System and method for correcting the effects of wafer tilt on offset measurements

Abstract

A method for correcting errors in offset measurements of a semiconductor wafer due to wafer tilt, the method comprising: measuring, for at least one location on a wafer, a difference between a tool induced transfer (TIS) of a metrology device in a first illumination arrangement relative to the wafer and the TIS of the metrology device in a second illumination arrangement relative to the wafer, wherein in the first illumination arrangement a surface of the wafer is illuminated generally orthogonally by an illumination source of the metrology device, and wherein in the second illumination arrangement the surface is illuminated obliquely by the illumination source; and correcting errors in the offset measurements due to tilt of the wafer at the location by subtracting a weighted value of the difference between the TIS in the first and second illumination arrangements from an offset measurement measured by the metrology device at the at least one location.

Description

Technical Field

[0001] The present invention relates generally to metrology, and more particularly to offset measurement of semiconductor wafers. Background Art

[0002] Various systems and methods for measuring offsets in semiconductor wafer fabrication are known in the art. Summary of the invention

[0003] The present invention seeks to provide novel systems and methods for correcting for the effects of local wafer tilt in offset measurements performed on a semiconductor wafer.

[0004] Therefore, in accordance with a preferred embodiment of the present invention there is provided a method for correcting errors in offset measurements of a semiconductor wafer due to wafer tilt, the method comprising: measuring, for at least one location on a wafer, a difference between a tool induced transfer (TIS) of a metrology device in a first illumination arrangement relative to the wafer and the TIS of the metrology device in a second illumination arrangement relative to the wafer, wherein in the first illumination arrangement a surface of the wafer is substantially orthogonally illuminated by an illumination source of the metrology device, and wherein in the second illumination arrangement the surface is obliquely illuminated by the illumination source; and correcting errors in the offset measurements due to tilt of the wafer at the location by subtracting a weighted value of the difference between the TIS in the first and second illumination arrangements from an offset measurement measured by the metrology device at the at least one location.

[0005] Preferably, the difference between the TIS in the first and second lighting arrangements comprises a characteristic profile that varies as a function of a parameter of the metrology device.

[0006] Preferably, the metrology device illuminates the wafer at a plurality of wavelengths and measures the difference in the TIS of the metrology device as a function of the plurality of wavelengths.

[0007] Preferably, at a plurality of locations N on the wafer s The measurement of the difference in the TIS is performed at a location and the difference in the TIS of the metrology device is measured as a function of a plurality of wavelengths for each of the plurality of locations.

[0008] Preferably, the weighted value of the difference between the TIS in the first and second lighting arrangements is calculated by multiplying the difference between the TIS in the first and second lighting arrangements by a weighting coefficient.

[0009] Preferably, the weighting coefficients are calculated based only on the variable part of the offset measurement and the difference between the TIS in the first and second lighting arrangements.

[0010] Preferably, the weighting coefficient is calculated according to the following formula:

[0011]

[0012] Where α(N s ) is the weighting coefficient, is the variable part of the offset measurement, and is the variable part of the difference between the TIS in the first and second lighting arrangements.

[0013] Preferably, the variable portion of the offset measurement is calculated according to the following formula:

[0014]

[0015] Among them MIS measured (N s ,λ) is the offset measure, and MIS measured (N s ) is a shift measurement averaged over multiple illumination wavelengths.

[0016] Preferably, a weighted value of the difference between the TIS in the first and second lighting arrangements is subtracted from the offset measurement according to the following formula:

[0017] MIS corrected (N s )=MIS measured (N s ,λ)-α(N s )·ΔTIS(λ)

[0018] Among them MIS corrected (N s ) is the correction value for the offset measurement, and ΔTIS(λ) is the difference between the TIS in the first and second lighting arrangements.

[0019] According to a preferred embodiment of the method of the present invention, the method further comprises optimizing an operating parameter of the metering device based on the difference in the TIS of the metering device.

[0020] According to another preferred embodiment of the present invention, there is also provided a system for correcting errors in offset measurements on a semiconductor wafer due to wafer tilt, the system comprising: an illumination source forming part of a metrology device and operable to illuminate the wafer in at least a first illumination arrangement and a second illumination arrangement, wherein in the first illumination arrangement a surface of the wafer is substantially orthogonally illuminated by the illumination source, and wherein in the second illumination arrangement the surface is obliquely illuminated by the illumination source; a TIS calculator operable to find a difference between the TIS of the metrology device in the first and second illumination arrangements; and a wafer tilt corrector operable to correct errors in the offset measurements due to wafer tilt at a location on the wafer based on subtracting a weighted value of the difference between the TIS of the metrology device in the first and second illumination arrangements from an offset measurement made by the metrology device at the location.

[0021] Preferably, the difference between the TIS in the first and second lighting arrangements comprises a characteristic profile that varies as a function of a parameter of the metrology device.

[0022] Preferably, the illumination source is operable to illuminate the wafer at the plurality of wavelengths, and the TIS calculator is operable to find the difference in the TIS of the metrology device as a function of the plurality of wavelengths.

[0023] Preferably, the TIS calculator is operable to find a plurality of locations N on the wafer s The difference in TIS at the plurality of locations as a function of a plurality of wavelengths for each of the plurality of locations.

[0024] Preferably, the wafer tilt corrector is operable to calculate a weighted value of the difference between the TIS in the first and second illumination arrangements by multiplying the difference between the TIS in the first and second illumination arrangements by a weighting coefficient.

[0025] Preferably, the wafer tilt corrector is operable to calculate the weighting coefficient based solely on a variable portion of the offset measurement and the difference between the TIS in the first and second illumination arrangements.

[0026] Preferably, the wafer tilt corrector is operable to calculate the weighting coefficient according to the following formula:

[0027]

[0028] Where α(N s ) is the weighting coefficient, is the variable part of the offset measurement, is the variable part of the difference between the TIS in the first and second lighting arrangements.

[0029] Preferably, the wafer tilt corrector is operable to calculate the variable portion of the offset measurement according to the following formula:

[0030]

[0031] Among them MIS measured (N s ,λ) is the offset measure, and is a shift measurement averaged over multiple illumination wavelengths.

[0032] Preferably, the wafer tilt corrector is operable to subtract a weighted value of the difference between the TIS in the first and second illumination arrangements from the offset measurement according to the following formula:

[0033] MIS corrected (N s )=MIS measured (N s ,λ)-α(N s )·ΔTIS(λ)

[0034] Among them MIS corrected (N s ) is the correction value for the offset measurement, and ΔTIS(λ) is the difference between the TIS in the first and second lighting arrangements.

[0035] According to a preferred embodiment of the system according to the invention, operating parameters of the metering device are optimized based on the difference in TIS of the metering device. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention will be more fully understood and appreciated through the following specific embodiments in conjunction with the accompanying drawings, in which:

[0037] Figure 1 is a simplified schematic, partially pictorial, partially block diagram illustration of a system for correcting for the effects of wafer tilt in offset measurements, constructed and operative in accordance with a preferred embodiment of the present invention;

[0038] Figure 2A and 2B is a simplified schematic diagram of respective first and second illumination conditions of a metrology device relative to a semiconductor wafer for use in Figure 1 In a system of the type presented, data for correcting offset measurements is provided;

[0039] Figure 2C is Figure 2A and 2B A simplified graphical representation of the data obtained under the lighting conditions; and

[0040] Figure 3is a simplified flow chart illustrating the steps of correcting for the effects of wafer tilt on offset measurements in accordance with a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0041] Now refer to Figure 1 , Figure 1 is a simplified schematic, partially pictorial, partially block diagram illustration of a system for correcting for the effects of wafer tilt in offset measurements, constructed and operative in accordance with a preferred embodiment of the present invention.

[0042] like Figure 1 As seen, a metrology system 100 is provided that includes a metrology tool 102 for measuring offsets in the manufacture of semiconductor devices, such as semiconductor wafers 104. The metrology tool 102 preferably includes an illumination source, schematically represented here as an illumination source 110, which is operable to illuminate the wafer 104 so as to allow imaging of target structures formed on the layers of the wafer 104, thereby measuring offsets between the layers of the wafer 104. It should be understood that in addition to the illumination source 110, the metrology tool 102 typically includes various additional components that are well known in the art (omitted here for clarity) to facilitate imaging of the wafer 104 and measurement of offsets between the layers of the wafer 104.

[0043] According to a particularly preferred embodiment of the present invention, the metrology tool 102 may be embodied as a multi-wavelength tool, such as an Archer 700 tool available from KLA, Inc., California, USA, which is operable to perform multi-wavelength measurements on the wafer 104. The metrology tool 102 is preferably operable to output at least one offset measurement representing an offset between layers of the wafer 104 at at least one measurement location on the wafer 104. In the case where the metrology tool 102 is a multi-wavelength instrument, the offset measurement MIS measured The output can be expressed as MIS measured (N s ,λ), where N s represents a specific location on the wafer 104 relative to which the measurement is performed, and λ represents a plurality of illumination wavelengths provided by the illumination source 110 .

[0044] It should be appreciated that local variations in the tilt of the surface 120 of the wafer 104 may affect the offset measurements MIS output by the metrology tool 102 due to the effect of wafer tilt on the offset measurements. measured (N s ,λ) has an impact on the accuracy of the offset measurement and may therefore introduce errors therein. Preliminary measurements performed by the inventors have shown that the local wafer tilt at the target position may vary by about ±0.5 mrad. Such local wafer tilt may have a considerable impact on the offset measurement, which may become increasingly significant as the wafer stack height increases.

[0045] According to a preferred embodiment of the present invention, the value of the local wafer tilt at a specific location on the wafer 104 can be found and its effect on the offset measurement MIS can be quantified. measured (N s ,λ) to allow correction of errors in the offset measurement caused by local wafer tilt. This advantageously results in more accurately calculating an improved offset measurement to represent the actual offset value of the wafer 104. According to a preferred embodiment of the present invention, both a measurement of wafer tilt and a quantification of the error in the offset measurement caused thereby are found, based on the inventors' understanding that wafer tilt has a significant impact on the offset measurement MIS. measured (N s ,λ) is equivalent to the effect of the tilt of the illumination source 110 relative to the surface 120 of the wafer 104 illuminated thereby, due to the same telecentric effect of both tilts.

[0046] Illumination source tilt contributes to the inherent limited measurement accuracy of the metrology tool 102, which can be quantified as the tool induced shift (TIS) of the metrology tool 102, and does not change after a 180° rotation of the wafer 104. However, wafer tilt directly contributes to the TIS-corrected offset measurement, and does change after a 180° rotation of the wafer 104. Based on this understanding, measuring the change in TIS of the metrology tool 102 under intentionally tilted illumination conditions compared to non-tilted illumination conditions can serve as a basis for finding the corresponding change in offset measurement due to equivalent wafer tilt, and thereby both quantifying wafer tilt and correcting the offset measurement for the effect of wafer tilt thereon.

[0047] like Figure 1 As can be seen, the effect of oblique lighting conditions on the TIS of the metrology tool 102 can be found by the TIS difference calculator 130. Figures 2A to 2C The preferred operation of the TIS difference calculator 130 is best understood.

[0048] like Figure 2A As can be seen, the TIS of the metrology tool 102 is preferably initially measured in a first non-tilted illumination arrangement, wherein the illumination source 110 is preferably centered relative to the illumination position on the surface 120 of the wafer 104, such that the surface 120 is generally orthogonally illuminated by the illumination source 110 along the illumination axis 200. The TIS of the metrology tool 102 can be found by any suitable method, various types of methods are well known in the art. Preferably, the TIS can be quantified by measuring the same feature on the surface 120 at 0° and 180° rotations of the wafer 104, the TIS being equal to half the sum of the measurements in each wafer orientation.

[0049] like Figure 2BAs can be seen, the TIS of the metrology tool 102 is preferably additionally measured in a second oblique illumination arrangement, wherein the illumination source 110 is preferably offset to be off-center relative to the illumination position on the surface 120 of the wafer 104, such that the surface 120 is illuminated by the illumination source 110 generally obliquely relative to the illumination axis 200. Here, as an example, the illumination source 110 is shown offset by 10 μm, such that the illumination provided thereby is incident on the surface 120 at an oblique angle of about 5 mrad.

[0050] It should be appreciated that such measurements relative to the surface 120 of the wafer 104, under the first and second illumination conditions, are preferably made prior to performing metrology measurements on the wafer 104 by the metrology tool 102, optionally as part of a preliminary training procedure performed on the metrology tool 102 prior to operating the metrology tool 102. Such measurements may be performed for multiple locations on the wafer 104, and in the case of a multi-wavelength imaging metrology tool, at multiple illumination wavelengths.

[0051] Under the first central lighting condition (e.g. Figure 2A ) and under a second off-center illumination condition relative to the surface 120 of the wafer 104 (such as, for example, Figure 2B ), for a plurality of measurement positions, the difference in measurement accuracy of the metrology tool 102 (preferably expressed as a difference in TIS) may be plotted as a function of illumination wavelength. Figure 2C An example of such a plot is shown in FIG. 1 , where the TIS (ΔTIS) of the metrology tool 102 is Figure 2A and 2B The difference between the first and second illumination conditions is plotted as a function of the illumination wavelength for the 10 measurement positions, with the ΔTIS for each measurement position being plotted as Figure 2C The single line in the graph is represented.

[0052] from Figure 2C It can be understood from the consideration of , that ΔTIS appears to vary significantly with illumination wavelength, but not with illumination position. Figure 2C As shown, the variation in ΔTIS as a function of wavelength can be considered to correspond to a differential feature profile or landscape representing the effect of intentional, controlled illumination tilt, and thus to the equivalent effect of wafer tilt on the measurement accuracy of the metrology tool 102. Based on this profile, the effect of local wafer tilt on offset measurements made by the metrology tool 102 can be corrected, as described in further detail below.

[0053] It should be understood that Figure 2C A profile of the type shown in FIG. 1 may be generated by the TIS difference calculator 130 based on the Figure 2A and 2BIt will be appreciated that this profile is specific to both the wafer 104 and to a given layer of the wafer 104, and therefore, is preferably obtained by the TIS differential calculator 130 for each layer of the wafer 104 for which offset measurements are performed by the metrology tool 102. The output of this profile by the TIS differential calculator 130 is Figure 1 In a preferred embodiment of the present invention, the TIS difference calculator 130 may be embodied as a computing module, which includes a computer code operable to find the ΔTIS profile. It should be understood that although the TIS difference calculator 130 is Figure 1 102 as embodied as a separate module, but this is for clarity only, and the functionality of the TIS differential calculator 130 may alternatively be included in the metrology tool 102.

[0054] The ΔTIS profile obtained by the TIS difference calculator 130 is preferably provided to a wafer tilt corrector, shown here as embodied as a wafer tilt correction calculator module 140 included in the system 100. The wafer tilt corrector 140 is preferably operable to correct for an error in at least one offset measurement measured by the metrology device 102 at a given location on the wafer 104 due to the tilt of the wafer 104 at the given location. Preferably, the at least one offset measurement is corrected by the wafer tilt corrector 140 based on subtracting a weighted value of the difference between the TIS of the metrology device 102 in the first and second illumination arrangements (quantized and output by the TIS difference calculator 130) from the offset measurement.

[0055] For a specific location N s Wafer tilt effect correction for offset measurement MIS corrected (N s ) can be expressed as:

[0056] MIS corrected (N s )=MIS measured (N s ,λ)-α(N s )·ΔTIS(λ) (1)

[0057] Among them MIS measured (N s ,λ) denotes at least one offset measurement, which is preferably provided as an offset profile, as a measurement position N s and the function of the illumination measurement wavelength λ, ΔTIS(λ) is expressed as above with respect to Figures 2A to 2C The TIS differential feature profile measured as described above, and α(N s) represents a position-specific weighting factor, representing a specific local wafer tilt at a given position. It should be understood that the weighting factor α(N s The product of ) and the TIS differential feature profile ΔTIS(λ) represents the contribution of the local value of wafer tilt of the wafer 104 to the corresponding local measured offset value, and therefore must be subtracted from the measured offset profile in order to provide a 'clean' offset profile corrected for the error caused by the local wafer tilt. As detailed above, the correction of the offset measurement based on the TIS differential feature profile ΔTIS(λ) is based on the equivalence between TIS variations due to illumination tilt and wafer tilt.

[0058] It should be understood that in order to find out MIS corrected (N s ), which is the desired output of the wafer tilt correction calculator module 140, the weighting coefficient α (N s ). As the weighting coefficient α(N s ), consider only the variable part of the measured offset at each position according to the following formula:

[0059]

[0060] in is the measured shift averaged over all measured wavelengths.

[0061] Next, the weighting coefficient α (N) can be found by calculating the projection of the variable part of ΔTIS on the variable part of the measured offset at each location according to the following formula: s ):

[0062]

[0063] wherein the variable portion of the ΔTIS signature is defined for the same set of multiple wavelengths λ over which the offset is measured by subtracting the value of the ΔTIS signature averaged over the multiple wavelengths from the ΔTIS signature. It will be appreciated that using only the variable portion of the measured offset profile and the variable portion of the difference in TIS, rather than the full values ​​of these parameters, to calculate the weighting coefficients at each location allows the components of these parameters caused by wafer tilt to be separated from the actual offset value at each location.

[0064] The weighting coefficient α(N) found according to equations (2) and (3) s ) can then be substituted into equation (1) to produce the offset measurement corrected for wafer tilt according to

[0065]

[0066] It will be appreciated that the calculations described above with reference to equations (1) to (4) are preferably performed by the wafer tilt correction calculator module 140, and preferably thereby output a correction offset value that is cleaned for inaccuracies introduced therein due to wafer tilt. In a preferred embodiment of the present invention, the wafer tilt correction calculator module 140 may be embodied as a calculation module that includes computer code operable to perform calculations according to equations (1) to (4). It will be appreciated that although the wafer tilt correction calculator module 140 is Figure 1 1 as embodied as a separate module, but this is for clarity only, and the functionality of the wafer tilt correction calculator module 140 may alternatively be included in the metrology tool 102.

[0067] It should be appreciated that the correction procedure performed by the system 100 may be implemented for correcting offset measurements performed on any type of symmetrical target formed on the wafer 104 and used as a reference structure for offset measurements in the fabrication of the wafer 104. In the event that the reference target is asymmetrical, the asymmetry of the target must be additionally considered when correcting the offset measurements in order to distinguish between inaccuracies in the offset measurements caused by local wafer tilt and components of the offset measurements caused by target asymmetry.

[0068] It should be further appreciated that in some preferred embodiments of the present invention, the measurement of ΔTIS as a function of wavelength can be used to optimize the settings of the metrology tool 102, for example, by selecting a measurement wavelength that has minimal sensitivity to illumination source tilt and, therefore, local wafer tilt. In such cases, the output of the TIS differential calculator 130 can be fed back to the metrology tool 102 and its settings adjusted accordingly, such as Figure 1 Optional bi-directional communication between the metrology tool 102 and the TIS differential calculator 130 is indicated by the double-headed arrow shown in FIG.

[0069] It should be further understood that although the operation of the TIS difference calculator 130 is described above with reference to the measurement of the dependence of the variation of TIS due to illumination source tilt on the wavelength of the metrology illumination, this is by way of example only. In alternative embodiments of the present invention, the variation of TIS due to illumination source tilt may be characterized with respect to other parameters of the metrology tool (e.g., by way of example only, the focus position of the metrology tool).

[0070] Now refer to Figure 3 , Figure 3 is a simplified flow chart illustrating the steps of correcting for the effects of wafer tilt on offset measurements in accordance with a preferred embodiment of the present invention.

[0071] like Figure 3As can be seen, the method 300 for correcting for the effect of wafer tilt in offset measurements can begin with a first step 302 in which a characteristic profile of the difference in the TIS of a metrology tool under tilted and non-tilted illumination conditions is obtained. The characteristic profile can be obtained as a function of a variable characteristic of the metrology tool (for example, as a function of wavelength). The characteristic profile can be obtained by a computerized TIS differential calculator module (e.g., Figure 1 Module 130) is calculated.

[0072] As seen in the second step 304, the offset of the semiconductor device is preferably measured for at least one location on the semiconductor device by the metrology tool characterized in the first step 302. It should be appreciated that while the first step 302 may generally be performed before the second step 304, this is not necessarily required and the order of steps 302 and 304 may be reversed.

[0073] As seen at the third step 306, a weighted value of the characteristic profile of the difference in the TIS is preferably found, which preferably corresponds to the value of the local wafer tilt at the measurement location on the semiconductor device under test. This correspondence is based on the understanding that the effect of wafer tilt on the offset measurement is equivalent to the effect of illumination source tilt on the offset measurement. Preferably, the weighted value is found according to equations (2) and (3) detailed above.

[0074] As seen at fourth step 308, the weighted value found at third step 306 is preferably subtracted from the offset measurement in order to correct for inaccurate offset measurements therein due to local wafer tilt. It will be appreciated that the corrected offset measurement thus obtained more accurately represents the actual offset between layers of the semiconductor device under test. Preferably, the subtraction is performed according to equation (4) detailed above.

[0075] It should be understood by those skilled in the art that the present invention is not limited to what is particularly shown and described above. The scope of the present invention includes combinations and sub-combinations of the above-mentioned various features and modifications thereof, all of which are not in the prior art.

Claims

1. A method for correcting errors in offset measurement of a semiconductor wafer caused by tilt of the wafer, comprising: measuring, for at least one location on a wafer, a difference between a tool induced transfer (TIS) of a metrology device in a first illumination arrangement relative to the wafer, wherein a surface of the wafer is illuminated generally orthogonally by an illumination source of the metrology device, and the TIS of the metrology device in a second illumination arrangement relative to the wafer; and correcting an error in the offset measurement due to tilt of the wafer at the location by subtracting a weighted value of the difference between the TIS in the first and second illumination arrangements from an offset measurement measured by the metrology device at the at least one location, wherein the difference between the TIS in the first and second lighting arrangements comprises a characteristic profile that varies as a function of a parameter of the metering device, wherein the metrology device illuminates the wafer with a plurality of wavelengths and measures the difference in the TIS of the metrology device as a function of the plurality of wavelengths, Wherein a plurality of locations N on the wafer s performing the measuring of the difference in the TIS at a location and measuring the difference in the TIS of the metrology device as a function of the plurality of wavelengths for each of the plurality of locations, and Wherein the weighted value of the difference between the TIS in the first and second lighting arrangements is calculated by multiplying the difference between the TIS in the first and second lighting arrangements by a weighting coefficient.

2. The method of claim 1, wherein the weighting coefficient is calculated based only on a variable portion of the offset measurement and the difference between the TIS in the first and second lighting arrangements.

3. The method according to claim 2, wherein the weighting coefficient is calculated according to the following formula: Where α(N s ) is the weighting coefficient, is the variable portion of the offset measurement, and is the variable portion of the difference between the TIS in the first and second lighting arrangements.

4. The method of claim 3, wherein the variable portion of the offset measurement is calculated according to the following formula: Among them MIS measured (N s ,λ) is the offset measure, and is the shift measurement averaged over the plurality of illumination wavelengths.

5. The method of claim 4, wherein subtracting a weighted value of the difference between the TIS in the first and second lighting arrangements from the offset measurement is performed according to the following formula: MIS corrected (N s )=MIS measured (N s ,λ)-α(N s )·ΔTIS(λ) MIS corrected (N s ) is the correction value of the offset measurement, and ΔTIS(λ) is the difference between the TIS in the first and second lighting arrangements. 6 . The method of claim 1 , and further comprising optimizing an operating parameter of the metering device based on the difference in the TIS of the metering device.

7. A system for correcting errors in offset measurements on a semiconductor wafer due to tilt of the wafer, the system comprising: an illumination source forming part of a metrology device and operable to illuminate a wafer in at least a first illumination arrangement and a second illumination arrangement, wherein in the first illumination arrangement a surface of the wafer is illuminated substantially orthogonally by the illumination source, and wherein in the second illumination arrangement the surface is illuminated obliquely by the illumination source; a tool induced transfer (TIS) calculator operable to find a difference between the TIS of the metering device in the first and second lighting arrangements; and a wafer tilt corrector operable to correct an error in the offset measurement due to tilt of the wafer at the location on the wafer based on subtracting a weighted value of the difference between the TIS of the metrology devices in the first and second illumination arrangements from an offset measurement made by the metrology device at the location on the wafer, wherein the difference between the TIS in the first and second lighting arrangements comprises a characteristic profile that varies as a function of a parameter of the metering device, wherein the illumination source is operable to illuminate the wafer at a plurality of wavelengths, and the TIS calculator is operable to find the difference in the TIS of the metrology device as a function of the plurality of wavelengths, wherein the TIS calculator is operable to find the difference in TIS at a plurality of locations Ns on the wafer as a function of the plurality of wavelengths for each of the plurality of locations, Wherein the wafer tilt corrector is operable to calculate the weighted value of the difference between the TIS in the first and second illumination arrangements by multiplying the difference between the TIS in the first and second illumination arrangements by a weighting coefficient.

8. The system of claim 7, wherein the wafer tilt corrector is operable to calculate the weighting coefficient based only on a variable portion of the offset measurement and the difference between the TIS in the first and second illumination arrangements.

9. The system of claim 8, wherein the wafer tilt corrector is operable to calculate the weighting coefficient according to the following formula: Where α(N s ) is the weighting coefficient, is the variable portion of the offset measurement, and is the variable portion of the difference between the TIS in the first and second lighting arrangements.

10. The system of claim 9, wherein the wafer tilt corrector is operable to calculate the variable portion of the offset measurement according to: MIS measured (N s ,λ) is the offset measure, and is the shift measurement averaged over the plurality of illumination wavelengths.

11. The system of claim 10, wherein the wafer tilt corrector is operable to subtract a weighted value of the difference between the TIS in the first and second illumination arrangements from the offset measurement according to the following formula: MIS corrected (N s )=MIS measured (N s ,λ)-α(N s )·ΔTIS(λ) Among them MIS corrected (N s ) is the correction value of the offset measurement, and ΔTIS(λ) is the difference between the TIS in the first and second lighting arrangements.

12. The system of claim 7, wherein an operating parameter of the metering device is optimized based on the difference in the TIS of the metering device.

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