Abstract

A novel balanced detector interferometric ellipsometer (BDIE), composed of a polarized common-path optical heterodyne interferometer incorporating a novel balanced detector, provides an amplitude-sensitive method for measurement of the elliptical parameters of a thin film. The requirement for equal amplitude of the polarized heterodyne signals for balanced detection results in the simultaneous measurement of the elliptical parameters in terms of the azimuth angle of a half-wave plate and the output intensity from the differential amplifier, respectively. The common-path feature of BDIE shows a common phase noise rejection mode and this enhances the sensitivity of the phase measurement. At the same time, the balanced detector configuration of BDIE reduces excess noise of laser intensity fluctuation to give better sensitivity during measurement. The error of measurement of BDIE is derived and analyzed. Finally, the elliptical polarization effect of the laser beam is found to be independent of the measurement of the elliptical parameters.

© 2006 Optical Society of America

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References

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  1. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1980), pp. 153-268.
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    [Crossref]
  8. L. R. Watkins and M. D. Hoogerland, "Interferometric ellipsometer with wavelength modulation laser diode source," Appl. Opt. 43, 4362-4366 (2004).
    [Crossref] [PubMed]
  9. C. Chou, C. W. Lyu, and L. C. Peng, "Polarized differential-phase laser scanning microscope," Appl. Opt. 40, 95-99 (2001).
    [Crossref]
  10. "Liquid-crystal light control system Model 932," Newport Resource (2004), p. 519, http://www.newport.com.
  11. Calibration data sheet of step wafer SiO2 on Si serial number ID0153, Dipl-Ing (FH), Michael Kaiser, Labor für Mikrosystemtechnik FH-München, Germany.
  12. H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
    [Crossref]
  13. K. X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, "Balanced heterodyne signal extraction in postmodulated Sagnac interferometer at low frequency," Opt. Lett. 22, 1485-1488 (1997).
    [Crossref]
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  15. A. Kolomenskii, P. Gershou, and H. Schuessler, "Sensitivity and detection limit of concentration and absorption measurement by laser-induced surface plasmon resonance," Appl. Opt. 36, 6539-6547 (1997).
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2004 (1)

2002 (1)

H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
[Crossref]

2001 (2)

C. Chou, C. W. Lyu, and L. C. Peng, "Polarized differential-phase laser scanning microscope," Appl. Opt. 40, 95-99 (2001).
[Crossref]

P. Karageorgiev, H. Orendi, B. Stiller, and L. Brehmer, "Scanning near-field ellipsometric microscope-imaging ellipsometry with a lateral resolution in nanometer range," Appl. Phys. Lett. 79, 1730-1732 (2001).
[Crossref]

1998 (1)

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

1997 (3)

1995 (1)

1990 (1)

1986 (1)

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, "Excess noise suppression in a fiber optic balanced detection system," Opt. Quantum Electron. 18, 445-454 (1986).
[Crossref]

Amaratunga, G. A. J.

Azzam, R. M.

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1980), pp. 153-268.

Bashara, N. M.

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1980), pp. 153-268.

Battig, R.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, "Excess noise suppression in a fiber optic balanced detection system," Opt. Quantum Electron. 18, 445-454 (1986).
[Crossref]

Bender, H.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Brehmer, L.

P. Karageorgiev, H. Orendi, B. Stiller, and L. Brehmer, "Scanning near-field ellipsometric microscope-imaging ellipsometry with a lateral resolution in nanometer range," Appl. Phys. Lett. 79, 1730-1732 (2001).
[Crossref]

Byer, R. L.

Chang, C. N.

H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
[Crossref]

Chang, K. S.

Chou, C.

De Laet, J.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Fejer, M. M.

Gershou, P.

Gustafson, E. K.

Hamstra, M. A.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Hemmes, K.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Henchoz, P. D.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, "Excess noise suppression in a fiber optic balanced detection system," Opt. Quantum Electron. 18, 445-454 (1986).
[Crossref]

Hoogerland, M. D.

Huang, Y. C.

H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
[Crossref]

Jellison, G. E.

Karageorgiev, P.

P. Karageorgiev, H. Orendi, B. Stiller, and L. Brehmer, "Scanning near-field ellipsometric microscope-imaging ellipsometry with a lateral resolution in nanometer range," Appl. Phys. Lett. 79, 1730-1732 (2001).
[Crossref]

Kolomenskii, A.

Koops, K. R.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Lin, C. H.

Lyu, C. W.

H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
[Crossref]

C. Chou, C. W. Lyu, and L. C. Peng, "Polarized differential-phase laser scanning microscope," Appl. Opt. 40, 95-99 (2001).
[Crossref]

Modine, F. A.

Orendi, H.

P. Karageorgiev, H. Orendi, B. Stiller, and L. Brehmer, "Scanning near-field ellipsometric microscope-imaging ellipsometry with a lateral resolution in nanometer range," Appl. Phys. Lett. 79, 1730-1732 (2001).
[Crossref]

Peng, L. C.

Riedling, K.

K. Riedling, Ellipsometry for Industrial Applications (Springer-Verlag, 1988), pp. 1-14.
[Crossref]

Rusli, R.

Schram, T.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Schuessler, H.

Stierlin, R.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, "Excess noise suppression in a fiber optic balanced detection system," Opt. Quantum Electron. 18, 445-454 (1986).
[Crossref]

Stiller, B.

P. Karageorgiev, H. Orendi, B. Stiller, and L. Brehmer, "Scanning near-field ellipsometric microscope-imaging ellipsometry with a lateral resolution in nanometer range," Appl. Phys. Lett. 79, 1730-1732 (2001).
[Crossref]

Sun, K. X.

Teng, H. K.

H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
[Crossref]

Watkins, L. R.

Weber, H. P.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, "Excess noise suppression in a fiber optic balanced detection system," Opt. Quantum Electron. 18, 445-454 (1986).
[Crossref]

Wind, M. M.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

P. Karageorgiev, H. Orendi, B. Stiller, and L. Brehmer, "Scanning near-field ellipsometric microscope-imaging ellipsometry with a lateral resolution in nanometer range," Appl. Phys. Lett. 79, 1730-1732 (2001).
[Crossref]

Jpn. J. Appl. Phys., Part 1 (1)

H. K. Teng, C. Chou, C. N. Chang, C. W. Lyu, and Y. C. Huang, "Linear birefringence measurement with a differential-phase optical heterodyne polarimeter," Jpn. J. Appl. Phys., Part 1 41, 3140-3144 (2002).
[Crossref]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, "Excess noise suppression in a fiber optic balanced detection system," Opt. Quantum Electron. 18, 445-454 (1986).
[Crossref]

Thin Solid Films (1)

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. De Laet, and H. Bender, "Evaluation of interferometric ellipsometer systems with a resolution of one microsecond and faster," Thin Solid Films 313-314, 40-46 (1998).
[Crossref]

Other (4)

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1980), pp. 153-268.

K. Riedling, Ellipsometry for Industrial Applications (Springer-Verlag, 1988), pp. 1-14.
[Crossref]

"Liquid-crystal light control system Model 932," Newport Resource (2004), p. 519, http://www.newport.com.

Calibration data sheet of step wafer SiO2 on Si serial number ID0153, Dipl-Ing (FH), Michael Kaiser, Labor für Mikrosystemtechnik FH-München, Germany.

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Figures (4)

Fig. 1
Fig. 1

Optical setup. HWP, half-wave plate; BS1, BS2, BS3, beam splitters; PBS, polarized beam splitter; AOM1, AOM2, acousto-optic modulators; M1, M2, M3, plane mirrors; D P , D S , photodetectors; BPF, bandpass filter; DA, differential amplifier; DVM, digital voltmeter; PC, personal computer; SPU, signal processor unit; SA, spectrum analyzer; BSC, Babinet–Soliel compensator.

Fig. 2
Fig. 2

Measurement of BDIE under the condition of (a) Δ Φ = 180 ° (in phase), (b) Δ Φ = 0 ° (out of phase), and (c) without laser beam (shot-noise limited) ( Δ ω = 33 kHz ) .

Fig. 3
Fig. 3

(a) Ratio of δ Δ Δ versus Δ Φ and (b) the ratio of δ ψ ψ versus 2 Θ r as a function of the ratio Δ κ κ 1 .

Fig. 4
Fig. 4

Error δ ψ e versus A P A S as a function of small δ θ of elliptical polarization.

Tables (1)

Tables Icon

Table 1 Measured Data of Si O 2 Thin Film Deposited on a Silicon Substrate at Incident Angle α = 70 ° a

Equations (64)

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I P 1 + P 2 ( Δ ω t ) = A P 1 2 + A P 2 2 + 2 A P 1 A P 2 cos ( Δ ω t + Δ Φ P ) ,
I S 1 + S 2 ( Δ ω t ) = A S 1 2 + A S 2 2 + 2 A S 1 A S 2 cos ( Δ ω t + Δ Φ S ) ,
I P 1 + P 2 ( Δ ω t ) = 2 A P 1 A P 2 cos ( Δ ω t + Δ Φ P ) ,
I S 1 + S 2 ( Δ ω t ) = 2 A S 1 A S 2 cos ( Δ ω t + Δ Φ S ) .
I P 1 + P 2 ( Δ ω t ) = 2 κ cos ( Δ ω t + Δ Φ P ) ,
I S 1 + S 2 ( Δ ω t ) = 2 κ cos ( Δ ω t + Δ Φ S ) .
I P 1 + P 2 ( Δ ω t ) = 2 κ cos ( Δ ω t + Δ Φ 2 ) ,
I S 1 + S 2 ( Δ ω t ) = 2 κ cos ( Δ ω t Δ Φ 2 )
I out ( Δ ω t ) = 4 γ κ sin ( Δ Φ 2 ) sin ( Δ ω t ) ,
Δ Φ = 2 sin 1 [ I out 4 κ ] ,
I out + ( Δ ω t ) = 4 γ κ cos ( Δ Φ 2 ) cos ( Δ ω t ) .
Δ Φ = 2 tan 1 [ I out I out + ] .
Δ Φ = 2 ( δ P 1 δ S 1 ) = 2 Δ ,
Δ = sin 1 [ I out 4 κ ] ,
A P 1 = A P 2 = A 0 2 cos ( 2 Θ ) ,
A S 1 = A S 2 = A 0 2 sin ( 2 Θ ) ,
r ̃ P 1 2 A P 1 A P 2 = r ̃ S 1 2 A S 1 A S 2 = k ,
r ̃ P 1 2 r ̃ S 1 2 = tan 2 ( ψ ) = A S 1 A S 2 A P 1 A P 2 = tan 2 ( 2 Θ ) ,
ψ = 2 Θ .
I P 1 + P 2 ( Δ ω t ) = 2 A P 1 r A P 2 r cos ( Δ ω t + Δ Φ P ) ,
I S 1 + S 2 ( Δ ω t ) = 2 A S 1 r A S 2 r cos ( Δ ω t + Δ Φ S ) ,
r P 1 = r P 1 exp ( i δ P 1 ) ,
r S 1 = r S 1 exp ( i δ S 1 ) .
r P 2 = r P 2 exp ( i δ P 2 ) ,
r S 2 = r S 2 exp ( i δ S 2 ) .
r P 1 r P 2 A P 1 A P 2 = r S 1 r S 2 A S 1 A S 2 .
A P 1 = A P 2 = A 0 2 cos ( 2 Θ r ) ,
A S 1 = A S 2 = A 0 2 sin ( 2 Θ r ) ,
r P 1 r P 2 r S 1 r S 2 = tan 2 ( 2 Θ r ) .
φ 0 = Δ Φ P Δ Φ S = ( δ P 1 δ P 2 ) ( δ S 1 δ S 2 ) = 2 sin 1 [ I out r 4 κ r ] ,
I P 1 + P 2 ( Δ ω t ) = 2 A P 1 A P 2 cos ( Δ ω t + Δ Φ P ) ,
I S 1 + S 2 ( Δ ω t ) = 2 A S 1 A S 2 cos ( Δ ω t + Δ Φ S ) ,
r P 1 r P 2 r ̃ P 1 2 A P 1 A P 2 = r S 1 r S 2 r ̃ S 1 2 A S 1 A S 2 .
A P 1 = A P 2 = A 0 2 cos ( 2 Θ S ) ,
A S 1 = A S 2 = A 0 2 sin ( 2 Θ S ) .
tan 2 ( ψ ) = ( r ̃ P 1 r ̃ S 1 ) 2 = tan 2 ( 2 Θ S ) r S 1 r S 2 r P 1 r P 2 = tan 2 ( 2 Θ S ) tan 2 ( 2 Θ r ) ,
tan ( ψ ) = tan ( 2 Θ S ) tan ( 2 Θ r ) ,
φ = φ 0 + 2 ( δ P 1 δ S 1 ) = 2 sin 1 [ I out S 4 κ S ] .
Δ = δ P 1 δ S 1 = sin 1 [ I out S 4 κ S ] sin 1 [ I out r 4 κ r ] ,
I P 1 + P 2 ( Δ ω t ) = 2 κ 1 cos ( Δ ω t + Δ Φ P ) ,
I S 1 + S 2 ( Δ ω t ) = 2 κ 2 cos ( Δ ω t + Δ Φ S ) .
I out ( Δ ω t ) = I P 1 + P 2 ( Δ ω t ) I S 1 + S 2 ( Δ ω t ) = ( κ 1 κ 2 ) cos ( Δ Φ 2 ) cos ( Δ ω t ) ( κ 1 + κ 2 ) sin ( Δ Φ 2 ) sin ( Δ ω t ) .
I out ( Δ ω t ) 4 κ 1 sin ( Δ Φ 2 ) 1 + [ Δ κ 2 κ 1 tan ( Δ Φ 2 ) ] 2 sin ( Δ ω t ) .
I out ( Δ ω t ) 4 κ 1 sin [ Δ Φ 2 + δ ( Δ Φ ) 2 ] sin ( Δ ω t ) ,
( Δ κ κ 1 ) tan ( Δ Φ 2 ) 2
δ Δ Δ = ( Δ κ κ 1 ) 2 4 Δ Φ tan ( Δ Φ 2 ) .
r P 1 r P 2 r ̃ P 1 2 A P 1 A P 2 = r S 1 r S 2 r ̃ S 1 2 A S 1 A S 2 + Δ κ ,
r P 1 r P 2 r ̃ P 1 2 A P 1 A P 2 = r S 1 r S 2 r ̃ S 1 2 ( A 0 2 4 ) sin 2 ( 2 Θ S )
r S 1 r S 2 r ̃ S 1 2 ( A 0 2 4 ) sin 4 ( 2 Θ S ) + Δ κ = r S 1 r S 2 r ̃ S 1 2 ( A 0 2 4 ) sin 2 ( 2 Θ S ) .
δ Θ S = ( Δ κ κ 1 ) tan ( 2 Θ S ) 4 .
tan ( ψ + δ ψ ) = tan ( 2 Θ S + 2 δ Θ S ) tan ( 2 Θ r ) .
δ ψ ψ = ( Δ κ κ 1 ) tan 2 ( 2 Θ r ) 2
( E P E S ) = ( A P exp ( i θ P ) A S exp ( i θ S ) ) exp ( i ω 0 t ) ,
( E P E S ) = R ( Θ ) J H R ( Θ ) ( E P E S ) = ( A P cos ( 2 Θ ) exp ( i θ P ) + A S cos ( 2 Θ ) exp ( i θ S ) A P sin ( 2 Θ ) exp ( i θ P ) A S sin ( 2 Θ ) exp ( i θ S ) ) exp [ i ( ω 0 t π 2 ) ] ,
( E P 1 E S 1 ) = ( A P 1 cos ( 2 Θ ) exp ( i θ P ) + A S 1 sin ( 2 Θ ) exp ( i θ S ) A P 1 sin ( 2 Θ ) exp ( i θ P ) A S 1 cos ( 2 Θ ) exp ( i θ S ) ) exp { i [ ( ω 0 + ω 1 ) t π 2 ] } ,
( E P 2 E S 2 ) = ( A P 2 cos ( 2 Θ ) exp ( i θ P ) + A S 2 sin ( 2 Θ ) exp ( i θ S ) A P 2 sin ( 2 Θ ) exp ( i θ P ) A S 2 cos ( 2 Θ ) exp ( i θ S ) ) exp { i [ ( ω 0 + ω 2 ) t π 2 ] } .
J t = [ r ̃ P 1 exp ( i δ P 1 ) 0 0 r ̃ S 1 exp ( i δ S 1 ) ]
( E P 1 E S 1 ) = J t J t ( E P 1 E S 1 ) .
I P = E P 1 + E P 2 2 = 2 r ̃ P 1 2 K P cos ( Δ ω t + 2 δ P 1 σ P ) ,
I S = E S 1 + E S 2 2 = 2 r ̃ S 1 2 K S cos ( Δ ω t + 2 δ S 1 σ S ) ,
I P = 2 K cos [ Δ ω t + δ P 1 δ S 1 ( σ P σ S ) 2 ] ,
I S = 2 K cos [ Δ ω t + δ P 1 δ S 1 + ( σ P σ S ) 2 ] .
I out e ( Δ ω t ) = I P I S = 4 K sin ( Δ Φ 2 ) sin ( Δ ω t ) ,
Δ Φ = δ P 1 δ S 1 ( σ P σ S ) 2 = Δ ( σ P σ S ) 2 .

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