Method for reducing the effect of phase grating asymmetry on position measurement accuracy.

Abstract

The method for reducing the influence of the asymmetry of the phase grating on the position measurement accuracy includes the steps of: determining the asymmetry change range according to the design value and processing accuracy of the phase grating, and then determining the asymmetric grating structure; establishing an asymmetric grating simulation model; inputting the asymmetric grating structure into the asymmetric grating simulation model, simulating the position error curve of each diffraction order within the range of the asymmetry change; and determining the weight of each diffraction order according to the obtained position error difference of each diffraction order, thereby reducing the influence of the asymmetry change. The method proposed in the present invention does not need to measure the shape of the grating, and only determines the range of the asymmetry change of the grating according to the processing accuracy, and can reduce the influence of the asymmetry change in the range on the position measurement accuracy.

Description

[Technical field]

[0001] The present invention relates to the technical fields of semiconductors, integrated circuits, and precision measurement, and in particular to a method for reducing the effect of phase grating asymmetry on position measurement accuracy. [Background technology]

[0002] The position measurement technology of phase gratings has the characteristics of high measurement accuracy and low environmental impact, and is widely used in the fields of integrated circuits, precision processing and precision measurement. This technology uses spatially coherent light to illuminate a phase grating, generate diffracted beams of each order, interfere with the +mth diffraction order and the -mth diffraction order, scan the phase grating to generate a measurement signal that changes sinusoidally, and finally obtain the position information of the grating by fitting the measurement signal. With the continuous development of the application field, especially the continuous shrinkage of technology nodes in the field of integrated circuits, higher requirements have been put forward for the measurement accuracy of the grating position sensor. However, during the processing process and subsequent processing processes, the structure of the phase grating will change, especially due to the effects during etching, deposition, chemical mechanical polishing and temperature changes. According to the principle of position measurement of phase gratings, the asymmetric change of the grating structure will cause measurement errors. Therefore, it is necessary to analyze the effect of the asymmetry of the grating on the measurement accuracy and reduce the effect.

[0003] When analyzing the effect of the asymmetry of the grating on the position measurement accuracy, the shape of the grating is usually measured accurately using a scanning electron microscope or other means, and the diffraction field of the asymmetric grating is calculated by rigorously solving Maxwell's equations such as the rigorous coupled wave method (RCWA) or the finite difference time domain method (FDTD), to obtain the effect of the asymmetry on the position measurement accuracy, and reduce the effect of the asymmetry on the position measurement accuracy. However, different grating marks have different asymmetries, and the same grating mark may have different changes in asymmetry due to factors such as clamping. At the same time, the scanning electron microscope has strict requirements on the environment, has a slow measurement speed and is destructive, and the method of rigorously solving Maxwell's equations is highly accurate but time-consuming. Therefore, this method is very time-consuming and expensive. Summary of the Invention [Problem to be solved by the invention]

[0004] In light of this, a main object of the present invention is to provide a method for reducing the effect of phase grating asymmetry on position measurement accuracy, in order to partially solve at least one of the above technical problems. [Means for solving the problem]

[0005] In order to achieve the above object, one aspect of the present invention is to determining a range of change in asymmetry according to the design value and processing accuracy of the phase grating, and determining an asymmetric grating structure; establishing an asymmetric lattice simulation model; inputting the asymmetric grating structure into the asymmetric grating simulation model, and simulating the position error curve of each diffraction order within a change range of asymmetry; A method for reducing the effect of phase grating asymmetry on position measurement accuracy has been provided, the method including a step of determining a weight for each diffraction order according to the difference in position error of each obtained diffraction order, thereby reducing the effect of the asymmetry change.

[0006] wherein the step of establishing the asymmetric lattice simulation model comprises: According to the principle of phase grating position measurement, a formula for the effect of asymmetry on measurement accuracy is derived; According to the scalar diffraction theory, an asymmetric grating model is established to obtain the diffraction field of the asymmetric grating, and the influence of the asymmetry on the position measurement accuracy is obtained according to a calculation formula.

[0007] Here, the method further includes a validation step that includes validating the corrected position error curve and determining that the weights are all valid within the determined asymmetry range.

[0008] Here, the principle of the phase grating position measurement is that an incident beam of wavelength λ is perpendicularly incident on the phase grating to generate diffracted beams of each order, and in an optical model, interference occurs between the +mth diffraction order and the −mth diffraction order. Periodic measurement signals are generated by scanning the phase grating, and the position information of the phase grating is obtained from the measurement signals.

[0009] Here, the formula for calculating the effect of asymmetry on the measurement accuracy is:

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[0010] Here, to obtain the diffraction field of the asymmetric grating, it is necessary to first analyze the diffraction field of the top tilt grating, and then derive the diffraction field of any asymmetric grating.

[0011] Here, the diffraction field of the top tilt grating is

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[0012] Here, the asymmetric lattice model includes top, bottom, sidewall, and top angle symmetries.

[0013] Here, the ridge of the asymmetric grating model is divided into four parts G1, G2, G3, and G4, respectively, and the diffraction field of the asymmetric grating is

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[0014] Here, in order to reduce the asymmetric position error, the weight vector of the diffraction orders {w m} is the position error vector {Δx m} and w m We need to ensure that the sum of is 1.

[0015] As can be seen based on the above technical proposals, the method for reducing the influence of phase grating asymmetry on position measurement accuracy of the present invention has at least some of the following beneficial effects compared with the prior art.

[0016] The method proposed by the present invention does not require measuring the shape of the grating; it is possible to reduce the effect of the asymmetry change in the grating within a range determined according to the processing accuracy, on the position measurement accuracy.

[0017] The method proposed by the present invention has strong process adaptability, because different processes have different asymmetries, and the asymmetries at different positions on the same silicon wafer are not consistent, so the method can reduce the impact of the asymmetry change in this range on the position measurement accuracy according to the range of change.

[0018] The method proposed by the present invention has low cost and strong real-time performance. This method does not need to increase hardware to complete the test, so it can avoid the measurement of asymmetry by means such as electronic scanning lens and process test verification, and can reduce costs; the change range of asymmetry can be pre-determined according to process and processing accuracy, and the impact of asymmetry on position measurement accuracy can be reduced, so it has strong real-time performance.

[0019] For a more complete understanding of the present disclosure, and the advantages thereof, reference is now made to the following detailed description taken in conjunction with the accompanying drawings, in which: [Brief description of the drawings]

[0020] [Figure 1] FIG. 1 is a schematic flow chart of a method for reducing the effect of phase grating asymmetry on position measurement accuracy in the present invention. [Diagram 2] FIG. 2 is a schematic diagram for determining the asymmetric lattice structure. [Diagram 3] FIG. 3 is a schematic diagram of the structure of a top tilt grating in one period. [Figure 4] FIG. 4 is a schematic diagram of an arbitrary asymmetric lattice structure. [Diagram 5] FIG. 5 is a schematic diagram of an exploded view of the marking structure. [Figure 6]FIG. 6 shows the position error of each diffraction order when the top tilt asymmetry is changed in the range of [−30 nm, 30 nm]. [Figure 7] FIG. 7 shows the position error curves when the asymmetry of the top tilt is changed in the range of [−30 nm, 30 nm] after setting weights on the measurement positions of different diffraction orders. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0021] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail hereinafter in combination with specific embodiments with reference to the accompanying drawings.

[0022] The present invention proposes a method for reducing the influence of the asymmetry of the phase grating on the position measurement accuracy. In this method, the rough shape of the grating is first determined according to the design value of the phase grating and the grating processing range, and then a grating analysis model is established according to the scalar diffraction theory to obtain the influence of the asymmetry change on the measurement accuracy within the processing range, and weights are set for the measurement positions of different diffraction orders according to the difference in sensitivity of each diffraction order to the asymmetry change to reduce the influence of the asymmetry on the position measurement accuracy. In this method, it is not necessary to measure the shape of the diffraction grating, and it is only necessary to determine the range of the asymmetry change of the grating according to the processing accuracy, so that the influence of the asymmetry change within this range on the position measurement accuracy can be reduced.

[0023] As shown in FIG. 1, this is a schematic flowchart of a method for reducing the effect of phase grating asymmetry on position measurement accuracy, which includes the following steps:

[0024] 1. Determine the extent of change in asymmetric lattice structure The range of change in asymmetry is determined according to the design value and processing accuracy of the phase grating, as shown in Figure 2. For example, the design period of the grating is d = 16 μm, the groove depth h = 200 nm, and the grating ridge width fd = 8 μm. If it is assumed that the grating only has asymmetry in the top tilt according to the processing accuracy, the asymmetry range of the top tilt is determined to be Δh ∈ [-30 nm, 30 nm].

[0025] 2. Establish an asymmetric lattice simulation model First, according to the principle of phase grating position measurement, a calculation formula for the influence of asymmetry on the measurement accuracy is derived, then, according to the scalar diffraction theory, an asymmetric grating model is established to obtain the diffraction field of the asymmetric grating, and further, according to the calculation formula, the influence of asymmetry on the position measurement accuracy is obtained.

[0026] 1) Effect of asymmetry on measurement accuracy The principle of the phase grating position sensor is that an incident beam with wavelength λ is perpendicularly incident on a phase grating, generating diffracted beams of each order, and the +mth diffraction order and -mth diffraction order are made to interfere with each other by the optical module. By scanning the phase grating, a periodic measurement signal is generated. The position information of the phase grating is obtained from the measurement signal.

[0027] Assuming that the phase grating is located at x0, the incident beam is a collimated beam of unit amplitude, and the initial phase is 0, then the complex amplitude of the +mth diffraction order is

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[0028] The complex amplitude of the mth diffraction order is:

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[0029] If the phase grating is a symmetric grating, A m =A -m And φ m =φ -m Then, equation (5) can be expressed as follows:

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[0030] If the phase grating is an asymmetric grating, A m ≠A -m And φ m ≠φ -m and the resulting position error is

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[0031] Therefore, when the phase grating is an asymmetric grating, not only does the contrast V of the measurement signal decrease, but also a measurement position error occurs.

[0032] 2) Asymmetric lattice model In order to analyze the effect of asymmetry on the measurement accuracy, it is necessary to obtain the form of the diffraction field of the asymmetric grating. The method is based on scalar diffraction theory, which first analyzes the diffraction field of a top-tilted grating and then estimates the diffraction field of any asymmetric grating.

[0033] A. Top tilt asymmetric diffraction field The top-tilt asymmetric grating structure is shown in Figure 3, where d is the grating period, l is the grating ridge width, f is the duty defined as l / d, h is the center height of the grating ridge, and Δh is the asymmetry height. Assume that the grating has an infinite number of periods along the x-axis and extends infinitely perpendicular to the page.

[0034] Establishing a coordinate system as shown in FIG. 3, the lattice structure can be expressed as follows:

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[0035] Substituting equation (9) into equation (10), we get:

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[0036] B. Asymmetric grating diffraction field Assume that an asymmetric lattice G has asymmetric bottom, sidewall, and top angles, as shown in Figure 4. Divide the entire ridge into four parts, G1, G2, G3, and G4, and let the center positions of each part be x1, x2, x3, and x4, respectively, and their widths be f1d, f2d, f3d, and f4d, respectively.

[0037] According to Fourier's theorem, the diffracted field E of a grating G m G can be expressed as follows:

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[0038] E m G1 , E m G2 , E m G3 , and E m G4 is the diffraction field E of the top tilt marker m According to the Fourier translation theorem, E m G1 , E m G2 , E m G3 , and E m G4 can be expressed as follows:

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[0039] By substituting equations (11) and (13) into equation (12), we obtain the diffraction field E of the grating G. m G Using the same method, any asymmetric grating diffraction field can be obtained, and the signal contrast V and position error Δx can be calculated using equations (4) and (7).

[0040] 3. Simulate the position error of each diffraction order According to the formula in step 2, the position error of each diffraction order when the top tilt asymmetry changes in the range of [-30 nm, 30 nm] can be obtained by simulation as shown in Figure 7. From this, it can be seen that when the asymmetry changes, a difference occurs in the position error of each diffraction order. The larger the diffraction order, the smaller the position error Δx caused by the asymmetry, and the larger the asymmetry, the larger the position error of each diffraction order.

[0041] 4. Obtain the weights for each diffraction order In order to improve the measurement accuracy, it is necessary to control the position error due to asymmetry. From equation (7), we can see that the position error Δx is a function of the diffraction order m, so Δx will be different if m is different. Therefore, it is possible to reduce Δx due to asymmetry depending on the difference.

[0042] The position measurement sensor can collect the measurement signals of the 1st to nth diffraction orders, and the position error of each diffraction order m is Δx m and assuming that the actual position of the grating is x0, the measured result of the mth diffraction order is

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[0043] The lattice position measurement result x

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[0044] Therefore, in the case where there is no position error, i.e., x=x0, we need

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[0045] Therefore, to reduce the asymmetric position error, the weight vector of the diffraction orders {w m} is the position error vector {Δx m} and w m It is necessary to ensure that the sum of {w m}={0, 0.0817, -0.8872, 0.5107, 1.2947} and it can be determined that m=1, 3, 5, 7, 9.

[0046] 5. Verification When this weight is used, the corrected position error is shown in Fig. 6. When the asymmetry of the top tilt varies in the range of [-30 nm, 30 nm], the maximum position error is 4 × 10 -8 nm and can be ignored.

[0047] Although the above-mentioned specific embodiments have further described the objectives, technical solutions and beneficial effects of the present invention in detail, it should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. 1. A method for reducing the effect of phase grating asymmetry on position measurement accuracy, comprising the steps of: determining a range of change in asymmetry according to the design value and processing accuracy of the phase grating, and determining an asymmetric grating structure; establishing an asymmetric lattice simulation model; inputting the asymmetric grating structure into the asymmetric grating simulation model, and simulating the position error curve of each diffraction order within a change range of asymmetry; determining a weight for each diffraction order according to a difference in position error of each diffraction order obtained, thereby reducing an effect of asymmetry change; Establishing the asymmetric lattice simulation model comprises: Derive a formula for the effect of asymmetry on measurement accuracy according to the phase grating position measurement principle; Establishing an asymmetric grating model according to scalar diffraction theory to obtain the diffraction field of the asymmetric grating, and obtaining the influence of the asymmetry on the position measurement accuracy according to a calculation formula; The formula for calculating the effect of asymmetry on the measurement accuracy is: [0023] and where V is the signal contrast, A m is the amplitude of the +mth diffraction order, A −m is the amplitude of the −mth diffraction order, Δx m is the position error, Δφ m is the phase after grating diffraction, and d is the grating period. To reduce the asymmetric position error, it is necessary to ensure that the weight vector of the diffraction orders {w m} is orthogonal to the position error vector {Δx m} and that the sum of w m is 1. A method for reducing the effect of phase grating asymmetry on position measurement accuracy.

2. and a validation step including validating the corrected position error curve and determining that the weights are all valid within the determined asymmetry range.

2. The method of claim 1 .

3. The principle of measuring the phase grating position is as follows: An incident beam of wavelength λ is incident perpendicularly to the phase grating to generate diffracted beams of each order, and in the optical model, interference occurs between the +mth diffraction order and the −mth diffraction order; A periodic measurement signal is generated by scanning the phase grating. The aim is to obtain the position information of the phase grating from the measurement signal.

2. The method of claim 1 .

4. To obtain the diffraction field of the asymmetric grating, it is necessary to first analyze the diffraction field of the top tilt grating and then derive the diffraction field of any asymmetric grating.

2. The method of claim 1 .

5. The diffraction field of the top tilt grating is [0024] It is expressed as: where h is the height of the center of the grating ridge, Δh is the asymmetric height, f is the duty defined as l / d, d is the grating period, and l is the grating ridge width.

5. The method of claim 4.

6. The asymmetric lattice model includes top, bottom, sidewall, and top angle symmetries.

2. The method of claim 1 .

7. The ridges of the asymmetric grating model are divided into four parts G1, G2, G3, and G4, respectively, and the diffraction field of the asymmetric grating is expressed as follows: [0025] It is expressed as: Here, E ｍ Ｇ１ , E ｍ Ｇ２ , E ｍ Ｇ３ , and E ｍ Ｇ４ are the diffracted fields of the phase gratings G1, G2, G3, and G4, respectively, [0026] h １ , h ２ , h ３ , and h ４ represent the heights of the grating ridges of G1, G2, G3, and G4, respectively, and x １ , x ２ , x ３ , x ４ represents the center position of each part, and f １ , f ２ , f ３ , f ４ respectively represent the duties of G1, G2, G3 and G4 7. The method of claim 6.

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