Polar coordinate sampling-based cross transfer function quick decomposition method

A transfer function and polar coordinate technology, applied in electrical digital data processing, special data processing applications, instruments, etc., to achieve the effect of easy singular value decomposition, fast and efficient calculation, and meet the needs of lithography process design

Inactive Publication Date: 2018-01-30
SUZHOU COGENDA ELECTRONICS CO LTD
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Problems solved by technology

On the other hand, FFT has a coupling relationship between discrete sampling in the frequency domain and discrete sampling in the space domain, and discrete sampling can only be orthogonal sampling

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  • Polar coordinate sampling-based cross transfer function quick decomposition method
  • Polar coordinate sampling-based cross transfer function quick decomposition method
  • Polar coordinate sampling-based cross transfer function quick decomposition method

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Embodiment

[0048] Based on the imaging theory of Hopkins diffractive optics, the formula of imaging light intensity distribution function is as follows:

[0049]

[0050] 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:

[0051] 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)

[0052] 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. The above-mentioned cross transfer function definition is a description on the frequency domain space, then the expression of the cross transfer function on the space domain can be obtained by Fourier transfor...

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Abstract

The invention discloses a polar coordinate sampling-based cross transfer function quick decomposition method. The method comprises the following steps of 1) obtaining optical parameters of an imagingsystem; 2) obtaining coordinates (ri, theta j) of sampling points on a spatial domain by adopting a polar coordinate sampling method; 3) calculating light source mutual intensity functions, defined inthe specification, and pupil functions, defined in the specification, corresponding to the sampling points through non-uniform inverse Fourier transform; 4) calculating a cross transfer function value, defined in the specification, of the spatial domain corresponding to the sampling points, and establishing a sampling matrix defined in the specification; 5) establishing a group of orthogonal basis functions defined in the specification, calculating function values, defined in the specification, of the orthogonal basis functions in corresponding polar coordinate sampling positions, and establishing a matrix Q=[q1, q2, ...qk]; 6) performing QR matrix decomposition, defined in the specification, on the matrix Q; 7) calculating a projection matrix and performing singular value decomposition on the projection matrix P to obtain P=UU*; 8) obtaining a kernel function, defined in the specification, of the cross transfer function, defined in the specification, on the spatial domain. Quick analysis can be performed to obtain the TCC kernel function, so that light intensity distribution calculation is quick and efficient, and actual photoetching process design demands are met.

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 polar coordinate sampling. 【Background technique】 [0002] In the production process of semiconductor devices, the traditional top-down photolithography process of pattern transfer technology has the advantages of high production efficiency and relatively low cost, and is the main means of industrial production at present. The lithography process simulation technology mainly includes the lithography system imaging model and the reverse optimization process. The reverse optimization is an iterative process. Each iteration needs to call the lithography imaging model to correctly estimate the silicon wafer under specific lithography conditions. image. The optical imaging model is the key to the lithography process. At present, the ba...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
Inventor 贡顶沈忱崔绍春陈雪莲鄢丽萍
Owner SUZHOU COGENDA ELECTRONICS CO LTD
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