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Partial Coherence: On-Axis Imaging
Microlithography Systems Laboratory
Microelectronic Engineering Department
1. GOAL
The goal of this lab is to demonstrate the effects of partially coherent imaging. We will modify the SMFL
GCA 6700 wafer stepper with apertures to control the degree of partial coherence and evaluate image
fidelity through a focus exposure matrix.
2. INTRODUCTION AND THEORY
2.1 Coherence
Partial coherence is an important and ubiquitous degree of freedom present on most optical lithography
projection tools. Partial Coherence, σ, is defined as the ratio of condenser NA to objective NA.

NAC
NAO
(1)
In order to gain an understanding of partially coherent imaging and the effect the degree of coherence has
on an image, it is useful to consider the extremes in each direction: coherent (σ = 0) and incoherent imaging

(σ = 1).
Resolution (or as in this case, the half pitch) can be expressed in terms of the coherence value using the k1
factor, as shown in equation 2.
p k1

2 NA
(2)
Where k1 is given by equation 3.

k1 
1
2  1
(3)
2.2 Coherent imaging
In fully coherent imaging, there is no spreading of diffraction orders, since the illumination in this case

consists of a plane wave propagating normally to the mask surface. This lack of angular spread in the
illuminating radiation results in diffraction orders with the same absence. Diffraction orders below a certain
NA can be collected completely, resulting in full modulation until a certain feature pitch. Further decreases
in pitch below a critical cutoff value result in no part of the ±1st diffraction orders being collected, and no
resolution is possible. In this case, the cutoff frequency (the minimum resolvable frequency of a system) is
sharp. The minimum resolution for a perfectly coherent system is given by equation 4. The amplitude
transfer function for coherent imaging can be seen in Figure 1.
R
0.5
NA

Microlithography Systems – Phase Shifting Masks
(4)
Figure 1: Comparison of amplitude transfer function and optical transfer function. Cutoff frequencies are shown for
each case.
Modulation is defined in equation 5.
Modulation 
Imax  Imin
Imax  Imin
(5)
2.3 Incoherent imaging
In fully incoherent imaging, the diffraction orders have a spread that causes them to fill the entire pupil.
This results in an imaging condition
where the minimum resolvable pitch is smaller than that possible using

coherent imaging, however modulation of the features decreases linearly to 0, based on equation 6.
R
0.25
NA
(6)
The Optical Transfer Function for incoherent imaging can also be seen in Figure 1. Although the
modulation decreases linearly with decreasing feature half-pitch, the ultimate resolution of the incoherent
system is doubled from its coherent counterpart.

2.4 GCA 6700 g-line wafer stepper
The SMFL g-line stepper has an NA of 0.29 and a partial coherence (σ) of 0.68. Although these parameters
are normally not adjustable, we will attempt to modify the partial coherence of the system and evaluate the
effects of such modification.
Removing several covers in the illumination system of the GCA will allow access to various beam shaping
optics responsible for producing the eventual 0.68 σ light. Using apertures made of aluminum foil, we will
attempt to find an aperture stop plane in the illumination system and stop down the acceptance angle of the
system’s input. Exposures made with this system using appropriate spatial frequency objects should show
decreased ultimate resolution at low partial coherence values.
Microlithography Systems – Phase Shifting Masks
3. PLANNED PROCEDURE
3.1 Focus exposure matrix at 0.68 σ
Run a focus exposure matrix with an un-modified exposure system.
1.
2.
3.
Obtain several bare 4” silicon wafers
Coat multiple wafers with photoresist on the SVG track, and measure the thickness with either the
Nanospec or SpectraMap. Record the average thickness, t0, for each.
Expose a single wafer on the GCA stepper with an exposure matrix.
a. Using a radiometer to measure intensity, calculate exposure time for an approximate dose
that will result in equal lines and spaces, which could be about twice as long the dose to
clear (~110 mJ/cm2). Homing the aperture blades of the field stop may assist data
collection.
b. Set the “Exposure Mode” switch under the keyboard to “Time Mode”
c. Load the engineering test mask (ETM) and first wafer.
d. Type: EXPO EMCR221
e. PASS: 1
f. Knowing that there are 81 die in a 9x9 array, choose initial and increment dose values
that will center around the approximate dose to size.
i. Begin with an exposure range from the dose to clear (E 0) to 3E0. This will center
the array on twice the dose to clear. If this is too broad, conduct a second more
precise FEM.
At the time of this writing, the first die in a 9x9 array lies off the wafer’s edge. Doing an 8x8 array starting
at (row 2, column 2) avoids the resulting auto-focus error.
g.
h.
4.
5.
6.
OVER: R
Choose initial and incremental focus values so that the most recent best focus value,
written on the console, is centered in the array. The GCA focus increments are in
machine units, and there are about 50 machine units per micron. Use a focus step size of
about 5 machine units.
i. Do not run an open frame test.
j. RETICLE BAR CODE: NONE (just hit “ENTER”)
k. FLOOR #: enter the number of the slot where you loaded the mask.
l. ALIGNMENT MARK PHASE (P/N/X): X
m. After the keyboard prompts, press “RES”, wait for the laser sensor LED’s near the input
boat to light up, then press “1st L” followed by “S/C”
n. If a mistake is made, hold down the “CTRL” key and type a “C”. The screen should show
a double colon. Type and “A”. This will abort the chain of commands, and you can start
over at step 3d.
Develop the wafer on the SVG track
Observing the 1.0 µm lines, find the best die and determine focus and exposure window via
microscope inspection. Refer to Figure 2. Remember to record the criteria used to define
acceptable features, such as equal lines and spaces. This is the process latitude.
Determine the smallest pitch resolved. The unmodified GCA should be able to resolve 0.8 µm
equal lines and spaces.
Figure 2: Focus and exposure progression on the GCA 6700.
Microlithography Systems – Phase Shifting Masks
3.2 Modifying the coherence of the GCA 6700
Collect the following tools and supplies:







A small hex wrench
Scissors or an X-ACTO knife
A drafting compass (the pencil can be replaced with a wafer scribe if it’s an issue)
A single hole punch (optional)
Metal foil
Tape
A ruler
With the hex wrench, remove the screws on top of the GCA’s front most lid above the condenser lens,
which is shown top-down in Figure 3. Remove the lid and peer into the exposed cavity; the view should
resemble that illustrated in Figure 4. With the hex wrench, remove the screws in the “L”-shaped structure
extending beyond the surface of the light-pipe – this is the aperture stop. Slide the aperture stop out of its
slot in the pipe; it should resemble the illustration in Figure 5.
Figure 3: Top of the GCA looking backwards toward the
rear of the environmental chamber. The ovals mark the
locations of the screws to remove the lid.
Figure 4: Angled view down into the GCA once the lid
has been removed. The circles mark the locations of the
screws to remove the aperture stop.
Microlithography Systems – Phase Shifting Masks
Figure 5: Detailed view of the GCA 6700 aperture stop.
Knowing that the diameter of the unmodified aperture stop correlates to a sigma of 0.68, use a ratio to
derive the diameter of the desired coherence value. Construct a new aperture in a sheet of metal foil,
superimpose it over the stock aperture stop, and re-insert it into the GCA. Remember to take a new
irradiance measurement.
3.2 Focus exposure matrix at 0.34 σ
Repeat section 3.1 after modifying the GCA’s coherence to 0.34. Remember to re-measure the irradiance
and adjust the exposure times so an identical dose range is delivered; otherwise, use identical FEM settings.
3.3 Focus exposure matrix at 0.17 σ
Repeat section 3.1 after modifying the GCA’s coherence to 0.17. The diameter of the single hole punch
may closely approximate the calculated diameter. Remember to re-measure the irradiance and adjust the
exposure times so an identical dose range is delivered; otherwise, use identical FEM settings.
4. DATA ANALYSIS
Which coherence value resolves the smallest pitch? Determine how coherence affects the process latitude.
Is there a tradeoff? Explain your results in terms of the modulation and k1 value. When does incoherence
offer improved imaging capability? Is an incoherent source ever a disadvantage?
REFERENCES
J. R. Sheats, and B. W. Smith, “Optics for Photolithography,” Microlithography: Science and Technology,
“Optics for Photolithography,” Marcel Dekker, New York, 1998, pp. 205.
J. W. Goodman, “Frequency Analysis of Optical Imaging Systems,” Introduction to Fourier Optics,
“Frequency Analysis of Optical Imaging Systems,” McGraw-Hill, New York, 1996, pp. 127.
Microlithography Systems – Phase Shifting Masks
APPENDIX
GCA illuminator assembly
Figure 6: Maximus 2000 Optical Path. C3 is the aperture stop that we will use in order to modify the partial
coherence/illumination of the system.
Figure 7: The cross section view of the kaleidoscope assembly
Microlithography Systems – Phase Shifting Masks