CN106780600A - Pattern density computational methods - Google Patents
Pattern density computational methods Download PDFInfo
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- CN106780600A CN106780600A CN201710079130.2A CN201710079130A CN106780600A CN 106780600 A CN106780600 A CN 106780600A CN 201710079130 A CN201710079130 A CN 201710079130A CN 106780600 A CN106780600 A CN 106780600A
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- Prior art keywords
- pattern density
- computational methods
- wavelet transformation
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- area
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T5/00—Image enhancement or restoration
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20048—Transform domain processing
- G06T2207/20064—Wavelet transform [DWT]
Abstract
Present invention is disclosed a kind of pattern density computational methods.The pattern density computational methods that the present invention is provided include：The sample area of figure is determined according to sample rate；Scanned along graphic limit, set up wavelet transformation index；Calculate the area that wavelet transformation each sub-block intersects with graphic limit, acquisition sub-block coefficient；Each rank wavelet transform matrix is built according to sub-block coefficient；Each rank wavelet transform matrix is added successively, the pattern density distribution under different levels is obtained.Thus wavelet transformation is employed, the Density Distribution of multiple scopes can be simultaneously given, and can significantly reduces amount of calculation, improve computational efficiency.
Description
Technical field
The present invention relates to technical field of semiconductors, more particularly to a kind of pattern density computational methods.
Background technology
, it is necessary to be related to pattern density in the model of CMP (cmp) is set up, judged according to pattern density
Whether figure is uniform, further to complete to the perfect of technique.
Under normal circumstances, industry is estimated that pattern density is distributed according to the area that each lattice point is capped.Such as Fig. 1 and
Shown in Fig. 2, Fig. 1 is a schematic diagram of figure A covering lattice points B；Fig. 2 is Density Distributions of the figure A in lattice point B.Specifically may be used
To represent figure A by lattice point color range in each lattice point occupied area, and then represent pattern density distribution situation.Such as Fig. 2
In illustrated by different fillings, the lattice point B of top 3 shows the distribution of no figure without filling；Two, the left side lattice point of lower section
Filling is most light, and the lattice point filling of two, right side is taken second place, and middle two lattice points filling is most dense, can be right further combined with different filling institutes
The density range answered, calculates specific pattern density distribution situation.
But, it is complicated that for complicated and large-scale IC domains, in each lattice point, graphics area is calculated.In addition,
The Density Distribution in different range is usually used in CMP model, such as it is simultaneously close in 100 μm, 50 μm of needs and 10 μ ms
Degree is distributed to judge the uniformity of figure.The estimation of different range is, it is necessary to repartition lattice point, reference area is considerably increased
Amount of calculation.
Therefore, this situation how is improved, to improving computational efficiency, improved production plays the role of great.
The content of the invention
It is an object of the present invention to provide a kind of pattern density computational methods, improve computational efficiency.
In order to solve the above technical problems, the present invention provides a kind of pattern density computational methods, including：
The sample area of figure is determined according to sample rate；
Scanned along graphic limit, set up wavelet transformation index；
Calculate the area that wavelet transformation each sub-block intersects with graphic limit, acquisition sub-block coefficient；
Each rank wavelet transform matrix is built according to sub-block coefficient；
Each rank wavelet transform matrix is added successively, the pattern density distribution under different levels is obtained.
Optionally, for described pattern density computational methods, the wavelet transformation is two-dimentional haar wavelet transform.
Optionally, for described pattern density computational methods, scanned along graphic limit, set up wavelet transformation and index it
Before, set up orthogonal basis function.
Optionally, for described pattern density computational methods, the orthogonal basis function is Ψ (0,0), Ψ (1,0), Ψ
(0,1), Ψ (1,1).
Optionally, for described pattern density computational methods, after orthogonal basis function is set up, swept along graphic limit
Retouch, before setting up wavelet transformation index, also include：
Delete the basic function Ψ (1,1) for 0 after launching.
Optionally, for described pattern density computational methods, for the sample area more than 10 grades of wavelet transformations, carry out
Segmentation is calculated using parallel multiprocessor.
Optionally, for described pattern density computational methods, the sample area scope of 10 grades of small echos is the length of side
5000 μm of square.
Optionally, for described pattern density computational methods, become by calculating graphic limit and small echo in sample area
The value of the intersection point for changing calculates the area.
Optionally, for described pattern density computational methods, described each sub-block of calculating wavelet transformation and graphic limit
Intersecting area is calculated using parallel multiprocessor.
Optionally, for described pattern density computational methods, the sample area be some skirts into Closed Graph
Shape.
Compared with prior art, in the pattern density computational methods that the present invention is provided, including：Figure is determined according to sample rate
Sample area；Scanned along graphic limit, set up wavelet transformation index；Wavelet transformation each sub-block is calculated to intersect with graphic limit
Area, obtain sub-block coefficient；Each rank wavelet transform matrix is built according to sub-block coefficient；By each rank wavelet transform matrix successively phase
Plus, obtain the pattern density distribution under different levels.Thus wavelet transformation is employed, the density of multiple scopes can be simultaneously given
Distribution, and can significantly reduce amount of calculation, improve computational efficiency；
Further, calculated by parallel multiprocessor, it is also possible to improve computational efficiency.
Brief description of the drawings
Fig. 1 is the schematic diagram of figure A covering lattice point B in the prior art；
Fig. 2 is Density Distributions of the figure A in lattice point B；
Fig. 3 is the flow chart of pattern density computational methods in the present invention；
Fig. 4 is the basic function selected in one embodiment of the invention；
Fig. 5 is the schematic diagram of determination sample area in one embodiment of the invention；
Fig. 6 be one embodiment of the invention in set up wavelet transformation index schematic diagram；
The schematic diagram that Fig. 7 intersects for graphic limit in one embodiment of the invention with wavelet transformation；
Fig. 8 is the pattern density distribution under different levels in one embodiment of the invention.
Specific embodiment
Pattern density computational methods of the invention are described in more detail below in conjunction with schematic diagram, which show
The preferred embodiments of the present invention, it should be appreciated that those skilled in the art can change invention described herein, and still realize
Advantageous effects of the invention.Therefore, description below be appreciated that it is widely known for those skilled in the art, and not
As limitation of the present invention.
For clarity, not describing whole features of practical embodiments.In the following description, it is not described in detail known function
And structure, because they can make the present invention chaotic due to unnecessary details.It will be understood that opening in any practical embodiments
In hair, it is necessary to make a large amount of implementation details to realize the specific objective of developer, such as according to relevant system or relevant business
Limitation, another embodiment is changed into by one embodiment.Additionally, it should think that this development is probably complicated and expends
Time, but it is only to those skilled in the art routine work.
The present invention is more specifically described by way of example referring to the drawings in the following passage.Will according to following explanation and right
Book is sought, advantages and features of the invention will become apparent from.It should be noted that, accompanying drawing is in the form of simplifying very much and using non-
Accurately ratio, is only used to conveniently, lucidly aid in illustrating the purpose of the embodiment of the present invention.
Core concept of the invention is, there is provided a kind of pattern density computational methods, by using wavelet transformation, Neng Goutong
When provide the Density Distribution of multiple scopes and the efficiency of area reckoning can be improved.
The method includes：
Step S11, the sample area of figure is determined according to sample rate；
Step S12, scans along graphic limit, sets up wavelet transformation index；
Step S13, calculates the area that wavelet transformation each sub-block intersects with graphic limit, acquisition sub-block coefficient；
Step S14, each rank wavelet transform matrix is built according to sub-block coefficient；
Step S15, each rank wavelet transform matrix is added successively, obtains the pattern density distribution under different levels.
The preferred embodiment of the pattern density computational methods is exemplified below, with clear explanation present disclosure, should
It is clear that, present disclosure is not restricted to following examples, and other pass through the conventional skill of those of ordinary skill in the art
The improvement of art means is also within thought range of the invention.
Fig. 3 is refer to, and combines Fig. 4-Fig. 8, the computational methods to pattern density in the present invention are described in detail.
As shown in Fig. 2 in the present embodiment, the pattern density computational methods include：
Specifically, in step s 11, as shown in figure 4, determining the sample area of figure 10 according to sample rate.In the present invention
In, pattern density calculating is carried out using wavelet transformation, in such as Fig. 4, figure 10 is arranged in wavelet transform function image 20, institute
State sample area be some skirts into closed figure.The series of wavelet transformation launches according to 2 power, is with minimum dimension
As a example by 5 μm, the size that 10 grades of wavelet transformation can sample is 5*210μm, that is to say the foursquare model that the about length of side is 5000 μm
Enclose.The calculating brought in order to avoid data are excessive is complicated, for that beyond the region of the square scope, then can be divided
Cut, so as to be calculated using parallel multiprocessor, efficiency can be improved.Certainly, use region in the present embodiment is defined as side
About 5000 μm long of foursquare scope, foundation actual conditions, such as difference of processor function, required sample rate etc.,
Sample area can also be other scopes.
Specifically, the present embodiment is calculated by taking two-dimentional haar wavelet transform as an example, it is to be understood that two-dimentional Ha Er is small
Wave conversion is relatively simple with respect to other wavelet transformations, while needs of the invention are disclosure satisfy that, therefore two dimension is breathed out in the present embodiment
Your wavelet transformation is not to define range of choice of the invention, and other kinds of wavelet transformation can also be used in the present invention
In.
Specifically, in step s 12, being scanned along graphic limit, wavelet transformation index is set up.First, as shown in figure 5, building
Vertical orthogonal basis function.The orthogonal basis function includes 4, respectively Ψ (0,0), Ψ (1,0), Ψ (0,1), Ψ (1,1).Each
Orthogonal basis function is connect including four sub-blocks in matrix pattern, and each sub-block is constant (+1 or -1).Then, Fig. 6 is refer to,
In wavelet transform function image 20, it is scanned along graphic limit 30, sets up wavelet transformation index.This allows for small echo change
Change after deployment, be only not zero at graphic limit, in center section, that is to say the region that correspond to basic function Ψ (1,1),
Its value is 0, thus can delete Ψ (1,1) this basic function.
Specifically, in step s 13, the area that wavelet transformation each sub-block intersects with graphic limit, acquisition sub-block are calculated
Coefficient.As shown in fig. 7, to be illustrated as a example by graphic limit and basic function Ψ (1,0) intersection.Figure can first be calculated
Border and four intersection points of sub-block of basic function Ψ (1,0), then, to each sub-block difference reference area integration.Herein, can be with
According to green theorem, area integral is changed into and is integrated along the curve on border, and consider that the sub-block of basic function Ψ is constant (+1
Or -1), therefore, the phasor function in integration is linear function, and is straight line in view of border, therefore only needs to the every of calculation
The value of individual intersection point, you can the area is obtained, so as to obtain sub-block coefficient.
Further, can be calculated using parallel multiprocessor, to improve computational efficiency.
Specifically, in step S14, each rank wavelet transform matrix is built according to sub-block coefficient.The building process of this matrix
It is known to those skilled in the art, is not described in detail herein.
Specifically, in step S15, each rank wavelet transform matrix is added successively, the figure obtained under different levels is close
Degree distribution.As shown in figure 8, schematically illustrate the pattern density distribution situation under the rank wavelet transformation of 1 rank -6, i.e., can be simultaneously
Provide the Density Distribution of multiple scopes.For the ease of identification wherein in 1-4 ranks, with separated by dashed lines.In production application
In, it is possible to use gray scale is not come to each sub-box is filled out according to actual graphical density using gray scale under same order small echo in Fig. 8
Fill.
In sum, in the pattern density computational methods that the present invention is provided, wavelet transformation is employed, can simultaneously provides many
The Density Distribution of individual scope, and can significantly reduce amount of calculation, improve computational efficiency.
Obviously, those skilled in the art can carry out various changes and modification without deviating from essence of the invention to the present invention
God and scope.So, if these modifications of the invention and modification belong to the scope of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to comprising these changes and modification.
Claims (10)
1. a kind of pattern density computational methods, including：
The sample area of figure is determined according to sample rate；
Scanned along graphic limit, set up wavelet transformation index；
Calculate the area that wavelet transformation each sub-block intersects with graphic limit, acquisition sub-block coefficient；
Each rank wavelet transform matrix is built according to sub-block coefficient；
Each rank wavelet transform matrix is added successively, the pattern density distribution under different levels is obtained.
2. pattern density computational methods as claimed in claim 1, it is characterised in that the wavelet transformation is two-dimentional Haar wavelet transform
Conversion.
3. pattern density computational methods as claimed in claim 2, it is characterised in that scanned along graphic limit, set up small echo
Before manipulative indexing, orthogonal basis function is set up.
4. pattern density computational methods as claimed in claim 3, it is characterised in that the orthogonal basis function is Ψ (0,0), Ψ
(1,0), Ψ (0,1), Ψ (1,1).
5. pattern density computational methods as claimed in claim 4, it is characterised in that after orthogonal basis function is set up, on edge
Graphic limit is scanned, and before setting up wavelet transformation index, is also included：
Delete the basic function Ψ (1,1) for 0 after launching.
6. pattern density computational methods as claimed in claim 2, it is characterised in that for the sampling more than 10 grades of wavelet transformations
Region, is carried out segmentation and is calculated using parallel multiprocessor.
7. pattern density computational methods as claimed in claim 6, it is characterised in that the sample area scope of 10 grades of small echos
It is 5000 μm of square of the length of side.
8. pattern density computational methods as claimed in claim 2, it is characterised in that by calculating graphic limit in sample area
The area is calculated with the value of the intersection point of wavelet transformation.
9. pattern density computational methods as claimed in claim 1, it is characterised in that described each sub-block of calculating wavelet transformation with
The intersecting area of graphic limit is calculated using parallel multiprocessor.
10. pattern density computational methods as claimed in claim 1, it is characterised in that the sample area is some skirts
Into closed figure.
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| CN201710079130.2A CN106780600A (en) | 2017-02-14 | 2017-02-14 | Pattern density computational methods |
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105590338A (en) * | 2015-12-07 | 2016-05-18 | 中国科学院微电子研究所 | Three-dimensional reconstruction method for image of scanning electron microscope |
| CN106200279A (en) * | 2016-09-22 | 2016-12-07 | 上海华虹宏力半导体制造有限公司 | A kind of method of sampling for lithography layout OPC and device |
-
2017
- 2017-02-14 CN CN201710079130.2A patent/CN106780600A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105590338A (en) * | 2015-12-07 | 2016-05-18 | 中国科学院微电子研究所 | Three-dimensional reconstruction method for image of scanning electron microscope |
| CN106200279A (en) * | 2016-09-22 | 2016-12-07 | 上海华虹宏力半导体制造有限公司 | A kind of method of sampling for lithography layout OPC and device |
Non-Patent Citations (1)
| Title |
|---|
| 张宗新.: "《证券投资基金行为与市场质量冲击》", 31 July 2014 * |
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Application publication date: 20170531 |