CN110703438B - Method and device for calculating photoetching model based on polar coordinate vector - Google Patents

Method and device for calculating photoetching model based on polar coordinate vector Download PDF

Info

Publication number
CN110703438B
CN110703438B CN201911288282.9A CN201911288282A CN110703438B CN 110703438 B CN110703438 B CN 110703438B CN 201911288282 A CN201911288282 A CN 201911288282A CN 110703438 B CN110703438 B CN 110703438B
Authority
CN
China
Prior art keywords
light source
polarization
representing
light
cross
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.)
Active
Application number
CN201911288282.9A
Other languages
Chinese (zh)
Other versions
CN110703438A (en
Inventor
陈雪莲
周洁云
崔绍春
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.)
Moyan Computing Science Nanjing Co ltd
Original Assignee
Moyan Computing Science Nanjing Co ltd
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 Moyan Computing Science Nanjing Co ltd filed Critical Moyan Computing Science Nanjing Co ltd
Priority to CN201911288282.9A priority Critical patent/CN110703438B/en
Publication of CN110703438A publication Critical patent/CN110703438A/en
Application granted granted Critical
Publication of CN110703438B publication Critical patent/CN110703438B/en
Priority to PCT/CN2020/136830 priority patent/WO2021121272A1/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • 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
    • G03F7/70058—Mask illumination systems
    • G03F7/70091—Illumination settings, i.e. intensity distribution in the pupil plane or angular distribution in the field plane; On-axis or off-axis settings, e.g. annular, dipole or quadrupole settings; Partial coherence control, i.e. sigma or numerical aperture [NA]

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)

Abstract

The application relates to the technical field of photoetching processes for semiconductor production, in particular to a method and a device for calculating a photoetching model based on polar coordinate vectors. The application provides a method for calculating a lithography model based on polar coordinate vectors, which comprises the following steps: determining a polarization type of the light source; establishing a transmission matrix of the incident ray field strength entering the pupil based on the polarization type, the transmission matrix describing transmission changes of the incident ray field strength; establishing a vector calculation photoetching model to obtain a plurality of cross transfer functions for describing physical optics based on the polarization type of the light source and the transmission relation of the incident light field intensity; and calculating the light intensity distribution of the vector lithography model on the photoresist layer based on the plurality of cross transfer functions of the physical optics.

Description

Method and device for calculating photoetching model based on polar coordinate vector
Technical Field
The application relates to the technical field of photoetching processes for semiconductor production, in particular to a method and a device for calculating a photoetching model based on polar coordinate vectors.
Background
In the modern integrated circuit manufacturing industry, in the photolithography process of advanced process nodes, aiming at a mainstream light source with a wavelength of 193nm, immersion photolithography is generally adopted to improve the numerical aperture NA so as to improve the resolution of the photolithography process, and the photolithography process is a resolution enhancement technology RET which is generally used for semiconductor device production. As the numerical aperture increases, incoming rays enter the photoresist layer at a larger incident angle, and the phase and amplitude of the rays are greatly different from those of normal incident rays. The photolithography process starts from a 45nm process node, and the 193nm wavelength immersion photolithography technique is commonly used in the photolithography process of semiconductor device production, and increases the numerical aperture by refraction of incident light, and the immersion liquid is deionized water with a refractive index of 1.44. The immersion lithography technology has been adopted in domestic wafer factories even at the 55nm process node. Aiming at the photoetching process with high numerical aperture, a scalar calculation photoetching model can meet the requirement of simulation calculation, and researchers begin to consider a vector model. At the 45nm process node, it becomes important to consider a vector model of the light source polarization.
In some implementations of vector-computed lithography models, when a simulated prediction of reticle pattern imaging on a photoresist is made, for incident light rays emitted by a polarized light source in the pupil, a photochemical reaction occurs on the photoresist to form a pattern profile approximating the mask pattern. Vector calculation photoetching is described by a group of complex mathematical models based on a standard Cartesian coordinate system, a transmission matrix and a cross transfer function of field intensity are calculated, then, sampling errors are introduced by standard sampling and fast Fourier transform calculation, and therefore the calculation photoetching model can be used for predicting the imaging of a mask plate pattern on a photoresist to a certain extent.
However, in the actual calculation process, the transmission matrix M of the field strength is a full matrix, and considering the effect caused by polarized light, up to five types of cross transfer functions need to be calculated, the analytical calculation process is very complex and difficult to implement, more simulation calculation time is needed, and standard sampling and fast fourier transform calculation are limited by an orthogonal coordinate system, a sampling error is bound to be introduced, error accumulation causes the failure of final calculation of lithography model modeling, that is, the calculation lithography model cannot be used for effective prediction of imaging of other reticle patterns on photoresist.
Disclosure of Invention
The invention aims to provide a method and a device for calculating a photoetching model based on polar coordinate vectors, which provides a description device for light polarization under polar coordinate description through a polarized light source device, a polarized light field intensity transmission matrix device, a physical optical description device and a vector calculation photoetching model device. .
The embodiment of the application is realized as follows:
a first aspect of an embodiment of the present application provides a method for computing a lithography model based on a polar coordinate vector, including: determining a polarization type of a light source, the polarization type comprising: x line, Y line, TE, TM, Circular and XY4 Sector; establishing a transmission matrix of the incident ray field strength entering the pupil based on the polarization type, the transmission matrix describing transmission changes of the incident ray field strength; establishing a vector calculation photoetching model to obtain a plurality of cross transfer functions for describing physical optics based on the polarization type of the light source and the transmission relation of the incident light field intensity; and calculating the light intensity distribution of the vector lithography model on the photoresist layer based on the plurality of cross transfer functions of the physical optics.
Optionally, the incident light includes a polarized portion of the light source and an unpolarized portion of the light source, and the electric field of the polarized portion of the light source can be resolved on a radial describing electric field and an angular describing electric field.
Alternatively, the transmission matrix may describe the effect of the radial and angular ray polarizations on the field strength of the incident ray, which is expressed as follows:
Figure 401034DEST_PATH_IMAGE001
wherein the first column
Figure 91909DEST_PATH_IMAGE002
Representing radial ray pairs
Figure 167751DEST_PATH_IMAGE003
Influence of the polarization term in the direction, second column
Figure 133433DEST_PATH_IMAGE004
Representing angular ray pairs
Figure 252698DEST_PATH_IMAGE005
The influence of the polarization term in the direction;
the radial field strength only influences the radial direction
Figure 645634DEST_PATH_IMAGE006
Direction and z-direction, angular
Figure 217560DEST_PATH_IMAGE007
Is only relevant to itself;
the Jones matrix describes the pupil-to-light polarization change,
Figure 721354DEST_PATH_IMAGE008
representing the effect of the pupil lens on the radial ray polarization,
Figure 695126DEST_PATH_IMAGE009
represents the effect of the pupil lens on the polarization of the diagonal rays;
the refractive effect of the photoresist layer and the pupil, i.e., the creation of M.
Alternatively, the model of the transfer matrix at infinite depth in the photoresist layer can be described as:
Figure 256033DEST_PATH_IMAGE010
wherein the content of the first and second substances,
Figure 315256DEST_PATH_IMAGE011
which represents the transmission coefficient in the medium,
Figure 888320DEST_PATH_IMAGE012
which represents the transmission coefficient in the photoresist,
Figure 716598DEST_PATH_IMAGE013
is the angle of incidence of the light rays,
Figure 451336DEST_PATH_IMAGE014
is the angle of refraction.
Alternatively, the transmission matrix may be described as:
Figure 997855DEST_PATH_IMAGE015
wherein the content of the first and second substances,
Figure 577872DEST_PATH_IMAGE016
which is the reflection coefficient in the TM mode,
Figure 526237DEST_PATH_IMAGE017
for the reflection coefficient in the TE mode,
Figure 434806DEST_PATH_IMAGE013
is the angle of incidence of the light rays,
Figure 203041DEST_PATH_IMAGE014
is the angle of refraction.
Optionally, based on the polarization type of the light source and the transmission relationship of the incident light field intensity, a vector calculation lithography model is established, which is expressed as:
Figure 117908DEST_PATH_IMAGE018
wherein the content of the first and second substances,
Figure 655199DEST_PATH_IMAGE019
in order to obtain the position coordinates of the resist image,
Figure 731740DEST_PATH_IMAGE020
to describe the cross-transfer function of the physical optics,
Figure 252851DEST_PATH_IMAGE021
which is a vector in the frequency domain,
Figure 971408DEST_PATH_IMAGE022
as a function of the reticle(s),
Figure 628786DEST_PATH_IMAGE023
is the conjugate of the mask function.
Optionally, the plurality of cross-transfer functions of the physical optics comprises a cross-transfer function of the light source to a non-polarized part and a cross-transfer function of the polarized part of the light source, which is expressed as follows:
Figure 873298DEST_PATH_IMAGE024
Figure 616126DEST_PATH_IMAGE025
Figure 607216DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure 384679DEST_PATH_IMAGE027
，
Figure 803022DEST_PATH_IMAGE028
representing a vector in the frequency domain and,
Figure 298725DEST_PATH_IMAGE029
the value of the integral variable is represented by,
Figure 562347DEST_PATH_IMAGE030
the representation of the pupil function is shown,
Figure 459896DEST_PATH_IMAGE031
the conjugate of the pupil function is represented,
Figure 610710DEST_PATH_IMAGE032
the function of the light source is represented,
Figure 593709DEST_PATH_IMAGE033
a description of an electric field representing a particular direction;
Figure 661022DEST_PATH_IMAGE034
represents the cross-transfer function of a non-polarized light source,
Figure 413078DEST_PATH_IMAGE035
indicating a location
Figure 173223DEST_PATH_IMAGE036
Direction of light emission
Figure 377940DEST_PATH_IMAGE037
Respectively to the direction
Figure 514523DEST_PATH_IMAGE038
The influence of the polarization term of the upper electric field,
Figure 118155DEST_PATH_IMAGE039
the conjugates representing the respective functions, orthogonal and independent of each other, result in:
Figure 49202DEST_PATH_IMAGE040
Figure 741215DEST_PATH_IMAGE041
which represents the radial cross-transfer function of the,
Figure 150330DEST_PATH_IMAGE042
the angular cross-transfer function is represented as,
Figure 611399DEST_PATH_IMAGE043
and
Figure 978926DEST_PATH_IMAGE044
representing radial and angular field strength transfer functions, in which
Figure 158235DEST_PATH_IMAGE045
Figure 371041DEST_PATH_IMAGE046
In the formula (I), the compound is shown in the specification,
Figure 955125DEST_PATH_IMAGE047
a description of the electric field in the radial direction is shown,
Figure 696816DEST_PATH_IMAGE048
representing an angular electric field description.
Optionally, the calculating the light intensity distribution of the vector lithography model on the photoresist layer based on the plurality of cross transfer functions of the physical optics comprises the steps of:
based on the multiple cross transfer functions, matrix decomposition is carried out on the multiple cross transfer functions to obtain kernel functions
Figure 629000DEST_PATH_IMAGE049
And satisfies the following conditions:
Figure 645498DEST_PATH_IMAGE050
in the formula (I), the compound is shown in the specification,
Figure 815579DEST_PATH_IMAGE051
is a vector coordinate in space and is,
based on the kernel function and the mask pattern function, the sum of the light intensity distribution of the non-polarized part of the light source on the photoresist layer and the light intensity distribution of the polarized part of the light source on the photoresist layer is calculated and represented as follows:
Figure 524909DEST_PATH_IMAGE052
Figure 413230DEST_PATH_IMAGE053
wherein the content of the first and second substances,
Figure 233419DEST_PATH_IMAGE054
a vector of spatial coordinates is represented, and,
Figure 520656DEST_PATH_IMAGE055
a function of the reticle is represented and,
Figure 135308DEST_PATH_IMAGE056
a kernel function representing a non-polar cross-transfer function decomposition,
Figure 510926DEST_PATH_IMAGE057
a kernel function representing a cross-transfer function decomposition corresponding to the polarized light source;
based on the light intensity distribution of the polarized part of the light source and the light intensity distribution of the non-polarized part of the light source, a final light intensity distribution is obtained by calculation, which is expressed as follows:
Figure 869226DEST_PATH_IMAGE058
wherein the content of the first and second substances,
Figure 279479DEST_PATH_IMAGE059
representing a spatial coordinate vector, p representing a light source polarization factor,
Figure 330612DEST_PATH_IMAGE060
representing the light intensity distribution of the non-polarized part of the light source,
Figure 193525DEST_PATH_IMAGE061
representing the light intensity distribution of the polarized part of the light source.
Optionally, the plurality of cross transfer functions of the physical optics are in a bilinear function form, and are used for obtaining a kernel function prediction graph through fast calculation.
A second aspect of an embodiment of the present application provides an apparatus for computing a lithography model based on polar coordinate vectors, including;
polarized light source means for field strength configuration of a polarized light source and determining a polarization type of the light source;
a polarized light field intensity transmission matrix device for establishing a transmission matrix of the incident light field intensity entering the pupil, the transmission matrix describing the transmission variation of the incident light field intensity;
the physical optics description device is used for establishing a vector calculation photoetching model to obtain a plurality of cross transfer functions for describing physical optics;
and the vector calculation photoetching model device is used for establishing a vector calculation photoetching model and calculating the light intensity distribution of the vector photoetching model on the light resistance layer by integrating a plurality of cross transfer functions of the physical optics, a transmission matrix of the incident light field intensity and the polarization type of the light source.
The beneficial effects of the embodiment of the application include: in a key instrument photoetching machine in the integrated circuit manufacturing industry, a key part lens is of a circular symmetrical structure, and a vector calculation photoetching model under the polar coordinate condition provided by the application is more fit with physical parameters of the key part lens; a group of brand-new orthogonal field intensity descriptions are given through a polarized light source device, the field intensity of any incident ray can be decomposed on the group of orthogonal field intensity, the field intensity change of the incident ray from an entrance pupil to a light resistance layer is described as a polarized light field intensity transmission matrix M of a non-full matrix with half elements of 0, so that only 3 types of cross transfer functions need to be calculated in a vector calculation photoetching model, in the whole simulation process, more calculation time is occupied by analyzing the cross transfer functions, the types of the cross transfer functions are reduced, the time required by simulation calculation is directly reduced, the calculation efficiency can be improved, and the precision and the prediction speed of the vector calculation photoetching model can be improved to a certain extent.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.
FIG. 1 depicts a step diagram of a method of computing a lithography model based on polar coordinate vectors according to an embodiment of the present application;
FIG. 2 is a diagram illustrating a step of a light intensity distribution obtaining method on a photoresist layer according to an embodiment of the present application;
FIG. 3 shows a computer lithography simple principle schematic according to an embodiment of the present application;
FIG. 4 shows a radial depiction of an electric field under polar coordinate system conditions in accordance with an embodiment of the present application;
FIG. 5 shows a schematic diagram illustrating an angular description of an electric field under polar coordinate system conditions according to an embodiment of the present application;
FIG. 6 illustrates a simple vector model diagram in an infinite depth photoresist layer model according to one embodiment of the present application;
FIG. 7 shows a simplified block diagram of an apparatus for computing a lithography model based on polar coordinate vectors according to an embodiment of the present application;
FIG. 8 shows a schematic diagram of a polarized light source type of polarized light source apparatus according to an embodiment of the present application;
FIG. 9 is a graph illustrating a comparison of lithography model calculations using polar coordinate vector based calculations to typical scalar model calculations according to an embodiment of the present application;
FIG. 10 shows a plot of intensity distribution in photoresist for a Dense special pattern of a standard test mask pattern according to one embodiment of the present application;
icon: 100-calculating a lithography model device based on the amount of polar coordinates; 110-polarized light source means; 120-polarized light field intensity transmission matrix device; 130-a physical optics description means; 140-vector calculation lithography model apparatus.
Detailed Description
Certain exemplary embodiments will now be described to provide an overall understanding of the principles of the structure, function, manufacture, and use of the devices and methods disclosed herein. One or more examples of these embodiments are illustrated in the accompanying drawings. Those of ordinary skill in the art will understand that the devices and methods specifically described herein and illustrated in the accompanying drawings are non-limiting exemplary embodiments and that the scope of the various embodiments of the present application is defined solely by the claims. Features illustrated or described in connection with one exemplary embodiment may be combined with features of other embodiments. Such modifications and variations are intended to be included within the scope of the present application.
Reference throughout this specification to "embodiments," "some embodiments," "one embodiment," or "an embodiment," etc., means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases "in various embodiments," "in some embodiments," "in at least one other embodiment," or "in an embodiment," or the like, throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. Thus, the particular features, structures, or characteristics shown or described in connection with one embodiment may be combined, in whole or in part, with the features, structures, or characteristics of one or more other embodiments, without limitation. Such modifications and variations are intended to be included within the scope of the present application.
The application provides a vector calculation photoetching model under a polar coordinate condition. In the present application, the vector computing lithography model will be presented in a more compact form.
The critical instrument lithography machine in the integrated circuit manufacturing industry is used for realizing the pattern transfer of a design circuit through an optical instrument. The key lens of the optical instrument is circularly symmetrical, and the polar coordinate condition is more suitable for the physical parameters of the optical instrument.
The simple bilinear function form bi-linear is given for the cross transfer function, and the decomposition of the bilinear function form bi-linear is easy to realize. Finally, the precision of the vector calculation lithography model is improved, and the purpose of quickly predicting any graph through the kernel function is achieved.
As shown in fig. 3, computational lithography can be described simply as being made up of a light source, reticle, pupil, and imaging plane. The photoetching process mainly solves the problem of how to transfer the pattern on the mask plate to an imaging plane and can effectively ensure that the outline formed by the photoresist on the imaging plane is consistent with the pattern on the mask plate.
FIG. 1 is a flowchart illustrating a method of computing a lithography model based on polar coordinate vectors according to one embodiment of the present application.
In step S1, the polarization type of the light source is first determined. In a vector computational lithography model, the polarization of the light source is typically considered for producing polarized light.
Polarized light is beneficial to improving the imaging resolution of certain mask patterns on photoresist, but causes great negative effects on other patterns due to the polarization effect of incident light. Therefore, the vector model with a high numerical aperture NA has to consider the influence of polarized light.
For a polarized light source, the field strength of the polarized light emitted by the light source is divided into two orthogonal independent parts according to the transmission physical characteristics of the wave. Under the condition of a polar coordinate system, two orthogonal field intensity descriptions are given.
The first mode is the TM mode, i.e. the radial describing electric field, denoted as
Figure 815569DEST_PATH_IMAGE062
As shown in fig. 4.
The second mode is the TE mode, i.e. the azimuthal describing electric field, denoted as
Figure 814749DEST_PATH_IMAGE063
As shown in fig. 5.
For any polarized light source, the electric field can be resolved on the two orthogonal electric fields. There are six types of polarization of the light source, including X line, Y line, TE, TM, Circular, and XY 4Sector, as shown in FIG. 8.
In the present embodiment, the position of the incident ray on the polar coordinate is represented as:
Figure 36783DEST_PATH_IMAGE064
，
wherein the content of the first and second substances,
Figure 121414DEST_PATH_IMAGE065
is the radius of the location at which it is located,
Figure 352675DEST_PATH_IMAGE066
is at an angle to the horizontal. In this embodiment, an X Linear mode polarized light source is selected, and the field strengths at the positions are:
Figure 206361DEST_PATH_IMAGE067
in some embodiments, e.g., the polarization type is Y linear, with the field strength expressed as:
Figure 333717DEST_PATH_IMAGE068
in some embodiments, e.g., the polarization type is TE, the field strength is expressed as:
Figure 902714DEST_PATH_IMAGE069
in some embodiments, e.g., the polarization type is TM, the field strength is expressed as:
Figure 406508DEST_PATH_IMAGE070
in some embodiments, for example, the polarization type is Circular, and the field strength is expressed as:
Figure 645859DEST_PATH_IMAGE071
in some embodiments, such as when the polarization type is XY 4Sector,
when in use
Figure 678537DEST_PATH_IMAGE072
Its field strength is expressed as:
Figure 3340DEST_PATH_IMAGE073
when in use
Figure 310824DEST_PATH_IMAGE074
When, its field strength is expressed as:
Figure 139103DEST_PATH_IMAGE075
the field intensity of the polarized light source in the application can be selected from the configuration, and a vector model corresponding to the polarized light source is established. It should be noted that, for non-polarized light sources,
Figure 873841DEST_PATH_IMAGE062
and
Figure 423289DEST_PATH_IMAGE063
orthogonal to each other, giving the following results:
Figure 268886DEST_PATH_IMAGE076
with continued reference to FIG. 1, in step S2, based on the polarization type, a transmission matrix is established for the incident ray field strength entering the pupil that describes the transmission variation in the incident ray field strength.
The polarized light source emits polarized light through the pupil to the image plane, and through the refraction of the surface of the photoresist layer, enters the image plane where the photoresist is located, which is shown in the simplified schematic diagram of fig. 3.
The polarized light field intensity transmission matrix device 120 provided by the present application can describe the effect of the pupil and the photoresist layer on the light polarization, i.e. the transmission change of the field intensity of the light in the pupil light and the photoresist layer. Under polar coordinates, the effect of polarized light source on the transmission of polarized light can be expressed by the transmission matrix description as:
Figure 217250DEST_PATH_IMAGE077
wherein the first column
Figure 122889DEST_PATH_IMAGE078
Representing radial ray pairs
Figure 891125DEST_PATH_IMAGE079
Influence of the polarization term in the direction, second column
Figure 540412DEST_PATH_IMAGE080
Representing angular ray pairs
Figure 343283DEST_PATH_IMAGE081
Influence of polarization terms in the direction ofIn this application, the radial field strength only affects the radial direction
Figure 151315DEST_PATH_IMAGE082
Direction and z-direction, angular
Figure 875688DEST_PATH_IMAGE083
Is only associated with itself. The Jones matrix describes the pupil-to-light polarization change; the refractive effect of the photoresist layer and the pupil, i.e., the creation of M.
For the common model, the Jones matrix is described simply as a 2 x 2 matrix:
the ideal pupil Jones matrix is described as:
Figure 63087DEST_PATH_IMAGE084
the jones matrix in TE mode is described as:
Figure 986044DEST_PATH_IMAGE085
the jones matrix in TM mode is described as:
Figure 967906DEST_PATH_IMAGE086
in some embodiments, for an infinite depth photoresist layer model, a simple vector model is shown in FIG. 6. According to the optical theory, the refractive indexes of the front and the back of the surface of the photoresist layer are respectively
Figure 976313DEST_PATH_IMAGE087
And
Figure 967403DEST_PATH_IMAGE088
then, the transmission coefficients corresponding to the two modes are:
Figure 228356DEST_PATH_IMAGE089
wherein the content of the first and second substances,
Figure 381120DEST_PATH_IMAGE013
is the angle of incidence of the light rays,
Figure 611244DEST_PATH_IMAGE014
is the angle of refraction.
According to the vector model shown in the figure, the incident ray
Figure 406025DEST_PATH_IMAGE090
The field strength description of (a) is expressed as:
Figure 37995DEST_PATH_IMAGE091
in the TE mode, only the azimuthal electric field needs to be considered
Figure 627239DEST_PATH_IMAGE092
In the direction of the electric field of
Figure 610238DEST_PATH_IMAGE093
Perpendicular to the plane of the paper. The present application indicates that in this mode, the electric field in the photoresist layer
Figure 943131DEST_PATH_IMAGE093
The direction not changing, i.e.
Figure 161098DEST_PATH_IMAGE094
In TM mode, only the azimuthal electric field needs to be considered
Figure 186823DEST_PATH_IMAGE095
In the direction of the electric field of
Figure 391539DEST_PATH_IMAGE096
Parallel to the paper. The present application indicates that in this mode, the electric field in the photoresist layer
Figure 528122DEST_PATH_IMAGE097
Angle with parallel direction
Figure 869105DEST_PATH_IMAGE014
It can be decomposed into two directional effects, which are expressed as:
Figure 800152DEST_PATH_IMAGE098
the variation for the entrance and exit pupils of the light is described by the Jone matrix, i.e.
Figure 492164DEST_PATH_IMAGE099
. The above process describes the refraction of light at the surface of the photoresist layer, and the change in field strength is expressed as:
Figure 638631DEST_PATH_IMAGE100
in summary, the M matrix can be expressed as:
Figure 834120DEST_PATH_IMAGE101
for the inside of the photoresist layer, the influence of refraction and reflection of light needs to be considered at the same time, and the M matrix is expressed as:
Figure 201647DEST_PATH_IMAGE102
wherein the content of the first and second substances,
Figure 115377DEST_PATH_IMAGE016
and
Figure 593762DEST_PATH_IMAGE103
the reflection coefficient is in two modes.
In some embodiments, the polarized light source emits polarized light through the pupil lens and the surface of the photoresist layer to the inside of the photoresist layer, and a certain light intensity distribution is presented. The distance between the pupil lens and the photoresist layer, thick, and the refractive index n of the immersion liquid are respectively as follows:
Figure 174916DEST_PATH_IMAGE104
the light resistance layer is composed of a plurality of layers of photoresist materials, and the refractive index and the reflection coefficient of the light resistance layer are respectively as follows:
Figure 447766DEST_PATH_IMAGE105
Figure 845862DEST_PATH_IMAGE106
Figure 862359DEST_PATH_IMAGE107
calculating the transmission coefficients of refraction and reflection according to the parameters
Figure 298020DEST_PATH_IMAGE108
And
Figure 741771DEST_PATH_IMAGE109
establishing a transmission matrix of the incident light corresponding to the field intensity:
Figure 630092DEST_PATH_IMAGE110
wherein the content of the first and second substances,
Figure 450281DEST_PATH_IMAGE111
in order to be a refractive transmission factor,
Figure 740448DEST_PATH_IMAGE016
is the reflection transmission factor.
With continued reference to fig. 1, in step S3, a vector computation lithography model is built based on the polarization type of the light source and the transmission relationship of the incident light field strength to obtain a plurality of cross transfer functions describing physical optics. The vector model is represented as:
Figure 355100DEST_PATH_IMAGE018
wherein the content of the first and second substances,
Figure 721928DEST_PATH_IMAGE019
in order to obtain the position coordinates of the resist image,
Figure 80229DEST_PATH_IMAGE020
to describe the cross-transfer function of the physical optics,
Figure 490481DEST_PATH_IMAGE112
which is a vector in the frequency domain,
Figure 276035DEST_PATH_IMAGE022
as a function of the reticle(s),
Figure 873369DEST_PATH_IMAGE113
is the conjugate of the mask function.
The cross-transfer function describing the physical optics described in this application is built on polar coordinates, so that the amount of computation required is reduced, and on the other hand, the optical lens itself is defined to be more closely matched to the physical optics in polar coordinates.
The cross transfer function is established respectively for the polarized part and the non-polarized part of the light source.
For non-polarized light sources, a cross-transfer function is established, the description of which is expressed as follows:
Figure 35360DEST_PATH_IMAGE114
in the formula (I), the compound is shown in the specification,
Figure 300120DEST_PATH_IMAGE115
，
Figure 519224DEST_PATH_IMAGE116
representing a vector in the frequency domain and,
Figure 869434DEST_PATH_IMAGE117
the value of the integral variable is represented by,
Figure 569536DEST_PATH_IMAGE118
the representation of the pupil function is shown,
Figure 423223DEST_PATH_IMAGE119
the conjugate of the pupil function is represented,
Figure 816158DEST_PATH_IMAGE120
the function of the light source is represented,
Figure 653664DEST_PATH_IMAGE121
a description of an electric field representing a particular direction;
Figure 157458DEST_PATH_IMAGE122
represents the cross-transfer function of a non-polarized light source,
Figure 131230DEST_PATH_IMAGE123
indicating a location
Figure 697996DEST_PATH_IMAGE124
Direction of light emission
Figure 22798DEST_PATH_IMAGE125
Respectively to the direction
Figure 64704DEST_PATH_IMAGE126
The influence of the polarization term of the upper electric field,
Figure 158562DEST_PATH_IMAGE127
represents the conjugate of the corresponding function;
due to the fact that
Figure 893299DEST_PATH_IMAGE062
And
Figure 439818DEST_PATH_IMAGE063
are orthogonal and independent of each other, thereby
Figure 550994DEST_PATH_IMAGE128
。
For polarized light sources, a cross-transfer function is established, the description of which is expressed as follows:
Figure 499358DEST_PATH_IMAGE129
from the polarized light field strength transmission matrix device 120, it is easy to find:
Figure 402068DEST_PATH_IMAGE130
Figure 170304DEST_PATH_IMAGE131
then in this polar condition only two cross transfer functions need to be calculated:
Figure 819591DEST_PATH_IMAGE132
Figure 622462DEST_PATH_IMAGE133
wherein
Figure 964581DEST_PATH_IMAGE134
Figure 485693DEST_PATH_IMAGE135
In the formula (I), the compound is shown in the specification,
Figure 407512DEST_PATH_IMAGE136
a description of the electric field in the radial direction is shown,
Figure 64890DEST_PATH_IMAGE137
representing an angular electric field description.
With continued reference to FIG. 1, in step S4, the light intensity distribution of the vector lithography model on the photoresist layer is calculated based on the plurality of cross-transfer functions of the physical optics, which is illustrated in FIG. 2.
In step S1, a kernel function is obtained based on the plurality of cross transfer functions.
The cross transfer function is a bilinear function, and a group of kernel functions can be easily obtained through decomposition
Figure 326980DEST_PATH_IMAGE049
And satisfies the following conditions:
Figure 335387DEST_PATH_IMAGE138
in the formula (I), the compound is shown in the specification,
Figure 326477DEST_PATH_IMAGE139
is a vector coordinate in space and is,
in step S2, based on the kernel function and the mask pattern function, a light intensity distribution of the non-polarized portion of the light source on the photoresist layer and a light intensity distribution of the polarized portion of the light source on the photoresist layer are calculated and expressed as follows,
Figure 103940DEST_PATH_IMAGE140
Figure 522283DEST_PATH_IMAGE141
wherein the content of the first and second substances,
Figure 486828DEST_PATH_IMAGE117
a vector of spatial coordinates is represented, and,
Figure 281609DEST_PATH_IMAGE142
a function of the reticle is represented and,
Figure 379490DEST_PATH_IMAGE143
a kernel function representing a non-polar cross-transfer function decomposition,
Figure 703155DEST_PATH_IMAGE144
the kernel function obtained by decomposing the cross transfer function represents the kernel function of the cross transfer function decomposition corresponding to the polarized light source;
in step S3, a final light intensity distribution is obtained by calculation based on the light intensity distribution of the polarized part of the light source and the light intensity distribution of the non-polarized part of the light source, which is expressed as follows:
Figure 951734DEST_PATH_IMAGE058
wherein the content of the first and second substances,
Figure 284626DEST_PATH_IMAGE145
representing a spatial coordinate vector, p representing a light source polarization factor,
Figure 771102DEST_PATH_IMAGE146
representing the light intensity distribution of the non-polarized part of the light source,
Figure 796827DEST_PATH_IMAGE147
representing the light intensity distribution of the polarized part of the light source.
FIG. 9 shows a graph of a profile plot formed on a photoresist by computer lithography under certain threshold conditions, showing a comparison of the vector model calculations and the scalar model calculations in general, based on the apparatus of the present application, where it can be seen that the image obtained on the photoresist using the apparatus of the present application is more accurate. FIG. 10 shows a plot of intensity distribution in photoresist for a Dense special pattern of a standard test mask pattern, demonstrating that the vector computing lithography model described in the embodiments of the present application can more effectively predict the pattern transfer characteristics of a mask pattern onto an imaging plane at advanced process nodes.
As shown in FIG. 7, the present application further provides a polar coordinate quantity-based lithography model calculation apparatus 100, which includes a polarized light source apparatus, a polarized light field strength transmission matrix apparatus 120, a physical optics description apparatus 130, and a vector calculation lithography model apparatus 140.
The polarized light source arrangement 110 is used to configure the field strength of the polarized light source and determine the type of polarization of the light source.
The polarized light field strength transmission matrix arrangement 120 is used to establish a transmission matrix of the incident light field strength into the pupil that describes the transmitted change in the incident light field strength.
The physical optics description device 130 is used for establishing a vector computation lithography model to obtain a plurality of cross transfer functions describing physical optics.
The vector calculation lithography model device 140 is used for establishing a vector calculation lithography model and calculating the light intensity distribution of the vector lithography model on the photoresist layer by integrating a plurality of cross transfer functions of the physical optics, the transmission matrix of the incident light field intensity and the polarization type of the light source.
The beneficial effects that this application embodiment probably brought lie in: in a key instrument photoetching machine in the integrated circuit manufacturing industry, a key part lens is of a circular symmetrical structure, and a vector calculation photoetching model under the polar coordinate condition provided by the application is more fit with physical parameters of the key part lens; a group of brand-new orthogonal field intensity descriptions are given through a polarized light source device, the field intensity of any incident ray can be decomposed on the group of orthogonal field intensity, the field intensity change of the incident ray from an entrance pupil to a light resistance layer is described as a polarized light field intensity transmission matrix M of a non-full matrix with half elements of 0, so that only 3 types of cross transfer functions need to be calculated in a vector calculation photoetching model, in the whole simulation process, more calculation time is occupied by analyzing the cross transfer functions, the types of the cross transfer functions are reduced, the time required by simulation calculation is directly reduced, the calculation efficiency can be improved, and the precision and the prediction speed of the vector calculation photoetching model can be improved to a certain extent.
Moreover, those skilled in the art will appreciate that aspects of the present application may be illustrated and described in terms of several patentable species or situations, including any new and useful combination of processes, machines, manufacture, or materials, or any new and useful improvement thereon. Accordingly, various aspects of the present application may be embodied entirely in hardware, entirely in software (including firmware, resident software, micro-code, etc.) or in a combination of hardware and software. The above hardware or software may be referred to as "data block," module, "" engine, "" unit, "" component, "or" system.
Computer program code required for the operation of various portions of the present application may be written in any one or more programming languages, including an object oriented programming language such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C + +, C #, VB.NET, Python, and the like, a conventional programming language such as C, Visual Basic, Fortran 2003, Perl, COBOL2002, PHP, ABAP, a dynamic programming language such as Python, Ruby, and Groovy, or other programming languages, and the like.
Additionally, the order in which elements and sequences of the processes described herein are processed, the use of alphanumeric characters, or the use of other designations, is not intended to limit the order of the processes and methods described herein, unless explicitly claimed. While various presently contemplated embodiments of the invention have been discussed in the foregoing disclosure by way of example, it is to be understood that such detail is solely for that purpose and that the appended claims are not limited to the disclosed embodiments, but, on the contrary, are intended to cover all modifications and equivalent arrangements that are within the spirit and scope of the embodiments herein. For example, although the system components described above may be implemented by hardware devices, they may also be implemented by software-only solutions, such as installing the described system on an existing server or mobile device.
Similarly, it should be noted that in the preceding description of embodiments of the application, various features are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure aiding in the understanding of one or more of the embodiments. This method of disclosure, however, is not intended to require more features than are expressly recited in the claims. Indeed, the embodiments may be characterized as having less than all of the features of a single embodiment disclosed above.
The entire contents of each patent, patent application publication, and other material cited in this application, such as articles, books, specifications, publications, documents, and the like, are hereby incorporated by reference into this application. Except where the application is filed in a manner inconsistent or contrary to the present disclosure, and except where the claim is filed in its broadest scope (whether present or later appended to the application) as well. It is noted that the descriptions, definitions and/or use of terms in this application shall control if they are inconsistent or contrary to the statements and/or uses of the present application in the material attached to this application.

Claims (4)

1. A method of computing a lithography model based on polar coordinate vectors, comprising:
determining a polarization type of a light source, the polarization type comprising: x line, Y line, TE, TM, Circular and XY4 Sector;
the electric field of the polarized light of the light source can be resolved on the radial description electric field and the angular description electric field
Figure 696678DEST_PATH_IMAGE001
；
Based on the polarization type, establishing a transmission matrix of the incident ray field intensity entering the pupil, wherein the transmission matrix describes the transmission change of the incident ray field intensity, and the transmission matrix can describe the influence of radial ray polarization and angular ray polarization on the incident ray field intensity, and the formula is as follows:
Figure 328648DEST_PATH_IMAGE002
wherein the first column
Figure 917892DEST_PATH_IMAGE003
Representing radial ray pairs
Figure 564206DEST_PATH_IMAGE004
Influence of the polarization term in the direction, second column
Figure 897099DEST_PATH_IMAGE005
Representing angular lightThe lines are respectively paired
Figure 321258DEST_PATH_IMAGE004
The influence of the polarization term in the direction; the radial field strength only influences the radial direction
Figure 612562DEST_PATH_IMAGE006
Direction and z-direction, angular
Figure 817278DEST_PATH_IMAGE007
Is only relevant to itself; the Jones matrix describes the pupil-to-light polarization change,
Figure 688282DEST_PATH_IMAGE008
representing the effect of the pupil lens on the radial ray polarization,
Figure 294844DEST_PATH_IMAGE009
represents the effect of the pupil lens on the polarization of the diagonal rays; the refractive effect of the photoresist layer and the pupil, i.e., the creation of M, the transmission matrix can be described in the infinite depth model of the photoresist layer as:
Figure 488541DEST_PATH_IMAGE010
wherein the content of the first and second substances,
Figure 649395DEST_PATH_IMAGE011
which represents the transmission coefficient in the medium,
Figure 589669DEST_PATH_IMAGE012
which represents the transmission coefficient in the photoresist,
Figure 50737DEST_PATH_IMAGE007
is the angle of incidence of the light rays,
Figure 152686DEST_PATH_IMAGE013
is the angle of refraction;
establishing a vector calculation photoetching model based on the polarization type of the light source and the transmission relation of the incident light field intensity to obtain a plurality of cross transfer functions for describing physical optics
Figure 66415DEST_PATH_IMAGE014
，
Figure 544801DEST_PATH_IMAGE015
，
Figure 863305DEST_PATH_IMAGE016
，
Figure 136155DEST_PATH_IMAGE014
Represents the cross-transfer function of a non-polarized light source,
Figure 271601DEST_PATH_IMAGE015
which represents the radial cross-transfer function of the,
Figure 553678DEST_PATH_IMAGE016
representing an angular cross-transfer function, wherein the cross-transfer function of the unpolarized light source is represented as:
Figure 723759DEST_PATH_IMAGE017
wherein the content of the first and second substances,
Figure 167510DEST_PATH_IMAGE018
，
Figure 321411DEST_PATH_IMAGE019
representing a vector in the frequency domain and,
Figure 873090DEST_PATH_IMAGE020
the value of the integral variable is represented by,
Figure 163257DEST_PATH_IMAGE021
the representation of the pupil function is shown,
Figure 777909DEST_PATH_IMAGE022
the conjugate of the pupil function is represented,
Figure 153527DEST_PATH_IMAGE023
the function of the light source is represented,
Figure 777406DEST_PATH_IMAGE024
a description of the electric field representing a particular direction,
Figure 922080DEST_PATH_IMAGE025
indicating a location
Figure 973213DEST_PATH_IMAGE026
In the direction of light
Figure 570547DEST_PATH_IMAGE027
Respectively to the direction
Figure 747187DEST_PATH_IMAGE028
The influence of the polarization term of the upper electric field,
Figure 746367DEST_PATH_IMAGE029
represents the conjugate of the corresponding function;
and calculating the light intensity distribution of the vector lithography model on the photoresist layer based on the plurality of cross transfer functions of the physical optics.
2. The method of claim 1, wherein the transmission matrix when considering refraction and reflection effects inside the photoresist layer can be described as:
Figure 702821DEST_PATH_IMAGE030
wherein the content of the first and second substances,
Figure 521873DEST_PATH_IMAGE031
which is the reflection coefficient in the TM mode,
Figure 753134DEST_PATH_IMAGE032
for the reflection coefficient in the TE mode,
Figure 606821DEST_PATH_IMAGE033
is the angle of incidence of the light rays,
Figure 999756DEST_PATH_IMAGE034
is the angle of refraction.
3. A method of computing a lithography model based on polar coordinate vectors as claimed in claim 1, wherein said plurality of cross transfer functions of the physical optics further comprises a cross transfer function of a polarized part of the light source, which is expressed as follows:
Figure 834332DEST_PATH_IMAGE035
Figure 338126DEST_PATH_IMAGE036
wherein the content of the first and second substances,
Figure 46319DEST_PATH_IMAGE018
，
Figure 610155DEST_PATH_IMAGE019
representing a vector in the frequency domain and,
Figure 669378DEST_PATH_IMAGE020
the value of the integral variable is represented by,
Figure 976863DEST_PATH_IMAGE037
the representation of the pupil function is shown,
Figure 70721DEST_PATH_IMAGE022
the conjugate of the pupil function is represented,
Figure 805458DEST_PATH_IMAGE038
the function of the light source is represented,
Figure 354907DEST_PATH_IMAGE024
a description of an electric field representing a particular direction;
bonding of
Figure 934924DEST_PATH_IMAGE039
The cross-transfer function of the non-polarized light source,
Figure 617709DEST_PATH_IMAGE025
indicating a location
Figure 257769DEST_PATH_IMAGE026
In the direction of light
Figure 291584DEST_PATH_IMAGE027
Respectively to the direction
Figure 940871DEST_PATH_IMAGE028
The influence of the polarization term of the upper electric field,
Figure 9322DEST_PATH_IMAGE029
the conjugates representing the respective functions, orthogonal and independent of each other, result in:
Figure 82932DEST_PATH_IMAGE040
Figure 72885DEST_PATH_IMAGE041
which represents the radial cross-transfer function of the,
Figure 525863DEST_PATH_IMAGE042
the angular cross-transfer function is represented as,
Figure 448820DEST_PATH_IMAGE043
and
Figure 696262DEST_PATH_IMAGE044
representing radial and angular field strength transfer functions, in which
Figure 173510DEST_PATH_IMAGE045
Figure 899021DEST_PATH_IMAGE046
In the formula (I), the compound is shown in the specification,
Figure 942063DEST_PATH_IMAGE047
a description of the electric field in the radial direction is shown,
Figure 820459DEST_PATH_IMAGE048
representing an angular electric field description.
4. An apparatus for computing a lithography model based on polar coordinate vectors, comprising;
polarized light source device for configuring the field strength of a polarized light source and determining the polarization type of the light source, the electric field of the polarized light of the light source being resolvable in a radially describing electric field and in an angularly describing electric field
Figure 316162DEST_PATH_IMAGE001
；
A polarized light field strength transmission matrix apparatus for establishing a transmission matrix of incident light field strength into a pupil, the transmission matrix describing transmission changes in the incident light field strength, the transmission matrix describing the effects of radial and angular light polarization on the incident light field strength, the formula being as follows:
Figure 314205DEST_PATH_IMAGE049
wherein the first column
Figure 946175DEST_PATH_IMAGE003
Representing radial ray pairs
Figure 269840DEST_PATH_IMAGE004
Influence of the polarization term in the direction, second column
Figure 987260DEST_PATH_IMAGE005
Representing angular ray pairs
Figure 51644DEST_PATH_IMAGE004
The influence of the polarization term in the direction; the radial field strength only influences the radial direction
Figure 803699DEST_PATH_IMAGE006
Direction and z-direction, angular
Figure 563845DEST_PATH_IMAGE007
Is only relevant to itself; the Jones matrix describes the pupil-to-light polarization change,
Figure 768561DEST_PATH_IMAGE008
representing the effect of the pupil lens on the radial ray polarization,
Figure 639565DEST_PATH_IMAGE009
represents the effect of the pupil lens on the polarization of the diagonal rays; the refractive effect of the photoresist layer and the pupil, i.e., the creation of M, the transmission matrix can be described in the infinite depth model of the photoresist layer as:
Figure 246127DEST_PATH_IMAGE010
wherein the content of the first and second substances,
Figure 177174DEST_PATH_IMAGE050
which represents the transmission coefficient in the medium,
Figure 869186DEST_PATH_IMAGE051
which represents the transmission coefficient in the photoresist,
Figure 812390DEST_PATH_IMAGE033
is the angle of incidence of the light rays,
Figure 7879DEST_PATH_IMAGE034
is the angle of refraction;
a physical optics description device for building a vector computational lithography model to obtain a plurality of cross transfer functions describing physical optics
Figure 375407DEST_PATH_IMAGE014
，
Figure 289136DEST_PATH_IMAGE015
，
Figure 767522DEST_PATH_IMAGE016
，
Figure 83097DEST_PATH_IMAGE014
Represents the cross-transfer function of a non-polarized light source,
Figure 355946DEST_PATH_IMAGE015
which represents the radial cross-transfer function of the,
Figure 754042DEST_PATH_IMAGE016
representing an angular cross-transfer function, wherein the cross-transfer function of the unpolarized light source is represented as:
Figure 36119DEST_PATH_IMAGE052
wherein the content of the first and second substances,
Figure 206200DEST_PATH_IMAGE018
，
Figure 915530DEST_PATH_IMAGE019
representing a vector in the frequency domain and,
Figure 538272DEST_PATH_IMAGE020
the value of the integral variable is represented by,
Figure 358461DEST_PATH_IMAGE021
the representation of the pupil function is shown,
Figure 648628DEST_PATH_IMAGE022
the conjugate of the pupil function is represented,
Figure 263280DEST_PATH_IMAGE023
the function of the light source is represented,
Figure 387967DEST_PATH_IMAGE024
a description of the electric field representing a particular direction,
Figure 11846DEST_PATH_IMAGE025
indicating a location
Figure 156520DEST_PATH_IMAGE026
In the direction of light
Figure 207652DEST_PATH_IMAGE027
Respectively to the direction
Figure 70566DEST_PATH_IMAGE028
The influence of the polarization term of the upper electric field,
Figure 966978DEST_PATH_IMAGE029
represents the conjugate of the corresponding function;
and the vector calculation photoetching model device is used for establishing a vector calculation photoetching model and calculating the light intensity distribution of the vector photoetching model on the light resistance layer by integrating a plurality of cross transfer functions of the physical optics, a transmission matrix of the incident light field intensity and the polarization type of the light source.
CN201911288282.9A 2019-12-16 2019-12-16 Method and device for calculating photoetching model based on polar coordinate vector Active CN110703438B (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
CN201911288282.9A CN110703438B (en) 2019-12-16 2019-12-16 Method and device for calculating photoetching model based on polar coordinate vector
PCT/CN2020/136830 WO2021121272A1 (en) 2019-12-16 2020-12-16 Method and device for vector calculation photoetching model based on polar coordinates

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911288282.9A CN110703438B (en) 2019-12-16 2019-12-16 Method and device for calculating photoetching model based on polar coordinate vector

Publications (2)

Publication Number Publication Date
CN110703438A CN110703438A (en) 2020-01-17
CN110703438B true CN110703438B (en) 2020-04-17

Family

ID=69207123

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911288282.9A Active CN110703438B (en) 2019-12-16 2019-12-16 Method and device for calculating photoetching model based on polar coordinate vector

Country Status (2)

Country Link
CN (1) CN110703438B (en)
WO (1) WO2021121272A1 (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110703438B (en) * 2019-12-16 2020-04-17 墨研计算科学（南京）有限公司 Method and device for calculating photoetching model based on polar coordinate vector

Family Cites Families (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007273560A (en) * 2006-03-30 2007-10-18 Toshiba Corp Light intensity distribution simulation method
US7889315B2 (en) * 2006-04-13 2011-02-15 Asml Netherlands B.V. Lithographic apparatus, lens interferometer and device manufacturing method
JP2008076683A (en) * 2006-09-20 2008-04-03 Canon Inc Mask data generation program, mask data generation method, mask fabrication method, exposure method and device manufacturing method
JP4484909B2 (en) * 2007-07-24 2010-06-16 キヤノン株式会社 Original data creation method, original data creation method, exposure method, and original data creation program
NL1036189A1 (en) * 2007-12-05 2009-06-08 Brion Tech Inc Methods and System for Lithography Process Window Simulation.
CN101923278B (en) * 2009-06-17 2012-01-04 复旦大学 Modeling method of phase shift mask in photolithographic process
JP5662762B2 (en) * 2009-11-20 2015-02-04 キヤノン株式会社 Method and program for calculating effective light source, exposure method and device manufacturing method
NL2007306A (en) * 2010-09-23 2012-03-26 Asml Netherlands Bv Source polarization optimization.
WO2015120070A1 (en) * 2014-02-05 2015-08-13 Kla-Tencor Corporation Grazing order metrology
NL2015160A (en) * 2014-07-28 2016-07-07 Asml Netherlands Bv Illumination system, inspection apparatus including such an illumination system, inspection method and manufacturing method.
CN107644131A (en) * 2017-09-13 2018-01-30 苏州珂晶达电子有限公司 Intersection transmission function quick decomposition method based on polar coordinates sampling
CN110703438B (en) * 2019-12-16 2020-04-17 墨研计算科学（南京）有限公司 Method and device for calculating photoetching model based on polar coordinate vector

Also Published As

Publication number Publication date
CN110703438A (en) 2020-01-17
WO2021121272A1 (en) 2021-06-24

Similar Documents

Publication Publication Date Title
JP6421237B2 (en) Metrology method, target and substrate
KR100436831B1 (en) Method and apparatus for fast aerial image simulation
CN102692823B (en) Methods and apparatus for calculating electromagnetic scattering properties of a structure and for reconstruction of approximate structures
TWI486801B (en) Mask, mask layout data, non-transitory computer-readable storage medium and method for placing sub-resolution assist features in mask layout
CN101846886A (en) Delta TCC (transmission cross coefficient) for high-speed sensibility model calculation
CN106062634A (en) Measuring a process parameter for a manufacturing process involving lithography
US11875101B2 (en) Method for patterning process modelling
KR20130008662A (en) Method of forming photomask layout
TW200900872A (en) Method for predicting resist pattern shape, computer readable medium storing program for predicting resist pattern shape, and computer for predicting resist pattern shape
US9411223B2 (en) On-product focus offset metrology for use in semiconductor chip manufacturing
CN110703438B (en) Method and device for calculating photoetching model based on polar coordinate vector
US8230369B2 (en) Simulation method and simulation program
US20230288815A1 (en) Mapping metrics between manufacturing systems
Adam et al. Using machine learning in the physical modeling of lithographic processes
KR102411551B1 (en) Method and apparatus for determining alignment properties of a radiation beam
US10067425B2 (en) Correcting EUV crosstalk effects for lithography simulation
KR20110102688A (en) Method of etch proximity correction, method of creating photomask layout using the same, computer readable media including a sequence of programmed instructions stored thereon for implementing the same and mask imaging system
CN104865799B (en) A kind of photoetching projection objective lens polarize simulating analysis
US20090210851A1 (en) Lithography simulation method and computer program product
CN115639731A (en) Method, device, system and medium for predicting telecentric deviation of projection objective of photoetching machine
US10496780B1 (en) Dynamic model generation for lithographic simulation
JP2009204823A (en) Simulation method and program for simulation
CN116745701A (en) Measurement target simulation
Shim et al. Verification of directed self-assembly (DSA) guide patterns through machine learning
Zhang et al. Efficient full-chip mask 3D model for off-axis illumination

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
GR01 Patent grant
GR01 Patent grant