CN105372948A - Rapid modeling based wave aberration detection method for large-numerical aperture photoetching projection lens - Google Patents

Abstract

A detection method for wave aberration of large numerical aperture lithography projection objective lens based on rapid modeling, which is divided into two stages: rapid modeling and aberration extraction. In the rapid modeling stage, the polarization state of light and the polarization aberration of projection objective lens are set first. As well as numerical aperture and other parameters, use the unary linear sampling method to simulate the spatial image, perform principal component analysis and multiple linear regression analysis on the simulated spatial image, obtain the corresponding principal components and regression matrix, and establish a detection model that matches the large numerical aperture lithography machine In the aberration extraction stage, the measured spatial image is collected, the principal component coefficient is obtained by fitting the principal component of the measured spatial image, and the regression matrix is used to perform least squares fitting on the principal component coefficient to obtain the Zernike aberration of the measured spatial image. The invention realizes rapid modeling and high-precision detection of the Zernike aberrations Z ₅ -Z ₃₇ of the large numerical aperture lithographic projection objective lens.

Description

Detection method of wave aberration in large numerical aperture lithography projection objective lens based on rapid modeling

technical field

The invention relates to a lithography projection objective lens, in particular to a method for detecting wave aberration of a large numerical aperture lithography projection objective lens based on rapid modeling.

Background technique

The lithography machine is one of the core equipment for the manufacture of very large scale integrated circuits. The projection objective lens is one of the most important subsystems of the lithography machine. The wave aberration of the projection objective lens is the main factor affecting the engraving accuracy and imaging resolution of the lithography machine. With the development of lithography technology from dry to immersion, the aberration tolerance of the projection objective lens of lithography machines has become more and more stringent, and the speed and accuracy of wave aberration detection have also become higher and higher. In order to meet the requirements of engraving accuracy and imaging resolution of lithography machines, it is of great significance to develop a fast and high-precision wave aberration detection technology for large numerical aperture lithography projection objectives.

The wave aberration detection technology of lithography projection objective lens based on aerial image measurement is a common type of technology, which has the advantages of fast detection speed, low cost, and real-time detection of wave aberration of lithography projection objective lens. In 2015, Zhu Boer et al. proposed a method for detecting wave aberration of the projection objective lens of a large numerical aperture lithography machine (see prior art 1, Zhu Boer, Li Sikun, Wang Xiangchao, Yan Guanyong, Shen Lina, Wang Lei, "A large Numerical aperture lithography machine projection objective lens wave aberration detection method", patent application number: 201510166998.7, publication number: 104777718A). This method adopts the Box-BehnkenDesign statistical sampling method, uses polarized light illumination and vector imaging model, establishes a detection model that matches the large numerical aperture lithography machine, and realizes the measurement of 33rd-order Zernike aberration (Z ₅ ~ Z ₃₇ ), but it takes a long time to establish the detection model, which is not conducive to the rapid detection of wave aberration of lithography projection objective lens.

Contents of the invention

The object of the present invention is to provide a method for detecting wave aberration of a large numerical aperture lithography projection objective lens based on rapid modeling, which can detect wave aberration of a large numerical aperture lithography projection objective lens quickly and with high precision.

Technical solution of the present invention is as follows:

A method for detecting wave aberration of a large numerical aperture lithography projection objective lens based on rapid modeling. The measurement system used in the method includes a light source for generating a laser beam, an illumination system, and a camera for carrying a test mask and having precise positioning capabilities. Mask table, projection objective lens system for imaging detection marks on mask pattern onto silicon wafer, work table capable of carrying silicon wafer and capable of three-dimensional scanning and precise positioning, aerial image installed on the work table sensor and a data processing computer connected with the aerial image sensor.

The light source can be traditional lighting, ring lighting, dipole lighting, quadrupole lighting and free lighting light source, the partial coherence factor of the traditional lighting source is σ; the partial coherence factor of the ring lighting source is [σ _out , σ _in ], σ _out represents the external coherence factor, σ _in represents the internal coherence factor; the partial coherence factor of dipole lighting is [σ _out , σ _in ], σ _out represents the external coherence factor, σ _in represents the internal coherence factor, and the polar angle is θ; The partial coherence factor of the quadrupole illumination is [σ _out , σ _in ], σ _out represents the external coherence factor, σ _in represents the internal coherence factor, and the pole opening angle is θ.

The illumination system is used to adjust the light intensity distribution and polarization state of the illumination light field generated by the light source.

The detection mark is composed of 6 isolated spaces with different orientations, and the 6 different orientations are respectively 0°, 30°, 45°, 90°, 120°, and 135°.

The method includes two stages of rapid modeling and aberration extraction.

The Rapid Modeling phase consists of the following steps:

1) Use the unary linear sampling method to set the combination ZU of the 33rd order Zernike aberration Z ₅ ~ Z ₃₇ , and randomly set a set of polarization aberration PT of the projection objective lens of the large numerical aperture lithography machine, and a sampling matrix of 33×67 The D formula is as follows:

2) Select the lithography simulation parameters: the illumination mode of the illumination system and its partial coherence factor. The numerical aperture NA of the objective lens, set the value range of NA as NA≥0.93;

3) Place a test mask on the mask table, the test mark on the test mask is an isolated empty combination;

4) Aerial image acquisition range: the X direction acquisition range is [-L, L], set the value range of L as 300nm≤L≤3000nm, the Z direction acquisition range is [-F, F], set the value range of F The value range is The number of spatial image acquisition points: the number of acquisition points in the X direction is M, the value range of M is set to M≥20, the number of acquisition points in the Z direction is N, and the value range of N is set to N≥13; the above parameters and the Zernike image Input the difference combination ZU into the computer, use the vector imaging formula shown in formula ②, and use the lithography simulation software for simulation to obtain the simulated spatial image set AIU.

$\begin{array}{c}\hat{I}(x,\mathrm{the\; y})={\mathrm{no}}_{image}\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}...\∫J(f,g)h(f+f^{\′},g+g^{\′})h^{*}(f+f^{\′\′},g+g^{\′\′})\\ o(f^{\′},g^{\′})m_0(f+f^{\′},g+g^{\′}){\mathrm{E.}}_0\&Center\; Dot;o^{*}(f^{\′\′},g^{\′\′})m_0^{*}(f+f^{\′\′},g+g^{\′\′}){\mathrm{E.}}_0^{*}\\ e^{-i2\mathrm{\π}\[(f^{\′}-f^{\′\′})x+(g^{\′}-g^{\′\′})\mathrm{the\; y}\]}{\mathrm{dfdgdf}}^{\′}{\mathrm{d\; g}}^{\′}{\mathrm{df}}^{\′\′}{\mathrm{dg}}^{\′\′}\end{array}$ ②

Among them, n _image is the refractive index of the image space, J(f,g) is the normalized effective light source intensity distribution, H(f,g) is the pupil function, O(f,g) is the diffraction of the mask spectrum, M ₀ (f, g) is the 3×2 transmission matrix, E ₀ is the Jones vector of the incident light, ^* represents the conjugate transpose, x and y, f and g are the normalized image plane coordinates, The pupil surface coordinates, the normalization formula is as follows:

$\begin{array}{cc}x=\frac{x}{\mathrm{\λ}/NA},& \mathrm{the\; y}=\frac{\mathrm{the\; y}}{\mathrm{\λ}/NA},\\ f=\frac{f}{NA/\mathrm{\λ}},& g=\frac{g}{NA/\mathrm{\λ}},\end{array}$ ③

Among them, NA is the numerical aperture of the projection objective lens, λ is the exposure wavelength of the lithography machine, x and y, f and g are the coordinates of the image plane and the pupil plane, respectively.

5) Perform principal component analysis on the artificial space image set AIU to obtain the principal components of the simulated space image and the corresponding principal component coefficients, the formula is as follows:

AIU＝PC·V④

Among them, PC is the principal component of the simulated spatial image set, and V is the corresponding principal component coefficient.

6) Using the principal component coefficient V and the Zernike aberration combination ZU as known data, adopt the least squares fitting method to calculate the linear regression matrix RM, the formula is as follows:

V＝ZU·RM⑤

The aberration extraction stage consists of the following steps:

1) Set the parameters of the lithography machine to be tested, and the parameters are the same as those in the modeling stage;

2) Start the lithography machine, the illumination light emitted by the light source is adjusted by the illumination system to obtain the illumination mode corresponding to the modeling stage, irradiate the test mask on the mask table, and use the spatial image sensor to measure the multi-directional light converged by the projection objective lens. The aerial image corresponding to the test mark is obtained, and the measured aerial image is input into the computer for storage.

3) Utilize computer to carry out principal component fitting to measured spatial image, obtain the principal component coefficient of measured spatial image, then carry out fitting with described linear regression matrix RM according to least square method, obtain the Zernike of measured lithographic projection objective lens aberrations.

Compared with the prior art, the present invention has the following advantages:

The present invention reduces the number of samples and simplifies the modeling process through the unary linear sampling method; and adopts the polarized light illumination method and the vector imaging model to accurately characterize the spatial image of the large numerical aperture lithography machine, and finally realizes the large numerical aperture photolithography Rapid modeling and high-precision detection of Zernike aberrations Z ₅ ~ Z ₃₇ in engraved projection objective lenses.

Description of drawings

Fig. 1 is a structural diagram of the detection system used in the present invention.

Fig. 2 is a schematic diagram of the illumination method used in the present invention, wherein (a) is the structure of the illumination method, and (b) is the polarization state of the illumination light.

FIG. 3 is a schematic diagram of the mask mark structure used in the present invention.

Fig. 4 is a wave aberration accuracy diagram of a large numerical aperture lithography projection objective lens measured by the present invention.

detailed description

The present invention will be further described below in conjunction with the embodiments and accompanying drawings, but the protection scope of the present invention should not be limited by this embodiment.

Fig. 1 is a schematic structural diagram of the detection system used in the present invention. A light source 1 for generating a laser beam, an illumination system 2, a mask table 4 for carrying a test mask 3 and capable of precise positioning, and a projection objective lens system 6 for imaging the detection marks 5 on the mask pattern onto the silicon wafer , a workpiece table 7 capable of carrying silicon wafers and capable of three-dimensional scanning and precise positioning, an aerial image sensor 8 installed on the workpiece table 7 , and a data processing computer 9 connected to the aerial image sensor 8 .

The method includes two stages of rapid modeling and aberration extraction.

The Rapid Modeling phase consists of the following steps:

1) Using the unary linear sampling method to set The combination ZU of the 33rd-order Zernike aberration Z ₅ to Z ₃₇ in the amplitude range and randomly set the polarization aberration PT of a group of large numerical aperture lithography projection objectives. The formula of the sampling matrix D of 33×67 is as follows:

2) Select the lithography simulation parameters: the illumination mode of the illumination system is selected ring illumination, its partial coherence factor is [σ _out ,σ _in ]=[0.9,0.7], the polarization state of the illumination light is selected linearly polarized light, the linearly polarized The vibration direction of the light-light vector is parallel to the X-axis direction, as shown in Figure 2, the exposure wavelength of the lithography machine is λ=193nm, and the numerical aperture of the projection objective lens is NA=1.35;

3) Place a test mask on the mask table, the test mark on the test mask is a combination of isolated voids, the combination has 6 isolated voids with different orientations, and the orientations of the 6 isolated voids are respectively 0°, 30°, 45°, 90°, 120°, 135°, as shown in Figure 3;

4) Aerial image acquisition range: X direction acquisition range is [-900nm, 900nm], Z direction acquisition range is [-2000,2000]; Aerial image acquisition points: X direction acquisition points are 61, Z direction acquisition points are 57; Input the above parameter design and Zernike aberration combination ZU into the computer, use the vector imaging formula shown in formula ②, and use lithography simulation software for simulation to obtain the simulated spatial image set AIU.

$\begin{array}{c}\hat{I}(x,\mathrm{the\; y})={\mathrm{no}}_{image}\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}...\∫J(f,g)h(f+f^{\′},g+g^{\′})h^{*}(f+f^{\′\′},g+g^{\′\′})\\ o(f^{\′},g^{\′})m_0(f+f^{\′},g+g^{\′}){\mathrm{E.}}_0\&Center\; Dot;o^{*}(f^{\′\′},g^{\′\′})m_0^{*}(f+f^{\′\′},g+g^{\′\′}){\mathrm{E.}}_0^{*}\\ e^{-i2\mathrm{\π}\[(f^{\′}-f^{\′\′})x+(g^{\′}-g^{\′\′})\mathrm{the\; y}\]}{\mathrm{dfdgdf}}^{\′}{\mathrm{d\; g}}^{\′}{\mathrm{df}}^{\′\′}{\mathrm{d\; g}}^{\′\′}\end{array}$ ②

Among them, n _image is the refractive index of the image space, J(f,g) is the normalized effective light source intensity distribution, H(f,g) is the pupil function, O(f,g) is the diffraction of the mask spectrum, M ₀ (f, g) is the 3×2 transmission matrix, E ₀ is the Jones vector of the incident light, ^* represents the conjugate transpose, x and y, f and g are the normalized image plane coordinates, The pupil surface coordinates, the normalization formula is as follows:

$\begin{array}{cc}x=\frac{x}{\mathrm{\λ}/NA},& \mathrm{the\; y}=\frac{\mathrm{the\; y}}{\mathrm{\λ}/NA};\\ f=\frac{f}{NA/\mathrm{\λ}},& g=\frac{g}{NA/\mathrm{\λ}};\end{array}$ ③

Among them, NA is the numerical aperture of the projection objective lens, λ is the exposure wavelength of the lithography machine, x and y, f and g are the coordinates of the image plane and the pupil plane, respectively.

5) Perform principal component analysis on the artificial space image set AIU to obtain the principal components of the simulated space image and the corresponding principal component coefficients, the formula is as follows:

AIU＝PC·V④

Among them, PC is the principal component of the simulated spatial image set, and V is the corresponding principal component coefficient.

6) Using the principal component coefficient V and the Zernike aberration combination ZU as known data, adopt the least squares fitting method to calculate the linear regression matrix RM, the formula is as follows:

V＝ZU·RM⑤

The aberration extraction stage consists of the following steps:

1) Set the parameters of the lithography machine to be tested, and the parameters are the same as those in the modeling stage;

2) Start the lithography machine, the illumination light emitted by the light source is adjusted by the illumination system to obtain the illumination mode corresponding to the modeling stage, irradiate the test mask on the mask table, and use the spatial image sensor to measure the multi-directional light converged by the projection objective lens. The aerial image corresponding to the test mark is obtained, and the measured aerial image is input into the computer for storage.

3) Utilize computer to carry out principal component fitting to measured spatial image, obtain the principal component coefficient of measured spatial image, then carry out fitting with described linear regression matrix RM according to least square method, obtain the Zernike of measured lithographic projection objective lens Aberrations, as shown in Figure 4. The fast modeling part takes 10 minutes, and the average error and standard deviation of the detected Zernike aberration are both below 0.07nm.

Compared with the prior art, the present invention reduces the number of samples, simplifies the modeling process, and greatly shortens the modeling time through the unary linear sampling method; and adopts the polarized light illumination method and the vector imaging model to accurately characterize the large numerical aperture The aerial image of the lithography machine finally realized the rapid modeling and high-precision detection of the Zernike aberrations Z ₅ to Z ₃₇ of the large numerical aperture lithography projection objective lens.

The above embodiments are only exemplary embodiments adopted to illustrate the principles of the present invention, but the present invention is not limited thereto. For those of ordinary skill in the art, without departing from the spirit and essence of the present invention, various modifications and improvements can be made, so all equivalent technical solutions also belong to the scope of the present invention, and the patent of the present invention The scope of protection should be defined by the claims.

Claims (5)

1. A method for detecting wave aberration of a large numerical aperture lithography projection objective lens based on rapid modeling. The measurement system used in the method includes a light source (1) for generating a laser beam, an illumination system (2), and a load-bearing test A mask (3) and a mask table (4) with precise positioning capabilities, a projection objective lens system (6) for imaging the detection marks (5) on the mask pattern onto the silicon wafer, capable of carrying the silicon wafer and having A workpiece table (7) with three-dimensional scanning capability and precise positioning capability, an aerial image sensor (8) installed on the workpiece table (7), and a data processing computer (9) connected to the aerial image sensor (8); It is characterized in that the method includes two stages of rapid modeling and aberration extraction; The rapid modeling phase described includes the following steps: 1) Set the combination ZU of 33rd-order Zernike aberration Z ₅ ~ Z ₃₇ by using the unary linear sampling method, and randomly set a set of polarization aberration PT. The formula of the sampling matrix D of 33×67 is as follows: 2) Select the lithography simulation parameters: the illumination mode of the illumination system, that is, polarized illumination, the partial coherence factor of the light source, the exposure wavelength λ of the lithography machine, and the numerical aperture NA of the projection objective lens; 3) Place a test mask (3) on the mask table, the test mark on the test mask is an isolated empty combination; 4) Set the spatial image acquisition range and the number of acquisition points: the acquisition range in the X direction is [-L, L] and the number of acquisition points is M, the acquisition range in the Z direction is [-F, F] and the number of acquisition points is N; 5) Input the parameters of above-mentioned steps 1)-step 4) into the computer, and use lithography simulation software to simulate to obtain the simulation spatial image set AIU; 6) Carry out principal component analysis on the simulated spatial image set AIU to obtain the principal components of the simulated spatial image and the corresponding principal component coefficients, the formula is as follows: AIU＝PC·V④ Among them, PC is the principal component of the simulated spatial image set, and V is the corresponding principal component coefficient; 7) Using the principal component coefficient V and the Zernike aberration combination ZU as known data, adopt the least squares fitting method to calculate the linear regression matrix RM, the formula is as follows: V＝ZU·RM⑤ The described aberration extraction stage comprises the following steps: 1) Set the parameters of the lithography machine to be tested, and the parameters are the same as those in the modeling stage; 2) Start the lithography machine, the illumination light emitted by the light source is adjusted by the illumination system to obtain the illumination mode corresponding to the modeling stage, irradiate the test mask on the mask table, and use the spatial image sensor to measure the multi-directional light converged by the projection objective lens. Test the spatial image corresponding to the mark, obtain the measured spatial image, and input it into the computer for storage; 3) Utilize computer to carry out principal component fitting to measured spatial image, obtain the principal component coefficient of measured spatial image, then carry out fitting with described linear regression matrix RM according to least square method, obtain the Zernike of measured lithographic projection objective lens aberrations. 2. the rapid modeling based large numerical aperture lithography projection objective lens wave aberration detection method according to claim 1, is characterized in that, described light source is conventional lighting, ring lighting, dipole lighting, quadrupole lighting or Free lighting source, the partial coherence factor of traditional lighting source is σ; the partial coherence factor of ring lighting source is [σ _out , σ _in ], σ _out represents the external coherence factor, σ _in represents the internal coherence factor; the partial coherence factor of dipole lighting The factor is [σ _out ,σ _in ], σ _out represents the external coherence factor, σ _in represents the internal coherence factor, and the pole opening angle is θ; the partial coherence factor of quadrupole lighting is [σ _out ,σ _in ], σ _out represents the external Coherence factor, σ _in represents the internal coherence factor, and the pole angle is θ; The lighting system is used to adjust the light intensity distribution and polarization state of the lighting light field generated by the light source; The detection mark is composed of 6 isolated spaces with different orientations, and the 6 different orientations are 0°, 30°, 45°, 90°, 120° and 135° respectively. 3. The method for detecting wave aberration of a large numerical aperture lithography projection objective lens based on rapid modeling according to claim 1, wherein the polarization state of the polarized illumination is fully polarized, partially polarized or completely non-polarized. 4. The large numerical aperture lithography projection objective wave aberration detection method based on rapid modeling according to claim 1, wherein the value range of the acquisition range L in the X direction is 300nm≤L≤3000nm; The value range of the collection range F in the Z direction is 2000nm≤F≤6000nm; the value range of the collection point M in the X direction is M≥20, and the value range of the collection point N in the Z direction is N≥13. 5 . The method for detecting wave aberration of a large numerical aperture lithography projection objective lens based on rapid modeling according to claim 1 , wherein the numerical aperture NA of the projection objective lens is ≥ 0.93.