CN114675508A - Electron beam lithography dose shape correction method based on edge iteration - Google Patents

Electron beam lithography dose shape correction method based on edge iteration Download PDF

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CN114675508A
CN114675508A CN202210381947.6A CN202210381947A CN114675508A CN 114675508 A CN114675508 A CN 114675508A CN 202210381947 A CN202210381947 A CN 202210381947A CN 114675508 A CN114675508 A CN 114675508A
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layout
pixel
edge
delta
offset
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刘杰
徐宏成
姚文泽
赵浩杰
张思媛
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Hunan 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
    • G03F7/20—Exposure; Apparatus therefor
    • G03F7/2051—Exposure without an original mask, e.g. using a programmed deflection of a point source, by scanning, by drawing with a light beam, using an addressed light or corpuscular source
    • G03F7/2059—Exposure without an original mask, e.g. using a programmed deflection of a point source, by scanning, by drawing with a light beam, using an addressed light or corpuscular source using a scanning corpuscular radiation beam, e.g. an electron beam
    • G03F7/2061—Electron scattering (proximity) correction or prevention methods
    • 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
    • G03F7/70383—Direct write, i.e. pattern is written directly without the use of a mask by one or multiple beams
    • 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
    • G03F7/7055—Exposure light control in all parts of the microlithographic apparatus, e.g. pulse length control or light interruption
    • G03F7/70558—Dose control, i.e. achievement of a desired dose
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention relates to an edge iteration-based electron beam lithography dose shape correction method, which carries out iterative correction by judging and storing exposure conditions of each point position of a layout edge until the convergence standard is met. The invention is divided into six steps: step S1: dividing grids of the electron beam exposure layout; step S2: judging and storing the position of each pixel edge point in the exposure layout; step S3: simulating the exposure and development processes of the electron beam exposure layout, and calculating the offset of the corresponding pixel at the edge of each pixel; step S4: correcting the edge exposure position of each pixel according to the offset of the pixel corresponding to the edge of each pixel; step S5: calculating an error and judging whether iteration converges; step S6: and obtaining the layout after shape correction. The correction time is short because only the boundary of the layout needs to be calculated, and the energy of all points of the edge is accurately corrected and calculated, so the method has the characteristics of high calculation efficiency and high calculation precision.

Description

Electron beam lithography dose shape correction method based on edge iteration
Technical Field
The invention relates to an electron beam lithography dose shape correction method based on edge iteration, which is used for quickly correcting an electron beam lithography layout on the premise of ensuring the precision, realizes exposure layout shape correction by single dose and belongs to the field of computational lithography.
Background
The electron beam lithography is a high-resolution maskless direct-writing lithography technology, and because the spot size of the electron beam is very small, the electron beam lithography can be used for manufacturing a layout with the characteristic size below 10 nanometers. Due to collision and scattering of electrons in the resist and the substrate, the developed layout and the design layout are seriously distorted, and negative effects such as electron beam lithography Proximity Effect (Proximity Effect), atomization Effect (Fogging Effect), etching Loading Effect (Etch Loading Effect), charge accumulation Effect (Charging Effect) and the like are generated. Correction of these negative effects, especially for lithographic layouts with very small or dense feature sizes, is an indispensable critical step in the electron beam lithography process flow.
Two types of correction methods currently exist: dose correction and shape correction. Wherein the dose correction has the advantage of high accuracy, but the electron beam lithography requires a fast exposure dose change, which is highly demanding for the lithography apparatus. The shape correction achieves the purpose of using the same dose to expose the whole layout by correcting the shape of the layout, and can be compatible with all photoetching equipment. At present, in the traditional shape correction algorithm, the whole exposure layout needs to be solved iteratively, so that the calculation efficiency of the large-scale exposure layout is very low. Therefore, it is highly desirable to invent a shape correction algorithm that is compatible with all lithographic apparatuses and can perform efficient calculation while ensuring calculation accuracy.
Compared with the existing shape correction method, the method does not need to divide the layout into small rectangles, does not need to judge the connection part of the rectangles, only needs to receive energy according to each point of the edge for processing, greatly reduces the calculation pixel points, can effectively improve the calculation efficiency particularly aiming at the calculation of the exposure layout with super-large scale, and also greatly improves the precision.
Disclosure of Invention
The invention relates to an electron beam lithography dose shape correction method based on edge iteration, aiming at modifying an input layout to overcome the negative effect generated by electron beam lithography on the premise of ensuring that the dose is not changed, thereby realizing the shape correction by single dose.
The technical solution of the invention is as follows: by correcting the exposure condition of the edge of the analysis layout, on the premise of ensuring the precision and time, recording according to the exposure condition of all points of the edge of the layout, and iteratively correcting the layout according to the result, the invention comprises the following steps:
step S1: dividing grids of the electron beam exposure layout;
reading in an electron beam lithography original layout, dividing a part of the layout needing exposure into square grids (which can also be expressed as pixels) at equal intervals, wherein each grid is an exposure point, the original layout is assigned with 1, the rest blank grids are assigned with 0, and the converted original layout is expressed by P (x, y) (x is more than or equal to 0 and less than M, y is more than or equal to 0 and less than N, wherein M and N are the length and the width of the layout respectively).
Step S2: judging and storing the position of each pixel edge point in the exposure layout;
according to the original layout matrix P (x, y) obtained in S1, four groups of data lists, i.e., upper (T), right (R), lower (B), and left (L), are divided according to the edges, and are respectively determined and stored according to four conditions of formulas (1), (2), (3), and (4), as shown in fig. 2, that is:
1) judging conditions that each pixel in the layout is positioned at the upper edge are as follows:
Figure BDA0003593240450000021
in the formula, P (x, y) is an original layout matrix. T is a list that stores all the points and offsets of the top edge, and δ is the offset of a point of the top edge (i.e., the amount the top edge moves up, or down). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (1) to be a group according to three variables of x, y and delta, sequentially storing the groups into an upper edge list T, and initializing the delta to be 0.
2) Judging conditions that each pixel in the layout is positioned at the right edge:
Figure BDA0003593240450000022
in the formula, P (x, y) is an original layout matrix. R is a list that stores all the points and offsets of the right edge, and δ is the offset of a point of the right edge (i.e., the amount by which the point of the right edge is moved to the left, or to the right). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (2) to be a group according to three variables of x, y and delta, sequentially storing the groups into a right edge list R, and initializing the delta to be 0.
3) Judging conditions that each pixel in the layout is positioned at the lower edge:
Figure BDA0003593240450000023
in the formula, P (x, y) is an original layout matrix. B is a list that stores all points of the lower edge and the offset, δ is the offset of a point of the lower edge (i.e., the amount the point of the lower edge moves up, or down). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (3) to be a group according to three variables of x, y and delta, sequentially storing the group into a lower edge list B, and initializing the delta to be 0.
4) Judging conditions that each pixel in the layout is positioned at the left edge are as follows:
Figure BDA0003593240450000024
in the formula, P (x, y) is an original layout matrix. L is a list that stores all the points and offsets of the left edge, and δ is the offset of a point of the left edge (i.e., the amount by which the point of the left edge is moved to the left, or to the right). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (4) to be a group according to three variables of x, y and delta, sequentially storing the groups into a left edge list L, and initializing the delta to be 0.
Step S3: simulating the exposure and development processes of the electron beam exposure layout, and calculating the offset of the corresponding pixel at the edge of each pixel;
performing energy deposition exposure calculation on the iterative layout matrix D (x, y),defining the energy distribution after exposure as ED(x, y), the exposure calculation method is as follows:
Figure BDA0003593240450000025
in the formula (I), the compound is shown in the specification,
Figure BDA0003593240450000026
is a two-dimensional discrete convolution; PSF (x, y) is an electron beam spot spread function that contains functional forms that describe various effects in e-beam lithography including, but not limited to, e-beam lithography Proximity Effect (Proximity Effect), fogging Effect (FoggingEffect), Etch Loading Effect (Etch Loading Effect), charge Effect (Charging Effect). The initial value of the iterative layout matrix D (x, y) is equal to P (x, y), i.e., D (x, y) ═ P (x, y). The energy deposition result of the exposure is subjected to development calculation (development threshold tau, 0)<τ<1) Developing model SDThe definition method of (x, y) is as follows:
Figure BDA0003593240450000027
in the formula, max is the calculation EDMaximum point of (x, y), τ is developing threshold, SD(x, y) is the development of the exposed layout.
Next, the shift amount δ per pixel of each edge is sequentially calculated in accordance with the edge position list T, R, B and L acquired in S2, as shown in fig. 3, that is:
1) let the length of the T list be NTAnd the upper boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000031
in the formula, delta3i+2The offset of the ith pixel at the upper edge is (i is more than or equal to 0 and less than or equal to NT/3)，SD(x, y) is the development of the exposed layout.
2) Let the length of the R list be NRRight boundary offsetThe calculation method comprises the following steps:
Figure BDA0003593240450000032
in the formula, delta3i+2Is the offset of the ith pixel at the right edge (i is more than or equal to 0 and less than or equal to NR/3)，SD(x, y) is the development of the exposed layout.
3) Let the length of the B list be NBThe lower boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000033
in the formula, delta3i+2The offset of the ith pixel at the lower edge is (i is more than or equal to 0 and less than or equal to NB/3)，SD(x, y) is the development of the exposed layout.
4) Let L list be N in lengthLThe left boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000034
in the formula, delta3i+2The offset of the ith pixel at the left edge is (i is more than or equal to 0 and less than or equal to NL/3)，SD(x, y) is the development of the exposed layout.
Step S4: correcting the edge exposure position of each pixel according to the offset of the corresponding pixel of each pixel edge;
the initial value of the iterative layout matrix D (x, y) is equal to P (x, y), i.e., D (x, y) ═ P (x, y). The edges of the respective pixels are sequentially corrected in accordance with the shift amounts of the respective points of the pixel edge acquired in S3, as shown in fig. 4, that is:
1) correction method of boundary on pixel according to stored list T and T length NTSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NTAnd/3), namely:
when delta3i+2<At time 0:
D(x3i+n-1,y3i+1)＝0,n＝0,1,2,…,|δ3i+2| (11)
in the formula, the point x3i,y3i+1By shifting down one pixel, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i-n,y3i+1)＝1,n＝0,1,2,…,|δ3i+2| (12)
in the formula, the point x3i,y3i+1Moving one pixel up, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
2) Correction method of pixel right boundary according to stored list R and R length NRSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NRAnd/3), namely:
when delta3i+2<At time 0:
D(x3i,y3i+1-n+1)＝0,n＝0,1,2,…,|δ3i+2| (13)
in the formula, the point x3i,y3i+1By one pixel to the left, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i,y3i+1+n)＝1,n＝0,1,2,…,|δ3i+2| (14)
in the formula, the point x3i,y3i+1Shifted by one pixel to the right, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
3) Correction method of lower boundary of pixel according to stored list B and length N of BBSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NBAnd/3), namely:
when delta3i+2<At time 0:
D(x3i-n+1,y3i+1)＝0,n＝0,1,2,…,|δ3i+2| (15)
in the formula, the point x3i,y3i+1Moving one pixel up, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i+n,y3i+1)＝1,n＝0,1,2,…,|δ3i+2| (16)
in the formula, the point x3i,y3i+1By shifting down one pixel, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
4) Correction method of pixel left boundary based on stored list L and L length NLSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NLAnd/3), namely:
when delta3i+2<At time 0:
D(x3i,y3i+1+n-1)＝0,n＝0,1,2,…,|δ3i+2| (17)
in the formula, the point x3i,y3i+1Shifted by one pixel to the right, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2<At time 0:
D(x3i,y3i+1-n)＝1,n＝0,1,2,…,|δ3i+2| (18)
in the formula, the point x3i,y3i+1By one pixel to the left, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
Since the layout D (x, y) is composed of 0 and 1, the effect of correcting the layout is achieved through assignment of each point of the four edges. The updated iterative layout D (x, y) is then saved.
Step S5: calculating an error and judging whether iteration converges;
the corrected iterative layout D (x, y) obtained in S4 is exposed and developed, and the calculation process is the same as in equations (5) and (6). Setting the nth time (n)>1) Convergence error of HnNamely:
Figure BDA0003593240450000041
in the formula, HnAs a result of the nth development SDNumber of pixels, H, different from the original layout P (x, y)1＝∞。
If H isn>Hn-1Taking the iterative layout D (x, y) calculated in S4 as the input of S3, returning to S3 to continue calculating the offset of each point of the edge, then entering S4 to reinitialize D (x, y) to continue correcting according to the updated offset, and then entering S5 to judge and cycle. If H isn<Hn-1The cycle is stopped. And (5) obtaining a final iteration layout D (x, y), namely the layout after shape correction.
Step S6: obtaining a layout after shape correction;
and when the iteration of S5 is finished, obtaining the final iteration layout D (x, y), namely the layout after the shape correction.
Drawings
FIG. 1 is a flow chart of the operation of the present invention;
FIG. 2 is a schematic diagram of obtaining pixel edge coordinates;
FIG. 3 is a schematic illustration of calculating an edge point offset;
FIG. 4 is a schematic diagram of correcting a layout according to an edge point offset;
FIG. 5 is a diagram of the dose correction effect of the simple layout shape;
FIG. 6 is a comparison of the rate of convergence and accuracy of the present invention with other shape correction algorithms.
Detailed Description
The invention will be described in further detail below with reference to the drawings and specific examples.
The invention relates to an electron beam lithography dose shape correction method based on edge iteration, aiming at determining the offset of the edge of an iterative layout by modifying and comparing the results of the original layout and the iterative layout after development on the premise of ensuring the dose not to be changed, and further correcting the layout according to the offset. Under the condition allowable range, the correction time can be controlled by setting the convergence accuracy, and finally, the layout is generated according to the corrected data by pixels. The steps of the invention are shown in figure 1 and are divided into six steps: dividing grids of the electron beam exposure layout; judging and storing the position of each pixel edge point in the exposure layout; simulating the exposure and development processes of the electron beam exposure layout, and calculating the offset of the corresponding pixel at the edge of each pixel; correcting the edge exposure position of each pixel according to the offset of the pixel corresponding to the edge of each pixel; calculating an error and judging whether iteration converges; and obtaining the layout after shape correction. The technical solution of the invention is as follows: exposing the corrected layout by using the same dose, calculating the edge offset of the iteratively corrected layout each time on the premise of ensuring the precision, and correcting the layout of the next iteration, wherein the specific implementation steps are as follows:
step S1: dividing grids of the electron beam exposure layout;
reading in an electron beam lithography original layout, dividing a part of the layout needing exposure into square grids (which can also be expressed as pixels) at equal intervals, wherein each grid is an exposure point, the original layout is assigned with 1, the rest blank grids are assigned with 0, and the converted original layout is expressed by P (x, y) (x is more than or equal to 0 and less than M, y is more than or equal to 0 and less than N, wherein M and N are the length and the width of the layout respectively).
Step S2: judging and storing the position of each pixel edge point in the exposure layout;
according to the original layout matrix P (x, y) obtained in S1, four groups of data lists, namely, upper (T), right (R), lower (B) and left (L), are divided according to the edges, and are respectively judged and stored according to four conditions of formulas (1), (2), (3) and (4), as shown in fig. 2, that is:
1) judging conditions that each pixel in the layout is positioned at the upper edge are as follows:
Figure BDA0003593240450000051
in the formula, P (x, y) is an original layout matrix. T is a list that stores all the points and offsets of the top edge, and δ is the offset of a point of the top edge (i.e., the amount the top edge moves up, or down). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (1) to be a group according to three variables of x, y and delta, sequentially storing the groups into an upper edge list T, and initializing the delta to be 0.
2) Judging conditions that each pixel in the layout is positioned at the right edge:
Figure BDA0003593240450000061
in the formula, P (x, y) is an original layout matrix. R is a list that stores all the points and offsets of the right edge, and δ is the offset of a point of the right edge (i.e., the amount by which the point of the right edge is moved to the left, or to the right). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (2) to be a group according to three variables of x, y and delta, sequentially storing the groups into a right edge list R, and initializing the delta to be 0.
3) Judging conditions that each pixel in the layout is positioned at the lower edge:
Figure BDA0003593240450000062
in the formula, P (x, y) is an original layout matrix. B is a list that stores all points of the lower edge and the offset, δ is the offset of a point of the lower edge (i.e., the amount the point of the lower edge moves up, or down). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (3) to be a group according to three variables of x, y and delta, sequentially storing the groups into a lower edge list B, and initializing the delta to be 0.
4) Judging conditions that each pixel in the layout is positioned at the left edge are as follows:
Figure BDA0003593240450000063
in the formula, P (x, y) is an original layout matrix. L is a list that stores all the points and offsets of the left edge, and δ is the offset of a point of the left edge (i.e., the amount by which the point of the left edge is moved to the left, or to the right). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (4) to be a group according to three variables of x, y and delta, sequentially storing the groups into a left edge list L, and initializing the delta to be 0.
Step S3: simulating the exposure and development processes of the electron beam exposure layout, and calculating the offset of the corresponding pixel at the edge of each pixel;
performing energy deposition exposure calculation on the iteration layout matrix D (x, y), and defining the energy distribution after exposure as ED(x, y), the exposure calculation method is as follows:
Figure BDA0003593240450000064
in the formula (I), the compound is shown in the specification,
Figure BDA0003593240450000065
is a two-dimensional discrete convolution; PSF (x, y) is an electron beam spot spread function that contains functional forms that describe various effects in e-beam lithography including, but not limited to, e-beam lithography Proximity Effect (Proximity Effect), fogging Effect (FoggingEffect), Etch Loading Effect (Etch Loading Effect), charge Effect (Charging Effect). The initial value of the iterative layout matrix D (x, y) is equal to P (x, y), i.e., D (x, y) ═ P (x, y). The exposed energy deposition result is subjected to development calculation (development threshold τ, 0)<τ<1) Developing model SDThe definition method of (x, y) is as follows:
Figure BDA0003593240450000066
in the formula, max is the calculation EDMaximum point of (x, y), τ is developing threshold, SD(x, y) is the development of the exposed layout.
Next, the shift amount δ per pixel of each edge is sequentially calculated in accordance with the edge position list T, R, B and L acquired in S2, as shown in fig. 3, that is:
1) let the length of the T list be NTAnd the upper boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000071
in the formula, delta3i+2The offset of the ith pixel at the upper edge is (i is more than or equal to 0 and less than or equal to NT/3)，SD(x, y) is the development of the exposed layout.
2) Let the length of the R list be NRAnd the right boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000072
in the formula, delta3i+2Is the offset of the ith pixel at the right edge (i is more than or equal to 0 and less than or equal to NR/3)，SD(x, y) is the development of the exposed layout.
3) Let the length of the B list be NBAnd the lower boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000073
in the formula, delta3i+2The offset of the ith pixel at the lower edge is (i is more than or equal to 0 and less than or equal to NB/3)，SD(x, y) is the development of the exposed layout.
4) Let L list be N in lengthLThe left boundary offset calculation method comprises the following steps:
Figure BDA0003593240450000074
in the formula, delta3i+2For the offset of the ith pixel at the left edge (0 ≦ i ≦ N)L/3)，SD(x, y) is the development of the exposed layout.
Step S4: correcting the edge exposure position of each pixel according to the offset of the corresponding pixel of each pixel edge;
the initial value of the iterative layout matrix D (x, y) is equal to P (x, y), i.e., D (x, y) ═ P (x, y). The edges of the respective pixels are sequentially corrected in accordance with the shift amounts of the respective points of the pixel edge acquired in S3, as shown in fig. 4, that is:
1) correction method of boundary on pixel according to stored list T and T length NTSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NTAnd/3), namely:
when delta3i+2<At time 0:
D(x3i+n-1,y3i+1)＝0,n＝0,1,2,…,|δ3i+2| (11)
in the formula, the point x3i,y3i+1Moving one pixel down, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i-n,y3i+1)＝1,n＝0,1,2,…,|δ3i+2| (12)
in the formula, the point x3i,y3i+1Moving one pixel up, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
2) Correction of pixel right boundary based on stored list R, and R length NRSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NRAnd/3), namely:
when delta3i+2<At time 0:
D(x3i,y3i+1-n+1)＝0,n＝0,1,2,…,|δ3i+2| (13)
in the formula, the point x3i,y3i+1By one pixel to the left, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i,y3i+1+n)＝1,n＝0,1,2,…,|δ3i+2| (14)
in the formula, the point x3i,y3i+1Shifted by one pixel to the right, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
3) Correction method of lower boundary of pixel according to stored list B and length N of BBSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NBAnd/3), namely:
when delta3i+2<At time 0:
D(x3i-n+1,y3i+1)＝0,n＝0,1,2,…,|δ3i+2| (15)
in the formula, the point x3i,y3i+1Moving one pixel up, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i+n,y3i+1)＝1,n＝0,1,2,…,|δ3i+2| (16)
in the formula, the point x3i,y3i+1By shifting down one pixel, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
4) Correction of left boundary of pixel based on stored list L and length N of LLSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NLAnd/3), namely:
when delta3i+2<At time 0:
D(x3i,y3i+1+n-1)＝0,n＝0,1,2,…,|δ3i+2| (17)
in the formula, the point x3i,y3i+1Shifted by one pixel to the right, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2<At time 0:
D(x3i,y3i+1-n)＝1,n＝0,1,2,…,|δ3i+2| (18)
in the formula, the point x3i,y3i+1By one pixel to the left, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
Since the layout D (x, y) is composed of 0 and 1, the effect of correcting the layout is achieved through assignment of each point of the four edges. The updated iterative layout D (x, y) is then saved.
Step S5: calculating an error and judging whether iteration converges;
the corrected iterative layout D (x, y) obtained in S4 is exposed and developed, and the calculation process is the same as in equations (5) and (6). Setting the nth time (n)>1) Convergence error of HnNamely:
Figure BDA0003593240450000081
in the formula, HnAs a result of the nth development SDNumber of pixels, H, different from the original layout P (x, y)1＝∞。
If H isn>Hn-1Taking the iterative layout D (x, y) calculated in S4 as the input of S3, returning to S3 to continue calculating the offset of each point of the edge, then entering S4 to reinitialize D (x, y) to continue correcting according to the updated offset, and then entering S5 to judge and cycle. If H isn<Hn-1The cycle is stopped. And (5) obtaining a final iteration layout D (x, y), namely the layout after shape correction.
Step S6: obtaining a layout after shape correction;
and when the iteration of S5 is finished, obtaining a final iteration layout D (x, y), namely the layout after the shape correction.
As shown in fig. 5, (a) is the original layout, i.e., P (x, y) in S1; (b) is the development of the original layout after direct exposure, i.e. SD(x, y), where D (x, y) is P (x, y); (c) is the corrected uniform dose shape layout, i.e. D obtained by S6 iteration(x, y); (d) is the corrected uniform dose shape development result, i.e., S after iterative convergence in S6D(x, y). According to the electron beam lithography dose shape correction method based on edge iteration, only the boundary condition of the layout needs to be calculated by adopting an edge iteration algorithm, so that the calculated amount is greatly reduced, and the calculation speed is high. And the energy deposition value of the edge pixel is considered, the error between the correction result and the original layout after the correction result is developed is small, and the requirement on the experimental precision can be met. As shown in fig. 6, which is a comparison of the convergence rate and accuracy of the present invention with the LBFGS algorithm and the PID algorithm, it can be seen that the efficiency and accuracy of the present method are significantly better than those of the other two methods. Therefore, the method has the characteristics of high calculation efficiency and high calculation precision.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention, and do not limit the protection scope of the present invention. With reference to the description of the embodiment, those skilled in the art will understand and make modifications or substitutions related to the technical solution of the present invention without departing from the spirit and scope of the present invention.

Claims (6)

1. An electron beam lithography dose shape correction method based on edge iteration is characterized by comprising the following steps:
step S1, dividing the grid of the electron beam exposure layout;
step S2, judging and storing the position of each pixel edge point in the exposure layout;
step S3, simulating the exposure and development process of the electron beam exposure layout, and calculating the offset of the pixel corresponding to each pixel edge;
step S4, correcting the edge exposure position of each pixel according to the offset of the corresponding pixel of each pixel edge;
step S5, calculating error and judging whether iteration converges;
and step S6, obtaining the layout after shape correction.
2. The method of claim 1, wherein the correction comprises: in step S1, the original layout of the electron beam lithography is read in, the part of the layout that needs to be exposed is divided into square grids (which may also be referred to as "pixels") at equal intervals, each grid is an exposure point, the original layout is assigned with 1, the remaining blank grids are assigned with 0, and the converted original layout is represented by P (x, y) (x is greater than or equal to 0 and less than M, y is greater than or equal to 0 and less than N, where M and N are the length and width of the layout, respectively).
3. The method of claim 1, wherein the correction comprises: in step S2, the positions of each point on the edge of each pixel in the exposure layout are determined and stored, and the exposure layout is divided into four groups of data lists, i.e., an upper (T), a right (R), a lower (B) and a left (L) according to the original layout matrix P (x, y) obtained in S1, and the four groups of data lists are determined and stored according to the four conditions of formulas (1), (2), (3) and (4), that is:
1) judging conditions that each pixel in the layout is positioned at the upper edge are as follows:
Figure FDA0003593240440000011
in the formula, P (x, y) is an original layout matrix. T is a list that stores all the points and offsets of the top edge, and δ is the offset of a point of the top edge (i.e., the amount the top edge moves that point up, or down). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (1) to be a group according to three variables of x, y and delta, sequentially storing the groups into an upper edge list T, and initializing the delta to be 0.
2) Judging conditions that each pixel in the layout is positioned at the right edge:
Figure FDA0003593240440000012
in the formula, P (x, y) is an original layout matrix. R is a list that stores all the points and offsets of the right edge, and δ is the offset of a point of the right edge (i.e., the amount by which the point of the right edge is moved to the left, or to the right). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (2) to be a group according to three variables of x, y and delta, sequentially storing the groups into a right edge list R, and initializing the delta to be 0.
3) Judging conditions that each pixel in the layout is positioned at the lower edge:
Figure FDA0003593240440000013
in the formula, P (x, y) is an original layout matrix. B is a list that stores all points of the lower edge and the offset, δ is the offset of a point of the lower edge (i.e., the amount the point of the lower edge moves up, or down). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (3) to be a group according to three variables of x, y and delta, sequentially storing the groups into a lower edge list B, and initializing the delta to be 0.
4) Judging conditions that each pixel in the layout is positioned at the left edge are as follows:
Figure FDA0003593240440000021
in the formula, P (x, y) is an original layout matrix. L is a list that stores all the points and offsets of the left edge, and δ is the offset of a point of the left edge (i.e., the amount by which the point of the left edge is moved to the left, or to the right). Traversing x and y coordinates in an original layout matrix P (x, y), enabling the coordinates meeting the formula (4) to be a group according to three variables of x, y and delta, sequentially storing the groups into a left edge list L, and initializing the delta to be 0.
4. The edge-iteration-based electron beam lithography dose shape correction method of claim 1, wherein: in step S3, simulating the exposure and development process of the electron beam exposure layout, calculating the offset of the pixel corresponding to the edge of each pixel, performing energy deposition exposure calculation on the iterative layout matrix D (x, y), and defining the energy distribution after exposure as ED(x, y), the exposure calculation method is as follows:
Figure FDA0003593240440000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003593240440000023
is a two-dimensional discrete convolution; PSF (x, y) is an electron beam spot spread function that contains functional forms that describe various effects in e-beam lithography including, but not limited to, e-beam lithography Proximity Effect (Proximity Effect), Fogging Effect (Fogging Effect), Etch Loading Effect (Etch Loading Effect), charge Effect (Charging Effect). The initial value of the iterative layout matrix D (x, y) is equal to P (x, y), i.e., D (x, y) ═ P (x, y). The exposed energy deposition result is subjected to development calculation (development threshold τ, 0)<τ<1) Developing model SDThe definition method of (x, y) is as follows:
Figure FDA0003593240440000024
in the formula, max is the calculation EDMaximum point of (x, y), τ is developing threshold, SD(x, y) is the development of the exposed layout.
Next, the shift amount δ per pixel of each edge is calculated in turn in accordance with the edge position list T, R, B and L acquired in S2, that is:
1) let the length of the T list be NTAnd the upper boundary offset calculation method comprises the following steps:
Figure FDA0003593240440000025
in the formula, delta3i+2The offset of the ith pixel at the upper edge is (i is more than or equal to 0 and less than or equal to NT/3)，SD(x, y) is the development of the exposed layout.
2) Let the length of the R list be NRAnd the right boundary offset calculation method comprises the following steps:
Figure FDA0003593240440000026
in the formula, delta3i+2Is the offset of the ith pixel at the right edge (i is more than or equal to 0 and less than or equal to NR/3)，SD(x, y) is the development of the exposed layout.
3) Let the length of the B list be NBAnd the lower boundary offset calculation method comprises the following steps:
Figure FDA0003593240440000027
in the formula, delta3i+2The offset of the ith pixel at the lower edge is (i is more than or equal to 0 and less than or equal to NB/3)，SD(x, y) is the development of the exposed layout.
4) Let L list be N in lengthLThe left boundary offset calculation method:
Figure FDA0003593240440000028
in the formula, delta3i+2The offset of the ith pixel at the left edge is (i is more than or equal to 0 and less than or equal to NL/3)，SD(x, y) is the development of the exposed layout.
5. The edge-iteration-based electron beam lithography dose shape correction method of claim 1, wherein: in step S4, the edge exposure position of each pixel is corrected according to the offset of the pixel corresponding to each pixel edge, so that the initial value of the iterative layout matrix D (x, y) is equal to P (x, y), i.e., D (x, y) ═ P (x, y). The edges of the respective pixels are sequentially corrected in accordance with the shift amounts of the respective points of the edges of the pixels acquired in S3, that is:
1) correction method of boundary on pixel according to stored list T and T length NTSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NTAnd/3), namely:
when delta3i+2<At time 0:
D(x3i+n-1,y3i+1)＝0,n＝0,1,2,…,|δ3i+2| (11)
in the formula, the point x3i,y3i+1By shifting down one pixel, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i-n,y3i+1)＝1,n＝0,1,2,…,|δ3i+2| (12)
in the formula, the point x3i,y3i+1Moving one pixel up, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
2) Correction of pixel right boundary based on stored list R, and R length NRSequentially taking out each group of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NRAnd/3), namely:
when delta3i+2<At time 0:
D(x3i,y3i+1-n+1)＝0,n＝0,1,2,…,|δ3i+2| (13)
in the formula, the point x3i,y3i+1Move one pixel to the left, move by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i,y3i+1+n)＝1,n＝0,1,2,…,|δ3i+2| (14)
in the formula, the point x3i,y3i+1By shifting by one pixel to the right by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
3) Correction of lower boundary of pixel based on stored list B and length N of BBSequentially taking out each group of coordinates x3i,y3i+1Deviation from harmonyAmount of displacement delta3i+2，(0≤i≤NBAnd/3), namely:
when delta3i+2<At time 0:
D(x3i-n+1,y3i+1)＝0,n＝0,1,2,…,|δ3i+2| (15)
in the formula, the point x3i,y3i+1Moving one pixel up, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2>At time 0:
D(x3i+n,y3i+1)＝1,n＝0,1,2,…,|δ3i+2| (16)
in the formula, the point x3i,y3i+1Moving one pixel down, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
4) Correction of left boundary of pixel based on stored list L and length N of LLSequentially taking out each set of coordinates x3i,y3i+1And offset delta3i+2，(0≤i≤NLAnd/3), namely:
when delta3i+2<At time 0:
D(x3i,y3i+1+n-1)＝0,n＝0,1,2,…,|δ3i+2| (17)
in the formula, the point x3i,y3i+1Shifted by one pixel to the right, by | δ3i+2And l-1 time, and assigning the pixel position corresponding to the iteration layout D (x, y) to be 0 after each movement.
When delta3i+2<At time 0:
D(x3i,y3i+1-n)＝1,n＝0,1,2,…,|δ3i+2| (18)
in the formula, the point x3i,y3i+1By one pixel to the left, by | δ3i+2And l, assigning the position of the pixel corresponding to the iteration layout D (x, y) to be 1 after each movement.
Since the layout D (x, y) is composed of 0 and 1, the effect of correcting the layout is achieved through assignment of each point of the four edges. The updated iterative layout D (x, y) is then saved.
6. The edge-iteration-based electron beam lithography dose shape correction method of claim 1, wherein: in step S5, an error is calculated and it is determined whether the iteration converges, and the corrected iteration layout D (x, y) obtained in S4 is exposed and developed, and the calculation process is the same as in formulas (5) and (6). Setting the nth time (n)>1) Convergence error of Hn：
Figure FDA0003593240440000041
In the formula, HnAs a result of the nth development SDThe number of pixels, H, different from the original layout P (x, y)1＝∞。
If H isn>Hn-1Taking the iterative layout D (x, y) calculated in S4 as the input of S3, returning to S3 to continue calculating the offset of each point of the edge, then entering S4 to reinitialize D (x, y) to continue correcting according to the updated offset, and then entering S5 to judge and cycle. If Hn<Hn-1The cycle is stopped. And (5) obtaining a final iteration layout D (x, y), namely the layout after shape correction.
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