CN105069194B - A kind of optimization method of the photoetching attenuation type mask based on genetic algorithm - Google Patents
A kind of optimization method of the photoetching attenuation type mask based on genetic algorithm Download PDFInfo
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Abstract
A kind of optimization method of the photoetching attenuation type mask based on genetic algorithm belongs to attenuation type photomask optimization method field, and this method solve the existing attenuated phase shift mask structure under lighting system used by consideration system of prior art does not have the technical problem of specific optimization method.The optimization method of the present invention is based on genetic algorithm, fitness function is formed with the aerial image contrast of mask, x-ray reflectivity etc., and cooperate with lighting system and state used by consideration projection lithography system, the light that different incident directions are balanced using optimized algorithm is differed in the position of the bright dark areas of mask graph, so that under the conditions of specific illumination, the contrast highest of projection lithography system aerial image, realize the acquisition of the attenuation type mask vertical structure parameter of optimal imaging quality.
Description
Technical field
The invention belongs to attenuation type photomask optimization method field, and in particular to a kind of photoetching attenuation type based on genetic algorithm
The optimization method of mask.
Background technology
Phase shifting mask (Phase-Shifting Mask, PSM) be most prospect projection lithography RET it
One, it can be realized is imaged towards the super resolution rate of 10nm and following technology node.Wherein, attenuated phase shift mask
Due to designing the advantages such as simple, manufacturing cost is low, turn into calculate field of lithography emphasis of interest at present.
Utopian resolution ratio enhancing hypothesized model is pointed out, if its lighting system can be taken into full account in projection lithography system
Influence, then can be such that the resolution ratio of system is further improved to caused by attenuated phase shift mask.However, existing attenuation type phase
The optimization for moving mask only stays in rationale, and the not specifically mask arrangement used by consideration system under lighting system
Optimization.
Genetic algorithm is a kind of optimized algorithm for simulating natural evolution selection course, and it is directly grasped to structure objects
Make, limited without existence function derivation and continuity, there is inherent disguise and global optimizing ability, at the beginning of mainly including colony
The steps such as beginningization, coding, fitness calculating, cross and variation and decoding.Consider the attenuation type phase of the specific lighting parameter of etching system
It is numerous to move mask arrangement Optimal Parameters, the selection of such as phase shift layer material, thickness, multilayer film cycle, and extreme ultraviolet lithography system
Needed for attenuated phase shift mask performance in addition to contrast is improved, also need to realize the maximization of reflectivity, and the performance is joined
Number change is with seriously non-linear.
The content of the invention
In order to solve existing for prior art for the attenuated phase shift mask under lighting system used by consideration system
Structure does not have the technical problem of specific optimization method, and the present invention provides a kind of the excellent of photoetching attenuation type mask based on genetic algorithm
Change method, this method takes full advantage of the advantages of derivation and continuity restrictive condition is not present in genetic algorithm, to mask performance
(i.e. highest image contrast and reflectivity) carries out parameter optimization with its structural parameters in the mask arrangement of nonlinear change.
The technical solution adopted for solving the technical problem of the present invention is as follows：
A kind of optimization method of the photoetching attenuation type mask based on genetic algorithm, it comprises the following steps：
Step 1: one population of initialization, its scale is Pop, and the whole that each individual in population carries mask is treated
Optimal Parameters information, the parameter information to be optimized include the absorption phase shift layer material of mask, absorb phase shift layer thickness, multilayer film
Periodic thickness, initialization genetic algebra are a boundary conditions of the Gen as optimization；
Step 2: population is encoded using binary coding, so as to follow-up individual intersection, mutation operator；
Step 3: as genetic algebra i≤Gen, population is decoded, obtains to use during simulation calculation
Decimal number, and using decoding obtained by include absorb phase shift layer material, absorb phase shift layer thickness, Periodic-thickness for Multilayer
Optimal Parameters information data construction mask inside；
Step 4: the mask under the conditions of specific illumination is carried out with Abbe image-forming principles and Kirchhoff approximate models
Imaging calculates, and obtains the aerial image of the mask in population corresponding to each individual；
Step 5: image quality evaluation is carried out to all aerial images that step 4 obtains, using its performance characterization as fitness function
Fitness, to the fitness function Fitness of any individualnIt is expressed as：
In formula, Con is aerial image contrast, and NILS is that aerial image normalizes log slope, and R is the transmitance or anti-of mask
Penetrate rate；
Enter Step 6: obtaining the individual that fitness function Fitness is maximum in this generation i.e. the i-th generation as this generation optimized individual
Row filing storage, while individual in this generation is selected according to fitness function size, its selection result is as parent；
Step 7: all individuals obtained by being selected through step 6 are intersected, mutation operation obtains filial generation, i.e. i+1 generations,
Judge whether genetic algebra i exceedes maximum genetic algebra Gen, if it is not, then entering next suboptimization；If so, then exiting circulation, tie
Shu Youhua, now corresponding phase shift layer material, absorption phase shift layer thickness, the Periodic-thickness for Multilayer of absorbing is optimal after optimizing
Parameter.
The beneficial effects of the invention are as follows：The optimization method is based on genetic algorithm, and cooperates with and consider that projection lithography system is adopted
Lighting system and state, position phase of the light in the bright dark areas of mask graph of different incident directions is balanced using optimized algorithm
Difference, so that under the conditions of specific illumination, the contrast highest of projection lithography system aerial image, realize the decay of optimal imaging quality
The acquisition of type mask vertical structure parameter.
Brief description of the drawings
Fig. 1 is typical transmission-type attenuation type mask arrangement schematic diagram.
Fig. 2 is the optimization method flow chart of the photoetching attenuation type mask of the invention based on genetic algorithm.
Fig. 3 is for the reflective attenuated phase shift mask structural representation in extreme ultraviolet photolithographic optical projection system.
Fig. 4 is the two poles illumination schematic diagram in lithographic projection system.
Embodiment
The present invention is described in further details with reference to the accompanying drawings and examples.
As shown in figure 1, typical transmission-type attenuation type mask arrangement generally comprises substrate 10 and Cr made of fused silica
The absorbed layer 11 that the material such as (chromium) or Mo (molybdenum) is formed.Absorbed layer 11 both adjusts the amplitude of transmission optical electric field vector, while again
Adjust its phase.Generally, for normal incidence light beam 13 after the attenuation type mask, through the light of absorbed layer (dark space)
132 in addition to there is decay compared to the light 131 through clear zone in amplitude, is also attached with π position difference.Therefore, directional light is worked as
After beam incides a cycle on mask (clear zone+dark space) generation diffraction, its 0 grade of meeting weakens because of π additional phase difference, ±
1 grade can then strengthen.According to Abbe's theory of image formation, can interfere after diffraction light at least two levels of object pass through system pupil
Imaging, and according to interference theory, when the light amplitude of two levels is closer, then its image contrast is higher.For specific direction
For incident light, to reach theoretic optimal imaging contrast, then light 131,132 will just be in bright, dark space position difference
π, while also have particular/special requirement to its amplitude transmittance ratio.Then, when for two beam parallel input lights 13,14 shown in Fig. 1 and
Speech, will make to be optimal image quality in theory, then need to meet four conditions simultaneously, i.e., the amplitude of light beam 131,132 passes through
Rate, position phase condition, and the amplitude transmittance of light beam 141,142, position phase condition.And the free degree of absorbed layer 11 only has two, i.e.,
Material and thickness.Obviously, it is above-mentioned hardly possible to have solution.And for the off-axis of infinite incident direction can be equivalent in etching system
Illumination, it is impossible to have a solution, i.e., attenuation type mask can not possibly meet strict amplitude transmission simultaneously to the directive incident light of institute
Rate, position phase condition.The present invention is only capable of by optimized algorithm, is sought between the amplitude transmittance, position phase condition in each incident light direction
Seek balance so that its image quality optimizes.Therefore, the present invention is based on genetic algorithm, considers the specific photograph that lithographic objective uses
Bright mode, the optimized design of attenuated phase shift mask structure corresponding to realization.
As shown in Fig. 2 the optimization method specific implementation process of the photoetching attenuation type mask of the invention based on genetic algorithm is such as
Under：
1) population is initialized, its scale is Pop, and each individual in population carries the whole ginseng to be optimized of mask
Number information, specifically include the absorption phase shift layer material of mask, absorb phase shift layer thickness, Periodic-thickness for Multilayer, initialization heredity
Algebraically is a boundary conditions of the Gen as optimization；
2) population is encoded using binary coding (0-1 codings), is easy to follow-up individual intersection, mutation operator；
3) as genetic algebra i≤Gen, population is decoded, obtains can be used during simulation calculation ten
System number, and include absorbing phase shift layer material, absorption phase shift layer thickness, including Periodic-thickness for Multilayer using obtained by decoding
Optimal Parameters information data construction mask；
4) the mask imaging meter under the conditions of specific illumination is carried out with Abbe image-forming principles and Kirchhoff approximate models
Calculate (see open source literature [1] Wang Jun, Jin Chunshui, Wang Liping et al..Study on the Off-
Axis Illumination for Extreme Ultraviolet Lithography[J].Acta Optica Sinica,
2012,32(12):1211003. and open source literature [2] Xu Ma, Gonzalo R.Arce.Computational
Lithography[M].Hoboken:Wiley＆Sons, 2010.) sky of the mask in population corresponding to each individual, is obtained
Between picture；
5) image quality evaluation is carried out to all aerial images of acquisition, using its performance characterization as fitness function, such as aerial image pair
, herein can be specifically by any than degree Con, aerial image normalization log slope NILS, the transmitance of mask or reflectivity R etc.
The fitness function Fitness of bodynIt is expressed as：
6) individual that fitness function Fitness is maximum in this generation (the i-th generation) is obtained as this generation optimized individual to be returned
Shelves storage, while individual in this generation is selected according to fitness function size, its selection result is as parent；
7) all individuals obtained by being selected through step 6) are intersected, mutation operation obtains filial generation, i.e. after i+1 generations, sentence
It is disconnected whether to exceed maximum genetic algebra Gen, if it is not, then entering next suboptimization, if so, then exiting circulation, terminate optimization, now
It is corresponding to absorb phase shift layer material, absorb the optimized parameter after phase shift layer thickness, Periodic-thickness for Multilayer as optimize.
As shown in figure 3, the reflective attenuated phase shift mask structure used in extreme ultraviolet lithography system is mainly by substrate
20th, multilayer film 21 and absorbed layer 22 are formed, and wherein multilayer film 21 is made up of Mo layers 211 and Si layers 212, but are not limited only to the knot
Structure, as other because the structure as derived from the functional requirements such as increase mask lifetime does not represent herein.Its main structure parameters includes
The periodic thickness d of multilayer film 21, the material Material of absorbed layer 22AbAnd the thickness d of absorbed layer 22Ab, three arranges jointly
The amplitude reflectance ratio of mask light and shade region reflected light and position difference.The reflected light of parallel entrance beam 23 is 231 respectively,
232, the reflected light of parallel entrance beam 24 is 241,242 respectively.
It is periodic thickness d, the absorbed layer 22 of multilayer film 21 to above three parameter using Optimizing Flow figure as shown in Figure 2
Material MaterialAbAnd the thickness d of absorbed layer 22AbOptimize.Using two pole lighting systems as shown in Figure 4, σout
=0.7, σin=0.4, pole subtended angle is 90 °, and two pole lines are vertical with exposing intensive lines L/S, optical projection system image-side numerical aperture
For 0.3, intensive linear feature size CD is 15nm, exposure wavelength 13.5nm.The periodic thickness d constant intervals of multilayer film 21 are
[6.8,7.1], the thickness d of absorbed layer 22AbConstant interval is [0,100], the candidate materials Material of absorbed layer 22AbThere are four kinds, point
Wei not Mo, SnO2, SnO and Cr, its optical constant it is as shown in table 1 below.
| Material | n | k |
| Mo | 0.92163807 | 0.0063653732 |
| SnO2 | 0.92909952 | 0.066637260 |
| SnO | 0.94045556 | 0.062663801 |
| Cr | 0.93257187 | 0.038773484 |
Population scale is 1600, and genetic algebra 50, crossover probability 0.9, mutation probability 0.01, evaluation function is (i.e.
Fitness function in genetic algorithm) transmission of log slope NILS, mask is normalized by aerial image contrast Con, aerial image
Rate or reflectivity R are formed, and its optimum results is as shown in table 2 below.
| d | MaterialAb | dAb | R | Con |
| 7.035nm | Cr | 33.66nm | 73.1% | 0.80 |
Claims (1)
1. a kind of optimization method of the photoetching attenuation type mask based on genetic algorithm, it is characterised in that this method includes following step
Suddenly：
Step 1: one population of initialization, its scale is Pop, and the whole that each individual in population carries mask is to be optimized
Parameter information, the parameter information to be optimized include the absorption phase shift layer material of mask, absorb phase shift layer thickness, multilayer film cycle
Thickness, initialization genetic algebra are a boundary conditions of the Gen as optimization；
Step 2: population is encoded using binary coding, so as to follow-up individual intersection, mutation operator；
Step 3: as genetic algebra i≤Gen, population is decoded, obtains can be used during simulation calculation ten
System number, and include absorbing phase shift layer material, absorption phase shift layer thickness, including Periodic-thickness for Multilayer using obtained by decoding
Optimal Parameters information data construction mask；
Step 4: the mask under the conditions of specific illumination is carried out with Abbe image-forming principles and Kirchhoff approximate models is imaged
Calculate, obtain the aerial image of the mask in population corresponding to each individual；
Step 5: image quality evaluation is carried out to all aerial images that step 4 obtains, using its performance characterization as fitness function
Fitness, to the fitness function Fitness of any individualnIt is expressed as：
<mrow>
<msub>
<mi>Fitness</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>NILS</mi>
<mi>n</mi>
</msub>
<mo>*</mo>
<msub>
<mi>R</mi>
<mi>n</mi>
</msub>
<mo>*</mo>
<msub>
<mi>Con</mi>
<mi>n</mi>
</msub>
</mrow>
</msup>
</mrow>
In formula, Con is aerial image contrast, and NILS is that aerial image normalizes log slope, and R is transmitance or the reflection of mask
Rate；
Returned Step 6: obtaining the individual that fitness function Fitness is maximum in this generation i.e. the i-th generation as this generation optimized individual
Shelves storage, while individual in this generation is selected according to fitness function size, its selection result is as parent；
Step 7: all individuals obtained by being selected through step 6 are intersected, mutation operation obtains filial generation, i.e. i+1 generations, judge
Whether genetic algebra i exceedes maximum genetic algebra Gen, if it is not, then entering next suboptimization；If so, then exiting circulation, terminate excellent
Change, it is now corresponding to absorb phase shift layer material, absorb the optimal ginseng after phase shift layer thickness, Periodic-thickness for Multilayer as optimize
Number.
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| CN105631193A (en) * | 2015-12-21 | 2016-06-01 | 中国科学院长春光学精密机械与物理研究所 | Hybrid genetic algorithm-based extreme ultraviolet multilayer film structure parameter inversion method |
| CN105446087A (en) * | 2015-12-21 | 2016-03-30 | 中国科学院长春光学精密机械与物理研究所 | Extreme ultraviolet wave band optical constant inversion method based on genetic algorithm |
| US20180196349A1 (en) * | 2017-01-08 | 2018-07-12 | Mentor Graphics Corporation | Lithography Model Calibration Via Genetic Algorithms with Adaptive Deterministic Crowding and Dynamic Niching |
| CN109283685B (en) * | 2018-09-27 | 2020-10-09 | 中山大学 | Design method of nano unit of super-structured lens and super-structured lens |
| CN111399335B (en) * | 2020-02-04 | 2023-12-22 | 中国科学院微电子研究所 | Mask defect repairing method and device |
| CN115469555B (en) * | 2022-11-14 | 2023-03-31 | 中国科学院光电技术研究所 | Space image prediction and image quality optimization method for sensor chip projection lithography machine |
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