## 1.

## Introduction

A wafer aligner is a semiconductor exposure apparatus that aligns a wafer to a mask for each exposure field. Using a stage that sequentially moves field by field, the exposure apparatus can expose a field with a series of alignment sequence steps until the entire wafer surface is exposed. An optical registration metrology system (ORMS) measures the amount of exposure displacement error. Using some form of photolithography registration metrology, ORMS measurements are possible during the alignment process using wafer alignment optics installed in the wafer aligner. Occasionally, these measurements are done with an independent ORMS, which is a commercially available tool. Hereafter, we define ORMS to measure the photoresist marks on bare silicon wafers only. ORMS will then be used mainly for analysis of machine performance, which is very useful for wafer aligners.

The precision of the ORMS sensors has two limitations. The first limitation relates to one-dimensional (1-D) laser spot sensors.^{1} When a wafer must be moved beneath a fixed optical sensor,^{1} a scanning stage for providing object movement is required for 1-D scanning optical sensors. The error in the position of the laser metrology system for stage monitoring is generally larger than that of the optical sensor due to air temperature fluctuations and high frequency vibrations of machine components,^{2} which are beyond the frequency response of laser metrology, so the measurement precision can never be small when using conventional metrological methods. The second limitation occurs when a two-dimensional (2-D) imaging sensor is used to measure a motionless mark.^{3} It is difficult to improve the measurement precision in this imaging mode due to the limits associated with the optical image magnification and sensor pixel size reduction. Other types of difficulties also arise when ensuring adequate intensity to the solid state imaging pixels. In the conventional approach, reducing the measurement error involves moving the wafer stage very slowly and taking a large number of data points, $N$. However, the reducing factor of the error is proportional to $1/\sqrt{N}$, and so an increasing $N$ is time consuming. An alternative approach to overlay measurements employs scatterometry,^{4} which is used to reconstruct the three-dimensional (3-D) shape of a registration mark from diffracted light. Although this method has the potential to meet the requirements for registration metrology, lengthy electromagnetic field calculations are required.

In the field of optical measurements, the Moire effect is a well-studied phenomenon.^{5}^{,}^{6} The Moire method has a particularly unique advantage in that it can significantly improve the precision with no further demands on the sensitivity of the optical sensor. For this reason, the Moire method is widely used for optical displacement measurements in optical encoders^{2}^{,}^{7}^{,}^{8} and curved surface metrology.^{9}10.11.^{–}^{12} We attempt here to implement Moire technologies into ORMS in order to improve the measurement precision.

There is much previous research in Moire, in particular for measuring 3-D topology. However, in the context of ORMS applications, our implementation to photolithography belongs to 2-D Moire measurements, similar to that found in optical encoders. With regard to an optical encorder, Ref. 8 has proposed an electrical signal process using two independent Moire fringe signals with the same phase. Many types of Moire measurements utilize a 2-D monitor camera to observe a real-time topological deformation.^{12}^{,}^{13} Kafri has studied a double exposure technique^{5}^{,}^{11} in which the camera film realizes a Moire fringe image by exposing a shifted grating on a previously exposed grating as a reference pattern.

In registration metrology, measurement of the displacement between two points by photoresist images through double exposure is required. The photoresist image can indicate problems in the exposure of a wafer aligner, such as registration error, machine vibration, and exposure stage error. Such information is valuable because one can perform a calibration for the wafer aligner. The biggest advantage of using Moire technology for ORMS is that the physical quantity to be measured is highly magnified. For a double-exposed wafer, we measure the distance between two sequentially exposed marks. The distance is magnified by the Moire phenomena and calculated by dividing the Moire magnification factor from the measured distance. In this case, theoretically, the measurement error is not magnified. Therefore, the division operation reduces the measurement error with the inverse of the Moire magnification factor. As compared to conventional approaches for reducing the error, our method does not require slow machine movements to record a large number of data points.

In Sec. 2, we describe our derived Moire method, called the alternating direction Moire (ADM). Applications to ORMS measurements are described in Sec. 3. From exposure experiments under i-line illumination, we verify the advantages of the ADM method in Sec. 4. In Sec. 5, future applications to the most advanced immersion ArF tools and the possible merit of ADM are discussed.

## 2.

## ADM and ORMS

## 2.1.

### ORMS and Bar-in-Bar Method

ORMS measurement precision is expressed by ${\sigma}_{\text{metrology}}$. A first mark or set of marks is created on a wafer by a first exposure. A second mark or set of marks is created by a second exposure. Assume that $\sigma $ denotes the measurement precision of any one of the photoresist marks obtained with metrology optics. Then, $\sigma $ is the measurement error of the sensor defined as the statistical error distribution from numerous data points, as described in the Appendix. Assuming that a conventional ORMS measures the distance between two marks, ${\sigma}_{\text{metrology}}$ is given by

In our case, the marks are photoresist marks so that there is less waveform error for the optical signal.In conventional systems, the fundamental mark arrangements for ORMS are the box-in-box^{14}^{,}^{15} or bar-in-bar.^{15} In Fig. 1, the sequential process of the double exposure for the bar-in-bar system is shown. In this process, two types of reticles, $R1$ and $R2$, are used for the photomask. After the reticle $R1$ is exposed on the wafer and the reticle $R2$ is also exposed with the stage in motion to make the bar-in-bar pattern on the photoresist. In the case of the bar-in-bar system, a line is exposed between the two previously exposed lines. The relative position of the center line from the two outside lines corresponds to both the polarity of the direction and the amount of displacement. In this paper, we call this metrology method the differential method. This bar-in-bar system is also known as electrical micromeasurement.^{16}

## 2.2.

### Alternating Direction Moire

To implement Moire metrology into the bar-in-bar method for ORMS, we develop a new concept using two types of Moire, $+\theta $ and $-\theta $, with opposite phases. Figure 2 shows the schematics of the general principle of ADM where the $-\theta $ Moire is assigned to $A$ and ${A}^{\prime}$, and the $+\theta $ Moire is assigned to $B$. The Moire $A$ and ${A}^{\prime}$ correspond to the two outside lines in the bar-in-bar system. Moire $B$ corresponds to the center line of the bar-in-bar system. As in the bar-in-bar system, the offset term is cancelled by the differentiation operation without loss of the precision as

This equation shows the displacement error between gratings $G1$ and $G2$ as shown in Fig. 2.It is notable that there is a large magnification factor for the ADM in comparison to the bar-in-bar mark, which strongly reduces the measurement errors.

## 3.

## Double Exposure ADM Method with Photoresist Mark

## 3.1.

### Basic Concept in Practice

We propose the ADM method for ORMS. The first and the second exposures are initially performed for two different mask patterns consisting of arrays of lines. Resist development leads to marks on the wafer with positions that are very sensitive to stage alignment errors. Chromium lines on one mask have an inclination angle, $\theta $, with respect to the lines on the other mask. The overlapped areas of the chromium lines of the two masks lead to wedge-shaped unexposed areas on the wafer, which emerge as a positive photoresist pattern after development. The resulting set of unexposed patterns is in the form of a Moire pattern. Assuming the stage moves in the $Y$-direction in order to overlap the two patterns, the resulting marks are displaced in the $X$-direction by an amount related to the inclination angle and the displacement. In particular, a change in displacement $DY$ causes a change of $DX=DY(1/\mathrm{tan}\text{\hspace{0.17em}}\theta )$ in the $X$-direction. The factor ($1/\mathrm{tan}\text{\hspace{0.17em}}\theta $) is referred to as the Moire multiplication ratio.

This procedure is used to measure the distances between adjacent marks and then to divide the measured distances by the Moire multiplication ratio. It should be noted that all measurement errors are reduced by a factor of the Moire multiplication ratio. In creating Moire photoresist images, the marks should meet the requirements for the ADM method, a zero point of the position should exist, and the amount of its shift from the zero point should include directional information concerning the positional error.

Figure 3 shows how Moire photoresist images are created with the double exposure process. A $Y$-direction shift of the wafer, $\mathrm{\Delta}$, causes an $X$-direction shift of the mark, $\mathrm{\Lambda}$. The shift $\mathrm{\Delta}$ is multiplied by the ratio, $1/\mathrm{tan}\text{\hspace{0.17em}}\theta $, to create the latter shift through the double exposure of a zigzag mark and a straight line mark. $\theta $ is an angle between the zigzag and straight lines. At least three points of Moire photoresist images are needed to meet the requirements for the ADM method. The changes in the coordinates of $X1$ to $X2$ and that of $X2$ to $X3$ are related to alignment errors through the Moire effect. Figure 4 shows the Moire photoresist images when $\mathrm{\Delta}$ is zero. The zigzag line in this figure is the centerline of the zigzag pattern of the second mask pattern. The finite $\mathrm{\Delta}$ case is shown in Fig. 5.

## 3.2.

### Error Analysis of Measurements

We discuss the estimation of ADM measurement errors, where the following analysis is applicable to any type of ORMS sensor. We analyze the ADM measurement error in ORMS, assuming measurement error follows a normalized Gaussian distribution, hereafter called the normal distribution in this paper, without loss of generality. The measurement error is reduced by a factor equal to the inverse Moire multiplication ratio. The coordinates of three Moire photoresist marks are given by

The measurement error of the detection for each mark is written as ${\epsilon}_{i}$. The physical quantity measured in this method ${\mathrm{\Lambda}}_{\text{measured}}$ is defined as the difference between the distance of $X1$ and $X2$ and that of $X2$ and $X3$, as depicted in Figs. 4 and 5.${\mathrm{\Lambda}}_{\text{measured}}$ can be expressed in terms of the true value $\mathrm{\Lambda}$.

## (7)

$${\mathrm{\Lambda}}_{\text{measured}}=[(X3-X2)/2-(X2-X1)/2]/2=\mathrm{\Lambda}+[({\epsilon}_{1}+{\epsilon}_{3}-2{\epsilon}_{2})/2]/2.$$Using Eqs. (6) and (7), $\mathrm{\Delta}$ can be rewritten as

## (8)

$${\mathrm{\Delta}}_{\text{measured}}=\mathrm{tan}\text{\hspace{0.17em}}\theta [(X3-X2)/4-(X2-X1)/4]\phantom{\rule{0ex}{0ex}}=\mathrm{\Delta}+\mathrm{tan}\text{\hspace{0.17em}}\theta ({\epsilon}_{1}+{\epsilon}_{3}-2{\epsilon}_{2})/4$$The measurement error of each mark ${\epsilon}_{i}$ is assumed to have a constant variance regardless of $\theta $, although the shape of the Moire photoresist mark appears different depending on the angle. This assumption is discussed in Sec. 5.1 in detail. In order to discuss the $\theta $ dependence of $\epsilon $, we introduce

We can show that for which the derivation is given in the Appendix.Referring to Eqs. (11) and (10), $\epsilon $ is expressed as

From Eq. (12), the ORMS precision ${\sigma}_{\text{metrology}}$ of ADM is## (13)

$${\sigma}_{\text{metrology}}=\sqrt{{(\mathrm{tan}\text{\hspace{0.17em}}\theta /4)}^{2}\xb76{\sigma}^{2}}.$$## 4.

## Experimental Results

## 4.1.

### Laser Step Alignment

We focus our attention on wafer alignment optics that use a laser spot.^{1} Under this assumption, the laser spot can produce a significant amount of scattered light even for small wedge shapes in Moire photoresist images. Experiments are performed to validate the ADM precision of the 1-D alignment optics equipped with an exposure apparatus and a laser step alignment (LSA) measurement system installed in a Nikon NSR-1755iA ($\mathrm{NA}=0.50$, illumination $\mathrm{NA}=0.30$), which is an i-line exposure apparatus. A normally incident laser sheet beam creates an oblong spot on the wafer. As shown in Fig. 6, a periodic array of die-shaped marks is situated on the wafer. When the laser spot is positioned on the marks during the stage scan, the laser beam is diffracted by the marks and detected by an optical device located at an angle $\varphi =\mathrm{si}{\mathrm{n}}^{-1}(\lambda /d)$ relative to the wafer surface. The angle is determined by the period of the marks and the wavelength of the laser light.

## 4.2.

### LSA for ADM Measurement

In Fig. 7, the ADM mark arrangement is displayed as three columns of marks along the $X$-axis in seven rows with a $d=4\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mu \mathrm{m}$ pitch. The LSA diffraction signal along the $X$-axis is shown in Fig. 8. In the process of the stage scans, the light signal consists mostly of light diffracted by the columns of marks.^{1}^{,}^{17}^{,}^{18} In the discussion below, the ORMS precision $\sigma $ is multiplied by a factor of three. In the $3\sigma $ expression, all measured values lie within 3 sigma of the mean, or approximately 99.7%. Note that in Sec. 3, the ORMS precision for ADM is calculated for $1\sigma $.

## 4.3.

### ADM Magnification and Precision Improvement

We experimentally investigate the validity of ADM by demonstrating that precision improves in inverse proportion to the increasing magnification factor. Masks with several different angles are prepared for the experiment. In Fig. 9, there are two masks with $2\text{-}\mu \mathrm{m}$ line width periodic gratings for the double exposures. The masks are designed to have four different values of $K$: 10, 16, 20, and 32, corresponding to four different $\theta $ of 21.8, 14, 11.3, and 7.1 deg, respectively. As an example, in Table 1, a 2-D of the largest and smallest angle patterns (labeled as $10x$ and $32x$, respectively) are shown. Regarding $K=1$, we adapt the conventional ORMS experimental data with the arrangement shown in Fig. 6. The ORMS data for $K=1$ gives a $3\sigma $ precision of

## (15)

$$3{\sigma}_{\mathrm{i}\text{-}\text{line},\text{Metrology}}=14\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{nm}.$$## Table 1

Design rules for 10× and 32× ADM marks in experiments.

Magnification | 10× | 32× |

Length (X) | 25 μm | 50 μm |

Cross angle (θ) | 21.8 deg | 7.1 deg |

Line width (W) | 2 μm | 2 μm |

Range (Y) | ±3 μm | ±1.1 μm |

Four different magnification data points for ORMS of ADM are repeatedly taken. From this data, the measurement precision is shown as five dots in Fig. 10, where the vertical and the horizontal axes are expressed on a logarithmic scale. According to the theory of the ADM method, the precision in the experimental data in Fig. 10 has a slope of $-1$ with respect to magnification. The data fit well to a linear model, with a coefficient of determination ${R}^{2}$ of over 0.93 for five data points, indicating good agreement with the data.

The increased multiplication of ADM in our experiments is consistent with the theoretical prediction calculated according to Eq. (14). At $32x$ ($\theta =7.1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{deg}$), the $3\sigma $ precision of ORMS using ADM for an i-line exposure apparatus is derived from the linear curve in Fig. 10 as

## (16)

$$3{\sigma}_{\mathrm{i}\text{-}\text{line},\text{Moiremetrology}}=0.50\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{nm}.$$## 5.

## Discussion

## 5.1.

### Verification of Assumptions

Based on the experimental results shown in Fig. 10, the errors ${\epsilon}_{\mathrm{i}}$ in Eqs. (3)–(5) reach a constant value. Thus, the assumption in Sec. 3.2, namely that the error expressed by a normal distribution is not influenced by the shape of the mark, is valid under experimental conditions. The LSA system has a constant measurement error, despite the fact that the wedge-shaped mark becomes narrower with an increase in magnification factor $K$, at least up to $K=32$.

## 5.2.

### Mask Error Robustness of ADM

Mask manufacturing errors, including angle error and line roughness error, are discussed in this section. In Fig. 3, given three overlapping exposure points with different line segment angles $\alpha $, $\beta $, and $\gamma $, the magnification factor $K$ can be derived from Eqs. (3) to (6) as

## (17)

$$K=(1/\mathrm{tan}\text{\hspace{0.17em}}\alpha +2/\mathrm{tan}\text{\hspace{0.17em}}\beta +1/\mathrm{tan}\text{\hspace{0.17em}}\gamma )/4.$$## 5.3.

### Future Precision Improvement

The ADM method is a new methodology that combines the Moire principle with a conventional sensor to detect a resist wedge mark. This method would be relevant to an advanced generation immersion ArF exposure apparatus if mark edge measurements employ a nonstage-scanning sensor, such as a 2-D CMOS image sensor. This assumes that equally precise measurements are possible for CMOS image sensors in comparison to 1-D laser spot sensors.

For a typical immersion ArF exposure apparatus with a 2-D CMOS alignment sensor, the $3\sigma $ sensor precision is usually assumed as $3{\sigma}_{\mathrm{ArF},\mathrm{CMOS}}=0.5\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{nm}$,^{19} where ${\sigma}_{\mathrm{ArF},\mathrm{CMOS}}$ is the sensor precision of the ArF tool with the 2-D CMOS sensor. Then, from Eq. (1)

## (18)

$$3{\sigma}_{\mathrm{ArF},\text{metrology}}=\sqrt{2}\xb73{\sigma}_{\mathrm{ArF},\mathrm{CMOS}}=0.707\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{nm},$$The estimated ORMS precision of a $32\times $ angle pattern using ADM for an exposure ArF tool is calculated from Eqs. (15), (16), and (18) as

## (19)

$$3{\sigma}_{\mathrm{ArF},\text{Moiremetrology}}\phantom{\rule{0ex}{0ex}}=(3{\sigma}_{\mathrm{i}\text{-}\text{line},\text{Moiremetrology}})(3{\sigma}_{\mathrm{ArF},\text{metrology}})/(3{\sigma}_{\mathrm{i}\text{-}\text{line},\text{Metrology}})\phantom{\rule{0ex}{0ex}}=0.025\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{nm}.$$^{20}given present semiconductor manufacturing processes. Furthermore, by selecting an appropriate $\theta $, the sensitivity, $K$, can be adjusted to provide further improvement if needed. It is notable that the ADM technology can offer a new possibility for “pico-meter” order optical registration metrology.

## 5.4.

### Positive and Negative Resist

ADM can be applied using either a positive or negative resist. However, the single exposure dose energy for a double exposure is different for positive and negative resists. For a positive resist, ${E}_{\mathrm{p}}$ is greater than ${E}_{\mathrm{t}}$, where ${E}_{\mathrm{p}}$ is the single dose energy for a positive resist image and ${E}_{\mathrm{t}}$ is the threshold energy above which the positive resist disappears or the negative resist remains after development. For negative resists, ${E}_{\mathrm{n}}$ is less than ${E}_{\mathrm{t}}$, but $2{E}_{\mathrm{n}}$ is greater than ${E}_{\mathrm{t}}$, where ${E}_{\mathrm{n}}$ is the single dose energy for the negative resist image.

## 5.5.

### Nonphotoresist Application

Our experiment for the ADM is performed in the case of photolithography where the Moire pattern is printed on the photoresist. However, the concept of ADM is general because it is fundamentally derived from the bar-in-bar method. Therefore, beyond the case of photolithography, our ADM pattern is one of the candidates for Moire position measuring metrology for wide areas.

To obtain the ADM marks, we require two sequential exposures, $G1$ and $G2$, in Fig. 2. Thus, it is impossible for ADM to be applied to real-time Moire measurements. If the pattern $G1$ has already been exposed on the wafer plane and the $G2$ reticle is fixed, real-time measurements are possible using a camera. This mode of ADM is not applicable for registration metrology.

## 6.

## Conclusions

We developed a new concept for ORMS measurements called the ADM method, which utilizes the double exposure photoresist marks with opposite phases to create a Moire pattern. This measurement method greatly improves precision in inverse proportion to the Moire multiplication ratio. Experiments showed a 0.50 nm ($3\sigma $) precision using the optical alignment sensor of an i-line exposure apparatus, a precision 32 times higher than conventional methods. Given an alignment sensor sensitivity adequate for wedge detection using ADM, this method can be applied to the most advanced immersion ArF scanners, with a possible 25 pm ($3\sigma $) precision. As compared to the conventional approach to reduce error, our method does not require a large number of slow machine movements because the error is reduced in inverse proportion to the Moire magnification. The concept of ADM is not limited to ORMS and can be applied to other Moire metrologies.

## Appendices

## Appendix:

### ${\epsilon}_{i}$ and Summation of $\sigma $

The notation ${\epsilon}_{i}$ denotes an amount of error in the ORMS measurement in mark detection $i$, subject to a normal distribution $N(\mu ,{\sigma}^{2})$, with mean $\mu $ and variance ${\sigma}^{2}$. We define the expression

Since the mean value of the measurement error in this paper is generally zero, ${\epsilon}_{i}$ can be expressed as

With respect to $\epsilon $, the calculation of a unified variance for three marks can be defined as follows. Define $\rho $ as the error associated with three marks combined

Here, $\rho $ is the random variable and is the equation represented as Eq. (22). It can be represented as where ${\sigma}_{\mathrm{p}}^{2}$ is the variance of three point measurements. Since $\{{\epsilon}_{i}\}$ can be represented by a uniform value subject to a normal distribution, the unified variance can be calculated as Upon substitution of Eq. (24) into Eq. (23), we have Eq. (11).## Acknowledgments

The authors thank Dr. Michael Sogard, Mr. Koichi Matsumoto, Dr. Shinichi Nakajima, Dr. Kazuya Okamoto, and Dr. Tomoya Noda for their valuable suggestions.

## References

## Biography

**Kyoichi Suwa** received an MS degree from Osaka University in 1973, and participated in the development of the wafer aligner, macroinspection, and the LCD aligner. He was a previous member of the Nikon board of directors. His most recent published paper appeared in *Applied Optics*.