Milster, Socha, Brooker

1
Basics of Optical Imaging in Microlithography A
"Hands-on" Approach

• Tom D. Milster (University of Arizona)
• Robert Socha (ASML)
• Peter Brooker (SYNOPSYS)

• Thanks to
• Del Hansen
• Phat Lu
• Warren Bletscher

2
What we want to do with this course
From This
To This

• Take a complicated optical system, like a
  lithographic projection camera used to make
  computer chips, and simplify it to a working
  model that demonstrates basic principles.
• Use a simple optical system for the student to
  work with hands on and observe the results.
• Demonstrate the relationship of the simple system
  to a real lithographic system through a
  commercial simulator.
• Have fun and demonstrate our unparalled acting
  abilities

3
OUTLINE

• Intro
• Basic Imaging What we do in lithography
• The goal of making a small image
• What limits the size of the image?
• Basic Illumination and Imaging
• Koehler Illumination
• Definition of coherence factor sigma
• Binary Mask
• Contrast versus pitch for sigma 0
• Contrast versus pitch for sigma gt 0
• 2-Beam and 3-Beam Imaging
• Focus behavior
• Phase Mask
• Contrast versus pitch
• Focus behavior
• Off-Axis Illumination
• Contrast versus pitch
• Focus behavior
• Summary

4
Introduction

• What is photo lithography ?

• Optical image is recorded in the resist via
  changes in concentrations of species.
• Concentration level controls development

Object reticle or mask
Optics
Aerial Image
Photoresist
Wafer films
Latent Image
Photoresist Development
Resist Cross sections
Negative Photoresist
Positive Photoresist
Etymology Photolithography Light Stone
Writing
5
Introduction

• 1st approximation is that Aerial image propagates
  into photoresist normal to the wafer plane,
  creating a latent image
• Reality is more complicated you need to
  calculate E fields in photoresist at many
  propagation angles

0.25mm 5-BAR Structures Focus0.0mm, NA0.57
NA0.6, 248nm
Z
Image Cross Section
Z
Resist Cross Section (not top down!)
6
Introduction

• The goal of making a small image
• Transfer image into a photosensitive material,
  i.e., photoresist, for subsequent processing that
  results in a desired pattern to be used as a
  stencil

photoresist
7
Introduction

• Imaging Resolution and Lord Rayleigh
• Q When can you resolve the image of 2 distance
  stars?
• A When the 1st Intensity min of one lines up
  with peak of other

Large l
Small NA
Decrease l
Increase NA
Large NA
From the math of the Airy function
Web Top Optics, 1999
8

• Oh Master-Litho
• ..what limits the size of the photoresist
  pattern?
• Grasshopper, there are three paths to improve
  resolution
• Reduce Wavelength (Lambda)
• Increase numerical aperture (NA)
• Decrease k1 Process knob
• Includes off-axis illumination, complex masks,
  high contrast photoresist, acid diffusion, etc
• .now go away Grasshopper I am busy.

9

• What is it now Grasshopper
• Master, what affects the contrast of the image?
• The answer is found in the values of
• NA
• CD and Pitch
• Partial Coherence or illumination (s)
• s0 Coherent Limit
• s1 Incoherent Limit

10

• You again grasshopper
• Master
• look at the following data

11
Effect of Varying s
l193nm, NA0.75 Dense Lines vs. s (circular)
150nm L/S
100nm L/S

• Master, how come in one case increasing sigma is
  good (100nm L/S) and in the other case,
  increasing sigma is bad (200nm L/S)?
• It depends on the amount of diffraction orders
  that are being collected by the lensnow go away!

12

• Master, I am sure that your answers are correct
  but
• yes Grasshopper
• But I find these facts confusing. What is sigma?
  How can in some cases a larger sigma be good and
  in other cases a larger sigma be bad? And what
  the heck is k1?
• MasterI do not want only the answersI want to
  understandplease help me understand master
• Grasshopper you are finally asking the right
  question
• Go to the optical bench now
• It holds the answer to your questions!!

13
Basics of Imaging in Lithography Experimental
Layout
14
First Light Get An Image

• Lets do an experiment
• Set up the bench with
• Pinhole Source
• Aperture Stop of 6.35 mm (1/4 in) diameter.
• Put in the L (25.2µm) pitch mask and observe the
  aerial image.
• The grating simulates a mask.
• The aerial image simulates what is used to expose
  the resist.
• In our system, the aerial image is reimaged onto
  a CCD camera, which is like an Aerial Image
  Measurement System (AIMS).
• Draw picture of the light pattern at the stop.

15
Basic Illumination and Imaging

• Kohler Illumination

Image of source
Stop
Mask Plane
Source Aperture
Aerial Image
Lens 1
Lens 2
Condenser
Imaging Lens

• Field Stop of Imaging Lens is Aperture stop
  condenser and vice versa
• Lithographic systems use Koehler illumination
  where the illumination source aperture is imaged
  into the stop of the imaging lens.

16
Basic Illumination and Imaging

• Definition of Coherence Factor Sigma

Stop Diameter
Source Image Diameter
Mask Plane
Pupil Edge (the NA)
Source
Source Image
Imaging Lens
View of Entrance Pupil with blank mask
Condenser
17
Simple Binary Mask

• Model a Cr on quartz grating mask as an
  infinitely thin grating

Note For 11 lines and spaces, P 2 LW LW
Line Width
P
SiO2
Cr
E-Field
Position
3
-3
Grating Equation
q
Diffraction Orders
2
-2
1
-1
0
Lens/Pupil
18
Effect of Varying Pitch

• Lets do an experiment
• Set up the bench with
• Pinhole Source
• Aperture Stop of 6.35 mm (1/4 in) diameter.
• Use the S(8.4µm), M(12.6µm) and L(25.2µm) pitches
  of the mask and observe the effects in the image
  plane and at the stop.
• Draw the light pattern at the stop on the next
  page.
• What is the relationship between the light
  pattern at the stop and the image?
• What is the smallest pitch for which we can
  obtain an image?
• This system is very similar to what would be
  observed if an on-axis laser beam was used to
  illuminate the mask. Therefore, we call this
  case coherent imaging.
• Notice that the lines in the image are either
  completely resolved, or they are not. There is
  no partially resolved case.

19
Effect of Varying Pitch
20
Binary Mask and Diffraction Orders

• Must have more than 1 order in pupil to have
  image modulation

3
Pupil (stop)
1
o
Strong Image Modulation
-1
We see diffraction orders emanating from the mask
that are necessary for imaging.
-3
For 11 grating
Coherent limit
pupil
1
qMax
o
Pmin is the minimum pitch that is at the limit of
resolution.
-1
NAsin(qMax)
k11/2
1
pupil
qMax
No Image just constant Irradiance
o
-1
21
Coffee Break
22

• Time for the Late Shows new and exciting quiz
  game sensation.
• Do you want to play
• Know your Current events?
• Know your Cuts of Beef?
• Know your Optics Bench Basics?
• Know your Bench Basics! Excellent choice!!!

23
Bench basics

• Where is the Source Aperture relative to the
  condenser lens?
• Is it
• A at minus infinity
• B it refuses to reveal its location
• C The source aperture is located at the front
  focus of the condenser lens
• Answer is C The source aperture (effective
  source for the system) is located at the focus of
  the condenser lens. Collimated light from the LED
  illuminates the grating. Light from every part of
  the source aperture illuminates each point on the
  grating.

24
Bench basics
fc
f1
f2
fc
f1
f2
2fcam
2fcam

• Q Where does the image of the Source Aperture
  appear?
• Does it appear
• A only in the Borg space time continuum
• B at the grating
• C in the plane of the Stop.
• Correct answer is C The image of the Source
  Aperture appears in the plane of the stop.

25
Bench basics

• Q Collimated light from the Source Aperture
  illuminates the Grating. This is because.
• A The grating is not worthy of the sources
  focused attention
• B The source is the gratingquestion is
  irrelevant
• C Kohler Illumination of the grating averages
  out non uniformities in the source.
• Answer is C

26

• Comedy writers strike
• No more multiple choice answers
• Lets continue to cement the concepts associated
  with the bench

27
Bench Basics

• Q Where is the grating located with respect to
  Lens1?
• A The grating is located at the focus of lens 1.
• Q Where does the image of the grating appear?
• A The image of the grating appears at the Image
  plane

28
Bench Basics

• Q If the Image occurs at the image plane, why is
  the microscope needed?
• A The image of the source at the image plane
  cannot be seen with the eye. The microscope is
  needed to magnify the image so it can be seen by
  your eye.

29
Bench Basics Grating off axis point

• Q Look at the above picture. Estimate the
  vertical magnification?
• 3.7
• How can the vertical magnification be decreased?
• Decrease f2 but keep Stop at focus of Lens2.

30
Connection back to real Scanner Optics

• Q Where is the mask plane and image of the mask?
• A First plane on the left and last plane on
  right.
• Q Can you find the stop in the lens column?
• A On the right side of center.
• Q What is the magnification?
• A 4x demagnification.

31
Effect of Varying Sigma

• Lets do an experiment
• Set up the bench with
• Pinhole Source
• Aperture Stop of 6.35 mm diameter.
• S(8.4µm) grating
• Use the PH, 3.18mm (1/8 in) and 6.35mm (1/4in)
  diameter sources and observe the effect at the
  stop and at the image plane. Estimate ? for each
  source.
• Draw the light pattern at the stop on the next
  page.
• Is there a point where we can resolve the lines
  in the image?
• By changing ?, we are allowing more light through
  the stop that can interfere to form an image.
• Not all of the light that is passed through the
  stop can interfere, thus giving us background
  light that reduces our contrast. The amount of
  background light is a function of the pitch,
  therefore the contrast is a function of the
  pitch.
• This case is called partially coherent imaging,
  because of the dependence of the contrast on
  pitch.

32
Effect of Varying Sigma
33
Contrast Curves versus Pitch Sigma

• Sigma0.05 ---Coherent
• Sigma0.5 -----Partially Coherent
• Sigma1 ---Incoherent limit

34
Modulation Transfer Function (MTF)

• Optics types love this plot!!!!
• Can you find the Coherent frequency cut off?

35
Binary Mask Influence of Sigma

• Pupil diagrams with Partial Coherence

We must have at least 2 conjugate sources points
in the pupil to form an image.
NA
s
Imaging!!

• Each source point is projected by the diffraction
  orders from the mask
• These will interfere with each other for a given
  source point
• need more than 1 for interference and hence image
  modulation

36
Binary Mask Sigma lt 1
Resolution limit with 0ltslt1 for a circular source

• No grating - just blank mask

• Grating period at cut-off frequency

• Grating period resolution limit at given ?

1st
-1st
0th order
37
Binary Mask Sigma 1
Resolution limit with s1 for a circular source

• No grating - just blank mask

• Grating period at cut-off frequency

• Grating period corresponds to incoherent cut-off

38
Binary Mask, l248nm, NA0.63
39
s0.05 s 0.7 for k10.5
40
Different cases for on axis, k10.5

• Assume circular, on axis illumination
• Assume dense L/S
• k10.5
• ? Center of n1 diffraction orders are at edge of
  lens
• ? CD LW 0.5Lambda/NA
• For 248nm illumination, NA0.63
• CD 0.5248nm/0.63 197nm ? 200nm L/S give
  k10.5
• For 193nm illumination, NA0.93
• CD 0.5193nm/0.93 104nm ? 104nm L/S give
  k10.5
• For 193nm illumination, NA 1.2
• CD 0.5193/1.2 80.4nm ? 80nm L/S gives k1
  0.5
• Results above are only good for on axis
  illumination.
• The usual off-axis case is different.

41
Binary Mask Round and Annular Illumination
Small s and k1gt0.5
Larger s and k1lt0.5

• All power is inside pupil (for 0th and ?1st
  orders)
• Coherent source points have 3-beam interaction

• Some power is inside pupil (center of ?1st
  orders is outside)
• Coherent source points have 2-beam interaction

Conventional or Circular Source
Annular Source
42
Binary Mask 3-Beam Imaging

• Lets do an experiment
• Set up the bench with
• L(25µm) Pitch grating
• PH Source
• Observe the behavior (position and contrast) of
  the image as the observation plane is moved from
  the perfect focus. Write down your observations.
• What happens as the observation plane is moved
  beyond the point of zero contrast?

43
Binary Mask 3-Beam Imaging

• Do you see reversed-contrast lines?
• This type of focus behavior is indicative of
  three-beam imaging, where all of the power from
  the 0 and /- 1st diffraction orders passes the
  stop.
• Every point in the image is derived from three
  conjugate source points in the pupil.
• Three-beam imaging has the characteristic that
  reversed-contrast planes can occur if the focus
  is too far or the resist is too thick.

44
Binary Mask, l248nm, NA0.63, 300nm L/S
3-Beam Imaging
45
Missing Orders

• Lets do an experiment
• Set the bench with
• L(25 µm) pitch
• PH source
• Draw a sketch of the image on the next page.
• Block the zero diffraction order at the stop.
• Draw a sketch of the image on the next page.
• Does the pitch of the image change?
• This type of focus behavior is indicative of
  two-beam imaging.
• Every point in the image is derived from two
  conjugate source points in the pupil, which are
  widely separated and lead to a double-frequency
  image.
• Now change the system to block either the 1 or
  -1 order, but let the zero order pass the stop.
• Draw a sketch of the image on the next page.
• Observe the image pitch and defocus behavior.
  Write down your observations.

46
Missing Orders
47
Binary Mask, l248nm, NA0.63, 250nm L/S
48
Phase Mask
P
E
E-Field
-5
Diffraction Orders
Grating Equation
5
-3
3
q
1
-1
Lens/Pupil
1st
-1st
49
Pure Phase Chromeless
E
1
P
E-Field
-1
Position
Diffraction Orders
-5
Grating Equation
5
-3
3
q
1
-1
Lens/Pupil
1st
-1st
50
Phase Mask

• The phase mask produces no zero order

3
Pupil (stop)
1
Strong Image Modulation
-1
No zero order is emitted from the phase mask.
-3
For alternating phase shift grating
Coherent limit
pupil
1
qMax
pmin is the minimum Cr pitch that is at the limit
of resolution.
-1
NAsin(qMax)
k11/4
1
pupil
qMax
No Image just constant Irradiance
-1
51
Phase Mask

• Lets do an experiment
• Set the bench with ?.
• 12.5µm Pitch Phase Mask
• 14.25mm Diameter stop (No Magnet)
• 3mm Diameter Source (? 0.3)
• Observe the light pattern at the stop. How many
  diffraction orders do you see?
• Draw a sketch of image and the light pattern at
  the stop on the next page.
• Note the relative brightness of the zero order
  and the /-1st orders. If needed, remove the
  grating to identify where the zero order occurs.
• Observe the line pattern at the observation
  plane. (Block the zero order if present)
• How does the image pitch compare to using a
  simple grating mask?

52
Phase Mask

• Change the observation plane location. How
  sensitive is the observationplane location to
  focus changes?
• The phase mask has no zero order, and it produces
  a double-frequency pitch in the aerial image
  compared to a binary mask.
• The minimum pitch in the image is half the
  minimum pitch of a simple grating mask.
• The phase-mask image is relatively insensitive to
  focus changes, due to the missing zero order.

53
l248nm, NA0.63, sigma 0.3
54
Off-Axis Illumination

• Illumination source shapes that do not have axial
  intensity as usually known as off-axis sources
• Examples are annular, quadrupole, and dipole
• Off-axis illumination helps to enable k1lt0.5 with
  binary masks
• Reduction of on axis source reduces DC terms
  and enhances contrast
• A conventional on axis small source
• Some Off-axis sources

55
Coherent Off-Axis Illumination and a Binary Mask

• Orders shift relative to pupil

Image Modulation
For 11 grating
Incoherent limit
qMax
Pmin is the minimum pitch that is at the limit of
resolution.
NAsin(qMax)
k11/4
pupil
0
qMax
No Image just constant Irradiance
-1
56
Binary Mask with Annular Illumination
Resolution limit with 0ltslt1 for a circular source
?outer

• No grating - just blank mask

?center
?inner
0th order

• Grating period at cut-off frequency

-1st
1st
0th order

• Grating period resolution limit at given ?

-1st
1st
0th order
57
Off-Axis Illumination with a Binary Mask

• Lets do an experiment
• Set up the bench with system for minimum ?.
• S(8.2µm) pitch mask
• PH Source centered on axis
• Observe the pattern at the stop. Draw the light
  pattern at the stop on the next page.
• Do you see an image? Sketch the camera output on
  the next page.
• Move the source until at least two orders pass
  through the stop. Draw the pattern at the stop
  and the image on the next page.

58
Off-Axis Illumination with a Binary Mask
59
l248nm, NA0.63, sigma 0.3
60
Different cases for off axis, k10.25

• Assume off axis illumination
• Assume dense L/S
• k10.25
• ? Center of n0 and n1 diff. orders are at edge
  of lens
• ? CD LW 0.25Lambda/NA
• For 248nm illumination, NA0.63
• CD 0.5248nm/0.63 98nm ? 100nm L/S give
  k10.25
• For 193nm illumination, NA0.93
• CD 0.25193nm/0.93 52nm ? 50nm L/S give
  k10.25
• For 193nm illumination, NA 1.2
• CD 0.25193/1.2 40.2nm ? 40nm L/S gives k1
  0.25
• Current off-axis results.
• Actually might want whole orders inside with
  sigma0.3

61
Summary

• What have we learned?
• The basic optical components of a lithography
  system are the source, condenser and imaging
  lens.
• The size and shape of the source influence
  properties of the aerial image.
• The stop of the system determines the maximum
  angle of diffraction orders that can pass to the
  image.
• It takes at least two diffraction orders passing
  the stop to form a line-space image.
• By increasing ?, we can change from coherent-like
  illumination to partially-coherent illumination.
• Partially coherent illumination can allow higher
  pitch in the image at the expense of reduced
  contrast.
• 2-Beam and 3-Beam geometries have different focus
  characteristics.
• By using a phase-shift mask, the zero order is
  eliminated and the first diffraction orders move
  closer to the center.
• Off-axis illumination can produce a half-pitch
  image, but the contrast is lower than with a
  phase-shift mask.

62
References

• Introductory Articles
• SPIE Proceedings for Microlithography
• Journal of Microlithography, Microfabrication,
  and Microsystems (JM3) SPIE Press
• Industry Magazines
• Microlithography World
• www.pennwell.com
• Books
• Intro to Fourier Optics and Statistical Optics
• by J. Goodman
• Resolution Enhancement Techniques and Optical
  Imaging in Projection Microlithography
• Alfred Wong, SPIE Press
• Microlithography Science and Technology
• Ed James Sheats and Bruce Smith
• Pub Marcel Dekker

63
References

• Intro Papers
• Using location of diffraction orders to predict
  performance of future scanners,
• Peter Brooker Publication Proc. SPIE Vol.
  5256, p. 973-984, 23rd BACUS (2003)
• Roles of NA, sigma, and lambda in low-k1 aerial
  image formation,
• Peter D. Brooker Publication Proc. SPIE Vol.
  4346, p. 1575-1586, (2001)
• Advanced Papers
• U of A Dissertation by Doug Goodman (1979),
  Stationary Optical Projectors
• Papers by H.H. Hopkins for partial coherent
  imaging, Richards and Wolf for high NA

64
Thank You for Taking This Course!
65
Backup Slides
66
Basic Illumination and Imaging

• Pupil or the aperture stop Physical Limiting
  aperture of system
• Location and size defined by Chief Ray and
  Marginal Ray
• Chief Ray Starts at edge of object (field) goes
  through center of pupil
• Marginal Ray Starts at axial object and goes
  through edge of pupil

Pupil
Object
n image side refractive index
Chief ray
Aerial Image
h
Marginal ray
h
n object side refractive index

• NA numerical aperture
• defined by marginal ray
• maximum angle accepted by system

67
Basic Illumination and Imaging
Imaging Lens

• Lets do an experiment
• Calculate NA at the image plane for rs _______
  .
• Calculate the coherent resolution limit in terms
  of pitch in the aerial image.

rs
?m
68
Optimum DOF and Modulation for Annular (and
dipole)
0
1
-1

• Optimum when phase differences between 0th and
  1st orders are minimum

69
Optimum DOF and Modulation for Quadrupole
0
1
-1
NA scenter
l/Pitch

• Optimum when phase differences between 0th and
  1st orders are minimum

70
Off-axis Illumination PrinciplesEffects of
different illumination modes

• Periodic features benefit most from QUASAR
  illumination
• Optimum illumination is specific to reticle
  features

71
More Facts Aerial Image Cross Section
l193nm, NA0.75 Dense Lines vs. s (circular)
Varying s
100nm L/S
150nm L/S

• Increase sigma and contrast goes up (100nm L/S)
• Increase sigma and contrast goes down (200 nm
  L/S)
• Very confusing!!! What is going on??

72
Lithography Imaging Laws

• What limits the size of the photoresist pattern ?
• Three paths to improve resolution
• Wavelength (l)
• Numerical Aperture (NA)
• k1 Process knob
• Includes off-axis illumination, complex masks,
  high contrast photoresist, acid diffusion, etc
• What limits the size of the optical (and/or
  aerial) image? (Assuming circular illumination
  source and binary reticle)
• NA
• l
• Partial Coherence or illumination (s)
• s0 Coherent Limit
• s1 Incoherent Limit
• Finebut where do these come from??

• Note resolution is often written as Linewidth
  (LW) or critical dimension (CD) in the context
  with photoresist

73
Basic Illumination and Imaging

• Definition of Coherence Factor Sigma

Stop Diameter
Source Image Diameter
Mask Plane
Pupil Edge (the NA)
Source
Source Image
Imaging Lens
View of Entrance Pupil with blank mask
Condenser
If pupil diameter NA, then source size NA
s (pupil or NA units)