JP2000155051A - Phase state analyzing method for equiphase stripes - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the precision of a phase state analysis in an observation region by applying a masking process to portions corresponding to regions where no stripe information exists in the phase distribution applied with a phase unlapping process in the analyzing method for the phase state of a checked body having an observation region split into multiple portions by separation bands where no stripe information exists. SOLUTION: In this phase state analyzing method, stripes scanning is applied in four steps to a checked face split into multiple observation regions by separation bands (S1). The phase distribution of the checked face is obtained from four interference stripes intensities obtained by the stripes scanning (S2). The phase distribution is folded between -π and π, thus phase unlapping is applied by the phase unlapping method, and the continuous phase distribution is obtained (S3). A masking process is applied to portions having 0 modulation corresponding to the separation bands (S4). Finally, an inclination correction is made to the continuous phase distribution applied with the masking process by the method of least squares (S5).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing the phase state of equiphase fringes when analyzing and measuring the shape of the surface of a light reflector or the thickness unevenness or refractive index distribution of a light transmitting body using interference fringes or moiré fringes. Regarding, particularly, when the subject surface is composed of a plurality of observation areas set to be substantially flush with each other,
Alternatively, in the case where a plurality of observation regions in which the refractive index distribution inside the subject is set to be substantially uniform, even if there is a separation band for which stripe information cannot be obtained for region division, the plurality of observation regions are The present invention relates to a phase state analysis method for equiphase fringes, which can analyze and measure a phase state over a range.

[0002]

2. Description of the Related Art Conventionally, there has been known a method of analyzing contour fringes such as interference fringes and measuring the surface shape of a subject with high accuracy.

For example, in a suction chuck apparatus for suction-supporting a silicon wafer used as an IC substrate and performing surface checking and surface processing of the wafer, a reference surface for suction-supporting a sample is provided with surface accuracy on the order of light wavelength. In order to measure the surface accuracy of the reference surface, a technique based on reflection-type interference fringe measurement is used.

By the way, this suction chuck device is shown in FIG.
A reference surface 2 with high surface accuracy is formed on the upper surface of the pedestal main body 1, and a plurality of suction holes 3 are evenly distributed in the surface. By the suction action, for example, a thin silicon wafer 4 is sucked and held on the reference surface 2.

When the surface accuracy of the reference plane 2 is measured using the technique based on interference fringe measurement, interference fringe information in the entire area of the reference plane 2 is acquired (if necessary, fringe scanning is performed. ), A predetermined operation is performed based on the acquired information to obtain a phase distribution (height data).

However, since the obtained phase value is folded into the range of the main value of (-π, π) (phase wrapping) according to the above-mentioned predetermined calculation, the phase value is large for a phase having a large dynamic range. It becomes discontinuous and has an uncertain value that is an integral multiple of 2π. Therefore, in order to obtain the phase distribution along the actual surface shape, the phase distribution Φ folded in the range of the main value of (−π, π) as described above is obtained.
It is necessary to perform a phase unwrapping process for obtaining an original continuous phase distribution from (x, y).

When such a phase unwrapping process is performed, a highly accurate continuous phase distribution Φ is obtained using a simple algorithm for a smooth phase distribution with little noise.
Although it is possible to obtain (x, y), it becomes a very difficult problem when a region including a large amount of noise and low modulation (an amount depending on the interference fringe amplitude) is included, and the continuous phase distribution Φ (x, y) is obtained. ) Is difficult to obtain.

[0008] Under such circumstances, in recent years, there has been proposed a technique capable of performing a phase unwrapping process satisfactorily even when noise is large or modulation is low.

This method focuses on a portion where interference fringes have higher contrast (higher modulation) and sequentially unwraps the phase from such a portion. In the field of computer science, the minimum tree problem (Minimum Spanning) is used.
Tree Problem) is an application of a graph problem, and the maximum-amplitude tree method using it is known to be particularly effective (The 55th (1994) Proceedings of the Japan Society of Applied Physics) P803).

[0010]

However, in the suction chuck device and the like shown in FIG. 7, the wafer 4 can be removed from the reference surface 2 without requiring excessive force after the predetermined processing is completed. As described above, the reference surface 2 is divided into a plurality of regions by the lattice-shaped grooves 5.

In the case where the observation area is completely divided into a plurality of areas by the groove 5, effective interference fringe information cannot be obtained from the groove 5, so that observation interference information can be obtained. Since the area is a completely divided area on the interference fringe data, the area is obtained by performing a predetermined calculation based on the interference fringe information with respect to the reference plane 2 while including the area without the interference fringe information. When the phase unwrapping process is performed on the phase distribution, there is a problem that an error occurs in the analysis data.

That is, in the case where the above-described phase unwrapping method is used, a portion corresponding to the groove 5 where the interference fringes do not occur on the reference surface 2 is an error factor, and the entire shape of the reference surface 2 is accurately determined. Difficult to analyze.

When the surface shape of the test surface is obtained by using the interference fringe measurement technique, the test surface set in the test object setting section is necessarily slightly inclined. When obtaining data, a process of correcting the inclination using the least squares method or the like is finally required. However, such a tilt correction process is added to data obtained by performing phase unwrapping. In addition, there is also a problem that the above-described step portion where no interference fringe occurs becomes a weight for the entire data and accurate tilt correction cannot be performed.

[0014] Such a problem is caused by the fact that a subject is composed of a transmissive object and its observation area is divided into a plurality of parts by a separation band in which it is difficult to obtain interference fringe information. This also occurs when the rate distribution and the thickness unevenness of the observation area are measured using a transmission interference fringe measurement technique.

The present invention has been made in view of such circumstances, and when measuring the surface shape, refractive index distribution, or thickness unevenness of an object by analyzing equiphase fringes, the object is separated by a plurality of separation bands. Is divided into observation regions, and even when the stripe information of the separation band cannot be obtained, the data in the separation band does not affect the phase analysis of the observation region. It is an object of the present invention to provide a phase state analysis method of equiphase fringes that can perform measurement.

[0016]

According to the method for analyzing the phase state of equiphase fringes according to the present invention, a separating band having no fringe information and a plurality of divided bands separated by the separating band are adjacent to each other with the separating band interposed therebetween. The phase difference at the end of the region is 1
The fringe information of the subject including the observation region having a fringe information value smaller than / 2 fringes is taken in, the phase is calculated based on the fringe information of the subject including the separation band in the observation region, and then, A phase unwrapping process is performed on a phase distribution that has been phase-wrapped by phase calculation, and a masking process is performed on a portion of the phase distribution that has been subjected to the phase unwrapping process, the portion corresponding to the separation band where the fringe information does not exist. It is assumed that.

Further, the present invention is characterized in that a predetermined function correction process is performed on the phase distribution subjected to the masking process.

The above-mentioned "ends of the regions adjacent to each other with the separator in between" mean the boundary portions of the opposing separators in the two observation regions adjacent to each other with the separator in between.

[0019]

Embodiments of the present invention will be specifically described below with reference to the drawings.

FIG. 1 is a flowchart for explaining a phase state analysis method for equiphase fringes according to the present embodiment.
In the method of the present embodiment, a Fizeau-type reflection laser interferometer is used. First, as shown in step 1 (S1), a test object which is a light reflector divided into a plurality of observation regions by a separation band. A four-step fringe scan is performed on the surface. It should be noted that the separation band does not generate interference fringes when focused on the observation area. Further, the phase difference at the boundary between the opposing separators in the two observation regions adjacent to each other with the separation band interposed therebetween is better than 縞 fringe (の of the incident light wavelength by a vertically incident light wave interferometer). It is necessary to obtain fringe information with high modulation in the observation region.

Next, the phase distribution Φ (x, y) of the test surface is determined from the _four interference fringe intensities I ₁ , I ₂ , I ₃ and I ₄ obtained by the fringe scanning (S2). In this case, the phase distribution Φ (x, y) is obtained based on stripe information on a straight line in the plane (on the white arrow in FIG. 2).

Since this phase distribution Φ (x, y) is assumed to be phase wrapping data convolved between −π and π, the phase unwrapping method such as the above-mentioned maximum amplitude tree method is used. Lapping is performed to obtain a continuous phase distribution Φ (x, y) (S3).

Next, in the continuous phase distribution Φ (x, y), a masking process is performed on a portion where the modulation is 0, which corresponds to the above-mentioned separation band (S4). Here, the masking process means that, for example, 0
Is multiplied by 1 with respect to the data to be left as it is. However, if only unnecessary data can be removed, masking processing in another mode can be used.

Finally, inclination correction is performed on the masked continuous phase distribution Φ (x, y) using the least squares method (S5). At this time, other function corrections such as power correction, correction using a function of Seidel aberration, and correction using a Zernike polynomial may be performed at the same time.

If the masking process for extracting only a desired observation region is performed before the phase unwrapping calculation between the above-mentioned steps 1 (S1) and 2 (S2), the subsequent calculation process The time can be reduced, and the shape analysis processing can be speeded up.

Hereinafter, the present embodiment will be described in more detail.

When a fringe scanning method is used in a laser interferometer, for example, in the case of a four-step method, the interference fringe intensities I ₁ , I ₂ , I ₃ , and I _{4 in four} fringe scans are represented by the following equations (1). , (2), (3), and (4). I ₁ (x, y) = I ₀ (x, y) [1 + γ (x, y) cos {Φ (x, y)}] (1) I ₂ (x, y) = I ₀ (x , Y) [1 + γ (x, y) cos {Φ (x, y) + π / 2}] (2) I ₃ (x, y) = I ₀ (x, y) [1 + γ (x, y ) cos {Φ (x, y) + π}] (3) I ₄ (x, y) = I ₀ (x, y) [1 + γ (x, y) cos {Φ (x, y) + 3π / 2}] ... (4)

Here, x and y are coordinates, Φ (x, y) is a phase, I ₀ (x, y) is an average light intensity at each point, and γ (x, y)
y) represents the interference fringe modulation, respectively. The modulation may be considered to have a substantially correlation with the interference fringe amplitude, and is specifically expressed by the following equation (5).

[0029]

(Equation 1)

The above four equations (1), (2),
When the phase Φ (x, y) is obtained from (3) and (4), the following equation (6) is obtained.

[0031]

(Equation 2)

At this time, as apparent from the fact that the above equation (6) is an arctangent function, the phase Φ (x, y)
Is convolved between -π and π. The data in such a state is usually called phase wrapping data. When the denominator is 0 in this formula (that is, I ₁ (x, y)
= I ₃ (x, y)) is π / 2 if the molecule is positive
And if negative, -π / 2.

Further, a portion where no interference fringes exist (10 in FIG. 2)
Character part) is I₁(X, y) = I ₂(X, y) = I₃
(X, y) = I₄Since (x, y) = 0, the phase
It becomes π / 2 or -π / 2 in the ping data.
In other words, data in an area where no interference fringes exist is considered to be an error.
turn into.

However, the heights (phases) of the separation zone boundary portions of the observation areas on both sides divided by such an area where no interference fringes exist (separation zones) are substantially the same height (at least the phase difference is π). In other words, in the case of a Fizeau interferometer using a He-Ne laser, the height difference is 0.16 μm or less in consideration of the wavelength of incident light. If the analysis is performed using the above-described phase unwrapping method such as the maximum amplitude tree method, no calculation error occurs when only the observation region where the interference fringe exists is analyzed. In other words, a calculation error occurs in the separation band where no interference fringes exist.

Taking this fact into consideration, in the present embodiment, the phase unwrapping method is applied to the entire region including the separation band where no interference fringes exist and the plurality of observation regions where the interference fringes exist. , The masking process is performed on the region where the modulation is 0 (the modulation value is easy to judge at this stage) to eliminate the data of the region where the interference fringes do not exist, and the separation where the interference fringes do not exist is performed. The calculation error for the band portion does not affect the analysis value of the observation region.

Further, when the surface shape of the test surface is obtained by using the interference fringe measurement technique, the test surface set in the test object setting section is inevitably slightly inclined. When the shape data is obtained, a process of correcting the inclination using the least square method or the like is finally required.
However, when such a slope correction process is applied to the continuous phase distribution obtained by performing the phase unwrapping, a portion corresponding to the above-described separation band where no interference fringe is generated becomes a weight for the entire data. Although there is a problem that accurate tilt correction cannot be performed, in the present embodiment, masking processing is performed on an area where modulation is 0 to eliminate data in an area where the interference fringes do not exist. Accurate inclination correction can be performed, and correct shape measurement can be performed. In addition,
The condition is that the phase difference between the regions adjacent to each other across the separation band having no interference fringe information has a slope smaller than 1/2 fringe.

Further, in the above fringe scanning method, it is possible to use another step method of three or more steps such as a five step method instead of the four step method.

<Embodiments> Specific embodiments will be described below by analyzing simulation data in comparison with the prior art.

First, the observation area is divided by two cross lines (separation zones) in which no interference fringes occur in the surface to be inspected.
It is assumed that the observation region is completely flat, and the subject having such a test surface is slightly tilted (the height difference in the region sandwiching the separation band is less than 1/2 fringe). It is assumed that the state is set in a Fizeau laser interferometer.

FIG. 2 shows simulation data of interference fringes for the test surface assumed as described above. Note that FIG.
(A) shows the interference fringe data corresponding to the above equation (1), and (B) shows the interference fringe data corresponding to the above equation (3).

With respect to this interference fringe data, the surface shape of the center cross section (on the white arrow line) of the phase wrapping data is shown in FIG.
Is formed in a sawtooth shape as shown in FIG. Note that the portion corresponding to the crosshair has no interference fringes and is set to π / 2 radians, so that a distortion is formed on the graph, which causes an analysis error. Note that, depending on the setting of the software program for performing the analysis process, the value may be -π / 2 radians instead of the above-mentioned π / 2 radians.

Next, when the phase wrapping data shown in FIG. 3 is subjected to phase unwrapping by the above-described maximum amplitude tree method, a graph shown in FIG. 4 is obtained. It can be seen that the portion corresponding to the crosshair and having no interference fringes is distorted on the straight line graph.

Next, when the data shown in FIG. 4 is subjected to the inclination correction by the least square method, the error component becomes a weight over the entire area, and as shown in FIG. 5, accurate inclination correction is performed. It will be difficult. That is, the straight line portion of the graph has a predetermined slope in FIG.

Therefore, before performing the inclination correction by the least-squares method, masking processing is performed on the data of the portion where the modulation is 0 (the portion corresponding to the cross hair). Here, a change in the value of the modulation is shown in FIG. The masking process multiplies the data by 1 if the modulation value is 1, and multiplies the data by 0 if the modulation value is 0.

As described above, by performing the masking process on the area where the modulation becomes 0 before performing the inclination correction, the inclination of the straight line portion of the graph can be surely corrected even when the inclination is corrected.

Hereinafter, points to be noted in obtaining a better analysis result in the embodiment will be enumerated.

(1) It is preferable that the observation region has good modulation, that is, the observation region has almost the same reflectance with the reference surface and has good contrast of interference fringes.

(2) It is preferable to adjust the irradiation light amount of the interferometer so that the interference fringe contrast always becomes the best.

(3) It is preferable that the interferometer is focused on the surface to be measured. If not focused, interference fringes
Due to the effect of the diffraction phenomenon, it flows as if at the edge, which causes an error.

(4) It is preferable to perform measurement in a measurement environment in which air fluctuation and vibration are as small as possible. If such requirements are not satisfied, fringe scanning will not be performed accurately, causing measurement errors and lowering the modulation in the region where the interference fringes exist.

(5) It is preferable that the measurement is performed in a state where the flatness of the surface to be inspected is good and the alignment is minimized.

The method for analyzing the phase state of equiphase fringes of the present invention is not limited to the above-described embodiment, and various other modifications can be made. For example, in the above-described embodiment, when the object is a light reflector, the method is applied to measurement of the surface shape (irregular shape or step shape) of the light reflector. In this case, the method can be applied to the measurement of the thickness unevenness and the refractive index distribution.

However, when the subject is a light transmitting body,
When applying the method of the present invention, it is necessary to satisfy the same prerequisites as in the above embodiment.

That is, the phase difference in the light incident direction (the phase difference accompanying the thickness unevenness and the refractive index distribution) at the boundary between the opposite separation zones of the two observation regions divided by the separation zone is equal to 1/2 of the equal phase fringe. It is necessary to be less than the fringes. Therefore, the height difference between the opposing separation zones is, for example, less than λ / 4 when a Fizeau type or Michelson type interferometer is used, and λ / It is necessary to be less than 2 (where λ is the light wavelength from the light source). In addition, it is necessary that no stripe information exists in the separation band, the stripe information in the measurement area needs to have good contrast, and the inclination has the presence of interference fringes sandwiching the separation band. It is necessary that the phase difference of the region is less than 1/2 fringe.

Furthermore, in the method of the present embodiment, a light reflection type Fizeau laser interferometer is used as the interferometer device, but various other interferometers may be used. Further, as the irradiation light source, a white light source may be used instead of the laser light source.

The type of fringe information is not limited to the above-described interference fringe information, but may be moire fringe information. However, in the fringe information of the moire fringe, the amount corresponding to one fringe is different from the fringe information of the interference fringe.
For example, in a grid irradiation method for vertical observation using parallel light illumination, when a grid pitch is P and an illumination angle is θ, one fringe corresponds to the amount of P / tan θ.

Further, the phase state analysis method of equiphase fringes of the present invention is not limited to the case where the phase distribution Φ (x, y) of the subject is obtained based on a plurality of pieces of fringe information obtained by the fringe scanning method. The present invention can also be applied to a case where the phase distribution Φ (x, y) is obtained based on the stripe information obtained by one capture.

[0058]

As described above, according to the phase state analysis method for equiphase fringes of the present invention, masking is performed on a portion corresponding to a region where no fringe information exists in the phase distribution subjected to the phase unwrapping process. In the final stage, the data on the separation zone is removed, and the influence of the data on the separation zone on the entire analysis value can be eliminated, thus improving the accuracy of the phase state analysis in the observation region of the subject. Can be achieved. Further, if a function correction process such as a tilt correction is performed on the phase distribution thereafter, the accuracy of the correction can be improved.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining an embodiment according to a phase state analysis method of equiphase fringes of the present invention.

FIG. 2 is a diagram showing interference fringe data used in a simulation according to an embodiment of the method of the present invention.

FIG. 3 is a graph showing phase wrapping data corresponding to the interference fringe data of FIG. 2;

FIG. 4 is a graph showing data obtained by performing a phase unwrapping process on the phase wrapping data of FIG. 3;

5 is a graph showing data obtained by correcting the inclination of the data of FIG. 4 by a least squares method in a state including an analysis error.

FIG. 6 is a graph showing a change in modulation value.

FIG. 7 is a perspective view showing a shape of a test surface to which a measurement technique based on interference fringe measurement is applied.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Pedestal main body 2 Reference surface 3 Suction hole 4 Silicon wafer 5 Groove

Claims (2)

[Claims] 1. A separation band having no fringe information and a plurality of divisions by the separation band, and a phase difference between end portions of regions adjacent to each other with the separation band therebetween is 1 /
Taking in fringe information of the subject consisting of an observation region having a fringe information value smaller than two fringes, performing a phase calculation based on the fringe information of the subject including the separation band in the observation region; Performing a phase unwrapping process on the phase distribution that has been phase-wrapped by calculation, and performing a masking process on a portion corresponding to a separation band where the fringe information does not exist in the phase distribution on which the phase unwrapping process has been performed. To analyze the phase state of equiphase fringes. 2. The method according to claim 1, wherein a predetermined function correction process is performed on the phase distribution subjected to the masking process.
The phase state analysis method for the described equiphase fringes.