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 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

Fig. 1

Double exposure to print bar-in-bar marks on the wafer using reticle 1 and reticle 2.

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

Fig. 2

General principle of alternating direction Moire (ADM); the notation is different from that of chapter 3. The Moire pattern $A$ observed when two grating images $G1$ and $G2$ are tilted with an angle $-\theta$; if the grating $G1$ is moved a distance $\mathrm{\Delta }y$ in the $y$-direction, the Moire pattern will move a distance $\mathrm{\Delta }X=-\mathrm{\Delta }Y/\tan \theta$ in the $x$-direction. The Moire pattern B tilted with an angle $+\theta$; if the grating $G1$ is moved a distance $\mathrm{\Delta }y$ in the $y$-direction, the Moire pattern will move a distance $\mathrm{\Delta }X=\mathrm{\Delta }Y/\tan \theta$ in the $x$-direction. Pattern $A$ and pattern $B$ have opposite phase. Pattern $A^{\prime }$ is identical to pattern $A$, but the position is the opposite of pattern $A$.

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.

3.1.

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 $DX=DY(1/\tan \theta )$ in the $X$-direction. The factor ($1/\tan \theta$) 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, $1/\tan \theta$, 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.

Fig. 3

Combination of Moire photoresist patterns. (a) The first mask pattern. (b) The second mask pattern. (c) Double exposed image. (d) Patterns after development used for ADM. There are seven pairs of zigzag and straight lines.

Fig. 4

Example of double exposed patterns. Dot-dashed line represents the case where the $Y$-direction shift $\mathrm{\Delta }$ is zero.

Fig. 5

Solid line represents the case where the $Y$-direction shift is $\mathrm{\Delta }$. $X1$, $X2$, and $X3$ are the coordinates of the marks shifted by the multiplied shift, $\mathrm{\Lambda }$.

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

${\mathrm{\Lambda }}_{\text{measured}}$ can be expressed in terms of the true value $\mathrm{\Lambda }$.

Using Eqs. (6) and (7), $\mathrm{\Delta }$ can be rewritten as

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

Referring to Eqs. (11) and (10), $\epsilon$ is expressed as

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.

Fig. 6

Laser beam shaped into an elliptic spot. The short axis is about $4\text{-}\mu \mathrm{m}$ long with a $40\text{-}\mu \mathrm{m}$ long axis. Seven marks make up a row with a pitch of $d=4\mu \mathrm{m}$.

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 $d=4\mu \mathrm{m}$ 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 $1\sigma$.

Fig. 7

ADM patterns and one-dimensional laser scanning system (LSA). There are three rows of seven wedge-shaped patterns along the $X$-direction with a pitch of $4\mu \mathrm{m}$.

Fig. 8

Waveform of LSA signals.

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

Fig. 9

Design details of ADM patterns.

Table 1

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

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.

Fig. 10

Relationship between the precision and the magnification, $K$. The vertical axis shows the optical registration metrology system $3\sigma$ precision. The horizontal axis shows ADM magnification $K$. Five data points for different $K$ values are plotted. The solid line corresponds to a $x^{-1}$ dependence.

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

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

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 $3{\sigma }_{\mathrm{ArF},\mathrm{CMOS}}=0.5\mathrm{nm}$,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)

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

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 $2E_{\mathrm{n}}$ 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.