(a)

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

1

0.0 0.2 0.4 0.6 0.8 1.0 0

20

40

60

80

100

Deve

lopm

ent R

ate

(nm

/s)

Relative Inhibitor Concentration m

n = 16

n = 2

Figure 7.1 Development rate plot of the original kinetic model as a function of the dissolution selectivity parameter (rmax = 100 nm/s, rmin = 0.1 nm/s, mth = 0.5, and n = 2, 4, 8, and 16).


2

0.0 0.2 0.4 0.6 0.8 1.0 0

20

40

60

80

100

Deve

lopm

ent R

ate

(nm

/s)


n = 9

n = 1

n = 5

l = 5

0.0 0.2 0.4 0.6 0.8 1.0 0

20

40

60

80

100

Deve

lopm

ent R

ate

(nm

/s)


l = 15

l = 1

(a) (b)

Figure 7.2 Plots of the enhanced kinetic development model for rmax = 100 nm/s, rresin = 10 nm/s, rmin = 0.1 nm/s with: (a) l = 9; and (b) n = 5.


3

0.1

1

10

100

1000

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Initial Inhibitor Concentration (w t fraction)

Dev

elo

pme

nt R

ate

(n

m/s

)

0.1

1

10

100

1000

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Initial Inhibitor Concentration (w t fraction)

Dev

elo

pme

nt R

ate

(n

m/s

) (a) (b)

Figure 7.3 An example of a Meyerhofer plot, showing how the addition of increasing concentrations of inhibitor increases rmax and decreases rmin: a) idealized plot showing a log-linear dependence on initial inhibitor concentration, and b) the enhanced kinetic model assuming kenh M0 and kinh M0

2.


4

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0

10

20

30

40

50

Dev

elop

me

nt R

ate

(nm

/s)


Figure 7.4 Comparison of experimental dissolution rate data (symbols) exhibiting the so-called ‘notch’ shape to best fits of the original (dotted line) and enhanced (solid line) kinetic models. The data shows a steeper drop in development rate at about 0.5 relative inhibitor concentration than either model predicts.


5

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0

10

20

30

40

50

Deve

lopm

ent R

ate

(nm

/s)


mth_notch = 0.4 mth_notch = 0.5

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0

10

20

30

40

50

Deve

lopm

ent R

ate

(nm

/s)


n_notch = 60 n_notch = 15

(a) (b)

Figure 7.5 Plots of the notch model: (a) mth_notch equal to 0.4, 0.45, and 0.5 with n_notch equal to 30; and (b) n_notch equal to 15, 30, and 60 with mth_notch equal to 0.45.


6

0.0 0.2 0.4 0.6 0.8 1.0 0.00

0.25

0.50

0.75

1.00

1.25

Rel

ativ

e D

evel

opm

ent

Rat

e

Relative Depth into Resist

Figure 7.6 Example surface inhibition with r0 = 0.1 and d = 100 nm for a 1000 nm thick resist.


7

0 100 200 300 400 500 0

20

40

60

80

100

Dev

elop

me

nt R

ate

(nm

/s)

Exposure Dose (mJ/cm2)

30 °C

14 °C

Figure 7.7 Development rate of THMR-iP3650 (averaged through the middle 20% of the resist thickness) as a function of exposure dose for different developer temperatures shows a change in the shape of the development dose response.


8

0.0 0.2 0.4 0.6 0.8 1.0 0

40

80

120

160

200

Dev

elop

me

nt R

ate

(nm

/s)


30 °C

14 °C

Figure 7.8 Comparison of the best-fit models of THMR-iP3650 for different developer temperatures shows the effect of increasing rmax and increasing dissolution selectivity parameter n on the shape of the development rate curve.


9

50

100

200

3.25 3.30 3.35 3.40 3.45 3.50

1000/Developer Temperature (K)

Dis

solu

tion r

max

(nm

/s)

3

8

3.25 3.30 3.35 3.40 3.45 3.50

1000/Developer Temperature (K)

Dis

solu

tion n

5

4

7

6

(a) (b)

Figure 7.9 Arrhenius plots of the maximum dissolution rate rmax and the dissolution selectivity parameter n for THMR-iP3650.


10

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Log (Exposure Dose)

Optic

al D

ensi

ty

Figure 7.10 An example Hurter-Driffield (H-D) curve for a photographic negative.


11

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 10 100 1000


Rela

tive T

hic

kness

Rem

ain

ing

Figure 7.11 Positive resist characteristic curve used to measure contrast.


12

0.01

0.1

1

10

100

1000

1 10 100 1000


Deve

lopm

ent R

ate

(nm

/s)

Figure 7.12 A lithographic H-D curve used to define the theoretical contrast.


13

0

1

2

3

4

5

6

1 10 100 1000


Theore

tical C

ontrast

Figure 7.13 A typical variation of theoretical contrast with exposure dose. For this data, the FWHM dose ratio is about 5.5.


14

Resist

Substrate

Development Path

Figure 7.14 Typical development path.


15

Path

s

x

z

Figure 7.15 Section of a development path relating path length s to x and z.


16

0

50

100

150

200

250

300

350

400

-200 -100 0 100 200 x (nm)

z (n

m)

Resist

Figure 7.16 Example of how the calculation of many development paths leads to the determination of the final resist profile.


17

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.1 0.2 0.3 0.4 0.5

x/pitch

Rel

ativ

e In

tens

ity

Aerial Image

Gaussian

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.1 0.2 0.3 0.4 0.5

x/pitch

Rel

ativ

e In

tens

ity

Aerial Image

Gaussian

(a) (b)

Figure 7.17 Matching a three-beam image (a0 = 0.45, a1 = 0.55, a2 = 0.1) with a Gaussian using a) a value of s given by equation (7.91); and b) the best fit s. Note the goodness of the match in the region of the space (x/pitch < 0.25).


18

0

2

4

6

8

10

12

14

16

18

20

-0.15 -0.10 -0.05 0 0.05 0.10

Distance from nominal edge (k1 units)

Image L

og-s

lope

(1/

m)

Space Line

-0.15 -0.10 -0.05 0 0.05 0.10

Distance from nominal edge (k1 units)

Image L

og-s

lope

(1/

m)

Space Line

0

2

4

6

8

10

12

14

16

18

20

(a) (b)

Figure 7.18 Simulated aerial images over a range of conditions show that the image log-slope varies about linearly with distance from the nominal resist edge in the region of the space: a) k1 = 0.46 and b) k1 = 0.38 for isolated lines, isolated spaces, and equal lines and spaces and for conventional, annular and quadrupole illumination.


19

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6

z

Dw

(z)

Figure 7.19 A plot of Dawson’s Integral, Dw(z).


20

20

40

60

80

100

120

140

160

180

0.9 1.4 1.9 2.4 2.9

E/E(0)

CD

(nm

)

VTR

LPM and Approximate LPM

Figure 7.20 CD versus dose curves as predicted by the LPM equation (7.98), the LPM using the approximation for the Dawson’s integral, and the VTR. All models assumed a Gaussian image with g = 0.0025 1/nm2 (NILS1 = 2.5 and CD1 = 100 nm), = 10, and Deff = 200 nm.


21

Res

ist

Thi

ckne

ss (

nm)


0

240

480

720

960

1200

0 100 200 300 400 500

Exposure Dose (mJ/cm2) 0 20 40 60 80 100

Res

ist

Thi

ckne

ss (

nm)

0

240

480

720

960

1200

(a) (b)

Figure 7.21 Measured contrast curves for an i-line resist at development times ranging from 9 to 201 seconds (shown here over two different exposure scales).


22

Deve

lopm

ent R

ate

(n

m/s

)


0

24

48

72

96

120

0.0 0.2 0.4 0.6 0.8 1.0

rmax = 100.3 nm/s

rmin = 0.10 nm/s

mth = 0.06

n = 4.74

RMS Error: 2.7 nm/s

Figure 7.22 Analysis of the contrast curves generates an r(m) data set, which was then fit to the original kinetic development model (best fit is shown as the solid line).

(a)

Documents

development rate curve

development rate of

development rate plot

notch model

notch equal

typical development

development dose response

maximum dissolution