A Design Method for Random Phase Plates Based on Genetic Algorithms

Abstract

The application discloses a random phase plate design method based on a genetic algorithm, which is suitable for an energy homogenization unit of a photolithography illumination system, and the energy homogenization unit at least comprises a first array of microlenses, a second array of microlenses and a condenser arranged along an optical path in sequence, and the energy homogenization unit is characterized in that a random phase plate designed by using the genetic algorithm is added in the energy homogenization unit based on the double arrays of microlenses. Laser is expanded and passes through the array of microlenses to obtain array sub-beams, the sub-beams are superimposed on a back focal plane by the condenser to obtain a homogenized light field, and the coherence of the laser corresponds to the interference effect of the homogenized light field. The random phase plate is designed according to the coherence of the laser and the structural parameters of the energy homogenization unit, the random phase plate adds a phase to each sub-beam, thereby changing the angular spectrum distribution of the sub-beams when the sub-beams are partially coherent superimposed on the back focal plane, and the effect of eliminating the interference pattern and improving the uniformity of the light field is achieved.

Description

Technical Field

[0001] This invention relates to laser homogenization technology, specifically a design method for a random phase plate based on a genetic algorithm, which is particularly suitable for decoherence operations in the energy homogenization unit of a photolithography illumination system. Background Technology

[0002] As integrated circuit patterns become increasingly complex, photolithography requires customized illumination patterns for specific patterns to further improve resolution. Ensuring critical dimension uniformity within the photolithography exposure field is crucial, as is the uniformity of the illumination field within the exposure area. To guarantee stable and uniform energy for the pupil, an energy homogenization unit is introduced before the free pupil shaping system. Currently, the mainstream homogenization scheme uses microlens arrays, with dual-row microlens arrays requiring coordination with a condenser lens assembly. The microlens array first splits the incident beam into many sub-beams, which are then superimposed on the back focal plane of the condenser lens assembly to obtain a uniform illumination field, thus achieving beam homogenization. In photolithography machines, excimer lasers with low spatial coherence are used as the light source. In immersion lithography illumination systems, the precise critical dimension requirements within the exposure field make the influence of the light source's coherence on the uniformity of the illumination field significant.

[0003] Currently, commonly used decoherence methods include rotating frosted glass (patent number CN209764030U), rapidly rotating scattering sheet (patent number CN 116382040 A), and random phase plate (patent number CN209560211U). Rotating frosted glass causes severe beam scattering, and in nanosecond pulse-width photolithography scanning exposure, rotating scattering sheets cannot achieve homogenization. Furthermore, actively moving optical elements introduce vibrations into the optical path, making them unsuitable for high-precision photolithography illumination systems. Typical random phase plates alter the beam divergence direction, and their homogenization capability is uncertain for specific energy homogenization units. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a design method for a random phase plate based on a genetic algorithm, which can realize the decoherence of the energy homogenization unit of the photolithography illumination system.

[0005] The technical solution of the present invention is as follows:

[0006] Step S1. Set the receive vector length L of the random phase plate to be designed, and L = M × N × q, where q is the order of the random phase plate, and generate the initial population chromosome through binary encoding:

[0007] Step S2. Randomly generate an initial population P, which includes a phase distribution P.phase and the corresponding fitness P.adapt, and set the offspring size n of the initial population P. C nC =n Pop ×n Pc , where n Pc Let n be the crossover probability. Pop The initial population size P;

[0008] Step S3. Using the beam transmission in the pre-formed photolithography illumination system energy homogenization unit transmission model as the fitness function, and the non-uniformity of the light intensity distribution at the back focal plane of the condenser lens group as the fitness, calculate the fitness INU using the following formula:

[0009]

[0010]

[0011] Among them, I top (x,y) represents the integrated intensity at the top of the light field;

[0012] Constructing a population fitness INU z It consists of the fitness of Z chromosomes;

[0013] Step S4. Randomly select individuals P(a) and P(b) from the initial population P, compare the fitness values ​​of P(a) and P(b), and select the individual with the best fitness value to enter the next generation population. Repeat this process twice to obtain two chromosomes P1 and P2.

[0014] Step S5. Randomly generate random numbers s, 1≤s≤L-1. Cross over the chromosome P1 after P1(s) and the chromosome after P2(s) to obtain new chromosomes P1' and P1', and store them in the next generation population P. t (n), when 1≤n≤n C When / 2, repeat steps S4 and S5 until n is satisfied. C / 2 times, proceed to the next step;

[0015] Step S6. For the new population P t The operation is as follows:

[0016] Generate a random number r, 0 ≤ r ≤ 1. If r is less than the mutation probability mu, generate a random number g, 1 ≤ g ≤ L-1. If P t If the gene at p(g) on ​​chromosome p of chromosome (n) is 0, then p(g) = 1. t If the gene at p(g) on ​​chromosome p of chromosome (n) is 1, then p(g) = 0. The mutated chromosome P... t (n) The input is fed into the fitness function constructed in step S3, and the output fitness is stored in the structure P. t In .adapt(n), when 1≤n≤n CIf / 2, repeat step S6; otherwise, proceed to the next step.

[0017] Step S7. Based on fitness P t .adapt from small to large population P t Sort;

[0018] Step S8. Return to step S4 until the termination condition is met, and output the chromosome P with the optimal fitness. t (1), that is, the individual with the lowest light field inhomogeneity;

[0019] Step S9. For chromosome P t (1) Perform binary decoding, specifically:

[0020] For a second-order phase plate, binary 0 corresponds to phase 0, and binary 1 corresponds to phase π.

[0021] For a fourth-order phase plate, binary 00 corresponds to phase 0, 01 corresponds to phase π / 2, 10 corresponds to phase π, and 11 corresponds to phase 3π / 2.

[0022] Similarly, for a q-order phase plate, log2 q genes represent a binary numerical value, and the product of this value and π / q is its corresponding phase value;

[0023] 2. The design method of the random phase plate based on genetic algorithm according to claim 1, characterized in that the method for constructing the pre-constructed energy homogenization unit transport model of the photolithography illumination system is as follows:

[0024] ① Since the sub-beams on the second row of microlens array are independent and do not crosstalk, the integral operation of the mutual intensity can be discretized, based on the coherence length l of the laser. c and the size p of the microlens x ×p y Calculate the number of microlenses within the coherence length, I = l cx / p x J = l cy / p y I and J are integers, (ε,η) is the back focal plane of the condenser lens group, and the mutual intensity of the back focal planes of the condenser lens group is J. f (ε,η), and set as J f (ε,η)=0;

[0025] ②(u,v) is the incident surface of the first row of microlens arrays, (ε,η) is the back focal plane of the condenser lens group, J in (u m ,v n Let (m,n,u) be the incident sub-beam passing through the microlens with index (m,n). Calculate the sub-beam (m,n,u) m ,vn The mutual intensity distribution of the light field on the back focal plane (ε,η) of the condenser lens group J m,n (ε,η), the formula is as follows:

[0026]

[0027] ③ Perform the mutual intensity superposition of sub-beams on the back focal plane (ε,η) of the condenser lens group, as shown in the following formula:

[0028] J f (ε,η)=J f (ε,η)+J m,n (ε,η)

[0029] Let m = (-M / 2…0…M / 2), n = (-N / 2…0…N / 2), repeat step ② until the mutual intensity of all sub-beams is superimposed to obtain the mutual intensity of the light field at the back focal plane of the condenser lens;

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] 1) This invention uses a genetic algorithm to design a random phase plate, which can be specially designed according to the required decoherence system, and the decoherence capability is controllable;

[0032] 2) The random phase plate designed by the genetic algorithm in this invention has a wide range of applications. Compared with the existing decoherence elements, it can be applied to photolithography scanning exposure with nanosecond pulse width.

[0033] 3) This invention constructs a transmission model for the energy homogenization unit of a photolithography illumination system. This model is based on the mutual intensity theory and more accurately simulates the transmission results of partially coherent beams.

[0034] 4) The present invention discretizes the quadruple integral when calculating the mutual intensity results. This method is based on the premise that the sub-beams on the second row of microlens array are independent and do not crosstalk.

[0035] 5) The random phase plate designed in this invention has a significant homogenization effect in the energy homogenization unit of the photolithography illumination system, and the decoherence effect is more obvious for light fields with large coherence lengths. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of a design method for a random phase plate based on a genetic algorithm according to the present invention;

[0037] Figure 2 This is a schematic diagram illustrating the application of the random phase plate designed using the present invention in the energy homogenization unit of a photolithography illumination system.

[0038] Figure 3This is a comparison chart showing the effect of decoherence using the random phase plate designed in this invention. Detailed Implementation

[0039] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the scope of protection of the present invention.

[0040] Please see Figure 1 , Figure 1 This is a schematic diagram of a design method for a random phase plate based on a genetic algorithm according to the present invention, as shown in the figure, which includes the following steps:

[0041] Constructing a beam transport model within an energy homogenization unit involves the following steps:

[0042] 1) Since the beam distribution on the second row of microlens array consists of non-intersecting array sub-beams, the integral operation of mutual intensity can be discretized, based on the coherence length l of the laser. c and the size p of the microlens x ×p y Calculate the number of microlenses within the coherence length, I = l cx / p x J = l cy / p y I and J are integers, (ε,η) is the back focal plane of the condenser lens group, and the mutual intensity of the back focal planes of the condenser lens group is J. f (ε,η), and set as J f (ε,η)=0;

[0043] 2)(u,v) is the incident surface of the first row of microlens arrays, (ε,η) is the back focal plane of the condenser lens group, J in (u m ,v n Let (m,n,u) be the incident sub-beam passing through the microlens with index (m,n). Calculate the sub-beam (m,n,u) m ,v n The mutual intensity distribution of the light field on the back focal plane (ε,η) of the condenser lens group J m,n (ε,η), the formula is as follows:

[0044]

[0045] 3) Perform mutual intensity superposition of sub-beams on the back focal plane (ε,η) of the condenser lens group, using the following formula:

[0046] J f (ε,η)=J f (ε,η)+J m,n (ε,η)

[0047] Let m = (-M / 2…0…M / 2), n = (-N / 2…0…N / 2), repeat step ② until the mutual intensity of all sub-beams is superimposed to obtain the mutual intensity of the light field at the back focal plane of the condenser lens;

[0048] The design of a random phase plate using a genetic algorithm includes the following steps:

[0049] 1) Set the receiving vector length L of the random phase board. For a second-order random phase board, the receiving vector length L is M×N. For a fourth-order random phase board, the receiving vector length L is M×N×2.

[0050] 2) Population chromosome binary encoding; For a second-order phase plate, binary 0 corresponds to phase 0, binary 1 corresponds to phase π, and for a fourth-order phase plate, binary 00 corresponds to phase 0, 01 corresponds to phase π / 2, 10 corresponds to phase π, and 11 corresponds to phase 3π / 2.

[0051] 3) Generate the initial population P using a random function; the initial population P is a structure array containing the binary encoded phase distribution P.phase and the corresponding fitness P.adapt;

[0052] 4) Set the size of the offspring to n C n C =n Pop ×n Pc , where n Pc Let n be the crossover probability. Pop Let P be the population size.

[0053] 5) The beam transmission model in the energy homogenization unit is used as the fitness function, and the non-uniformity of the light intensity distribution at the back focal plane of the condenser lens is used as the fitness. The population fitness is calculated using the following formula:

[0054]

[0055] Among them I top (x,y) represents the integrated intensity at the top of the light field;

[0056] 6) Randomly select individuals P(i) and P(j) from the population P, compare the fitness values ​​of P(i) and P(j), and select the individual with the best fitness value to enter the next generation of the population. Repeat this process twice to obtain two chromosomes P1 and P2.

[0057] 7) Generate random numbers s using a random function, 1 ≤ s ≤ L-1. Cross over the chromosomes following P1(s) and P2(s) to obtain new chromosomes P1' and P1', and store them in the next generation population P. t (n), when 1≤n≤n C When / 2, repeat steps (6) and (7) for n. C / 2 times, otherwise proceed to the next step;

[0058] 8) For the new population P t , for P t Perform the following operations: Generate a random number r, 0 ≤ r ≤ 1. If r is less than the mutation probability mu, generate a random number s, 1 ≤ s ≤ L-1. If P t If the gene at p(s) on chromosome p of chromosome (n) is 0, then p(s) = 1. t If the gene at p(s) on chromosome p of chromosome (n) is 1, then p(s) = 0. The mutated chromosome P... t (n) is input into the fitness function constructed in step (5), and the output fitness is stored in the structure P. t In .adapt(n), when 1≤n≤n C If the result is 2, repeat step (8); otherwise, proceed to the next step.

[0059] 9) Based on fitness P t .adapt from small to large population P t Sort;

[0060] 10) Return to step (6) until the termination condition is met, and output the chromosome P with the best fitness. t (1), that is, the individual with the lowest light field inhomogeneity;

[0061] 11) Regarding chromosome P t (1) Perform binary decoding, specifically:

[0062] For a second-order phase plate, binary 0 corresponds to phase 0, and binary 1 corresponds to phase π.

[0063] For a fourth-order phase plate, binary 00 corresponds to phase 0, 01 corresponds to phase π / 2, 10 corresponds to phase π, and 11 corresponds to phase 3π / 2.

[0064] Figure 2 This is a schematic diagram illustrating the application of the random phase plate designed using the method of this invention in the energy homogenization unit of a lithography illumination system. As shown in the figure, the energy homogenization unit of the lithography illumination system consists of a double-row microlens array and a condenser lens group. The microlens array first divides the incident beam into many sub-beams, and then these sub-beams are superimposed on the back focal plane of the condenser lens group to obtain the illumination light field. In the immersion lithography illumination system, the front end of the energy homogenization unit is a beam expander system, and the output end is the input of a free pupil shaping system. The random phase plate obtained by the design method of this invention is placed in front of or behind the second row of microlens array, thereby changing the angular spectrum distribution when the sub-beams are coherently superimposed on the back focal plane, eliminating interference patterns, and improving the uniformity of the light field.

[0065] Figure 3 These are comparison images showing the effects of decoherence using the random phase plate designed in this invention. Figure 3 (a) shows the light field distribution of the energy homogenization unit of the photolithography illumination system on the back focal plane of the condenser lens group. The interference fringes of the light field in the longitudinal direction are obvious. Figure 3 (b) is the light field distribution diagram after using the random phase plate. It can be seen that the uniformity of the light field is improved in both the longitudinal and transverse directions, with the improvement effect being more obvious in the longitudinal direction.

Claims

1. A design method of a random phase plate based on a genetic algorithm, suitable for an energy homogenization unit of a photolithography illumination system, the photolithography illumination system energy homogenization unit comprising at least a first array of microlenses, a second array of microlenses and a condenser lens group placed in sequence along an optical path; the number of each array of microlenses is MxN; characterized in that, The application relates to a method for designing a random phase plate. Step S1: setting the receiving vector length L of a random phase plate to be designed, and L=M*N*q, q is the order of the random phase plate, and an initial population chromosome is generated through binary coding: Step S2. Randomly generate an initial population P, the initial population P including a phase distribution P.phase and a corresponding fitness P.adapt, and set the offspring size n of the initial population P C , n C = n Pop x n Pc , where n Pc is a crossover probability, and n Pop is the number of the initial population P; Step S3: taking the transmission of a light beam in a pre-constructed lithography illumination system energy homogenization unit transmission model as a fitness function, taking the non-uniformity of the light intensity distribution on the back focal plane of the condenser group as the fitness, calculating the fitness INU, and the formula is as follows: where I top (x,y) is the integrated intensity at the top of the light field; Constructing population fitness INU z consisting of the fitness of Z chromosomes; Step S4: randomly selecting individuals P(a) and P(b) in the initial population P, comparing the fitness values of P(a) and P(b), selecting the individual with the best fitness value into the next generation population, and repeating twice to obtain two chromosomes P1 and P2; Step S5. Randomly generate a random number s, 1≤s≤L-1, cross the chromosome P1 after P1(s) with the chromosome after P2(s) to obtain new chromosomes P1' and P1', and store them in the next generation population P t (n), when 1≤n≤n C / 2, repeat steps S4 and S5 until n C / 2 times, and enter the next step; Step S6. For the new population P t The operation is as follows: A random number r, 0≤r≤1, is generated, and if r is less than the mutation probability mu, a random number g, 1≤g≤L-1, is generated, and if P t If the gene at p(g) of chromosome p of (n) is 0, then p(g) = 1, and if P t If the gene at p(g) of chromosome p of (n) is 1, then p(g) = 0, and the mutated chromosome P t (n) is input into the fitness function constructed in step S3, and the output fitness is stored in the structure P t .adapt(n). When 1≤n≤n C / 2, step S6 is repeated, otherwise the next step is executed. Step S7. Adapt P according to fitness P t .adapt population P from small to big t Sort; Step S8. Return to Step S4. until a termination condition is met, and output the chromosome P of the optimal fitness t (1), i.e., the individual with the lowest light field inhomogeneity Step S9. Chromosome P t (1) Perform binary decoding to obtain a random phase plate of order q, the log2q bases being a binary representation of a number whose product with π / q is the corresponding phase value.

2. The design method of a random phase plate based on a genetic algorithm according to claim 1, characterized by, The pre-constructed lithography illumination system energy homogenization unit transmission model is constructed in the following manner: ①Based on the coherence length l of the laser c and the size p of the microlens x ×p y Calculate the number of microlenses within the coherence length, I = l cx / p x J = l cy / p y I and J are integers, (ε,η) is the back focal plane of the condenser lens group, and the mutual intensity of the back focal planes of the condenser lens group is J. f (ε,η), and set as J f (ε,η)=0; (u,v) is the entrance plane of the first microlens array, (ε,η) is the back focal plane of the condenser lens group, J in (u m ,v n ) is the incident sub-beam passing through the microlens with serial number (m,n), and the light field mutual intensity distribution J m (ε,η) of the sub-beam (m,n,u n ,v m,n ) on the back focal plane (ε,η) of the condenser lens group is calculated according to the following formula: III. performing mutual intensity superposition of the sub-beams on the back focal plane (epsilon, eta) of the condenser group, and the formula is as follows: J f (ε,η) = J f (ε,η) + J m,n (ε,η) Let m=(-M / 2...0...M / 2), n=(-N / 2...0...N / 2), repeat step ② until the mutual intensity of all sub-beams is superimposed, and the light field mutual intensity of the back focal plane of the condenser is obtained.

3. The design method of a random phase plate based on a genetic algorithm according to claim 1, wherein, The population chromosome is generated through binary coding, and the specific method is as follows: For a second-order phase plate, phase 0 corresponds to 0, and phase pi corresponds to 1; For a fourth-order phase plate, phase 0 corresponds to 00, phase pi / 2 corresponds to 01, phase pi corresponds to 10, and phase 3pi / 2 corresponds to 11; Similarly, for a q-order phase plate, the quotient of the phase and pi / q is the decimal value of the corresponding gene, which is converted into a binary expression of log2q genes.

4. The design method of a random phase plate based on a genetic algorithm according to claim 1, wherein The pair of chromosomes P t (1) performing binary decoding, specifically: For a second-order phase plate, binary 0 corresponds to phase 0, and binary 1 corresponds to phase pi; For a fourth-order phase plate, binary 00 corresponds to phase 0, binary 01 corresponds to phase pi / 2, binary 10 corresponds to phase pi, and binary 11 corresponds to phase 3pi / 2; Similarly, for a q-order phase plate, log2q genes are a binary expression of a numerical value, and the product of the numerical value and pi / q is the corresponding phase value.

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