Modulation Transfer Function
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Fraunhofer Diffraction

The measure of the quality of the aerial image is given
by
MTF 




I MAX  I MIN
I MAX  I MIN
The MTF is really a measure of the contrast in the aerial
image
The optical system needs to produce MTFs of 0.5 or
more for a resist to properly resolve the features
The MTF depends on the feature size in the image; for
large features MTF=1
As the feature size decreases, diffractions effects casue
MTF to degrade
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Change in MTF versus Wavelength
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Contact and Proximity Systems



These systems operate in the near field or Fresnel
regime
– Assume the mask and the resist are separated by
some small distance “g”
– Assume a plane wave is incident on the mask.
Because of diffraction, light is bent away for the
aperture edges
– The effect is shown in the next slide
– Note the small maximum at the edge; this results
from constructive interference
– Also note the ringing
To reduce these effect, we often use light sources with
multiple wavelengths
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Fresnel Diffraction
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Fresnel Diffraction


As g increases, the quality of the image
decreases because diffraction effects become
more important
The aerial image can generally be computed
accurately when
g

W2

where W is the feature size
Within this regime, the minimum resolvable
feature size is
Wmin  g
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Resolution

A more exact solution for the theoretical resolution for
proximity or contact aligners is given by:
3 
z
R
 g  
2 
2

Where  is the wavelength of light used to exposure the
pattern, g is the distance between the bottom of the
mask and the top of the photoresist, z is the thickness
of the photoresist (typically 0.8-1.2mm).
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Fresnel Number


Fresnel diffraction when F ≥ 1
Fraunhofer diffraction when F << 1
2
W
F
g
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Summary of the Three Systems
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Comparison of Depth of Focus
http://www.research.ibm
.com/journal/rd/411/hol
m1.gif
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Photoresists



Photoresists change their chemical properties when
exposed to light
– Almost all photoresists are based on hydrocarbons
– There are some inorganic resists (e.g., As2S3)
The light breaks chemical bonds in these materials
The photoresist then chemically rearranges itself into a
more stable compound
– Some positive photoresists may form smaller
polymer chains, which are more soluble in developer
after exposure
– Negative photoresist forms larger polymer chains,
which are less soluble in developer after exposure
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Photoresists



Most resists in use today are positive resists because
they have better resolution
– Negative resists swell when exposed to light
Generally, resists are liquid at room temperature and
are applied by placing a drop on the wafer and then
spinning at high angular velocity (3-6k rpm)
– The viscosity and spin speed determine the resist
thickness.
Controlled by the type and volume of solvent
Once spun on, the wafer undergoes a pre-bake to drive
off the solvent
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http://www.lithoguru.com/scientist/lithobasics.html
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Photoresists



Following pre-bake, the resist is exposed and developed
– Developing is performed either by immersion or by
spraying a developer (base)
After developing, the resist is baked again (postbake) to
harden it and improve its resistance to etches
– Long UV exposure can also be used to cross-link the
polymer chains in the remaining photoresist
After the etch step, the resist is removed in an oxygen
plasma or by a wet removal
– Acetone if minimal hardbake
– Variation on RCA etch or nitric acid
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Photoresists

Parameters that determine the usefulness of the resist
include
– Sensitivity
- a measure of how much light is required to
expose the resist
- typically 100mJ/cm2
– Resolution
- exposure, baking, developing must not degrade
the quality of the image
– Polymer used in Resist
- it must withstand the etching or ion implantation
after the mask pattern is transferred to the resist
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Photoresists


Photoresists usually contain three components
– An inactive resin (usually a hydrocarbon
which forms the base material)
– Photoactive compound (PAC)
– Solvent that is used to adjust the viscosity
The most common g- and i-line resists use
– Diazonaphthoquinones (DNQ) as the PAC
– Novolac as the resin
– Propylene Glycol Monomethyl Ether Acetate
(PGMEA) as the solvent
- this has replaced Cellosolve Acetate,
which is a toxic hazard
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Basic Structure of Novolac


Novolac is a polymer containing hydrocarbon rings with 2
methyl groups and 1 OH group
– The basic ring structure is repeated to form a long chain
polymer
Novolac readily dissolves in developer at a rate of ~15 nm/s
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Diazoquinone


The photoactive part of the molecule is the part above the SO2
The remainder of the molecule is represented by “R”
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Diazoquinone



The function of the PAC is to inhibit the
dissolution of the resin in the developer
DNQ is essentially insoluble in developer prior
to exposure to light
– When dissolved in the resin, they reduce
the resist dissolution rate to 1—2 nm/s
When the resist is exposed to light, the
diazoquinone molecule changes chemically
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Decomposition of DNQ
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Diazoquinone




When exposed to light, the bonds to the weakly bound
nitrogen are broken leaving a highly active carbon site
The molecule stabilizes itself by moving a carbon
outside the ring and covalently bonding to an oxygen
becoming a ketene molecule
– This is known as the Wolf rearrangement
The ketene transform into carbolic acid in the presence
of water
– The carbolic acid is readily soluble in a basic
developer
- TMAH – tetramethyl ammonium hydroxide, KOH
or NaOH dissolved in water
The exposed resist now dissolves at about 100 – 200
nm/s
– 10-100 times faster than the unexposed resist
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Properties and Characteristics of Resists

Two parameters are used to define the
properties of photoresists
– Contrast
- Contrast is the ability of the photoresist
to distinguish between dark and light
- It is experimentally determined by
exposing the resist to differing amounts
of light, developed for a fixed time, and
measuring the thickness of resist
remaining after developing
– Critical modulation transfer function (CMTF)
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Photoresist Contrast
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Photoresist Contrast


For positive resists, material exposed to low light will
not be attacked by the developer; material exposed to
large doses will be completely removed
– Intermediate doses will result in partial removal
The contrast is the slope of this curve and is given by

1
log 10
Qf
QO
– Typical g- and i-line resists will achieve a contrast of
2—3 and Qf values of 100 mJ/cm2
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Photoresist Contrast


The contrast is not a constant, but depends on
process variables such as
– development chemistry,
– bake times,
– temperatures before and after exposure,
– wavelength of light,
– age of resist, and
– underlying structure
It is desirable to have as high a contrast as
possible in order to produce the sharpest
edges in the developed pattern
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http://www.research.
ibm.com/journal/rd/
411/holm4.gif
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Photoresist Contrast
This ‘poor’ quality image has been used to create periodic sine wave patterns in resist for optical gratings.
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Modulation Transfer Function


We defined the MTF before in terms of a measure of the
dark versus light intensities in the aerial image
produced by the projection system
We define a similar quantity for the resist—the critical
modulation transfer function (CMTF)
CMTFresist


Q f  Q0
101/   1

 1/ 
Q f  Q0 10  1
The CMTF is the minimum optical transfer function
necessary to resolve a pattern in the resist
– For g- and i-line resists, CMTF  0.4
The CMTF must be less than the aerial image MTF if the
resist is to resolve the aerial image
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Effect of Resist Thickness

Resists usually do not have uniform thickness on the
wafer
– Edge bead: The build-up of resist along the
circumference of the wafer
- There are edge bead removal systems
– Step coverage
Centrifugal Force
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Effect of Resist Thickness


The resist can be underexposed where it is thicker and
overexposed where it is thinner
– This can lead to linewidth variations
Light intensity varies with depth below the surface due
to absorption
I ( x)  I 0 exp( x)

where  is the optical absorption coefficient
Thus, the resist near the surface is exposed first
– We have good fortune. There is a process called
bleaching in which the exposed material becomes
almost transparent
i.e.,  decreases after exposure to light
- Therefore, more light goes to deeper layers
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Photoresist Absorption



If the photoresist becomes transparent, and if
the underlying surface is reflective, reflected
light from the wafer will expose the
photoresist in areas we do not want it to.
However, this leads to the possibility of
standing waves (due to interference), with
resultant waviness of the developed resist
We can solve this by putting an antireflective
coating on the surface before spinning the
photoresist  increases process complexity
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Standing Waves due to Reflections
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Standing Waves Due to Reflections
http://www.lithoguru.com/scientist/lithobasics.html
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Removal of Standing Wave Pattern
(a)
(b)
(c)
Diffusion during a post-exposure bake (PEB) is often used to
reduce standing waves.
Photoresist profile simulations as a function of the PEB
diffusion length: (a) 20nm, (b) 40nm, and (c) 60nm.
http://www.lithoguru.com/scientist/lithobasics.html
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Mask Engineering





There are two ways to improve the quality of
the image transferred to the photoresist
– Optical Proximity Correction (OPC)
– Phase Shift Masks (PSM)
We note that the lenses in projections systems
are both finite and circular
Most features on the mask are square
We lose the high frequency components of the
pattern
We thus lose information about the
“squareness” of the corners
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Mask Engineering


The effects are quite predictable
We can correct them by adjusting feature
dimensions and shapes in the masks
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Mask Engineering
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Phase Shift Masks



In a projection system, the amplitudes of the diffracted
light at the wafer add
– Closely spaced lines interact; the intensity at the
wafer is smeared
If we put a material of proper index of refraction on part
of the mask, we can retard some of the light and change
its phase by 180 degrees
– Properly done, the amplitudes interfere
The thickness of the PS layer is
d

2n  1
n is the index of refraction of the phase shift material
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Phase Shift Masks (PSM)
Intensity
pattern is
barely
sufficient
to resolve
the two
patterns.
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