CN114297975B - Mask pattern optimization design method for manufacturing curved surface relief contour device - Google Patents

Mask pattern optimization design method for manufacturing curved surface relief contour device Download PDF

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CN114297975B
CN114297975B CN202111616388.4A CN202111616388A CN114297975B CN 114297975 B CN114297975 B CN 114297975B CN 202111616388 A CN202111616388 A CN 202111616388A CN 114297975 B CN114297975 B CN 114297975B
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CN114297975A (en
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刘志祥
徐富超
贾辛
谢强
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Chengdu Tongli Precision Photoelectric Instrument Manufacturing Co ltd
Institute of Optics and Electronics of CAS
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Chengdu Tongli Precision Photoelectric Instrument Manufacturing Co ltd
Institute of Optics and Electronics of CAS
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Abstract

The invention discloses a mask pattern optimization design method for manufacturing a curved surface relief contour device, which comprises the steps of establishing a response model of photosensitive mixture (PAC) concentration distribution of photoresist to exposure light intensity according to the relationship of the exposure light intensity distribution and parameters such as absorption coefficients and photosensitive coefficients of different components of the photoresist; establishing a photoresist developing model according to parameters such as the developing rate of complete exposure of the photoresist, the developing rate of unexposed exposure of the photoresist, the threshold value of the relative concentration of photosensitive substances, a developing selection constant and the like; calculating the PAC concentration distribution and the developing rate distribution of each point of the photoresist in a layering manner, and establishing a simulation flow from the exposure to the actual developing figure outline by combining a micro cell removal method; establishing a relation between a binary mask opening function and exposure according to a mask moving exposure principle; and then, obtaining a mask plate pattern required by the manufacture of the curved surface relief contour device through an iterative optimization algorithm and an optimization design.

Description

Mask pattern optimization design method for manufacturing curved surface relief contour device
Technical Field
The invention relates to the technical field of curved surface relief contour device manufacturing in the fields of integrated circuits, flat panel displays, micro electro mechanical systems, micro optics and the like, in particular to a mask pattern optimization design method for manufacturing a curved surface relief contour device.
Background
The mask is a graphic master mask used by a common photoetching process of a micro-nano processing technology, a mask graphic structure is formed on a transparent substrate by an opaque shading film, and graphic information is transferred to a product substrate in a step-and-repeat or step-and-scan exposure mode and the like. The mask is a graphic 'negative film' in the chip manufacturing process, is used for transferring high-precision circuit design and bears intellectual property information such as graphic design, process technology and the like. The mask is used for batch production of chips, is a key part of connection of downstream production processes, and is one of determinants of chip precision and quality.
The mask to be processed is composed of a glass/quartz substrate, a chromium layer and a photoresist layer. The pattern structure can be obtained by plate making process, and the common processing equipment is direct-writing photoetching equipment, such as a laser direct-writing photoetching machine, an electron beam photoetching machine and the like. The mask is widely used, and the mask needs to be used in the field related to the photolithography process, such as IC (Integrated Circuit), FPD (Flat Panel Display), MEMS (Micro Electro Mechanical Systems ), and the like.
The conventional mask plate is mainly subjected to the processes of exposure, development, etching and the like to obtain various required structures such as lines, grooves, steps, holes and the like, parameters describing the structures mainly comprise line width, side wall angle, depth and the like, and the patterns are binary structure patterns. But is difficult to achieve using conventional masks if one wants to make continuously varying relief profiles, such as micro-optical elements like prisms, blazed gratings, fresnel lenses, micro-lens arrays, etc. Mask-shift exposure techniques can be used to produce such special continuously varying relief profiles. The principle of the method is that a code lithography mask is designed according to a target structure, the exposure dose distribution of an illumination surface is modulated through the code mask, then the mask or a substrate is moved simultaneously in the exposure process, and the continuous modulation of the exposure dose by each gray unit is realized, so that a relatively smooth and continuously-changed relief outline is obtained. The method can realize continuous modulation of exposure dose by using a conventional binary mask, simplifies the process, and can obtain arbitrary exposure distribution by changing the shape of the mask, so that the method is more suitable for manufacturing micro-optical devices and micro-electro-mechanical devices with curved surface relief profiles.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: an optimized design method of a mask graph is provided, so that the method is suitable for mask moving exposure equipment, and a curved surface relief contour device is obtained on a substrate through subsequent exposure, development, etching and other processes.
The technical scheme adopted by the invention for solving the technical problems is as follows: a mask plate pattern optimization design method for manufacturing a curved surface relief contour device comprises the following steps:
establishing a response model of photosensitive mixture (PAC) concentration distribution of photoresist to exposure light intensity according to the relationship between the exposure light intensity distribution and the absorption coefficient of a photosensitive material, the absorption coefficient of the photoresist which does not participate in photochemical reaction and the photosensitive coefficient of the photoresist;
step (2), calculating the concentration distribution of the photosensitive mixture (PAC) after photochemical reaction of the photosensitive mixture (PAC) at each point in the photoresist in a layering manner in the exposure process according to the exposure model, the initial condition and the boundary condition;
step (3), establishing a photoresist development model according to the developing rate of complete exposure of the photoresist, the developing rate of unexposed of the photoresist, the threshold value of the relative concentration of the photosensitive substance and the developing selection constant parameter, and establishing the relation between the concentration distribution of the photosensitive mixture (PAC) and the developing rate;
step (4), carrying out computer simulation by adopting a micro cell removal method, and converting the developing rate into an actual figure outline after photoresist development;
step (5), establishing a relation between a binary mask opening function and exposure light intensity according to a mask moving exposure principle, and establishing an overall simulation flow from the mask opening function to a development contour according to the photoresist exposure model, the development model and the development contour computer simulation method in the steps (1) to (4);
and (6) setting initial conditions and termination conditions according to the requirements of the curved surface relief contour device, and designing the shape of the opening of the mask through the development contour overall simulation flow established in the steps (1) to (5) and an iterative optimization algorithm.
Further, the curved surface relief contour may be a spherical surface, a cylindrical surface, a quadric surface, an aspheric surface, or the like.
Further, the curved relief contour device includes, but is not limited to, a micro-optical device, a micro-electro-mechanical device, etc.
Compared with the prior art, the invention has the advantages that:
(1) The invention adopts the mask moving exposure technology, is beneficial to realizing the continuous modulation of the exposure light intensity and realizing the high-precision manufacture of micro-optical devices and micro-electro-mechanical devices with continuously changed appearance.
(2) The photoresist exposure model, the developing model and the mask iterative optimization process established by the invention can realize the mask iterative optimization of any curved surface contour.
Drawings
FIG. 1 is a schematic cross-sectional view of a photoresist layer;
FIG. 2 is a schematic diagram of the principle of mask shift exposure;
FIG. 3 is a flowchart of a mask pattern optimization design method for manufacturing a curved relief contour device according to the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The invention establishes the relation between the exposure and the development contour based on a photoresist exposure model, a development model and a development contour computer simulation method, obtains the exposure distribution by using an iterative optimization algorithm optimization design, and calculates the mask opening shape distribution according to the mask moving exposure principle.
The invention relates to a mask plate pattern optimization design method for manufacturing a curved surface relief outline device, which comprises the following steps of:
step (1), establishing a photoresist exposure model, describing light intensity distribution of each point in the photoresist and photosensitive mixture (PAC) concentration distribution caused by photochemical reaction of the photosensitive mixture in the exposure process according to the relationship between exposure light intensity distribution and parameters such as absorption coefficients and photosensitive coefficients of different components of the photoresist, establishing a response model of the photosensitive mixture (PAC) concentration distribution of the photoresist to the exposure light intensity, and laying a foundation for finally determining the developed photoresist relief contour.
The exposure process is actually a process in which the absorption and scattering of light energy by the photoresist undergo a physicochemical reaction, and, macroscopically, the absorption of light can be described by the Lambert-Beer law, which describes the relationship between the absorption of light by a medium and the density of the medium and the propagation path of light. Microscopically, absorption of light by a medium can be seen as absorption of a photon by an atom or molecule of the medium, causing an electron to jump to a higher energy level. Both of these analytical methods provide useful information describing the process of light decay in the photoresist.
For positive photoresist, dill describes the dynamic processes of light absorption and photochemical reaction of the photoresist in the exposure process by utilizing Lambert-Beer law, and establishes a famous photoresist exposure model. The expression of the Dill model is:
Figure BDA0003436573470000031
Figure BDA0003436573470000032
wherein: i (x, z, t) -light intensity distribution at the position of the photoresist (x, z) at the moment of exposure t, M (x, z, t) -concentration percentage of the photosensitive mixture PAC at the position of the photoresist (x, z) at the moment of exposure t, A-absorption coefficient of photosensitive material, B-absorption coefficient of the photoresist which does not participate in photochemical reaction, C-representing the photosensitive coefficient of the photoresist, x-lateral coordinates of the cross section of the photoresist layer, z-vertical coordinates of the cross section of the photoresist layer, and t-exposure time of the photoresist.
The model describes the relationship between the concentration of the photosensitive mixture PAC and factors such as light intensity, time, depth and the like during the exposure process of the photoresist. Under the condition of giving initial conditions and boundary conditions, solving the equation system can obtain the light intensity of each point inside the photoresist after exposure and the concentration distribution of the photosensitive mixture PAC. Three of the parameters A, B, C are called Dill parameters or exposure parameters. These three parameters are related to the photosensitive properties of the photoresist and can be determined experimentally. For the same photoresist, under different wavelengths and different baking temperatures, the numerical values and the refractive index of the photoresist are different.
Step (2), calculating the concentration distribution of the photosensitive mixture (PAC) at different positions in the photoresist, and firstly setting initial conditions (before exposure):
M(x,z,0)=1
I(x,z,0)=I 0 exp[-(A+B)z]
wherein: m (x, z, 0) -photosensitive mixture PAC concentration percentage at time of exposure 0 (unexposed) photoresist (x, z), A-absorption coefficient of photosensitive material, B-absorption coefficient of photoresist not participating in photochemical reaction, x-cross coordinate of photoresist layer cross section, z-vertical coordinate of photoresist layer cross section, I 0 Initial exposure intensity of the photoresist.
And the boundary conditions are as follows:
I(x,0,t)=I 0
M(x,0,t)=exp(-I 0 Ct)
wherein: m (x, 0, t) -photosensitive mixture PAC concentration percentage of photoresist (x, 0) position (photoresist surface layer) at exposure time t, C-represents photosensitive coefficient of photoresist, x-horizontal coordinate of photoresist layer section, z-vertical coordinate of photoresist layer section, I 0 Initial exposure intensity of the photoresist.
Integrating the time t of the equation set of the Dill model by combining the initial condition and the boundary condition to obtain:
Figure BDA0003436573470000041
M(x,z,t total )=e -Q(x,z)C
wherein: q (x, z) -Exposure (integral of Exposure intensity), M (x, z, t) total ) Exposure t total At time of photoresist (x, z) position of photosensitive mixture PAC concentration percentage, A-absorption coefficient of photosensitive material, BAbsorption coefficient of the photoresist which does not participate in the photochemical reaction, C-representing the photosensitivity coefficient of the photoresist, t total -total photoresist exposure time.
Then, the layer separation calculation is carried out from the surface of the photoresist, and the concentration distribution M of the photosensitive mixture (PAC) at different positions is obtained.
And (3) establishing a photoresist developing model. After the photoresist is exposed, the concentration of a photosensitive mixture (PAC) at each point in the photoresist is changed, a latent image is formed in the photoresist, and a photoresist relief pattern can be obtained after the latent image is dissolved by a developing solution. The method for researching the photoresist development is to establish a proper development model by researching the relation between the concentration distribution of the photosensitive mixture PAC and the development rate after exposure. According to experimental research, various photoresist developing rate formulas are summarized at present, and a photoresist developing model is established. The current more mature visualization models are: a Dill model, a Mack model, a modified Mack model, a Notch model, and the like. And selecting a correspondingly matched developing model according to different characteristics of the photoresist.
A commonly used development model is the Mack model, which assumes that the developer gradually dissolves the surface layer of the resist, i.e. the development process always occurs at the outermost surface of the photoresist, without penetrating into the photoresist and dissolving at the same time with the surface. Thus, the development process can be divided into three steps: the developer molecules diffuse to the surface of the photoresist, the developer molecules react with the resin molecules on the surface of the photoresist, and the reaction product is dissolved in the developing solution. The model describes the development process of the photoresist based on molecular diffusion kinetics and chemical reaction kinetics, and gives physical significance to model parameters, so that the development process of the photoresist is easier to understand.
The expression of the model is:
Figure BDA0003436573470000051
Figure BDA0003436573470000052
wherein: r-development Rate of Photoresist, M-PAC relative concentration, M th Threshold value of the relative concentration of PAC, R max Development Rate, R, at full Photoresist Exposure min The development rate when the photoresist is unexposed, n-development selectivity constant, α -PAC relative concentration influence factor.
And (3) calculating the local developing rates of different positions according to the developing model and the PAC concentration distribution calculated in the step (2).
And (4) after determining the response relation between the PAC concentration of the photosensitive mixture and the local developing rate through a photoresist exposure model and a developing model, converting the developing rate into an actual graph outline, and performing simulation calculation by adopting a tiny cell removal method.
The basic idea of the tiny cell removal method is to consider the photoresist layer as a whole composed of many tiny cells (as shown in fig. 1), and determine the relief profile of the photoresist by examining the development state of each cell during the development process. If the cells are subdivided small enough, the development rate in each cell can be considered the same, with the development rate values found by the previous model.
After the development is started, the upper surface of the photoresist is firstly contacted with a developing solution, and the time required for removing the unit cell by the developing solution is as follows:
Figure BDA0003436573470000053
wherein: Δ t i,j Developer removal time, Δ Z-microcell depth, R i,j -local development rate, i-horizontal ith cell on photoresist profile, j-vertical jth cell on photoresist profile.
When only one side of the cell is contacted with the developing solution, the time required for removing the cell is as follows:
Figure BDA0003436573470000054
wherein, Δ X — microcell width;
when two sides (side and surface) of a cell are contacted with the developer, the time required to remove the cell is as follows:
Figure BDA0003436573470000055
wherein Δ X-microcell width, Δ Z-microcell depth.
During development, it is specified that only one of three states, namely, not yet developed, being developed and being developed, can occur in each cell, and 0, 1 and 2 are respectively used for representing the states after the development is completed. During computer simulation, the developing state of each unit is updated forward step by step according to the removal time of each unit, the developing profile of the photoresist is actually the connecting line of the cells in the developing state, and after the developing time is up, all the cells in the developing state 1 are found, so that the developing profile of the photoresist can be determined.
Step (5), if a curved profile is to be obtained on the photoresist, the corresponding exposure distribution should also be a close curve distribution, which is difficult to be realized by the conventional binary mask, but is realized by moving the binary mask at a constant speed by the mask moving exposure method (see fig. 2). The basic principle is to install a mask plate above a substrate coated with photoresist and keep a certain separation gap, wherein the opening function of a pattern on the mask plate is a continuous function f (x), and the pattern is periodically distributed along the y direction. During exposure, the optical power of the parallel light is P, and the mask plate moves linearly along the y direction at a speed V (y). If the moving distance is an integral multiple k of the pattern period in the exposure process, after the exposure light passes through the mask, the exposure energy distribution I (x) along the x direction on the photoresist is as follows:
I(x)=kPf(x)/V(y)
after exposure, the depth of the relief pattern obtained after the photoresist on the substrate is developed has a direct relationship with the magnitude of the exposure energy. And (5) calculating the photoresist development contour according to the given exposure distribution through the photoresist exposure model, the development model and the development contour computer simulation flow established in the steps (1) to (4).
And (6) iteratively optimizing the mask. Due to the non-linearity of the photoresist exposure model and the development model, the mask opening function needs to be designed by selecting some iterative optimization algorithm if the desired development profile is desired. The basic iterative optimization process comprises the following steps: firstly, setting photoresist exposure parameters and developing parameters, and establishing an exposure model and a developing model; then inputting a target curved surface equation as an initial mask opening function, determining the maximum exposure, and calculating the exposure distribution according to the mask opening function in an equal proportion manner; calculating the PAC concentration distribution in the photoresist by using a photoresist exposure model according to the exposure distribution to obtain the PAC concentration distribution, and then calculating a development profile by using a development model; and then calculating a difference value between the development contour and the theoretical surface shape, judging whether the difference value meets the requirement, if so, finishing the iteration output result, if not, converting the difference value into an exposure difference, superposing the exposure difference to the initial exposure, and then iterating again.
Expressed in functional form as:
y=f(x)
the iteration equation is:
Figure BDA0003436573470000061
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003436573470000062
-the kth iteration value of the exposure value->
Figure BDA0003436573470000063
The value of the k +1 th iteration of the exposure quantity->
Figure BDA0003436573470000064
-difference of the developed profile from the theoretical value after the kth iteration, ω -profile difference/maximum profile x maximum exposure.
And performing repeated iterative optimization, and exiting the iterative loop after the conditions are met. And after iteration is finished, converting the final exposure distribution into mask opening shape distribution in an equal proportion according to the maximum height of the mask unit, normalizing the mask opening shape according to the machinable minimum line width of a mask manufacturer to obtain mask unit data, and manufacturing a mask plate. And mounting the manufactured mask plate on a movable exposure machine, exposing the substrate, and then carrying out processes such as development, etching and the like to obtain the required continuous curved surface contour structure on the substrate.
It will be appreciated by those skilled in the art that the above embodiments are illustrative only and not intended to be limiting of the invention, and that changes and modifications to the above described embodiments may be made within the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A mask pattern optimization design method for manufacturing curved surface relief contour devices is characterized by comprising the following steps: comprises the following steps:
establishing a response model of photosensitive mixture (PAC) concentration distribution of photoresist to exposure light intensity according to the relationship between the exposure light intensity distribution and the absorption coefficient of a photosensitive material, the absorption coefficient of the photoresist which does not participate in photochemical reaction and the photosensitive coefficient of the photoresist;
step (2), according to the exposure model, the initial condition and the boundary condition, the concentration distribution of the photosensitive mixture (PAC) after the photochemical reaction of the photosensitive mixture (PAC) at each point in the photoresist in the exposure process is calculated in a layering way;
step (3), establishing a photoresist development model according to the developing rate of complete exposure of the photoresist, the developing rate of unexposed of the photoresist and a developing selection constant parameter, and establishing a relation between the concentration distribution of a photosensitive mixture (PAC) and the developing rate;
step (4), carrying out computer simulation by adopting a micro cell removal method, and converting the developing rate into an actual figure outline after photoresist development;
step (5), establishing a relation between a binary mask opening function and exposure light intensity according to a mask moving exposure principle, and establishing an overall simulation flow from the mask opening function to a development contour according to the photoresist exposure model, the development model and the development contour computer simulation method in the steps (1) to (4);
and (6) setting initial conditions and termination conditions according to the requirements of the curved surface relief contour device, and designing the shape of the opening of the mask through the development contour overall simulation flow established in the steps (1) to (5) and an iterative optimization algorithm.
2. The method of claim 1, wherein: the curved surface relief contour is a spherical surface, a quadric surface, an aspheric surface or a conical surface relief contour.
3. The method of claim 1, wherein: the curved surface relief contour device is a micro-optical device and a micro-electro-mechanical device.
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