consortium for metrology of semiconductor nanodefects © 2000 asu all rights reserved. pyramidal...

Consortium for Metrology ofSemiconductor Nanodefects

© 2000 ASU All rights reserved.

Pyramidal Pits and Optical Wafer Inspection Systems

M. Jordan, Jr., R.E. Díaz, and E.D. Hirleman

13 January 2000



Presentation overview

• Design and pre-characterization of a pit standard

• Angle-resolved scatter from pyramidal pits• A model of light scatter from pyramidal pits• Comparison of scatter from pits and

particles



Design and pre-characterization of a pit

standard

• Electron beam lithography was used to pattern the defect field.

• Critically-dimensioned pit sizes were generated.• Individual pits were thoroughly characterized.• Pit standard provided a continuous range of pit sizes.



Angle-resolved scatter from pyramidal pits

• Used combinations of p- and s-polarization, incidence angles of 45° and 65°, and wavelength 0.6328 µm.

• Pits used in measurements range in size from 0.34 µm to 0.76 µm.

• A characteristic null moves forward with increasing pit size only with p-polarization.

• A characteristic peak increases with increasing pit size regardless of polarization and incidence angle.



A model of light scatter from pyramidal pits

• A simple model explains the scattering phenomenon.• High refractive index of silicon and large electrical

size of pits in the silicon foiled DDSUB.• Developed a simple yet accurate model for s-

polarization based on diffraction theory.



Comparison of scatter from pits and particles

• Scatter was compared using pyramidal pits and equal diameter silicon dioxide spheres.

• Comparison was made using 65° incidence and wavelength 0.6328 µm for both s- and p-polarization.

• In s-polarization, the null and peak of the pit remain stationary with increasing size, but the null and peak of the particle move forward.

• In p-polarization, the null of the pit moves forward with increasing size, but the first peak of the particle remains within 5°.



Floor plan of the defect field

Target widths (µm) by row and column

0.05 0.10 0.15 0.20 0.22 0.24 0.26 0.28

0.30 0.32 0.34 0.35 0.36 0.37 0.38 0.40

0.05 0.10 0.15 0.20 0.22 0.24 0.26 0.28

0.30 0.32 0.34 0.35 0.36 0.37 0.38 0.40

0.05 0.10 0.15 0.20 0.22 0.24 0.26 0.28

0.30 0.32 0.34 0.35 0.36 0.37 0.38 0.40

0.05 0.10 0.15 0.20 0.22 0.24 0.26 0.28

0.30 0.32 0.34 0.35 0.36 0.37 0.38 0.40



Pyramidal pit of size 0.34 µm



Average pit widths and aspect ratios by column

number

column no. in width (µm) aspect ratio pitnumber average average s.d. average s.d. orientation——————————————————————————1 2 0.34 0.007 1.25 0.07 vertical2 2 0.37 0.014 1.25 0.21 both3 4 0.49 0.027 1.13 0.13 both4 4 0.53 0.031 1.13 0.13 both5 4 0.63 0.082 1.14 0.17 horizontal7 4 0.64 0.093 1.18 0.05 both8 4 0.66 0.061 1.10 0.08 both——————————————————————————



In-plane, differential scatter of pyramidal pits as

measured

s-polarizationincidence angle 65°wavelength 0.6328 µm

scattering angle (degrees)

DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100

0.76 µm

0.69 µm

0.63 µm

0.51 µm

0.41 µm

0.35 µm

Frame 001 09 Jan 2000 Differential scatter of pyramidal pits, 65° incidence, s-polarizationFrame 001 09 Jan 2000 Differential scatter of pyramidal pits, 65° incidence, s-polarization



Peak/null values, positions for s-polarization, i=65°,

=0.6328 µm

size peak position, value null position, value peak-to-null(µm) (µm²/sr) (µm²/sr) difference——————————————————————————0.35 * ~0.034 – – –0.41 * 0.056 – – –0.51 45° 0.110 ~0° 0.0111 0.099 µm²/sr0.63 49° 0.130 2° 0.0046 0.125 µm²/sr0.69 39° 0.268 2° 0.0067 0.261 µm²/sr0.76 41° 0.385 ~2° 0.0170 0.368 µm²/sr——————————————————————————* unlocalized




measured

p-polarizationincidence angle 65°wavelength 0.6328 µm


DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100

0.76 µm

0.69 µm

0.63 µm

0.51 µm

0.41 µm

0.35 µm

Frame 001 09 Jan 2000 Differential scatter of pyramidal pits, 65° incidence, p-polarizationFrame 001 09 Jan 2000 Differential scatter of pyramidal pits, 65° incidence, p-polarization



Peak/null values, positions for p-polarization, i=65°,

=0.6328 µm

size peak position,value null position, value peak-to-null(µm) (µm²/sr) (µm²/sr) difference——————————————————————————0.34 35° 0.047 – 42° 0.0009 0.046 µm²/sr0.41 38° 0.060 – 16° 0.0028 0.057 µm²/sr0.51 40° 0.096 – 4° 0.0041 0.092 µm²/sr0.63 38° 0.092 3° 0.0035 0.089 µm²/sr0.69 40° 0.143 12° 0.0086 0.134 µm²/sr0.76 45° 0.154 12° 0.0024 0.152 µm²/sr——————————————————————————




measured



DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100

0.76 µm0.69 µm

0.63 µm0.51 µm0.41 µm0.35 µm

Frame 001 09 Jan 2000 Differential scatter of pyramidal pits, 45° incidence, s-polarizationFrame 001 09 Jan 2000 Differential scatter of pyramidal pits, 45° incidence, s-polarization



Peak/null values, positions for s-polarization, i=45°,

=0.6328 µm

size peak position, value null position, value peak-to-null(µm) (µm²/sr) (µm²/sr) difference——————————————————————————0.35 28° 0.075 – – –0.41 24° 0.135 – – –0.51 28° 0.145 – 5° 0.028 0.117 µm²/sr0.63 31° 0.316 – 2° 0.007 0.309 µm²/sr0.69 30° 0.391 – 3° 0.007 0.384 µm²/sr0.76 31° 0.663 – 3° 0.012 0.651 µm²/sr——————————————————————————




measured



DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100

0.76 µm

0.69 µm

0.63 µm

0.51 µm

0.41 µm

0.35 µm

Frame 001 09 Jan 2000 Differential scatter of pyramidal pits, 45° incidence, p-polarizationFrame 001 09 Jan 2000 Differential scatter of pyramidal pits, 45° incidence, p-polarization



Peak/null values, positions for p-polarization, i=45°,

=0.6328 µm

size peak position, value null position, value peak-to-null(µm) (µm²/sr) (µm²/sr) difference——————————————————————————0.35 28° 0.066 – – –0.41 25° 0.100 – – –0.51 28° 0.131 – 11° 0.011 0.120 µm²/sr0.63 29° 0.165 1° 0.009 0.156 µm²/sr0.69 26° 0.214 2° 0.006 0.208 µm²/sr0.76 31° 0.216 0° 0.001 0.215 µm²/sr——————————————————————————



Qualitative comparison of trends by increase in size

i polari- peak null peak-to-null

zation position value position value difference

————————————————————————

65° s no trend ~0° no trend 65° p no trend 45° s no trend ~0° no trend 45° p no trend ————————————————————————



Reflectance of air-Si interface for a wavelength of 0.6328

µm

angle of incidence (degrees)

refle

cta

nce

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RsRp

Frame 001 08 Jan 2000 Reflectance versus angle of incidence using wavelength 0.6328 µmFrame 001 08 Jan 2000 Reflectance versus angle of incidence using wavelength 0.6328 µm



Model of light scatter from a pit – the physical equivalent

b

x

z

ya

H

E

i

i

i

( , , )r s s

s

s

Frame001 06Nov1999 InvertedPyramidPitFrame001 06Nov1999 InvertedPyramidPit



Model of light scatter from a pit – the equation

• Assumes behavior approaching that of a perfect electric conductor

• Incorporates duality and physical equivalence• Based on the Fraunhoffer diffraction approximation

2 2dC

d

ab b

bs

ss i

s i

+ for

for s

s

cossin[ ( sin sin ) / ]

( sin sin ) /

/

/2 2

2

2

3 2



In-plane, differential scatter for a pyramidal pit of size

0.35 µm



DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100

101

measuredcalculated

Frame 001 08 Jan 2000 Differential scatter of a 0.35 µm pyramidal pit, 65° incidence, s-polarizationFrame 001 08 Jan 2000 Differential scatter of a 0.35 µm pyramidal pit, 65° incidence, s-polarization



In-plane, differential scatter of a pit and a particle, s-

polarization


DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100

0.35 µm SiO2 sphere0.35 µm pyramidal pit

Frame 001 08 Jan 2000 Differential scatter from a 0.35 µm SiO2 sphere, 65° incidence, s-polarizationFrame 001 08 Jan 2000 Differential scatter from a 0.35 µm SiO2 sphere, 65° incidence, s-polarization




In-plane, differential scatter of a pit and a particle, s-

polarization


DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100


Frame 001 08 Jan 2000 Differential scatter from a 0.41 µm SiO2 sphere, 65° incidence, s-polarizationFrame 001 08 Jan 2000 Differential scatter from a 0.41 µm SiO2 sphere, 65° incidence, s-polarization




In-plane, differential scatter of a pit and a particle, p-

polarization


DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100


Frame 001 09 Jan 2000 Differential scatter from a 0.35 µm SiO2 sphere, 65° incidence, p-polarizationFrame 001 09 Jan 2000 Differential scatter from a 0.35 µm SiO2 sphere, 65° incidence, p-polarization




In-plane, differential scatter of a pit and a particle, p-

polarization



DS

C(µ

m²/

sr)

-90 -60 -30 0 30 60 9010-3

10-2

10-1

100


Frame 001 09 Jan 2000 Differential scatter from a 0.41 µm SiO2 sphere, 65° incidence, p-polarizationFrame 001 09 Jan 2000 Differential scatter from a 0.41 µm SiO2 sphere, 65° incidence, p-polarization



Conclusions

• A pit standard enabled the observation of light scatter as a function of size and shape.

• A characteristic null moves forward with increasing pit size using p-polarization.

• An analytical model predicts the light scatter of pyramidal pits using s-polarization and high incidence angle.

• Light scatter trends by size of pits and particles are switched as polarization is changed.



Acknowledgements

Howard Huff SEMATECH

John C. Stover ADE Optical Systems Corporation

Stanley D. Duke Duke Scientific Corporation

Robert Johnston Sumitomo Sitix Silicon, Inc.

consortium for metrology of semiconductor nanodefects © 2000 asu all rights reserved. pyramidal...

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