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Indicator function-based fast decomposition method for cross transfer function

A technology of indicator function and transfer function, which is applied in the direction of complex mathematical operations, photolithography exposure devices, micro-lithography exposure equipment, etc., can solve the problem of affecting the efficiency of lithography process design, the efficiency of affecting the calculation of light intensity distribution, time-consuming, etc. problems, to meet the requirements of lithography process design, fast and efficient calculation of light intensity distribution

Inactive Publication Date: 2018-01-23
SUZHOU COGENDA ELECTRONICS CO LTD
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Problems solved by technology

However, according to the Hopkins optical imaging theory, a four-dimensional cross-transfer function TCC is established, and the calculation of the cross-transfer function TCC involves quadruple integral operations, which is very time-consuming
If the corresponding optical parameters change, TCC has to be recalculated, and the calculation of TCC according to the normal calculation method will seriously affect the efficiency of light intensity distribution calculation, thereby affecting the design efficiency of lithography process

Method used

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  • Indicator function-based fast decomposition method for cross transfer function
  • Indicator function-based fast decomposition method for cross transfer function
  • Indicator function-based fast decomposition method for cross transfer function

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Embodiment

[0035] Based on the imaging theory of Hopkins diffractive optics, the formula of imaging light intensity distribution function is as follows:

[0036]

[0037] Among them, i is the imaginary number unit, M(f,g)=F[m(x,y)] is the two-dimensional Fourier transform (FFT, Fast Fourier Transform) of the spatial distribution of the mask plate, and TCC is the corresponding four-dimensional cross transfer function , which is defined as:

[0038] TCC(f 1 , g 1 ; f 2 , g 2 )=∫∫J(f,g)·P(f+f 1 ,g+g 1 )·P * (f+f 2 ,g+g 2 )dfdg (2)

[0039] Among them, J(f,g) is the light source function, P(f,g) is the pupil function of the imaging system, P * (f, g) is the complex conjugate of P(f, g) of the pupil function, expressing the optical parameters of the optical imaging system. According to Cobb's decomposition algorithm, there is a singular value decomposition of TCC as follows:

[0040]

[0041] Among them, Ker i (f, g) is the kernel function of TCC, then the light intensity d...

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Abstract

The invention discloses an indicator function-based fast decomposition method for a cross transfer function. The method comprises the steps of (1) obtaining a light source function J(f, g) of an imaging system; (2) dividing a region omega of describing a light source to obtain a group of orthogonal sub-regions omegaij and describing the light source function J(f, g) by using an indictor function Iij(f, g) on the orthogonal sub-regions; (3) calculating inverse Fourier transform of the indictor function Iij(f, g), obtaining a primary function Lij(x, y) in a spatial domain, projecting a light source mutual intensity function as shown in the specification in the spatial domain to a group of primary functions as shown in the specification and obtaining decomposition of the light source mutual intensity function as shown in the specification; (4) building a core function as shown in the specification of the cross transfer function as shown in the specification in the spatial domain; and (5)calculating a convolution of the core function as shown in the specification and a mask pattern as shown in the specification and obtaining an exposure pattern as shown in the specification on an image plane. The light source function is expressed by using the indicator function Iij(f, g) on the orthogonal sub-regions, the decomposition of the light source mutual intensity function as shown in thespecification is directly obtained by using an orthogonality relationship of the indicator function and a projection coefficient of the light source, the core function as shown in the specification of the cross transfer function as shown in the specification is easily obtained, so that light intensity distribution calculation is fast and efficient.

Description

【Technical field】 [0001] The invention belongs to the technical field of lithographic resolution enhancement in semiconductor device process simulation, and in particular relates to a fast decomposition method of a cross transfer function based on an indicator function established in the Hopkins imaging principle. 【Background technique】 [0002] Photolithography is the main means of pattern transfer technology in the production process of semiconductor devices, which has the advantages of high production efficiency and relatively low cost. The lithography process is based on diffractive optics, which obtains the light intensity distribution of a specific pattern on the imaging plane, that is, optical imaging. With the development of semiconductor technology, the size of semiconductor devices is getting smaller and smaller. When the feature size is close to or even smaller than the wavelength of light used in the photolithography process, optical diffraction will cause the ex...

Claims

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Application Information

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IPC IPC(8): G03F7/20G06F17/14
Inventor 贡顶沈忱崔绍春陈雪莲鄢丽萍
Owner SUZHOU COGENDA ELECTRONICS CO LTD
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