[go: up one dir, main page]

CN112558428A - Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process - Google Patents

Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process Download PDF

Info

Publication number
CN112558428A
CN112558428A CN202011470885.3A CN202011470885A CN112558428A CN 112558428 A CN112558428 A CN 112558428A CN 202011470885 A CN202011470885 A CN 202011470885A CN 112558428 A CN112558428 A CN 112558428A
Authority
CN
China
Prior art keywords
layer
rectangular thin
thin layer
electromagnetic field
light intensity
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011470885.3A
Other languages
Chinese (zh)
Inventor
耿子辰
周再发
代辉
黄庆安
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southeast University
Original Assignee
Southeast University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southeast University filed Critical Southeast University
Priority to CN202011470885.3A priority Critical patent/CN112558428A/en
Priority to PCT/CN2020/138373 priority patent/WO2022126692A1/en
Publication of CN112558428A publication Critical patent/CN112558428A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
    • G03F7/705—Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)

Abstract

本发明公开了一种SU‑8胶紫外光背面光刻工艺的二维光强分布模拟方法，步骤1：将需要进行光强分布模拟的光刻仿真区域进行空间离散，细分成网格组成的二维阵列；步骤2：将整个光刻仿真区域沿水平方向划分成若干矩形薄层；步骤3：对每一矩形薄层分别建立麦克斯韦方程，并对麦克斯韦方程进行分离变量得到一个特征值问题，然后将每一矩形薄层中的材料参数和电磁场用傅里叶级数展开，通过数值求解特征值问题得到每一矩形薄层中的电磁场分布情况；步骤4：根据连续性条件施加电磁场边界条件将每一矩形薄层耦合起来，求得光在透过掩模版后的电磁场分布情况；步骤5：根据电磁场分布情况计算得到SU‑8胶背面入射紫外光的二维光强分布的模拟结果。

Figure 202011470885

The invention discloses a two-dimensional light intensity distribution simulation method of SU-8 glue ultraviolet light backside lithography process. Step 1: spatially discretize a lithography simulation area that needs to perform light intensity distribution simulation, and subdivide it into grids. Step 2: Divide the entire lithography simulation area into several rectangular thin layers along the horizontal direction; Step 3: Establish Maxwell's equations for each rectangular thin layer separately, and separate variables from Maxwell's equation to obtain an eigenvalue problem , and then expand the material parameters and electromagnetic fields in each rectangular thin layer with Fourier series, and obtain the electromagnetic field distribution in each rectangular thin layer by numerically solving the eigenvalue problem; Step 4: Apply the electromagnetic field boundary according to the continuity condition Conditionally couple each rectangular thin layer to obtain the electromagnetic field distribution of the light after passing through the reticle; Step 5: Calculate the simulation result of the two-dimensional light intensity distribution of the incident ultraviolet light on the back of the SU-8 glue according to the electromagnetic field distribution .

Figure 202011470885

Description

SU-8胶紫外光背面光刻工艺的二维光强分布模拟方法Two-dimensional light intensity distribution simulation method for SU-8 glue UV backside lithography process

技术领域technical field

本发明涉及一种SU-8厚光刻胶紫外光背面入射光刻工艺的二维光强分布模拟方法，属于微电子机械系统(MEMS)加工工艺过程计算机模拟领域。The invention relates to a two-dimensional light intensity distribution simulation method of SU-8 thick photoresist ultraviolet light incident photolithography process on the back surface, belonging to the field of computer simulation of micro-electromechanical system (MEMS) processing technology.

背景技术Background technique

目前采用SU-8厚胶的紫外光(UV)光刻技术是MEMS领域的重要微细加工技术，它克服了普通光刻胶光刻深宽比不足的问题，十分适合于制造超厚、高深宽比的MEMS微结构。传统的SU-8胶紫外光垂直入射光刻工艺只能制造垂直的SU-8胶微结构。随着MEMS器件的日益丰富，出现了如嵌入式沟道、V形槽和倾斜圆柱等这类的倾斜结构，采用斜入射光刻工艺可以摆脱垂直入射的限制，制造各种复杂的SU-8胶微结构。然而，由于SU-8胶在涂覆过程中厚度不均匀以及边珠效应等原因，衬底边缘的SU-8胶会比衬底中央的SU-8胶厚。而且，由于光刻胶顶部和底部曝光剂量的不均匀，会出现光刻胶顶部过度曝光、底部曝光不足的现象，影响最终显影的尺寸。同时，在SU-8胶紫外光斜入射光刻过程中，掩模版与SU-8胶之间不可避免地会出现空气间隙。由于空气间隙产生的衍射效应对光刻精度影响很大，导致难以加工高深宽比的SU-8胶微结构。为了解决这个问题，有学者提出了采用SU-8胶紫外光背面光刻工艺来制造高深宽比的SU-8胶微结构。这种方法直接将掩模版作为衬底，将SU-8胶直接涂覆在掩模版上，光刻过程中，入射紫外光直接透过掩模版背面曝光SU-8胶。该方法使用的工艺设备简单，加工成本低，避免了由于SU-8胶表面不平整产生的衍射效应的影响，同时也避免了衬底反射对SU-8胶微结构的影响，可以更有效地加工高深宽比的SU-8胶微结构。At present, ultraviolet (UV) lithography technology using SU-8 thick glue is an important microfabrication technology in the field of MEMS. It overcomes the problem of insufficient aspect ratio of ordinary photoresist lithography, and is very suitable for the manufacture of ultra-thick and high aspect ratio. than the MEMS microstructure. The traditional SU-8 glue UV vertical incident photolithography process can only produce vertical SU-8 glue microstructures. With the increasing abundance of MEMS devices, inclined structures such as embedded channels, V-shaped grooves and inclined cylinders have appeared. The oblique incident lithography process can get rid of the limitation of vertical incidence and manufacture various complex SU-8 glue microstructure. However, due to the uneven thickness of the SU-8 glue during the coating process and the edge bead effect, the SU-8 glue at the edge of the substrate will be thicker than the SU-8 glue in the center of the substrate. Moreover, due to the non-uniform exposure dose at the top and bottom of the photoresist, the phenomenon of over-exposure at the top of the photoresist and under-exposure at the bottom of the photoresist will occur, which affects the size of the final development. At the same time, in the process of SU-8 glue oblique incident ultraviolet light lithography, an air gap will inevitably appear between the reticle and the SU-8 glue. Since the diffraction effect caused by the air gap has a great influence on the lithography accuracy, it is difficult to process the SU-8 glue microstructure with high aspect ratio. In order to solve this problem, some scholars have proposed to use SU-8 glue UV backside lithography process to fabricate high aspect ratio SU-8 glue microstructures. In this method, the reticle is directly used as the substrate, and the SU-8 glue is directly coated on the reticle. During the photolithography process, the incident ultraviolet light directly exposes the SU-8 glue through the back of the reticle. The process equipment used in the method is simple, the processing cost is low, the influence of the diffraction effect caused by the uneven surface of the SU-8 glue is avoided, and the influence of the reflection of the substrate on the microstructure of the SU-8 glue is avoided, and the SU-8 glue can be more effectively Processing high aspect ratio SU-8 glue microstructures.

采用仿真工具来优化工艺性能，既可以避免反复制版、流片、实验所带来的高成本、耗时长问题，也可以利用计算仿真技术寻求最佳工艺条件，大幅提升制造性能，缩短相关MEMS产品的设计周期，降低其开发成本，并且更加深入地了解光刻技术的内在原理。SU-8胶光刻过程中，由于光刻胶显影后的最终形貌很大程度上取决于曝光工艺，它是整个光刻过程中最重要的一步工艺。通过模拟光刻后光刻胶内的光强分布情况，可以对显影后的光刻胶形貌进行预测。因此，进行SU-8厚胶背面入射光刻工艺的光强分布仿真是一项极具发展潜力的研究。Using simulation tools to optimize process performance can not only avoid the high cost and time-consuming problems caused by anti-replication, tape-out, and experiments, but also use computational simulation technology to find the best process conditions, greatly improve manufacturing performance, and shorten related MEMS products. design cycles, reduce their development costs, and gain a deeper understanding of the underlying principles of lithography. In the SU-8 photolithography process, since the final morphology of the photoresist after development largely depends on the exposure process, it is the most important step in the entire photolithography process. By simulating the light intensity distribution in the photoresist after photolithography, the morphology of the photoresist after development can be predicted. Therefore, it is a research with great development potential to carry out the simulation of light intensity distribution of SU-8 thick paste backside incident lithography process.

发明内容SUMMARY OF THE INVENTION

发明目的：针对上述现有技术，提出一种SU-8胶紫外光背面光刻工艺的二维光强分布模拟方法，用于模拟光刻后光刻胶内的光强分布情况。Purpose of the invention: In view of the above prior art, a method for simulating two-dimensional light intensity distribution of SU-8 glue ultraviolet light backside lithography process is proposed, which is used to simulate the light intensity distribution in the photoresist after lithography.

技术方案：SU-8胶紫外光背面光刻工艺的二维光强分布模拟方法，包括如下步骤：Technical solution: a two-dimensional light intensity distribution simulation method of SU-8 glue ultraviolet light backside lithography process, including the following steps:

步骤1：将需要进行光强分布模拟的光刻仿真区域进行空间离散，细分成网格组成的二维阵列，并采用二维矩阵代表所述二维阵列；Step 1: spatially discretize the lithography simulation area that needs to perform light intensity distribution simulation, subdivide it into a two-dimensional array composed of grids, and use a two-dimensional matrix to represent the two-dimensional array;

步骤2：将整个光刻仿真区域沿水平方向划分成若干矩形薄层，所述矩形薄层在Z轴方向上光学性质连续；Step 2: Divide the entire lithography simulation area into several rectangular thin layers along the horizontal direction, and the rectangular thin layers have continuous optical properties in the Z-axis direction;

步骤3：对每一所述矩形薄层分别建立麦克斯韦方程，并对所述麦克斯韦方程进行分离变量得到一个特征值问题，然后将每一所述矩形薄层中的材料参数和电磁场用傅里叶级数展开，通过数值求解所述特征值问题得到每一所述矩形薄层中的电磁场分布情况；Step 3: Establish Maxwell's equations for each of the rectangular thin layers, and separate variables for the Maxwell's equations to obtain an eigenvalue problem, and then use the Fourier transform for the material parameters and electromagnetic fields in each of the rectangular thin layers. Series expansion, the electromagnetic field distribution in each of the rectangular thin layers is obtained by numerically solving the eigenvalue problem;

步骤4：根据连续性条件施加电磁场边界条件将每一所述矩形薄层耦合起来，求得光在透过掩模版后的电磁场分布情况；Step 4: According to the continuity condition, the electromagnetic field boundary condition is applied to couple each of the rectangular thin layers, and the electromagnetic field distribution of the light after passing through the reticle is obtained;

步骤5：根据电磁场分布情况计算得到SU-8胶背面入射紫外光的二维光强分布的模拟结果。Step 5: Calculate the simulation result of the two-dimensional light intensity distribution of the incident ultraviolet light on the back of the SU-8 adhesive according to the electromagnetic field distribution.

进一步的，所述步骤3包括如下步骤：Further, the step 3 includes the following steps:

步骤3-1：对每一所述矩形薄层分别建立麦克斯韦方程，将电磁场E分离成X(x)和Z(z)两个变量，并代入麦克斯韦方程，从而将麦克斯韦方程分解为如式(1)所示的两个微分方程，所述微分方程含有复数势k2ε和特征值α2；Step 3-1: Establish Maxwell's equations for each of the rectangular thin layers, separate the electromagnetic field E into two variables, X(x) and Z(z), and substitute them into Maxwell's equations, thereby decomposing Maxwell's equations into the following formula ( 1) The two differential equations shown, the differential equations contain complex potential k 2 ε and eigenvalue α 2 ;

Figure BDA0002833602040000021
Figure BDA0002833602040000021

其中，ε为每一所述矩形薄层的材料介电常数，k为波数；Wherein, ε is the material permittivity of each of the rectangular thin layers, and k is the wave number;

步骤3-2：掩模结构在x方向上以长度d为周期重复地排列，将介电常数ε进行傅里叶级数展开，如式(2)所示；Step 3-2: The mask structure is repeatedly arranged in the x direction with a length d as a period, and the dielectric constant ε is expanded by a Fourier series, as shown in formula (2);

Figure BDA0002833602040000022
Figure BDA0002833602040000022

其中，εj(x)表示第j层矩形薄层的介电常数，

Figure BDA0002833602040000031
为傅里叶级数展开后的第q项的系数，L为傅里叶展开级数，i表示复数，b是d的倒数；where ε j (x) represents the dielectric constant of the jth thin rectangular layer,
Figure BDA0002833602040000031
is the coefficient of the qth term after the Fourier series expansion, L is the Fourier expansion series, i is a complex number, and b is the reciprocal of d;

步骤3-3：通过如式(3)所示逆傅里叶变换求出傅里叶级数展开后的每一项的系数：Step 3-3: Calculate the coefficient of each term of the Fourier series expansion through the inverse Fourier transform as shown in equation (3):

Figure BDA0002833602040000032
Figure BDA0002833602040000032

步骤3-4：对变量X(x)进行如式(4)所示傅里叶变换；Step 3-4: Perform Fourier transform on the variable X(x) as shown in formula (4);

Figure BDA0002833602040000033
Figure BDA0002833602040000033

其中，Bl为傅里叶展开后第l项系数；Among them, B l is the lth coefficient after Fourier expansion;

步骤3-5：将傅里叶展开级数代入式(1)中第一个微分方程，得到特征值矩阵方程，如式(5)所示；Step 3-5: Substitute the Fourier expansion series into the first differential equation in equation (1) to obtain the eigenvalue matrix equation, as shown in equation (5);

Figure BDA0002833602040000034
Figure BDA0002833602040000034

其中，B是矩阵D的特征向量，Dl,m为矩阵D中第l行第m列的元素，εl-m为经傅里叶展开后的第(l-m)项介电常数值；Among them, B is the eigenvector of matrix D, D l, m is the element of the l-th row and m-th column of matrix D, ε lm is the (lm)-th dielectric constant value after Fourier expansion;

步骤3-6：建立如式(6)所示的第j层矩形薄层的电磁场数学模型；Step 3-6: establish a mathematical model of the electromagnetic field of the j-th rectangular thin layer as shown in formula (6);

Figure BDA0002833602040000035
Figure BDA0002833602040000035

其中，

Figure BDA0002833602040000036
为第j层矩形薄层的电场y方向分量，
Figure BDA0002833602040000037
及
Figure BDA0002833602040000038
表示第j层矩形薄层的第m阶本征模振幅，即矩阵Aj及A'j的第m列元素；
Figure BDA0002833602040000039
表示第j层矩形薄层的特征值矩阵的第m列元素，
Figure BDA00028336020400000310
表示第j层矩形薄层的特征向量矩阵的第l行第m列元素，并通过式(5)求解得到；zj表示第j层矩形薄层的坐标；
Figure BDA00028336020400000311
为第j层矩形薄层的磁场x方向分量，
Figure BDA00028336020400000312
为第j层矩形薄层的磁场z方向分量。in,
Figure BDA0002833602040000036
is the y-direction component of the electric field of the j-th rectangular thin layer,
Figure BDA0002833602040000037
and
Figure BDA0002833602040000038
represents the m-th order eigenmode amplitude of the j-th rectangular thin layer, that is, the m-th column elements of the matrices A j and A'j;
Figure BDA0002833602040000039
represents the m-th column element of the eigenvalue matrix of the j-th rectangular thin layer,
Figure BDA00028336020400000310
represents the element of the lth row and mth column of the eigenvector matrix of the jth layer of rectangular thin layer, and is obtained by solving the formula (5); zj represents the coordinates of the jth layer of rectangular thin layer;
Figure BDA00028336020400000311
is the x-direction component of the magnetic field of the jth rectangular thin layer,
Figure BDA00028336020400000312
is the z-direction component of the magnetic field of the jth rectangular thin layer.

进一步的，所述步骤4中，空气与第一层界面处根据电磁场连续边界条件，用矩阵形式表示，得到如式(7)所示的边界条件方程；Further, in the step 4, the interface between the air and the first layer is expressed in matrix form according to the continuous boundary condition of the electromagnetic field, and the boundary condition equation shown in formula (7) is obtained;

Figure BDA0002833602040000041
Figure BDA0002833602040000041

Figure BDA0002833602040000042
Figure BDA0002833602040000042

其中，

Figure BDA0002833602040000043
表示第1层形貌信息，A1、A'1表示第1层衍射结果信息，矩阵R表示光照信息，Rl表示矩阵R的第l列元素，l0为斜入射时入射波阶次，λ0为入射光波长，
Figure BDA0002833602040000044
表示初始光照强度，θ表示入射角度；in,
Figure BDA0002833602040000043
represents the topography information of the first layer, A 1 and A' 1 represent the diffraction result information of the first layer, the matrix R represents the illumination information, R l represents the element in the lth column of the matrix R, and l 0 is the incident wave order at oblique incidence, λ 0 is the wavelength of incident light,
Figure BDA0002833602040000044
represents the initial light intensity, and θ represents the incident angle;

最后一层界面处根据边界条件得如式(9)所示的边界条件方程：According to the boundary conditions at the interface of the last layer, the boundary condition equation shown in Eq. (9) is obtained:

Figure BDA0002833602040000045
Figure BDA0002833602040000045

其中，

Figure BDA0002833602040000046
为第n层形貌信息，An、A'n为第n层衍射结果信息；in,
Figure BDA0002833602040000046
is the topography information of the nth layer, An and A' n are the diffraction result information of the nth layer;

将第j层和第(j+1)层矩形薄层的电场、磁场进行连续性匹配得到：The electric field and magnetic field of the jth layer and the (j+1)th rectangular thin layer are successively matched to obtain:

Figure BDA0002833602040000047
Figure BDA0002833602040000047

其中，

Figure BDA0002833602040000048
为第j层形貌信息，Aj、A'j为第j层衍射结果信息；Aj+1、A'j+1为第(j+1)层衍射结果信息，
Figure BDA0002833602040000049
为第(j+1)层电场值；in,
Figure BDA0002833602040000048
is the topography information of the j-th layer, A j and A' j are the diffraction result information of the j-th layer; A j+1 and A' j+1 are the diffraction result information of the (j+1)-th layer,
Figure BDA0002833602040000049
is the electric field value of the (j+1)th layer;

根据电磁场边界条件求得Aj及A'j矩阵，代入式(6)进行积分计算进而得到第j层矩形薄层的电磁场值

Figure BDA00028336020400000410
According to the boundary conditions of the electromagnetic field, the A j and A' j matrices are obtained, and they are substituted into formula (6) for integral calculation to obtain the electromagnetic field value of the jth thin rectangular layer.
Figure BDA00028336020400000410

进一步的，所述步骤5中，SU-8胶背面入射紫外光的二维光强分布的模拟结果如式(11)所示；Further, in the step 5, the simulation result of the two-dimensional light intensity distribution of the incident ultraviolet light on the back of the SU-8 glue is shown in formula (11);

Figure BDA00028336020400000411
Figure BDA00028336020400000411

其中，Il,m为所述二维阵列中坐标(l,m)处光照强度值，

Figure BDA00028336020400000412
为所述二维阵列中坐标(l,m)处电场
Figure BDA00028336020400000413
值，nr为光刻胶折射率实部。Wherein, I l, m is the light intensity value at the coordinates (l, m) in the two-dimensional array,
Figure BDA00028336020400000412
is the electric field at coordinates (l, m) in the two-dimensional array
Figure BDA00028336020400000413
value, n r is the real part of the photoresist refractive index.

有益效果：本发明采用基于严格电磁场理论的波导法计算光刻胶内的光强分布情况，由于背面入射直接将掩模版作为衬底，将SU-8胶直接涂覆在掩模版上，不需考虑空气间隙的影响，同时也避免了衬底反射的影响。同时，在背面入射紫外光的二维光强计算模型中，也综合考虑了不同参数对光强分布的影响，如光刻胶的深度、斜入射时的入射角。将模拟结果与实际的实验结果进行对比以验证模型准确性得出，本发明方法可以精确模拟紫外光背面入射这一光刻工艺过程中SU-8胶内部的光强分布情况。Beneficial effects: the present invention adopts the waveguide method based on strict electromagnetic field theory to calculate the light intensity distribution in the photoresist, because the backside incident directly uses the reticle as the substrate, and the SU-8 glue is directly coated on the reticle, without the need for The effects of air gaps are considered, while the effects of substrate reflections are also avoided. At the same time, in the two-dimensional light intensity calculation model of the incident ultraviolet light on the back side, the influence of different parameters on the light intensity distribution, such as the depth of the photoresist and the incidence angle of oblique incidence, is also comprehensively considered. Comparing the simulation results with the actual experimental results to verify the accuracy of the model, the method of the present invention can accurately simulate the light intensity distribution inside the SU-8 glue during the photolithography process of incident ultraviolet light on the backside.

附图说明Description of drawings

图1是基于二维波导法的光刻仿真模型示意图；1 is a schematic diagram of a lithography simulation model based on a two-dimensional waveguide method;

图2是垂直入射时不同光刻胶深度的光强分布曲线图与对应的光强等高线图。FIG. 2 is a light intensity distribution curve diagram and a corresponding light intensity contour diagram at different photoresist depths under vertical incidence.

具体实施方式Detailed ways

下面结合附图对本发明做更进一步的解释。The present invention will be further explained below in conjunction with the accompanying drawings.

如图1所示为基于二维波导法的光刻仿真模型示意图，入射光具有入射光强I0以及入射角θ这二个维度的信息，坐标系的建立如图所示，其中沿着掩模版水平方向建立x轴，沿着垂直于掩模版方向建立z轴，每一层在z轴方向上都有连续的光学性质。掩模不透光区域和透光区域的坐标定义可从图中明显看出。根据背面入射的特点，光刻过程中将掩模版作为衬底，将SU-8胶直接涂覆在掩模版上，入射紫外光直接透过掩模版背面曝光SU-8胶。因此，在矩形薄层的划分过程中，将玻璃定义为第一层材料，即为图中材料c，掩模版作为第二层材料，即为图中材料b，SU-8光刻胶作为第三层材料，即为图中材料a，每一层在z方向上的坐标值分别是0、z1、z2、z3。这样一来，每一层材料在z方向上的介电常数均满足一致性的原则。Figure 1 is a schematic diagram of the lithography simulation model based on the two-dimensional waveguide method. The incident light has two dimensions of information, the incident light intensity I 0 and the incident angle θ. The establishment of the coordinate system is shown in the figure, where along the mask The x-axis is established horizontally on the reticle and the z-axis is established along the direction perpendicular to the reticle, and each layer has continuous optical properties in the z-axis direction. The coordinate definitions of the opaque area and the transparent area of the mask can be clearly seen from the figure. According to the characteristics of the backside incident, the reticle is used as the substrate in the photolithography process, the SU-8 glue is directly coated on the reticle, and the incident ultraviolet light directly passes through the back of the reticle to expose the SU-8 glue. Therefore, in the process of dividing the rectangular thin layer, the glass is defined as the first layer material, which is the material c in the figure, the mask is used as the second layer material, which is the material b in the figure, and the SU-8 photoresist is the first layer material. There are three layers of material, namely material a in the figure, and the coordinate values of each layer in the z direction are 0, z1, z2, and z3, respectively. In this way, the dielectric constant of each layer of material in the z direction satisfies the principle of consistency.

SU-8胶紫外光背面光刻工艺的二维光强分布模拟方法，包括如下步骤：The two-dimensional light intensity distribution simulation method of SU-8 glue ultraviolet light backside lithography process includes the following steps:

步骤1：将需要进行光强分布模拟的光刻仿真区域进行空间离散，细分成网格组成的二维阵列，并采用二维矩阵代表该二维阵列。Step 1: The lithography simulation area that needs to perform light intensity distribution simulation is spatially discretized, subdivided into a two-dimensional array composed of grids, and a two-dimensional matrix is used to represent the two-dimensional array.

步骤2：将整个光刻仿真区域沿水平方向划分成若干矩形薄层，每一矩形薄层在Z轴方向上光学性质连续。Step 2: Divide the entire lithography simulation area into several rectangular thin layers along the horizontal direction, and each rectangular thin layer has continuous optical properties in the Z-axis direction.

步骤3：对每一矩形薄层分别建立麦克斯韦方程，并对麦克斯韦方程进行分离变量得到一个特征值问题，然后将每一矩形薄层中的材料参数和电磁场用傅里叶级数展开，通过数值求解特征值问题得到每一矩形薄层中的电磁场分布情况。Step 3: Establish Maxwell's equations for each rectangular thin layer separately, and separate the variables of Maxwell's equation to obtain an eigenvalue problem, and then expand the material parameters and electromagnetic fields in each rectangular thin layer with Fourier series, through the numerical value Solve the eigenvalue problem to get the electromagnetic field distribution in each rectangular thin layer.

步骤4：根据连续性条件施加电磁场边界条件将每一矩形薄层耦合起来，求得光在透过掩模版后的电磁场分布情况。Step 4: According to the continuity condition, the electromagnetic field boundary condition is applied to couple each rectangular thin layer, and the electromagnetic field distribution of the light after passing through the reticle is obtained.

步骤5：根据电磁场分布情况计算得到SU-8胶背面入射紫外光的二维光强分布的模拟结果。Step 5: Calculate the simulation result of the two-dimensional light intensity distribution of the incident ultraviolet light on the back of the SU-8 adhesive according to the electromagnetic field distribution.

具体的，步骤3包括如下步骤：Specifically, step 3 includes the following steps:

步骤3-1：对每一矩形薄层分别建立麦克斯韦方程，运用分离变量法的思想，将电磁场E分离成X(x)和Z(z)两个变量，并代入麦克斯韦方程，从而将麦克斯韦方程分解为如式(1)所示的两个微分方程，所述微分方程含有复数势k2ε和特征值α2；Step 3-1: Establish Maxwell's equations for each rectangular thin layer, and use the idea of the separation of variables method to separate the electromagnetic field E into two variables, X(x) and Z(z), and substitute them into Maxwell's equations, thereby converting Maxwell's equations is decomposed into two differential equations as shown in equation (1), the differential equations contain complex potential k 2 ε and eigenvalue α 2 ;

Figure BDA0002833602040000061
Figure BDA0002833602040000061

其中，ε为每一所述矩形薄层的材料介电常数，X(x)和Z(z)为分离出的变量,k为波数。where ε is the material permittivity of each of the rectangular thin layers, X(x) and Z(z) are separated variables, and k is the wave number.

步骤3-2：掩模结构在x方向上以长度d为周期重复地排列，将介电常数ε进行傅里叶级数展开，如式(2)所示；Step 3-2: The mask structure is repeatedly arranged in the x direction with a length d as a period, and the dielectric constant ε is expanded by a Fourier series, as shown in formula (2);

Figure BDA0002833602040000062
Figure BDA0002833602040000062

其中，εj(x)表示第j层矩形薄层的介电常数，

Figure BDA0002833602040000063
为傅里叶级数展开后的第q项的系数，L为傅里叶展开级数，i表示复数，b是d的倒数。where ε j (x) represents the dielectric constant of the jth thin rectangular layer,
Figure BDA0002833602040000063
is the coefficient of the qth term after the Fourier series expansion, L is the Fourier expansion series, i is a complex number, and b is the reciprocal of d.

步骤3-3：通过如式(3)所示逆傅里叶变换求出傅里叶级数展开后的每一项的系数。Step 3-3: Calculate the coefficient of each term after Fourier series expansion by inverse Fourier transform as shown in equation (3).

Figure BDA0002833602040000064
Figure BDA0002833602040000064

步骤3-4：对变量X(x)进行如式(4)所示傅里叶变换；Step 3-4: Perform Fourier transform on the variable X(x) as shown in formula (4);

Figure BDA0002833602040000065
Figure BDA0002833602040000065

其中，Bl为傅里叶展开后第l项系数。Among them, B l is the lth coefficient after Fourier expansion.

步骤3-5：将傅里叶展开级数代入式(1)中第一个微分方程，得到特征值矩阵方程，如式(5)所示；Step 3-5: Substitute the Fourier expansion series into the first differential equation in equation (1) to obtain the eigenvalue matrix equation, as shown in equation (5);

Figure BDA0002833602040000071
Figure BDA0002833602040000071

其中，B是矩阵D的特征向量，Dl,m为矩阵D中第l行第m列的元素，εl-m为经傅里叶展开后的第(l-m)项介电常数值。Among them, B is the eigenvector of matrix D, D l,m is the element in the lth row and mth column of matrix D, and εlm is the ( lm )th dielectric constant value after Fourier expansion.

步骤3-6：根据式(4)中X(x)表达式和对式(1)第二个微分方程求解得到的Z(z)表达式，计算出电磁场表达式的值，从而建立如式(6)所示的第j层矩形薄层的电磁场数学模型；Step 3-6: Calculate the value of the electromagnetic field expression according to the X(x) expression in Equation (4) and the Z(z) expression obtained by solving the second differential equation of Equation (1), thereby establishing the formula (6) Mathematical model of the electromagnetic field of the j-th rectangular thin layer shown;

Figure BDA0002833602040000072
Figure BDA0002833602040000072

其中，

Figure BDA0002833602040000073
为第j层矩形薄层的电场y方向分量，
Figure BDA0002833602040000074
及
Figure BDA0002833602040000075
表示第j层矩形薄层的第m阶本征模振幅，即矩阵Aj及A'j的第m列元素；
Figure BDA0002833602040000076
表示第j层矩形薄层的特征值矩阵的第列元素，
Figure BDA0002833602040000077
表示第j层矩形薄层的特征向量矩阵的第l行第m列元素，并通过式(5)求解得到；z表示z轴坐标，zj表示第j层矩形薄层的坐标；
Figure BDA0002833602040000078
为第j层矩形薄层的磁场x方向分量，
Figure BDA0002833602040000079
为第j层矩形薄层的磁场z方向分量。in,
Figure BDA0002833602040000073
is the y-direction component of the electric field of the j-th rectangular thin layer,
Figure BDA0002833602040000074
and
Figure BDA0002833602040000075
represents the m-th order eigenmode amplitude of the j-th rectangular thin layer, that is, the m-th column elements of the matrices A j and A'j;
Figure BDA0002833602040000076
represents the column-th element of the eigenvalue matrix of the j-th rectangular thin layer,
Figure BDA0002833602040000077
Represents the elements of the lth row and mth column of the eigenvector matrix of the jth layer of rectangular thin layer, and is obtained by formula (5); z represents the z-axis coordinate, and zj represents the jth layer of rectangular thin layer coordinates;
Figure BDA0002833602040000078
is the x-direction component of the magnetic field of the jth rectangular thin layer,
Figure BDA0002833602040000079
is the z-direction component of the magnetic field of the jth rectangular thin layer.

步骤4中，空气与第一层界面处根据电磁场连续边界条件，用矩阵形式表示，得到如式(7)所示的下边界条件方程；In step 4, the interface between the air and the first layer is expressed in matrix form according to the continuous boundary condition of the electromagnetic field, and the lower boundary condition equation shown in formula (7) is obtained;

Figure BDA00028336020400000710
Figure BDA00028336020400000710

其中，in,

Figure BDA00028336020400000711
Figure BDA00028336020400000711

Figure BDA00028336020400000712
Figure BDA00028336020400000712

Figure BDA00028336020400000713
Figure BDA00028336020400000713

上式中，

Figure BDA0002833602040000081
表示第1层形貌信息，A1、A'1表示第1层衍射结果信息，矩阵R表示光照信息，Rl表示矩阵R的第l列元素，l0为斜入射时入射波阶次，λ0为入射光波长，
Figure BDA0002833602040000082
表示初始光照强度，θ表示入射角度，
Figure BDA0002833602040000083
表示第1层形貌信息的第l行第m列元素。In the above formula,
Figure BDA0002833602040000081
represents the topography information of the first layer, A 1 and A '1 represent the diffraction result information of the first layer, the matrix R represents the illumination information, R l represents the element in the lth column of the matrix R, and l 0 is the incident wave order at oblique incidence, λ 0 is the wavelength of incident light,
Figure BDA0002833602040000082
represents the initial light intensity, θ represents the incident angle,
Figure BDA0002833602040000083
Indicates the element in the lth row and the mth column of the topography information of the first layer.

最后一层界面处根据边界条件得如式(11)所示的边界条件方程：According to the boundary conditions at the interface of the last layer, the boundary condition equation shown in Eq. (11) is obtained:

Figure BDA0002833602040000084
Figure BDA0002833602040000084

其中：in:

Figure BDA0002833602040000085
Figure BDA0002833602040000085

Figure BDA0002833602040000086
Figure BDA0002833602040000086

上式中，

Figure BDA0002833602040000087
为第n层形貌信息，An、A'n为第n层衍射结果信息；
Figure BDA0002833602040000088
表示第n层形貌信息的第l行第m列元素，εs为最后一矩形薄层材料的介电常数，T为最后一矩形薄层的坐标。In the above formula,
Figure BDA0002833602040000087
is the topography information of the nth layer, An and A'n are the diffraction result information of the nth layer;
Figure BDA0002833602040000088
It represents the element in the lth row and mth column of the topography information of the nth layer, εs is the dielectric constant of the material of the last rectangular thin layer, and T is the coordinate of the last rectangular thin layer.

将第j层和第(j+1)层矩形薄层的电场、磁场进行连续性匹配得到：The electric field and magnetic field of the jth layer and the (j+1)th rectangular thin layer are successively matched to obtain:

Figure BDA0002833602040000089
Figure BDA0002833602040000089

上式中各个元素的表达式如下：The expression of each element in the above formula is as follows:

Figure BDA00028336020400000810
Figure BDA00028336020400000810

Figure BDA00028336020400000811
Figure BDA00028336020400000811

Figure BDA00028336020400000812
Figure BDA00028336020400000812

Figure BDA00028336020400000813
Figure BDA00028336020400000813

Figure BDA00028336020400000814
Figure BDA00028336020400000814

Figure BDA00028336020400000815
Figure BDA00028336020400000815

Figure BDA0002833602040000091
Figure BDA0002833602040000091

Figure BDA0002833602040000092
Figure BDA0002833602040000092

其中，

Figure BDA0002833602040000093
为第j层形貌信息，Aj、A'j为第j层衍射结果信息；Aj+1、A'j+1为第(j+1)层衍射结果信息，
Figure BDA0002833602040000094
为第(j+1)层电场值，
Figure BDA0002833602040000095
Figure BDA0002833602040000096
表示第j层形貌信息的第l行第m列元素，
Figure BDA0002833602040000097
表示第(j+1)层电场值的第l行第m列元素。in,
Figure BDA0002833602040000093
is the topography information of the j-th layer, A j and A' j are the diffraction result information of the j-th layer; A j+1 and A' j+1 are the diffraction result information of the (j+1)-th layer,
Figure BDA0002833602040000094
is the electric field value of the (j+1)th layer,
Figure BDA0002833602040000095
Figure BDA0002833602040000096
represents the element of the lth row and the mth column of the topography information of the jth layer,
Figure BDA0002833602040000097
The element in the lth row and the mth column representing the electric field value of the (j+1)th layer.

最后，根据电磁场边界条件求得Aj及A'j矩阵，代入式(6)进行积分计算进而得到第j层矩形薄层的电磁场值

Figure BDA0002833602040000098
Finally, according to the boundary conditions of the electromagnetic field, the A j and A' j matrices are obtained, and they are substituted into the formula (6) for integral calculation to obtain the electromagnetic field value of the jth thin rectangular layer.
Figure BDA0002833602040000098

步骤5中，SU-8胶背面入射紫外光的二维光强分布的模拟结果如式(23)所示；In step 5, the simulation result of the two-dimensional light intensity distribution of the incident ultraviolet light on the back of the SU-8 adhesive is shown in formula (23);

Figure BDA0002833602040000099
Figure BDA0002833602040000099

其中，Il,m为二维阵列中坐标(l,m)处光照强度值，

Figure BDA00028336020400000910
为二维阵列中坐标(l,m)处电场
Figure BDA00028336020400000911
值，nr为光刻胶折射率实部。Among them, I l, m is the light intensity value at the coordinates (l, m) in the two-dimensional array,
Figure BDA00028336020400000910
is the electric field at coordinates (l,m) in the two-dimensional array
Figure BDA00028336020400000911
value, n r is the real part of the photoresist refractive index.

图2是垂直入射时不同光刻胶深度的光强分布曲线图与对应的光强等高线图。光刻仿真时，初始入射光强为2.6mW/cm2，入射光波长为365nm，光刻胶厚度为300μm，掩模版长度为200μm，掩模孔大小为100μm。图2(a)为垂直入射时不同光刻胶深度的光强分布曲线图，曲线从上至下光刻胶深度依次为5μm、100μm、200μm和300μm。图2(b)为对应的光强等高线图。本发明将模拟结果与实际的实验结果进行对比，以验证模型准确性。经验证发现模拟结果与实验结果比较一致，可以用于SU-8胶紫外光背面入射光刻过程的二维模拟。FIG. 2 is a light intensity distribution curve diagram and a corresponding light intensity contour diagram at different photoresist depths under vertical incidence. During the lithography simulation, the initial incident light intensity was 2.6 mW/cm2, the incident light wavelength was 365 nm, the photoresist thickness was 300 μm, the mask length was 200 μm, and the mask hole size was 100 μm. Figure 2(a) is a graph of the light intensity distribution at different photoresist depths at vertical incidence. The photoresist depths of the curve are 5 μm, 100 μm, 200 μm and 300 μm in sequence from top to bottom. Figure 2(b) is the corresponding light intensity contour map. The present invention compares the simulation results with the actual experimental results to verify the accuracy of the model. After verification, it is found that the simulation results are consistent with the experimental results, and can be used for the two-dimensional simulation of the SU-8 glue UV back incident lithography process.

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. It should be regarded as the protection scope of the present invention.

Claims (4)

  1. The two-dimensional light intensity distribution simulation method of the SU-8 photoresist ultraviolet light back side photoetching process is characterized by comprising the following steps of:
    step 1: carrying out space dispersion on a photoetching simulation area needing light intensity distribution simulation, subdividing the photoetching simulation area into a two-dimensional array consisting of grids, and representing the two-dimensional array by adopting a two-dimensional matrix;
    step 2: dividing the whole photoetching simulation area into a plurality of rectangular thin layers along the horizontal direction, wherein the rectangular thin layers are continuous in optical property in the Z-axis direction;
    and step 3: respectively establishing Maxwell equations for each rectangular thin layer, separating variables from the Maxwell equations to obtain a characteristic value problem, then expanding material parameters and electromagnetic fields in each rectangular thin layer by Fourier series, and solving the characteristic value problem through numerical values to obtain the electromagnetic field distribution condition in each rectangular thin layer;
    and 4, step 4: applying electromagnetic field boundary conditions according to continuity conditions to couple the rectangular thin layers, and obtaining the electromagnetic field distribution condition of light after penetrating through the mask;
    and 5: and calculating according to the distribution condition of the electromagnetic field to obtain a simulation result of the two-dimensional light intensity distribution of the SU-8 glue back incident ultraviolet light.
  2. 2. The method for simulating the two-dimensional light intensity distribution of the SU-8 photoresist ultraviolet light backside lithography process according to claim 1, wherein the step 3 comprises the steps of:
    step 3-1: respectively establishing Maxwell equations for each rectangular thin layer, separating the electromagnetic field E into two variables of X (x) and Z (z), substituting the variables into the Maxwell equations, and decomposing the Maxwell equations into two differential equations shown in the formula (1), wherein the differential equations contain complex potential k2Epsilon and a characteristic value alpha2；
    Figure FDA0002833602030000011
    Wherein epsilon is the dielectric constant of the material of each rectangular thin layer, and k is the wave number;
    step 3-2: the mask structures are repeatedly arranged in the x direction with the length d as a period, and the dielectric constant epsilon is subjected to Fourier series expansion as shown in formula (2);
    Figure FDA0002833602030000012
    wherein epsilonj(x) Represents the dielectric constant of the j-th rectangular thin layer,
    Figure FDA0002833602030000013
    is the coefficient of the q-th term after Fourier expansion, L is the Fourier expansion series, i represents the complex number, b is the reciprocal of d;
    step 3-3: the coefficient of each term after the expansion of the fourier series is found by the inverse fourier transform as shown in equation (3):
    Figure FDA0002833602030000021
    step 3-4: performing Fourier transform on the variable X (x) as shown in the formula (4);
    Figure FDA0002833602030000022
    wherein, BlThe coefficients of the ith term after Fourier expansion;
    step 3-5: substituting Fourier expansion series into a first differential equation in the formula (1) to obtain a characteristic value matrix equation shown in a formula (5);
    Figure FDA0002833602030000023
    where B is the eigenvector of the matrix D, Dl,mIs the element of the ith row and mth column in matrix D, epsilonl-mIs the dielectric constant value of the (l-m) th item after Fourier expansion;
    step 3-6: establishing an electromagnetic field mathematical model of the j-th rectangular thin layer as shown in the formula (6);
    Figure FDA0002833602030000024
    wherein,
    Figure FDA0002833602030000025
    is the j-th momentThe y-direction component of the electric field of the conformal thin layer,
    Figure FDA0002833602030000026
    and
    Figure FDA0002833602030000027
    representing amplitude of eigenmodes of m-th order of rectangular layer of j-th layer, i.e. matrix AjAnd A'jThe m-th column element of (1);
    Figure FDA0002833602030000028
    the mth column element of the eigenvalue matrix representing the jth rectangular sheet,
    Figure FDA0002833602030000029
    the ith row and mth column elements of the eigenvector matrix representing the jth rectangular thin layer are obtained by solving the formula (5); z is a radical ofjRepresenting the coordinates of the j-th rectangular thin layer;
    Figure FDA00028336020300000210
    is the x-direction component of the magnetic field of the j-th rectangular thin layer,
    Figure FDA00028336020300000211
    is the z-direction component of the magnetic field of the j-th rectangular thin layer.
  3. 3. The method for simulating the two-dimensional light intensity distribution of the SU-8 photoresist ultraviolet light back lithography process according to claim 2, wherein in the step 4, the boundary condition equation shown in the formula (7) is obtained by expressing the interface between the air and the first layer in a matrix form according to the continuous boundary condition of the electromagnetic field;
    Figure FDA0002833602030000031
    Figure FDA0002833602030000032
    wherein,
    Figure FDA0002833602030000033
    representing layer 1 profile information, A1、A'1Representing diffraction result information of layer 1, matrix R representing illumination information, RlThe l column element, l, of the representation matrix R0At oblique incidence, of the incident order, λ0In the wavelength of the incident light,
    Figure FDA0002833602030000034
    representing the initial illumination intensity, and theta represents the incident angle;
    and obtaining a boundary condition equation shown as the formula (9) at the interface of the last layer according to the boundary condition:
    Figure FDA0002833602030000035
    wherein,
    Figure FDA0002833602030000036
    is the n-th layer of profile information, An、A'nDiffraction result information of the nth layer;
    and (3) continuously matching the electric field and the magnetic field of the j-th layer and the (j +1) -th rectangular thin layer to obtain:
    Figure FDA0002833602030000037
    wherein,
    Figure FDA0002833602030000038
    as the j-th layer of profile information, Aj、A'jDiffraction result information of the j layer; a. thej+1、A'j+1Diffraction result information of the (j +1) th layer,
    Figure FDA0002833602030000039
    is the (j +1) th layer electric field value;
    determining A from electromagnetic field boundary conditionsjAnd A'jThe matrix is substituted for the formula (6) to carry out integral calculation so as to obtain the electromagnetic field value of the j-th rectangular thin layer
    Figure FDA00028336020300000310
  4. 4. The method for simulating the two-dimensional light intensity distribution of the SU-8 photoresist ultraviolet light back side lithography process according to claim 2, wherein in the step 5, the simulation result of the two-dimensional light intensity distribution of the SU-8 photoresist back side incident ultraviolet light is as shown in formula (11);
    Figure FDA00028336020300000311
    wherein, Il,mIs the illumination intensity value at coordinate (l, m) in the two-dimensional array,
    Figure FDA00028336020300000312
    for the electric field at coordinate (l, m) in the two-dimensional array
    Figure FDA00028336020300000313
    Value nrIs the real part of the refractive index of the photoresist.
CN202011470885.3A 2020-12-14 2020-12-14 Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process Pending CN112558428A (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
CN202011470885.3A CN112558428A (en) 2020-12-14 2020-12-14 Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process
PCT/CN2020/138373 WO2022126692A1 (en) 2020-12-14 2020-12-22 Two-dimensional light intensity distribution simulation method for uv-light back lithography process using su-8 photoresist

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011470885.3A CN112558428A (en) 2020-12-14 2020-12-14 Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process

Publications (1)

Publication Number Publication Date
CN112558428A true CN112558428A (en) 2021-03-26

Family

ID=75063104

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011470885.3A Pending CN112558428A (en) 2020-12-14 2020-12-14 Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process

Country Status (2)

Country Link
CN (1) CN112558428A (en)
WO (1) WO2022126692A1 (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116702524A (en) * 2023-08-09 2023-09-05 华芯程(杭州)科技有限公司 Etching simulation method, device and equipment using diffusion boundary layer
CN117008428A (en) * 2023-09-26 2023-11-07 全芯智造技术有限公司 Lithographic simulation method, apparatus and medium
WO2023216336A1 (en) * 2022-05-13 2023-11-16 东南大学 Light intensity distribution simulation method for thick photoresist lithography process

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN119045272B (en) * 2024-10-30 2025-02-11 江苏第三代半导体研究院有限公司 Mask plate design method and micro light-emitting diode preparation method

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10355264B4 (en) * 2003-11-26 2008-08-14 Qimonda Ag Method for improving a simulation model of the photolithographic projection
CN101776849A (en) * 2010-03-08 2010-07-14 东南大学 Light intensity distribution analogy method of heavy-rubber ultraviolet light oblique incidence back etching process
CN102081311A (en) * 2010-12-20 2011-06-01 东南大学 Method for simulating three-dimensional light intensity distribution of thick photoresist backside oblique incidence photoetching process
WO2017063839A1 (en) * 2015-10-12 2017-04-20 Asml Netherlands B.V. Methods and apparatus for simulating interaction of radiation with structures, metrology methods and apparatus, device manufacturing method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
ZI-CHEN GENG 等: "A 2D Waveguide Method for Lithography Simulation of Thick SU-8 Photoresist", 《MICROMACHINES》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023216336A1 (en) * 2022-05-13 2023-11-16 东南大学 Light intensity distribution simulation method for thick photoresist lithography process
CN116702524A (en) * 2023-08-09 2023-09-05 华芯程(杭州)科技有限公司 Etching simulation method, device and equipment using diffusion boundary layer
CN116702524B (en) * 2023-08-09 2023-10-20 华芯程(杭州)科技有限公司 Etching simulation method, device and equipment using diffusion boundary layer
CN117008428A (en) * 2023-09-26 2023-11-07 全芯智造技术有限公司 Lithographic simulation method, apparatus and medium
CN117008428B (en) * 2023-09-26 2024-01-26 全芯智造技术有限公司 Lithographic simulation method, apparatus and medium

Also Published As

Publication number Publication date
WO2022126692A1 (en) 2022-06-23

Similar Documents

Publication Publication Date Title
WO2022126692A1 (en) Two-dimensional light intensity distribution simulation method for uv-light back lithography process using su-8 photoresist
JP2021505942A (en) 3D beam shaping using metasurface
US9523800B2 (en) Computation efficiency by iterative spatial harmonics order truncation
Liu et al. Machine learning aided solution to the inverse problem in optical scatterometry
WO2023216336A1 (en) Light intensity distribution simulation method for thick photoresist lithography process
CN104750917A (en) Determination method for layered medium rough surface electromagnetic scattering coefficients
CN102708229A (en) Matrix decomposition and novel singular value decomposition combined method for complex layered medium structures
Budhu et al. Unit cell design for aperiodic metasurfaces
Wongviboonsin et al. Microstructural effects on the response of a multi-layered elastic substrate
CN104238282B (en) The extreme ultraviolet photolithographic quick strict emulation mode containing defect mask diffraction spectra
US10739583B2 (en) Method for obtaining at least one structure approximating a sought structure by reflow
US8560270B2 (en) Rational approximation and continued-fraction approximation approaches for computation efficiency of diffraction signals
CN103279612B (en) The multi grid Preconditioning method of complex target radar return quick obtaining
CN110287549B (en) RCS prediction method for multi-position thin coating aircraft with uncertain sources
Xionggui et al. Analysis and simulation of diffractive imaging field in thick film photoresist by using angular spectrum theory
Oshima et al. Development of a physics-informed neural network to enhance wind tunnel data for aerospace design
CN116027639A (en) Plasma photoetching imaging method and device
Sun et al. On-demand Quick Metasurface Design with Neighborhood Attention Transformer
CN103472686B (en) Method for simulating three-dimensional light intensity distribution in thick resist ultraviolet (UV) shifting mask lithography
Strojwas et al. Layout manufacturability analysis using rigorous 3-D topography simulation
WO2020032092A1 (en) Substrate for cell culturing, production method, and prediction method
Dai et al. Preconditioned Richardson numerical method for thermal analysis in X-ray lithography with cylindrical geometry
CN102081311A (en) Method for simulating three-dimensional light intensity distribution of thick photoresist backside oblique incidence photoetching process
Yeung et al. A very fast and accurate rigorous EMF simulator for EUVL masks based on the pseudo-spectral time-domain method
CN102621801B (en) Calculation method of conical diffraction field of double-layer attenuation phase-shift L/S mask with assist lines

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20210326

RJ01 Rejection of invention patent application after publication