WO1997030378A1

WO1997030378A1 - Positional measurements

Info

Publication number: WO1997030378A1
Application number: PCT/GB1997/000341
Authority: WO
Inventors: Shimon Dov Yanowitz; Nigel Peter Smith; Andrew Michael Christian Smout; Andrew Peter Keens
Original assignee: Bio-Rad Micromeasurements Limited
Priority date: 1996-02-16
Filing date: 1997-02-07
Publication date: 1997-08-21
Also published as: AU1612597A; GB9603262D0

Abstract

The invention relates to a method and apparatus for determining the centre and displacement of rectilinear structures or images and the relative concentricity of structures or images during photolithography. The method and apparatus is sufficiently sensitive to measure image centres and thus reduce overlay errors. Additionally improvements are achieved in the accuracy of instances where tool or processing conditions have adversely altered the apparent symmetry of an image. The invention lies in the realisation that in instances of low contrast and/or strong asymmetry and thus where symmetry and/or detail has been degraded, existing techniques can be used providing one compensates by improving the nature of the image line that is used for the purpose of the measurements and is specifically achieved by using a second order derivative of an image cross section profile. Thus in one instance the invention presents a method for determining displacement between rectilinear marks or images by firstly adding or averaging a number of image signals in at least a part of a given row and/or column above a given axis and then using the Laplacian function so as to provide an improved 2D image of said mark.

Description

POSITIONAL MEASUREMENTS

The invention relates to a method and apparatus for determining the centre of structures or images and the relative concentricity of structures or images, and particularly, but not exclusively, the relative concentricity of overlay marks or patterns.

There are instances when it is necessary to determine the centre and possibly also the relative concentricity of aligned, or overlaid, patterns which may be rectilinear patterns. For example, such patterns are typically used in the semiconductor industry to monitor photolithography during the wafer fabrication process.

In a semiconductor multilayer wafer fabrication process, there is a repeated step involving the printing of a new layer on top of a previous reference layer through a process of photolithography. Technology requirements make ever increasing demands on the degree of accuracy to which these layers should be aligned. The error in alignment is known as overlay error or misregistration error. This overlay error is carefully monitored. Some manual monitoring techniques exist, but in recent years this has become mostly an automated process performed by machines known as Overlay Metrology Tools.

An overlay metrology tool operates on an overlay target which often comprises two rectilinear marks. Typically, the bigger mark which is called the Outer, is printed as part of the selected reference layer. The smaller mark, called the Inner, is then printed inside the outer as part of the new layer that is being superimposed. A typical overlay mark is illustrated in Figure 1.

The tool determines the overlay error by first determining the centrepoint of each mark, and then computing the distance between these two centrepoints.

Optical inspection of small overlay marks or patterns has been performed using imaging apparatus of a conventional nature such as a microscope in combination with electronic image processing. In this way overlain images have been viewed in order to determine the nature of the alignment. However, particularly in the semiconductor industry, chemical and mechanical processes are now being used to polish and so planarize wafer surfaces and these techniques undesirably degrade the optical appearance of the mark on the wafer surface. Thus using conventional apparatus it is difficult to view the marks and thus make the appropriate measurements. Moreover the polishing process itself may introduce asymmetries into the appearance of the mark that undesirably distort any measurements of overlay error that are made.

Figure 1 shows two camera images of overlay marks, each consisting of a plurality of pixels or image points with various intensities arranged in rows and columns. The right hand side of the Figure shows an image in which the contrast between the two overlay marks and the wafer substrate is relatively high and which is therefore suitable for conventional analysis. The left hand side of the Figure shows an image where the contrast between the outer mark and the wafer substrate has been degraded as a consequence of chemical and/or mechanical processing. It is of note that instances may occur where more than one mark is degraded and in these instances an image would be presented where both marks were difficult to distinguish.

Conventionally, the first step in measuring the overlay error represented by an image such as those in Figure 1 is to take one or more lines passing through the selected mark. Ideally such lines are selected having regard to the geometry of the mark. For example, where a rectangular mark is used such lines are typically vertical and/or horizontal and lie along rows or columns in the image. The line gives rise to an image cross-section profile where the displacement at each point in the profile represents the image signal level in each corresponding pixel along said line.

In an alternative example, where a non-rectangular mark is used such lines are either vertical and/or horizontal or at an angle thereto.

Referring to Figure 1 it can be seen that two cross-section profiles 1 and 2 are provided. Towards the left hand side of the Figure the outer mark is represented with relatively low image contrast and therefore the corresponding displacements A are relatively shallow. Towards the right hand side of Figure 1 the outer mark provides a relatively strong signal. Accordingly the signal data in each image point is relatively strong and therefore displacements H corresponding to the two outer vertical lines of the outer mark are relatively large.

Conventionally using one prior art technique, once an image cross-section profile is created for a given mark, selected parts thereof are firstly duplicated and then the duplicated parts are folded over the original at some nominal centreline position. This folding position is then moved in single pixel increments, thus sliding the folded and original signals over one another. At each folding position the value of correlation between the profiles at that point, is computed. The correlation between two profiles { } and {r, } is by given by

Equation 1

where / and t are the means of / and t respectively. At a certain location there will be a best match between the rotated profiles. This best match will produce a maximum in the correlation. Detecting the location where the maximum lies, points at where the centre of the mark is. The centre calculation is further refined by taking more values of the correlation around the point of maximum, and interpolating them.

The correlation operation is capable of matching vectors that differ in both gain and offset. The offset is treated by subtracting the mean of each vector from all points of that vector. The gain is handled by normalising the expression by means of the energies of the two vectors. This is the term that appears in the denominator. This flexibility of the correlation is achieved at a cost of many addition and multiplication operations.

In practice, a plurality of such measurements along a plurality of profiles are made and then data relating to the centre of each edge is averaged so that the centre point of each mark is determined as the average of the centre locations of its east and west (or north and south) edges. It will be apparent that because the mark is square the profiles will all be of a similar nature and therefore data relating to the centre of edges in profiles taken along X and Y axes can be averaged or processed in some other statistical manner to improve the precision of the overall measurement.

Once the centre point of each mark is determined the overlay measurement is represented as the distance between the centre point of the two marks.

In summary, the art of overlay measurement involves taking image cross- section profiles of the image ideally in both horizontal and vertical orientations, which, in terms of the image, is looking at rows and columns. These image cross-section profiles typically contain edge patterns corresponding to both the inner and outer marks.

A prior measurement art relies on the quality of symmetry between east and west (or north and south) edges of a mark, for centre point determination. However, there are contributing factors that tend to degrade this symmetry. Some of these are tool related, such as uneven illumination across the field of view, camera and optical distortion and background noise. Although the art of producing metrology tools attempts to minimise these problems, it is never possible to eliminate them completely. Another, major, source of asymmetry may be induced by the properties of the wafer. In some production processes, chemical and/or mechanical polishing processes are used to planarize the layers. These flatten the topography of the marks. An undesired side effect of this is that the contrast of the optical image of such marks is heavily disrupted, as is the symmetry quality of the corresponding profiles. In addition, the pattern itself may be eroded in an asymmetric manner. All these factors may contribute to a significant total degradation in the quality of the results.

In view of the problems associated with undertaking metrology measurements using prior art techniques and equipment we have developed an invention which is designed to overcome, or at least mitigate, the problems associated with the prior art. The invention incorporates a principle which will be described hereinafter in greater detail.

The principle used in this invention is not to solely use the image cross- section profile signal itself. Instead, some function of that signal is used in which the embedded symmetry is enhanced and the asymmetry is suppressed. This function is the Laplacian of the signal. In one dimensional geometry, which is the case with cross-sections, the Laplacian is reduced to the second order derivative of the profile pattern. A schematic illustration of the effect of taking the second order derivative is shown in Figure 2.

A preferred embodiment of this invention involves an improvement to the symmetry quality of the signal that is achieved by filtering it by means of a Low Pass Filter. This filter is based on and is tightly matched to the physical properties of the optical transfer function of the tool's imaging system. This optical transfer function determines the useful spatial frequency range in the image. It depends primarily on both the geometry of the objective, expressed in terms of its NA - the Numerical Aperture, and on λ, the wavelength of the light source illuminating the object. Any components of the profile signal which lie outside this useful spatial frequency range, are guaranteed to be noise rather than useful information. Tlierefore these components are filtered out. This operation is illustrated in Figure 3. The removal of these components further improves the symmetry quality of the signal. The cutoff spatial frequency of the low-pass filter can only be approximately determined mathematically, mainly because a white light source is used, the spectrum of which contains a multitude of wavelengths. The exact cutoff spatial frequency is, therefore, empirically matched.

A further preferred embodiment used in this invention involves a simplification of the centre point determination once a profile has been provided. This simplification involves a modulus technique for determining a centre point and is described in greater detail hereinafter.

We have therefore devised methods and apparatus for enabling the centre point of images to be determined especially, but not exclusively, in conditions where the clarity or contrast of the image with respect to background or other images may be reduced.

It is an object of the invention to provide a method and apparatus which is sufficiently sensitive to measure image centres and so relative concentricity such as overlay error in instances where the contrast between at least a part of one mark is diminished having regard to at least a part of the remainder of the image.

It is another object of the invention to provide a method and apparatus which is sufficiently immune to asymmetry in the image so as to be able to measure image centres and so relative concentricity such as overlay error with improved accuracy in instances where tool or processing conditions have adversely affected the apparent symmetry in the image. In one broad aspect the invention is provided by way of taking a one dimensional Laplacian operation on an image cross-section profile.

According to a first aspect of the invention there is therefore provided a method for measuring the centre point of a mark comprising:

a) providing an image of said mark which includes at least a 2D representation of said mark made up of a plurality of image points arranged in rows and columns;

b) measuring each image signal in each image point along at least a first axis of said mark so as to provide a first image cross-section profile and then taking a one dimensional Laplacian operation on this profile to provide a second derivative profile; and

c) using detection techniques to determine the centre point of said second derivative profile so as to determine the centre point of said mark.

In a preferred method of the invention the above procedures are undertaken on a rectilinear mark and ideally repeated in respect of a second mark, preferably also rectilinear, so that the two centre points can be compared and in the instance where alignment is required an alignment error can be determined having regard to the distance between the two centre points.

Preferably in b) above the intensity at each image point is measured.

In the above, the reference to and corresponding image includes reference to an image which may be directly taken or indirectly derived from the mark. In the instance where an indirect derivation is made one may measure, for example, phase or topography in b) above.

Ideally said detection technique preferably comprises determining an approximate centre location of said second derivative profile; folding said second derivative profile through 180° about said approximate centre location; and moving said folding position until a point of maximum profile overlap is achieved.

According to a second aspect of the invention there is provided a method for measuring displacement between at least two marks comprising:

a) providing an image of said marks which includes at least a 2D representation of said marks made up of a plurality of image points arranged in rows and columns;

b) measuring each image signal in each image point along at least a first axis of a first of said marks so as to provide a first image cross-section profile and then taking a one dimensional Laplacian operation on this profile to provide a second derivative profile; and

c) using detection techniques to determine the centre point of said second derivative profile.

d) repeating steps b) and c) above for at least a second mark; and e) comparing the at least two identified centre points for each of the at least two marks in order to determine the degree of displacement between same.

In a preferred embodiment of the invention steps b) and c) are repeated, in respect of each mark, along a plurality of axes.

Ideally said detection technique comprises determining an approximate centre location of said second derivative profile; folding said second derivative profile through 180° about said approximate centre location; and moving said folding position until a point of maximum profile overlap is achieved.

In a further preferred embodiment of the invention said method for said first and second aspects of the invention involves filtering said image signals so that any signals which lie outside the useful spatial frequency range are eliminated. In other words signals which lie outside the useful spatial frequency range of the metrology tool and/or objective are filtered.

In the above first and second aspects of the invention one example is provided as to how a centre point of a second derivative profile can be determined. However, it is within the scope of the invention to use any alternative technique to determine a centre once said profile has been provided.

In the above method of said first and second aspects said Laplacian operation is used in order to provide a second derivative profile along at least a first axis of each of said marks because it provides for a purer signal. This is because background non-uniformity is reduced or mitigated.

Thus, the invention lies in the realisation that in instances of low contrast and/or strong asymmetry and thus where detail and/or symmetry has been degraded, existing techniques can be used providing one compensates by improving the nature of the image line that is used for the purpose of the above measurements. This is done by using not, as is conventionally the case, the zero order derivative of the image cross-section profile, but rather the second order derivative of the image cross-section profile. Using this technique one can surprisingly significantly enhance the accuracy of centreline, overlay, misregistration or displacement measurements and one is thus provided with a technique which is applicable in instances where contrast is low or asymmetry is present.

In other words, the invention lies in the realisation that the symmetry quality of a profile of a symmetrical image pattern can be improved by reducing or mitigating background non-uniformity by employing the second order derivative of a signal.

In addition, in our copending application no. 9526015.4, herein incoφorated by way of reference, we describe a method and apparatus which enables rectilinear images to be viewed especially in instances where contrast is poor. Thus, where it is required to determine a centre point or displacement measurement for marks which comprise rectilinear images in addition to use of the above method one may also use the invention described in our copending application. That is to say, instead of determining an image cross-section profile as above described, the first and second aspect methods for determining a first image cross-section profile under b) may be amended so that said profile comprises creating at least a first profile along at least a first axis, selected having regard to one side of said mark, by adding or averaging an image signal at each image point in at least a part of a row and/or column perpendicular to said axis so as to provide a first image cross-section profile including displacements which represent points along said axis where a rectilinear image is observed and then taking a one dimensional Laplacian operation on this first profile to provide a second derivative profile.

In yet a further preferred method the procedure under b) above may be modified so that, in addition to adding or averaging as described in the preceding paragraph to provide an image cross-section profile the said method may further also include positioning either said first or second profile about said image so that image signals creating either said first or second profile are aligned with the corresponding displacement readings of said first or second profile; examining said positioned profile or said 2D representation in order to identify points where an image pattern exists; comparing said profile points with corresponding image points or vice versa in order to determine whether a selected image point corresponds with a position on said first or second profile where a mark is observed or vice versa and if this is the case; either enhancing that selected image point and/or suppressing other image points. In this way, an improved 2D image of the mark to be viewed is created and once this improved image is created the steps under b) and c) of the first aspect of the invention may be executed and/or the steps under b), c), d) and e) of the second aspect of the invention may be executed. Thus it will be apparent to those skilled in the art that the modified method that has particular application in determining displacement between rectilinear marks or images is advantageously undertaken by firstly adding or averaging a number of image signals in at least a part of a given row and/or column above a given axis and then using the Laplacian function of the signal; or by firstly adding or averaging a number of image signals in at least part of a given row and/or column above a given axis to provide an improved first image cross-section profile and then using this profile, by positioning same about said image, in order to enhance and/or suppress the selected parts of this image so as to provide for an improved 2D image of said mark and then using this improved 2D image to execute the procedures under b) and c) of the first aspect of the invention and/or under b), c), d) and e) of the second aspect of the invention.

In the above method of the invention said axis is selected having regard to a side of said mark.

According to a third aspect of the invention there is provided an apparatus for measuring the centre point of a mark comprising:

a) imaging means for viewing said mark to create at least a 2D representation of said mark made up of a plurality of image points arranged in rows and columns;

b) means for providing an image cross-section profile along at least a first axis of said mark which means measures an image signal at each image point along said axis and then takes a one dimensional Laplacian operation of this profile to provide a second derivative profile; and

c) means for determining a centre point of said second derivative profile along said first axis of said mark.

In a preferred embodiment of the invention the apparatus may be adapted so as to repeat the above method for a second mark and then compare the two centre points in order to determine the degree of displacement between same.

In a further preferred embodiment of the invention said means under c) above comprises means for determining an approximate centre point of said second derivative profile; means for folding said second derivative profile through 180° about said approximate centre point; and means for matching said folded parts in order to determine the point of best fit.

More preferably still a plurality of profiles are provided along a plurality of axes so that data relating to a plurality of centre points are determined. Alternatively, a plurality of profiles are provided along a plurality of axis and data relating to such profiles is averaged or processed in some other way, in order to improve the provision of the overall measurement, prior to the determination of a centre point.

According to a fourth aspect of the invention there is provided an apparatus for measuring displacement between at least two marks comprising:

a) imaging means for viewing said marks so as to create at least a 2D representation of said marks made up of a plurality of image points arranged in rows and columns;

b) means for providing a first image cross-section profile along at least a first axis through a first of said marks which means measures an image signal at each image point along said axis and then takes a one dimensional Laplacian operation of this profile to provide a second derivative profile;

c) means for determining the centre point of said second derivative profile;

d) repeating steps b) and c) above for at least a second mark; and

e) comparing at least two identified centre points for each of the at least two marks in order to determine the degree of displacement between same.

In a preferred embodiment of the invention said means relating to b) and c) above are adapted to provide a plurality of second derivative profiles along a plurality of axis and then determine the centre point of said profiles, respectively, or alternatively the average centre point of said profiles.

In a further preferred embodiment of the invention said means under c) above comprises-β means for determining an approximate centre point of said second derivative profile; means for folding said second derivative profile through 180° about said approximate centre point; and means for matching said folded parts in order to determine the point of best fit.

In the instance where one or more second derivative profiles of a second mark is provided means is provided for determining the degree of displacement between said marks.

In a preferred embodiment of the invention said apparatus further includes means for providing an image cross-section profile through more than one axis of each of said marks and comparing centre points of corresponding image lines, that is to say the centre points of image lines taken through the same axis of each mark.

In yet a further preferred embodiment of the invention the means for providing a first image cross-section profile comprises a means for obtaining a first profile of at least a first mark along at least a first axis selected having regard to, and preferably parallel to, one side of said mark which means comprises a further means for adding or averaging an image signal in each image point in either at least a part of a row and/or column perpendicular to or above said axis so as to produce a profile comprising a first graph with displacements) where the addition or average of image signals in a given row or column increases observable signal and then performing a one dimensional Laplacian function on this original profile to provide a second derivative profile.

In yet a further embodiment of the invention the means for providing the first image cross-section profile, in addition to providing adding or averaging as described in the preceding paragraph also comprises a means for positioning said first or second profile about said image so that image signals creating either said first or second profile are aligned with the corresponding displacement readings of said first or second profile; means for examining each point in said profile or said 2D representation in order to identify where an image pattern exists; means for comparing said profile point with image points or vice versa in order to determine whether a selected image point corresponds with a position on either said first or said second profile where a mark is observed or vice versa and if this is the case; means for either enhancing the selected image point or suppressing other image points so as to provide an improved 2D image of said mark which image can then be used for executing steps b) and c) in accordance with the third aspect of the invention or b), c), d) and e) in accordance with the fourth aspect of the invention.

In respect of both said third and fourth aspects of the invention said apparatus further includes filtering means for filtering signals that are outside the useful spatial frequency range of the metrology tool and/or objective of the imaging means.

In any of the first, second, third or fourth aspects of the invention a centre point of at least one mark may be determined either by using a plurality of a 2D representations as one scans through focus; or alternatively, by repeatedly extracting data from a single representation, ideally provided at the point of focus.

An embodiment of the invention will now be described by way of example only with reference to the accompanying Figures wherein;

Figure 1 is a representation of marks and their corresponding image lines/profiles; Figure 2 shows the effect of second order derivative on symmetry quality;

Figure 3 shows the frequency spectrum of the image profile signal and its match low pass filter;

Figure 4 shows a schematic description of the line processing system;

Figure 5 shows a schematic illustration of a mark centre determination by folding and matching.

a: approximate centre location is determined

b: the profile is folded at this location.

c: two folded parts are matched.

Figure 6 shows a schematic description of an overlay measurement procedure.

Referring to the Figures there is shown a schematic representation of a way in which displacement between two marks is currently determined. The representation describes a way particularly adapted to a determination of displacement or overlay error in the semiconductor industry where the two marks typically comprise rectilinear images, and usually discontinuous images, of different sizes such that a first image can be positioned so as to be surrounded by a second image. Clearly if the two images are of the same shape and also the same orientation then it should be possible to concentrically position one image with respect to another. Concentricity may need to be determined for a number of reasons but in the semiconductor industry it is usually used as a measure of alignment when successive layers are deposited during semiconductor wafer manufacture.

Thus, firstly, an image is provided of the overlay layers and the field of view includes an image of the overlay marks. Typically an image cross-section profile is provided; that is to say a line through each mark, ie an inner-mark image cross-section profile and an outer-mark image cross-section profile, comprising a measure of image signal in each image point along said profile, is provided. Standard folding correlation techniques are then used to find the centre of each mark. Ideally, a plurality of image cross-section profiles along a plurality of axes are used in order to determine the mark centres and data relating to a number of edge centres are averaged in order to improve the accuracy of the measurement. The difference between centre points of the inner-mark and outer-mark profiles is determined in order to provide a measure of the degree of displacement or overlay error.

The above method works relatively well when the marks to be analysed are readily viewable. But this is not always the case, and this is clearly illustrated towards the left hand side of Figure 1 where an outer mark is represented by a relatively weak, or poor contrast, signal. Thus the image line for this signal, represented by displacements A along image cross-section profile 1 are relatively flat. Use of conventional folding correlation techniques results in unacceptable levels of error and therefore such profiles do not lend themselves to the above method.

We have therefore modified the above method and we provide an inventive solution to the problem of imaging poor contrast marks or patterns by way of using the Laplacian function of an image line. When an image line of this nature is used, background non-uniformity or impurity in the image line is reduced. This is clearly illustrated in Figure 2 which shows the effect of use of the Laplacian function which in one dimension is reduced to the second order derivative of the profile pattern. The top graph shows the original signal image cross-section profile which suffered from both uneven illumination and distortion. The bottom graph shows the same signal after the method of the invention has been applied that is to say after the Laplacian function of the profile has been used. Thus although the signal is still relatively weak and thus displacements may still be relatively small the nature of the image lines is much clearer and therefore it is possible to determine a centre point. It is of considerable note that the symmetrical qualities of the profile have been considerably enhanced following the Laplacian operation. With this enhanced symmetry it is possible now to use standard techniques to determine the centre point of the symmetrical profile, for example, it is possible to use standard folding correlation techniques to determine the centre point of the profile.

The Laplacian, or second order derivative operator, is also digitally approximated on a computer. This is achieved by replacing infinitesimal differentials by sample differences. A digital second derivative of a function is thus given by

/ (t - n) ~ J n * I J n ■ 1 ^" *^• J n

where /, is the sampled value of the function at the point x = n. A schematic illustration of the system is shown in Figure 4.

The symmetry quality of the profile may also be enhanced by use of a low pass spatial filter. The spatial filter is configured so that it is matched to the physical properties of the imaging tool's microscope. In particular, it is matched to the optical transfer function of the microscope objective and/or the optical components of the microscope. The optical transfer function determines the useful spatial frequency range of the objective. Thus a filter can be provided as illustrated in Figure 3 which removes components which fall outside the useful spatial frequency range of the objective and/or the optical components of the microscope.

As previously mentioned in this application in our copending application no. 95260105.4 we describe a method which is particularly suited to rectilinear marks which method involves improved viewing of such marks and we consider that this method has application for determining displacements. In particular, the method and apparatus of the invention can be modified so that when providing a first image cross-section profile one provides a profile of each mark along at least a first axis selected having regard to one side of each mark by adding or averaging an image signal in each image point in at least a part of a row and/or column perpendicular to said axis so as to provide a graph including displacements which represents points along said axis where a rectilinear image is observed and then one takes a one dimensional Laplacian operation on this first profile to provide a second derivative profile.

We have found that by adding or averaging image signals, in either at least a part of a row and/or a column above said selected axis, the strength of the image signal is increased and this provides for greater displacements in a given profile. Thus when such "enhanced" profiles are used, following the Laplacian operation, a centre point can be yet more accurately determined.

Alternatively, the method of the invention may be further refined by positioning either said first or second profile about a 2D representation of at least one mark and then examining each point in said profile or said 2D representation in order to identify a mark pattern or contrast, and where such pattern exists, comparing said profile point with said image points or vice versa in order to determine whether a selected image point corresponds with the position on either said first or said second profile where a displacement occurs or vice versa and if this is the case, either enhancing that selected image point or suppressing other image points. In this way an improved 2D image of at least one mark can be provided and this new improved 2D image can then be subject to the method of the invention.

In addition to the above, the invention also includes a further refinement which involves a simplification of the determination of a centre point once a profile is provided.

This essentially involves a shortcut to determine the centre point of a mark; thus time is saved at no performance cost. Please see Figures 5 and 6.

The shortcut is achieved by the embodiment using a different matching method to correlation for matching two vectors { } and {t, } . This method is to be known as the modulus matcher which is given by Equation 2 mmat h(f , t) = ∑|/[ - /_:

This method does not normally handle well offset and gain changes between the vectors. However, the preferred embodiment uses this method in conjunction with the second order derivative method, described above.

Since the second order differential eliminates gain and offset effects, it is no longer required to determine the mean value of the second differential and to subtract it from the individual point values. Similarly, it is not necessary to scale the signal. These two changes imply that the computation time and speed are enhanced by not using the correlation expression of Equation 1, which involves a lot of costly and unnecessary computer operations. Instead, by employing the much simpler expression of Equation 2, the preferred embodiment is capable of achieving a much faster speed of operation.

Unlike the correlation method, the modulus matcher is a measure of the degree of mismatch between two vectors. Therefore, at the point of best match, this operator will produce a minimum. By taking more points around that minimum, interpolation of the location of the minimum is performed, to achieve a greater level of precision.

We therefore provide in this document the description of a method and corresponding apparatus which can be used to measure the centre point of a mark or degree of displacement between at least two, and if required a plurality, of marks which method and apparatus may be refined in accordance with our copending UK patent application no. 9526015.4 to increase the accuracy of displacement measurements between rectilinear marks.

Claims

1. A method for measuring the centre point of a mark comprising:

2. A method according to claim 1 wherein the above procedures are undertaken on a rectilinear mark.

3. A method according to any preceding claim wherein the procedures are undertaken repeatedly in respect of a second rectilinear mark, so that the two centre points can be compared and in the instance where alignment is required an alignment error can be determined having regard to the distance between the two centre points.

4. A method according to any preceding claim wherein in step b) intensity at each image point is measured.

5. A method according to claim 1 wherein said image is provided on a screen, film or the like so as to provide an indirect image of the mark and in step b) above a measurement of phase is made.

6. A method according to claim 1 wherein said image is provided on a screen, film or the like so as to provide an indirect image of the mark and in step b) above a measurement of topography is made.

7. A method according to claim 1 wherein said detection technique comprises determining an approximate centre location of said second derivative profile; folding said second derivative profile through 180° about said approximate centre location.

8. A method according to claim 7 wherein said detection technique further comprises moving said folded position until a point of maximum profile overlap is achieved.

9. A method according to any preceding claim for measuring displacement between at least two marks comprising:

a) providing an image of said marks which includes at least a 2D representation of said marks made up a plurality of image points arranged in rows and columns;

b) measuring each image signal in each image point along at least a first axis of a first of said marks so as to provide a first image cross- section profile and then taking a one dimensional Laplacian operation on this profile to provide a second derivative profile; and c) using detection techniques to determine the centre point of said second derivative profile.

d) repeating steps b) and c) above for at least a second mark; and

e) comparing the at least two identified centre points for each of the at least two marks in order to determine the degree of displacement between same.

10. A method according to claim 9 wherein steps b) and c) are repeated, in respect of each mark, along a plurality of axes.

11. A method according to claims 9 and 10 wherein said detection technique comprises determining an approximate centre location of said second derivative profile; folding said second derivative profile through 180° about said approximate centre location.

12. A method according to claim 1 1 wherein said detection technique further comprises moving said folded position until a point of maximum profile overlap is achieved.

13. A method according to any preceding claim wherein filtering of said image signals, eliminates any signals which lie outside the useful spacial frequency range.

14. A method according to any preceding claim under step b) comprising amendment so that said profile comprises creating at least a first profile along at least a first axis, selected having regard to one side of said mark, by 28 adding or averaging an image signal at each image point in at least a part of a row and/or column peφendicular to said axis so as to provide a first image cross-section profile including displacements which represent points along said axis where a rectilinear image is observed and then taking a one dimensional Laplacian operation on said first profile so as to provide a second derivative profile.

15. A method according to claim 14 wherein the procedure under step b) is modified so that, in addition to adding or averaging so as to provide an image cross-section profile the method may further also include positioning either said first or second profile about said image so that image signals creating either first or second profile are aligned with corresponding displacement readings of first said or second profile; examining said positioned profile or said 2D representation in order to identify points where an image pattern exists; comparing said profile points with corresponding image points or vice versa in order to determine whether the selected image point corresponds with the position on said first or second profile where a mark is observed or vice versa and if this is the case; either enhancing that selected image point and/or suppressing other image points so as to provide an improved 2D image of said mark which can then be used for executing steps b) and c) or claim 1 or b), c), d) and e) of claim 9.

16. A method according to claim 15 wherein an axis is selected having regard to a side of said mark.

17. An apparatus according to any preceding claim for measuring a centre point of a mark comprising; a) imaging means for viewing said mark to create at least a 2D representation of said mark made up of a plurality of image points arranged in rows and columns;

18. An apparatus according to claim 17 which is adapted so as to repeat the steps outlined in claim 17 for a second mark and then compare the two centre points in order to determine the degree of displacement between same.

19. An apparatus according to claims 17 and 18 which means under c) for determining an approximate centre point of said second derivative profile comprises means for folding said second derivative profile through 180° about said approximate centre point; and means for matching said folded parts in order to determine the point of best fit.

20. An apparatus according to claim 17 to 19 which is adapted to provide a plurality of profiles along a plurality of axes so that data relating to a plurality of centre points are determined.

21. An apparatus according to claim 17 to 19 which is adapted to provide a plurality of profiles along a plurality of axes and data relating to such profiles is averaged or processed in some other way, in order to improve the precision of the overall measurement, prior to the determination of a centre point.

22. An apparatus according to any preceding claim for measuring displacement between at least two marks comprising:

a) imaging means for viewing said mark so as to create at least a 2D representation of said mark made up of a plurality of image points arranged in rows and columns;

c) means for determining the centre point of said second derivative profile;

d) repeating steps b) and c) above for at least a second mark; and

e) comparing at least two identified centre points for each of at least two marks in order to determine the degree of displacement between the same.

23. An apparatus according to claim 22 further comprising a means relating to b) and c) which is adapted to provide a plurality of second derivative profiles along a plurality of axes and then determine the centre point of said profile, respectively.

24. An apparatus according to claim 22 further comprising a means relating to b) and c) which is adapted to provide a plurality of second derivative profiles along a plurality of axes and then determine the average centre point of said profile.

25. An apparatus according to claims 22 to 24 which comprises a means under c) for determining an approximate centre point of said second derivative profile; means for folding said derivative profile through 180°C about said approximate centre point.

26. An apparatus according to claim 25 which comprises a means for matching said folded parts in order to determine the point of best fit.

27. An apparatus according to claims 22 to 26 wherein in the instance where one of more second derivative profiles of a second mark is provided there is provided a means for determining the degree of displacement between said marks.

28. An apparatus according to claims 22 to 27 which further comprises a means for providing an image cross-section profile through more than one axis of each of said marks and comparing centre points of corresponding image lines.

29. An apparatus according to claim 22 to 28 which means b) for providing a first image cross-section profile further comprises a means for obtaining a first profile of at least a first mark along at least a first axis selected having regard to, and preferably parallel to, one side of said mark which means further comprises a means for adding or averaging an image signal in each image point in either at least a part of a row and/or column peφendicular to or above said axis so as to produce a profile comprising a first graph with displacement(s) where the addition or average of images, signals in a given row or column increases observable signals and then forming one dimensional Laplacian function on this original profile to provide a second derivative profile.

30. An apparatus according to claim 29 which means b) for providing a first image cross-section profile, in addition to providing adding or averaging further comprises a means for positioning said first or second profile about said image so that image signals creating either said first or second profile are aligned with the corresponding displacement reading of said first or second profile; means for examining each point in said profile or said 2D representation in order to identify where an image pattern exists; means for comparing said profile point with image points or vice versa in order to determine whether a selected image point corresponds with a position on either said first or second profile where a mark is observed or vice versa and if this is the case; means for either enhancing the selected image point or suppressing other image points so as to provide an improved 2D image of said mark which image can then be used for executing steps b) and c) of claim 17 or b), c), d) and e) of claim 22.

31. An apparatus according to claims 17 to 30 wherein said apparatus further includes a filtering means for filtering signals outside the useful spacial frequency range of the metrology tool and/or objective of the imaging means.

32. A method and apparatus according to any preceding claim wherein a centre point of at least one mark may be determined either by using a plurality or 2D representation as one scans through focus; or alternatively, by repeatedly extracting data from a single representation, provided at the point of focus.