Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
c
d
b
g
e
a
f
h
i
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).
1
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.0
High leakage
current, device
fails
Devices are
too slow, poor
bin sort
0.6
0.4
Range affects
timing, which
affects max clock
speed possible
0.2
0
75
0.8
Frequency
Frequency
0.8
1.0
Leakage
current
limit
bin sort
limit
0.6
0.4
0.2
0
80
85
90
95
100
105
75
80
85
90
95
Gate CD (nm)
Gate CD (nm)
(a)
(b)
100
105
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.
2
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
140
Resist Linewidth
(nm)
120
100
80
EL =
E(CD – 10%) – E(CD + 10%)
Enominal
100%
60
20
25
30
35
40
2
45
Exposure Energy (mJ/cm )
Figure 8.3 The common CD versus exposure dose (E) curve is used to
measure exposure latitude (EL).
3
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Table 8.1 Examples of random focus errors (mm, 6s) for different lithographic generations.
Error Source
Lens Heating (Compensated)
Environmental (Compensated)
Mask Tilt (actual/16)
Mask Flatness (actual/16)
Wafer Flatness (over one field)
Chuck Flatness (over one field)
Laser Bandwidth
Autofocus Repeatability
Best Focus Determination
Vibration
Total RSS random focus errors
19911
i-line
0.50 m
0.10
0.20
0.05
0.12
0.30
0.14
0.0
0.20
0.30
0.10
0.60
19952
i-line
0.35 m
0.10
0.20
0.05
0.12
0.33
0.03
0.0
0.08
0.15
0.10
0.50
1995 2 [3]
KrF stepper
0.35 m
0.00
0.10
0.10
0.12
0.33
0.03
0.20
0.10
0.10
0.05
0.45
2001
KrF scanner
0.18 m
0.00
0.10
0.05
0.12
0.15
0.03
0.1
0.07
0.10
0.05
0.28
2005
ArF scanner
0.09 m
0.00
0.05
0.05
0.07
0.07
0.03
0.04
0.04
0.05
0.03
0.15
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.
1
4
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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.
Error Source
Topography
Field curvature & astigmatism
Resist Thickness
Total Systematic Errors (range)
Total Random Errors (6s)
Range/s
Total BIFE (6s equivalent)
1991
i-line
0.50 m
0.5
0.4
0.2
1.1
0.60
11
1.5
1995
i-line
0.35 m
0.3
0.4
0.2
0.9
0.50
10.8
1.2
1995
KrF stepper
0.35 m
0.3
0.3
0.2
0.8
0.45
10.7
1.1
2001
KrF scanner
0.18 m
0.10
0.08
0.10
0.28
0.28
6
0.47
2005
ArF scanner
0.09 m
0.05
0.05
0.05
0.15
0.15
6
0.25
5
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
D

w
Figure 8.4 Example photoresist profile and its corresponding “best fit” trapezoidal
feature model.
6
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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.
7
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1000
Feature Width (nm)
900
800
700
600
500
Threshold Fit
400
-1.5
-1.0
Straight Line Fit
-0.5
0.0
0.5
1.0
Focus (m)
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.
8
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Wafer
Pattern of
Exposure
Fields
Slit
Scan
Direction
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.
9
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Box-in-Box
Frame-in-Frame
Bar-in-Bar
Figure 8.8 Typical ‘box-in-box’ style overlay measurement targets, showing topdown 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.)
10
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
wXL
w
XL
wXR
w
XR
x-overlay = 0.5(wXL - wXR)
Figure 8.9 Measuring overlay as a difference in width measurements.
11
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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.)
12
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
y
y
(x*,y*)
(x*,y*)
(x,y)
(x,y)
x
(a)
x
(b)
Figure 8.11 Examples of two simple overlay errors: a) rotation, and b)
magnification errors.
13
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
(a)
(b)
Figure 8.12 Different types of rotation errors as exhibited on the wafer: a) reticle
rotation, and b) wafer rotation.
14
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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.
15
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Error Term
Picture
Coefficients
Translation
x, y
Rotation
xy
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 .
16
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Figure 8.15 Example of a stepper lens fingerprint showing in this case nearly
random distortion across the lens field.
17
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
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.
18
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Resist Feature Width, CD
(nm)
250
Exposure Dose
(mJ/cm2)
200
14
16
18
20
22
24
26
30
34
150
100
50
0
-0.3
-0.2
-0.1
0.0
0.1
0.2
Focus (m)
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.
19
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
160
CD (nm)
140
d ln CD
 0.7
d ln E E , F
1 0
120
 = 0.17 m
CD1 = 100 nm
100
80
E1 = 30 mJ/cm2
60
40
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Focus (um)
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.
20
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Aerial Image
Resist Profile
Aerial
Image
Resist Profile
Top
Top
Bottom
Bottom
(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.
21
Exposure (mJ/cm2)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
30
30
28
28
70
26
26
80
24
24
90
22
22
100
20
CD
120
18
140
16
14
-0.3
20
CD = 110nm
18
Sidewall Angle
16
Resist Loss
14
-0.2
-0.1
0.0
0.1
0.2
-0.4 -0.3
-0.2 -0.1
0.0
Focus (m)
Focus (m)
(a)
(b)
0.1
0.2
Figure 8.20 Displaying the data from a focusexposure matrix in an alternate form:
a) contours of constant CD versus focus and exposure, and b) as a focusexposure
process window constructed from contours of the specifications for linewidth,
sidewall angle, and resist loss.
22
30
30
28
28
Exposure (mJ/cm2)
Exposure (mJ/cm2)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
26
24
22
20
18
26
24
22
20
18
16
16
14
-0.4
14
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
-0.3
-0.2
-0.1
0.0
Focus (m)
Focus (m)
(a)
(b)
0.1
0.2
Figure 8.21 Measuring the size of the process window: (a) finding maximum
rectangles; and (b) comparing a rectangle to an ellipse.
23
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Exposure Latitude (%)
20
18
Ellipse
16
14
12
10
Rectangle
8
6
4
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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).
24
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
200
Resist Linewidth (nm)
Resist Linewidth (nm)
200
160
120
80
40
160
120
80
40
0
-0.3
-0.2
-0.1
0.0
0.1
0
14
0.2
18
22
26
30
34
Exposure Energy (mJ/cm2)
Focal Position (microns)
Isofocal
point
Figure 8.23 Two ways of plotting the focusexposure 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).
25
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
180
Resist Feature Width (nm)
Resist Feature Width (nm)
250
200
150
100
50
0
-0.4
-0.3
-0.2
-0.1
0.0
Focus (m)
(a)
0.1
0.2
160
Dose
140
8
9
10
11
12
13
14
15
16
17
18
120
100
80
60
40
20
0
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
Focus (m)
(b)
Figure 8.24 Bossung plots for (a) dense and (b) isolated 130nm lines showing
the difference in isofocal bias.
26
26
26
24
24
24
22
20
2
22
20
18
18
16
-0.5
Dose (mJ/cm )
26
Dose (mJ/cm2)
Dose (mJ/cm2)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.0
0.5
16
-0.5
22
20
18
0.0
0.5
16
-0.5
0.0
Focus (microns)
Focus (microns)
Focus (microns)
(a)
(b)
(c)
0.5
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.
27
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Exposure (mJ/cm2)
26
25
24
23
22
21
20
19
18
-0.2
-0.1
0.0
0.1
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.
28
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
27
120
26
(a)
CD (nm)
110
CDdense - CDiso (nm)
130
Dense
100
90
80
Isolated
70
24
(b)
23
22
21
60
50
30
25
32
34
36
38
40
20
30
Exposure Dose (mJ/cm2)
32
34
36
38
40
2
Exposure Dose (mJ/cm )
45
120
CD (nm)
(c)
CDdense - CDiso (nm)
Dense
100
80
60
40
20
0
-0.3
Isolated
-0.2
-0.1
Focus (m)
0
0.1
40
35
(d)
30
25
20
-0.3
-0.2
-0.1
0
0.1
Focus (m)
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
29
difference through focus.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
- Focus
Best
Focus
+ 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).
30
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
3.0
2.0
H-V Bias
(nm)
1.0
0.0
Equal Line/Space
-1.0
-2.0
-3.0
-0.20
Isolated Line
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Defocus (microns)
Figure 8.29 PROLITH simulations of HV bias through focus showing approximately
linear behavior (l = 193nm, NA = 0.75, s = 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.
31
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
130
Horizontal
Linewidth (nm)
128
126
124
Vertical
122
120
118
0.00
0.05
0.10
0.15
0.20
Sigma X-Shift
Figure 8.30 Example of how an x-shift in the center of a conventional source (s =
0.6) affects mainly the vertical (y-oriented) lines and spaces (CD = 130nm, pitch =
650nm, PROLITH simulations).
32
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
-1st order
0th order
(a)
+1st order
-1st order
0th order
+1st order
(b)
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.
33
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
(a)
(b)
+1st order
-1st order
0th order
(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 (s = 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.
34
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1100
Resist Feature Width, CD
(nm)
1000
900
800
700
600
Line/Space
500
400
300
200
100
Isolated Line
0
0
100 200 300 400 500 600 700 800 900 1000 1100
Mask Width (constant duty)
(nm)
Figure 8.33 Typical mask linearity plot for isolated lines and equal lines and
spaces (i-line, NA = 0.56, s = 0.5).
35
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
3
Equal Line/Space
MEEF
2
1
0
200
Isolated Line
300
400
500
600
700
800
Mask CD (nm)
Figure 8.34 The mask error enhancement factor (MEEF) for the data of Figure 8.33.
36
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
2.5
Image MEEF
2.0
Incoherent
1.5
Coherent
1.0
0.5
0.0
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Spacewidth/Linewidth
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.
37
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Relative Intensity
1.2
Effective
dose error at
the nominal
line edge
0.9
0.6
0.3
0.0
-200
-100
0
100
200
Horizontal Position (nm)
Figure 8.36 Mask errors can be thought of as creating effective dose errors near
the edge of the feature.
38
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
MEEF
3.5
3.0
high contrast
2.5
mid contrast
low contrast
2.0
1.5
1.0
0.5
0.0
100
200
300
400
500
600
Nominal Feature Width (nm)
Figure 8.37 Resist contrast affects the mask error enhancement factor (MEEF)
dramatically near the resolution limit.
39
600
600
400
400
Y Position (nm)
Y Position (nm)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
200
0
-200
200
0
-200
-400
-400
-600
-800 -600 -400 -200
-600
-400 -200
0
200
X Position (nm)
400
600
800
0
200
400
X Position (nm)
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).
40
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
400
FocusExposure Data
Linewidth
350
Gap Width (nm)
Gap Width
300
Ideal Behavior
250
200
150
150
Target Operating Point
200
250
300
350
Isolated Line Width (nm)
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.
41
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
+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, s = 0.5, l = 248, positive focus defined as shifting the focal
plane up).
42
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
80
60
75
55
LES (nm)
LES (nm)
70
65
60
55
50
45
50
45
40
40
35
35
0.6
0.7
0.8
0.9
1.0
0
0.2
0.4
0.6
0.8
Numerical Aperture
Partial Coherence
(a)
(b)
1.0
Figure 8.41 Response of line-end shortening to imaging parameters (130 nm
isolated line, l = 248 nm): a) numerical aperture (s = 0.5), and b) partial coherence
(NA = 0.85).
43
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
50
50
Increase in LES (nm)
Increase in LES (nm)
60
40
30
20
10
0
0
20
40
60
80
Diffusion Length (nm)
(a)
100
40
30
20
10
0
0
50
100
150
Diffusion Length (nm)
(b)
Figure 8.42 Diffusion can have a dramatic effect on line-end shortening of an
isolated line: a) 180 nm line, l = 248 nm, NA = 0.688, s = 0.5, conventional resist,
and b) 130 nm line, l = 248 nm, NA = 0.85, s = 0.5, chemically amplified resist.
44
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
35
Frequency
30
CSE90
25
20
15
10
5
0
0
10
20
30
40
50
Point-by-point Error (nm)
(a)
(b)
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.
45
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Figure 8.44 Examples of photoresist pattern collapse, both in cross-section (left)
and top down (Courtesy of Joe Ebihara of Canon).
46
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007

H
wl
ws
(a)
(b)
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.
47