chris a. mack, fundamental principles of optical lithography, (c) 2007 1 design mask aerial image...

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

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Design

Mask

Aerial Image

Latent Image

Developed Resist Image

Image in Resist

PEB Latent Image

Figure 9.1 The lithography process expressed as a sequence of information transfer steps.


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Imin

mask

image

Imax

Figure 9.2 Image contrast is the conventional metric of image quality used in photography and other imaging applications, but is not directly related to lithographic quality.


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mask

image

Figure 9.3 Image Log-Slope (or the Normalized Image Log-Slope, NILS) is the best single metric of image quality for lithographic applications.


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0.0 -150 -100 -50 0 50 100 150

Horizontal Position (nm)

Rel

ativ

e In

tens

ity

0.2

0.4

0.6

0.8

1.0

1.2

1.4 In Focus

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

-0.2 -0.1 0 0.1 0.2

Defocus (microns)

Nor

ma

lize

d Im

age

Log

-slo

pe

(a) (b)

Figure 9.4 The effect of defocus is to (a) ‘blur’ an aerial image, resulting in (b) reduced log-slope as the image goes out of focus (150 nm space on a 300 nm pitch, NA = 0.93, = 193 nm).


5

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 Defocus (microns)

NIL

S

365 nm

248 nm

193 nm

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8

Defocus (microns)

NIL

S

NA = 0.5

NA = 0.6

NA = 0.7

(a) (b)

Figure 9.5 Using the log-slope defocus curve to study lithography: (a) lower wavelengths give better depth of focus (NA = 0.6, = 0.5, 250 nm lines and spaces), and (b) there is an optimum NA for maximizing depth of focus ( = 248 nm, = 0.5, 250 nm lines and spaces).


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0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 NILS

Exp

osur

e La

titud

e (%

) %EL = 8.9(NILS – 0.5)

Figure 9.6 Typical correlation between NILS and exposure latitude (simulated data, = 248 nm, NA = 0.6, = 0.5, 500 nm of UV6 on ARC on silicon, printing 250 nm lines and spaces through focus).


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1.2

1.05

0.3

0.9

Partial Coherence 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.90

0.85

0.80

0.70

0.60

0.50

0.75

0.65

0.55

Num

eric

al A

pert

ure

Figure 9.7 One approach to the optimum stepper problem is the pick a fixed amount of defocus (0.2 m) and find the settings that maximize the NILS ( = 248 nm, 130 nm lines on a 360 nm pitch, contours of constant NILS).


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0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Sine(incident angle)

Res

ist R

efle

ctiv

ity

TM-pol.

TE-pol.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

TE-pol.

TM-pol.

Res

ist R

efle

ctiv

ity

0.0 0.2 0.4 0.6 0.8 1.0

Sine(incident angle)

(a) (b)

Figure 9.8 Intensity reflectivity between air and resist of plane waves as a function of incident angle and polarization for a) resist on silicon, and b) resist on an optically matched substrate ( = 248 nm, resist n = 1.768 + i0.009868).


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0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Relative Sensitizer Concentration, m

-m ln

(m)

Figure 9.9 Plot revealing the existence of an optimum exposure, the value of m at which the latent image gradient is maximized. Note that m = 1 corresponds with unexposed resist, while m = 0 is completely exposed resist.


10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1.0

Relative Sensitizer Concentration m(z)

Rel

ativ

e La

tent

Imag

e G

radi

ent

Az = 0

Az = 1

Az = 2

Figure 9.10 Bleaching (increasing values of Az) results in increased latent image gradient at the bottom of the resist (shown here is the special case where B = 0).


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0.5

0.6

0.7

0.8

0.9

1.0

0.00 0.05 0.10 0.15 0.20

nD/pitch

a n*/

a n

Figure 9.11 Effect of diffusion on the latent image frequency components for a dense line.


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0.70

0.75

0.80

0.85

0.90

0.95

1.00

0.0 0.05 0.10 0.15 0.20 0.25 0.30

D/L

Fra

ctio

nal L

IG a

fter

PE

B

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (D/L)

2 F

ract

iona

l LIG

afte

r P

EB

(a) (b)

Figure 9.12 Increased diffusion (shown by the dimensionless quantity D/L, the diffusion length over the width of the edge region) causes a decease in the latent image gradient (LIG) after PEB.


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0.0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

Relative Sensitizer Concentration, m = 1-h

-mln

(m)/

(1-m

)

Figure 9.13 For a chemically amplified resist with a given required amount of amplification, the exposure dose (and thus relative sensitizer concentration m) is optimum as the dose approaches zero (m 1), assuming negligible diffusion.


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0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.00 0.05 0.10 0.15 0.20 0.25

nD/pitch

DPSF

RDPSF

a n*/

a n

Figure 9.14 Effect of diffusion on the latent image frequency components for a dense line, comparing pure diffusion (DPSF) to reaction diffusion (RDPSF).


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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 20 40 60 80 100

PEB time (sec) or 10f

Rel

ativ

e LI

G (

afte

r P

EB

)

Total Gradient Amplification Diffusion

Figure 9.15 Including diffusion with amplification, there is an optimum PEB to maximize the latent image gradient (LIG), shown here relative to the maximum possible LIG. For this example, Kamp = 0.1 s-1, = 200 s and the exposure dose is chosen to give the maximum gradient for each PEB time.


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0 0.2 0.4 0.6 0.8 1

= 2D/(L2Kamp)

0

1

2

3

4

5

6

7

8

9

10

f

0.35

0.40

0.45

0.50

0.55

0.60

0 0.2 0.4 0.6 0.8 1

Opt

imum

m*

= 2D/(L2Kamp)

(a) (b)

Figure 9.16 The optimum value of a) the amplification factor, and b) the deblocked concentration in order to maximize the final latent image gradient, as a function of .


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0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 0.2 0.4 0.6 0.8 1

-(dm

*/dx

)/IL

S

= 2D/(L2Kamp)

Figure 9.17 The optimum value of the final latent image gradient (relative to the image log-slope), as a function of .


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0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

-(dm

*/dx

)/IL

S

= 2D/(L2Kamp)

q0 = 0

q0 = 0.1

q0 = 0.2

0 0.5 1.0 1.5

Figure 9.18 The optimum value of the final latent image gradient (relative to the image log-slope), as a function of for cases with and without quencher.


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0

1

2

3

4

5

0.0 0.5 1.0 1.5

= 2D/(L2Kamp)

Op

timu

m

f

q = 0

q = 0.1

q = 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.5 1.0 1.5 O

ptim

um

m*

= 2D/(L2Kamp)

q = 0

q = 0.1

q = 0.2

(a) (b)

Figure 9.19 The optimum value of a) the amplification factor, and b) the deblocked concentration in order to maximize the final latent image gradient, as a function of for different quencher loadings.


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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.05 0.10 0.15 0.20 0.25 0.30

q0

Crit

ical

Figure 9.20 Numerically determined values of the critical value (c) for different quencher loadings.


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10

Exposure Dose (mJ/cm2)

1

10

100

Dev

elop

me

nt R

ate

(nm

/s)

100 1000

Figure 9.21 Typical development rate function of a positive photoresist (one type of HurterDriffield curve).


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0

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1.0

Relative Concentration m*

ln

r/m

* n = 5

n = 10

Figure 9.22 One component of the overall photoresist contrast is the variation in development rate r with chemical species m*, shown here for the reaction-controlled version of the original kinetic development rate model (rmax = 100 nm/s, rmin = 0.1 nm/s).


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0

10

20

30

40

50

60

70

80

0.5 0.6 0.7 0.8 0.9 1.0

Relative Concentration m*

n = 5

n = 10

n = 20

lnr/m

*

Figure 9.23 Development rate gradient with inhibitor concentration for the original kinetic development rate model (rmax = 100 nm/s, rmin = 0.1 nm/s, mth = 0.7).


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0

2

4

6

8

10

12

14

16

18

0.5 0.6 0.7 0.8 0.9 1.0 Relative Concentration m

Ga

mm

a

n = 5

n = 20

n = 10

Figure 9.24 Photoresist contrast as a function of inhibitor concentration for the original kinetic development rate model, assuming no diffusion (rmax = 100 nm/s, rmin = 0.1 nm/s, mth = 0.7) and different values of the dissolution selectivity parameter n.


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0

1

2

3

4

5

010

2030

4050

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Gamma

Amplification Factor

Exposure Dose (mJ/cm2)

Figure 9.25 The overall photoresist contrast (gamma) as a function of exposure dose (E) and amplification factor (f) for a chemically amplified resist with no diffusion ( = 0, rmax = 100 nm/s, rmin = 0.1 nm/s, n = 5, C = 0.05 cm2/mJ).


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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1 3 5 7 9 11 13

LPM Gamma

dln(

CD

)/dl

n(E

)

2/NILS

Figure 9.26 A plot of equation (9.88) showing how the exposure latitude term approaches its limiting value of 2/NILS as the lumped photoresist contrast increases. In this case, the resist aspect ratio is 2, the ratio I(CD/2)/I(0) is 0.5 and the NILS is 2.


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Figure 9.27 SEM pictures of photoresist features exhibiting line edge roughness.


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0

1

2

3

4

5

0 5 10 15 20 25 30

Acid Diffusion Length (nm)

LER

(A

rb. U

nits

)

a = 0.5 nm

a = 1.5 nm

0

1

2

3

4

5

0 5 10 15 20 25 30

Acid Diffusion Length (nm) L

ER

(A

rb. U

nits

)

a = 0.5 nm

a = 1.5 nm

(a) (b)

Figure 9.28 Prediction of LER trends for a 45 nm feature using the generic conditions found in equation (9.99) and using three values of the deblocking reaction capture range a (0.5, 1, and 1.5 nm): a) assuming a 2-dimensional problem, and b) for a 3-dimensional problem.


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Process Step Information Error Sources Information Metric

Design Polygons, binary (usually assumed perfect) Mask Amplitude transmittance,

tm(x,y) CD and registration errors, corner rounding, phase and transmittance

Aerial Image I(x,y) Diffraction limitation, aberrations, defocus, flare, polarization

NILS

Image in Resist

I(x,y,z) Substrate reflections/thin film effects, polarization effects, defocus through the resist

NILS

Exposure Latent Image m(x,y,z) or h(x,y,z) (before PEB)

Exposure dose errors Latent image gradient

Post-exposure Bake

Latent Image m*(x,y,z) (after PEB)

Thermal dose errors, diffusion Latent image gradient

Development Development Rate r(x,y,z) + Resist Profile (CD, sidewall angle, resist loss)

Finite contrast, rmax/rmin Development rate log-slope, gamma + exposure latitude, CD error

Table 9.1 Summary of lithography process steps and their corresponding information metrics.

chris a. mack, fundamental principles of optical lithography, (c) 2007 1 design mask aerial image...

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