Download Chapter4_Figures

Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
EI
Air
Resist
n1
D
Substrate
(a)
Air
z=0
n2
Resist
n3
Substrate
(b)
Figure 4.1 Film stack showing (a) the geometry for the standing wave derivation,
and (b) a normally incident electric field EI.
1
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.8
Relative Intensity
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
200
400
600
800
1000
Depth into Resist (nm)
Figure 4.2 Standing wave intensity in one micron of photoresist on a silicon
substrate for an i-line exposure.
2
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.6
Relative Intensity
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
200
400
600
800
1000
Depth into Resist (nm)
Figure 4.3 Standing wave intensity within a photoresist film at the start of exposure
(850nm of resist on 100nm SiO2 on silicon, l = 436nm). Note the impact of the
oxide film on the phase of the effective substrate reflectivity, which affects the
intensity at the bottom of the resist.
3
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
x
Substrate

k
(x,z)

r

z
Plane
wave
z=0
Figure 4.4 Geometry used for describing plane waves and standing waves for
oblique incidence.
4
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.50
Intensity Reflectivity (|12|2)
0.45
p-polarization
0.40
s-pol.
0.35
air
resist
0.30
0.25
0.20
s-polarization
0.15
0.10
0.05
p-polarization
0.00
0
10
20
30
40
50
60
70
80
90
Incident Angle (degrees)
Figure 4.5 Reflectivity (square of the reflection coefficient) as a function of the
angle of incidence showing the difference between s- and p-polarization (n1 = 1.0,
n2 = 1.7). Both air and resist layers are assumed to be infinitely thick.
5
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
2.5
angle = 0
angle = 30
Relative Intensity
2.0
1.5
1.0
0.5
0.0
0
100
200
300
400
500
Depth into Resist (nm)
Figure 4.6 Standing wave intensity within a photoresist film (500 nm of resist on
silicon, l = 248 nm) as a function of incident angle (s-polarization assumed).
6
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Relative Intensity
1.0
I-Line
H-Line
0.8
G-Line
0.6
E-Line
0.4
0.2
0.0
200
250
300
350
400
450
500
550
600
Wavelength (nm)
Figure 4.7 Spectral output of a typical high-pressure mercury arc lamp. The
illumination spectrum of an i-line or g-line lithographic exposure tool is usually a
filtered portion of this lamp spectrum.
7
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
3.0
single wavelength
broadband
Relative Intensity
2.5
2.0
1.5
1.0
0.5
0.0
0
200
400
600
800
1000
Depth into Resist (nm)
Figure 4.8 Standing wave intensity within a photoresist film (1000 nm of resist on
silicon), for monochromatic (l = 365 nm) and broadband illumination (350 – 450 nm
range of the mercury spectrum).
8
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Resist Linewidth (m)
0.65
0.60
0.55
0.50
0.45
0.40
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Resist Thickness (m)
Figure 4.9 CD swing curve showing a sinusoidal variation in the resist linewidth
with resist thickness (i-line exposure of resist on silicon).
9
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Dose to Clear (mJ/cm2)
100
90
80
70
60
50
40
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Resist Thickness (m)
Figure 4.10 Eo swing curve showing a sinusoidal variation in the resist dose-toclear with resist thickness (i-line exposure of resist on silicon).
10
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.30
Reflectivity
0.25
0.20
0.15
0.10
0.05
0.00
0.90
0.95
1.00
1.05
1.10
1.15
1.20
Resist Thickness (m)
Figure 4.11 Reflectivity swing curve showing a sinusoidal variation in the resist
coated wafer reflectivity with resist thickness (i-line exposure of resist on silicon).
11
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Air
Air
n1
EI
Er0 Er1
z=0
Resist
Substrate
D
n2
Resist
n3
Substrate
Figure 4.12 Film stack showing (a) geometry for swing curve derivation, and (b)
incident, transmitted, and reflected waves (oblique angles are shown for
diagrammatical purposes only).
12
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Dose-to-Clear, E0 (mJ/cm2)
150
140
NA = 0.0
NA = 0.2
NA = 0.3
NA = 0.4
NA = 0.5
130
120
110
100
90
1.00
1.05
1.10
1.15
1.20
Resist Thickness (microns)
Figure 4.13 The phase and amplitude of a dose-to-clear swing curve are affected
by the range of angles striking the resist, which is controlled by the product of the
partial coherence and the numerical aperture (NA) for conventional illumination.13
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Resist Feature Width, CD (nm)
260
240
220
200
180
160
140
200
220
240
260
280
300
320
340
360
380
400
Resist Thickness (nm)
Figure 4.14 Proper balancing of absorption and reflectivities can make the
minimum of a swing curve (D = 310 nm) achieve the same CD as the previous
swing curve maximum (D = 280 nm).
14
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Substrate Reflectivity
Substrate Reflectivity
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
First Minimum BARC
0.2
0.2
0.1
0.1
0.0
0
20
40
60
80
100
Thickness Layer #2 (nm)
120
140
0.0
0
Second Minimum BARC
20
40
60
80
100
120
140
Thickness Layer #2 (nm)
Figure 4.15 Typical examples of substrate reflectivity versus BARC thickness for
different resist/BARC/substrate stacks.
15
2.4
0.75

2.2
0.70
0.65
2.0
0.60
1.8
0.55
n
0.50
1.6
0.45
1.4
0.40
1.2
1.0
10
0.35
0.30
20
30
40
50
BARC Thickness (nm)
(a)
60
0.41
2.8
2.6
0.36
2.4

2.2
2.0
0.31
n
0.26
1.8
1.6
0.21
1.4
1.2
50
70
90
110
Refractive Index - imaginary
0.80
Refractive Index - real
2.6
Refractive Index - imaginary
Refractive Index - real
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.16
130
BARC Thickness (nm)
(b)
Figure 4.16 Optimum BARC refractive index (real and imaginary parts, n and k)
as a function of BARC thickness for normal incidence illumination (resist index =
1.7 + i0.01536 and silicon substrate index = 0.8831 + i2.778) at 193 nm. a) First
minimum BARCs, and b) second minimum BARCs.
16
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.005
1.4
1.2
1.0
2
0.003
R/|n|
2
2
R/ (1/nm )
0.004
0.002
0.8
0.6
0.4
0.001
0.2
0.000
0.0
0
20
40
60
Optimum BARC Thickness (nm)
(a)
80
0
10
20
30
40
50
60
70
Optimum BARC Thickness (nm)
(b)
Figure 4.17 Sensitivity of substrate reflectivity for the optimum first minimum
BARCs of Figure 4.16a as a function of a) BARC thickness errors, or b) BARC
refractive index errors.
17
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.0016
2.5
2.0
0.0012
2
R/ (1/nm )
0.0014
R/|n|
2
0.0010
2
0.0008
0.0006
0.0004
1.5
1.0
0.5
0.0002
0.0000
50
70
90
110
130
0.0
50
70
90
110
Optimum BARC Thickness (nm)
Optimum BARC Thickness (nm)
(a)
(b)
130
Figure 4.18 Sensitivity of substrate reflectivity for the optimum second minimum
BARCs of Figure 4.16b as a function of a) BARC thickness errors, or b) BARC
refractive index errors.
18
2.19
0.715
2.18
0.710
2.17
0.705
0.700
2.16
0.695
2.15

n
2.14
0.690
0.685
2.13
0.680
2.12
0.675
D = 20 nm
2.11
0.670
2.10
0.665
0
10
20
30
40
50
60
70
1.68
0.510
1.66
0.505
1.64
0.500
1.62
1.60

n
1.58
0.495
0.490
1.56
0.485
1.54
D = 40 nm
0.480
1.52
1.50
Refractive Index - imaginary
0.720
Refractive Index - real
2.20
Refractive Index - imaginary
Refractive Index - real
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.475
0
10
20
30
40
50
Angle (in air, degrees)
Angle (in air, degrees)
(a)
(b)
60
70
Figure 4.19 Optimum BARC parameters to achieve minimum substrate reflectivity
as a function of incident angle (angle defined in air, before entering the photoresist)
for two different BARC thicknesses (resist index = 1.7 + i0.01536 and silicon
substrate index = 0.8831 + i2.778) at 193 nm exposure: a) 20 nm BARC thickness,
and b) 40 nm BARC thickness.
19
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Minimum Intensity Reflectivity
0.0030
D = 20nm
0.0025
0.0020
0.0015
D = 40nm
0.0010
0.0005
0.0000
0
10
20
30
40
50
60
70
Angle (in air, degrees)
Figure 4.20 The best case (minimum) reflectivity (using the BARC parameters
shown in Figure 4.19) of the substrate as a function of incident angle for 20nm and
40nm thick BARC films. Note that 60º corresponds to the maximum angle in air
allowed for NA = 0.866.
20
Resist/BARC Electric Field Reflectivity
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.20
B: s-polarized
0.15
A: p-polarized
0.10
0.05
A: s-polarized
B: p-polarized
0.00
0
10
20
30
40
50
60
70
80
Angle in Air (degrees)
Figure 4.21 An example of the variation of BARC reflectivity as a function of light angle
and polarization for two different BARCs. The intensity reflectivity is the square of the
electric field reflectivity plotted here, but interference makes the field reflectivity a better
measure of the standing wave effects. (Resist index = 1.7 + i0.01536, silicon substrate
index = 0.8831 + i2.778, BARC A index = 1.80 + i0.48, BARC A thickness = 30 nm,
BARC B index = 1.53 + i0.54, BARC B thickness = 39 nm.)
21
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.7
Oxide Thickness
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
Substrate Reflectivity
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
20
40
60
80
100
120
140
Thickness Layer #2
(nm)
Figure 4.22 Substrate reflectivity versus BARC thickness over a range of underlying
oxide thicknesses (oxide on top of a silicon substrate).
22
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Resist Feature Width, CD (nm)
130
120
R = 0.07%
110
100
90
80
150
R = 0.43%
160
170
180
190
200
210
220
230
240
250
Resist Thickness (nm)
Figure 4.23 CD swing curves (100nm lines with a 280nm pitch are printed with a
stepper using annular illumination, with a center sigma given by NA = 0.54) for two
different BARCs with different levels of optimization, as given by the resulting
23
substrate reflectivity R.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Side View
resist
Swing Curve
Maximum
Top View
or
Swing Curve
Minimum
Top of Step
Bottom of Step
Figure 4.24 Example of how resist thickness variations over topography produce
linewidth variations due to swing curve effects when a BARC is not used.
24
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
resist
Figure 4.25 Reflective notching occurs when nearby topography reflects light
obliquely into an adjacent photoresist feature.
25
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Figure 4.26 Imaging of lines and spaces over reflective topography without BARC
(left) showing reflective notching, and with BARC (right) showing the reflective
notching effectively suppressed (photos courtesy of AZ Photoresist, used with
permission).
26
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Incident Aerial Image
CEL
Image Transmitted
Through the CEL
Figure 4.27 Contrast Enhancement Layer (CEL) bleaching improves the quality of
the aerial image transmitted into the photoresist.
27
0.85
200
0.80
100
0.75
0
0.70
-100
0.65
25
75
125
175
Phase (degrees)
Magnitude, ||
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
-200
225
Nitride Thickness (nm)
Figure 4.28 Variation of the magnitude and phase of the resist/substrate reflection
coefficient as a function of silicon nitride thickness for a film stack of resist on nitride
on 40 nm of oxide on silicon.
28
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Dose to Clear (mJ/cm2)
175
93nm Nitride
136nm Nitride
150
125
100
75
0.90
0.95
1.00
1.05
1.10
Resist Thickness (microns)
Figure 4.29 Changes in nitride thickness cause a shift in the phase of the resist
swing curve, making nitride thickness control as critical as resist thickness control.
29
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Substrate Reflectivity
1.0
0.8
0.6
0.4
0.2
0.0
25
75
125
175
225
Nitride Thickness (nm)
Figure 4.30 Nitride thickness also affects the shape of the resist profile, causing
resist footing, undercuts, or vertical profiles. Substrate reflectivity (the square of the
magnitude of the reflection coefficient) is shown for comparison.
30
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007

E1

E2
TE or s-polarization

E1

E2
TM or p-polarization
Figure 4.31 Two plane waves with different polarizations will interfere very
differently. For transverse electric (TE) polarization (electric field vectors pointing
out of the page), the electric fields of the two vectors overlap completely regardless
of the angle between the interfering beams.
31
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.2
Contrast or NILS/
1.0
0.8
0.6
0.4
Aerial Image
0.2
Image in Resist
0.0
0
10
20
30
40
50
Angle in Air (degrees)
Figure 4.32 The interference between two TM polarized planes waves produces an
image whose contrast and NILS depends on the angle. Since the angle in resist is
reduced by refraction, the contrast and NILS of the image in resist is better than the
32
aerial image.
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
(a)
(b)
Figure 4.33 Focusing of plane waves arriving at different angles a) in air, and b) in
resist, showing that the resist induces spherical aberration.
33
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Mask
0.30
0.25
SWAR
0.20
2(0)
Center
of
Space
0.15
Line
Edge
0.10
Line
Edge
0.05
0.00
-100
-80
-60
-40
-20
0
20
40
60
80
100
Horizontal Position (nm)
Figure 4.34 The standing wave amplitude ratio (SWAR) at different positions on the
feature for coherent three-beam imaging and s-polarization. For this example of
three-beam imaging of 100 nm lines and spaces, ao = 0.5, a1 = 0.3183.
34
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.0
T, s-pol.
T, p-pol.
T or It/Ii
0.8
0.6
It/Ii, p-pol.
0.4
0.2
It/Ii, s-pol.
0.0
0
20
40
60
80
Incident Angle (degrees)
Figure 4.35 Intensity transmitted into layer 2 relative to the incident intensity (solid
lines) and the transmittance T (dashed lines) as a function of the angle of incidence
for both s and p polarization (n1 = 1.0, n2 = 1.5).
35