Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Development Rate (nm/s)
100
n = 16
80
60
n=2
40
20
0
0.0
0.2
0.4
0.6
0.8
1.0
Relative Inhibitor Concentration m
Figure 7.1 Development rate plot of the original kinetic model as a function of the
dissolution selectivity parameter (rmax = 100 nm/s, rmin = 0.1 nm/s, mth = 0.5, and n =
2, 4, 8, and 16).
1
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
100
Development Rate (nm/s)
Development Rate (nm/s)
100
80
n=1
60
40
n=5
20
n=9
0
0.0
0.2
0.4
0.6
0.8
Relative Inhibitor Concentration m
(a)
1.0
80
60
40
20
l=1
l=5
0
0.0
0.2
l = 15
0.4
0.6
0.8
1.0
Relative Inhibitor Concentration m
(b)
Figure 7.2 Plots of the enhanced kinetic development model for rmax = 100 nm/s,
rresin = 10 nm/s, rmin = 0.1 nm/s with: (a) l = 9; and (b) n = 5.
2
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1000
100
Development Rate (nm/s)
Development Rate (nm/s)
1000
10
1
0.1
0.00
0.05
0.10
0.15
0.20
0.25
0.30
100
10
1
0.1
0.00
0.05
0.10
0.15
0.20
0.25
Initial Inhibitor Concentration (w t fraction)
Initial Inhibitor Concentration (w t fraction)
(a)
(b)
0.30
Figure 7.3 An example of a Meyerhofer plot, showing how the addition of increasing
concentrations of inhibitor increases rmax and decreases rmin: a) idealized plot
showing a log-linear dependence on initial inhibitor concentration, and b) the
enhanced kinetic model assuming kenh  M0 and kinh  M02.
3
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Development Rate (nm/s)
50
40
30
20
10
0
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Relative Inhibitor Concentration m
Figure 7.4 Comparison of experimental dissolution rate data (symbols) exhibiting
the so-called ‘notch’ shape to best fits of the original (dotted line) and enhanced
(solid line) kinetic models. The data shows a steeper drop in development rate at
about 0.5 relative inhibitor concentration than either model predicts.
4
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
50
Development Rate (nm/s)
Develo pment Rate (nm/s)
50
40
30
20
10
mth_notch = 0.5
m th_notch = 0.4
0
0.30
0.35
0.40
40
30
20
10
n_notch = 15
n_notch = 60
0.45
0.50
0.55
Relative Inhibitor Concentration m
(a)
0.60
0
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Relative Inhibitor Concentration m
(b)
Figure 7.5 Plots of the notch model: (a) mth_notch equal to 0.4, 0.45, and 0.5 with
n_notch equal to 30; and (b) n_notch equal to 15, 30, and 60 with mth_notch equal to
0.45.
5
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Relative Development Rate
1.25
1.00
0.75
0.50
0.25
0.00
0.0
0.2
0.4
0.6
0.8
1.0
Relative Depth into Resist
Figure 7.6 Example surface inhibition with r0 = 0.1 and d = 100 nm for a 1000 nm
thick resist.
6
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Development Rate (nm/s)
100
30 °C
80
60
14 °C
40
20
0
0
100
200
300
400
500
2
Exposure Dose (mJ/cm )
Figure 7.7 Development rate of THMR-iP3650 (averaged through the middle 20% of
the resist thickness) as a function of exposure dose for different developer
temperatures shows a change in the shape of the development dose response. 7
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Development Rate (nm/s)
200
160
120
30 °C
80
40
14 °C
0
0.0
0.2
0.4
0.6
0.8
1.0
Relative Inhibitor Concentration m
Figure 7.8 Comparison of the best-fit models of THMR-iP3650 for different
developer temperatures shows the effect of increasing rmax and increasing
dissolution selectivity parameter n on the shape of the development rate curve.
8
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
200
8
Dissolution n
Dissolution rmax (nm/s)
7
100
50
3.25
3.30
3.35
3.40
3.45
3.50
6
5
4
3
3.25
3.30
3.35
3.40
3.45
1000/Developer Temperature (K)
1000/Developer Temperature (K)
(a)
(b)
3.50
Figure 7.9 Arrhenius plots of the maximum dissolution rate rmax and the
dissolution selectivity parameter n for THMR-iP3650.
9
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
4.0
Optical Density
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Log (Exposure Dose)
Figure 7.10 An example Hurter-Driffield (H-D) curve for a photographic negative.
10
Relative Thickness R emaining
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1
10
100
1000
Exposure Dose (mJ/cm2 )
Figure 7.11 Positive resist characteristic curve used to measure contrast.
11
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Development Rate (nm/s)
1000
100
10
1
0.1
0.01
1
10
100
1000
Exposure Dose (mJ/cm2 )
Figure 7.12 A lithographic H-D curve used to define the theoretical contrast.
12
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Theoretical Contrast
6
5
4
3
2
1
0
1
10
100
1000
Exposure Dose (mJ/cm2 )
Figure 7.13 A typical variation of theoretical contrast with exposure dose. For this
data, the FWHM dose ratio is about 5.5.
13
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Development
Path
Resist
Substrate
Figure 7.14 Typical development path.
14
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
z
s
x
Path
Figure 7.15 Section of a development path relating path length s to x and z.
15
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
x (nm)
-200
0
-100
0
100
200
50
z (nm)
100
150
200
250
300
350
Resi st
400
Figure 7.16 Example of how the calculation of many development paths leads to
the determination of the final resist profile.
16
1.2
1.2
1.0
1.0
Relative Intensity
Relative Intensity
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.8
0.6
0.4
Gaussian
0.8
0.6
0.4
Gaussian
0.2
0.2
Aerial Image
Aerial Image
0.0
0.0
0
0.1
0.2
0.3
x/pitch
(a)
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
x/pitch
(b)
Figure 7.17 Matching a three-beam image (a0 = 0.45, a1 = 0.55, a2 = 0.1) with a
Gaussian using a) a value of s given by equation (7.91); and b) the best fit s.
Note the goodness of the match in the region of the space (x/pitch < 0.25).
17
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
20
20
Space Line
16
14
12
10
8
6
4
2
0
-0.15
Space Line
18
Image Log -slope (1/ m)
Image Log -slope (1/ m)
18
16
14
12
10
8
6
4
2
-0.10
-0.05
0
0.05
Distance from nominal edge (k1 units)
(a)
0.10
0
-0.15
-0.10
-0.05
0
0.05
0.10
Distance from nominal edge (k1 units)
(b)
Figure 7.18 Simulated aerial images over a range of conditions show that the
image log-slope varies about linearly with distance from the nominal resist edge in
the region of the space: a) k1 = 0.46 and b) k1 = 0.38 for isolated lines, isolated
spaces, and equal lines and spaces and for conventional, annular and quadrupole
illumination.
18
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.6
0.5
Dw(z)
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
z
Figure 7.19 A plot of Dawson’s Integral, Dw(z).
19
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
180
160
CD (nm)
140
120
VTR
100
80
60
LPM and Approximate LPM
40
20
0.9
1.4
1.9
2.4
2.9
E/E(0)
Figure 7.20 CD versus dose curves as predicted by the LPM equation (7.98), the
LPM using the approximation for the Dawson’s integral, and the VTR. All models
assumed a Gaussian image with g = 0.0025 1/nm2 (NILS1 = 2.5 and CD1 = 100
nm), g = 10, and Deff = 200 nm.
20
1200
1200
960
960
Resist Thickness (nm)
Resist Thickness (nm)
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
720
480
240
0
720
480
240
0
0
100
200
300
400
2
Exposure Dose (mJ/cm )
(a)
500
0
20
40
60
80
100
2
Exposure Dose (mJ/cm )
(b)
Figure 7.21 Measured contrast curves for an i-line resist at development times
ranging from 9 to 201 seconds (shown here over two different exposure scales).
21
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
120
r max = 100.3 nm/s
96
Development Rate
(nm/s)
r min = 0.10 nm/s
mth = 0.06
72
n = 4.74
RMS Error: 2.7 nm/s
48
24
0
0.0
0.2
0.4
0.6
0.8
1.0
Relative Inhibitor Concentration m
Figure 7.22 Analysis of the contrast curves generates an r(m) data set, which was
then fit to the original kinetic development model (best fit is shown as the solid line).
22