Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007 1 Figure 4.1 Film stack showing (a) the geometry for the standing wave derivation,

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

1

Resist

Substrate

Air n1

D z = 0

Resist

Substrate

Air EI

n2

n3

Figure 4.1 Film stack showing (a) the geometry for the standing wave derivation, and (b) a normally incident electric field EI.

(a) (b)


2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 200 400 600 800 1000

Depth into Resist (nm)

Rel

ativ

e In

tens

ity

Figure 4.2 Standing wave intensity in one micron of photoresist on a silicon substrate for an i-line exposure.


3

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 200 400 600 800 1000


Rel

ativ

e In

ten

sity

Figure 4.3 Standing wave intensity within a photoresist film at the start of exposure (850nm of resist on 100nm SiO2 on silicon, = 436nm). Note the impact of the oxide film on the phase of the effective substrate reflectivity, which affects the intensity at the bottom of the resist.


4

z

x

(x,z)

Substrate

x

z = 0

Plane wave

k

r

Figure 4.4 Geometry used for describing plane waves and standing waves for oblique incidence.


5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 10 20 30 40 50 60 70 80 90

Incident Angle (degrees)

Inte

nsi

ty R

efle

ctiv

ity (

|12

|2 )

p-polarization

s-polarization

air

resist

p-polarization

s-pol.

Figure 4.5 Reflectivity (square of the reflection coefficient) as a function of the angle of incidence showing the difference between s- and p-polarization (n1 = 1.0, n2 = 1.7). Both air and resist layers are assumed to be infinitely thick.


6

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500


Rel

ativ

e In

tens

ity

angle = 0 angle = 30

Figure 4.6 Standing wave intensity within a photoresist film (500 nm of resist on silicon, = 248 nm) as a function of incident angle (s-polarization assumed).


7

0.0

0.2

0.4

0.6

0.8

1.0

200 250 300 350 400 450 500 550 600

Wavelength (nm)

Re

lativ

e In

ten

sity

I-Line

H-Line G-Line

E-Line

Figure 4.7 Spectral output of a typical high-pressure mercury arc lamp. The illumination spectrum of an i-line or g-line lithographic exposure tool is usually a filtered portion of this lamp spectrum.


8

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 200 400 600 800 1000


Rel

ativ

e In

tens

ity

single wavelength broadband

Figure 4.8 Standing wave intensity within a photoresist film (1000 nm of resist on silicon), for monochromatic ( = 365 nm) and broadband illumination (350 – 450 nm range of the mercury spectrum).


9

0.40

0.45

0.50

0.55

0.60

0.65

0.90 0.95 1.00 1.05 1.10 1.15 1.20

Resist Thickness (m)

Re

sist

Lin

ew

idth

(m

)

Figure 4.9 CD swing curve showing a sinusoidal variation in the resist linewidth with resist thickness (i-line exposure of resist on silicon).


10

40

50

60

70

80

90

100

0.90 0.95 1.00 1.05 1.10 1.15 1.20


Do

se t

o C

lea

r (m

J/cm

2 )

Figure 4.10 Eo swing curve showing a sinusoidal variation in the resist dose-to-clear with resist thickness (i-line exposure of resist on silicon).


11

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.90 0.95 1.00 1.05 1.10 1.15 1.20


Re

flect

ivity

Figure 4.11 Reflectivity swing curve showing a sinusoidal variation in the resist coated wafer reflectivity with resist thickness (i-line exposure of resist on silicon).


12

Resist

Substrate

Air n1

D z = 0

EI Er0

n2

n3

Resist

Substrate

Air Er1

Figure 4.12 Film stack showing (a) geometry for swing curve derivation, and (b) incident, transmitted, and reflected waves (oblique angles are shown for diagrammatical purposes only).


13

1.00 1.05 1.10 1.15 1.20 90

100

110

120

130

140

150

Do

se-t

o-C

lea

r, E

0 (m

J/cm

2 )

Resist Thickness (microns)

NA = 0.2 NA = 0.3 NA = 0.4 NA = 0.5

NA = 0.0

Figure 4.13 The phase and amplitude of a dose-to-clear swing curve are affected by the range of angles striking the resist, which is controlled by the product of the partial coherence and the numerical aperture (NA) for conventional illumination.


14

140

160

180

200

220

240

260

200 220 240 260 280 300 320 340 360 380 400

Re

sist

Fe

atu

re W

idth

, CD

(n

m)

Resist Thickness (nm)

Figure 4.14 Proper balancing of absorption and reflectivities can make the minimum of a swing curve (D = 310 nm) achieve the same CD as the previous swing curve maximum (D = 280 nm).


15

Substrate Reflectivity

Thickness Layer #2 (nm)

Second Minimum BARC First Minimum BARC

0.0

0.1

0.2

0.3

0.4

0.5

0.6 Substrate Reflectivity

Thickness Layer #2 (nm) 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 4.15 Typical examples of substrate reflectivity versus BARC thickness for different resist/BARC/substrate stacks.


16

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

10 20 30 40 50 60

BARC Thickness (nm)

Ref

ract

ive

Inde

x -

real

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

Ref

ract

ive

Inde

x -

imag

inar

y

n

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

50 70 90 110 130

BARC Thickness (nm)

Ref

ract

ive

Inde

x -

real

0.16

0.21

0.26

0.31

0.36

0.41

Ref

ract

ive

Inde

x -

imag

inar

y

n

(a) (b)

Figure 4.16 Optimum BARC refractive index (real and imaginary parts, n and k) as a function of BARC thickness for normal incidence illumination (resist index = 1.7 + i0.01536 and silicon substrate index = 0.8831 + i2.778) at 193 nm. a) First minimum BARCs, and b) second minimum BARCs.


17

0.000

0.001

0.002

0.003

0.004

0.005

0 20 40 60 80

Optimum BARC Thickness (nm)

R/

2 (1

/nm

2 )

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70


R/|n

|2 (a) (b)

Figure 4.17 Sensitivity of substrate reflectivity for the optimum first minimum BARCs of Figure 4.16a as a function of a) BARC thickness errors, or b) BARC refractive index errors.


18

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

50 70 90 110 130


R/

2 (

1/n

m2)

0.0

0.5

1.0

1.5

2.0

2.5

50 70 90 110 130


R/|n

|2

(a) (b)

Figure 4.18 Sensitivity of substrate reflectivity for the optimum second minimum BARCs of Figure 4.16b as a function of a) BARC thickness errors, or b) BARC refractive index errors.


19

2.10

2.11

2.12

2.13

2.14

2.15

2.16

2.17

2.18

2.19

2.20

0 10 20 30 40 50 60 70

Angle (in air, degrees)

Re

fra

ctiv

e In

dex

- re

al

0.665

0.670

0.675

0.680

0.685

0.690

0.695

0.700

0.705

0.710

0.715

0.720

Re

fra

ctiv

e In

dex

- im

agin

ary

n

D = 20 nm

1.50

1.52

1.54

1.56

1.58

1.60

1.62

1.64

1.66

1.68

0 10 20 30 40 50 60 70


Re

fra

ctiv

e In

dex

- re

al

0.475

0.480

0.485

0.490

0.495

0.500

0.505

0.510

Re

fra

ctiv

e In

dex

- im

ag

ina

ry

n

D = 40 nm

(a) (b)

Figure 4.19 Optimum BARC parameters to achieve minimum substrate reflectivity as a function of incident angle (angle defined in air, before entering the photoresist) for two different BARC thicknesses (resist index = 1.7 + i0.01536 and silicon substrate index = 0.8831 + i2.778) at 193 nm exposure: a) 20 nm BARC thickness, and b) 40 nm BARC thickness.


20

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0 10 20 30 40 50 60 70


Min

imu

m In

ten

sity

Re

flect

ivity

D = 20nm

D = 40nm

Figure 4.20 The best case (minimum) reflectivity (using the BARC parameters shown in Figure 4.19) of the substrate as a function of incident angle for 20nm and 40nm thick BARC films. Note that 60º corresponds to the maximum angle in air allowed for NA = 0.866.


21

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60 70 80

Angle in Air (degrees)

Re

sist

/BA

RC

Ele

ctric

Fie

ld R

efle

ctiv

ity

A: p-polarized

A: s-polarized

B: s-polarized

B: p-polarized

Figure 4.21 An example of the variation of BARC reflectivity as a function of light angle and polarization for two different BARCs. The intensity reflectivity is the square of the electric field reflectivity plotted here, but interference makes the field reflectivity a better measure of the standing wave effects. (Resist index = 1.7 + i0.01536, silicon substrate index = 0.8831 + i2.778, BARC A index = 1.80 + i0.48, BARC A thickness = 30 nm, BARC B index = 1.53 + i0.54, BARC B thickness = 39 nm.)


22

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 120 140

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200

Oxide Thickness S

ubst

rate

Ref

lect

ivity

Thickness Layer #2 (nm)

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200

Figure 4.22 Substrate reflectivity versus BARC thickness over a range of underlying oxide thicknesses (oxide on top of a silicon substrate).


23

80

90

100

110

120

130

Re

sist

Fe

atu

re W

idth

, CD

(n

m)

Resist Thickness (nm)

R = 0.43%

R = 0.07%

150 160 170 180 190 200 210 220 230 240 250

Figure 4.23 CD swing curves (100nm lines with a 280nm pitch are printed with a stepper using annular illumination, with a center sigma given by NA = 0.54) for two different BARCs with different levels of optimization, as given by the resulting substrate reflectivity R.


24

Swing Curve Maximum

Top View

Side View resist

Swing Curve Minimum

Top of Step Bottom of Step

or

Figure 4.24 Example of how resist thickness variations over topography produce linewidth variations due to swing curve effects when a BARC is not used.


25

resist

Figure 4.25 Reflective notching occurs when nearby topography reflects light obliquely into an adjacent photoresist feature.


26

Figure 4.26 Imaging of lines and spaces over reflective topography without BARC (left) showing reflective notching, and with BARC (right) showing the reflective notching effectively suppressed (photos courtesy of AZ Photoresist, used with permission).


27

Image Transmitted Through the CEL

CEL

Incident Aerial Image

Figure 4.27 Contrast Enhancement Layer (CEL) bleaching improves the quality of the aerial image transmitted into the photoresist.


28

25 75 125 175 225 0.65

0.70

0.75

0.80

0.85 M

ag

nitu

de

, |

|

Nitride Thickness (nm)

-200

-100

0

100

200

Ph

ase

(d

eg

ree

s)

Figure 4.28 Variation of the magnitude and phase of the resist/substrate reflection coefficient as a function of silicon nitride thickness for a film stack of resist on nitride on 40 nm of oxide on silicon.


29

0.90 0.95 1.00 1.05 1.10

Do

se t

o C

lea

r (m

J/cm

2 )

Resist Thickness (microns)

93nm Nitride

136nm Nitride

75

100

125

150

175

Figure 4.29 Changes in nitride thickness cause a shift in the phase of the resist swing curve, making nitride thickness control as critical as resist thickness control.


30

25 75 125 175 225 0.0

0.2

0.4

0.6

0.8

1.0

Su

bst

rate

Ref

lect

ivity

Nitride Thickness (nm)

Figure 4.30 Nitride thickness also affects the shape of the resist profile, causing resist footing, undercuts, or vertical profiles. Substrate reflectivity (the square of the magnitude of the reflection coefficient) is shown for comparison.


31

1 E

2 E 1 E

2 E 1 E

2 E

1 E

2 E

TE or s-polarization TM or p-polarization

Figure 4.31 Two plane waves with different polarizations will interfere very differently. For transverse electric (TE) polarization (electric field vectors pointing out of the page), the electric fields of the two vectors overlap completely regardless of the angle between the interfering beams.


32

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 50

Angle in Air (degrees)

Co

ntr

ast

or

NIL

S/

Aerial Image

Image in Resist

Figure 4.32 The interference between two TM polarized planes waves produces an image whose contrast and NILS depends on the angle. Since the angle in resist is reduced by refraction, the contrast and NILS of the image in resist is better than the aerial image.


33

Figure 4.33 Focusing of plane waves arriving at different angles a) in air, and b) in resist, showing that the resist induces spherical aberration.

(a) (b)


34

0.00

0.05

0.10

0.15

0.20

0.25

0.30

-100 -80 -60 -40 -20 0 20 40 60 80 100

Horizontal Position (nm)

SW

AR

Line Edge

2(0)

Mask

Line Edge

Center of

Space

Figure 4.34 The standing wave amplitude ratio (SWAR) at different positions on the feature for coherent three-beam imaging and s-polarization. For this example of three-beam imaging of 100 nm lines and spaces, ao = 0.5, a1 = 0.3183.


35

0.0 0 20 40 60 80

Incident Angle (degrees)

T o

r I t/

I i

0.2

0.4

0.6

0.8

1.0

It/Ii, s-pol.

It/Ii, p-pol.

T, p-pol. T, s-pol.

Figure 4.35 Intensity transmitted into layer 2 relative to the incident intensity (solid lines) and the transmittance T (dashed lines) as a function of the angle of incidence for both s and p polarization (n1 = 1.0, n2 = 1.5).

Documents

Chris A. Mack, Fundamental Principles of Optical Lithography, (c) 2007 1 Figure 4.1 Film stack showing (a) the geometry for the standing wave derivation,