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

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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
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rectangular thin
layer
thin layer
electromagnetic field
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耿子辰
周再发
代辉
黄庆安
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Southeast University
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Southeast University
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    • 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

Abstract

The invention discloses a two-dimensional light intensity distribution simulation method of an SU-8 photoresist ultraviolet light back photoetching process, which comprises the following steps of: carrying out space dispersion on a photoetching simulation area needing light intensity distribution simulation, and subdividing the photoetching simulation area into a two-dimensional array consisting of grids; step 2: dividing the whole photoetching simulation area into a plurality of rectangular thin layers along the horizontal 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 the material parameters and the electromagnetic field 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 each rectangular thin layer, 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.

Description

Two-dimensional light intensity distribution simulation method for SU-8 photoresist ultraviolet light back photoetching process
Technical Field
The invention relates to a two-dimensional light intensity distribution simulation method for an SU-8 thick photoresist ultraviolet light back incidence photoetching process, and belongs to the field of computer simulation of a micro-electro-mechanical system (MEMS) processing process.
Background
The Ultraviolet (UV) photoetching technology using SU-8 thick photoresist is an important micromachining technology in the field of MEMS, overcomes the problem of insufficient photoetching depth-to-width ratio of common photoresist, and is very suitable for manufacturing an ultra-thick MEMS microstructure with high depth-to-width ratio. The traditional SU-8 photoresist ultraviolet light vertical incidence photoetching process can only manufacture vertical SU-8 photoresist microstructures. With the increasing abundance of MEMS devices, inclined structures such as embedded channels, V-shaped grooves, inclined cylinders and the like appear, and the limit of vertical incidence can be eliminated by adopting an oblique incidence photoetching process to manufacture various complicated SU-8 photoresist microstructures. However, due to uneven thickness of the SU-8 glue during the coating process and edge bead effect, the SU-8 glue at the edge of the substrate may be thicker than the SU-8 glue at the center of the substrate. Moreover, due to the uneven exposure dose on the top and bottom of the photoresist, the phenomena of overexposure on the top of the photoresist and underexposure on the bottom of the photoresist occur, which affects the final developed dimension. Meanwhile, in the oblique incidence photoetching process of the SU-8 photoresist ultraviolet light, an air gap inevitably exists between the mask and the SU-8 photoresist. The diffraction effect generated by the air gap has great influence on the photoetching precision, so that the SU-8 glue microstructure with high aspect ratio is difficult to process. To solve this problem, researchers have proposed using SU-8 photoresist uv backside lithography to fabricate high aspect ratio SU-8 photoresist microstructures. The method directly uses the mask as a substrate, and directly coats the SU-8 glue on the mask, and during the photoetching process, incident ultraviolet light directly penetrates through the back of the mask to expose the SU-8 glue. The method has the advantages of simple used process equipment and low processing cost, avoids the influence of diffraction effect caused by uneven surface of the SU-8 glue, simultaneously avoids the influence of substrate reflection on the SU-8 glue microstructure, and can more effectively process the SU-8 glue microstructure with high depth-to-width ratio.
The simulation tool is adopted to optimize the process performance, so that the problems of high cost and long time consumption caused by repeated plate making, flow sheet and experiment can be avoided, the optimal process condition can be searched by utilizing the computational simulation technology, the manufacturing performance is greatly improved, the design cycle of related MEMS products is shortened, the development cost of the related MEMS products is reduced, and the internal principle of the photoetching technology is further understood. In the SU-8 photoresist photoetching process, the final appearance of the developed photoresist depends on the exposure process to a great extent, and is the most important one-step process in the whole photoetching process. The shape of the developed photoresist can be predicted by simulating the light intensity distribution condition in the photoresist after photoetching. Therefore, the simulation of the light intensity distribution of the SU-8 thick photoresist back-side incident lithography process is a research with great development potential.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the prior art, a two-dimensional light intensity distribution simulation method of an SU-8 photoresist ultraviolet light back side photoetching process is provided, which is used for simulating the light intensity distribution condition in the photoresist after photoetching.
The technical scheme is as follows: the two-dimensional light intensity distribution simulation method of the SU-8 photoresist ultraviolet light back photoetching process comprises the following steps:
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.
Further, the step 3 comprises the following steps:
step 3-1: respectively establishing each rectangular thin layerMaxwell's equation, which separates the electromagnetic field E into two variables of X (x) and Z (z) and substitutes the variables into Maxwell's equation, thereby decomposing Maxwell's equation into two differential equations as shown in formula (1), the differential equations containing complex potential k2Epsilon and a characteristic value alpha2；
Figure BDA0002833602040000021
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 BDA0002833602040000022
wherein epsilonj(x) Represents the dielectric constant of the j-th rectangular thin layer,
Figure BDA0002833602040000031
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 BDA0002833602040000032
step 3-4: performing Fourier transform on the variable X (x) as shown in the formula (4);
Figure BDA0002833602040000033
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 BDA0002833602040000034
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 BDA0002833602040000035
wherein the content of the first and second substances,
Figure BDA0002833602040000036
is the y-direction component of the electric field of the j-th rectangular thin layer,
Figure BDA0002833602040000037
and
Figure BDA0002833602040000038
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 BDA0002833602040000039
the mth column element of the eigenvalue matrix representing the jth rectangular sheet,
Figure BDA00028336020400000310
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 BDA00028336020400000311
is the x-direction component of the magnetic field of the j-th rectangular thin layer,
Figure BDA00028336020400000312
is the z-direction component of the magnetic field of the j-th rectangular thin layer.
Further, in the step 4, the interface between the air and the first layer is expressed in a matrix form according to the continuous boundary condition of the electromagnetic field, so as to obtain a boundary condition equation shown in a formula (7);
Figure BDA0002833602040000041
Figure BDA0002833602040000042
wherein the content of the first and second substances,
Figure BDA0002833602040000043
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 BDA0002833602040000044
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 BDA0002833602040000045
wherein the content of the first and second substances,
Figure BDA0002833602040000046
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 BDA0002833602040000047
wherein the content of the first and second substances,
Figure BDA0002833602040000048
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 BDA0002833602040000049
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 BDA00028336020400000410
Further, in the step 5, a simulation result of two-dimensional light intensity distribution of the SU-8 glue back incident ultraviolet light is shown as a formula (11);
Figure BDA00028336020400000411
wherein, Il,mIs the illumination intensity value at coordinate (l, m) in the two-dimensional array,
Figure BDA00028336020400000412
for the electric field at coordinate (l, m) in the two-dimensional array
Figure BDA00028336020400000413
Value nrIs the real part of the refractive index of the photoresist.
Has the advantages that: the invention adopts a waveguide method based on strict electromagnetic field theory to calculate the light intensity distribution condition in the photoresist, and because the back incidence directly takes the mask as the substrate and the SU-8 glue is directly coated on the mask, the influence of air gap is not needed to be considered, and the influence of substrate reflection is also avoided. Meanwhile, in the two-dimensional light intensity calculation model of the back incident ultraviolet light, the influence of different parameters on the light intensity distribution, such as the depth of the photoresist and the incident angle during oblique incidence, is also comprehensively considered. The simulation result is compared with the actual experiment result to verify the accuracy of the model, and the method can accurately simulate the light intensity distribution condition inside the SU-8 photoresist in the photoetching process of ultraviolet light back incidence.
Drawings
FIG. 1 is a schematic diagram of a lithography simulation model based on a two-dimensional waveguide method;
FIG. 2 is a graph of light intensity distribution at different photoresist depths at normal incidence with corresponding light intensity contour plots.
Detailed Description
The invention is further explained below with reference to the drawings.
FIG. 1 is a schematic diagram of a two-dimensional waveguide-based lithography simulation model, in which incident light has incident light intensity I0And the incidence angle theta, where the x-axis is established along the horizontal direction of the reticle and the z-axis is established along the direction perpendicular to the reticle, each layer has continuous optical properties in the z-axis direction. The coordinate definition of the opaque and transparent areas of the mask is apparent from the figure. According to the characteristics of back incidence, the mask is used as a substrate in the photoetching process, SU-8 glue is directly coated on the mask, and incident ultraviolet light directly penetrates through the back of the mask to expose the SU-8 glue. Therefore, in the dividing process of the rectangular thin layer, the glass is defined as a first layer material, namely, a material c in the drawing, the mask is defined as a second layer material, namely, a material b in the drawing, the SU-8 photoresist is defined as a third layer material, namely, a material a in the drawing, and the coordinate values of each layer in the z direction are 0, z1, z2 and z3 respectively. Thus, the dielectric constant of each layer material in the z direction satisfies the principle of uniformity.
The two-dimensional light intensity distribution simulation method of the SU-8 photoresist ultraviolet light back photoetching process comprises the following steps:
step 1: and 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: and dividing the whole photoetching simulation area into a plurality of rectangular thin layers along the horizontal direction, wherein each rectangular thin layer has continuous optical properties 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 the material parameters and the electromagnetic field 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: and applying electromagnetic field boundary conditions according to the continuity conditions to couple each rectangular thin layer, and obtaining the electromagnetic field distribution condition of light after transmitting 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.
Specifically, the step 3 comprises the following steps:
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) by using the idea of a separation variable method, substituting the variables into the Maxwell equations, and decomposing the Maxwell equations into two differential equations shown in a formula (1), wherein the differential equations contain complex potential k2Epsilon and a characteristic value alpha2；
Figure BDA0002833602040000061
Wherein ε is the material dielectric constant of each of said rectangular thin layers, X (x) and Z (z) are the isolated variables, and k is the wavenumber.
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 BDA0002833602040000062
wherein epsilonj(x) Represents the dielectric constant of the j-th rectangular thin layer,
Figure BDA0002833602040000063
is the coefficient of the q-th term after Fourier expansion, L is the Fourier expansion series, i represents the complex number, and b is the reciprocal of d.
Step 3-3: the coefficient of each term after the fourier series expansion is obtained by inverse fourier transform as shown in formula (3).
Figure BDA0002833602040000064
Step 3-4: performing Fourier transform on the variable X (x) as shown in the formula (4);
Figure BDA0002833602040000065
wherein, BlIs the ith coefficient 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 BDA0002833602040000071
where B is the eigenvector of the matrix D, Dl,mIs the element of the ith row and mth column in matrix D, epsilonl-mThe dielectric constant value of the (l-m) th item after Fourier expansion.
Step 3-6: calculating the value of the electromagnetic field expression according to the X (x) expression in the formula (4) and the Z (z) expression obtained by solving the second differential equation in the formula (1), thereby establishing an electromagnetic field mathematical model of the j-th rectangular thin layer as shown in the formula (6);
Figure BDA0002833602040000072
wherein the content of the first and second substances,
Figure BDA0002833602040000073
is the y-direction component of the electric field of the j-th rectangular thin layer,
Figure BDA0002833602040000074
and
Figure BDA0002833602040000075
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 BDA0002833602040000076
the first column element of the eigenvalue matrix representing the j-th rectangular sheet,
Figure BDA0002833602040000077
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 denotes the z-axis coordinate, zjRepresenting the coordinates of the j-th rectangular thin layer;
Figure BDA0002833602040000078
is the x-direction component of the magnetic field of the j-th rectangular thin layer,
Figure BDA0002833602040000079
is the z-direction component of the magnetic field of the j-th rectangular thin layer.
In the step 4, expressing the interface between the air and the first layer in a matrix form according to the continuous boundary condition of the electromagnetic field to obtain a lower boundary condition equation shown as a formula (7);
Figure BDA00028336020400000710
wherein the content of the first and second substances,
Figure BDA00028336020400000711
Figure BDA00028336020400000712
Figure BDA00028336020400000713
in the above formula, the first and second carbon atoms are,
Figure BDA0002833602040000081
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 BDA0002833602040000082
representing the initial illumination intensity, theta representing the angle of incidence,
Figure BDA0002833602040000083
the mth row and mth column elements represent the layer 1 shape information.
And obtaining a boundary condition equation shown as the formula (11) at the interface of the last layer according to the boundary condition:
Figure BDA0002833602040000084
wherein:
Figure BDA0002833602040000085
Figure BDA0002833602040000086
in the above formula，
Figure BDA0002833602040000087
Is the n-th layer of profile information, An、A'nDiffraction result information of the nth layer;
Figure BDA0002833602040000088
row mth column element, epsilon, representing the n-th layer of profile informationsIs the dielectric constant of the material of the last rectangular thin layer, and T is the coordinate of the last rectangular thin 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 BDA0002833602040000089
the expressions for the respective elements in the above formula are as follows:
Figure BDA00028336020400000810
Figure BDA00028336020400000811
Figure BDA00028336020400000812
Figure BDA00028336020400000813
Figure BDA00028336020400000814
Figure BDA00028336020400000815
Figure BDA0002833602040000091
Figure BDA0002833602040000092
wherein the content of the first and second substances,
Figure BDA0002833602040000093
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 BDA0002833602040000094
is the value of the electric field of the (j +1) th layer,
Figure BDA0002833602040000095
Figure BDA0002833602040000096
the mth row and mth column elements representing the jth layer of shape information,
Figure BDA0002833602040000097
row i and column m elements representing the (j +1) th layer electric field value.
Finally, according to the boundary condition of the electromagnetic field, A is obtainedjAnd 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 BDA0002833602040000098
In the step 5, the simulation result of the two-dimensional light intensity distribution of the SU-8 adhesive back incident ultraviolet light is shown as the formula (23);
Figure BDA0002833602040000099
wherein, Il,mThe illumination intensity value at the coordinate (l, m) in the two-dimensional array,
Figure BDA00028336020400000910
is an electric field at coordinates (l, m) in a two-dimensional array
Figure BDA00028336020400000911
Value nrIs the real part of the refractive index of the photoresist.
FIG. 2 is a graph of light intensity distribution at different photoresist depths at normal incidence with corresponding light intensity contour plots. During photoetching simulation, the initial incident light intensity is 2.6mW/cm2, the incident light wavelength is 365nm, the photoresist thickness is 300 μm, the mask plate length is 200 μm, and the mask hole size is 100 μm. FIG. 2(a) is a graph showing the intensity distribution of light at different depths of the photoresist at normal incidence, the curves being, from top to bottom, 5 μm, 100 μm, 200 μm and 300 μm in the order of photoresist depth. Fig. 2(b) is a corresponding light intensity contour diagram. The invention compares the simulation result with the actual experiment result to verify the accuracy of the model. The simulation result is proved to be consistent with the experimental result, and the method can be used for two-dimensional simulation of the SU-8 photoresist ultraviolet light back incidence photoetching process.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also 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 the content of the first and second substances,
    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 the content of the first and second substances,
    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 the content of the first and second substances,
    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 the content of the first and second substances,
    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)

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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

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
NL2017510A (en) * 2015-10-12 2017-04-24 Asml Netherlands Bv 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

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