CN108614390A - A kind of source mask optimization method using compressed sensing technology - Google Patents

A kind of source mask optimization method using compressed sensing technology Download PDF

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CN108614390A
CN108614390A CN201810645227.XA CN201810645227A CN108614390A CN 108614390 A CN108614390 A CN 108614390A CN 201810645227 A CN201810645227 A CN 201810645227A CN 108614390 A CN108614390 A CN 108614390A
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optimization
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CN108614390B (en
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马旭
王志强
赵琦乐
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Beijing Institute of Technology BIT
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    • GPHYSICS
    • G03PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03FPHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F1/00Originals for photomechanical production of textured or patterned surfaces, e.g., masks, photo-masks, reticles; Mask blanks or pellicles therefor; Containers specially adapted therefor; Preparation thereof
    • GPHYSICS
    • G03PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03FPHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F1/00Originals for photomechanical production of textured or patterned surfaces, e.g., masks, photo-masks, reticles; Mask blanks or pellicles therefor; Containers specially adapted therefor; Preparation thereof
    • G03F1/68Preparation processes not covered by groups G03F1/20 - G03F1/50
    • G03F1/70Adapting basic layout or design of masks to lithographic process requirements, e.g., second iteration correction of mask patterns for imaging

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Abstract

The invention discloses a kind of source mask optimization method using compressed sensing technology, the image that light source optimization SO problems are configured to solve 2 norms in the case where solving as Condition of Non-Negative Constrains by the present invention restores problem, i.e.,:s.t.Wherein constraints system of linear equationsThe corresponding aerial image of light source is as possible close to target imaging value after making optimization.On the other hand, photomask optimization MO problems are configured to the image optimization problem containing sparse regular terms and low-rank regular terms by the present invention, i.e.,:Wherein constraints Nonlinear System of EquationsMake the mask after optimization and light source corresponding aerial image observation data as possible close to the observation data on targeted graphical,Constraints can further decrease the number of equation group in optimization process,Constraints can ensure that the complexity of mask in optimization process reduces as possible.

Description

A kind of source mask optimization method using compressed sensing technology
Technical field
The present invention relates to photoetching resolutions to enhance technical field, and in particular to a kind of to be covered using the light source of compressed sensing technology Mould optimization method.
Background technology
Optical lithography is current mainstream photoetching technique, it utilizes optical projection image-forming principle, is exposed by step-scan Mode the integrated circuit pattern on mask is transferred on the chip for being coated with photoresist.With the quick hair of semicon industry Exhibition, the characteristic size of super large-scale integration are also constantly reducing.And lithography system is essential core in IC manufacturing industry sets Standby, the photoetching technique of mainstream mainly uses the deep ultraviolet immersion lithography of optical source wavelength 193nm at present.
As photoetching technique node enters 45-14nm, the critical size of integrated circuit has been enter into deep sub-wavelength range, at this time RET (resolution enhancement technique, abbreviation RET) must be used to further increase The resolution ratio of lithography system and imaging fidelity.Light source-photomask optimization (source-mask optimization, abbreviation SMO) Technology is to improve one of the important method of optical patterning resolution ratio and anti-aliasing degree, and SMO had been imaged using light source and mask Coupled relation in journey optimizes the intensity distribution of light source while carrying out predistortion to mask, can further decrease technique The factor and raising lithography system imaging performance.Previous SMO technologies mainly use the optimization algorithm of gradient descent method to pixelation Light source and mask optimize, but the light source and mask due to pixelation need to handle huge number during optimization According to amount, the operation efficiency of traditional optimization algorithm will significantly reduce, for this purpose, for SMO technologies operation efficiency problem need into One step solves.
Pertinent literature (Journal of the Optical Society of America A, 2013,30:112-123) A kind of SMO technologies based on gradient descent method are proposed, this method is directed to the optimization order of light source and mask, it is proposed that three kinds are not Same optimization method, is synchronized model, alternate type and hybrid optimized method respectively, wherein the effect of optimization with mixed type is managed the most Think, but the above method needs a large amount of run time, operational efficiency needs to further increase in optimization process.
Pertinent literature (Optics Express, 2017,25:It 7131-7149) proposes a kind of based on self-adapting compressing sense Know that the quick SO methods of technology, this method assume that light source figure is sparse in certain group sparse basis, i.e., light source figure is in the group Most coefficient values on base are equal to 0 or close to 0.Later, this method according to
The blue noise method of sampling chooses several observation points in the key area of circuit layout, and construction SO optimizes mathematical modulo Type, and above-mentioned SO problems are solved using linear Bu Laigeman algorithms, the light source figure after being optimized.
But there are 2 points of deficiencies for above method:First, the linear Bu Laigeman algorithms that the above method uses are needed every Zero setting is forced to the optimized variable of light source during suboptimization, this operates the optimal solution that will necessarily influence SO problems, to influence The imaging performance of lithography system;Second, the above method considers only linear compression cognition technology in light source optimization problem Using non-linear compression cognition technology not being applied in the optimization problem of mask, therefore final optical patterning performance is also It is not optimal result.
In conclusion the operation efficiency of tradition SMO methods, and the SO Optimal solution problems based on linear compression cognition technology It remains to be further improved and improves.
Invention content
In view of this, the present invention provides a kind of source mask optimization methods using compressed sensing technology, using gradient The sparse restructing algorithm GPSR of projection solves light source and optimizes SO problems, and each iteration updates obtained all right and wrong in optimization process Negative solution, does not force zero setting relevant operation, and similar in algorithm operation time, optimum results are more nearly practical true Value, can further increase optical patterning performance;And for photomask optimization MO problems, targeted graphical and aerial image are dropped Sampling, to reduce the number of optimization method group, can preferably improve operation efficiency.
In order to achieve the above objectives, technical scheme of the present invention includes the following steps:
Light source is initialized as N by step 101S×NSLight source figure J, by mask graph M and targeted graphicalRasterizing For the figure of N × N, wherein NSIt is integer value with N.
Step 102 carries out point by point scanning to the light source figure J, and converts the light source figure J to N2× 1 light Source vectorThe light source vectorElement value be equal to the light source figure J respective pixel value.
Point by point scanning is carried out to mask graph M, and converts M to N2× 1 mask vectorThe mask vector's Element value is equal to the respective pixel value of the mask graph M.
To targeted graphicalPoint by point scanning is carried out, and willIt is converted into N2× 1 object vectorThe object vector Element value be equal to targeted graphicalRespective pixel value.
Step 103 selectes two groups of group basic function ΨJAnd ΨMSo that light source vectorWith mask vectorRespectively in ΨJWith ΨMOn be sparse;By light source vectorIn ΨJUpper expansion obtainsMask vectorIn ΨMUpper expansion obtainsWhereinWithCoefficient after being respectively unfolded.
Step 104 calculates illumination interaction coefficent ICC matrixes I using initial mask graph Mcc, size N2×NS 2; And to targeted graphicalWith ICC matrixes IccIt is down-sampled to respectively obtainWith
Step 105, the form for being constructed in light source optimization SO problems:
WhereinRefer toOptimum results;For vector2 norms;λ is weight coefficient;For vector1 norm;As constraints.
Step 106 optimizes SO problems using the light source in the sparse restructing algorithm GPSR solution procedures 105 of gradient projection, Obtain corresponding optimal light source figureOptimum resultsLight source figure after calculation optimization isΨ'JIt is ΨJ Transposition.
Step 107 calculates aerial image I (θ according to the light source optimized in step 106M) and scan obtain the space at As I (θM) aerial image vectorAnd it is rightWithDown-sampled obtain is carried out respectivelyWith
Photomask optimization MO problems are constructed in form by step 108:
WhereinIt isOptimum results;For vectorLow-rank regular terms,For vectorIt is sparse just Then item, α and β are respectivelyWithThe weight coefficient of regular terms.
Step 109, using division Bu Laigeman algorithm Split Bregman solution procedures 108 in MO problems, obtain pair Answer the vector of optimal mask graphMask graph after calculation optimization isΨ'MFor ΨMTransposition.
Further, described right in step 107WithDown-sampled obtain is carried out respectivelyWithSpecifically For:
Step 201, the targeted graphicalThe matrix for being N × N for size;Lightproof part in middle corresponding targeted graphical Element value is set as 1, and light transmission part element value is set as 0, rightRow and column carry out value every K pixel respectively and obtainDrop Matrix after samplingSize is indicated with N/K × N/K.
Step 202, to the aerial image I (θM) row and column carry out value every K pixel respectively and obtain I (θM) drop and adopt Matrix I after samplekM), size is N/K × N/K.
Advantageous effect:
The object of the present invention is to provide a kind of source masks using compressed sensing technology to optimize SMO methods.First, for The method construct constraints system of linear equations that SO problems are combined using blue noise sampling and adaptive projection matrix, later, Light source optimization SO problems are converted to the image recovery problem for solving 2 norms, light source figure is carried out using GPSR restructing algorithms Optimization.Compared to existing linear Bu Laigeman algorithms, the GPSR restructing algorithms in the present invention can not only ensure similar operation Efficiency, and the negative solution that optimization process can be avoided to generate well, the result optimized are more nearly the reality of light source Actual value can further increase the imaging performance of lithography system, linear compression cognition technology answering in light source optimization problem With;It is secondly, down-sampled to targeted graphical and aerial image progress using the method for dot interlace value for photomask optimization MO problems, Using after down-sampled targeted graphical and aerial image construct the loss function of low-dimensional, in order to further speed up optimization efficiency and carry Sparse and two regular terms of low-rank are also added in loss function and use restraint by the manufacturability of high mask, the present invention.
Description of the drawings
Fig. 1 is the flow chart of the SMO methods of the present invention using compressed sensing technology.
Fig. 2 is the optimization light source figure obtained using conventional hybrid type SMO methods, mask graph and its in nominal exposure amount Imaging schematic diagram in the photoresist of best focal plane down.
When Fig. 3 is K=2, the optimization light source figure that is obtained using the SMO methods based on compressed sensing technology in the present invention Shape, mask graph and its imaging schematic diagram in the photoresist of best focal plane under nominal exposure amount.
When Fig. 4 is K=4, the optimization light source figure that is obtained using the SMO methods based on compressed sensing technology in the present invention Shape, mask graph and its imaging schematic diagram in the photoresist of best focal plane under nominal exposure amount.
Fig. 5 is to be obtained using after the SMO methods optimization based on compressed sensing technology in conventional hybrid type SMO methods and the present invention The lithography system process window contrast schematic diagram arrived.
Specific implementation mode
The present invention will now be described in detail with reference to the accompanying drawings and examples.
The principle of the present invention:Practical lithography system imaging performance generally use image error, mask complexity, process window Etc. indexs evaluated.In order to improve optical patterning fidelity, reducing mask complexity and expand process window, the present invention is by SO The image that problem is configured to solve 2 norms in the case where solving as Condition of Non-Negative Constrains restores problem, i.e.,:
Wherein constraints system of linear equationsThe corresponding aerial image of light source is as possible close to target imaging after making optimization Value.
On the other hand, MO problems are configured to the image optimization problem containing sparse regular terms and low-rank regular terms by the present invention, I.e.:
Wherein constraints Nonlinear System of EquationsMake the mask after optimization and the corresponding aerial image observation of light source Data as possible close to the observation data on targeted graphical,Constraints can further decrease equation group in optimization process Number,Constraints can ensure that the complexity of mask in optimization process reduces as possible.
The present invention provides a kind of source mask optimization method using compressed sensing technology, flow is as shown in Figure 1, packet It includes:
Light source is initialized as N by step 101S×NSLight source figure J, by mask graph M and targeted graphicalRasterizing For the figure of N × N, wherein NSIt is integer value with N.
Step 102 carries out point by point scanning to the light source figure J, and converts the light source figure J to N2× 1 light Source vectorThe light source vectorElement value be equal to the light source figure J respective pixel value.
Point by point scanning is carried out to mask graph M, and converts M to N2× 1 mask vectorThe mask vector's Element value is equal to the respective pixel value of the mask graph M.
To targeted graphicalPoint by point scanning is carried out, and willIt is converted into N2× 1 object vectorThe object vector's Element value is equal to targeted graphicalRespective pixel value.
Step 103 selectes two groups of group basic function ΨJAnd ΨMSo that light source vectorWith mask vectorRespectively in ΨJWith ΨMOn be it is sparse, i.e., light source vectorWith mask vectorIn ΨJAnd ΨMMost of coefficient after being unfolded on base is 0 or connects It is bordering on 0;By light source vectorIn ΨJUpper expansion obtainsMask vectorIn ΨMUpper expansion obtains WhereinWithCoefficient after being respectively unfolded.
Step 104 calculates illumination interaction coefficent ICC (illumination cross using initial mask graph M Coefficient) matrix Icc, size N2×NS 2;And to targeted graphicalWith ICC matrixes IccIt is down-sampled to respectively obtainWithS is mark, and blue noise and the adaptive matrix method of sampling are used in the present invention.
Step 105, the form for being constructed in light source optimization SO problems:
WhereinRefer toOptimum results;For vector2 norms;λ is weight coefficient;For vector1 norm;As constraints.
Step 106 optimizes SO problems using the light source in the sparse restructing algorithm GPSR solution procedures 105 of gradient projection, Obtain corresponding optimal light source figureOptimum resultsLight source figure after calculation optimization isΨ'JIt is ΨJ Transposition.
Step 107 calculates aerial image I (θ according to the light source optimized in step 106M) and scan obtain the space at As I (θM) aerial image vectorAnd it is rightWithDown-sampled obtain is carried out respectivelyWith
It is right in step 107 in the embodiment of the present inventionWithDown-sampled obtain is carried out respectivelyWithSpecifically For:
Step 201, the targeted graphicalThe matrix for being N × N for size;Lightproof part in middle corresponding targeted graphical Element value is set as 1, and light transmission part element value is set as 0, rightRow and column carry out value every K pixel respectively and obtainDrop Matrix after samplingSize is indicated with N/K × N/K;
Step 202, to the aerial image I (θM) row and column carry out value every K pixel respectively and obtain I (θM) drop and adopt Matrix I after samplekM), size is N/K × N/K.
Photomask optimization MO problems are constructed in form by step 108:
WhereinIt isOptimum results;For vectorLow-rank regular terms,For vectorIt is sparse just Then item, α and β are respectivelyWithThe weight coefficient of regular terms.
Step 109, using division Bu Laigeman algorithm Split Bregman solution procedures 108 in MO problems, obtain pair Answer the vector of optimal mask graphMask graph after calculation optimization isΨ'MFor ΨMTransposition.
The embodiment of the present invention:
Be illustrated in figure 2 the optimization light source figure obtained using conventional hybrid type SMO methods, optimization mask graph and its Imaging schematic diagram in the photoresist of best focal plane under nominal exposure amount.201 are obtained using conventional hybrid type SMO methods Optimize light source figure, white represents light-emitting zone, and black represents not light-emitting zone.202 be to be obtained using conventional hybrid type SMO methods The mask graph arrived, white represent open area, and black represents light, critical size 45nm.203 is using 201 As light source, 202 be used as mask, when not considering variation of exposure and defocusing effect, in the photoresist of ideal focal plane at Picture, image error 2888, wherein image error are defined as square of imaging and Euler's distance of targeted graphical in photoresist, cover Mould complexity is 197, and the calculating of wherein mask complexity is the test carried out using the Calibre simulation softwares of profession, entirely SMO Optimizing Flow operation times are 1170991 seconds.
It is the optimization light source figure that is obtained using the SMO methods based on CS technologies, excellent in the case of being illustrated in figure 3 K=2 Change mask graph and its imaging schematic diagram in the photoresist of best focal plane under nominal exposure amount.301 is using based on CS The optimization light source figure that the SMO methods of technology obtain, white represent light-emitting zone, and black represents not light-emitting zone.302 be use The mask graph that SMO methods based on CS technologies obtain, white represent open area, and black represents light, crucial ruler Very little is 45nm.303 is are used as mask using 301 as light source, 302, when not considering variation of exposure and defocusing effect, in ideal It is imaged in the photoresist of focal plane, image error 1376, mask complexity is 92, entire SMO Optimizing Flows operation time It is 118532 seconds.
It is the optimization light source figure that is obtained using the SMO methods based on CS technologies, excellent in the case of being illustrated in figure 4 K=4 Change mask graph and its imaging schematic diagram in the photoresist of best focal plane under nominal exposure amount.401 is using based on CS The optimization light source figure that the SMO methods of technology obtain, white represent light-emitting zone, and black represents not light-emitting zone.402 be use The mask graph that SMO methods based on CS technologies obtain, white represent open area, and black represents light, crucial ruler Very little is 45nm.403 is are used as mask using 401 as light source, 402, when not considering variation of exposure and defocusing effect, in ideal It is imaged in the photoresist of focal plane, image error 2580, mask complexity is 151, entire SMO Optimizing Flows operation time It is 96992 seconds.
The lithography system work obtained after the SMO methods optimization being illustrated in figure 5 in conventional hybrid type SMO methods and the present invention Skill window comparison diagram.501 process windows obtained for conventional hybrid type SMO methods, 502 when being K=2, the side SMO in the present invention The process window that method obtains, 503 when being K=4, the obtained process window of SMO methods in the present invention.
It is found that comparing existing conventional hybrid type SMO methods, the SMO methods in the present invention have more comparison diagram 2,3,4,5 High operation efficiency, mask complexity is lower, and the imaging performance of lithography system is more preferable after optimization.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention. All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in the present invention's Within protection domain.

Claims (2)

1. a kind of source mask optimization method using compressed sensing technology, which is characterized in that including:
Light source is initialized as N by step 101S×NSLight source figure J, by mask graph M and targeted graphicalGrid turn to N × The figure of N, wherein NSIt is integer value with N;
Step 102 carries out point by point scanning to the light source figure J, and converts the light source figure J to N2× 1 light source vectorThe light source vectorElement value be equal to the light source figure J respective pixel value;
Point by point scanning is carried out to mask graph M, and converts M to N2× 1 mask vectorThe mask vectorElement Respective pixel value of the value equal to the mask graph M;
To targeted graphicalPoint by point scanning is carried out, and willIt is converted into N2× 1 object vectorThe object vectorElement Value is equal to targeted graphicalRespective pixel value;
Step 103 selectes two groups of group basic function ΨJAnd ΨMSo that light source vectorWith mask vectorRespectively in ΨJAnd ΨMOn It is sparse;By light source vectorIn ΨJUpper expansion obtainsMask vectorIn ΨMUpper expansion obtainsWhereinWithCoefficient after being respectively unfolded;
Step 104 calculates illumination interaction coefficent ICC matrixes I using initial mask graph Mcc, size N2×NS 2;And it is right Targeted graphicalWith ICC matrixes IccIt is down-sampled to respectively obtainWith
Step 105, the form for being constructed in light source optimization SO problems:
WhereinRefer toOptimum results;For vector2 norms;λ is weight coefficient;For to Amount1 norm;As constraints;
Step 106 optimizes SO problems using the light source in the sparse restructing algorithm GPSR solution procedures 105 of gradient projection, obtains Corresponding optimal light source figureOptimum resultsLight source figure after calculation optimization isΨ'JIt is ΨJTurn It sets;
Step 107 calculates aerial image I (θ according to the light source optimized in step 106M) and scan obtain the aerial image I (θM) aerial image vectorAnd it is rightWithDown-sampled obtain is carried out respectivelyWith
Photomask optimization MO problems are constructed in form by step 108:
WhereinIt isOptimum results;For vectorLow-rank regular terms,For vectorSparse canonical , α and β are respectivelyWithThe weight coefficient of regular terms;
Step 109, using the MO problems in division Bu Laigeman algorithm Split Bregman solution procedures 108, obtain it is corresponding most The vector of excellent mask graphMask graph after calculation optimization isΨ'MFor ΨMTransposition.
2. the method as described in claim 1, which is characterized in that described right in the step 107WithIt is dropped respectively Sampling obtainsWithSpecially:
Step 201, the targeted graphicalThe matrix for being N × N for size;Lightproof part element in middle corresponding targeted graphical Value is set as 1, and light transmission part element value is set as 0, rightRow and column carry out value every K pixel respectively and obtainIt is down-sampled Matrix afterwardsSize is indicated with N/K × N/K;
Step 202, to the aerial image I (θM) row and column carry out value every K pixel respectively and obtain I (θM) it is down-sampled after Matrix IkM), size is N/K × N/K.
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