211 and 213 enter the detectors and the higher order diffractions do not enter the detectors and, thus, do not enter the optical system 220. In some embodiments, the overlay measurement patterns 206 and 208 are consistent with the overlay measurement patterns of FIGS. 6A, 6B, 7A, and 8.

FIGS. 3A, 3B and 3C respectively illustrate a substrate 232 having two overlay measurement patterns 206 and 208 having an overlay shift (FIG. 3A), negative and positive first order diffractions 210A and 210B as a function of the overlay shift (FIG. 3B), and a difference of the first order diffracted light intensities as a function of an overlay shift distance 302 (FIG. 3C). FIG. 3A is consistent with FIG. 2A with a difference that the overlay measurement pattern 206 of the resist material layer 203 on top of the second layer 202 is shifted with respect to the overlay measurement pattern 208 by the overlay shift distance 302 in the positive X-direction. The overlay shift distance 302 is a distance between the center (e.g., the center of mass or the center of the center pattern) of the two overlay measurement patterns 206 and 208.

FIG. 3B shows light intensities of the negative and positive first order diffractions 211 and 213 as a function of the overlay shift distance 302. In some embodiments, FIG. 3B respectively shows the signals corresponding to the negative and positive detected first order diffractions 211 and 213 that are detected by the detectors 222 of the optical system 220 of FIG. 2B. In some embodiments, the analyzer module 230 receives corresponding signals of detected negative and positive first order diffractions 211 and 213 and subtracts the signal corresponding to the negative first order diffractions 211 from the signal corresponding to the positive first order diffractions 213 to generate an asymmetry (AS) function 320 (FIG. 3C). As shown in FIG. 3B, the signal corresponding to the negative first order diffractions 211 has an intensity peak in the negative region of the overlay shift distance 302 and the signal corresponding to the positive first order diffractions 213 has an intensity peak in the positive region of the overlay shift distance 302. Also, FIG. 3B shows that the signals corresponding to the detected negative and positive first order diffractions 211 and 213 are symmetric with respect to the intensity coordinate 304. Although the overlay shift distance 302 is displayed as the shift between the edges of the boxes of the overlay measurement patterns 206 and 208, the origin of the overlay measurement patterns 206 and 208 may be defined as the center of the overlay measurement patterns 206 and 208 and the overlay shift distance 302 can be defined with respect to a shift in the center of the overlay measurement patterns 206 and 208. In some embodiments, the signals corresponding to the negative first order diffraction 211 and the positive first order diffraction 213 are consistent with the signals that are detected by the detectors 222 of FIG. 8.

FIG. 3C shows the AS function 320 as a function of the overlay shift distance 302. Because the signals corresponding to the detected negative and positive first order diffractions 211 and 213 are symmetric with respect to the intensity coordinate 304, the AS function 320 passes through the origin. In some embodiments, the AS function may be written as equation (1):

A
⁢
S

=

k
.

sin

[

(

2
⁢
Π

P

)

.

(
S
)

]

Eq
.

(
1
)

where P is a pattern (grating) pitch, S is the overlay shift distance 302, and k is determined based on the light wavelength and a layer structure (e.g., thickness, refractive index, and absorption coefficient) of the first layer, the second layer, and the resist material layer. In some embodiments, when the overlay shift distance 302 is small compared to the pattern pitch P, the AS function may be written as equation (2):

A
⁢
S

=

k
.

(

2
⁢
Π

P

)

.

(
S
)

Eq
.

(
2
)

K
=

k
.

(

2
⁢
Π

P

)

where is the slope 322 of the AS function 320 at the origin in FIG. 3C.

FIG. 4 illustrates an exemplary overlay measurement pattern. The overlay measurement pattern 400 of FIG. 4 that may be used as the overlay measurement pattern 206 of FIG. 2B or the overlay measurement pattern 516 of FIG. 8 and may be produced in the resist material layer 203 has four different overlay measurement patterns. In some embodiments, when the overlay measurement pattern 400 on the top coincides with the bottom overlay measurement pattern 208 of FIG. 2B, the upper right portion 402 and the lower left portion 404 of the overlay measurement pattern 400 respectively have an initial shift of −D and +D in the positive X-direction with respect to the bottom overlay measurement pattern 208. In some embodiments, the overlay measurement pattern 400 on the top is placed with an X-direction overlay error OV, e.g., overlay placement error in the X-direction, over the bottom overlay measurement pattern 208 and thus the AS function between the upper right portion 402 and the bottom overlay measurement pattern 208 becomes equation (3):

A
⁢
S
⁢
1

=

k
.

sin

[

(

2
⁢
Π

P

)

.

(

O
⁢
V

-
D

)

]

Eq
.

(
3
)

which is a point on the AS function 320 of FIG. 3C with a shift S=(OV−D). The AS function between the upper right portion 402 and the bottom overlay measurement pattern 208 may be approximated as AS1=K.(OV−D), which is a point on the slope 322 of the AS function 320 of FIG. 3C with the shift S=(OV−D). Also, the AS function between the lower left portion 404 and the bottom overlay measurement pattern 208 becomes equation (4):

A
⁢
S
⁢
2

=

k
.

sin

[

(

2
⁢
Π

P

)

.

(

O
⁢
V

+
D

)

]

Eq
.

(
4
)

which is a point on the AS function 320 of FIG. 3C with a shift S=(OV+D). The AS function between the lower left portion 404 and the bottom overlay measurement pattern 208 may be approximated as AS2=K.(OV+D), which is a point on the slope 322 of the AS function 320 of FIG. 3C with the shift S=(OV+D). Thus, by using the optical system 220 of FIG. 2B and measuring the detected negative and positive first order diffractions 211 and 213, the AS function value AS1 between the upper right portion 402 of the overlay measurement pattern 400 and the bottom overlay measurement pattern 208 and the AS function value AS2 between the lower left portion 404 of the overlay measurement pattern 400 and the bottom overlay measurement pattern 208 can be determined and the overlay error OV in the X-direction may be determined as:

O
⁢
V

=

D
.

(

AS
⁢
1

+

AS
⁢
2

A
⁢
S
⁢
2

-

A
⁢
S
⁢
1

)

Eq
.

(
5
)

In some embodiments, when the overlay measurement pattern 400 on the top coincides with the bottom overlay measurement pattern 208, the upper left portion 401 and the lower right portion 405 of the overlay measurement pattern 400 respectively have an initial shift of −D and +D in the positive Y-direction with respect to the bottom overlay measurement pattern 208. Thus, the overlay error in the Y-direction may similarly be determined.

In some embodiments, as shown in FIGS. 1A and 1B, the extent 113 of each portion of the overlay measurement pattern 400 or the overlay measurement patterns 206 and 208 is between 300 nm and 40,000 nm. A CD of the sub-patterns, e.g., boxes, of each portion of the overlay measurement pattern 400 or the overlay measurement patterns 206 and 208 is between 10 nm and 1400 nm. A pitch between the sub-patterns of each portion of the overlay measurement pattern 400 or the overlay measurement patterns 206 and 208 is between 100 nm and 1500 nm. In some embodiments, the upper layer and lower layer measurement patterns of FIGS. 6A, 6B, and 7A are repeated in the four quadrants similar to FIG. 4. Additionally, the measurement patterns of the upper layer in FIGS. 6A, 6B, and 7A respectively have the initial shifts of −D and +D in the positive Y-direction and in the positive X-direction in the four quadrants and, thus, the equations (3)-(5) may be used for determining the overlay error in FIGS. 6A, 6B, and 7A.

FIGS. 5A, 5B, 5C, and 5D respectively illustrate an overlay measurement pattern 520, e.g., a combination of two overlay measurement patterns in the same layer, with different pitches on a substrate, an incident light beam and first order diffractions reflected from the combination of the two overlay measurement patterns on the substrate, a graph of intensity/amplitude of the diffracted light from the substrate, and a top view of the overlay measurement pattern 520 in accordance with some embodiments of the present disclosure. FIG. 5A illustrates a substrate 500 that has the underlying substrate 200 and the overlay measurement pattern 520 disposed on the underlying substrate 200. The overlay measurement pattern 520 includes a first measurement pattern, e.g., a first grating, having sub-patterns 522, e.g., dark strips, consistent with the dark strips 114 of FIGS. 1A and 1B, that has an equal distance, a first pitch 535, between each two neighboring sub-patterns 522. The combination of two overlay measurement patterns also includes a second measurement pattern, e.g., a second grating, having sub-patterns 524, e.g., dark strips, consistent with the dark strips 114 of FIGS. 1A and 1B, that has an equal distance, a second pitch 537, between each two neighboring sub-patterns 524. In some embodiments, the first pitch 535 is between 2 to 10 times (e.g., natural number times) larger than the second pitch 537 and, thus, between 2 to 10 sub-patterns 524 are distributed in the interval of the first pitch 535 between each two neighboring sub-patterns 522. In some embodiments, the critical dimension (CD) is the size of a feature on a semiconductor circuit that impacts the electrical properties of the device and, thus, the semiconductor manufacturing process steps are designed to avoid affecting the CD of the layout pattern of the layers. As shown in FIG. 5A, in some embodiments, because the first pitch 535 of the sub-patterns 522 of a layer is much larger than the CD, by adding extra sub-patterns 524, between the sub-patterns 522, the pitch of the overlay measurement pattern is reduced and becomes comparable with the CD of the semiconductor circuit. Thus, the semiconductor manufacturing process steps do not impact the combination of the sub-patterns 522 and sub-patterns 524.

FIG. 5B shows the substrate 500 of FIG. 5A and additionally includes an incident light beam 542 that is incident on the substrate 500 and two first order diffractions 546 and 548 that are reflected from the substrate 500, e.g., reflected from the overlay measurement pattern 520. In some embodiments, the incident light beam 542 is transmitted along a perpendicular line 540, which is perpendicular to a surface 201 of the underlying substrate 200. The first order diffraction 546 is a negative first order diffraction that is reflected from the first grating, having the sub-patterns 522. The first order diffraction 546 has an angle θ₁with the line 540. Another first order diffraction 548 is a negative first order diffraction that is reflected from the second grating, having the sub-patterns 524. The first order diffraction 548 has an angle θ₃with the perpendicular line 540. In some embodiments, a ratio between the tangent of the angle θ₃to the tangent of the angle θ₁is the ratio between the first pitch 535 and the second pitch 537. Thus, in some embodiments, the angle θ₃is about 2 to about 4 times, e.g., about 3 times, the angle θ₁. For each one of the negative first order diffractions 546 and 548 a positive first order diffraction is also reflected from the substrate 500. The positive first order diffractions (not shown) are reflected in a direction such that the positive and negative first order diffractions are symmetrical with respect to perpendicular line 540. In some embodiments and consistent with FIGS. 2A and 2B, the overlay measurement pattern 520 is disposed in the first layer 204 such that the first layer 204 covers the overlay measurement pattern 520.

FIG. 5C shows the graphs of light intensity per reflected angle of the diffracted light from the overlay measurement pattern 520 of the substrate 500. The light intensity is shown on an intensity coordinate 502 and the reflected angles are shown on an angle coordinate 508. The diffraction patterns are reflected from the overlay measurement pattern 520 when the incident light beam 542 is directed to the surface 201 of the substrate 500 and irradiates the overlay measurement pattern 520 that includes the first grating of the sub-patterns 522 and the second grating of the sub-patterns 524. A graph 506 is the diffraction patterns associated with the sub-patterns 522 and a graph 504 is associated with the sub-patterns 524. As shown, the graphs 506 and 504 are displayed in the intensity coordinate 502 versus the angle coordinate 508. In some embodiments, the first bump of the graph 506 at the angle θ₁corresponds to the first order diffraction from the first grating of the sub-patterns 522 and the second bump of the graph 506 at the angle θ₂corresponds to the second order diffraction from the first grating of the sub-patterns 522. In some embodiments, the third bump of the graph 506 at the angle θ₃, corresponds to the third order diffraction from the first grating of the sub-patterns 522. In some embodiments, as shown in FIG. 5C, the third bump of the graph 506 coincides with the first bump of the graph 504 at the angle θ₃. In some embodiments and referring back to FIG. 5B, the first bump of the graph 506 at the angle θ₁is consistent with the negative first order diffraction 546 that is reflected from the first grating, however, the higher order diffractions having angles greater than θ₁with the perpendicular line 540 that are reflected from the first grating, having the sub-patterns 522, are not shown in FIG. 5B. In some embodiments, the first bump of the graph 504 at the angle θ₃is consistent with the negative first order diffraction 548 that is reflected from the second grating. The higher order diffractions having angles θ₄and θ₅that are reflected from the second grating, having the sub-patterns 524, are not shown in FIG. 5B.

In some embodiments, the first grating of the sub-patterns 522 and the second grating of the sub-patterns 524 are repeated and, thus, are period structures. In some embodiments, the first, second, third, etc. bumps at the angles θ₁, θ₂, θ₃, etc., of the graph 506, correspond to the frequency content, e.g., Fourier series components, of the first grating of the sub-patterns 522. Similarly, the first, second, third, etc. bumps at the angles θ₃, θ₄, θ₅, etc., of the graph 504, correspond to the frequency content, e.g., Fourier series components, of the second grating of the sub-patterns 524

FIG. 5D shows a top view of the overlay measurement pattern 520. The overlay measurement pattern 520 includes the sub-patterns 522 that are distributed in the X-direction with the first pitch 535 and extend in an interval 519 in the Y-direction. The overlay measurement pattern 520 also includes the sub-patterns 524 that are distributed in the X-direction with the second pitch 537 and extend in an interval 517 in the Y-direction.

FIGS. 6A and 6B respectively illustrate cross-sectional views of a substrate 602 having an underlying substrate 200, the first layer 204 on top of the underlying substrate 200 having an overlay measurement pattern, a second layer 202 on top of the first layer 204, and another overlay measurement pattern over the second layer 202 in accordance with some embodiments of the present disclosure. FIG. 6A shows the overlay measurement pattern 520 in the first layer 204 over the underlying substrate 200 and the overlay measurement pattern 516 that is above the second layer 202. As discussed, the second layer 202 is disposed above the first layer 204 and the resist material layer 203 that includes the overlay measurement pattern 516 is disposed over the second layer 202. FIG. 6A shows a pitch 535 between sub-patterns 518 of the overlay measurement pattern 516, e.g., the upper overlay measurement pattern. The overlay measurement pattern 520, e.g., the lower overlay measurement pattern includes a combination of two overlay measurement patterns, the sub-patterns 524 and the sub-patterns 522. In some embodiments, the pitch between the sub-patterns 522 is the same as the pitch 535 between the sub-patterns 518 of the overlay measurement pattern 516. In some embodiments, a pitch 537 exist between the sub-patterns 524, and the pitch 537 is smaller than the pitch 535, for example, the pitch 537 is one third of the pitch 535.

FIG. 6B shows an overlay measurement pattern 530 in the first layer 204 over the underlying substrate 200 and an overlay measurement pattern 526 that is above the second layer 202. As discussed, the second layer 202 is disposed above the first layer 204 and the resist material layer 203 that includes the overlay measurement pattern 526 is disposed over the second layer 202. FIG. 6B shows a pitch 536 between sub-patterns 528 of the overlay measurement pattern 526, e.g., the upper overlay measurement pattern. The overlay measurement pattern 530, e.g., the lower overlay measurement pattern has sub-patterns 534 and sub-patterns 532. In some embodiments, the pitch between the sub-patterns 532 is the same as the pitch 536 between the sub-patterns 528 of the overlay measurement pattern 526. The overlay measurement pattern 530 also includes sub-patterns 534 with a pitch 538 of, for example, one fourth of the pitch 536. In some embodiments, a material and the height 119 of the sub-patterns 532 and the sub-patterns 534 are the same and, thus, the sub-patterns 532 and 534 are disposed together by depositing a layer on the underlying substrate 200 and etching the layer to simultaneously generate both sub-patterns 532 and 534. In some embodiments, as shown in FIG. 6B, two or more sub-patterns 532 and sub-patterns 534 are etched as one segment and, thus, one sub-pattern 532 and an adjacent sub-pattern 534 are generated as one segment. As shown in FIG. 6B, every fourth of the sub-patterns 534 is connected from the left side to a right side of one of the sub-patterns 532.

FIG. 7A shows the substrate 602 of FIG. 6A that includes the overlay measurement pattern 520 in the first layer 204 over the underlying substrate 200 and the overlay measurement pattern 516 that is above the second layer 202. As shown in FIG. 7A, a light source of an optical system consistent with the light source 226 of the optical system 220 transmits an incident light beam 542 consistent with the incident light beam 214 of FIG. 2B to the overlay measurement patterns 516 and 520. As shown in FIG. 7A, a first order diffraction 544 that is consistent with the negative first order diffraction 210A of FIG. 2B is reflected from the overlay measurement pattern 516. Also, a first order diffraction 546 that is consistent with the negative first order diffraction 212A of FIG. 2B is reflected from the overlay measurement pattern 520. In addition, another negative first order diffraction 548 is reflected from the overlay measurement pattern 520. In some embodiments, the negative first order diffraction 546 is reflected from the sub-patterns 522 of the overlay measurement pattern 520 having the pitch 535 and the negative first order diffraction 548 is reflected from the sub-patterns 524 of the overlay measurement pattern 520 having the shorter pitch 537. The shorter pitch 537 is about ½ to ⅕, e.g., ⅓, of the pitch 535 in some embodiments.

In addition, as shown in FIG. 7A, the negative first order diffraction 544 from the sub-patterns 518 and the negative first order diffraction 546 from the sub-patterns 522 are in parallel and have an angle θ₁with respect to the perpendicular line 540 and, thus, may be combined. Also, as shown in FIG. 7A, the negative first order diffraction 548 from the sub-patterns 524 has an angle θ₃with the perpendicular line 540. In some embodiments, as discussed above, the pitch 535 is about two time to about five times, e.g., about 3 times, the pitch 537 and, thus, the tangent of the angle θ₃is about two time to about five times the tangent of the angle θ₁, e.g., is about 3 times the tangent of the angle θ₁. Thus, the negative first order diffraction 548 may be isolated from the negative first order diffraction 544 and the negative first order diffraction 546. As noted above, the positive first order diffractions (not shown) are also reflected from the overlay measurement pattern 516 and the overlay measurement pattern 520. The positive first order diffractions are in a direction such that the positive and negative first order diffractions are symmetrical with respect to the perpendicular line 540.

FIG. 7B shows the graphs of light intensity per reflected angle of the diffracted light from the overlay measurement pattern 516 and the overlay measurement pattern 520 of the substrate 602. The light intensity is shown on an intensity coordinate 712 and the reflected angles are shown on an angle coordinate 714. The diffraction patterns are reflected from the overlay measurement pattern 516 and the overlay measurement pattern 520 when the incident light beam 542 is directed to the substrate 602 as shown in FIG. 7A. A graph 702 is the diffraction patterns associated with the sub-patterns 522 of the overlay measurement pattern 520 and a graph 706 is associated with the sub-patterns 524 of the overlay measurement pattern 520. In addition, a graph 704 is associated with the sub-patterns 518 of the overlay measurement pattern 516. As shown, the graphs 702, 704, and 706 are displayed in the intensity coordinate 712 versus the angle coordinate 714. In some embodiments, the first bump of the graph 702 at the angle θ₁corresponds to the first order diffraction from the sub-patterns 522 of the overlay measurement pattern 520 and the second bump of the graph 702 at the angle θ₂corresponds to the second order diffraction from the sub-patterns 522. In addition, because the sub-patterns 522 of the overlay measurement pattern 520 and the sub-patterns 518 of the overlay measurement pattern 516, have the same pitch 535, the first bump of the graph 704 corresponding to the first order diffraction from the sub-patterns 518 of the overlay measurement pattern 516 is also observed at the angle θ₁. In addition, the first order diffraction from the sub-patterns 518 of the overlay measurement pattern 516 and the first order diffraction from the sub-patterns 522 of the overlay measurement pattern 520 that travel the same direction may be combined.

In some embodiments, as shown in FIG. 7B, the third bump of the graphs 702 and 704, coincide with the first bump of the graph 706 at the angle θ₃. Thus, the first order diffraction from the sub-patterns 522 of the overlay measurement pattern 520 and first order diffraction from the sub-patterns 518 of the overlay measurement pattern 516 travel at the same direction that is separate and distinct from the direction that the first order diffraction from the sub-patterns 524 of the overlay measurement pattern 520 travel. Therefore, the first order diffraction from the sub-patterns 522 of the overlay measurement pattern 520 and first order diffraction from the sub-patterns 518 of the overlay measurement pattern 516 may be isolated from the first order diffraction from the sub-patterns 524 of the overlay measurement pattern 520. As noted above, the semiconductor manufacturing process steps are designed to avoid affecting the CD of the layout pattern of a layer. As shown in FIGS. 6A, 6B, and 7A, in some embodiments, because the pitch of the sub-patterns 522/532 of the layer is much larger than the CD, by adding extra sub-patterns 524/534, between the sub-patterns 522/532, the pitch of the overlay measurement pattern is reduced and becomes comparable with the CD semiconductor circuit. Thus, the subsequent semiconductor manufacturing process steps do not impact the combination of the sub-patterns 522/532 and sub-patterns 524/534. In addition, the added sub-patterns 524/534 produce the negative first order diffraction 548 that may be isolated from the negative first order diffraction 544 and the negative first order diffraction 546. In some embodiments, the first order diffraction 548 is filtered, e.g., is physically blocked. Thus, only the negative first order diffraction 544 and the negative first order diffraction 546 are detected.

FIG. 7C shows the graphs 702, 704, and 706 that are displayed in the intensity coordinate 712 versus the angle coordinate 714. As shown in FIG. 7C, a segment 710 of the graphs 702, 704, and 706 is around the angle θ₁. Thus, as shown in segment 710, the first order diffraction from the sub-patterns 518 of the overlay measurement pattern 516 (the bump of the graph 702 at the angle θ₁) and the first order diffraction from the sub-patterns 522 of the overlay measurement pattern 520 (the bump of the graph 704 at the angle θ₁) may be combined. However, as the first order diffraction from the sub-patterns 524 is negligible in segment 710 (the graph 706 is negligible), the first order diffraction from the sub-patterns 524 may be isolated from the first order diffraction from the sub-patterns 518 of the overlay measurement pattern 516 and the first order diffraction from the sub-patterns 522 of the overlay measurement pattern 520.

FIG. 8 illustrates a measurement system for determining an overlay error in accordance with some embodiments of the disclosure. The measurement system of FIG. 8 shows the substrate 602 that is mounted on a stage 551 and the stage 551 that is coupled to and controlled by a stage controller 560. FIG. 8 also shows the optical system 220 that is mounted above the substrate 602. In some embodiments, one of the light sources of the optical system 220 transmits an incident light beam 515, consistent with the incident light beams 214 and 542 of FIGS. 2B and 7A, to the overlay measurement patterns 516 and 520. A portion of the incident light beam 515 is diffracted and reflected from the overlay measurement pattern 516 and produces the negative and positive first order diffractions 583A and 583B (at the angle θ₁with the perpendicular line 540) that are inner portions of first order diffractions 582 and 586 respectively. A remaining portion of the incident light beam 515 passes through the overlay measurement pattern 516 and the second layer 202 and gets diffracted and reflected from the sub-patterns 522 of the overlay measurement pattern 520 of the first layer 204 and produces the negative and positive first order diffractions 585A and 585B (at the angle θ₁with the perpendicular line 540) that are outer portions of first order diffractions 582 and 586 respectively. The negative and positive first order diffractions 582 and 586 are detected by the detector 222 of the optical system 220. The analyzer module 230 receives corresponding signals of the detected first order diffractions 582 and 586 and performs an analysis as described with respect to FIGS. 3B and 3C on the corresponding signals to determine a shift distance 302 between the overlay measurement patterns 516 and 520.

In addition, the remaining portion of the incident light beam 515 that passes through the overlay measurement pattern 516 and the second layer 202, also gets diffracted and reflected from the sub-patterns 524 of the overlay measurement pattern 520 of the first layer 204 and produces the negative and positive first order diffractions 525A and 525B (at the angle θ₃with the perpendicular line 540). Also, FIG. 8 shows apertures 550 (or pupil filters) of the detectors 222 of the optical system 220. The reflected and diffracted light may pass through the apertures 550 to the detectors 222. The barriers 601 outside the apertures 550 are used to block the diffractions from entering the optical system and being detected by the detectors 222. In some embodiments, the numerical aperture of the detectors 222 are designed such that the negative and positive first order diffractions 525A and 525B do not enter the detectors 222.

FIG. 9 illustrates an exemplary measurement system for determining an overlay error in accordance with some embodiments of the disclosure. The system 900 includes an analyzer module 930 and a main controller 940 coupled to each other. The analyzer module 930, which is consistent with the analyzer module 230 of FIGS. 2B and 8 receives one or more layout patterns 910 to be generated in the first layer 204 and the resist material layer 203. The analyzer module 930 may either directly connect to an optical system 904 or may connect to the optical system 904 via the main controller 940. In some embodiments, the analyzer module 930 receives a process information 912 that includes information of the semiconductor process steps for creating the semiconductor devices and also includes the sizes of the critical dimension of the devices and the connection lines. In some embodiments, a stage controller 902 is consistent with the stage controller 560 of FIG. 8.

In some embodiments, the main controller 940 is coupled to a process controller 906, the optical system 904, and the stage controller 902. In some embodiments and returning back to FIGS. 2B and 8 the optical system 904 is consistent with the optical system 220. The optical system 904, which is controlled by the main controller 940, generates the incident light beams 214, 515, and 542 of FIGS. 2B, 7A, and 8. In addition, the optical system 904 receives the diffracted light from the overlay measurement patterns and detects the diffracted light and generates corresponding signals of the detected diffracted light. The optical system 904 sends the corresponding signals of the detected diffracted light to the analyzer module 930 for analysis as described above to determine a shift distance between overlay measurement patterns 516 and 520 of the substrate 602.

In some embodiments, the analyzer module 930 sends the one or more layout patterns 910 directly or via the main controller 940 to the process controller 906 and commands the process controller 906 to produce, e.g., to deposit, the one or more layout patterns 910 in the first layer 204 and the resist material layer 203. As described, the overlay measurement pattern of the lower layer, e.g., the overlay measurement pattern 520 of FIGS. 6A, 7A, and 8 in addition to having the sub-patterns 522 with the same pitch as the sub-patterns 518 of the resist material layer 203, includes another more dense sub-patterns 524. In some embodiments, a pitch of the sub-patterns 522 is about 2 to about 20 times, e.g., about 3 times, longer than the pitch of the sub-patterns 524. In some embodiments, as the pitch of the sub-patterns 524 decreases, the angle θ₃, with respect to the perpendicular line 540, of the first order diffraction 548 generated by the sub-patterns 524 increases. Thus, in some embodiments, the pitch of the sub-patterns 524 and width of the sub-patterns 522 and/or 524 are selected such that the overlay measurement pattern 520 of FIGS. 6A, 7A, and 8 has about the same pitch size as the critical dimension of the devices that are created on the underlying substrate 200. In some embodiments, the critical dimension of the devices (e.g., a width of a fin structure or a width of a gate pattern) is between 10 nm and 50 nm and the pitch size of the overlay measurement pattern 520 is between about 10 nm and about 50 nm. In some embodiments, the overlay measurement pattern 520 has a pitch size that is in the range between 50 percent less than the average critical dimension of the devices and 50 percent more than the average critical dimension of the devices, e.g., the pitch size of the overlay measurement pattern 520 is between about 5 nm and about 75 nm.

FIG. 10 illustrates a flow diagram of an exemplary process 1000 for determining an overlay error, e.g., a shift distance 302, between the overlay measurement patterns 516 and 520, in accordance with some embodiments of the disclosure. The process 1000 may be performed by the measurement systems of FIGS. 8 and 9. In some embodiments, a portion of the process 1000 is performed and/or is controlled by the computer system 1100 described below with respect to FIGS. 11A and 11B. The method includes the operation S1002 that a first pattern having a first plurality of first sub-patterns with a first pitch is created, e.g., is disposed, in a lower-layer pattern (e.g., a lower-layer overlay measurement pattern) over a substrate. As shown in FIGS. 6A and 7A, the first pattern of the first plurality of sub-patterns 522 with a pitch 535 is created in the first layer 204.

In operation S1004, a second pattern having a second plurality of second sub-patterns with a second pitch smaller than the first pitch is created in the lower-layer pattern over the substrate. As shown in FIGS. 6A and 7A, the second pattern of the second plurality of second sub-patterns 524 with a pitch 537 smaller than the pitch 535 is created in the first layer 204 that is over the substrate 200 and the sub-patterns 524 are interleaved between the sub-patterns 522.

In operation S1006, a reflected first order diffracted light, e.g., the first order diffraction 548 or 525A of FIG. 7A or 8, associated with the pitch 537 from the lower-layer pattern is blocked and does not enter the detector 222.

In operation S1008, a third pattern having the first pitch is created in an upper-layer pattern (e.g., an upper-layer overlay measurement pattern). The upper-layer pattern at least partially overlapping the lower-layer pattern. As shown in FIGS. 6A and 7A, the third pattern of sub-patterns 518, which has the same pitch 535 as the sub-patterns 522, is created in the resist material layer 203. The third pattern of the sub-patterns 518 at least partially overlap the first pattern of the sub-patterns 522.

In operation S1010, an overlay error between the lower-layer pattern and the upper-layer pattern is determined based on diffracted light from the upper-layer pattern and diffracted light associated with the first pitch from the lower-layer pattern. As shown in FIGS. 8, the optical system 220 transmits the incident light beam 515 to the overlay measurement pattern