Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Mask
Light Source
Condenser Lens
Objective Lens
Wafer
Figure 2.1 Block diagram of a generic projection imaging system.
1
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Plane Wave Propagation
Diffraction by a Slit
Figure 2.2 Pictorial representation of Huygens’ principle, where any wavefront
can be thought of as a collection of point sources radiating spherical waves.
2
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Fraunhofer
Diffraction
Region
(z » w2/)
Kirchhoff
Diffraction Region
(z > /2)
Fresnel
Diffraction
Region
(z » w)
Figure 2.3 Comparison of the diffraction ‘regions’ where various approximations
become accurate. Diffraction is for a slit of width w illuminated by light of
wavelength , and z is the distance away from the mask.
3
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
mask
tm(x)
1
0
Tm(fx)
0
0
fx
Figure 2.4 Two typical mask patterns, an isolated space and an array of equal lines
and spaces, and the resulting Fraunhofer diffraction patterns assuming normally
incident plane wave illumination. Both tm and Tm represent electric fields.
4
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.0
Intensity
0.8
0.6
0.4
0.2
0.0
-3
-2
-1
0
1
2
3
w fx
Figure 2.5 Magnitude of the diffraction pattern squared (intensity) for a single
space (thick solid line), two spaces (thin solid line), and three spaces (dashed
lines) of width w. For the multiple-feature cases, the linewidth is also equal to w.
5
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Aperture
(x’, y’)-plane
Object
Plane
max
Entrance
Pupil
Objective
Lens
Figure 2.6 The numerical aperture is defined as NA = nsinmax where max is the
maximum half-angle of the diffracted light that can enter the objective lens, and
n is the refractive index of the medium between the mask and the lens.
6
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Mask
(Object)
Entrance Pupil
Objective
Lens
Exit Pupil
Wafer
(Image)
Figure 2.7 Formation of an aerial image: a pattern of lines and spaces
produces a diffraction pattern of discrete diffraction orders (in this case, three
orders are captured by the lens). The lens turns these diffraction orders into
plane waves projected onto the wafer, which interfere to form the image.
7
Amplitude
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.5

3
p
3
p

2
p

1
p
0
1
p
2
p
fx
Figure 2.8 Graph of the diffraction pattern for equal lines and spaces plotted out to
±3rd diffraction orders. For graphing purposes, the delta function is plotted as an
arrow, the height equal to the amplitude multiplier of the delta function.
8
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.4
Relative Intensity
1.2
N=1
N=3
N=9
1.0
0.8
0.6
0.4
0.2
0.0
-w
-w/2
0
w/2
w
Horizontal Position
Figure 2.9 Aerial images for a pattern of equal lines and spaces of width w as a
function of the number of diffraction orders captured by the objective lens (coherent
illumination). N is the maximum diffraction order number captured by the lens.
9
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Normalized Intensity
1.0
0.8
0.6
0.4
0.2
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Normalized Radius = rNA/
Figure 2.10 Ideal point spread function (PSF), the normalized image of an infinitely
small contact hole. The radial position is normalized by multiplying by NA/.
10
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Refractive index on
wafer side = nw
m
Refractive index on
mask side = nm
w
Entrance
Pupil
Aperture
Stop
Exit
Pupil
Figure 2.11 An imaging lens with reduction R scales both the lateral dimensions
and the sine of the angles by R.
11
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
2.0
Pupil Transmittance
1.8
1.6
1.4
1.2
1.0
0.8
0
0.2
0.4
0.6
0.8
1.0
sin(angle)
Figure 2.12 A plot of the radiometric correction as a function of the wafer-side
diffraction angle (R = 4, nw/nm = 1).
12
Wafer Plane Open Field Intensity
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.24
1.20
1.16
1.12
1.08
1.04
1.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Partial Coherence
Figure 2.13 One impact of the radiometric correction: the intensity at the wafer
plane for a unit amplitude mask illumination as a function of the partial coherence
factor (R = 4, NA = 0.9).
13
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Mask Pattern
(equal lines and spaces)
Diffraction Pattern
Lens Aperture
Figure 2.14 The effect of changing the angle of incidence of plane wave illumination
on the diffraction pattern is simply to shift its position in the lens aperture. A positive
illumination tilt angle is depicted here.
14
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Mask Pattern
(equal lines and spaces)
Diffraction Pattern
Lens Aperture
Figure 2.15 The diffraction pattern is broadened by the use of partially coherent
illumination (plane waves over a range of angles striking the mask).
15
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Lens Aperture
-1st
Lens Aperture
0th
(a)
+1st
-1st
0th
+1st
(b)
Figure 2.16 Top-down view of the lens aperture showing the diffraction pattern of
a line/space pattern when partially coherent illumination is used: a) s = 0.25; and
b) s = 0.5.
16
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
-1st order
0th order
+1st order
Figure 2.17 Example of dense line/space imaging where only the zero and first
diffraction orders are used. Black represents three beam imaging, lighter and
darker grays show the area of two beam imaging.
17
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Conventional
Annular
Quadrupole
Dipole
Figure 2.18 Conventional illumination source shape, as well as the most popular
off-axis illumination schemes, plotted in spatial frequency coordinates. The outer
circle in each diagram shows the cut-off frequency of the lens.
18
1.0
1.0
0.5
0.5
Y Pupil Position
Y Pupil Position
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
0.0
-0.5
-1.0
-1.0
-0.5
0.0
0.5
1.0
0.0
-0.5
-1.0
-1.0
-0.5
0.0
0.5
X Pupil Position
X Pupil Position
(a)
(b)
1.0
Figure 2.19 Examples of measured annular source shapes (contours of constant
intensity) from two different lithographic projection tools showing a more
complicated source distribution than the idealized ‘top-hat’ distributions.
19
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Lens Pupil
st
-1 order
st
+1 order
Figure 2.20 Annular illumination example where only the 0th and ±1st diffracted
orders pass through the imaging lens.
20
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Mask
Mask
Illumination
Wavefront
(a)
Objective Lens
(b)
Figure 2.21 The impact of illumination: a) when illuminated by a plane wave,
patterns at the edge of the mask will not produce diffraction patterns centered in
the objective lens pupil, but b) the proper converging spherical wave produces
diffraction patterns that are independent of field position.
21
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Entrance
Pupil
Mask
Source
Objective
Lens
Figure 2.22 Köhler illumination where the source is imaged at the entrance pupil
of the objective lens and the mask is placed at the exit pupil of the condenser
lens.
22
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.0
0.8
fx
0
MTF
NA

0.6
0.4
f
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
f/(2NA/)
(a)
(b)
Figure 2.23 The MTF(f) is the overlapping area of two circles of diameter NA/
separated by an amount f, as illustrated in a) and graphed in b).
23
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
Y Position (nm)
600
400
200
0
-200
-400
-600
-1000
-500
0
500
1000
X Position (nm)
Y Position (nm)
1000
Figure 2.24 Some examples of two-dimensional
aerial image calculations (shown as contours of
constant intensity), with the mask pattern on the
left (dark representing chrome).
500
0
-500
-1000
-1000
0
1000
X Position (nm)
24
Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007
1.4
Relative Intensity
1.2
1.0
0.8
s=0
s = 0.3
s = 0.6
s = 0.9
0.6
0.4
0.2
0.0
-0.8
-0.4
0.0
0.4
0.8
1.2
1.6
Horizontal Position (xNA/)
Figure 2.25 Aerial images of an isolated edge as a function of the partial coherence
factor.
25