CN102096336A - Method for determining illumination intensity distribution of light source of photoetching process - Google Patents
Method for determining illumination intensity distribution of light source of photoetching process Download PDFInfo
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Abstract
The invention relates to a method for determining the illumination intensity distribution of a light source of a photoetching process, and belongs to the technical field of integrated circuit manufacturing. The method comprises the following steps of: determining an initial shape and the initial illumination intensity of the light source; expressing the initial shape and the initial illumination intensity of the light source by using a matrix Gamma; converting the matrix Gamma into a matrix theta which is convenient to optimize; determining imaging accuracy and a focal depth in the photoetching process and establishing an objective function; acquiring a mask pattern and expressing the acquired mask pattern by using a pixel matrix m; computing the illumination intensity distribution of the mask pattern after the action of a photoetching system; expressing the illumination intensity distribution by using a matrix I which has the same scale as that of the matrix m; normalizing the matrix I; computing the pattern photoetched on a silicon chip by simulating a photoresist effect; expressing the pattern by using a matrix z; computing the matrix theta gradient Delta F (theta) of the objective function; updating the matrix theta by utilizing a formula theta <(n+1)>=theta <(n)>-s Delta F (theta) <(theta)>, wherein s represents step length and n represents iteration times; and repeating the four computation steps until a convergence condition is met. The method for optimizing the light source of the photoetching process has the advantages of short time and good optimization effect.
Description
Technical field
The invention belongs to the ic manufacturing technology field, relate to the method for a kind of light source light of definite photoetching process according to intensity distributions, be used to improve the performances such as imaging accuracy, depth of focus of photoetching, relate in particular to a kind of method of utilizing light source light that computer modeling technique determines photoetching process according to intensity distributions.
Background technology
Photoetching process is one of of paramount importance processing step during integrated circuit is made, main effect be with the graph copying on the mask plate to silicon chip, for next step carries out etching or ion injecting process is ready.The cost of photoetching is about 1/3 of whole silicon wafer manufacturing process, expends time in to account for 40～60% of whole silicon wafer technology.Therefore, the effect that improves photoetching can effectively reduce the cost that silicon chip is made.In order to improve the effect of photoetching, the light source that requires to adopt in photoetching process has that wavelength is little, the characteristics of high strength and high stability, and prior art provides the multiple method that the light source of photoetching process is optimized, and mainly contains:
(1) parameters optimization light source.This method adopts the linear combination of conventional light source shape or a plurality of conventional light source shapes, and the several parameters that determines the light source performance is optimized, and for example, chooses annular light source, optimizes the parameter of its internal diameter and external diameter.
(2), in spatial frequency domain, optimize arc array mode with some little arc light sources that are combined to form.
(3) represent that with pixel matrix the intensity of illumination of light source distributes, to determine that light source light is summed up as a non-negative least square problem according to the problem of the intensity distributions mode by mathematical derivation, utilize then and at present existingly separate by no means that the software of negative least square problem calculates.
(4) be to represent that with pixel matrix the intensity of illumination of light source distributes equally, determine that with genetic algorithm light source light is according to intensity distributions.
Yet, adopt degree of freedom that above-mentioned optimization method (1) and (2) optimize light source than represent the method that light source is optimized based on pixelation and want much less, it is also very limited to optimize effect; And adopt above-mentioned optimization method (3) and (4) to carry out light source when optimizing, optimize effect still can, but that it optimizes efficient is very low, computation process is consuming time very long.
Summary of the invention
The objective of the invention is in order to solve the problems referred to above of prior art, the method for a kind of light source light of definite photoetching process according to intensity distributions is provided, this method optimizes effective and computing time short.
To achieve these goals, the invention provides the method for a kind of light source light of definite photoetching process, may further comprise the steps according to intensity distributions:
(1) initial light of determining light source is according to intensity distributions, and represents with matrix Γ; The element of described matrix Γ is corresponding to the pixel in the described light source, and the element value of described each element of matrix Γ is corresponding to the intensity of illumination of this pixel;
(2) the described matrix Γ of normalization obtains matrix γ: obtain etching system the maximum intensity of illumination Γ max that can bear, and each element value among the described matrix Γ obtained matrix γ all divided by Γ max;
(3) adopt formula θ=arccos (2 γ-1) that described matrix γ is converted to matrix θ;
(4) obtain mask pattern, and represent with pixel matrix m, the element of described matrix m is corresponding to the pixel in the described mask pattern, and the element value of each described element is corresponding to the light transmission features of described pixel;
(5) determine the imaging accuracy and the depth of focus of mask pattern in the photoetching process, the pixel that calculates the figure that carves on the silicon chip respectively is on the focal plane and depart under the two kinds of situations in focal plane and the quadratic sum of error between the pixel of desirable figure, two described quadratic sums be multiply by given weight coefficient respectively, and addition is as objective function, and the described weight coefficient scope of getting is 0-1;
(6) calculate the intensity of illumination distribution of described mask pattern through imaging after the etching system effect, described intensity of illumination distributes and adopts the Abbe imaging model to calculate; Described intensity of illumination distribution is represented then this matrix I to be carried out normalization with the scale matrix I consistent with described matrix m;
(7) simulation photoresist effect is calculated the figure that carves on the described silicon chip and the figure that carves on this silicon chip is represented with matrix z, the element of described matrix z is corresponding to the described pixel that carves in the figure, whether the element value of each element of matrix z exposes for corresponding pixel, and described matrix z adopts the sigmoid function calculation to obtain;
(8) utilize described matrix z, I, m, θ to calculate the gradient of described objective function to described matrix θ
(θ);
(9) utilize formula
Upgrade described matrix θ, wherein s represents step-length, and n represents number of iterations;
(10) repeating step (6) up to satisfying the condition of convergence, obtains matrix γ to (9), and makes corresponding intensity of illumination distribution optimization light source with the element value of each element among the matrix γ.
Compared with prior art, the present invention has following beneficial effect: the method that the light source of photoetching process is optimized provided by the invention determines progressively that by the method that adopts iteration the light source light of photoetching process is according to intensity distributions, when satisfying the condition of convergence, finish optimizing process, than aforesaid optimization method (1) and (2), what the optimization effect of optimization method of the present invention will be good is many; Than aforesaid optimization method (3) and (4), significantly shorten the computing time of optimization method of the present invention, and it is also more better to optimize effect.
Description of drawings
Fig. 1 is the process flow diagram of the method that distributes of the intensity of illumination of definite photoetching process light source of the present invention.
Embodiment
Below in conjunction with accompanying drawing embodiments of the invention are elaborated.
Fig. 1 is the process flow diagram of the method that the light source of photoetching process is optimized of the present invention.As shown in Figure 1, the method for the intensity of illumination of definite photoetching process light source of the present invention distribution comprises following steps:
(1) initial light of determining light source is according to intensity distributions, and represents with matrix Γ;
Conventional light source according to photoetching process employing in the present integrated circuit manufacturing, for example circular, annular light source, the initial light of determining a light source is according to intensity distributions, and represent described light source with a matrix Γ, a pixel of relevant position in each element difference corresponding light source among the matrix Γ, the intensity of illumination of the element value corresponding pixel points of the element among the matrix Γ; In the present embodiment, the element of the pixel that expression is lighted in the light source among the matrix Γ (value that is intensity of illumination in the described light source is greater than the element among the matrix Γ of 0 pixel correspondence), the center that is limited in matrix Γ is the center of circle, is in the circle of radius with σ that σ is the partial coherence factor of etching system;
(2) normalization matrix Γ obtains matrix γ;
The method of normalization matrix Γ is: obtain etching system (mainly referring to lens combination) the maximum illumination intensity value Γ max that can bear, with each element value among the described matrix Γ all divided by Γ max, obtain a new matrix γ and represent light source, the scope of element value that is the element of described matrix γ is limited in the closed interval [0,1];
(3) adopt formula (1) that described matrix γ is converted to matrix θ;
Because the matrix γ of the expression light source that described step (2) obtains is a bounded, thereby has caused the difficulty that is optimized calculating; According to formula (1), described matrix γ is converted to the matrix θ of a unbounded, so that optimizing process is smooth;
θ＝arccos(2γ-1) (1)
(4) obtain mask pattern, and represent with pixel matrix m;
The flow process of obtaining mask pattern is: need the client of flow to give the chip foundries with domain; Foundries is processed into the mask pattern that etching system needs with described domain then, just can obtain mask pattern from foundry factory and office; According to the kind of mask pattern, mask pattern is represented with pixel matrix m the element of described matrix m is corresponding to the pixel in the described mask pattern, the element value of each described element is corresponding to the light transmission features of described pixel; Use M
mAnd N
mLine number and the columns of difference representing matrix m; Determine M
mAnd N
m, i.e. the scale of matrix m at first need be determined the size (pixel is square, and the length of side is generally got the 1/k of mask pattern minimum feature size, the integer between the desirable 3-10 of k) of a pixel then the wide of mask pattern to be obtained M divided by the pixel length of side
m, the length of mask pattern is obtained N divided by the pixel length of side
mMask graph can be selected the scale-of-two mask, and the diaphanous spot of scale-of-two mask represents with 1 that in matrix m the light tight of scale-of-two mask represented with 0 in described matrix m; Described mask graph also can be selected full phase deviation mask, complete the light tight of phase deviation mask represented with 0 in described matrix m, the diaphanous spot of the no phase deviation of described full phase deviation mask represents with 1 that in described matrix m the diaphanous spot that the phase deviation of described full phase deviation mask is 180 ° is represented with-1 in described matrix m.
(5) determine the imaging accuracy and the depth of focus of mask pattern in the photoetching process, the pixel that calculates the figure that carves on the silicon chip respectively be positioned on the focal plane and depart under the two kinds of situations in focal plane and the pixel of desirable figure (generally with mask pattern as desirable figure) between the quadratic sum of error, two quadratic sums that calculate under two kinds of situations be multiply by given weight coefficient respectively, and addition is as objective function;
Present embodiment calculates the method for the figure that carves on the silicon chip, adopts the computation process in the step (6) and (7);
Described weight coefficient generally is taken at open interval (0,1) in, two kinds of weight coefficient values can be weighed according to actual needs, if want to improve described depth of focus, the coefficient that then departs from the quadratic sum that obtains under the situation of focal plane is obtained the coefficient greater than the quadratic sum that obtains under the situation on the focal plane; If want to improve described imaging accuracy, then take opposite way.
(6) calculate the intensity of illumination distribution of described mask pattern through imaging after the etching system effect, described intensity of illumination distributes and adopts the Abbe imaging model to calculate; Described intensity of illumination distribution is represented with a scale matrix I consistent with matrix m, and this matrix I is carried out normalization;
Mask pattern described in the present embodiment adopts the Abbe imaging model to calculate through the intensity of illumination distribution of imaging after the etching system effect, and represent with a scale matrix I consistent with m, then described matrix I is carried out normalization, the Abbe imaging model after the normalization is provided by formula (2):
Wherein (i, j) and (a b) is respectively the label of the element of described matrix I and described matrix γ, M
sAnd N
sBe respectively line number and the columns of matrix γ, M
sAnd N
sGenerally be made as equally, generally get between the 20-100, value is big more, and the expression light source is meticulous more, k
A, bBe (a, the pupil function of the pixel of the element of b) locating, X among the described matrix γ of correspondence
2And Y
2Be described pupil function k
A, bLine number and columns (X
2Can be taken as M
mHalf, Y
2Can be taken as N
mHalf), (x, y) be shown in pupil function k
A, bThe label of element, symbol
The expression convolution algorithm; For the ease of calculating, the matrix I operational form that formula (3) provides formula (2) is as follows:
Wherein, subscript 1D represents the column vector form, and subscript T represents transposition; Q is that a line number is M
m* N
m, columns is M
s* N
sMatrix, formula (3) computation process is as follows: calculate in order
, the matrix that obtains is put in order in the broomrape of described matrix Q; Matrix S
1DStore each successively
Result of calculation, its element number equals the element number of described matrix γ; Q and S in whole optimizing process
1DAll only need to calculate once, can reuse later on; For convenience, represent S with V
1D Tγ
1DResult of calculation.
(7) simulation photoresist effect is calculated the figure that carves on the described silicon chip, and the figure that carves on this silicon chip is represented with matrix z;
This step need be simulated the effect of photoresist, the effect of general photoresist can be represented with a truncation funcation, a threshold value promptly is set, when intensity of illumination surpasses this threshold value, can on silicon chip, be carved, when being lower than this threshold value, then can not be carved, but, be unfavorable for being optimized calculating because truncation funcation is discontinuous, therefore present embodiment is similar to the truncation effect of described photoresist with the sigmoid function, is promptly provided by formula (4) by the process that goes out figure that intensity of illumination is finally carved:
In the formula: the matrix of the figure that z carves on the described silicon chip for expression, i, j are any one element among the matrix z, a is a constant of sigmoid function, generally is taken between the 50-200 t
rThreshold value (can search institute's data acquisition with photoresist) for described photoresist, the element of described matrix z is corresponding to the described pixel that carves in the figure, the element value of each element of matrix z is the whether exposure (exposure is 1, and not exposing is 0) of corresponding pixel.
(8) utilize described matrix z, I, m and θ to calculate the gradient of described objective function to described matrix θ
(θ); Use formula (5), can directly calculate gradient to be asked
(θ);
Wherein, described gradient
(θ) provide (according to general custom with matrix form, bold character is represented vector or matrix), symbol " ο " representing matrix or vector element multiply each other, subscript 1D → 2D represent the column vector calculated in order delegation follow delegation and arrange and be converted to matrix.
(9) utilize formula
Upgrade described matrix θ, wherein s represents step-length, and n represents number of iterations;
(10) repeating step (6) up to satisfying the condition of convergence, obtains matrix γ to (9), and makes corresponding intensity of illumination distribution optimization light source with the element value of each element among the matrix γ.
This optimizing process is considered as one of them that convergence condition can select to adopt following condition: (1) arrives predetermined greatest iteration step number; (2) objective function is less than a predetermined ideal value (generally getting between the 0-10); (3) a predetermined step number value X (generally getting between the 10-20) and an acceptable minimum target function decrement ε (generally get and be less than or equal to 0.001) reduction that continuous X goes on foot described objective function occurs less than the situation of ε.
After optimization is finished, obtain representing the matrix γ of light source, make the light source of optimization according to this result.
Above embodiment is an exemplary embodiment of the present invention only, is not used in restriction the present invention, and protection scope of the present invention is defined by the claims.Those skilled in the art can make various modifications or be equal to replacement the present invention in essence of the present invention and protection domain, this modification or be equal to replacement and also should be considered as dropping in protection scope of the present invention.
Claims (3)
1. the light source light of a definite photoetching process is characterized in that according to the method for intensity distributions, may further comprise the steps:
(1) initial light of determining light source is according to intensity distributions, and represents with matrix Γ; The element of described matrix Γ is corresponding to the pixel in the described light source, and the element value of described each element of matrix Γ is corresponding to the intensity of illumination of this pixel;
(2) the described matrix Γ of normalization obtains matrix γ: obtain etching system the maximum intensity of illumination Γ max that can bear, and each element value among the described matrix Γ obtained matrix γ all divided by Γ max;
(3) adopt formula θ=arccos (2 γ-1), described matrix γ is converted to matrix θ;
(4) obtain mask pattern, and represent with pixel matrix m, the element of described matrix m is corresponding to the pixel in the described mask pattern, and the element value of each described element is corresponding to the light transmission features of described pixel;
(5) determine the imaging accuracy and the depth of focus of mask pattern in the photoetching process, the pixel that calculates the figure that carves on the silicon chip respectively is on the focal plane and depart under the two kinds of situations in focal plane and the quadratic sum of error between the pixel of desirable figure, after two quadratic sums be multiply by given weight coefficient respectively, addition is as objective function again, and the described weight coefficient scope of getting is 0-1;
(6) calculate the intensity of illumination distribution of described mask pattern through imaging after the etching system effect, described intensity of illumination distributes and adopts the Abbe imaging model to calculate; Described intensity of illumination distribution is represented with the scale matrix I consistent with described matrix m, and this matrix I is carried out normalization;
(7) simulation photoresist effect is calculated the figure that carves on the described silicon chip, and the figure that carves on this silicon chip represented with matrix z, the element of described matrix z is corresponding to the described pixel that carves in the figure, whether the element value of each element of matrix z exposes for corresponding pixel, and described matrix z adopts the sigmoid function calculation to obtain;
(8) utilize described matrix z, I, m and θ to calculate the gradient of described objective function to described matrix θ
(θ);
(9) utilize formula
Upgrade described matrix θ, wherein s represents step-length, and n represents number of iterations;
(10) repeating step (6) up to satisfying the condition of convergence, obtains matrix γ to (9), and makes corresponding intensity of illumination distribution optimization light source with the element value of each element among the matrix γ.
2. method according to claim 1 is characterized in that, the mask pattern in the described step (4) is scale-of-two mask or full phase deviation mask; The diaphanous spot of described scale-of-two mask represents with 1 that in described matrix m the light tight of described scale-of-two mask represented with 0 in described matrix m; The light tight of described full phase deviation mask represented with 0 in described matrix m, the diaphanous spot of the no phase deviation of described full phase deviation mask represents with 1 that in described matrix m the diaphanous spot that the phase deviation of described full phase deviation mask is 180 ° is represented with-1 in described matrix m.
3. method according to claim 1 is characterized in that, the described condition of convergence is one of them of following condition:
1) arrives predetermined greatest iteration step number;
2) described objective function is less than a predetermined ideal value, and the ideal value span is 0-10;
3) predetermined step number value X, X gets between the 10-20, and an acceptable minimum target function decrement ε, and ε gets and is less than or equal to 0.001, reduction that continuous X goes on foot described objective function occurs all less than the situation of ε.
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| CN102707582A (en) * | 2012-06-18 | 2012-10-03 | 北京理工大学 | Light source-mask synchronous optimization based on Abbe vector imaging model |
| CN104133348A (en) * | 2014-08-07 | 2014-11-05 | 北京理工大学 | Light source optimization method for adaptive photoetching system |
| CN109407475A (en) * | 2018-12-29 | 2019-03-01 | 上海华力集成电路制造有限公司 | The method for controlling lighting source shape |
| CN110618584A (en) * | 2019-09-20 | 2019-12-27 | 上海华力微电子有限公司 | Light source optimization method, light source optimization device, photoetching system and photoetching method |
| CN113380204A (en) * | 2020-03-10 | 2021-09-10 | 咸阳彩虹光电科技有限公司 | Method and device for improving visual angle color cast and display panel |
| CN115598937A (en) * | 2022-12-13 | 2023-01-13 | 华芯程（杭州）科技有限公司（Cn） | Photoetching mask shape prediction method and device and electronic equipment |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102707582A (en) * | 2012-06-18 | 2012-10-03 | 北京理工大学 | Light source-mask synchronous optimization based on Abbe vector imaging model |
| CN102707582B (en) * | 2012-06-18 | 2013-11-27 | 北京理工大学 | Light source-mask synchronous optimization based on Abbe vector imaging model |
| CN104133348A (en) * | 2014-08-07 | 2014-11-05 | 北京理工大学 | Light source optimization method for adaptive photoetching system |
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| CN109407475A (en) * | 2018-12-29 | 2019-03-01 | 上海华力集成电路制造有限公司 | The method for controlling lighting source shape |
| CN110618584A (en) * | 2019-09-20 | 2019-12-27 | 上海华力微电子有限公司 | Light source optimization method, light source optimization device, photoetching system and photoetching method |
| CN110618584B (en) * | 2019-09-20 | 2022-04-05 | 上海华力微电子有限公司 | Light source optimization method, light source optimization device, photoetching system and photoetching method |
| CN113380204A (en) * | 2020-03-10 | 2021-09-10 | 咸阳彩虹光电科技有限公司 | Method and device for improving visual angle color cast and display panel |
| CN115598937A (en) * | 2022-12-13 | 2023-01-13 | 华芯程（杭州）科技有限公司（Cn） | Photoetching mask shape prediction method and device and electronic equipment |
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Application publication date: 20110615 |