CN104155852B - A kind of optimization method of litho machine light source - Google Patents

Abstract

A kind of litho machine light source optimization method, with the light source of pixelation for particle, the photoresist that Ideal graph is corresponding with mask under current light source light illumination mode as the quadratic sum of every bit difference as objective function, utilize the particle swarm optimization algorithm containing linear decrease weight and compressibility factor, by speed and the positional information iteration optimization light source figure of more new particle.The present invention effectively improves optical patterning quality, has the advantage that principle is simple, be easy to realization, fast convergence rate.

Description

A kind of optimization method of litho machine light source

Technical field

The present invention relates to litho machine, particularly relate to a kind of light source optimization method for litho machine.

Background technology

Photoetching technique is one of the most key technology during great scale integrated circuit manufactures, and photoetching resolution determines the characteristic dimension of integrated circuit pattern.When exposure wavelength and numerical aperture certain, need by improve photoresist process and adopt resolution enhance technology reduce process factor, thus improve photoetching resolution.Light source optimizes (SourceOptimization, SO) as a kind of important resolution enhance technology, adjusts intensity and the direction of incident light by changing intensity of light source distribution.SO both can be used alone, and also can use as a part for source mask optimization (SourceMaskOptimization, SMO) to improve optical patterning performance.

SO has the advantage of low, the easy realization of cost, thus obtains and studies widely.Recently, the free lighting engineering such as FlexRay is that SO provides higher degree of freedom.Granik has carried out classifying (see in first technology 1 to the different expression way of light source and optimization object function, Granik, Y, " Sourceoptimizationforimagefidelityandthroughput ", JournalofMicrolithographyMicrofabricationandMicrosystems, 2004.3 (4): p.509-522).Kehan etc. have carried out proving (see in first technology 2 to the advantage of the SO represented based on pixel from theoretical and emulation, Kehan, T., etal, " Benefitsandtrade-offsofglobalsourceoptimizationinoptical lithography ", ProceedingsoftheSPIE-TheInternationalSocietyforOpticalEn gineering, 2009.7274:p.72740C (12pp.)-72740C (12pp.)).On the other hand, SO is the important component part of SMO.Since first Rosenbluth etc. proposes the thought of light source and mask combined optimization, existing many algorithm application are in SMO.Wherein, the SMO based on genetic algorithm that Erdmann etc. propose is (see in first technology 3, Erdmann, A., etal, " Towardautomaticmaskandsourceoptimizationforopticallithog raphy ", Microlithography2004.InternationalSocietyforOpticsandPho tonics), do not need to be grasped the priori of photoetching, arbitrary imaging model and optimization aim can be selected, there is potential concurrency, avoid the problem that analytic method is difficult to be applied to complex optimization.But genetic algorithm encoding more complicated, its crossover and mutation all has typical assemblage characteristic, and optimizing process only operates chromosomal fragment, and speed of convergence is slower.In addition, the light source figure in first technology 3 by describing conventional illumination, ring illumination, throw light in two poles or the simple parameter of quadrupole illuminating represents, degree of freedom of its optimization is very restricted.

Summary of the invention

The invention provides a kind of litho machine light source optimization method based on particle swarm optimization algorithm.The light source of pixelation is encoded to particle by this method, utilizes the particle cluster algorithm containing Linear recurring series and compressibility factor, by speed and the positional information continuous iteration optimization light source figure of more new particle.The method principle is simple, is easy to realize, and adds optimization degree of freedom, effectively improves light source optimization efficiency.This method is applicable to the etching system needing light source to optimize.

Technical solution of the present invention is as follows:

Based on a light source optimization method for particle swarm optimization algorithm, concrete steps are:

1. the size of initialization light source figure J is N _s× N _s, the brightness value arranging light-emitting zone on light source figure J is 1, and the brightness value of light-emitting zone is not 0, and the coordinate of light source figure J is (f, g);

The size of initialization mask graph M is N _m× N _m, the transmissivity arranging light transmission part on mask graph M is 1, and the transmissivity of light-blocking part is 0, and the coordinate of mask graph M is (x, y);

Initialized target pattern I _t=M; Initialization photoresist threshold value t _rwith sensitivity α; Initialization population scale N, Studying factors c ₁and c ₂, inertia weight maximal value ω _maxwith minimum value ω _min; The position of each particle of initialization and speed wherein i (1≤i≤N) is particle numbering, and j (j>=1) is dimensionality of particle, and k (k=1) is iterations; Initialization evaluation function threshold value Fs, maximum iteration time k _m;

2. the control variable θ that initialization light source figure J is corresponding, θ (f, g) denotation coordination is the control variable θ of (f, g), corresponding to the positional information x of certain particle _i,j;

3. particle cluster algorithm optimal control variable θ is adopted, and light source figure J when calculating kth time iteration ^(k), formula is as follows:

$J^{\left(k\right)}=\frac{1+{\mathrm{\θ}}^{\left(k\right)}}{2},$

In formula, θ ^(k)represent kth (1≤k≤k _m, and k is positive integer) secondary iteration time control variable θ value;

4. lithography simulation software is adopted, by light source figure J ^(k)aerial image I when obtaining kth time iteration with mask graph M _a ^(k), and photoresist when calculating kth time iteration is as I _r ^(k), formula is as follows:

${I_r}^{\left(k\right)}(x,y)=\mathrm{sig}\left\{{I_a}^{\left(k\right)}(x,y)\right\}=\frac{1}{{1+e}^{-\mathrm{\α}(I_a(x,y)-t_r)}}\text{;}$

5. evaluation function value F during kth time iteration is calculated ^(k), formula is as follows:

$F^{\left(k\right)}={\left|\right|{I_r}^{\left(k\right)}-I_t\left|\right|}_2^2=\underset{y}{\mathrm{\Σ}}\underset{x}{\mathrm{\Σ}}{({I_r}^{\left(k\right)}(x,y)-I_t(x,y))}^2;$

Individual extreme value when the position making evaluation function value minimum that when 6. defining kth time iteration, particle itself finds is kth secondary iteration

During kth time iteration, by F ^(k)with corresponding evaluation function value compares, if F ^(k)be less than corresponding evaluation function value, then upgrade for θ ^(k)(f, g), wherein θ ^(k)(f, g) is the θ (f, g) during kth time iteration;

The global extremum when position making evaluation function value minimum that when 7. defining kth time iteration, in whole population, particle finds is kth time iteration

During kth time iteration, by F ^(k)with corresponding evaluation function value compares, if F ^(k)be less than corresponding evaluation function value, then upgrade for θ ^(k)(f, g);

8. the secondary speed of particle (k+1) is calculated and position

$x_{i,j}^{(k+1)}=x_{i,j}^{\left(k\right)}+v_{i,j}^{(k+1)},j=\mathrm{1,2}...d,$

In formula, compressibility factor c=c ₁+ c ₂,

Inertia weight $\mathrm{\ω}={\mathrm{\ω}}_{\max }-\frac{k({\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min })}{k_m},$

during iteration secondary to kth in i-th particle jth dimension

during iteration secondary to kth in g particle jth dimension

If 9. F ^(k)be less than Fs, or k is greater than k _m, enter step 10., otherwise return step 3.;

10. stop optimizing, for global extremum p _g, by p _grepresented information exports as light source after optimization.

With compared with first technology 3, the present invention has the following advantages:

1. the light source that the present invention relates to is represented by pixel, has higher optimization degree of freedom.

2. the present invention uses particle swarm optimization algorithm to carry out light source optimization, and compared to genetic algorithm, this optimization method has that principle is simple, parameter is less, the advantage of fast convergence rate, thus reduces optimization complexity, effectively improves optimization efficiency.

Accompanying drawing explanation

Fig. 1 is Optical Coatings for Photolithography principle schematic;

Fig. 2 is primary light source schematic diagram of the present invention;

Fig. 3 is mask graph schematic diagram of the present invention;

Fig. 4 is the mask aerial image schematic diagram that the present invention adopts mask graph shown in Fig. 3 to be obtained by primary light source illuminating imager;

Fig. 5 be the present invention adopt mask graph shown in Fig. 3 to be obtained by primary light source illuminating imager mask lithography glue as schematic diagram;

Fig. 6 is the light source schematic diagram obtained after adopting optimization of the present invention;

Fig. 7 is that the present invention adopts mask graph shown in Fig. 3 by the mask aerial image schematic diagram optimizing rear light illumination imaging acquisition;

Fig. 8 is that the present invention adopts mask graph shown in Fig. 3 by optimizing the mask lithography glue of rear light illumination imaging acquisition as schematic diagram;

Fig. 9 is the process flow diagram adopting the present invention to carry out light source optimization.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the invention will be further described, but should not limit the scope of the invention with this embodiment.

Fig. 1 is the Optical Coatings for Photolithography schematic diagram that the present invention adopts, and this method relates to and comprises lithography machine illumination system light source 1 as seen from the figure, mask 2, projection objective 3, silicon chip 4.Fig. 2 is primary light source light illumination mode schematic diagram of the present invention, and primary light source light illumination mode is quadrupole illuminating, and size is 11 × 11 pixels, and white portion brightness value is 1, and black region brightness value is 0, light illumination mode section coherence factor σ=0.2.Fig. 3 is mask graph schematic diagram of the present invention, and mask graph size is 81 × 81 pixels, and 210nm × 210nm, characteristic dimension CD are 45nm, and mask-type is binary mask, and white portion transmitance value is 1, and black region transmitance value is 0.Litho machine operation wavelength λ is the numerical aperture NA=1.35 of 193nm, litho machine, refractive index n=1.44, convergent-divergent multiplying power R=4.

The present invention is based on the litho machine light source optimization method of particle swarm optimization algorithm, step is as follows:

1. the size of initialization light source figure J is 11 × 11, and the brightness value arranging light-emitting zone on light source figure J is 1, and the brightness value of light-emitting zone is not 0, and light source figure coordinate is (f, g);

The size of initialization mask graph M is 81 × 81, and the transmissivity arranging light transmission part on mask graph M is 1, and the transmissivity of light-blocking part is 0, and mask graph coordinate is (x, y);

Initialized target pattern I _t=M; Initialization photoresist threshold value t _r=0.25 and sensitivity α=25; Initialization population scale N=30, Studying factors c ₁=c ₂=2.05, inertia weight maximal value ω _max=0.9 and minimum value ω _min=0.4; The initial position x of each particle _i,jrandom generation, the speed v of each particle _i,jbe the random number between 0 to π, wherein i (1≤i≤N) is particle numbering, and j (j>=1) is dimensionality of particle; Initialization evaluation function threshold value Fs=180, maximum iteration time k _m=60.

2. the control variable θ that initialization light source figure J is corresponding, θ (f, g) denotation coordination is the θ of (f, g), corresponding to the positional information x of certain particle _i,j.

3. particle cluster algorithm optimal control variable θ is adopted, and light source figure J when calculating kth time iteration ^(k), formula is as follows:

$J^{\left(k\right)}=\frac{1+{\mathrm{\θ}}^{\left(k\right)}}{2},$

In formula, θ ^(k)represent kth (1≤k≤k _m, and k is positive integer) secondary iteration time control variable θ value.

4. lithography simulation software is adopted, by light source figure J ^(k)aerial image I when obtaining kth time iteration with mask graph M _a ^(k), and photoresist when calculating kth time iteration is as I _r ^(k), formula is as follows:

${I_r}^{\left(k\right)}(x,y)=\mathrm{sig}\left\{{I_a}^{\left(k\right)}(x,y)\right\}=\frac{1}{{1+e}^{-\mathrm{\α}(I_a(x,y)-t_r)}}\text{.}$

5. evaluation function value F during kth time iteration is calculated ^(k), formula is as follows:

$F^{\left(k\right)}={\left|\right|{I_r}^{\left(k\right)}-I_t\left|\right|}_2^2=\underset{y}{\mathrm{\Σ}}\underset{x}{\mathrm{\Σ}}{({I_r}^{\left(k\right)}(x,y)-I_t(x,y))}^2.$

Individual extreme value when the position making evaluation function value minimum that when 6. defining kth time iteration, particle itself finds is kth secondary iteration

During kth time iteration, by F ^(k)with corresponding evaluation function value compares, if F ^(k)be less than corresponding evaluation function value, then upgrade for θ ^(k)(f, g), wherein θ ^(k)(f, g) is the θ (f, g) during kth time iteration.

The global extremum when position making evaluation function value minimum that when 7. defining kth time iteration, in whole population, particle finds is kth time iteration

During kth time iteration, by F ^(k)with corresponding evaluation function value compares, if F ^(k)be less than corresponding evaluation function value, then upgrade for θ ^(k)(f, g).

8. the secondary speed of particle (k+1) is calculated and position

$x_{i,j}^{(k+1)}=x_{i,j}^{\left(k\right)}+v_{i,j}^{(k+1)},j=\mathrm{1,2}...d,$

In formula, compressibility factor c=c ₁+ c ₂,

Inertia weight $\mathrm{\ω}={\mathrm{\ω}}_{\max }-\frac{k({\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min })}{k_m},$

during iteration secondary to kth in i-th particle jth dimension

during iteration secondary to kth in g particle jth dimension

If 9. F ^(k)be less than Fs, or k is greater than k _m, enter step 10., otherwise return step 3..

10. stop optimizing, for global extremum p _g, by p _grepresented information exports as light source after optimization.

Adopt the condition in the present embodiment, as shown in Figure 6, as shown in Figure 7, mask lithography glue picture as shown in Figure 8 for mask aerial image for the light illumination pattern after optimization.Adopt this light source optimization method, evaluation function and pattern error reduce 66.1%, effectively improve the resolution of etching system.

Claims (1)

1. a litho machine light source optimization method, is characterized in that, the method includes the steps of:

1. the size of initialization light source figure J is N _s× N _s, the brightness value arranging light-emitting zone on light source figure J is 1, and the brightness value of light-emitting zone is not 0, and the coordinate of light source figure J is (f, g);

The size of initialization mask graph M is N _m× N _m, the transmissivity arranging light transmission part on mask graph M is 1, and the transmissivity of light-blocking part is 0, and the coordinate of mask graph M is (x, y);

Initialized target pattern I _t=M; Initialization photoresist threshold value t _rwith sensitivity α; Initialization population scale N, Studying factors c ₁and c ₂, inertia weight maximal value ω _maxwith minimum value ω _min; The position of each particle of initialization and speed wherein i is particle numbering, and 1≤i≤N, j is dimensionality of particle, j>=1, and k is iterations, k=1; Initialization evaluation function threshold value Fs, maximum iteration time k _m;

2. the control variable θ that initialization light source figure J is corresponding, θ (f, g) denotation coordination is the control variable θ of (f, g), corresponding to the positional information x of certain particle _i,j;

3. particle cluster algorithm optimal control variable θ is adopted, and light source figure J when calculating kth time iteration ^(k), formula is as follows:

$J^{\left(k\right)}=\frac{1+{\mathrm{\θ}}^{\left(k\right)}}{2},$

In formula, θ ^(k)represent control variable θ value during kth time iteration, wherein k is span is 1≤k≤k _mpositive integer;

4. lithography simulation software is adopted, by light source figure J ^(k)aerial image I when obtaining kth time iteration with mask graph M _a ^(k), and photoresist when calculating kth time iteration is as I _r ^(k), formula is as follows:

${I_r}^{\left(k\right)}(x,y)=sig\left\{{I_a}^{\left(k\right)}(x,y)\right\}=\frac{1}{1+e^{-\mathrm{\α}\left(I_a\right(x,y)-t_r)}};$

5. evaluation function value F during kth time iteration is calculated ^(k), formula is as follows:

$F^{\left(k\right)}=\left|\right|{I_r}^{\left(k\right)}-I_t|{|}_2^2=\underset{y}{\Σ}\underset{x}{\Σ}{\left({I_r}^{\left(k\right)}\right(x,y)-I_t(x,y\left)\right)}^2;$

Individual extreme value when the position making evaluation function value minimum that when 6. defining kth time iteration, particle itself finds is kth secondary iteration

During kth time iteration, by F ^(k)with corresponding evaluation function value compares, if F ^(k)be less than corresponding evaluation function value, then upgrade for θ ^(k)(f, g), wherein θ ^(k)(f, g) is the θ (f, g) during kth time iteration;

The global extremum when position making evaluation function value minimum that when 7. defining kth time iteration, in whole population, particle finds is kth time iteration

During kth time iteration, by F ^(k)with corresponding evaluation function value compares, if F ^(k)be less than corresponding evaluation function value, then upgrade for θ ^(k)(f, g);

8. the secondary speed of particle (k+1) is calculated and position

$x_{i,j}^{(k+1)}=x_{i,j}^{\left(k\right)}+v_{i,j}^{(k+1)},j=1,2...d,$

In formula, compressibility factor

Inertia weight $\mathrm{\ω}={\mathrm{\ω}}_{max}-\frac{k({\mathrm{\ω}}_{max}-{\mathrm{\ω}}_{\min })}{k_m},$

individual extreme value during iteration secondary to kth in i-th particle jth dimension

global extremum during iteration secondary to kth in whole population jth dimension

If 9. F ^(k)be less than Fs, or k is greater than k _m, enter step 10., otherwise return step 3.;

10. stop optimizing, for global extremum p _g, by p _grepresented information exports as light source after optimization.