 3A and 3B.
FIG. 4 shows the distribution in data clusters for l.sub.trench and
l.sub.resist.
FIG. 5 is a block diagram of the method of clustering in accordance with
the invention.
FIG. 6 shows the results of the method in accordance with the present
invention.
FIG. 7 is a comparison of results obtained using a conventional intensity
linescan and the method of the present invention for measuring a dense
resist 1 .mu.m line structure.
FIG. 8 is a comparison of measurements of a 0.5 .mu.m thick resist wafer
with structures of varying widths.
FIG. 9 is a comparison of measurements of a 1.27 .mu.m thick resist wafer
with structures of varying widths.
FIG. 10 shows results obtained with a confocal microscope.
FIG. 11 illustrates use of the present invention to align structures.
DETAILED DESCRIPTION OF DRAWINGS
Referring to FIGS. 3A and 3B, it is observed that the two linescans are
different in two respects: first, the envelope of the scan through the
center of a photoresist line may experience two maximums due to
reflections from the top of the resist and the substrate underneath while
that through the center of a trench has only one maximum; second, the
envelopes of these two scans are offset in z by an amount approximately
equal to the resist thickness. We then classify all axial scans (scans
along the vertical axis) l.sub.x (z) at location x by processing the storm
signals into two groups, l.sub.resist and l.sub.trench, according to a
similarity measure, the location of the peaks in the z direction is used.
Each axial scan l.sub.x (z) may be thought of as a vector in N-dimensional
space. The distribution of the two data clusters l.sub.resist and
l.sub.trench is illustrated in FIG. 4 where, for simplicity, each vector
l.sub.x (z) is considered as three dimensional. The signals from the
resist line locations and the trench locations are clustered around the
resist line cluster and the trench cluster, respectively, while the edges
(or the transition region) are located between the two clusters. The
centroids l.sub.resist,centroid and l.sub.trench,centroid of the two
clusters 1.sub.resist and l.sub.trench may be defined as shown in FIG. 4,
which are very useful for data classification described below.
The signals l.sub.x (z) are usually represented by 64 or more data points
corresponding to 64 or more steps of the surface in the z-direction after
each image is taken in the x-y direction, and thus can be thought of as
vectors of at least 64 dimensions. This is too much information for fast
classification. To compress the information needed for classification one
can take a Fourier transform of the linescans, l.sub.x (z), in the z
direction, by writing (in continuous analog form):
l.sub.x (k.sub.z)=.intg.l.sub.x (z)e.sup.-jk.sbsp.z.sup.z dz(1)
where k.sub.z is called the spatial frequency in the z direction.
After the Fourier transform, only about 6 Fourier components (or
dimensions) are required, instead of 64 dimensions, to represent the same
signal l.sub.x. It should be noted that other transformations (for
example, Walsh or Karhunen-Louve transformations) can also be used for
dimensional reduction. With a Fourier transform, the magnitudes of the
spectrums of l.sub.resist (k.sub.z) and l.sub.trench (k.sub.z) are related
to the shape of their envelopes before the transform; the phase difference
of the spectrums of l.sub.resist (k.sub.z) and l.sub.trench (k.sub.z) is
related to the relative offset of their envelopes along the z-axis. The
transformed signal l.sub.x (k.sub.z) is now considered as a complex number
so that both the amplitude and phase of the spectrum are used for
classification.
In order to highlight the fact that all transformed signals of l.sub.x (z)
(in which the Fourier transform signal l.sub.x (k.sub.z) is one example)
and even the original signal l.sub.x (z) may be used for the data
clustering technique described in this disclosure, we will just use
l.sub.x to represent the signal at location x, without writing the
variables z or k.sub.z or any other transformed coordinates explicitly.
Up to now, the signals l.sub.x (z) are assumed to be single axial linescans
of intensities representing a well defined focal point along the z-axis
before Fourier transformation to spatial frequencies k.sub.z along the
transformed z-axis. However, l.sub.x may also be taken as a region of
linescans representing the focal area or spot along z or k.sub.z centered
at a horizontal location x. For example, the regional signal
l.sub.xn.sup.R with width (2 m+1) points is expressed as a
multidimensional vector:
##EQU1##
where l.sub.x(n-m), l.sub.x(n-m+1), l.sub.xn, l.sub.x(n+m-1) and
l.sub.x(n+m) are just linescans along z or k.sub.z at locations
x=x.sub.n-m, x.sub.n-m+1, x.sub.n, x.sub.n+m-1 and x.sub.n+m,
respectively. Since l.sub.x(n-m), l.sub.x(n-m+1), l.sub.xn, l.sub.x(n+m-1)
and l.sub.x(n+m) are all column vectors of the same dimension,
l.sub.xn.sup.R is now a column vector of dimension (2 m+1) times that of
the previous column vector 1.sub.xn.
The advantage of using a regional signal l.sub.x.sup.R over a line signal
l.sub.x is that the contribution of the neighboring pixels of the focal
spot x.sub.n-1, x.sub.n-2, etc. are taken into consideration in the
representation of the signal at x.sub.n. The underlying physical reason is
that the point spread function of an optical microscope extends over a
finite area on the sample so that the neighbors x.sub.n-1, x.sub.n-2, etc.
have their contributions even though the beam is supposed to be focused at
x.sub.n. However, in order to emphasize the contribution from the focused
point x=x.sub.n, the vector l.sub.xn.sup.R (Eq. 2) is weighted so that
l.sub.xn is unity and l.sub.x(n-m), l.sub.x(n-m+1), l.sub.xn,
l.sub.x(n+m-1) and l.sub.x(n+m) are weighted (with weights less than 1)
according to their distance from x.sub.n. For example, the point spread
function of the microscope may be used to assign the weights.
In the foregoing description it was stated that the axial linescans would
be classified in groups representing l.sub.trench and l.sub.resist at the
various l.sub.x locations. This is accomplished by a similarity measure.
After a dimensional reduction by transformation (if so desired), the line
signal l.sub.x or regional signals l.sub.x.sup.R are clustered by a
similarity measure. Some of the common similarity measures to measure the
similarity between two vectors l.sub.1 and l.sub.2 at locations x.sub.1
and x.sub.2 are:
Dot Product
##EQU2##
In a two-dimensional system if l.sub.1 and l.sub.2 are perpendicular, then
l.sub.1 .multidot.l.sub.2 =0. In a multidimensional system l.sub.1
.multidot.l.sub.2 is maximum when l.sub.1 and l.sub.2 lie along the same
directions.
Similarity Rule
##EQU3##
The denominator is zero when l.sub.1 =l.sub.2 and the numerator maximum
when l.sub.1 and l.sub.2 lie in the same direction.
Weighted Euclidean Distance
##EQU4##
This quantity is minimum when the vectors are identical.
Normalized Correlation
##EQU5##
This quantity is maximum when the vectors are parallel.
In Eqs. (3) and (5), we are summing over all the k dimensions of the
transformed domain.
The algorithm which we have found most satisfactory to date for clustering
is the Weighted Euclidean Distance measure (Eq. 5). There are many ways
the weights w.sub.k of the vector components l.sub.x (k) can be chosen:
for example, for the dimensionally reduced Fourier transform signal, each
dimension k represents a physical angular component of the reflected beam
collected by the microscope. A certain angular component is emphasized by
increasing the weight w.sub.k corresponding to that component. Moreover,
w.sub.k may be chosen statistically by weighting w.sub.k inversely
proportional to the variance of the k.sup.th dimension over a
predetermined set of prototype signals. This pattern recognition approach
is summarized in FIG. 5.
Thus the clustering process involves the following:
1. Obtain an x-z plot.
2. Optionally, the x-z plot is Fourier transformed along the z-axis. This
Fourier transform reduces the vector dimension of signal l.sub.x (at each
horizontal location x).
3. One or more prototypes representing l.sub.resist (or l.sub.trench) are
selected from the transformed x-z plot for calculating the centroid
l.sub.resist,centroid (or l.sub.trench,centroid) of class l.sub.resist,
(or l.sub.trench).
4. In the preferred method, the weighted Euclidean distance d.sub.x between
the line signal l.sub.x or region signal l.sub.x.sup.R and the chosen
class centroid l.sub.resist,centroid (or l.sub.trench,centroid) is
calculated (Eq. 5); d.sub.x is normalized and plotted as a function of x,
providing a similarity curve as shown in FIG. 3C and FIG. 6. The minimum
and maximum values represent trenches and lines, or vice versa. By
measuring the distance between the points in adjacent peaks of the curve
along a line which is parallel to the abscissa of the curve, which, for
example, is labeled x (.mu.m) in FIG. 6. The width of a trench or line is
then obtained from the measured distance between the peaks or troughs of
the similarity curve. In FIG. 6, the width of the resist strip (or trench)
is taken to be the width between the 50% points of the normalized distance
measure. Without prior knowledge of the cluster distribution, the width of
the resist lines or trenches is just taken at the plane equidistant from
the two clusters. Thus, we have classified the two regions, the trench and
the line, into two clusters. The surface between these two clusters is the
plane equidistant from the two clusters.
The other cluster methods, equations (3),, (4) and (6), can be used to find
a similarity curve which is a function of x. The curve would be of the
type illustrated and the analysis similar.
There are various ways to improve the current clustering algorithm. For
example, the estimation of the centroids l.sub.resist,centroid,
l.sub.trench,centroid of the two clusters l.sub.resist and l.sub.trench in
step (3) may be improved by iteration. After running through steps (1)
through (4), better locations of the lines and trenches is obtained and
therefore, the prototypes representing the lines and trenches can be
better selected. Then the process can be repeated to produce improved
results.
In step (4), width measurement by thresholding the Euclidean distance
measurement is not very satisfactory and may introduce errors in
partitioning the clusters. To avoid thresholding, one may first determine
the distances d.sub.x,trench between l.sub.x and l.sub.trench,centroid and
d.sub.x,resist between l.sub.x and l.sub.resist,centroid and then measure
the line-widths from the x-locations where d.sub.x,resist =d.sub.x,trench.
The method described above was used with the images obtained from a
confocal microscope. FIG. 7 shows a linescan at the bottom focus of a
dense resist line structure (1 .mu.m tall). The line structures cannot be
observed when an intensity linescan is obtained by traditional
thresholding. Using the clustering method in accordance with the
invention, the distance measure shows clearly the dense line structures
because the information contained in all focus locations are utilized.
FIG. 8 shows the measurement results on a 0.5 .mu.m thick E-beam resist
wafer with dense line structures of varying widths. The measurements were
obtained with a coherence microscope--the Mirau Correlation Microscope.
The diamonds show the measured widths obtained by thresholding the
intensity linescans at the trenches and the circles are the results
obtained by the clustering algorithm in accordance with this invention.
The irregular measurement results below 0.6 .mu.m are removed by the
clustering technique. FIG. 9 shows another set of measured data (1.27
.mu.m tall I-line resist wafer with dense line structures) acquired with a
Mirau Correlation Microscope. Again line structures below 0.6 .mu.m are
recognized by the clustering technique but not by a traditional
thresholdlug algorithm.
Similar improvement on the measurement data acquired by a confocal
microscope has also been observed. A confocal microscope (Conquest 2000 by
Prometrix Corp., Santa Clara, Calif.) was used to examine a focus/exposure
wafer of dense photoresist lines on polysilicon. Different dies on the
wafer were printed with different focus and exposure times so that the
widths of the printed lines changed slightly from die to die. The acquired
data were in the form of cloud plots as shown in FIG. 2B. The clustering
technique was then applied to the cloud plots and the measurement results
are shown in FIG. 10. Again, optical data produced by the clustering
technique correlates much better with SEM results than those obtained by
thresholding alone.
Although the present disclosure is mainly concerned with line-width
measurements, the same clustering technique, with little modifications,
may be applied to overlay metrology. In order to determine the alignment
accuracy of two alignment marks--typically achieved by centering a single
box inside a larger box (FIG. 11)--linescans are taken at several
locations on the alignment structures to determine the center of mass of
the two structures. However, it may sometimes be difficult to decide the
axial focusing since the two box-like structures are likely to be of
different heights. The clustering technique is very useful here since it
does not require the knowledge of the focal location of the alignment
structures. Furthermore, by utilizing the information from a range of
z-values instead of from a single focus, the irregularities near the edges
may be averaged out; thus, the center of mass may be determined more
accurately.
It is apparent that the image data obtained by the CCD camera can be line
scanned in various directions and locations to form cloud plots and
provide line-width measurement at any desired location of the
semiconductor device surface. It is also apparent that holes in masks as
well as lines and trenches can be measured during processing of
semiconductor devices.
* * * * *
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