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Photolithography:
The Basics of Projection Printing
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Photolithography
Photolithography is at the Center of the WaferFabrication Process
*
Thin Films
Implant
Diffusion Etch
Test/Sort
Polish
PhotoPatterned
wafer
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Photolithography Types
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Projection System
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
4
Light Source
Condenser Lens
Mask
Objective LensWafer
Block diagram of a generic projection imaging system
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Projection System
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
5
Light Source
Condenser Lens
Mask
Objective LensWafer
Illumination SystemIllumination system delivers light to the maskSufficient intensity
Proper directionality
Proper spectral characteristics
Adequate uniformity across the field
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Projection System
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
6
Light Source
Condenser Lens
Mask
Objective LensWafer
Illumination System
Mask
changes the transmittance of the light
Causes diffraction
Diffraction
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Projection System
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
7
Light Source
Condenser Lens
Mask
Objective LensWafer
Illumination System
Objective lens
Picks up a portion of the diffraction pattern
Projects the image onto the photoresist
Image Formation
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Diffraction Analysis
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
8
Light Source
Condenser Lens
Mask
Objective LensWafer
Illumination System
Mask
changes the transmittance of the light
Causes diffraction
Diffraction
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Diffraction
Theory of propagation of light
Solution to Maxwells Equations: complicated
Diffraction Integrals for far field: simpler
Light propagation in homogenous medium
FresnelDiffraction
Region
(z w)
KirchhoffDiffraction Region
(z > /2)
FraunhoferDiffractionRegion
(z w2/)
Fraunhofer Diffraction Integrals
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Fraunhofer Diffraction Integral
Mask Transmittance Function:
How does the mask transmit light?
Requires the solution of Maxwells equations for
that material: complicated!
Kirchhoff boundary condition
Feature size > 2 && chrome thickness < /2
Ignore diffraction caused by mask topography
),( yxtm
chrome0
regionnttranspare1),(
yxtm
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Fraunhofer Diffraction Integral
maskat theincidentfieldElectric:),(
functionmittancemask trans:),(
mediumtheofindexrefractive:
planendiffractiomask tofromdistance:
lightofhwavelengt:
planendiffractio:plane''
planemask:plane
yxE
yxt
n
z
yx
yx
Given
m
dxdyeyxtyxEffTyfxfi
myxmyx )(2),(),(),(
z
nyf
z
nxf
ff
ffT
where
yx
yx
yxm
',
'
patternndiffractioofsfrequencieSpatial:,
patternndiffractiotheoffieldElectric:),(
Fourier Optics
The diffraction pattern is
just the fourier transform
of the mask pattern
transmittance!
)),(),((),( yxtyxEFffT myxm
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Diffraction Examples
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
12
x00
mask
01
Tm(fx)
tm(x)
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.
x
xxm
f
wffT
)sin()(
j
x
x
xxm
p
jf
f
wf
p
fT )()sin(1
)(
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Chris A. Mack, Fundamental
Principles of Optical
Lithography, (c) 2007
13
0.0
0.2
0.4
0.6
0.8
1.0
-3 -2 -1 0 1 2 3
w fx
Intensity
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.
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Image Formation: Imaging Lens
Chris A. Mack, Fundamental Principles ofOptical Lithography, (c) 2007
14
Light Source
Condenser Lens
Mask
Objective LensWafer
Illumination System
Objective lens
Picks up a portion of the diffraction pattern
Projects the image onto the photoresist
Image Formation
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Imaging Lens
The diffraction pattern extends throughout
the x-y plane
The objective lens (finite size) can only capture
a part of this pattern
Higher spatial frequencies lost
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16
Aperture
(x, y)-plane
ObjectPlane
max
ObjectiveLens
EntrancePupil
maxsinnNA
NA
p
n
z
nyf
n
z
nxf
y
y
xx
min
1
sin'
sin'
NA/ : The maximum spatial frequency that can enter the lens
Large NA => larger portion of diffraction pattern is captured => better image
NA
KR
1
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Formation of the Image
Lens Pupil Function
Mathematical description of the amount of the
light entering the lens
Lens performs the inverse fourier transform of
the transmitted diffracted pattern
NA
ff
NAffffP
yx
yxyx
22
22
,0
,1),(
),(),(),(),(),(
1
yxyxM ffPffTFyxE
yxgyxgFF
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18
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-w -w/2 0 w/2 w
Horizontal Position
Rela
tiveIntensity N = 1
N = 3
N = 9
Aerial images for a pattern of equal lines and spaces of width was 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.
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PSF: Point Spread Function
Means of characterizing the resolving
capability of an imaging system
Normalized image of an infinitely small
contact hole
NANAR
JPSF
rNA
JffPFyxE
ffTyxt
ideal
yx
yxmm
7.0to66.0
)2(
)2(),(),(
1),()0,0(),(
2
1
11
0.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Normalized Radius = rNA/
0.2
0.4
0.6
0.8
1.0
NormalizedIn
tensity
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Oblique Illumination
Plane wave strikes at an angle
Phase differs for different points on mask
Shift in the position of the diffraction pattern
NA
kR
ffPffffTFffyxE
f
eyxE
yxyyxxmyx
x
xi
2
)},()','({)',',,(
'sin'
),(
1
1
'sin2
Diffraction Pattern
Lens Aperture
Mask Pattern(equal lines and spaces)
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