(a)

Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007

1

a

b

c

d

e f

g

i

ha

b

c

d

e f

g

i

h

Figure 8.1 A simple layout showing a two-transistor structure with source/drain contact holes. One design rule would dictate the minimum allowed spacing between the edge of the contact and the edge of the active area (dimension f).


2

Gate CD (nm)

Fre

que

ncy

Devices are too slow, poor

bin sort

High leakage current, device

fails

Range affects timing, which

affects max clock speed possible

0

0.2

0.4

0.6

0.8

1.0

75 80 85 90 95 100 105

0

0.2

0.4

0.6

0.8

1.0

75 80 85 90 95 100 105

Gate CD (nm)

Fre

que

ncy

bin sort limit

Leakage current

limit

(a) (b)

Figure 8.2 A distribution of polysilicon gate linewidths across a chip (a) can lead to different performance failures. Tightening up the distribution of polysilicon gate linewidths across a chip (b) allows for a smaller average CD and faster device performance.


3

100% Enominal

E(CD – 10%) – E(CD + 10%) EL =

20 25 30 35 40 45 60

80

100

120

140

Res

ist L

inew

idth

(n

m)

Exposure Energy (mJ/cm2)

Figure 8.3 The common CD versus exposure dose (E) curve is used to measure exposure latitude (EL).


4

Table 8.1 Examples of random focus errors (mm, 6) for different lithographic generations.

Error Source 19911 i-line

0.50 m

19952 i-line

0.35 m

1995 2 [3] KrF stepper

0.35 m

2001 KrF scanner

0.18 m

2005 ArF scanner

0.09 m Lens Heating (Compensated) 0.10 0.10 0.00 0.00 0.00 Environmental (Compensated) 0.20 0.20 0.10 0.10 0.05 Mask Tilt (actual/16) 0.05 0.05 0.10 0.05 0.05 Mask Flatness (actual/16) 0.12 0.12 0.12 0.12 0.07 Wafer Flatness (over one field) 0.30 0.33 0.33 0.15 0.07 Chuck Flatness (over one field) 0.14 0.03 0.03 0.03 0.03 Laser Bandwidth 0.0 0.0 0.20 0.1 0.04 Autofocus Repeatability 0.20 0.08 0.10 0.07 0.04 Best Focus Determination 0.30 0.15 0.10 0.10 0.05 Vibration 0.10 0.10 0.05 0.05 0.03 Total RSS random focus errors 0.60 0.50 0.45 0.28 0.15

1 C. A. Mack, “Understanding Focus Effects in Submicron Optical Lithography, part 3: Methods for Depth-of-Focus Improvement,” Optical/Laser Microlithography V, Proc., SPIE Vol. 1674 (1992) pp. 272-284. 2 S. Sethi, M. Barrick, J. Massey, C. Froelich, M. Weilemann, and F. Garza, “Lithography strategy for printing 0.35 um devices,” Optical/Laser Microlithography VIII, Proc., SPIE Vol. 2440 (1995), p. 619-632.


5

Error Source 1991 i-line

0.50 m

1995 i-line

0.35 m

1995 KrF stepper

0.35 m

2001 KrF scanner

0.18 m

2005 ArF scanner

0.09 m Topography 0.5 0.3 0.3 0.10 0.05 Field curvature & astigmatism 0.4 0.4 0.3 0.08 0.05 Resist Thickness 0.2 0.2 0.2 0.10 0.05 Total Systematic Errors (range) 1.1 0.9 0.8 0.28 0.15 Total Random Errors (6) 0.60 0.50 0.45 0.28 0.15 Range/ 11 10.8 10.7 6 6

Total BIFE (6 equivalent) 1.5 1.2 1.1 0.47 0.25

Table 8.2 Examples of systematic (mm, total range) and random focus error estimates combined to determine the Built-in Focus Errors (BIFE) of a process.


6

w

D

Figure 8.4 Example photoresist profile and its corresponding “best fit” trapezoidal feature model.


7

Focus below the resist

Focus above the resist

Figure 8.5 Resist profiles at the extremes of focus show how the curvature of a pattern cross-section can change.


8

400

500

600

700

800

900

1000

-1.5 -1.0 -0.5 0.0 0.5 1.0

Focus (m)

Fea

ture

Wid

th (

nm)

Straight Line Fit Threshold Fit

Figure 8.6 Using resist profiles at the extremes of focus as an example, the resulting measured feature size is a function of how the feature model is fit to the profile.


9

Wafer Pattern of Exposure

Fields

Wafer Pattern of Exposure

Fields

Scan Direction

Slit

Single Exposure Field

Scan Direction

Slit

Single Exposure Field

Figure 8.7 A wafer is made up of many exposure fields, each with one or more die. The field is exposed by scanning a slit across the exposure field.


10

Box-in-Box Frame-in-Frame Bar-in-BarBox-in-Box Frame-in-Frame Bar-in-Bar

Figure 8.8 Typical ‘box-in-box’ style overlay measurement targets, showing top-down optical images along the top and typical cross-section diagrams along the bottom. The outer box is typically 20 mm wide. (Courtesy of KLA-Tencor Corp.)


11

w XR w XL wXL

x-overlay = 0.5(wXL - wXR)

wXR

Figure 8.9 Measuring overlay as a difference in width measurements.


12

Figure 8.10 Typical AIM target where the inner bars (darker patterns in this photograph) are printed in one lithographic level and the outer (brighter) bars in another level. (Courtesy of KLA-Tencor Corp.)


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x

y

(x,y)

(x*,y*)

x

y

(x,y)

(x*,y*)

x

y

(x,y)

(x*,y*)

x

y

(x,y)

(x*,y*)

Figure 8.11 Examples of two simple overlay errors: a) rotation, and b) magnification errors.

(a) (b)


14

Figure 8.12 Different types of rotation errors as exhibited on the wafer: a) reticle rotation, and b) wafer rotation.

(a) (b)


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= +

Raw overlay value Modeled overlay value Residual value

= +

Raw overlay value Modeled overlay value Residual value

Figure 8.13 Separation of raw overlay data into modeled + residual values. The sampling shown here, four points per field and nine fields per wafer, is common for production monitoring.


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Error Term Picture Coefficients

Translation

x, y

Rotation

xy

Magnification

mx, my

Trapezoid (keystone)

t1, t2

Lens Distortion

d3, d5

Figure 8.14 Illustration of field (reticle) model terms including higher-order trapezoid and distortion .


17

Figure 8.15 Example of a stepper lens fingerprint showing in this case nearly random distortion across the lens field.


18

Scan Direction

Figure 8.16 Example of a scanner lens/scan fingerprint (figure used with permission). Note that errors in the scan direction are mostly averaged out by the scan.


19

-0.3 -0.2 -0.1 0.0 0.1

Focus (m)

Exposure Dose (mJ/cm2)

14 16 18 20 22 24 26 30 34

0

50

100

150

200

250

Res

ist

Fea

ture

Wid

th, C

D

(nm

)

0.2

Figure 8.17 Example of the effect of focus and exposure on the resulting resist linewidth. Here, focal position is defined as zero at the top of the resist with a negative focal position indicating that the plane of focus is inside the resist.


20

40

60

80

100

120

140

160

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Focus (um)

CD

(nm

)

7.0ln

ln

01,

FEEd

CDd

= 0.17 m

CD1 = 100 nm

E1 = 30 mJ/cm2

Figure 8.18 Plot of the simple Bossung model of equations (8.31) and (8.37) shows that it describes well the basic behavior observed experimentally.


21

Aerial Image Resist Profile

Top

Bottom

Top

Bottom

Aerial Image

Resist Profile

(a) (b)

Figure 8.19 Positioning the focal plane (a) above the top of the resist, or (b) below the bottom of the resist results in very different shapes for the final resist profile.


22

Focus (m)

140

120

100

90

80

70

CD = 110nm

Exp

osur

e (m

J/cm

2 )

16

18

20

22

24

26

28

30

14 -0.3 -0.2 -0.1 0.0 0.1 0.2

16

18

20

22

24

26

28

30

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

Focus (m)

14

CD

Sidewall Angle

Resist Loss

(a) (b)

Figure 8.20 Displaying the data from a focusexposure matrix in an alternate form: a) contours of constant CD versus focus and exposure, and b) as a focusexposure process window constructed from contours of the specifications for linewidth, sidewall angle, and resist loss.


23

16

18

20

22

24

26

28

30

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

Exp

osur

e (m

J/cm

2 )

Focus (m)

14

Focus (m)

16

18

20

22

24

26

28

30

Exp

osur

e (

mJ/

cm2 )

14 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

(a) (b)

Figure 8.21 Measuring the size of the process window: (a) finding maximum rectangles; and (b) comparing a rectangle to an ellipse.


24

18

0

2

4

6

8

10

12

14

16

20

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Exp

osu

re L

atitu

de (

%)

Ellipse

Rectangle

Depth of Focus (m)

Figure 8.22 The process window of Figure 8.20b is analyzed by fitting all the maximum rectangles and all the maximum ellipses, then plotting their height (exposure latitude) versus their width (depth of focus).


25

Res

ist L

ine

wid

th (

nm)

14 18 22 26 30 34

Focal Position (microns) -0.3 -0.2 -0.1 0.0 0.1 0.2

Exposure Energy (mJ/cm2)

Isofocal point

200

160

120

80

40

0

Res

ist L

ine

wid

th (

nm)

200

160

120

80

40

0

Figure 8.23 Two ways of plotting the focusexposure data set showing the isofocal point – the dose and CD that have minimum sensitivity to focus changes (for the left graph, each curve represents a different exposure dose; for the right graph, each curve is for a different focus).


26

0

50

100

150

200

250

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

Res

ist

Fea

ture

Wid

th (

nm)

Focus (m)

0

20

40

60

80

100

120

140

160

180

Res

ist

Fea

ture

Wid

th (

nm)

Focus (m)

8 9 10 11 12 13 14 15 16 17 18

Dose 8 9 10 11 12 13 14 15 16 17 18

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

(a) (b)

Figure 8.24 Bossung plots for (a) dense and (b) isolated 130nm lines showing the difference in isofocal bias.


27

16

18

20

22

24

26

-0.5 0.0 0.5 Focus (microns)

Dos

e (m

J/cm

2)

16

18

20

22

24

26


Dos

e (

mJ/

cm2)

16

18

20

22

24

26


Dos

e (m

J/cm

2)

(a) (b) (c)

Figure 8.25 Process windows calculated using equation (8.49) for a nominal line CD of 100 nm ±10 nm, nominal dose of 20 mJ/cm2, s = -1, and D = 0.45 microns: a) isofocal CD1 = 130 nm, b) isofocal CD1 = 100 nm, and c) isofocal CD1 = 70 nm.


28

18

19

20

21

22 23

24 25

26

-0.2 -0.1 0.0 0.1

Exp

osur

e (m

J/cm

2 )

Focus (m)

Figure 8.26 The overlapping process window for the dense (dashed lines) and isolated (solid lines) features shown to the right of the graph.


29

0

20

40

60

80

100

120

-0.3 -0.2 -0.1 0 0.1

Focus (m)

CD

(nm

)

Dense

Isolated

50

60

70

80

90

100

110

120

130

30 32 34 36 38 40


CD

(n

m)

Dense

Isolated

20

21

22

23

24

25

26

27

30 32 34 36 38 40


CD

den

se -

CD

iso

(nm

)

(a) (b)

20

25

30

35

40

45

-0.3 -0.2 -0.1 0 0.1

CD

dens

e -

CD

iso

(nm

)

Focus (m)

(c) (d)

Figure 8.27 A dual-target approach to monitoring dose and focus using a 90 nm dense line on a 220 nm pitch and an 80 nm isolated line: a) dense and isolated lines through dose; b) the iso-dense difference through dose; c) dense and isolated lines through focus; d) the iso-dense difference through focus.


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+ Focus - Focus Best Focus

Figure 8.28 The asymmetric response of resist sidewall angle to focus provides a means for monitoring focus direction as well as magnitude. Here , + focus is defined as placing the focal plane above the wafer (moving the wafer further away from the lens).


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-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Defocus (microns)

H-V

Bia

s (n

m)

Equal Line/Space

Isolated Line

Figure 8.29 PROLITH simulations of HV bias through focus showing approximately linear behavior ( = 193nm, NA = 0.75, = 0.6, 150 nm binary features, 20 milliwaves of astigmatism). Simulations of CD through focus and fits to equation (8.57) gave the CD curvature parameter a = -184 m-2 for the dense features and -403 m-2 for the isolated lines.


32

118

120

122

124

126

128

130

0.00 0.05 0.10 0.15 0.20

Sigma X-Shift

Line

wid

th (

nm)

Vertical

Horizontal

Figure 8.30 Example of how an x-shift in the center of a conventional source ( = 0.6) affects mainly the vertical (y-oriented) lines and spaces (CD = 130nm, pitch = 650nm, PROLITH simulations).


33

-1st order +1st order0th order-1st order +1st order0th order

-1st order +1st order0th order-1st order +1st order0th order-1st order +1st order0th order

Figure 8.31 Example of dense line/space imaging where only the zero and first diffraction orders are used (kpitch = 1.05). The middle segment of each source circle represents three beam imaging, the outer areas are two beam imaging. a) source shape is properly centered, b) source is offset in x (to the right) by 0.1. Note that the diffraction pattern represents vertical (y-oriented) features.

(a) (b)


34

-1st order +1st order

0th order

-1st order +1st order

0th order

(a) (b)

(c) (d)

Figure 8.32 Examples of how a telecentricity error affects the ratio of two beam to three beam imaging at the worst case pitch ( = 0.4, x-shift = 0.1, kpitch = 1.65). a) vertical lines, no telecentricity error, b) vertical lines, with telecentricity error, c) horizontal lines, no telecentricity error, and d) horizontal lines, with telecentricity error.


35

Res

ist

Fea

ture

Wid

th, C

D

(nm

)

Mask Width (constant duty) (nm)

Isolated Line

Line/Space

0 100 200 300 400 500 600 700 800 900 1000 1100 0

100

200

300

400

500

600

700

800

900

1000

1100

Figure 8.33 Typical mask linearity plot for isolated lines and equal lines and spaces (i-line, NA = 0.56, = 0.5).


36

200 300 400 500 600 700 800

Mask CD (nm)

ME

EF

Isolated Line

Equal Line/Space

0

1

2

3

Figure 8.34 The mask error enhancement factor (MEEF) for the data of Figure 8.33.


37

0.0

0.5

1.0

1.5

2.0

2.5

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Spacewidth/Linewidth

Ima

ge M

EE

F

Coherent

Incoherent

Figure 8.35 The impact of duty cycle (represented here as the ratio of spacewidth to linewidth for an array of line/space patterns) on the image CD based MEEF for both coherent and incoherent illumination. For the incoherent case, an MTF1 of 0.45 was used.


38

-200 -100 0 100 200 0.0

0.3

0.6

0.9

1.2

Horizontal Position (nm)

Rel

ativ

e In

tens

ity

Effective dose error at the nominal line edge

Figure 8.36 Mask errors can be thought of as creating effective dose errors near the edge of the feature.


39

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

100 200 300 400 500 600

Nominal Feature Width (nm)

ME

EF

high contrast

mid contrast

low contrast

Figure 8.37 Resist contrast affects the mask error enhancement factor (MEEF) dramatically near the resolution limit.


40

Y P

ositi

on (

nm)

X Position (nm)

-600

-400

-200

0

200

400

600

-800 -600 -400 -200 0 200 400 600 800

Y P

ositi

on (

nm)

X Position (nm)

-600

-400

-200

0

200

400

600

-400 -200 0 200 400

Figure 8.38 Outline of the printed photoresist pattern (solid) superimposed on an outline of the mask (dashed) shows two examples of line-end shortening (k1 = 0.6).


41

150

200

250

300

350

400

Isolated Line Width (nm)

Gap

Wid

th (

nm)

Linewidth

Gap Width

150 200 250 300 350

Focus Exposure Data

Ideal Behavior

Target Operating Point

Figure 8.39 Line-end shortening can be characterized by plotting the gap width of a structure like that in the insert as a function of the isolated linewidth under a variety of conditions. As shown here, changes in focus and exposure produce a linear gap width versus linewidth behavior.


42

+0.4 m Defocus In Focus -0.4 m Defocus

Figure 8.40 Simulated impact of focus on the shape of the end of an isolated line (250nm line, NA = 0.6, = 0.5, = 248, positive focus defined as shifting the focal plane up).


43

35

40

45

50

55

60

65

70

75

80

0.6 0.7 0.8 0.9 1.0

Numerical Aperture

LES

(nm

)

35

40

45

50

55

60

0 0.2 0.4 0.6 0.8 1.0

Partial Coherence LE

S (

nm)

(a) (b)

Figure 8.41 Response of line-end shortening to imaging parameters (130 nm isolated line, = 248 nm): a) numerical aperture ( = 0.5), and b) partial coherence (NA = 0.85).


44

0

10

20

30

40

50

60

0 20 40 60 80 100

Diffusion Length (nm)

Incr

ease

in L

ES

(nm

)

0

10

20

30

40

50

0 50 100 150

Diffusion Length (nm) In

crea

se in

LE

S (

nm)

(a) (b)

Figure 8.42 Diffusion can have a dramatic effect on line-end shortening of an isolated line: a) 180 nm line, = 248 nm, NA = 0.688, = 0.5, conventional resist, and b) 130 nm line, = 248 nm, NA = 0.85, = 0.5, chemically amplified resist.


45

0

5

10

15

20

25

30

35

10 20 30 40 50

Point-by-point Error (nm)

Fre

que

ncy

CSE90

0

Figure 8.43 Defining a metric of shape error begins with a) making point-by-point measurements comparing actual (dashed) to desired (solid) shapes, which produces b) a frequency distribution of errors (unsigned lengths of the vectors are used here). One possible critical shape error (the CSE90) is shown as an example of the analysis of this distribution.

(a) (b)


46

Figure 8.44 Examples of photoresist pattern collapse, both in cross-section (left) and top down (Courtesy of Joe Ebihara of Canon).


47

wlwlwsws

H

Figure 8.45 Pattern collapse of a pair of isolated lines: a) drying after rinse leaves water between the lines, and b) capillary forces caused by the surface tension of water pull the tops of the lines towards each other, leading to collapse.

(a) (b)

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