CN101556431A - Translational symmetrical mark and in-situ detection method of wave aberration of projection objective of photoetching machine - Google Patents

Abstract

The invention relates to a translational symmetrical mark and an in-situ detection method of wave aberration of a projection objective of a photoetching machine. The translational symmetrical mark consists of an X-direction translational symmetrical grating mark and a Y-direction translational symmetrical grating mark; the structure of one period of the translational symmetrical grating mark is as follows: each period consists of ten line areas which have a certain width and are parallelly and sequentially arranged without interval; the first and the sixth are light-tight areas, the second, the fourth, the eighth and the tenth are non-light tight areas with phase shift of 180 degrees; and the third, the fifth, the seventh and the ninth are non-light tight areas with phase shift of 0 degrees. The translational symmetrical phase-shifting mask grating mark is used for carrying out in-situ detection to wave aberration of the projection objective of the photoetching machine, so the sensitivity of wave aberration of the projection objective of the photoetching machine can be improved more.

Description

Translation symmetry mark and in-situ detection method of wave aberration of projection objective of photoetching machine

Technical field

The present invention relates to wave aberration of photo-etching machine projection objective in situ detection technology, relate in particular to a kind of translation symmetry mark and in-situ detection method of wave aberration of projection objective of photoetching machine.

Background technology

Litho machine is the nucleus equipment in the great scale integrated circuit manufacturing process.Projection objective system is one of most important subsystem of litho machine.The wave aberration of projection objective can reduce the optical patterning quality, reduces lithographic process window.In the projection objective imaging process, coma makes aerial image produce the lateral attitude skew, increases litho machine alignment error; Coma also can cause the live width of imaging figure asymmetric, increases the CD unevenness in the exposure visual field.Spherical aberration causes the optimal focal plane skew of exposure figure, and the litho machine depth of focus is reduced.Along with constantly reducing of lithographic feature size, the use of especially various resolution enhance technology, projection objective wave aberration is more and more outstanding to the influence of optical patterning quality.High-precision projection objective wave aberration in situ detection technology can provide in time data reliably for the correction of wave aberration, is an important photoetching machine technique.

TAMIS (TIS At Multiple Illumination Settings) technology is to be used to one of major technique that detects wave aberration of photo-etching machine projection objective at present in the world.(referring to technology 1 formerly, Hans van der Laan, Marcel Dierichs, Henk van Greevenbroek, Elaine McCoo, Fred Stoffels, RichardPongers, Rob Willekers. " Aerial image measurement methods for fastaberration set-up and illumination pupil verification. " Proc.SPIE 2001,4346,394-407.) the TAMIS technology adopts the test badge based on the binary mask figure, axial optimal focal plane side-play amount and lateral attitude side-play amount when measuring the test badge imaging calculate the spherical aberration and the coma of projection objective.This technology can reach 3nm and 2nm to the accuracy of detection of spherical aberration and coma respectively under the 3sigma condition.The wave aberration accuracy of detection of this technology is by the aberration sensitivity decision of test badge.Aberration sensitivity is big more, and its accuracy of detection is high more.The grating that the TAMIS choice of technology is made up of common binary mask figure is as test badge (as shown in Figure 1), ignore the difference between the aberration sensitivity of the test badge that the different types mask graph forms, limited the further raising of wave aberration accuracy of detection.

On the basis of TAMIS technology, people such as FAN WANG have proposed a kind of wave aberration of photo-etching machine projection objective in situ detection technology based on the phase shifting mask test badge.(referring to technology 2 formerly, Fan Wang, Xiangzhao Wang, Mingying Ma, Dongqing Zhang, Weijie Shi and Jianming Hu, " Aberrationmeasurement of projection optics in lithographic tools by use of analternating phase-shifting mask; " Appl.Opt.45,281-287 (2006) .) this technology utilizes phase shifting mask figure (as shown in Figure 2) to replace binary mask figure (as shown in Figure 1) as test badge, utilize the phase shifting mask advantage more highly sensitive, improve accuracy of detection than the aberration of binary mask.It is 250nm that this technology adopts live width, line empty than be 1: 1 symmetric form phase shifting mask grating as test badge, according to existing wave aberration computation model, calculate the spherical aberration and the coma of imaging optical system to be measured.Formerly technology 2 is by changing the mask graph of forming certification mark, makes the accuracy of detection of projection objective spherical aberration and coma has been improved 20% and 30% than technology 1 formerly respectively.

Because formerly technology 2 has been ignored the influence of phase shifting mask optical grating construction to wave aberration sensitivity, further do not improve accuracy of detection by optimizing optical grating construction, based on technology 2 formerly, people such as Zicheng Qiu have proposed a kind of asymmetric phase shifting mask grating marker (as shown in Figure 3) that is used for the projection objective wave aberration in situ detection.(referring to technology 3 formerly, Zicheng Qiu, Xiangzhao Wang, Qiongyan Yuan, and Fan Wang, " Coma measurement by use of an alternating phase-shifting mask mark witha specific phase width ", APPLIED OPTICS, Vol.48, No.2261-269 (2009)).People such as Ziheng Qiud are the scarce level that has realized mark ± 3 order diffraction light 2/3rds of the cycle by optimizing the structure of phase shifting mask grating thereby make the phase place peak width, the wave aberration sensitivity that has improved mark, and then improved accuracy of detection.Yet, formerly technology 3 does not have to consider to make the situation of more senior the scarce level of diffraction light, and the amplitude of the raising by original phase shifting mask optical grating construction being optimized the accuracy of detection of bringing is also limited, therefore utilize the principle of beam interference imaging, redesign new grating marker, make the more scarce level of diffraction light of multilevel, the wave aberration sensitivity that continues the raising test badge is an effective way that improves wave aberration in situ detection precision.

Summary of the invention

Present invention focuses on to provide a kind of translation symmetry mark and in-situ detection method of wave aberration of projection objective of photoetching machine, this method is improved the projection objective wave aberration accuracy of detection.

Technical solution of the present invention is as follows:

A kind of translation symmetry grating marker, its characteristics are to be made up of directions X translation symmetry grating marker and Y direction translation symmetry grating marker, the grating lines of described directions X translation symmetry grating marker are arranged along directions X, the grating lines of described Y direction translation symmetry grating marker are arranged along the Y direction, and the structure of the one-period of this translation symmetric form grating marker is:

Each cycle is made up of parallel no spaced 10 lines zones with certain width successively, 6th, the 7th, the 8th, the 9th, the 10th lines zone equates that with the width in the 1st, the 2nd, the 3rd, the 4th, the 5th lines zone the ratio of the width in described the 1st, the 2nd, the 3rd, the 4th, the 5th lines zone is: 90: 481: 43: 102: 83 respectively;

The the described the 1st and the 6th is light tight zone, and the described the 2nd, the 4th, the 8th and the 10th is 180 ° of phase shift transmission regions, and the described the 3rd, the 5th, the 7th and the 9th is the transmission region of 0 ° of phase shift;

The span in described cycle is: (wherein, λ is the wavelength of photo-etching machine illumination light source for 5.3846-0.6,5.3846+0.6) λ/NA, but NA is the interior maximal value of projection lens of lithography machine numerical aperture variation range and the mean value of minimum value;

The span of the transmitance of described transmission region is 95%～100%.

The deviation of the phase-shift phase of described transmission region is ± 10%.

The optimal value in described grating cycle is 5.3846 λ/NA, and the optimal value of the width in described the 1st, the 2nd, the 3rd, the 4th, the 5th lines zone is respectively: 0.3033 λ/NA, 1.6208 λ/NA, 0.1449 λ/NA, 0.3437 λ/NA and 0.2797 λ/NA.

Utilize above-mentioned translation symmetry grating marker to in-situ detection method of wave aberration of projection objective of photoetching machine, comprise the following steps:

(1) spherical aberration of labeling projection object lens, coma and astigmatism sensitivity coefficient: utilize lithography simulation software PROLITH to demarcate the wave aberration sensitivity coefficient: sensitivity coefficient changes with the numerical aperture of projection objective and the partial coherence factor of illuminator, the variation of lighting condition is by being provided with realization in PROLITH software, the partial coherence factor variation range is 0.3～0.8, and step-length is 0.1; The numerical aperture variation range is 0.5～0.8, and step-length is 0.1, can obtain 24 groups of different lighting conditions:

{(NA _i，σ _i)|i＝1，2......24}＝{(0.5，0.3)，(0.5，0.4)......(0.8，0.8)}。

Demarcating three rank coma Z ₇Sensitivity coefficient S ₂(NA _i, σ _i) time, set certain Z ₇Value and to get other zernike coefficient be zero uses the lithography simulation computed in software to obtain by Z ₇The imaging offset Δ X (NA that causes _i, σ _i), Ci Shi sensitivity coefficient S then ₂(NA _i, σ _i) be Δ X (NA _i, σ _i) and Z ₇The ratio;

Demarcate S with method ₁(NA _i, σ _i), S ₃(NA _i, σ _i), S ₄(NA _i, σ _i), S ₅(NA _i, σ _i), S ₆(NA _i, σ _i), S ₇(NA _i, σ _i), S ₈(NA _i, σ _i), S ₉(NA _i, σ _i), S ₁₀(NA _i, σ _i), S ₁₁(NA _i, σ _i), S ₁₂(NA _i, σ _i); Obtain following four sensitivity coefficient matrix at last:

$\left[\begin{array}{ccc}{S}_1({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_2({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_3({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_1({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_2({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_3({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_1({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_2({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_3({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right],$

$\left[\begin{array}{ccc}{S}_4({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_5({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_6({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_4({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_5({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_6({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_4({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_5({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_6({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right]$

$\left[\begin{array}{ccc}{S}_7({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_8({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_9({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_7({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_8({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_9({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_7({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_8({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_9({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right]$

$\left[\begin{array}{ccc}{S}_{10}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_{11}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_{12}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_{10}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{11}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{12}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_{10}({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_{11}({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_{12}({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right];$

(2) described translation symmetry grating marker is placed and accurately is positioned on the mask platform, by projection objective at different numerical aperture NA _iWith partial coherence factor σ _iImaging under the condition: regulate partial coherence factor by illuminator, its variation range is 0.3 ~ 0.8, and step-length is 0.1; Regulate numerical aperture by projection objective, its variation range is 0.5 ~ 0.8, and step-length is 0.1, ({ (NA under 24 groups of different lighting conditions _i, σ _i) | i=1,2......24}={ (0.5,0.3), (0.5,0.4) ... (0.8,0.8) }), the lateral attitude offset X of directions X when utilizing the described directions X translation of the aerial image sensor measurement symmetric form grating marker imaging on the work stage ₄₁(AN _i, σ _i) and optimal focal plane shifted by delta Z ₄₁(NA _i, σ _i), the lateral attitude offset Y of Y direction when measuring described Y direction translation symmetric form grating marker imaging ₄₂(NA _i, σ _i) and optimal focal plane shifted by delta Z ₄₂(NA _i, σ _i);

(3), calculate the spherical aberration and the coma of projection objective according to demarcation sensitivity matrix that obtains and the side-play amount that measures:

At first, utilize following formula, the aerial image that calculates directions X translation symmetric form grating marker is at the image space shifted by delta X of directions X (NA _i, σ _i), the aerial image of Y direction translation symmetric form grating marker is at the image space shifted by delta Y of Y direction (NA _i, σ _i) and optimal focal plane offset Z _s(NA _i, σ _i) and Δ Z _Hv(NA _i, σ _i):

Δ X (NA _i, σ _i) be in difference

With The aerial image of the test badge that measures under the condition is at the image space shifted by delta X of directions X ₄₁(NA _i, σ _i), promptly

ΔX(NA _i，σ _i)＝ΔX ₄₁(NA _i，σ _i)；

Δ Y (NA _i, σ _i) be in difference

With

The aerial image of the Y direction translation symmetric form grating marker that measures under the condition is at the image space shifted by delta Y of Y direction ₄₂(NA _i, σ _i), promptly

ΔY(NA _i，σ _i)＝ΔY ₄₂(NA _i，σ _i)

Δ Z _s(NA _i, σ _i) be in difference

With

The Δ Z that measures under the condition ₄₁(NA _i, σ _i) and Δ Z ₄₂(NA _i, σ _i) mean value, promptly

ΔZ _s(NA _i，σ _i)＝[ΔZ ₄₁(NA _i，σ _i)+ΔZ ₄₂(NA _i，σ _i)]/2；

Δ Z _Hv(NA _i, σ _i) be in difference With

The Δ Z that measures under the condition ₄₁(NA _i, σ _i) and Δ Z ₄₂(NA _i, σ _i) difference, promptly

ΔZ _hv(NA _i，σ _i)＝ΔZ ₄₁(NA _i，σ _i)-ΔZ ₄₂(NA _i，σ _i)；

Then, according to the position offset that measures with demarcate the sensitivity coefficient matrix obtain, utilize the following system of equations of least square method solving equation group, obtain representing zernike coefficient Z2, Z7, Z14, Z3, Z8, Z15, Z4, Z9, Z16, Z5, Z12 and the Z21 of projecting objective coma aberration, spherical aberration and astigmatism:

$\left[\begin{array}{c}\mathrm{\&Delta;X}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;X}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_1({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_2({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_3({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_1({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_2({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_3({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_2\\ Z_7\\ Z_{14}\end{array}\right],$

$\left[\begin{array}{c}\mathrm{\&Delta;Y}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;Y}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_4({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_5({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_6({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_4({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_5({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_6({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_3\\ Z_8\\ Z_{15}\end{array}\right],$

$\left[\begin{array}{c}\mathrm{\&Delta;}{Z}_s({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;}{Z}_s({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_7({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_8({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_9({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_7({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_8({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_9({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_4\\ Z_9\\ Z_{16}\end{array}\right],$

$\left[\begin{array}{c}\mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_{10}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_{11}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_{12}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_{10}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{11}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{12}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_5\\ Z_{12}\\ Z_{21}\end{array}\right].$

The present invention has been owing to adopted technique scheme, compares with technology formerly (formerly technology 1, formerly technology 2), has the following advantages:

The even level of the diffraction light of translation symmetric form phase shifting mask grating marker, ± 3 and ± 5 order diffraction light all lack level, so the wave aberration of this mark is highly sensitive in technology 1 formerly and the wave aberration sensitivity of the test badge in the technology 2 formerly.The coma linear model of three kinds of marks as shown in figure 10, as we know from the figure, the slope maximum of the straight line of translation symmetric form phase shifting mask grating marker, i.e. its coma sensitivity maximum, when using this marker detection coma, its precision is the highest.Process is to the simulation calculation of mark among the present invention to the sensitivity of coma, spherical aberration and astigmatism, can be sure of that translation symmetric form phase shifting mask grating marker has higher relatively wave aberration sensitivity, as test badge, can improve the in situ detection precision of wave aberration with it.

Description of drawings

Fig. 1: the test badge structural representation that uses in the technology 1 formerly.

Fig. 2: the test badge structural representation that uses in the technology 2 formerly.

Fig. 3: the test badge structural representation that uses in the technology 3 formerly.

Fig. 4: the synoptic diagram of translation symmetry grating marker of the present invention.

Fig. 5: the structural representation in the translation symmetry grating marker one-period of the present invention.

Fig. 6: the linear relationship curve of coma.

The linear relationship curve of Fig. 7 spherical aberration

The linear relationship curve of Fig. 8 astigmatism

Fig. 9: the wave aberration detection system structural representation that the present invention adopts.

Figure 10: the Coma-IPE linear relationship of binary mask mark, phase shifting mask mark and translation symmetric form phase shifting mask mark.

Figure 11: translation symmetric form phase shifting mask grating marker is to three rank coma Z ₇Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.

Figure 12: translation symmetric form phase shifting mask grating marker is to five rank coma Z ₁₄Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.

Figure 13: translation symmetric form phase shifting mask grating marker is to three rank spherical aberration Z ₉Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.

Figure 14: translation symmetric form phase shifting mask grating marker is to five rank spherical aberration Z ₁₆Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.

Figure 15: translation symmetric form phase shifting mask grating marker is to five rank astigmatism Z ₁₂Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.

Embodiment

The invention will be further described below in conjunction with embodiment and accompanying drawing, but do not limit protection scope of the present invention with this embodiment.

See also Fig. 4 earlier, Fig. 4: the synoptic diagram of translation symmetry grating marker of the present invention.As seen from the figure, translation symmetry grating marker of the present invention, form by directions X translation symmetry grating marker 41 and Y direction translation symmetry grating marker 42, the grating lines of described directions X translation symmetry grating marker 41 are arranged along directions X, the grating lines of described Y direction translation symmetry grating marker 42 are arranged along the Y direction, and the structure (referring to Fig. 5) of the one-period of this translation symmetric form grating marker 41,42 is:

Each cycle is made up of parallel no spaced 10 lines zones with certain width successively, the the the 6th (56), the 7th the (57), the 8th the (58), the 9th the (59), the 10th (510) the lines zone width with the the the 1st (51), the 2nd the (52), the 3rd the (53), the 4th the (54), the 5th (55) lines zone respectively is equal, and the ratio of the width in described the the the 1st (51), the 2nd the (52), the 3rd the (53), the 4th the (54), the 5th (55) lines zone is: 90: 481: 43: 102: 83;

The the described the 1st (51) and the 6th (56) is light tight zone, the described the the the 2nd (52), the 4th the (54), the 8th the (58) and the 10th (510) is 180 ° of phase shift transmission regions, and the described the the the 3rd (53), the 5th the (55), the 7th the (57) and the 9th (59) is the transmission region of 0 ° of phase shift;

The span in described cycle is: (wherein, λ is the wavelength of photo-etching machine illumination light source for 5.3846-0.6,5.3846+0.6) λ/NA, but NA is the interior maximal value of projection lens of lithography machine numerical aperture variation range and the mean value of minimum value;

The span of the transmitance of described transmission region is 95% ~ 100%.

The optimal value of each several part width is in the described translation symmetric form phase shifting mask grating one-period: mark 51 wide 0.3033 λ/NA, mark 52 wide 1.6208 λ/NA, mark 53 wide 0.1449 λ/NA, mark 54 wide 0.3437 λ/NA, mark 55 wide 0.2797 λ/NA.But NA is its mean value maximum and minimum value in the projection lens of lithography machine numerical aperture variation range.

The each several part width allows to produce ± 11.14% with interior deviation in the described grating one-period near optimal value, and promptly all grating markers that belongs in this deviation range are all regarded translation symmetric form phase shifting mask grating marker as.

A kind of in-situ detection method of wave aberration based on the wave aberration of photo-etching machine projection objective linear model

At first, based on (the linearrelationship between Coma and Image Placement Error (IPE) of the linear relationship model between coma and the imaging offset, the Coma-IPE linear model), based on (the linear relationshipbetween spherical aberration and Best Focus Shift (BFS) of the linear relationship model between spherical aberration and the optimal focal plane side-play amount, the Spherical-BFS linear model), and linear relationship model (thelinear relationship between astigmatism and relative best focus shift ofhorizontal and vertical grating images, the Astigmatism-BFS of astigmatism and vertical/relative optimal focal plane side-play amount of horizontal line grating _HvLinear model) sets up projection objective wave aberration in situ detection linear relationship model.

The optical lithography imaging system is an expansion thing (an extended object) becomes aerial image or photoresist picture by projection objective under the kohler's illumination condition a partial coherence imaging system.Its imaging performance is discussed for convenience,, is adopted based on intersecting the Hopkins partial coherence imaging theory of transport function to this system modelling with spatial domain and the normalization of frequency field Cartesian coordinate.Normalized Cartesian coordinates as the formula (1).

$x_o=-\frac{M\widehat{x_o}}{\mathrm{\&lambda;}/\mathrm{NA}}$ $y_o=-\frac{M\widehat{y_o}}{\mathrm{\&lambda;}/\mathrm{NA}}$

$x_i=-\frac{\widehat{x_i}}{\mathrm{\&lambda;}/\mathrm{NA}}$ $y_i=-\frac{\widehat{y_i}}{\mathrm{\&lambda;}/\mathrm{NA}},$

$f=\frac{\hat{f}}{\mathrm{NA}/\mathrm{\&lambda;}}$ $g=\frac{\hat{g}}{\mathrm{NA}/\mathrm{\&lambda;}}$

Wherein λ is the wavelength of monochromatic source, and NA is the picture number formulary value aperture of projection objective.The object plane coordinate

And image coordinates

All be normalized to (x respectively by the λ/NA of diffraction unit _o, y _o) and (x _i, y _i).Coordinate in the pupil plane

Then by cps NA/ λ be normalized to (f, g).The coordinate of every bit is according to horizontal amplification factor M convergent-divergent in the object plane, thus obtain with image planes on the corresponding identical coordinate figure of geometry picture point.The scalar form of Hopkins partial coherence imaging formula is as follows:

$I(x_i,y_i)=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;\&Integral;\&Integral;\&Integral;}}\mathrm{TCC}(f^{\&prime;},g^{\&prime;};f^{\&prime;\&prime;},g^{\&prime;\&prime;})O\left(f^{\&prime;},g^{\&prime;}\right)O^{*}(f^{\&prime;\&prime;},g^{\&prime;\&prime;})---\left(2\right)$

$e^{-\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;}[(f^{\&prime;}-f^{\&prime;\&prime;})x_i+(g^{\&prime;}-g^{\&prime;\&prime;})y_i]}{\mathrm{df}}^{\&prime;}{\mathrm{dg}}^{\&prime;}{\mathrm{df}}^{\&prime;\&prime;}{\mathrm{dg}}^{\&prime;\&prime;}$

Wherein, and TCC (f ', g '; F ", g ") is for intersecting transport function:

$\mathrm{TCC}(f^{\&prime;},g^{\&prime;};f^{\&prime;\&prime;},g^{\&prime;\&prime;})=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}\&Integral;J(f,g)H(f+f^{\&prime;},g+g^{\&prime;})H^{*}(f+f^{\&prime;\&prime;},g+g^{\&prime;\&prime;})\mathrm{dfdg}.---\left(3\right)$

In the following formula, and O (f ', g ') be the diffraction spectrum of mask.J (f g) is the intensity distributions of efficient light sources under the Kohler illumination condition, when adopting traditional partial coherence lighting system:

$J(f,g)=\left\{\begin{array}{cc}1/{\mathrm{\&pi;\&sigma;}}^2& \sqrt{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">g</figure-callout>}}^2}\&le;\mathrm{\&sigma;}\\ 0& \mathrm{otherwise}\end{array}\right..---\left(4\right)$

H (f is the pupil function of projection objective g), and expression formula is as follows:

$H(f,g)=\left\{\begin{array}{cc}{e}^{-\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{\&Phi;}(f,g)+\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;\&Delta;<figure-callout\; id="1"\; label="z"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">z</figure-callout>}\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}^2}\sqrt{1-{\mathrm{NA}}^2({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)},{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">g</figure-callout>}}^2<1}& \\ 0& \mathrm{others}\end{array}\right.---\left(5\right)$

Wherein, Ф (f g) is the projection objective wave aberration function, is expressed as follows with the striped zernike polynomial of quadrature:

$\mathrm{\&Phi;}(f,g)=\underset{n=1}{\overset{37}{\mathrm{\&Sigma;}}}{Z}_n{R}_n(f,g)$

$={\mathrm{<figure-callout\; id="1"\; label="Z"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">Z</figure-callout>}}_1+Z_{2}f+Z_{3}g+Z_4[2({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)-1]+Z_5(f^2-g^2)$

$+Z_7[3({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)-2]f+...$

$+Z_9[6{({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)}^2-6({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)+1]+...---\left(6\right)$

$+Z_{12}[4({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)-3](f^2-g^2)+...$

$+Z_{14}[10{({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)}^2-12({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)+3]f+...$

$+Z_{16}[20{({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)}^3-30{({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)}^2+12\left({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2{+g}^2\right)-1]+...$

$+Z_{21}[15{({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)}^2-20({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)+6](f^2-g^2)+...$

Formula (6) has been listed the coma (Z that will discuss ₇, Z ₁₄), spherical aberration (Z ₉, Z ₁₆) and astigmatism (Z ₁₂) zernike polynomial.Wherein, coma is strange aberration, can cause the lateral attitude skew of test badge aerial image; Spherical aberration and astigmatism are that idol is poor, can cause the optimal focal plane skew of test badge aerial image.Δ z is expressed as the defocusing amount of image planes, with Rayleigh length lambda/NA ²Be unit.During the aerial image of formula (5) on calculating the out of focus face, considered the influence of high-NA.

When the phase shifting mask grating marker passed through the projection objective imaging, its transmittance function was:

$t\left(x_o\right)=\underset{n=-\&infin;}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(x_o-2\mathrm{np})*[\mathrm{rect}\left(\frac{x_o+p/2}{\mathrm{pw}}\right)-\mathrm{rect}\left(\frac{x_o-p/2}{\mathrm{pw}}\right)]n\&Element;Z.---\left(7\right)$

The diffraction spectrum of mark is transmittance function t (x ₀) Fourier transform:

$O\left(f\right)=\frac{i\&CenterDot;\mathrm{pw}}{p}\underset{-N}{\overset{+N}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(f-\frac{n}{2p})\&CenterDot;\sin c(\mathrm{pw}\&CenterDot;f)\&CenterDot;\sin \left(\mathrm{\&pi;pf}\right).---\left(8\right)$

Wherein, p represents how much cycles, i.e. live width and phase region width sums of phase shifting mask grating.Pw represents the width of phase region.The condition of common phase shifting mask grating marker and optimize the phase shifting mask grating marker and satisfy+/-1 order diffraction light two-beam interference imaging is respectively:

λ/2 (1-σ) NA＜p≤3 λ/2 (σ+1) NA and λ/2 (1-σ) NA＜p≤5 λ/2 (σ+1) NA.Promptly

O(f)＝C _o[δ(f-f ₀)-δ(f+f ₀)]， (9)

Wherein, f ₀=1/2pand C _o=0.5isinc (0.25).According to (2)-(6) and (9) formula, the intensity distributions of label space picture is:

I(x _i，Δz)＝TCC(f ₀，0；f ₀，0)+TCC(-f ₀，0；f ₀，0)+

+exp(-i4f ₀x _i)∫∫J(f，g)exp(-iα)exp(iβ)dfdg+， (10)

+exp(i4f ₀x _i)∫∫J(f，g)exp(iα)exp(-iβ)dfdg

Wherein,

α＝2πФ(f+f ₀，g)/λ+πΔz[(f+f ₀) ²+g ²]

，(11)

β＝2πФ(f-f ₀，g)/λ+πΔz[(f-f ₀) ²+g ²]

To pupil function H (f, g) the out of focus item in is got approximate: $\sqrt{{\mathrm{NA}}^2({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)}\&ap;1-{\mathrm{NA}}^2({\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2+g^2)/2.$ Abbreviation gets:

I(x _i，Δz)＝2C ₀ ²[∫∫J(f，g)cos(α-β-4πf ₀x)dfdg+1] (12)

The difference solving equation $\&PartialD;I(x_i,\mathrm{\&Delta;z}=0)/{\&PartialD;x}_i=0$ With $\&PartialD;I(x_i=0,\mathrm{\&Delta;z})/\&PartialD;\mathrm{\&Delta;z}=0$ Obtain separating of imaging offset IPE and optimal focal plane side-play amount BFS:

$\mathrm{IPE}=\underset{n=1}{\overset{37}{\mathrm{\&Sigma;}}}{S}_{\mathrm{IPE}-n}\&CenterDot;Z_n=\frac{1}{{2\mathrm{\&lambda;<figure-callout\; id="0"\; label="f"\; filenames="A20091005132000251.png,A20091005132000252.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\underset{n=1}{\overset{37}{\mathrm{\&Sigma;}}}\frac{\&Integral;\&Integral;J(f,g)[R_n(f+{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="A20091005132000251.png,A20091005132000252.png"\; state="\{\{state\}\}">f</figure-callout>}}_0,g)-R_n(f-{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="A20091005132000251.png,A20091005132000252.png"\; state="\{\{state\}\}">f</figure-callout>}}_0,g)]\mathrm{dfdg}}{\&Integral;\&Integral;J(f,g)\mathrm{dfdg}}\&CenterDot;Z_n---\left(13\right)$

$\mathrm{BFS}=\underset{n=1}{\overset{37}{\mathrm{\&Sigma;}}}{S}_{\mathrm{BFS}-n}\&CenterDot;Z_n=\frac{-1}{{2\mathrm{\&lambda;<figure-callout\; id="0"\; label="f"\; filenames="A20091005132000251.png,A20091005132000252.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\underset{n=1}{\overset{37}{\mathrm{\&Sigma;}}}\frac{\&Integral;\&Integral;J(f,g)\&CenterDot;f\&CenterDot;[R_n(f+{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="A20091005132000251.png,A20091005132000252.png"\; state="\{\{state\}\}">f</figure-callout>}}_0,g)-R_n(f-{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="A20091005132000251.png,A20091005132000252.png"\; state="\{\{state\}\}">f</figure-callout>}}_0,g)]\mathrm{dfdg}}{\&Integral;\&Integral;J(f,g){\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">f</figure-callout>}}^2\mathrm{dfdg}}\&CenterDot;Z_n---\left(14\right)$

Wherein, S _IPE-nAnd S _BFS-nBe expressed as the sensitivity coefficient of image position side-play amount and optimal focal plane side-play amount.Know by formula (13) and formula (14), poor for idol, S _IPE-n≡ 0; For strange aberration, S _BFs-n≡ 0.When partial coherence factor σ, mark structure and numerical aperture NA one timing, imaging offset and strange aberration zernike coefficient are linear, and optimal focal plane side-play amount and idol difference zernike coefficient are linear.When p increased the restrictive condition of breaking through the two-beam interference imaging, the label space picture was formed by multiple-beam interference, and can't obtain the analytical expression of IPE and BFS this moment, can only analyze its linear relationship model by numerical evaluation.Fig. 6, Fig. 7 and Fig. 8 have provided coma respectively, the numerical solution of the linear relationship of spherical aberration and astigmatism.The corresponding test badge of tangent value difference at figure cathetus pitch angle is to the sensitivity coefficient of this wave aberration.In this article, a kind of sensitivity of wave aberration is represented when other wave aberration is zero, imaging offset or optimal focal plane side-play amount that per 1 nanometer wave aberration causes.

It is pointed out that two-beam interference imaging time space is not subjected to the modulation of senior diffraction light as the peak value of intensity, so can adopt extremum method to determine IPE and BFS.In actual detected, need determine IPE and CD as the threshold value of intensity by measurement space.Then need to scan the CD value in the different out of focus faces when determining BFS, determine the position of optimal focal plane according to the deviation of CD.The optimal focal plane side-play amount that causes with spherical aberration is different, astigmatism (Z ₁₂And Z ₂₁) the optimal focal plane side-play amount that causes comprises the component on level and the vertical both direction, usually by the grating marker and the vertical difference BFS that places the focal plane shift amount of grating marker of horizontal positioned _HvDecide.

Secondly, according to the analysis result of above-mentioned theory derivation and numerical evaluation, it is as follows to set up projection objective wave aberration in situ detection linear model:

ΔX(NA _i，σ _i)＝S ₁(NA _i，σ _i)Z ₂+S ₂(NA _i，σ _i)Z ₇+S ₃(NA _i，σ _i)Z ₁₄，(i＝1，2，3……n)，

(15)

ΔY(NA _i，σ _i)＝S ₄(NA _i，σ _i)Z ₃+S ₅(NA _i，σ _i)Z ₈+S ₆(NA _i，σ _i)Z ₁₅，(i＝1，2，3……n)， (16)

ΔZ _s(NA _i，σ _i)＝S ₇(NA _i，σ _i)Z ₄+S ₈(NA _i，σ _i)Z ₉+S ₉(NA _i，σ _i)Z ₁₆，(i＝1，2，3……n)，

(17)

ΔZ _hv(NA _i，σ _i)＝S ₁₀(NA _i，σ _i)Z ₅+S ₁₁(NA _i，σ _i)Z ₁₂+S ₁₂(NA _i，σ _i)Z ₂₁，(i＝1，2，3……n)，(18)

Above-mentioned equation can be represented by following matrix equation:

$\left[\begin{array}{c}\mathrm{\&Delta;X}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;X}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_1({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_2({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_3({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_1({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_2({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_3({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_2\\ Z_7\\ Z_{14}\end{array}\right],---\left(19\right)$

$\left[\begin{array}{c}\mathrm{\&Delta;Y}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;Y}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_4({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_5({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_6({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_4({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_5({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_6({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_3\\ Z_8\\ Z_{15}\end{array}\right],---\left(20\right)$

$\left[\begin{array}{c}\mathrm{\&Delta;}{Z}_s({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;}{Z}_s({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_7({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_8({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_9({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_7({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_8({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_9({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_4\\ Z_9\\ {\mathrm{<figure-callout\; id="16"\; label="Z"\; filenames="A20091005132000252.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{16}\end{array}\right],---\left(21\right)$

$\left[\begin{array}{c}\mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{ccc}{S}_{10}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_{11}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_{12}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_{10}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_{11}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_{12}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_5\\ Z_{12}\\ Z_{21}\end{array}\right],---\left(22\right)$

Wherein, Δ X (NA _i, σ _i) be the aerial image of the test badge that under different N A and σ condition, measures image space shifted by delta X at directions X ₄₁(NA _i, σ _i), promptly

ΔX(NA _i，σ _i)＝ΔX ₄₁(NA _i，σ _i)。(23)

Δ Y (NA _i, σ _i) be the aerial image of the test badge that under different N A and σ condition, measures image space shifted by delta Y in the Y direction ₄₂(NA _i, σ _i), promptly

ΔY(NA _i，σ _i)＝ΔY ₄₂(NA _i，σ _i)。(24)

Δ Z _s(NA _i, σ _i) be the Δ Z that under different N A and σ condition, measures ₄₁(NA _i, σ _i) and Δ Z ₄₂(NA _i, σ _i) mean value, promptly

ΔZ _s(NA _i，σ _i)＝[ΔZ ₄₁(NA _i，σ _i)+ΔZ ₄₂(NA _i，σ _i)]/2。(25)

Δ Z _Hv(NA _i, σ _i) be the Δ Z that under different N A and σ condition, measures ₄₁(NA _i, σ _i) and Δ Z ₄₂(NA _i, σ _i) difference, promptly

ΔZ _hv(NA _i，σ _i)＝ΔZ ₄₁(NA _i，σ _i)-ΔZ ₄₂(NA _i，σ _i)。(26)

S ₁(NA _i, σ _i), S ₂(NA _i, σ _i), S ₃(NA _i, σ _i), S ₄(NA _i, σ _i), S ₅(NA _i, σ _i), S ₆(NA _i, σ _i), S ₇(NA _i, σ _i), S ₈(NA _i, σ _i), S ₉(NA _i, σ _i), S ₁₀(NA _i, σ _i), S ₁₁(NA _i, σ _i), S ₁₂(NA _i, σ _i) be respectively and Z ₂, Z ₇, Z ₁₄, Z ₃, Z ₈, Z ₁₅, Z ₄, Z ₉, Z ₁₆, Z ₅, Z ₁₂And Z ₂₁Corresponding aberration sensitivity coefficient, by following formula definition:

${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;X}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">Z</figure-callout>}}_2},(i=\mathrm{1,2,3}......n),---\left(27\right)$

${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;X}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="7"\; label="Z"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">Z</figure-callout>}}_7},(i=\mathrm{1,2,3}......n),---\left(28\right)$

${\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_3=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;X}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;Z}_{14}},(i=\mathrm{1,2,3}......n),---\left(29\right)$

${\mathrm{<figure-callout\; id="4"\; label="S"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_4=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;Y}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="3"\; label="Z"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">Z</figure-callout>}}_3},(i=\mathrm{1,2,3}......n),---\left(30\right)$

${\mathrm{<figure-callout\; id="5"\; label="S"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_5=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;Y}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="8"\; label="Z"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">Z</figure-callout>}}_8},(i=\mathrm{1,2,3}......n),---\left(31\right)$

${\mathrm{<figure-callout\; id="6"\; label="S"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_6=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;Y}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;Z}_{15}},(i=\mathrm{1,2,3}......n),---\left(32\right)$

${\mathrm{<figure-callout\; id="7"\; label="S"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_7=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;}{Z}_s({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="4"\; label="Z"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">Z</figure-callout>}}_4},(i=\mathrm{1,2,3}......n),---\left(33\right)$

${\mathrm{<figure-callout\; id="8"\; label="S"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">S</figure-callout>}}_8=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;}{Z}_s({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;Z}_9},(i=\mathrm{1,2,3}......n),---\left(34\right)$

$S_9=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;}{Z}_s({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="16"\; label="Z"\; filenames="A20091005132000252.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{16}},(i=\mathrm{1,2,3}......n).---\left(35\right)$

$S_{10}=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;\mathrm{<figure-callout\; id="5"\; label="Z"\; filenames="A20091005132000262.png"\; state="\{\{state\}\}">Z</figure-callout>}}_5},(i=\mathrm{1,2,3}......n),---\left(36\right)$

$S_{11}=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;Z}_{12}},(i=\mathrm{1,2,3}......n),---\left(37\right)$

$S_{12}=\left({\mathrm{NA}}_i{,\mathrm{\&sigma;}}_i\right)=\frac{\&PartialD;\mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{NA}}_i,{\mathrm{\&sigma;}}_i)}{{\&PartialD;Z}_{21}},(i=\mathrm{1,2,3}......n).---\left(38\right)$

At last, according to above-mentioned linear model, a kind of in-situ detection method of wave aberration of projection objective of photoetching machine based on described translation symmetric form phase shifting mask grating marker is proposed.

The detection system that described method is used as shown in Figure 9.This system comprises the light source 1 that produces illuminating bundle; Be used to adjust the illuminator 2 of beam waist, light distribution, partial coherence factor and the lighting system of the light beam that described light source sends; Energy bearing test mask 3 and pinpoint mask platform 5; Can be with 4 imagings of the test badge on the test mask 3 and the adjustable projection objective 6 of numerical aperture; Can carry silicon chip and have the 3-D scanning ability and the accurate work stage 7 of station-keeping ability, be installed in the aerial image sensor 8 of the aerial image position that is used to measure test badge 4 on the test mask 3 on the work stage 7.

Described light source 1 can be ultraviolet and deep ultraviolet light sources such as mercury lamp, excimer laser, laser plasma light source and discharge plasma light source.

Described illuminator 2 comprises the extender lens group, beam shaping and beam homogenizer.

Described lighting system comprises traditional lighting, ring illumination, secondary illumination, level Four illumination etc.

Described test badge 4 is the translation symmetric form phase shifting mask grating marker of one of content of the present invention.

Described image-position sensor can be that CCD, photodiode array or other have the detector of photosignal translation function.When measuring the side-play amount of test badge 4 aerial images, at first work stage 7 focusing and levelings then, carry out 3-D scanning to test badge 4 through the aerial image that projection objective became, and measure the optimal focal plane side-play amount of aerial image and the imaging offset in the focal plane.

Described in-situ detection method of wave aberration of projection objective concrete operations step is as follows:

(1) the spherical aberration coma of labeling projection object lens 6 and astigmatism sensitivity coefficient.Utilize lithography simulation software PROLITH to demarcate the wave aberration sensitivity coefficient.Sensitivity coefficient changes with the numerical aperture of projection objective and the partial coherence factor of illuminator, in order to utilize (NA under the different lighting conditions _i, σ _i) imaging offset (Δ X (NA that measures _i, σ _i), Δ Y (NA _i, σ _i), Δ Z _s(NA _i, σ _i) and Δ Z _Hv(NA _i, σ _i)) calculate the zernike coefficient of representing projection objective wave aberration, need to demarcate the wave aberration sensitivity coefficient S (NA under the corresponding lighting condition _i, σ _i).The variation of lighting condition is by being provided with realization in PROLITH software, the partial coherence factor variation range is 0.3 ~ 0.8, and step-length is 0.1; The numerical aperture variation range is 0.5 ~ 0.8, and step-length is 0.1, can obtain 24 groups of different lighting conditions: { (NA _i, σ _i) | i=1,2......20}={ (0.5,0.3), (0.5,0.4) ... (0.8,0.8) }.The scaling method that illustrates sensitivity coefficient is as follows: demarcating three rank coma Z ₇Sensitivity coefficient S ₂(NA _i, σ _i) time, can set certain Z ₇Value and to get other zernike coefficient be zero uses the lithography simulation computed in software to obtain by Z ₇The imaging offset Δ X (NA that causes _i, σ _i), Ci Shi sensitivity coefficient S then ₂(NA _i, σ _i) be Δ X (NA _i, σ _i) and Z ₇The ratio.S ₁(NA _i, σ _i), S ₃(NA _i, σ _i), S ₄(NA _i, σ _i), S ₅(NA _i, σ _i), S ₆(NA _i, σ _i), S ₇(NA _i, σ _i), S ₈(NA _i, σ _i), S ₉(NA _i, σ _i), S ₁₀(NA _i, σ _i), S ₁₁(NA _i, σ _i), S ₁₂(NA _i, σ _i) scaling method and S ₂(NA _i, σ _i) similar.Obtain at last (19) ~ four 20 * 3 sensitivity coefficient matrix in (22) formula.(2) test badge 4 passes through projection objective 6 at different numerical aperture NA _iWith partial coherence factor σ _iImaging under the condition.Regulate partial coherence factor by illuminator 2, its variation range is 0.3 ~ 0.8, and step-length is 0.1; Regulate numerical aperture by projection objective 6, its variation range is 0.5 ~ 0.8, and step-length is 0.1.({ (NA under 24 groups of different lighting conditions _i, σ _i) | i=1,2......20}={ (0.5,0.3), (0.5,0.4) ... (0.8,0.8) }), the lateral attitude offset X of directions X when utilizing aerial image sensor 8 measurement test badges 51 imagings on the work stage 7 ₄₁(NA _i, σ _i) and optimal focal plane shifted by delta Z ₄₁(NA _i, σ _i), the lateral attitude offset Y of Y direction when measuring test badge 52 imagings ₄₂(NA _i, σ _i) and optimal focal plane shifted by delta Z ₄₂(NA _i, σ _i).(3), calculate the spherical aberration and the coma of projection objective according to demarcation sensitivity matrix that obtains and the side-play amount that measures.At first, utilize (23) ~ (26) formula, the aerial image that calculates test badge is at the image space shifted by delta X of directions X (NA _i, σ _i), the aerial image of test badge is at the image space shifted by delta Y of Y direction (NA _i, σ _i) and optimal focal plane offset Z _s(NA _i, σ _i) and Δ Z _Hv(NA _i, σ _i).Then,, utilize least square method solving equation group (19) ~ (22), obtain representing the zernike coefficient Z of projecting objective coma aberration, spherical aberration and astigmatism according to position offset that measures and the sensitivity coefficient matrix that demarcation obtains ₂, Z ₇, Z ₁₄, Z ₃, Z ₈, Z ₁₅, Z ₄, Z ₉, Z ₁₆, Z ₅, Z ₁₂And Z ₂₁

The litho machine system architecture that is adopted in the embodiment of the invention as shown in Figure 7, it is the ArF excimer laser of 193nm that light source 1 adopts wavelength, the lighting system that illuminator 2 provides is a traditional lighting, the partial coherence factor variation range is 0.3 ~ 0.8, step-length is 0.1.The numerical aperture variation range of projection objective 6 is 0.5 ~ 0.8, and step-length is 0.1.Test badge 4 on the test mask 3 adopts translation symmetric form phase shifting mask grating marker, and as shown in Figure 5, the cycle of test badge 4 (p) is 799nm, and 51,51,53,54 and 55 width is respectively 90nm, 481nm, 43nm, 102nm and 83nm.

In the present embodiment, utilize the spherical aberration and the coma of the asymmetric grating detection projection lens of lithography machine of one of content of the present invention, its step is as follows.

(1) utilize the wave aberration sensitivity coefficient matrix of lithography simulation software PROLITH labeling projection object lens, scaling method is as described in the summary of the invention, and it is as follows to obtain sensitivity coefficient matrix:

$\left[\begin{array}{ccc}{S}_1({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_2({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_3({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_1({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_2({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_3({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_1({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_2({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_3({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right],---\left(39\right)$

$\left[\begin{array}{ccc}{S}_4({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_5({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_6({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_4({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_5({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_6({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_4({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_5({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_6({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right],---\left(40\right)$

$\left[\begin{array}{ccc}{S}_7({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_8({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_9({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_7({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_8({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_9({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_7({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_8({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_9({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right].---\left(41\right)$

$\left[\begin{array}{ccc}{S}_{10}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_{11}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)& S_{12}({\mathrm{<figure-callout\; id="1"\; label="NA"\; filenames="A20091005132000262.png,A20091005132000272.png"\; state="\{\{state\}\}">NA</figure-callout>}}_1,{\mathrm{\&sigma;}}_1)\\ S_{10}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_{11}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)& S_{12}({\mathrm{<figure-callout\; id="2"\; label="NA"\; filenames="A20091005132000251.png,A20091005132000262.png"\; state="\{\{state\}\}">NA</figure-callout>}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_{10}({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_{11}({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})& S_{12}({\mathrm{<figure-callout\; id="20"\; label="NA"\; filenames="A20091005132000292.png"\; state="\{\{state\}\}">NA</figure-callout>}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right].---\left(42\right)$

(2) at different numerical aperture NA _iWith partial coherence factor σ _iMeasure the horizontal imaging offset Δ of the directions X X of test badge 41 under the condition ₄₁(NA _i, σ _i) and optimal focal plane offset Z ₄₁(NA _i, σ _i), the horizontal imaging offset Δ of the Y direction Y of measurement test badge 42 ₄₂(NA _i, σ _i) and optimal focal plane offset Z ₄₂(NA _i, σ _i).Under different lighting conditions, every kind of side-play amount measures 24 groups of data.

(3) according to demarcation clever brightness coefficient matrix that obtains and the side-play amount that measures, utilize least square method solving equation group (19) ~ (22), calculate spherical aberration, coma and the astigmatism of projection objective.Computing method are as described in the description.

When measuring projection objective wave aberration, the sensitivity matrix of demarcating test badge 4 is the key in measuring, and the variation range of sensitivity matrix medium sensitivity coefficient directly determines the wave aberration measuring accuracy, and its variation range is big more, and the wave aberration measuring accuracy is high more.Figure 11 is translation symmetric form phase shifting mask grating marker 4 pairs three rank coma Z of the present invention ₇Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.Figure 12 is translation symmetric form phase shifting mask grating marker 4 pairs five rank coma Z of the present invention ₁₄Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.Figure 13 is translation symmetric form phase shifting mask grating marker 4 pairs three rank spherical aberration Z of the present invention ₉Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.Figure 14 is translation symmetric form phase shifting mask grating marker 4 pairs five rank spherical aberration Z of the present invention ₁₆Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.Figure 15 is translation symmetric form phase shifting mask grating marker 4 pairs five rank astigmatism Z of the present invention ₁₂Sensitivity coefficient with the variation range of numerical aperture and partial coherence factor.Estimate the accuracy of detection of wave aberration according to the sensitivity coefficient variation range, in the present embodiment accuracy of detection of projection objective spherical aberration, coma and technology 1,2,3 formerly compared all and be improved significantly.

Claims (4)

1, a kind of translation symmetry grating marker, it is characterized in that forming by directions X translation symmetry grating marker (41) and Y direction translation symmetry grating marker (42), the grating lines of described directions X translation symmetry grating marker (41) are arranged along directions X, the grating lines of described Y direction translation symmetry grating marker (42) are arranged along the Y direction, and the structure of the one-period of this translation symmetric form grating marker (41,42) is:

Each cycle is made up of parallel no spaced 10 lines zones with certain width successively, the the the 6th (56), the 7th the (57), the 8th the (58), the 9th the (59), the 10th (510) the lines zone width with the the the 1st (51), the 2nd the (52), the 3rd the (53), the 4th the (54), the 5th (55) lines zone respectively is equal, and the ratio of the width in described the the the 1st (51), the 2nd the (52), the 3rd the (53), the 4th the (54), the 5th (55) lines zone is: 90: 481: 43: 102: 83;

The the described the 1st (51) and the 6th (56) is light tight zone, the described the the the 2nd (52), the 4th the (54), the 8th the (58) and the 10th (510) is 180 ° of phase shift transmission regions, and the described the the the 3rd (53), the 5th the (55), the 7th the (57) and the 9th (59) is the transmission region of 0 ° of phase shift;

The span in described cycle is: (wherein, λ is the wavelength of photo-etching machine illumination light source for 5.3846-0.6,5.3846+0.6) λ/NA, but NA is the interior maximal value of projection lens of lithography machine numerical aperture variation range and the mean value of minimum value;

The span of the transmitance of described transmission region is 95%～100%.

2, translation symmetry grating marker according to claim 1, the deviation that it is characterized in that the phase-shift phase of described transmission region is ± 10%.

3, translation symmetry grating marker according to claim 1, the optimal value that it is characterized in that the described grating cycle is 5.3846 λ/NA, and the optimal value of the width in described the the the 1st (51), the 2nd the (52), the 3rd the (53), the 4th the (54), the 5th (55) lines zone is respectively: 0.3033 λ/NA, 1.6208 λ/NA, 0.1449 λ/NA, 0.3437 λ/NA and 0.2797 λ/NA.

4, utilize the described translation symmetry of claim 1 grating marker to in-situ detection method of wave aberration of projection objective of photoetching machine, it is characterized in that comprising the following steps:

(1) spherical aberration of labeling projection object lens, coma and astigmatism sensitivity coefficient: utilize lithography simulation software PROLITH to demarcate the wave aberration sensitivity coefficient: sensitivity coefficient changes with the numerical aperture of projection objective and the partial coherence factor of illuminator, the variation of lighting condition is by being provided with realization in PROLITH software, the partial coherence factor variation range is 0.3～0.8, and step-length is 0.1; The numerical aperture variation range is 0.5～0.8, and step-length is 0.1, can obtain 24 groups of different lighting conditions:

{(NA _i，σ _i)|i＝1，2......24}＝{(0.5，0.3)，(0.5，0.4)......(0.8，0.8)}。

Demarcating three rank coma Z ₇Sensitivity coefficient S ₂(NA _i, σ _i) time, set certain Z ₇Value and to get other zernike coefficient be zero uses the lithography simulation computed in software to obtain by Z ₇The imaging offset Δ X (NA that causes _i, σ _i), Ci Shi sensitivity coefficient S then ₂(NA _i, σ _i) be Δ X (NA _i, σ _i) and Z ₇The ratio;

Demarcate S with method ₁(NA _i, σ _i), S ₃(NA _i, σ _i), S ₄(NA _i, σ _i), S ₅(NA _i, σ _i), S ₆(NA _i, σ _i), S ₇(NA _i, σ _i), S ₈(NA _i, σ _i), S ₉(NA _i, σ _i), S ₁₀(NA _i, σ _i), S ₁₁(NA _i, σ _i), S ₁₂(NA _i, σ _i); Obtain following four sensitivity coefficient matrix at last:

$\left[\begin{array}{ccc}{S}_1({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_2({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_3({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_1({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_2({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_3({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_1({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_2({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_3({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right],$

$\left[\begin{array}{ccc}{S}_4({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_5({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_6({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_4({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_5({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_6({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_4({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_5({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_6({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right]$

$\left[\begin{array}{ccc}{S}_7({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_8({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_9({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_7({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_8({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_9({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_7({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_8({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_9({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right]$

$\left[\begin{array}{ccc}{S}_{10}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_{11}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_{12}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_{10}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{11}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{12}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\\ S_{10}({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_{11}({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})& S_{12}({\mathrm{NA}}_{20},{\mathrm{\&sigma;}}_{20})\end{array}\right];$

(2) described translation symmetry grating marker (4) is placed and accurately is positioned on the mask platform (5), by projection objective (6) at different numerical aperture NA _iWith partial coherence factor σ _iImaging under the condition: regulate partial coherence factor by illuminator (2), its variation range is 0.3～0.8, and step-length is 0.1; Regulate numerical aperture by projection objective (6), its variation range is 0.5～0.8, and step-length is 0.1, ({ (NA under 24 groups of different lighting conditions _i, σ _i) | i=1,2, ..24}={ (0.5,0.3), (0.5,0.4),, .. (0.8,0.8) }), the lateral attitude offset X of directions X when utilizing aerial image sensor (8) measurement described directions X translation symmetric form grating marker (41) imaging on the work stage (7) ₄₁(NA _i, σ _i) and optimal focal plane shifted by delta Z ₄₁(NA _i, σ _i), the lateral attitude offset Y of Y direction when measuring described Y direction translation symmetric form grating marker (42) imaging ₄₂(NA _i, σ _i) and optimal focal plane shifted by delta Z ₄₂(NA _i, σ _i);

(3), calculate the spherical aberration and the coma of projection objective according to demarcation sensitivity matrix that obtains and the side-play amount that measures:

At first, utilize following formula, the aerial image that calculates directions X translation symmetric form grating marker (41) is at the image space shifted by delta X of directions X (NA _i, σ _i), the aerial image of Y direction translation symmetric form grating marker (42) is at the image space shifted by delta Y of Y direction (NA _i, σ _i) and optimal focal plane offset Z _s(NA _i, σ _i) and Δ Z _Hv(NA _i, σ _i):

Δ X (NA _i, σ _i) be different N A and The aerial image of the test badge 41 that measures under the condition is at the image space shifted by delta X of directions X ₄₁(NA _i, σ _i), promptly

ΔX(NA _i，σ _i)＝ΔX ₄₁(NA _i，σ _i)；

Δ Y (NA _i, σ _i) be different N A and

The aerial image of the Y direction translation symmetric form grating marker (42) that measures under the condition is at the image space shifted by delta Y of Y direction ₄₂(NA _i, σ _i), promptly

ΔY(NA _i，σ _i)＝ΔY ₄₂(NA _i，σ _i)

Δ Z _s(NA _i, σ _i) be different N A and

The Δ Z that measures under the condition ₄₁(NA _i, σ _i) and Δ Z ₄₂(NA _i, σ _i) mean value, promptly

ΔZ _s(NA _i，σ _i)＝[ΔZ ₄₁(NA _i，σ _i)+ΔZ ₄₂(NA _i，σ _i)]/2；

Δ Z _Hv(NA _i, σ _i) be different N A and

The Δ Z that measures under the condition ₄₁(NA _i, σ _i) and Δ Z ₄₂(NA _i, σ _i) difference, promptly

ΔZ _hv(NA _i，σ _i)＝ΔZ ₄₁(NA _i，σ _i)-ΔZ ₄₂(NA _i，σ _i)；

Then, according to the position offset that measures with demarcate the sensitivity coefficient matrix obtain, utilize the following system of equations of least square method solving equation group, obtain representing zernike coefficient Z2, Z7, Z14, Z3, Z8, Z15, Z4, Z9, Z16, Z5, Z12 and the Z21 of projecting objective coma aberration, spherical aberration and astigmatism:

$\left[\begin{array}{c}\mathrm{\&Delta;X}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;X}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]\left[\begin{array}{ccc}{S}_1({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_2({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_3({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_1({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_2({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_3({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_2\\ Z_7\\ Z_{14}\end{array}\right],$

$\left[\begin{array}{c}\mathrm{\&Delta;Y}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;Y}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]\left[\begin{array}{ccc}{S}_4({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_5({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_6({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_4({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_5({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_6({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_3\\ Z_8\\ Z_{15}\end{array}\right],$

$\left[\begin{array}{c}\mathrm{\&Delta;}{Z}_s({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;}{Z}_s({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]\left[\begin{array}{ccc}{S}_7({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_8({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_9({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_7({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_8({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_9({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_4\\ Z_9\\ Z_{16}\end{array}\right],$

$\left[\begin{array}{c}\mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ \mathrm{\&Delta;}{Z}_{\mathrm{hv}}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .\\ .\\ .\end{array}\right]\left[\begin{array}{ccc}{S}_{10}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_{11}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)& S_{12}({\mathrm{NA}}_1,{\mathrm{\&sigma;}}_1)\\ S_{10}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{11}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)& S_{12}({\mathrm{NA}}_2,{\mathrm{\&sigma;}}_2)\\ .& .& .\\ .& .& .\\ .& .& .\end{array}\right]\left[\begin{array}{c}{Z}_5\\ Z_{12}\\ Z_{21}\end{array}\right].$

Images