CN105629461B - A kind of ultra-fine laser accunputure field of hundred nanoscales focuses on design method - Google Patents
A kind of ultra-fine laser accunputure field of hundred nanoscales focuses on design method Download PDFInfo
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Abstract
The invention discloses a kind of ultra-fine laser accunputure field of hundred nanoscales to focus on design method, belongs to nanophotonics focusing and micro-processing technology field, including four steps：Thereafter the diffraction propagation behavior of light field during the firstth, using vector angular spectra theory to integrate description vector light beam illumination micro-structure metal film annulus piece；Secondth, equivalent numeric value aperture NA is utilizedeqWith normalization central shielding factor ε confined focusing light beam transversal yardsticks, and constraining to form ultra-fine laser accunputure field axially introduced into super-Gaussian function, thus establishing nonlinear constrained optimization model；3rd, above-mentioned Optimized model is solved using the genetic algorithm and Fast Hankel Transform arithmetic programming of configuration；The 4th, optimization initial parameter, including structural parameters and algorithm parameter are set, optimized algorithm, preferably micro-structure metal film annulus piece is performed a plurality of times.Flexible design different polarization beam lighting, a variety of scale micro-structure metal film annulus pieces based on the present invention, it can be applied to realize micro-nano photoetching, nanometer printing, super-resolution micro-imaging etc..
Description
Technical field
The invention belongs to nanophotonics focusing and micro-processing technology field, the more particularly to a kind of ultra-fine light of hundred nanoscales
Pin field focuses on design method.
Background technology
Since 2008, ultra-fine laser accunputure field focus issues cause scientific circles widely to pay close attention to, and turn into international forward position focus and grind
Study carefully one of problem.Ultra-fine laser accunputure field has important engineering application value, such as laser direct-writing micro-lithography, optical storage of data,
Scan the fields such as optical nano microtechnic, atom opticses, microcosmic particle acceleration, optical control.
At present, ultra-fine laser accunputure field focus modulation method is broadly divided into three major types, is based respectively on dioptric system, reflected light
System and diffraction optical system.Dioptric system modulator approach was proposed more with Data Memory Inst. of Singapore in 2008
Annulus pupil filtering, vector beam modulation, refractor be focused to represent (referring to document H.Wang, L.Shi,
B.Lukyanchuk,C.Sheppard,C.T.Chong.Creation of a needle of longitudinally
polarized light in vacuum using binary optics.Nature Photonics,2008,2:501-
505), this kind of technique study is concentrated the most, and advantage is theoretical clear, flexible design, and shortcoming is that radial polarisation vector beam produces
System complex, annulus shape iris filter processing request is harsh, high-end apochromatic micro objective is costly.Second class method
It is to be based on reflective optics, is mainly focused on using annular pupil filtering and parabolic mirror to realize (referring to document
H.Dehez,A.April,M.Piche.Needles of longitudinally polarized light:guidelines
for minimum spot size and tunable axial extent.Optics Express,2012,20:14891-
14905), advantage is easily to realize that limiting figure aperture (NA=1, air in) focuses in theory, and shortcoming is to focus on laser accunputure field to exist
Incident field side, and depend on ultraprecise aspherical mirror machining technique, metal parabolic mirror surface figure accuracy (PV) processing request
In the magnitude of λ/8~λ/6.3rd class method be directly focused using single plane piece type micro-structural (referring to document T.Liu,
J.Tan,J.Liu,H.Wang.Modulation of a super-Gaussian optical needle by high-NA
Fresnel zone plate.Optics Letters,2013,38:2742-2745), this is that one kind is spread out without lens, multiple beam
Blackberry lily relates to focusing system, and outstanding advantages are that light structure, cost be cheap, flexible design, and because Fresnel zone plate is in shortwave
Under long and large-numerical aperture situation, outer ring annulus radial width is close and radial width is in tens nanometer, and existing micro Process is carved
Etching technique proposes the requirement of harshness.
Above mentioned problem is the practical difficulty that ultra-fine laser accunputure field modulation at present faces, particularly existing report both at home and abroad there has been no
A kind of feasible method can realize that breadth wise dimension focuses on close to the ultra-fine laser accunputure field of hundred nanometer scales.
The content of the invention
The shortcomings that in order to overcome above-mentioned prior art, it is an object of the invention to provide a kind of ultra-fine laser accunputure of hundred nanoscales
Field focuses on design method, based on micro-structure metal film annulus piece, is illuminated using short wavelength laser, from deep ultraviolet (DUV) to extremely purple
(EUV) outside, there is the characteristics of cost is cheap, system architecture is simple, flexible design facilitates, available for micro-nano photoetching, nanometer printing,
The fields such as super-resolution micro-imaging, high-density optical storage.
To achieve these goals, the technical solution adopted by the present invention is：
A kind of ultra-fine laser accunputure field of hundred nanoscales focuses on design method, comprises the following steps：
Step 1, the diffraction biography of light field under the conditions of linearly polarized light and circularly polarized light illumination micro-structure metal film annulus piece is described
Process is broadcast, calculates each component of electric field and the distribution of total electric energy density after micro-structure metal film annulus piece；
Step 2, establishes nonlinear constrained optimization model, and Optimal Decision-making scalar is that each ring of micro-structure metal film annulus piece is saturating
Cross rate function tiWith normalization central shielding radius ε；
Step 3, utilize genetic algorithm and Fast Hankel Transform Algorithm for Solving Optimized model；
Step 4, optimization initial parameter is set, performs optimized algorithm, preferably micro-structure metal film annulus piece.
Compared with prior art, the beneficial effects of the invention are as follows：
Present system is simple, light structure, merely with single plane micro-structure metal film annulus piece；Utilize existing maturation
Micro fabrication i.e. can be achieved, cost is cheap, can batch making；Design method is flexible, suitable for a variety of Ultra-Violet Laser wavelength
Illumination, different radial direction annulus width, arbitrary diameter and operating distance design.
Brief description of the drawings
Fig. 1 is that the micro-structure metal film annulus piece Diffraction of Light in the present invention focuses on schematic diagram, and A represents micro-structural gold in figure
Belong to film annulus piece, B represents viewing plane.
Fig. 2 is micro-structure metal film annulus piece M of the present invention1Corresponding radial direction amplitude transmittance schematic diagram.
Fig. 3 is micro-structure metal film annulus piece M of the present invention1Corresponding axial normalized intensity (laser accunputure) field distribution signal
Figure.
Fig. 4 is micro-structure metal film annulus piece M of the present invention1Laser accunputure field intensity distribution schematic diagram in corresponding Y-Z plane.
Fig. 5 is micro-structure metal film annulus piece M of the present invention2Corresponding radial direction amplitude transmittance schematic diagram.
Fig. 6 is micro-structure metal film annulus piece M of the present invention2Corresponding axial normalized intensity (laser accunputure) field distribution signal
Figure.
Fig. 7 is micro-structure metal film annulus piece M of the present invention2Laser accunputure field intensity distribution schematic diagram in corresponding X-Z plane.
Embodiment
Describe embodiments of the present invention in detail with reference to the accompanying drawings and examples.
As shown in figure 1, short wavelength UV laser beam is directly focused on using micro-structure metal film annulus piece, in rang ring band
Modulation produces the ultra-fine laser accunputure field distribution of nanoscale at some tens of pm of surface after piece, utilizes vector angular spectra theory (Vectorial
Angular Spectrum Theory) carry out light propagation analysis.
(1) vector angular spectra theory light field integration represents
Assuming that along the linearly polarized light (LPB) of X-direction vibration along Z axis forward-propagating, as shown in figure 1, through micro-structure metal
After film annulus piece diffraction, in z>Any point in 0 perpendicular planeOpening position electric field E orthogonal components are according to vector
Angular spectra theory is derived by
In formula, Ex(r, z) represents x to component, Ey(r, z) represents y to component,Represent z to component, q (l)
=(1/ λ2-l2)1/2, l expression radial spatial frequency components；Wavelength is λ=λ in media as well0/ μ, λ0For vacuum wavelength, μ is to immerse
Medium refraction index；J0And J1It is first kind zero and first order Bessel function respectively, j is imaginary unit；A0(l) it is expressed as：
In formula, t (r) represents amplitude transmittance function corresponding to micro-structure metal film annulus piece, is 0 when light tight, printing opacity
When be 1；G (r) represents optical field amplitude distribution of the vector illuminating bundle in micro-structure metal film annulus piece aperture plane, false here
It is set to uniform plane wave irradiation, i.e. g (r)=1；Total electric energy density i.e. light after micro-structure metal film annulus piece is obtained by formula (1)
Qiang Wei
When illuminating bundle is (left-handed) circularly polarized light (CPB), each component that can be similarly derived by electric field E is
In formula, A0(l) provided by formula (2).Distribution of light intensity is distributed as Ivas(r, z)=2 | Ex(r,z)|2+|Ez(r,z)|2。
Obviously meet circular symmetry for circularly polarized light, intensity distribution, be different from linearly polarized light situation.
(2) multivariable, single goal, nonlinear constrained optimization model are established
According to formula (1) or formula (3), the required ultra-fine laser accunputure field fundamental characteristics of focusing is given, establishes multivariable, monocular
Mark, Solution of Nonlinear Optimal Problem.Row constraint, this hair must be entered to ultra-fine laser accunputure field in terms of transverse direction (X-Y) and axially (Z) two
It is bright to use following scheme：In transverse direction, it is specified that laser accunputure field centre position zfCorresponding equivalent numeric value aperture (NAeq), while to micro- knot
Structure metal film annulus piece center near axis area is blocked, and to suppress paraxial low frequency light field, is achieved in laser accunputure field transverse width
Further constraint；In axial direction, the super-Gaussian function (Super-Gaussian Function) with flat-top distribution characteristic is introduced
To limit axial laser accunputure field intensity distribution, the single-object problem mathematical description finally obtained is：
Subject to:
Ical=Ivas(0,Z；T)
T={ ti, Z={ zn}
|zn-zf|≤DOF/2
εmin≤ε≤εmax
In formula, parameterNAeq=η sin { [tan-1[D/(2zf)], K=Ivas
(0,zf)；NsgIt is super-Gaussian function order, is taken as 2 to 5 integer, DOF is the laser accunputure field axial direction depth of focus of design, and D represents micro- knot
Structure metal film annulus piece diameter；tiThe transmitance of each ring is represented, is 0 or 1；ε is to normalize central shielding radius, 0<ε<1, and 0<
εmin≤εmax<1, represent to carry out a certain degree of central shielding to micro-structure metal film annulus piece, can effectively realize axial laser accunputure
Field stretching and the compression of lateral beam；zfIt is the axially centered position of laser accunputure field, zn=zf± n Δs z is that the axial direction for participating in evaluation is adopted
Sampling point (n=0,1,2 ... Nzp), NzpNumber of sampling is determined, takes more than 2 integer, Δ z=DOF/ (2Nzp+1).Utilize root mean square
Error RMSE (Root Mean Square Error) evaluates the approximation ratio of actual optical field distribution and optimization aim.In transverse direction
Using FWHM (full width at half maximum), the fundamental characteristics of ultra-fine laser accunputure field is axially being evaluated using DOF (depth of focus).
(3) genetic algorithm and express delivery Hankel transform Algorithm for Solving optimization problem are utilized
Using genetic algorithm (Genetic Algorithm, GA) and Fast Hankel Transform algorithm (Fast Hankel
Transform Algorithm) carry out the optimization problem that solution formula (4) describes.GA is a kind of Gaussion mutation, simulation biology
The law of nature of evolution " survival of the fittest in natural selection ", using evolutionism and law of inheritance as theoretical foundation, have inherent hidden parallel
Property and ability of searching optimum.The basic operation of genetic algorithm includes：Initial configuration, genetic coding, the individual adaptation degree of population
Evaluation, selection, intersection and the variation of individual etc..Fitness function is the object function RMSE in formula (4), using { 0,1 }
The transmitance t of each annulus of binary code direct codingi, central shielding factor ε and axially using interval znDeng.GA is configured to
Two-point crossover and 2 points of variations, while retain elitist selection strategy, i.e., direct fitness highest individual in parent is directly lost
Reach in filial generation, population scale is set as M=10~60 by population scale, selection crossover probability is Pc>=0.75, variation is general
Rate is Pm≤ 0.15, iterations Ni≥10.Shown by a large amount of calculated examples, under above-mentioned configuration condition, GA being capable of fast and stable
Converge to approximate optimal solution.
When evaluating the fitness of any individual, it is necessary to perform substantial amounts of zero and first order Hankel transform, therefore entirely
The computational efficiency of Hankel transform and computational accuracy are the keys of design method in optimization process, in order to accelerate to optimize computing, are compiled
A kind of Fast Hankel Transform algorithms of Cheng Shixian (bibliography A.E.Siegman.Quasi Fast Hankel
Transform.Optics Letters,1977,1:13-15), the algorithm has that calculating speed is fast, precision is high, extremely low computer
The remarkable advantages such as memory requirement, in standard Hankel transform integral expression, replaced using nonlinear exponent function variable, will
The unilateral Hankel transform of standard is expressed as bilateral cross-correlation integral, Fourier transformation can be utilized to calculate after such conversion
Cross-correlation.
(4) design result and embodiment
193nm quasi-molecule immersion photolithography systems are the main flow sides of current below 100nm line widths yardstick micro-nano lithography
Method, therefore use wavelength X0=193nm, from water logging (η=1.44), laser illuminator polarization state takes LPB and CPB, micro- knot respectively
Radially basic loop bandwidth is set to Δ r=200nm to structure metal film annulus piece, and each annulus is specifically to open (printing opacity) or close (blocking) shape
State is determined by optimized algorithm.Classical ring strap structural parameters are shown in Table 1.
The micro-structure metal film annulus piece parameter of the optimization design of table 1
In table 1, device M150 μm of diameter, its structure is as shown in Figure 2.Using X polarization LPB (linearly polarized light beam) illuminations, work
It is 14.5 μm to make away from WD, and equivalent numeric value aperture is NAeq=1.25, the axial λ of depth of focus 12.40, as shown in Figure 3 in 13~16 μ ms
Interior axial normalized intensity (laser accunputure) distribution, Fig. 4 show M1Intensity distribution in corresponding Y-Z plane.14.5 μm of positions
It is asymmetric to put the horizontal hot spot in place, in vertical vibration direction hot spot FWHMy=0.31 λ0, and reach FWHM X-direction hot spot is widerx
=0.67 λ0。
In table 1, device M224 μm of diameter, its structure is as shown in Figure 5.Illuminated using CPB (circularly polarized light beam), working distance WD
For 10.5 μm, equivalent numeric value aperture is NAeq=1.08, the axial λ of depth of focus 6.60, as shown in Figure 6 in 8.5~12.5 μ ms
Axial normalized intensity (laser accunputure) distribution, Fig. 7 show M2Intensity distribution in corresponding X-Z plane.Due to being CPB illuminations,
So intensity field distribution meets axisymmetry, in 10.5 μm of opening position transverse direction hot spot FWHMx,y=0.60 λ0。
The embodiment of the present invention is described above in association with accompanying drawing, but these explanations can not be understood to limit
The scope of the present invention, protection scope of the present invention are limited by appended claims, any in the claims in the present invention base
Change on plinth is all protection scope of the present invention.
Claims (8)
1. a kind of ultra-fine laser accunputure field of hundred nanoscales focuses on design method, it is characterised in that comprises the following steps：
Step 1, the diffraction propagation mistake of light field under the conditions of linearly polarized light and circularly polarized light illumination micro-structure metal film annulus piece is described
Journey, calculate each component of electric field and the distribution of total electric energy density after micro-structure metal film annulus piece；
Step 2, establishes nonlinear constrained optimization model, and Optimal Decision-making scalar is each ring transmitance of micro-structure metal film annulus piece
Function tiWith normalization central shielding radius ε；
Step 3, utilize genetic algorithm and Fast Hankel Transform Algorithm for Solving Optimized model；
Step 4, optimization initial parameter is set, performs optimized algorithm, preferably micro-structure metal film annulus piece.
2. the ultra-fine laser accunputure field of hundred nanoscales focuses on design method according to claim 1, it is characterised in that the step 1
In, the diffraction propagation process of light field describes according to vector angular spectra theory, and each component of electric field is represented as Hankel transform
One-dimensional integrated form.
3. the ultra-fine laser accunputure field of hundred nanoscales focuses on design method according to claim 1, it is characterised in that the step 1
In, when illuminating bundle be vibration in X direction, along the positive transmission of Z axis linearly polarized light when, then spread out through micro-structure metal film annulus piece
After penetrating, in z>Any point in 0 perpendicular planeOpening position electric field E each orthogonal components are：
In formula, Ex(r,z)、Ey(r, z) andX respectively to, y to z to component；q( l The λ of)=(1/2- l 2
)1/2, l Represent radial spatial frequency component；Wavelength is λ=λ in media as well0/ μ, λ0For vacuum wavelength, μ is to immerse medium refraction
Rate；J0And J1It is first kind zero and first order Bessel function respectively, j is imaginary unit；A0(l) angular spectrum is represented, is expressed asIn formula, t (r) represents that amplitude corresponding to micro-structure metal film annulus piece is saturating
Rate function is crossed, is 0 when light tight, is 1 during printing opacity；G (r) represents that vector illuminating bundle is put down in micro-structure metal film annulus piece aperture
Optical field amplitude distribution in face, when being irradiated for uniform plane wave, g (r)=0；Then total electric energy after micro-structure metal film annulus piece
Density is that light intensity is
When illuminating bundle is Left-hand circular polarization light, then its electric field E each representation in components is
Distribution of light intensity is distributed as Ivas(r, z)=2 | Ex(r,z)|2+|Ez(r,z)|2。
4. the ultra-fine laser accunputure field of hundred nanoscales focuses on design method according to claim 1, it is characterised in that the step 3
In, genetic algorithm is configured, to tiBinary-coding is carried out with ε, is made a variation using two-point crossover and 2 points, and perform elitist selection plan
Slightly, while using Fast Hankel Transform algorithm integrated value is accelerated to calculate.
5. the ultra-fine laser accunputure field of hundred nanoscales focuses on design method according to claim 1, it is characterised in that the step 3
In, population scale is set as M=10~60, selection crossover probability is Pc>=0.75, mutation probability Pm≤ 0.15, iteration time
Number Ni≥10。
6. design method is focused on according to the ultra-fine laser accunputure field of hundred nanoscale of claim 1 or 4, it is characterised in that the step
In rapid three, the Fast Hankel Transform algorithm, refer in standard Hankel transform integral expression, utilize nonlinear exponent
Function variable is replaced, and the unilateral Hankel transform of standard is expressed as into bilateral cross-correlation integral, Fourier transformation is utilized so as to realize
Calculate cross-correlation.
7. the ultra-fine laser accunputure field of hundred nanoscales focuses on design method according to claim 1, it is characterised in that the step 4
In, optimization initial parameter includes system structure parameter：Illumination wavelengths and polarization state, immerse medium refraction index μ, micro-structure metal film
Annulus piece radial direction basic width Δ r and annulus number N, equivalent numeric value aperture NAeq, laser accunputure field axial direction depth of focus DOF, concurrently set heredity
Algorithm crossover probability Pc, mutation probability Pm, population scale M, iterations Ni。
8. design method is focused on according to the ultra-fine laser accunputure field of hundred nanoscale of claim 1 or 7, it is characterised in that the step
In rapid four, illumination wavelengths, from ultraviolet to extreme ultraviolet waveband, 10nm is taken<λ0<400nm, polarization state are liner polarization and circular polarization light；
Micro-structure metal film annulus piece radial direction basic width is taken as Δ r >=25nm.
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| CN106733573B (en) * | 2016-12-15 | 2019-10-15 | 南京大学 | A kind of three-dimensional wide band energy focusing device |
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