Abstract

We develop a paired circularly polarized heterodyne ellipsometer (PCPHE), in which a heterodyne interferometer based on a two-frequency circularly polarized laser beam is set up. It belongs to an amplitude-sensitive ellipsometer that is able to provide not only a wider dynamic range of polarization modulation frequency but also a higher detection sensitivity than that of a conventional photometric ellipsometer. A real-time and precise measurement of ellipsometric parameters, which demonstrated an accuracy of less than 1nm on thickness measurement of SiO2 thin film deposited on silicon substrate, can be applied with the PCPHE.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Greef, “An automatic ellipsometer for use in electrochemical investigations,” Rev. Sci. Instrum. 41, 532-538 (1970).
    [CrossRef]
  2. C. V. Kent, “A photoelectric method for the determination of the parameters of elliptically polarized light,” J. Opt. Soc. Am. 27, 117-119 (1937).
    [CrossRef]
  3. D. E. Aspnes, “Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers,” J. Opt. Soc. Am. A 21, 403-410 (2004).
    [CrossRef]
  4. S. N. Jasperson, D. K. Burge, and R. C. O'Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548-558 (1973).
    [CrossRef]
  5. S. N. Jasperson and S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761-767 (1969).
    [CrossRef]
  6. M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
    [CrossRef]
  7. K. Postava, A. Maziewski, T. Yamaguchi, R. Ossikovski, S. Višňovsky, and J. Pištora, “Null ellipsometer with phase modulation,” Opt. Express 12, 6040-6045 (2004).
    [CrossRef] [PubMed]
  8. J. Shamir and Y. Fainman, “Rotating linearly polarized light source,” Appl. Opt. 21, 364-365 (1982).
    [CrossRef] [PubMed]
  9. J. Shamir and A. Klein, “Ellipsometry with rotating plane-polarized light,” Appl. Opt. 25, 1476-1480 (1986).
    [CrossRef] [PubMed]
  10. L. Singher, A. Brunfeld, and J. Shamir, “Ellipsometry with a stabilized Zeeman laser,” Appl. Opt. 29, 2405-2408 (1990).
    [CrossRef] [PubMed]
  11. W. Mao, S. Zhang, L. Cui, and Y. Tan, “Self-mixing interference effects with a folding feedback cavity in Zeeman-birefringence dual frequency laser,” Opt. Express 14, 182-189 (2006).
    [CrossRef] [PubMed]
  12. D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precision Eng. 18, 161-163 (1996).
    [CrossRef]
  13. Y. L. Chen and D. C. Su, “Method for determining full-field absolute phases in the common-path heterodyne interferometer with an electro-optic modulator,” Appl. Opt. 47, 6518-6523 (2008).
    [CrossRef] [PubMed]
  14. Step wafer ID 0153 from Mikropack GmbH, Germany. The calibration data sheet of step wafer SiO2 on Si serial number ID0153, by Dipl-Ing (FH) Michael Kaiser, Labor für Mikrosystemtechnik FH-München, Germany.
  15. P. R. Berington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992).
  16. C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
    [CrossRef]
  17. S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
    [CrossRef]
  18. L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26, 349-351 (2001).
    [CrossRef]
  19. Y. L. Lo, H. W. Chih, C. Y. Yeh, and T. C. Yu, “Full-field heterodyne polariscope with an image signal processing method for principal axis and phase retardation measurements,” Appl. Opt. 45, 8006-8012 (2006).
    [CrossRef] [PubMed]

2008

2007

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
[CrossRef]

2006

2004

2001

1998

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

1996

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precision Eng. 18, 161-163 (1996).
[CrossRef]

1990

1986

1982

1973

S. N. Jasperson, D. K. Burge, and R. C. O'Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548-558 (1973).
[CrossRef]

1970

R. Greef, “An automatic ellipsometer for use in electrochemical investigations,” Rev. Sci. Instrum. 41, 532-538 (1970).
[CrossRef]

1969

S. N. Jasperson and S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

1937

Aspnes, D. E.

Berington, P. R.

P. R. Berington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992).

Bertucci, S.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Brunfeld, A.

Burge, D. K.

S. N. Jasperson, D. K. Burge, and R. C. O'Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548-558 (1973).
[CrossRef]

Chao, Y. F.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precision Eng. 18, 161-163 (1996).
[CrossRef]

Chen, S. S.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Chen, Y. L.

Chih, H. W.

Chiu, M. H.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precision Eng. 18, 161-163 (1996).
[CrossRef]

Chou, C.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
[CrossRef]

L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26, 349-351 (2001).
[CrossRef]

Cui, L.

El Ghemmaz, A.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Fainman, Y.

Greef, R.

R. Greef, “An automatic ellipsometer for use in electrochemical investigations,” Rev. Sci. Instrum. 41, 532-538 (1970).
[CrossRef]

Hsieh, J. C.

Huang, H. S.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Jasperson, S. N.

S. N. Jasperson, D. K. Burge, and R. C. O'Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548-558 (1973).
[CrossRef]

S. N. Jasperson and S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

Johann, L.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Kent, C. V.

Kleim, R.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Klein, A.

Leou, K. C.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Lin, T. L.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Liu, Y. W.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Lo, Y. L.

Lyu, C. W.

Mao, W.

Maziewski, A.

Nicolas, N.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

O'Handley, R. C.

S. N. Jasperson, D. K. Burge, and R. C. O'Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548-558 (1973).
[CrossRef]

Ossikovski, R.

Pawlowski, A.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Peng, L. C.

Pištora, J.

Postava, K.

Robinson, D. K.

P. R. Berington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992).

Schnatterly, S. E.

S. N. Jasperson and S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

Shamir, J.

Singher, L.

Stein, N.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Su, D. C.

Tan, Y.

Teng, H. K.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Tsai, F. H.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Višnovsky, S.

Wang, M. W.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Yamaguchi, T.

Yeh, C. Y.

Yu, C. J.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Yu, T. C.

Zhang, S.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827-832 (2004).
[CrossRef]

Opt. Commun.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, “Polarization modulation imaging ellipsometry for thin film thickness measurement,” Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Precision Eng.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precision Eng. 18, 161-163 (1996).
[CrossRef]

Rev. Sci. Instrum.

R. Greef, “An automatic ellipsometer for use in electrochemical investigations,” Rev. Sci. Instrum. 41, 532-538 (1970).
[CrossRef]

S. N. Jasperson and S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761-767 (1969).
[CrossRef]

Surf. Sci.

S. N. Jasperson, D. K. Burge, and R. C. O'Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548-558 (1973).
[CrossRef]

Thin Solid Films

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, and R. Kleim “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313-314, 73-78 (1998).
[CrossRef]

Other

Step wafer ID 0153 from Mikropack GmbH, Germany. The calibration data sheet of step wafer SiO2 on Si serial number ID0153, by Dipl-Ing (FH) Michael Kaiser, Labor für Mikrosystemtechnik FH-München, Germany.

P. R. Berington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

High-speed linear polarization rotator.

Fig. 2
Fig. 2

Optical setup of PCPHE. EOM, electro-optic modulator; Q, quarter-wave plate; S, specimen; BS, beam splitter; A t and A r , analyzers; D t and D r , photodetectors.

Fig. 3
Fig. 3

Measured error of Δ, δ Δ θ , at different values of ψ caused by unequal amplitude of the two-frequency laser beam in the range of (a)  0 ° Δ 65 ° and (b)  65 ° Δ 90 ° .

Fig. 4
Fig. 4

Computer simulation of δ ψ θ , which is induced by the unequal amplitude of a two-frequency laser beam at different ψ.

Tables (1)

Tables Icon

Table 1 Measured and Given Data of Si O 2 Thin Film Deposited on Silicon Substrate

Equations (45)

Equations on this page are rendered with MathJax. Learn more.

E PCP = 1 2 ( 1 i i 1 ) ( exp ( i ω t / 2 ) 0 0 exp ( i ω t / 2 ) ) 1 2 ( 1 1 ) a exp ( i ω 0 t ) = 1 2 ( 1 i ) a exp [ i ( ω 0 + ω 2 ) t ] + i 2 ( 1 i ) a exp [ i ( ω 0 ω 2 ) t ] ,
E PCP = ( cos ( ω t / 2 ) + sin ( ω t / 2 ) cos ( ω t / 2 ) sin ( ω t / 2 ) ) a 2 exp { i [ ω 0 t + ( π / 4 ) ] } = ( sin [ ( ω t / 2 ) + ( π / 4 ) ] cos [ ( ω t / 2 ) + ( π / 4 ) ] ) a exp { i [ ω 0 t + ( π / 4 ) ] } .
S PCP = ( 1 sin ω t cos ω t 0 ) t I 0 ,
M S = R ( 1 cos 2 ψ 0 0 cos 2 ψ 1 0 0 0 0 sin 2 ψ cos Δ sin 2 ψ sin Δ 0 0 sin 2 ψ sin Δ sin 2 ψ cos Δ ) ,
M A ( A ) = T A ( 1 cos 2 A sin 2 A 0 cos 2 A cos 2 2 A sin 2 A cos 2 A 0 sin 2 A sin 2 A cos 2 A sin 2 2 A 0 0 0 0 0 ) ,
S T = M A ( 45 ° ) M S S PCP ,
S R = M A ( 90 ° ) M S S PCP ,
I T = S T ( 1 ) = T I 0 ( 1 cos 2 ψ sin ω t + sin 2 ψ cos Δ cos ω t ) = T I 0 [ 1 + ( 1 sin 2 2 ψ sin 2 Δ ) 1 / 2 sin ( ω t + φ ) ] = I dc t + I ac t sin ( ω t + φ ) ,
T = T A R ,
I dc t = T I 0 ,
I a c t = T I 0 ( 1 sin 2 2 ψ sin 2 Δ ) 1 / 2 ,
φ = tan 1 ( tan 2 ψ cos Δ ) ,
I R = S R ( 1 ) = T I 0 ( 1 + cos 2 ψ ) ( 1 sin ω t ) = T I 0 ( 1 + cos 2 ψ ) [ 1 + sin ( ω t + π ) ] = I dc r + I ac r sin ( ω t + π ) .
I dc r = I ac r = T I 0 ( 1 + cos 2 ψ ) .
ψ = cos 1 [ ( I ac r / 2 I dc t ) 1 / 2 ] ,
sin 2 ψ sin Δ = [ 1 ( I ac t / I dc t ) 2 ] 1 / 2 ,
Δ = sin 1 { 1 ( I ac t / I dc t ) 2 1 [ ( I ac r / I dc t ) 1 ] 2 } 1 / 2 .
Δ = cos 1 ( tan Φ / tan 2 ψ ) .
S PME = ( 1 0 cos δ sin δ ) t I 0 , and     δ = δ 0 sin ω t .
θ = 1 2 tan 1 ( S 2 S 1 ) ,
ε = 1 2 sin 1 [ S 3 ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 ] ,
θ PCPHE = 45 ° ω t 2 , and     θ PME = 45 ° .
ε PCPHE = 0 ° , and     ε PME = δ 0 2 sin ω t .
( δ Δ θ ) 2 = [ ( Δ I dc t ) 2 ( I dc t θ ) 2 + ( Δ I ac t ) 2 ( I ac t θ ) 2 + ( Δ I ac r ) 2 ( I ac r θ ) 2 ] ( δ θ ) 2 ,
( δ ψ θ ) 2 = [ ( ψ I dc t ) 2 ( I dc t θ ) 2 + ( ψ I ac r ) 2 ( I ac r θ ) 2 ] ( δ θ ) 2 ,
Δ I dc t = 2 ( cos 2 Δ sin 2 Δ cos 2 ψ ) T I 0 sin 2 2 ψ sin 2 Δ ,
Δ I ac t = 2 ( 1 sin 2 2 ψ sin 2 Δ ) 1 / 2 T I 0 sin 2 2 ψ sin 2 Δ ,
Δ I ac r = 2 cos 2 ψ sin 2 Δ T I 0 sin 2 2 ψ sin 2 Δ ,
ψ I dc t = 1 2 T I 0 tan ψ ,
ψ I ac r = 1 2 T I 0 sin 2 ψ ,
S T = M A ( 45 ° ) M S M Q ( 45 ° ) M EOM S in ( θ ) ,
S R = M A ( 90 ° ) M S M Q ( 45 ° ) M EOM S in ( θ ) ,
S in ( θ ) = ( 1 cos 2 θ sin 2 θ 0 ) t I 0
M Q ( 45 ° ) = ( 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 ) ,
M EOM = ( 1 0 0 0 0 1 0 0 0 0 cos ω t sin ω t 0 0 sin ω t cos ω t ) ,
I T = T I 0 [ ( 1 + cos 2 θ sin 2 ψ sin Δ ) + sin 2 θ ( cos 2 ψ sin ω t + sin 2 ψ cos Δ cos ω t ) ] = I dc t + I ac t sin ( ω t + φ ) ,
I dc t = T I 0 ( 1 + cos 2 θ sin 2 ψ sin Δ ) ,
I ac t = T I 0 [ sin 2 θ ( 1 sin 2 2 ψ sin 2 Δ ) 1 / 2 ] ,
I R = T I 0 [ ( 1 + cos 2 ψ ) ( 1 sin 2 θ sin ω t ) ] = I dc r I ac r sin ω t ,
I dc r = T I 0 ( 1 + cos 2 ψ ) ,
I ac r = T I 0 sin 2 θ ( 1 + cos 2 ψ ) .
I ac t / θ = I ac r / θ = 0 ,
I dc t / θ = 2 T I 0 sin 2 ψ sin Δ .
δ Δ θ = | 2 ( cos 2 Δ sin 2 Δ cos 2 ψ ) sin 2 ψ cos Δ δ θ | .
δ ψ θ = | 2 cos 2 ψ sin Δ δ θ | .

Metrics