CN104155852A - Light source optimization method of photolithography machine - Google Patents

Abstract

A light source optimization method of a photolithography machine. A pixelated light source is employed as particles. Quadratic sum of a difference between each point in an ideal shape and each point in a photoresist image, which is corresponding to a mask, under a present light source illumination mode is used as an objective function. By means of particle swarm optimization containing a linearly decreasing weight and a compressibility factor, light source shape is iteratively optimized by updating speed information and position information of the particles. The method can effectively improve a photolithographic imaging quality, is simple in principle, is easy to carry out and is high in convergence speed.

Description

A kind of optimization method of litho machine light source

Technical field

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

Background technology

Photoetching technique is one of technology the most key during great scale integrated circuit is manufactured, and photoetching resolution determines the characteristic dimension of integrated circuit pattern.In exposure wavelength and numerical aperture certain in the situation that, need to be by improving photoresist process and adopting resolution enhance technology reduce process factor, thus improve photoetching resolution.Light source is optimized (Source Optimization, SO) as a kind of important resolution enhance technology, by changing the intensity of light source, distributes to adjust incident light intensity and direction.SO both can be used separately, and a part that also can be used as light source photomask optimization (Source Mask Optimization, SMO) is used to improve optical patterning performance.

SO has advantages of low, the easy realization of cost, thereby has obtained research widely.Recently, the free lighting engineering such as FlexRay provides higher degree of freedom for SO.Granik has carried out classifying (referring to technology 1 formerly to the different expression waies of light source and optimization aim function, Granik, Y, " Source optimization for image fidelity and throughput ", Journal of Microlithography Microfabrication and Microsystems, 2004.3 (4): p.509-522).Kehan etc. have carried out proving (referring to technology 2 formerly to the advantage of the SO representing based on pixel from theoretical and emulation, Kehan, T., et al, " Benefits and trade-offs of global source optimization in optical lithography ", Proceedings of the SPIE-The International Society for Optical Engineering, 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 (referring to technology 3 formerly, Erdmann, A., et al, " Toward automatic mask and source optimization for optical lithography ", Microlithography 2004.International Society for Optics and Photonics), do not need to be grasped the priori of photoetching, can select imaging model and optimization aim arbitrarily, there is potential concurrency, avoided analytic method to be difficult to be applied to the problem of complex optimization.Yet, genetic algorithm encoding more complicated, its crossover and mutation all has typical assemblage characteristic, and optimizing process is only to chromosomal fragment operation, and speed of convergence is slower.In addition, formerly the light source figure in technology 3 is represented by the simple parameter of describing conventional illumination, ring illumination, two utmost point illuminations or quadrupole illuminating, and the 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.This method is encoded to particle by the light source of pixelation, utilizes the particle cluster algorithm contain linear decrease inertia weight and compressibility factor, by more speed and the continuous iteration optimization light source of the positional information figure of new particle.The method principle is simple, is easy to realize, and has increased optimization degree of freedom, has effectively improved light source optimization efficiency.This method is applicable to the etching system that needs light source to optimize.

Technical solution of the present invention is as follows:

A light source optimization method based on particle swarm optimization algorithm, concrete steps are:

1. the size of initialization light source figure J is N _s* N _s, the brightness value that the upper light-emitting zone of light source figure J is set 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 that the upper light transmission part of mask graph M is set is 1, and the transmissivity of light-blocking part is 0, and the coordinate of mask graph M is (x, y);

Initialization targeted graphical I _t=M; Initialization photoresist threshold value t _rwith sensitivity α; Initialization population scale N, study factor 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. control variable θ corresponding to initialization light source figure J, the control variable θ that θ (f, g) denotation coordination is (f, g), corresponding to the positional information x of certain particle _i,j;

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

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

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

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

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

Evaluation function value F while 5. calculating the k time iteration ^(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 that makes evaluation function value minimum that while 6. defining the k time iteration, particle itself finds is the k time iteration

During the k time iteration, by F ^(k)with corresponding evaluation function value comparison, if F ^(k)be less than corresponding evaluation function value, upgrades for θ ^(k)(f, g), wherein θ ^(k)θ (f, g) when (f, g) is the k time iteration;

The global extremum when position that makes evaluation function value minimum that while 7. defining the k time iteration, in whole population, particle finds is the k time iteration

During the k time iteration, by F ^(k)with corresponding evaluation function value comparison, if F ^(k)be less than corresponding evaluation function value, upgrades for θ ^(k)(f, g);

8. calculate the inferior speed of particle (k+1) 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 $\mathrm{\ω}={\mathrm{\ω}}_{\max }-\frac{k({\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min })}{k_m},$

while being the k time iteration in i particle j dimension

while being the k time iteration in g particle j dimension

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

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

Compare with technology 3 formerly, the present invention has the following advantages:

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

2. the present invention uses particle swarm optimization algorithm to carry out light source optimization, and compared to genetic algorithm, this optimization method has advantages of that principle is simple, parameter is less, fast convergence rate, thereby has reduced optimization complexity, has effectively improved 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 illumination imaging;

Fig. 5 is that the present invention adopts mask lithography glue that mask graph shown in Fig. 3 obtains by primary light source illumination imaging as schematic diagram;

Fig. 6 adopts the light source schematic diagram obtaining after 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 of optimizing rear light illumination imaging acquisition;

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

Fig. 9 is the process flow diagram that adopts 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 photo-etching machine illumination system 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, 210nm * 210nm, and characteristic dimension CD is 45nm, and mask-type is two-value mask, and white portion transmitance value is 1, and black region transmitance value is 0.Litho machine operation wavelength λ is 193nm, the numerical aperture NA=1.35 of litho machine, refractive index n=1.44, convergent-divergent multiplying power R=4.

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

1. the size of initialization light source figure J is 11 * 11, and the brightness value that the upper light-emitting zone of light source figure J is set 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 that the upper light transmission part of mask graph M is set is 1, and the transmissivity of light-blocking part is 0, and mask graph coordinate is (x, y);

Initialization targeted graphical I _t=M; Initialization photoresist threshold value t _r=0.25 and sensitivity α=25; Initialization population scale N=30, study factor 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. control variable θ corresponding to initialization light source figure J, the θ that θ (f, g) denotation coordination is (f, g), corresponding to the positional information x of certain particle _i,j.

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

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

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

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

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

Evaluation function value F while 5. calculating the k time iteration ^(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 that makes evaluation function value minimum that while 6. defining the k time iteration, particle itself finds is the k time iteration

During the k time iteration, by F ^(k)with corresponding evaluation function value comparison, if F ^(k)be less than corresponding evaluation function value, upgrades for θ ^(k)(f, g), wherein θ ^(k)θ (f, g) when (f, g) is the k time iteration.

The global extremum when position that makes evaluation function value minimum that while 7. defining the k time iteration, in whole population, particle finds is the k time iteration

During the k time iteration, by F ^(k)with corresponding evaluation function value comparison, if F ^(k)be less than corresponding evaluation function value, upgrades for θ ^(k)(f, g).

8. calculate the inferior speed of particle (k+1) 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 $\mathrm{\ω}={\mathrm{\ω}}_{\max }-\frac{k({\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min })}{k_m},$

while being the k time iteration in i particle j dimension

while being the k time iteration in g particle j dimension

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

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

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 is that pattern error has reduced by 66.1%, has effectively improved 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 that the upper light-emitting zone of light source figure J is set 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 that the upper light transmission part of mask graph M is set is 1, and the transmissivity of light-blocking part is 0, and the coordinate of mask graph M is (x, y);

Initialization targeted graphical I _t=M; Initialization photoresist threshold value t _rwith sensitivity α; Initialization population scale N, study factor 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. control variable θ corresponding to initialization light source figure J, the control variable θ that θ (f, g) denotation coordination is (f, g), corresponding to the positional information x of certain particle _i,j;

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

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

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

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

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

Evaluation function value F while 5. calculating the k time iteration ^(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 that makes evaluation function value minimum that while 6. defining the k time iteration, particle itself finds is the k time iteration

During the k time iteration, by F ^(k)with corresponding evaluation function value comparison, if F ^(k)be less than corresponding evaluation function value, upgrades for θ ^(k)(f, g), wherein θ ^(k)θ (f, g) when (f, g) is the k time iteration;

The global extremum when position that makes evaluation function value minimum that while 7. defining the k time iteration, in whole population, particle finds is the k time iteration

During the k time iteration, by F ^(k)with corresponding evaluation function value comparison, if F ^(k)be less than corresponding evaluation function value, upgrades for θ ^(k)(f, g);

8. calculate the inferior speed of particle (k+1) 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 $\mathrm{\ω}={\mathrm{\ω}}_{\max }-\frac{k({\mathrm{\ω}}_{\max }-{\mathrm{\ω}}_{\min })}{k_m},$

while being the k time iteration in i particle j dimension

while being the k time iteration in g particle j dimension

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

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