CN105069194A - Genetic algorithm based optimization method for photoetching attenuation type mask - Google Patents

Abstract

A genetic algorithm based optimization method for a photoetching attenuation type mask belongs to the field of attenuation type mask optimization methods and solves the technical problem of no specific optimization method for an attenuation type phase shift mask structure in view of an illumination mode adopted by a system in the prior art. The optimization method is based on a genetic algorithm; space image contrast, multilayer film reflectivity and the like of the mask are used to form a fitness function; the illumination mode and state adopted by the projection photoetching system are cooperatively considered; and a phase difference of light, in different incident directions, in bright and dark regions of a mask pattern is balanced by utilizing an optimization algorithm, so that under a specific illumination condition, the space image contrast of the projection photoetching system is highest and the acquisition of longitudinal structural parameters of the attenuation type mask with the best imaging quality is realized.

Description

A kind of optimization method of the photoetching attenuation type mask based on genetic algorithm

Technical field

The invention belongs to attenuation type photomask optimization method field, be specifically related to a kind of optimization method of the photoetching attenuation type mask based on genetic algorithm.

Background technology

Phase shifting mask (Phase-ShiftingMask, PSM) is one of projection lithography resolution enhance technology of most prospect, and it can realize the super resolution rate imaging towards 10nm and following technology node.Wherein, attenuated phase shift mask, due to the advantage such as simplicity of design, low cost of manufacture, has become the emphasis calculating field of lithography and pay close attention at present.

Utopian resolution strengthens hypothesized model and points out, if can take into full account the impact that its lighting system causes attenuated phase shift mask in projection lithography system, then the resolution of system can be made to obtain raising further.But the optimization of existing attenuated phase shift mask only stays in rationale, and do not consider the mask arrangement optimization under the lighting system that system adopts particularly.

Genetic algorithm is a kind of optimized algorithm of simulating nature evolution selection course, it directly operates structure objects, and not existence function differentiate and continuity restriction, there is inherent disguise and global optimizing ability, mainly comprise the steps such as Population Initialization, coding, fitness calculating, cross and variation and decoding.Consider that the attenuated phase shift mask structure optimization parameter of the concrete lighting parameter of etching system is numerous, as the choosing of phase shift layer material, thickness, multilayer film cycle etc., and attenuated phase shift mask performance required in extreme ultraviolet etching system is except raising contrast, also need the maximization realizing reflectivity, and this performance parameter variations has serious non-linear.

Summary of the invention

In order to the attenuated phase shift mask structure solved under the lighting system adopted for consideration system that prior art exists does not have the technical matters of concrete optimization method, the invention provides a kind of optimization method of the photoetching attenuation type mask based on genetic algorithm, the method takes full advantage of the advantage that genetic algorithm does not exist differentiate and continuity restrictive condition, carries out parameter optimization to mask performance (i.e. the highest image contrast and reflectivity) with the mask arrangement that its structural parameters are nonlinearities change.

The technical scheme that technical solution problem of the present invention is taked is as follows:

Based on an optimization method for the photoetching attenuation type mask of genetic algorithm, it comprises the steps:

Step one, initialization one population, its scale is Pop, each individuality in population carries the parameter information whole to be optimized of mask, described parameter information to be optimized comprises absorption phase shift layer material, absorption phase shift layer thickness, the Periodic-thickness for Multilayer of mask, and initialization genetic algebra is that Gen is as the boundary condition optimized;

Step 2, binary coding is utilized to encode to population, so that follow-up individuality intersects, mutation operator;

Step 3, as genetic algebra i≤Gen, population is decoded, obtain operable decimal number in simulation calculation process, and the Optimal Parameters information data structure mask comprising absorption phase shift layer material, absorption phase shift layer thickness, Periodic-thickness for Multilayer utilizing decoding to obtain;

The mask imaging that step 4, utilization Abbe image-forming principle and Kirchhoff approximate model carry out under specific illumination condition calculates, and obtains the aerial image of the mask in population corresponding to each individuality;

Step 5, to step 4 obtain all aerial images carry out image quality evaluation, with its performance characterization for fitness function Fitness, to the fitness function Fitness of any individual _nbe expressed as:

${\mathrm{Fitness}}_n=e^{{\mathrm{NILS}}_n*R_n*{\mathrm{Con}}_n}$

In formula, Con is aerial image contrast, and NILS is aerial image normalization log slope, and R is transmitance or the reflectivity of mask;

Step 6, to obtain this generation be that individuality that in the i-th generation, fitness function Fitness is maximum carries out filing as this generation optimized individual and stores, and select individuality in this generation according to fitness function size, its selection result is as parent simultaneously;

Step 7, to select all individualities obtained to carry out intersecting through step 6, mutation operation obtains filial generation, i.e. i+1 generation, judge whether genetic algebra i exceedes maximum genetic algebra Gen, if not, then enter and optimize next time; If so, then exit circulation, terminate to optimize, now corresponding absorption phase shift layer material, absorption phase shift layer thickness, Periodic-thickness for Multilayer are the optimized parameter after optimization.

The invention has the beneficial effects as follows: this optimization method is based on genetic algorithm, and work in coordination with the lighting system and state of considering that projection lithography system adopts, optimized algorithm is utilized to balance the phasic difference of light in the bright dark areas of mask graph of different incident direction, to make under specific illumination condition, the contrast of projection lithography system aerial image is the highest, realizes the acquisition of the attenuation type mask vertical structure parameter of optimal imaging quality.

Accompanying drawing explanation

Fig. 1 is typical transmission-type attenuation type mask arrangement schematic diagram.

Fig. 2 is the optimization method process flow diagram of the photoetching attenuation type mask that the present invention is 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 two pole illumination schematic diagram in lithographic projection system.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further details.

As shown in Figure 1, typical transmission-type attenuation type mask arrangement generally comprises by melting substrate 10 that quartz makes and the absorption layer 11 that the material such as Cr (chromium) or Mo (molybdenum) is formed.Absorption layer 11 had both regulated the amplitude of transmitted light electric field intensity, regulated again its phase simultaneously.Generally speaking, for normal incidence light beam 13 after this attenuation type mask, through the light 132 of absorption layer (dark space) except amplitude has occurred decaying compared to the light 131 through clear zone, be also attached with the phasic difference of π.Therefore, after diffraction occurs one-period on parallel beam incident to mask (clear zone+dark space), its 0 grade of meeting weakens because of the additional phase difference of π, and ± 1 grade then can strengthen.According to Abbe's theory of image formation, just can interference imaging after the diffraction light of object has at least two-stage time through system pupil, and according to interference theory, when the light amplitude of two-stage time is more close, then its image contrast is higher.For the incident light of specific direction, reach theoretic optimal imaging contrast, then light 131,132 will be just π in phasic difference that is bright, dark space, simultaneously to its amplitude transmittance than also having particular/special requirement.So, when restrainting parallel input light 13,14 for two shown in Fig. 1, make to reach optimum image quality in theory, then need to meet four conditions, i.e. amplitude transmittance, the position phase condition of light beam 131,132, and the amplitude transmittance of light beam 141,142, position phase condition simultaneously.And the degree of freedom of absorption layer 11 only has two, i.e. material and thickness.Obviously, above-mentioned may have solution hardly.And for being equivalent to the off-axis illumination of infinite incident direction in etching system, solution can not be had, namely attenuation type mask can not to directive incident light meet strict amplitude transmittance, position phase condition all simultaneously.The present invention is only by optimized algorithm, and seeking balance between the amplitude transmittance in each incident light direction, position phase condition, makes its image quality optimization.Therefore, the present invention is based on genetic algorithm, consider the concrete lighting system that lithographic objective adopts, realize the optimized design of corresponding attenuated phase shift mask structure.

As shown in Figure 2, the optimization method specific implementation process that the present invention is based on the photoetching attenuation type mask of genetic algorithm is as follows:

1) initialization one population, its scale is Pop, each individuality in population carries the parameter information whole to be optimized of mask, specifically comprise the absorption phase shift layer material of mask, absorb phase shift layer thickness, Periodic-thickness for Multilayer, initialization genetic algebra is that Gen is as the boundary condition optimized;

2) utilize binary coding (0-1 coding) to encode to population, be convenient to follow-up individuality intersection, mutation operator;

3) as genetic algebra i≤Gen, population is decoded, obtain operable decimal number in simulation calculation process, and the Optimal Parameters information data structure mask comprising absorption phase shift layer material, absorption phase shift layer thickness, Periodic-thickness for Multilayer utilizing decoding to obtain;

4) the mask imaging of using Abbe image-forming principle and Kirchhoff approximate model to carry out under specific illumination condition calculates (see open source literature [1] WangJun, JinChunshui, WangLipingetal..StudyontheOff-AxisIlluminationforExtreme UltravioletLithography [J] .ActaOpticaSinica, 2012, 32 (12): 1211003. and open source literature [2] XuMa, GonzaloR.Arce.ComputationalLithography [M] .Hoboken:Wiley & Sons, 2010.), obtain the aerial image of the mask in population corresponding to each individuality,

5) image quality evaluation is carried out to all aerial images obtained, with its performance characterization for fitness function, as aerial image contrast Con, aerial image normalization log slope NILS, mask transmitance (reflectivity) R etc., can particularly by the fitness function Fitness of any individual at this _nbe expressed as:

${\mathrm{Fitness}}_n=e^{{\mathrm{NILS}}_n*R_n*{\mathrm{Con}}_n}$

6) obtain the individuality that in this generation (the i-th generation), fitness function Fitness is maximum and carry out filing storage as this generation optimized individual, select individuality in this generation according to fitness function size, its selection result is as parent simultaneously;

7) through step 6) select all individualities of obtaining to carry out intersecting, mutation operation obtains filial generation, namely after i+1 generation, judge whether to exceed maximum genetic algebra Gen, if not, then enter and optimize next time, if so, then exit circulation, terminate to optimize, now corresponding absorption phase shift layer material, absorption phase shift layer thickness, Periodic-thickness for Multilayer are the optimized parameter after optimization.

As shown in Figure 3, the reflective attenuated phase shift mask structure used in extreme ultraviolet etching system is formed primarily of substrate 20, multilayer film 21 and absorption layer 22, wherein multilayer film 21 is made up of Mo layer 211 and Si layer 212, but be not limited only to this structure, as other does not represent at this owing to such as increasing the derivative structure of the functional requirements such as mask lifetime.Its main structure parameters comprises the periodic thickness d of multilayer film 21, the material Material of absorption layer 22 _aband the thickness d of absorption layer 22 _ab, three arranges amplitude reflectivity ratio and the phasic difference of mask light and shade regional reflex light jointly.The reflected light of parallel entrance beam 23 is 231,232 respectively, and the reflected light of parallel entrance beam 24 is 241,242 respectively.

Utilization Optimizing Flow figure is as shown in Figure 2 to above-mentioned three parameters and the periodic thickness d of multilayer film 21, the material Material of absorption layer 22 _aband the thickness d of absorption layer 22 _abbe optimized.Adopt two pole lighting systems as shown in Figure 4, σ _out=0.7, σ _in=0.4, pole subtended angle is 90 °, and two pole lines are vertical with the intensive lines L/S of exposure, and optical projection system image-side numerical aperture is 0.3, and intensive linear feature size CD is 15nm, and exposure wavelength is 13.5nm.Multilayer film 21 periodic thickness d constant interval is [6.8,7.1], absorption layer 22 thickness d _abconstant interval is [0,100], absorption layer 22 candidate materials Material _abthere are four kinds, are respectively Mo, SnO ₂, SnO and Cr, its optical constant is as shown in table 1 below.

Material	n	k
			Mo	0.92163807	0.0063653732
SnO 2	0.92909952	0.066637260
			SnO	0.94045556	0.062663801
Cr	0.93257187	0.038773484

Population scale is 1600, genetic algebra is 50, and crossover probability is 0.9, and mutation probability is 0.01, evaluation function (fitness function in genetic algorithm) is made up of the reflectivity R in mask clear zone, intensive lines aerial image contrast Contrast, and its optimum results is as shown in table 2 below.

d	Material Ab	d Ab	R	Contrast
					7.035nm	Cr	33.66nm	73.1％	0.80

Claims (1)

1., based on an optimization method for the photoetching attenuation type mask of genetic algorithm, it is characterized in that, the method comprises the steps:

Step one, initialization one population, its scale is Pop, each individuality in population carries the parameter information whole to be optimized of mask, described parameter information to be optimized comprises absorption phase shift layer material, absorption phase shift layer thickness, the Periodic-thickness for Multilayer of mask, and initialization genetic algebra is that Gen is as the boundary condition optimized;

Step 2, binary coding is utilized to encode to population, so that follow-up individuality intersects, mutation operator;

Step 3, as genetic algebra i≤Gen, population is decoded, obtain operable decimal number in simulation calculation process, and the Optimal Parameters information data structure mask comprising absorption phase shift layer material, absorption phase shift layer thickness, Periodic-thickness for Multilayer utilizing decoding to obtain;

The mask imaging that step 4, utilization Abbe image-forming principle and Kirchhoff approximate model carry out under specific illumination condition calculates, and obtains the aerial image of the mask in population corresponding to each individuality;

Step 5, to step 4 obtain all aerial images carry out image quality evaluation, with its performance characterization for fitness function Fitness, to the fitness function Fitness of any individual _nbe expressed as:

${\mathrm{Fitness}}_n=e^{{\mathrm{NILS}}_n*R_n*{\mathrm{Con}}_n}$

In formula, Con is aerial image contrast, and NILS is aerial image normalization log slope, and R is transmitance or the reflectivity of mask;

Step 6, to obtain this generation be that individuality that in the i-th generation, fitness function Fitness is maximum carries out filing as this generation optimized individual and stores, and select individuality in this generation according to fitness function size, its selection result is as parent simultaneously;

Step 7, to select all individualities obtained to carry out intersecting through step 6, mutation operation obtains filial generation, i.e. i+1 generation, judge whether genetic algebra i exceedes maximum genetic algebra Gen, if not, then enter and optimize next time; If so, then exit circulation, terminate to optimize, now corresponding absorption phase shift layer material, absorption phase shift layer thickness, Periodic-thickness for Multilayer are the optimized parameter after optimization.