CHE323/CHE384
Chemical Processes for Micro- and Nanofabrication
Photoresist Contrast (H-D)
Curve
www.lithoguru.com/scientist/CHE323
(also called the characteristic curve)
Lecture 54
Lithography:
Resist Contrast
Relative Resist Thickness
1.25
Chris A. Mack
Adjunct Associate Professor
Note: can use log-10
or natural log
definitions of γ
1.00
0.75
0.50
x-intercept = E0
(dose-to-clear)
0.25
Slope at
intercept = -γ
0.00
1
www.lithoguru.com
© 2013 by Chris A. Mack
10
100
1000
Exposure Energy (mJ/cm2)
2
© Chris Mack
New Definition of
Contrast
H-D (Contrast) Curve
How does development rate respond to dose?
1.25
Development Rate (nm/s)
Relative Resist Thickness
1000
1.00
Developer B
γ = 2.4
0.75
Developer A
γ = 1.2
0.50
0.25
0.00
1
10
100
•
10
100
1000
Exposure Energy (mJ/cm2)
4
Photoresist Contrast
d ln r
d ln E
d ln r
d ln I
= γ th
dx
dx
Note that theoretical contrast is a function of dose.
Often the max value of γth is used.
Questions:
• The contrast “amplifies” the image gradient to
give a development rate gradient
– How does this definition relate to lithographic quality?
– What is the relationship of theoretical contrast to
measured contrast?
© Chris Mack
0.1
© Chris Mack
Theoretical Photoresist
Contrast
•
1
1
3
γ th =
γth = slope
10
0.01
1000
Exposure Energy (mJ/cm2)
© Chris Mack
100
• This is called the “Lithographic Imaging
Equation”
5
© Chris Mack
Page 1
6
Photoresist Contrast:
γth vs. γm
Conventional “Definition” of
Resist Contrast
γm =
1 dτ
D d ln E E = E
0
Relative Resist Thickness
1.00
Development Rate:
0.75
0.50
R=
t dev
dz
dt
∫
z
dt = t dev =
0
dz
∫ R( z )
0
(R = development rate, z = depth into the resist)
0.25
Now take the derivative with respect to ln(dose):
0.00
1
10
100
Exposure Energy (mJ/cm2)
D
γm =
τ = resist thickness remaining, D = initial resist thickness
Rbottom
dz
γ th
D
R( z )
∫
0
7
© Chris Mack
Theoretical Contrast
(a + 1)(1 − m) n
+ rmin
r = rmax
a + (1 − m) n
Resist Contrast Review
n +1
a=
(1 − mth ) n
n −1
18
• Theoretical contrast converts the image log-slope
16
mth = 0.7
n = 20
14
•
Gamma
12
10
n = 10
8
n=5
4
into a development rate log-slope
Measuring resist contrast is tricky using the
conventional characteristic curve method – it is
almost never worth using
– Anything that causes the development rate to vary with
depth into the resist (e.g., absorption, surface
inhibition) causes an error in contrast measurement
6
2
• Theoretical contrast can be measured using a
0
0.5
0.6
0.7
0.8
0.9
development rate monitor
1.0
Relative Concentration m
© Chris Mack
9
© Chris Mack
Lecture 54:
What have we Learned?
• How is the conventionally measured contrast
defined?
• How is the theoretical contrast defined?
• When do the conventionally measured and
theoretical contrasts give the same result?
• How is contrast related to the dissolution
selectivity parameter n?
© Chris Mack
8
© Chris Mack
11
Page 2
10