Download - (a)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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a
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i
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Figure 8.1 A simple layout showing a two-transistor structure with source/drain contact holes. One design rule would dictate the minimum allowed spacing between the edge of the contact and the edge of the active area (dimension f).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Gate CD (nm)
Fre
que
ncy
Devices are too slow, poor
bin sort
High leakage current, device
fails
Range affects timing, which
affects max clock speed possible
0
0.2
0.4
0.6
0.8
1.0
75 80 85 90 95 100 105
0
0.2
0.4
0.6
0.8
1.0
75 80 85 90 95 100 105
Gate CD (nm)
Fre
que
ncy
bin sort limit
Leakage current
limit
(a) (b)
Figure 8.2 A distribution of polysilicon gate linewidths across a chip (a) can lead to different performance failures. Tightening up the distribution of polysilicon gate linewidths across a chip (b) allows for a smaller average CD and faster device performance.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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100% Enominal
E(CD – 10%) – E(CD + 10%) EL =
20 25 30 35 40 45 60
80
100
120
140
Res
ist L
inew
idth
(n
m)
Exposure Energy (mJ/cm2)
Figure 8.3 The common CD versus exposure dose (E) curve is used to measure exposure latitude (EL).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Table 8.1 Examples of random focus errors (mm, 6) for different lithographic generations.
Error Source 19911 i-line
0.50 m
19952 i-line
0.35 m
1995 2 [3] KrF stepper
0.35 m
2001 KrF scanner
0.18 m
2005 ArF scanner
0.09 m Lens Heating (Compensated) 0.10 0.10 0.00 0.00 0.00 Environmental (Compensated) 0.20 0.20 0.10 0.10 0.05 Mask Tilt (actual/16) 0.05 0.05 0.10 0.05 0.05 Mask Flatness (actual/16) 0.12 0.12 0.12 0.12 0.07 Wafer Flatness (over one field) 0.30 0.33 0.33 0.15 0.07 Chuck Flatness (over one field) 0.14 0.03 0.03 0.03 0.03 Laser Bandwidth 0.0 0.0 0.20 0.1 0.04 Autofocus Repeatability 0.20 0.08 0.10 0.07 0.04 Best Focus Determination 0.30 0.15 0.10 0.10 0.05 Vibration 0.10 0.10 0.05 0.05 0.03 Total RSS random focus errors 0.60 0.50 0.45 0.28 0.15
1 C. A. Mack, “Understanding Focus Effects in Submicron Optical Lithography, part 3: Methods for Depth-of-Focus Improvement,” Optical/Laser Microlithography V, Proc., SPIE Vol. 1674 (1992) pp. 272-284. 2 S. Sethi, M. Barrick, J. Massey, C. Froelich, M. Weilemann, and F. Garza, “Lithography strategy for printing 0.35 um devices,” Optical/Laser Microlithography VIII, Proc., SPIE Vol. 2440 (1995), p. 619-632.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Error Source 1991 i-line
0.50 m
1995 i-line
0.35 m
1995 KrF stepper
0.35 m
2001 KrF scanner
0.18 m
2005 ArF scanner
0.09 m Topography 0.5 0.3 0.3 0.10 0.05 Field curvature & astigmatism 0.4 0.4 0.3 0.08 0.05 Resist Thickness 0.2 0.2 0.2 0.10 0.05 Total Systematic Errors (range) 1.1 0.9 0.8 0.28 0.15 Total Random Errors (6) 0.60 0.50 0.45 0.28 0.15 Range/ 11 10.8 10.7 6 6
Total BIFE (6 equivalent) 1.5 1.2 1.1 0.47 0.25
Table 8.2 Examples of systematic (mm, total range) and random focus error estimates combined to determine the Built-in Focus Errors (BIFE) of a process.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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w
D
Figure 8.4 Example photoresist profile and its corresponding “best fit” trapezoidal feature model.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Focus below the resist
Focus above the resist
Figure 8.5 Resist profiles at the extremes of focus show how the curvature of a pattern cross-section can change.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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400
500
600
700
800
900
1000
-1.5 -1.0 -0.5 0.0 0.5 1.0
Focus (m)
Fea
ture
Wid
th (
nm)
Straight Line Fit Threshold Fit
Figure 8.6 Using resist profiles at the extremes of focus as an example, the resulting measured feature size is a function of how the feature model is fit to the profile.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Wafer Pattern of Exposure
Fields
Wafer Pattern of Exposure
Fields
Scan Direction
Slit
Single Exposure Field
Scan Direction
Slit
Single Exposure Field
Figure 8.7 A wafer is made up of many exposure fields, each with one or more die. The field is exposed by scanning a slit across the exposure field.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Box-in-Box Frame-in-Frame Bar-in-BarBox-in-Box Frame-in-Frame Bar-in-Bar
Figure 8.8 Typical ‘box-in-box’ style overlay measurement targets, showing top-down optical images along the top and typical cross-section diagrams along the bottom. The outer box is typically 20 mm wide. (Courtesy of KLA-Tencor Corp.)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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w XR w XL wXL
x-overlay = 0.5(wXL - wXR)
wXR
Figure 8.9 Measuring overlay as a difference in width measurements.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Figure 8.10 Typical AIM target where the inner bars (darker patterns in this photograph) are printed in one lithographic level and the outer (brighter) bars in another level. (Courtesy of KLA-Tencor Corp.)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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x
y
(x,y)
(x*,y*)
x
y
(x,y)
(x*,y*)
x
y
(x,y)
(x*,y*)
x
y
(x,y)
(x*,y*)
Figure 8.11 Examples of two simple overlay errors: a) rotation, and b) magnification errors.
(a) (b)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Figure 8.12 Different types of rotation errors as exhibited on the wafer: a) reticle rotation, and b) wafer rotation.
(a) (b)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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= +
Raw overlay value Modeled overlay value Residual value
= +
Raw overlay value Modeled overlay value Residual value
Figure 8.13 Separation of raw overlay data into modeled + residual values. The sampling shown here, four points per field and nine fields per wafer, is common for production monitoring.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Error Term Picture Coefficients
Translation
x, y
Rotation
xy
Magnification
mx, my
Trapezoid (keystone)
t1, t2
Lens Distortion
d3, d5
Figure 8.14 Illustration of field (reticle) model terms including higher-order trapezoid and distortion .
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Figure 8.15 Example of a stepper lens fingerprint showing in this case nearly random distortion across the lens field.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Scan Direction
Figure 8.16 Example of a scanner lens/scan fingerprint (figure used with permission). Note that errors in the scan direction are mostly averaged out by the scan.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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-0.3 -0.2 -0.1 0.0 0.1
Focus (m)
Exposure Dose (mJ/cm2)
14 16 18 20 22 24 26 30 34
0
50
100
150
200
250
Res
ist
Fea
ture
Wid
th, C
D
(nm
)
0.2
Figure 8.17 Example of the effect of focus and exposure on the resulting resist linewidth. Here, focal position is defined as zero at the top of the resist with a negative focal position indicating that the plane of focus is inside the resist.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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40
60
80
100
120
140
160
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Focus (um)
CD
(nm
)
7.0ln
ln
01,
FEEd
CDd
= 0.17 m
CD1 = 100 nm
E1 = 30 mJ/cm2
Figure 8.18 Plot of the simple Bossung model of equations (8.31) and (8.37) shows that it describes well the basic behavior observed experimentally.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Aerial Image Resist Profile
Top
Bottom
Top
Bottom
Aerial Image
Resist Profile
(a) (b)
Figure 8.19 Positioning the focal plane (a) above the top of the resist, or (b) below the bottom of the resist results in very different shapes for the final resist profile.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Focus (m)
140
120
100
90
80
70
CD = 110nm
Exp
osur
e (m
J/cm
2 )
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30
14 -0.3 -0.2 -0.1 0.0 0.1 0.2
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30
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
Focus (m)
14
CD
Sidewall Angle
Resist Loss
(a) (b)
Figure 8.20 Displaying the data from a focusexposure matrix in an alternate form: a) contours of constant CD versus focus and exposure, and b) as a focusexposure process window constructed from contours of the specifications for linewidth, sidewall angle, and resist loss.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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30
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
Exp
osur
e (m
J/cm
2 )
Focus (m)
14
Focus (m)
16
18
20
22
24
26
28
30
Exp
osur
e (
mJ/
cm2 )
14 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
(a) (b)
Figure 8.21 Measuring the size of the process window: (a) finding maximum rectangles; and (b) comparing a rectangle to an ellipse.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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2
4
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16
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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Exp
osu
re L
atitu
de (
%)
Ellipse
Rectangle
Depth of Focus (m)
Figure 8.22 The process window of Figure 8.20b is analyzed by fitting all the maximum rectangles and all the maximum ellipses, then plotting their height (exposure latitude) versus their width (depth of focus).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Res
ist L
ine
wid
th (
nm)
14 18 22 26 30 34
Focal Position (microns) -0.3 -0.2 -0.1 0.0 0.1 0.2
Exposure Energy (mJ/cm2)
Isofocal point
200
160
120
80
40
0
Res
ist L
ine
wid
th (
nm)
200
160
120
80
40
0
Figure 8.23 Two ways of plotting the focusexposure data set showing the isofocal point – the dose and CD that have minimum sensitivity to focus changes (for the left graph, each curve represents a different exposure dose; for the right graph, each curve is for a different focus).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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0
50
100
150
200
250
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
Res
ist
Fea
ture
Wid
th (
nm)
Focus (m)
0
20
40
60
80
100
120
140
160
180
Res
ist
Fea
ture
Wid
th (
nm)
Focus (m)
8 9 10 11 12 13 14 15 16 17 18
Dose 8 9 10 11 12 13 14 15 16 17 18
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
(a) (b)
Figure 8.24 Bossung plots for (a) dense and (b) isolated 130nm lines showing the difference in isofocal bias.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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20
22
24
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-0.5 0.0 0.5 Focus (microns)
Dos
e (m
J/cm
2)
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18
20
22
24
26
-0.5 0.0 0.5 Focus (microns)
Dos
e (
mJ/
cm2)
16
18
20
22
24
26
-0.5 0.0 0.5 Focus (microns)
Dos
e (m
J/cm
2)
(a) (b) (c)
Figure 8.25 Process windows calculated using equation (8.49) for a nominal line CD of 100 nm ±10 nm, nominal dose of 20 mJ/cm2, s = -1, and D = 0.45 microns: a) isofocal CD1 = 130 nm, b) isofocal CD1 = 100 nm, and c) isofocal CD1 = 70 nm.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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19
20
21
22 23
24 25
26
-0.2 -0.1 0.0 0.1
Exp
osur
e (m
J/cm
2 )
Focus (m)
Figure 8.26 The overlapping process window for the dense (dashed lines) and isolated (solid lines) features shown to the right of the graph.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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0
20
40
60
80
100
120
-0.3 -0.2 -0.1 0 0.1
Focus (m)
CD
(nm
)
Dense
Isolated
50
60
70
80
90
100
110
120
130
30 32 34 36 38 40
Exposure Dose (mJ/cm2)
CD
(n
m)
Dense
Isolated
20
21
22
23
24
25
26
27
30 32 34 36 38 40
Exposure Dose (mJ/cm2)
CD
den
se -
CD
iso
(nm
)
(a) (b)
20
25
30
35
40
45
-0.3 -0.2 -0.1 0 0.1
CD
dens
e -
CD
iso
(nm
)
Focus (m)
(c) (d)
Figure 8.27 A dual-target approach to monitoring dose and focus using a 90 nm dense line on a 220 nm pitch and an 80 nm isolated line: a) dense and isolated lines through dose; b) the iso-dense difference through dose; c) dense and isolated lines through focus; d) the iso-dense difference through focus.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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+ Focus - Focus Best Focus
Figure 8.28 The asymmetric response of resist sidewall angle to focus provides a means for monitoring focus direction as well as magnitude. Here , + focus is defined as placing the focal plane above the wafer (moving the wafer further away from the lens).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Defocus (microns)
H-V
Bia
s (n
m)
Equal Line/Space
Isolated Line
Figure 8.29 PROLITH simulations of HV bias through focus showing approximately linear behavior ( = 193nm, NA = 0.75, = 0.6, 150 nm binary features, 20 milliwaves of astigmatism). Simulations of CD through focus and fits to equation (8.57) gave the CD curvature parameter a = -184 m-2 for the dense features and -403 m-2 for the isolated lines.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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120
122
124
126
128
130
0.00 0.05 0.10 0.15 0.20
Sigma X-Shift
Line
wid
th (
nm)
Vertical
Horizontal
Figure 8.30 Example of how an x-shift in the center of a conventional source ( = 0.6) affects mainly the vertical (y-oriented) lines and spaces (CD = 130nm, pitch = 650nm, PROLITH simulations).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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-1st order +1st order0th order-1st order +1st order0th order
-1st order +1st order0th order-1st order +1st order0th order-1st order +1st order0th order
Figure 8.31 Example of dense line/space imaging where only the zero and first diffraction orders are used (kpitch = 1.05). The middle segment of each source circle represents three beam imaging, the outer areas are two beam imaging. a) source shape is properly centered, b) source is offset in x (to the right) by 0.1. Note that the diffraction pattern represents vertical (y-oriented) features.
(a) (b)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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-1st order +1st order
0th order
-1st order +1st order
0th order
(a) (b)
(c) (d)
Figure 8.32 Examples of how a telecentricity error affects the ratio of two beam to three beam imaging at the worst case pitch ( = 0.4, x-shift = 0.1, kpitch = 1.65). a) vertical lines, no telecentricity error, b) vertical lines, with telecentricity error, c) horizontal lines, no telecentricity error, and d) horizontal lines, with telecentricity error.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Res
ist
Fea
ture
Wid
th, C
D
(nm
)
Mask Width (constant duty) (nm)
Isolated Line
Line/Space
0 100 200 300 400 500 600 700 800 900 1000 1100 0
100
200
300
400
500
600
700
800
900
1000
1100
Figure 8.33 Typical mask linearity plot for isolated lines and equal lines and spaces (i-line, NA = 0.56, = 0.5).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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200 300 400 500 600 700 800
Mask CD (nm)
ME
EF
Isolated Line
Equal Line/Space
0
1
2
3
Figure 8.34 The mask error enhancement factor (MEEF) for the data of Figure 8.33.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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0.0
0.5
1.0
1.5
2.0
2.5
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Spacewidth/Linewidth
Ima
ge M
EE
F
Coherent
Incoherent
Figure 8.35 The impact of duty cycle (represented here as the ratio of spacewidth to linewidth for an array of line/space patterns) on the image CD based MEEF for both coherent and incoherent illumination. For the incoherent case, an MTF1 of 0.45 was used.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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-200 -100 0 100 200 0.0
0.3
0.6
0.9
1.2
Horizontal Position (nm)
Rel
ativ
e In
tens
ity
Effective dose error at the nominal line edge
Figure 8.36 Mask errors can be thought of as creating effective dose errors near the edge of the feature.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
100 200 300 400 500 600
Nominal Feature Width (nm)
ME
EF
high contrast
mid contrast
low contrast
Figure 8.37 Resist contrast affects the mask error enhancement factor (MEEF) dramatically near the resolution limit.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Y P
ositi
on (
nm)
X Position (nm)
-600
-400
-200
0
200
400
600
-800 -600 -400 -200 0 200 400 600 800
Y P
ositi
on (
nm)
X Position (nm)
-600
-400
-200
0
200
400
600
-400 -200 0 200 400
Figure 8.38 Outline of the printed photoresist pattern (solid) superimposed on an outline of the mask (dashed) shows two examples of line-end shortening (k1 = 0.6).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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150
200
250
300
350
400
Isolated Line Width (nm)
Gap
Wid
th (
nm)
Linewidth
Gap Width
150 200 250 300 350
Focus Exposure Data
Ideal Behavior
Target Operating Point
Figure 8.39 Line-end shortening can be characterized by plotting the gap width of a structure like that in the insert as a function of the isolated linewidth under a variety of conditions. As shown here, changes in focus and exposure produce a linear gap width versus linewidth behavior.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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+0.4 m Defocus In Focus -0.4 m Defocus
Figure 8.40 Simulated impact of focus on the shape of the end of an isolated line (250nm line, NA = 0.6, = 0.5, = 248, positive focus defined as shifting the focal plane up).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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35
40
45
50
55
60
65
70
75
80
0.6 0.7 0.8 0.9 1.0
Numerical Aperture
LES
(nm
)
35
40
45
50
55
60
0 0.2 0.4 0.6 0.8 1.0
Partial Coherence LE
S (
nm)
(a) (b)
Figure 8.41 Response of line-end shortening to imaging parameters (130 nm isolated line, = 248 nm): a) numerical aperture ( = 0.5), and b) partial coherence (NA = 0.85).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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0
10
20
30
40
50
60
0 20 40 60 80 100
Diffusion Length (nm)
Incr
ease
in L
ES
(nm
)
0
10
20
30
40
50
0 50 100 150
Diffusion Length (nm) In
crea
se in
LE
S (
nm)
(a) (b)
Figure 8.42 Diffusion can have a dramatic effect on line-end shortening of an isolated line: a) 180 nm line, = 248 nm, NA = 0.688, = 0.5, conventional resist, and b) 130 nm line, = 248 nm, NA = 0.85, = 0.5, chemically amplified resist.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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0
5
10
15
20
25
30
35
10 20 30 40 50
Point-by-point Error (nm)
Fre
que
ncy
CSE90
0
Figure 8.43 Defining a metric of shape error begins with a) making point-by-point measurements comparing actual (dashed) to desired (solid) shapes, which produces b) a frequency distribution of errors (unsigned lengths of the vectors are used here). One possible critical shape error (the CSE90) is shown as an example of the analysis of this distribution.
(a) (b)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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Figure 8.44 Examples of photoresist pattern collapse, both in cross-section (left) and top down (Courtesy of Joe Ebihara of Canon).
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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wlwlwsws
H
Figure 8.45 Pattern collapse of a pair of isolated lines: a) drying after rinse leaves water between the lines, and b) capillary forces caused by the surface tension of water pull the tops of the lines towards each other, leading to collapse.
(a) (b)