CN102289146A - Method for optimizing two-phase phase shift mask based on generalized wavelet penalty function - Google Patents
Method for optimizing two-phase phase shift mask based on generalized wavelet penalty function Download PDFInfo
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- CN102289146A CN102289146A CN 201110272472 CN201110272472A CN102289146A CN 102289146 A CN102289146 A CN 102289146A CN 201110272472 CN201110272472 CN 201110272472 CN 201110272472 A CN201110272472 A CN 201110272472A CN 102289146 A CN102289146 A CN 102289146A
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Abstract
The invention provides a method for optimizing a phase shift mask based on a generalized wavelet function. In the method, by separating figures MO and M180 corresponding to opening parts of two-phase PSM 0DEG and 180DEG phases, and using wavelet penalty function of RO and R180 that corresponds to M0 and M180, a generalized wavelet penalty function R of two-phase PSM is obtained; two-phase PSM is optimized by using R; and the complexity and the manufacturing cost of the mask are reduced. and using wavelet penalty function of RO and R180 that corresponds to M0 and M180, a generalized wavelet penalty function R of two-phase PSM is obtained; two-phase PSM is optimized by using R; and the complexity and the manufacturing cost of the mask are reduced. Simultaneously, opening figures of 0DEG and 180DEG phases are independently processed and tokened respectively by a generalized wavelet penalty function method; and therefore, openings of 0DEG and 180DEG phases in the optimized mask are not mutually away from each other so that the advantage of phase modulation of two-phase PSM is reserved.
Description
Technical field
The present invention relates to a kind of method, belong to photoetching resolution enhancement techniques field based on broad sense small echo penalty function optimization two phase phase-shift mask.
Background technology
Current large scale integrated circuit generally adopts etching system manufacturing.Etching system mainly is divided into: four parts such as illuminator (comprising light source and condenser), mask, optical projection system and wafer.Photo etched mask adopts light transmission medium and resistance light medium to make, and the light transmission part is equivalent to opening to light.The light that light source sends is incident to mask, the opening portion printing opacity of mask after focusing on through condenser; Through behind the mask, light is incident on the wafer that scribbles photoresist via optical projection system, so just mask pattern is replicated on the wafer.
The etching system of main flow is the ArF degree of depth ultraviolet photolithographic system of 193nm at present, along with the photoetching technique node enters 45nm-22nm, the critical size of circuit has been far smaller than the wavelength of light source, so interference of light and diffraction phenomena are more remarkable, causes optical patterning to produce distortion and fuzzy.Etching system must adopt resolution enhance technology for this reason, in order to improve image quality.(phase-shifting mask PSM) is a kind of important photoetching resolution enhancement techniques to phase-shift mask.PSM adopts light transmission medium and resistance light medium to make, and the light transmission part is equivalent to opening to light.PSM is by changing the topological structure and the etch depth of mask light transmission part (being opening) in advance, and the amplitude and the phase place of modulation mask exit facet electric field intensity are to reach the purpose that improves imaging resolution.
But, the mask behind the employing PSM technical optimization, its manufacturing cost is higher, thereby causes great scale integrated circuit to make the raising of whole cost.The raising of mask manufacturing cost and difficulty mainly comes from following two aspects: the first, the PSM technology is added tiny auxiliary pattern on mask, thereby has increased the complexity of mask pattern.The second, in order to introduce the phase differential of transmitted light, PSM needs the etching depth of some opening is adjusted, thereby has increased the manufacture difficulty of mask.In order to design practical photo etched mask, must in the mask optimizing process, adopt and reduce the mask cost techniques.
Pertinent literature (Optics Express, 2007,15:15066~15079) has proposed a kind of small echo penalty function method of the PSM of reduction complexity.By utilizing wavelet function R and gradient matrix thereof
PSM is optimized, thereby effectively reduces the complexity of four phase PSM; Concrete principle is: make the neighbor pixel on the mask have identical transmissivity in the mask optimizing process as far as possible, thereby make the opening and the resistance light zone that have same phase on the mask concentrated relatively, finally reach the purpose that reduces the mask complexity.But for two phase PSM (as alternative expression PSM), it is made of 0 ° of phase place opening, 180 ° of phase place openings and light-blocking part.Utilize existing small echo penalty function method that two phase PSM is optimized, can make 0 ° and 180 ° of phase place openings mutually away from; But the advantage of two phase PSM just is to make 0 ° and 180 ° of phase place openings approaching mutually, utilizes the negative function Enhanced Imaging resolution of out of phase light; Therefore existing small echo penalty function method is not suitable for two phase PSM.
Summary of the invention
The purpose of this invention is to provide a kind of method of optimizing two phase PSM based on broad sense small echo penalty function; This method can effectively reduce the complexity of two phase PSM under the prerequisite that guarantees two phase PSM advantage, thereby reduces the manufacturing cost of two phase PSM.
Realize that technical scheme of the present invention is as follows:
A kind of method based on broad sense wavelet function optimization phase-shift mask, concrete steps are:
The transmissivity that the present invention sets 0 ° of phase place opening of two phase PSM is that the transmissivity of 1,180 ° of phase place opening is-1, and the transmissivity of light-blocking part is 0; With two phase PSM diagrammatic representation is the matrix M of N * N, and the element value of matrix M is the transmissivity of each pixel correspondence on the two phase PSM figure;
Described matrix M
0Be expressed as:
M
0=Γ{M} (1)
Described matrix M
180Be expressed as:
M
180=Γ{-1×M} (2)
Wherein, Γ x} is the hard decision function,
The sigmoid approximation to function M that utilizes of the present invention
0And M
180For: order
Get t
r=0, then (1) formula and (2) formula are approximately respectively:
Beneficial effect
The present invention is by separating 0 ° and 180 ° phase place opening portion graphs of a correspondence of two phase PSM M
0And M
180And utilize M
0And M
180Pairing small echo penalty function R
0And R
180Obtain the broad sense small echo penalty function R of two phase PSM, utilize R that two phase PSM is optimized, effectively reduce the complexity and the manufacturing cost of mask.The present invention simultaneously utilizes broad sense small echo penalty function method that 0 ° and 180 ° of phase place opening figure are carried out independent processing and sign respectively, therefore can not make 0 ° of optimizing in the mask of back and 180 ° of phase place openings mutually away from, thereby kept the phase modulation (PM) advantage of two phase PSM.
Description of drawings
Fig. 1 the present invention is based on the process flow diagram that broad sense small echo penalty function is optimized the method for two phase PSM.
Fig. 2 is the synoptic diagram of imaging in initial two phase PSM and the corresponding photoresist thereof.
Fig. 3 is under the situation of not using broad sense small echo penalty function method, the synoptic diagram of imaging in the photoresist of the two phase PSM of optimization and correspondence thereof.
Fig. 4 is the synoptic diagram of imaging in the two phase PSM that uses broad sense small echo penalty function method and optimize and the corresponding photoresist thereof.
Embodiment
Further the present invention is described in detail below in conjunction with accompanying drawing.
Inventive concept is: 0 ° of two phase PSM and 180 ° of phase place opening portion graphs of a correspondence are separated, calculate the high fdrequency component of 0 ° and the 180 ° pairing single order Haar of phase place opening figure wavelet transformation respectively, set up broad sense small echo penalty function R according to the high fdrequency component of above calculating, utilize R to combine with existing optimization aim function, PSM is optimized to two phase.
As shown in Figure 1, based on the method for broad sense small echo penalty function optimization two phase phase-shift mask, concrete steps are:
M in the present embodiment
0And M
180Can specifically be expressed as:
The transmissivity of setting PSM0 ° of phase place opening of two phase correspondence is that the transmissivity of 1,180 ° of phase place opening correspondence is-1, and the transmissivity of light-blocking part correspondence is 0.
With two phase PSM diagrammatic representation is the matrix M of N * N, the element value of matrix M is the transmissivity of each pixel correspondence on the two phase PSM figure, the element value that is the corresponding 0 ° of phase place opening of M is 1, and the element value of the corresponding 180 ° of phase place openings of M is-1, and the element value of the corresponding light-blocking part of M is 0.
Matrix M then
0Can be expressed as:
M
0=Γ{M} (1)
Matrix M
180Can be expressed as:
M
180=Γ{-1×M} (2)
Wherein, Γ x} is the hard decision function,
Wherein, the element of x representing matrix M;
Concrete process is:
Order
Wherein a represents slope, is used for controlling according to its different value the degree of tilt of curve; t
rThe expression threshold value.
{ x} is 0 to be the hard decision function of threshold value, therefore gets t because Γ
r=0, then (1) formula and (2) formula are approximately respectively
The detailed process of this step is:
M
0Horizontal high fdrequency component, vertical high frequency component and the oblique line high fdrequency component of single order Haar wavelet transformation be respectively
Matrix H
0, V
0And D
0, H
0(i, j), V
0(i, j) and D
0(i j) is respectively matrix element,
H
0(i,j)=M
0(2i-1,2j-1)-M
0(2i-1,2j)+M
0(2i,2j-1)-M
0(2i,2j)
V
0(i,j)=M
0(2i-1,2j-1)+M
0(2i-1,2j)-M
0(2i,2j-1)-M
0(2i,2j)
D
0(i,j)=M
0(2i-1,2j-1)-M
0(2i-1,2j)-M
0(2i,2j-1)+M
0(2i,2j)
M
180Horizontal high fdrequency component, vertical high frequency component and the oblique line high fdrequency component of single order Haar wavelet transformation be respectively
Matrix H
180, V
180And D
180, H
180(i, j), V
180(i, j) and D
180(i j) is respectively matrix element,
H
180(i,j)=M
180(2i-1,2j-1)-M
180(2i-1,2j)+M
180(2i,2j-1)-M
180(2i,2j)
V
180(i,j)=M
180(2i-1,2j-1)+M
180(2i-1,2j)-M
180(2i,2j-1)-M
180(2i,2j)
D
180(i,j)=M
180(2i-1,2j-1)-M
180(2i-1,2j)-M
180(2i,2j-1)+M
180(2i,2j)
With small echo penalty function R
0Be defined as M
0Single order Haar wavelet transformation level, vertically reach the energy summation of oblique line high fdrequency component, promptly
With small echo penalty function R
180Be defined as M
180Single order Haar wavelet transformation level, vertically reach the energy summation of oblique line high fdrequency component, promptly
Wherein, i, j=1,2, K,
P=1,2, q=1,2, the mod 2 of p '=(p+1), the mod 2 of q '=(q+1),
4 kinds of situations have been comprised: the first, p=1, q=1; The second, p=1, q=2;
Three, p=2, q=1; Four, p=2, q=2.
Pertinent literature (Optics Express, 2007,15:15066~15079) the optimization aim function D of mask is configured to the difference of imaging in the targeted graphical photoresist corresponding with mask Euler's distance square; Size as targeted graphical is N * N, then
Be the pixel value of each point in the targeted graphical, Z (x y) is the pixel value of imaging in the photoresist of mask correspondence, Z (x, y) with
Value be 0 or 1.With the broad sense small echo penalty function R structure fresh target function J that combines with D be:
J=D+R。
The gradient matrix of fresh target function J may be calculated:
Employing is based on the optimized Algorithm of gradient, the J and the utilization that can utilize R to obtain
The VJ that obtains carries out iteration optimization to mask pattern.
Embodiment of the present invention:
Fig. 2 is the synoptic diagram of imaging in initial two phase PSM and the corresponding photoresist thereof.201 is initial two phase PSM figure, and its shape is consistent with targeted graphical, and white is represented 0 ° of phase place opening portion, and black is represented 180 ° of phase place opening portions, and grey is represented light-blocking part, and its critical size is 45nm.202 for adopting 201 as behind the mask, imaging in the photoresist of etching system, image error is 1526 (image error is defined as the value of objective function here), and the CD error is 20nm, and wherein the CD error is the critical size of imaging in the actual photoresist in horizontal median axis place and the difference of desirable critical size.
Fig. 3 is under the situation of not using broad sense small echo penalty function method, the synoptic diagram of imaging in the photoresist of the two phase PSM of optimization and correspondence thereof.Under the situation of not using broad sense small echo penalty function method, adopt steepest prompt drop method that mask is optimized.301 are the two phase PSM figure after optimizing.302 is to adopt 301 as behind the mask, imaging in the photoresist of etching system, and image error is 277, the CD error is 0.
Fig. 4 is the synoptic diagram of imaging in the two phase PSM that uses broad sense small echo penalty function method and optimize and the corresponding photoresist thereof.Under the situation of using broad sense small echo penalty function method, adopt steepest prompt drop method that mask is optimized.401 are the two phase PSM figure after optimizing.402 is to adopt 401 as behind the mask, imaging in the photoresist of etching system, and image error is 321, the CD error is 0.
Comparison diagram 2,3,4 as can be known, though the broad sense small echo penalty function method among employing the present invention is optimized two phase PSM, the image error of two phase PSM is slightly larger than the situation of not using broad sense small echo penalty function method, but the opening figure of the two phase PSM after it is optimized more approaches regular rectangular shape or regular polygon.Therefore broad sense small echo penalty function method can effectively be controlled mask complexity and manufacturing cost thereof when being lowered into picture sum of errors CD error.
Only consider the situation of alternative expression PSM among the present invention, alternative expression PSM is: the opening portion transmissivity is 1 or-1, hinders the light zone simultaneously between different openings in addition; But on behalf of the present invention, this only be confined to the situation of alternative expression PSM, and the present invention also is applicable to various ways such as attenuation type PSM.
Though combine accompanying drawing the specific embodiment of the present invention has been described; but to those skilled in the art; under the prerequisite that does not break away from the principle of the invention, can also make some distortion, replacement and improvement, these also should be considered as belonging to protection scope of the present invention.
Claims (3)
1. optimize the method for phase-shift mask based on the broad sense wavelet function for one kind, it is characterized in that concrete steps are:
Step 101,0 ° and 180 ° phase place opening portion graphs of a correspondence of separation two phase phase-shift mask PSM; Wherein 0 ° of phase place opening portion graph of a correspondence is expressed as the matrix M of N * N
0, M
0The element value of corresponding 0 ° of phase place opening portion is 1, and the remainder element value is 0; 180 ° of phase place opening portion graphs of a correspondence are expressed as the matrix M of N * N
180, M
180The element value of corresponding 180 ° of phase place opening portions is 1, and the remainder element value is 0;
Step 102, utilize sigmoid curve sigmoid approximation to function M
0And M
180, obtain and have the M that can lead characteristic
0And M
180
Step 103, find the solution M
0And M
180The high fdrequency component of single order Ha Er Haar wavelet transformation, and according to M
0It is R that corresponding high fdrequency component is found the solution the small echo penalty function
0, according to M
180It is R that corresponding high fdrequency component is found the solution the small echo penalty function
180
Step 104, the broad sense small echo penalty function of two phase PSM is defined as R
0And R
180Linear combination, i.e. R=γ
0R
0+ γ
180R
180, γ wherein
0And γ
180Be respectively R
0And R
180Weight coefficient, and ask for the gradient matrix of broad sense small echo penalty function R
2. the method based on broad sense wavelet function optimization phase-shift mask according to claim 1 is characterized in that the transmissivity of setting PSM0 ° of phase place opening of two phase is that the transmissivity of 1,180 ° of phase place opening is-1, and the transmissivity of light-blocking part is 0; With two phase PSM diagrammatic representation is the matrix M of N * N, and the element value of matrix M is the transmissivity of each pixel correspondence on the two phase PSM figure;
Described matrix M
0Be expressed as:
M
0=Γ{M} (1)
Described matrix M
180Be expressed as:
M
180=Γ{-1×M} (2)
Wherein, Γ x} is the hard decision function,
3. the method based on broad sense wavelet function optimization phase-shift mask according to claim 2 is characterized in that the described sigmoid approximation to function M that utilizes
0And M
180For: order
Get t
r=0, then (1) formula and (2) formula are approximately respectively:
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CN102636882A (en) * | 2012-05-11 | 2012-08-15 | 北京理工大学 | Method for analyzing space images of high numerical aperture imaging system |
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US6503666B1 (en) * | 2000-07-05 | 2003-01-07 | Numerical Technologies, Inc. | Phase shift masking for complex patterns |
JP2008529066A (en) * | 2005-01-21 | 2008-07-31 | インターナショナル・ビジネス・マシーンズ・コーポレーション | Optimization of differential alternating phase shift mask |
CN102135725A (en) * | 2011-03-20 | 2011-07-27 | 北京理工大学 | Method for acquiring total number of cut rectangles of PBOPC (Pixel-Based Optical Proximity Correction) optimal mask pattern |
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US6503666B1 (en) * | 2000-07-05 | 2003-01-07 | Numerical Technologies, Inc. | Phase shift masking for complex patterns |
JP2008529066A (en) * | 2005-01-21 | 2008-07-31 | インターナショナル・ビジネス・マシーンズ・コーポレーション | Optimization of differential alternating phase shift mask |
CN102135725A (en) * | 2011-03-20 | 2011-07-27 | 北京理工大学 | Method for acquiring total number of cut rectangles of PBOPC (Pixel-Based Optical Proximity Correction) optimal mask pattern |
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
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CN102636882A (en) * | 2012-05-11 | 2012-08-15 | 北京理工大学 | Method for analyzing space images of high numerical aperture imaging system |
CN102636882B (en) * | 2012-05-11 | 2013-10-02 | 北京理工大学 | Method for analyzing space images of high numerical aperture imaging system |
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