Abstract

We present for the first time a universal expression for the combined standard uncertainty for all types of rotating-element spectroscopic ellipsometers (RE-SEs). Specifically, we introduce general model functions as universal analytic expressions for the combined standard uncertainties of the ellipsometric sample parameters. The model functions are expressed as functions of influencing quantities that are not known exactly. The detailed expressions for the model functions are provided for the common RE-SEs. Our approach can be used for instrumentation, standardization, simulation, metrology, optimization of measurement conditions, and performance comparison between RE-SEs.

© 2016 Optical Society of America

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References

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  1. R. W. Collins, I. An, J. Lee, and J. A. Zapien, “Multichannel ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, eds. (William Andrew Inc., 2005), Chap. 7.
  2. S. Zollner, “Spectroscopic ellipsometry for inline process control in the semiconductor industry,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, Berlin, 2013), Chap. 18.
  3. D. E. Aspnes, “Spectroscopic ellipsometry – A perspective,” J. Vac. Sci. Technol. A 31(5), 058502 (2013).
    [Crossref]
  4. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML, JCGM 100:2008, “Evaluation of measurement data - Guide to the expression of uncertainty in measurement,” (GUM 1995 with minor corrections) ( www.bipm.org ).
  5. D. E. Aspnes, “Spectroscopic ellipsometry – Past, present, and future,” Thin Solid Films 571, 334–344 (2014).
    [Crossref]
  6. E. Schmidt, “Precision of ellipsometric measurement,” J. Opt. Soc. Am. 60(4), 490–494 (1970).
    [Crossref]
  7. D. E. Aspnes, “Precision bounds to ellipsometer systems,” Appl. Opt. 14(5), 1131–1136 (1975).
    [Crossref] [PubMed]
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    [Crossref]
  9. D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” J. Opt. Soc. Am. A 7(4), 693–700 (1990).
    [Crossref]
  10. N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: Applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
    [Crossref]
  11. I. An and R. W. Collins, “Waveform analysis with optical multichannel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
    [Crossref]
  12. R. Kleim, L. Kuntzler, and A. El Ghemmaz, “Systematic errors in rotating-compensator ellipsometry,” J. Opt. Soc. Am. A 11(9), 2550–2559 (1994).
    [Crossref]
  13. Z. Huang and J. Chu, “Optimizing precision of fixed-polarizer, rotating-polarizer, sample, and fixed-analyzer spectroscopic ellipsometry,” Appl. Opt. 39(34), 6390–6395 (2000).
    [Crossref] [PubMed]
  14. D. E. Aspnes, “Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers,” J. Opt. Soc. Am. A 21(3), 403–410 (2004).
    [Crossref] [PubMed]
  15. B. Johs and C. M. Herzinger, “Precision in ellipsometrically determined sample parameters: simulation and experiment,” Thin Solid Films 455–456, 66–71 (2004).
    [Crossref]
  16. J. A. Zapien, A. S. Ferlauto, and R. W. Collins, “Application of spectral and temporal weighted error functions for data analysis in real-time spectroscopic ellipsometry,” Thin Solid Films 455–456, 106–111 (2004).
    [Crossref]
  17. K. M. Twietmeyer and R. A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16(15), 11589–11603 (2008).
    [Crossref] [PubMed]
  18. L. Broch, A. En Naciri, and L. Johann, “Systematic errors for a Mueller matrix dual rotating compensator ellipsometer,” Opt. Express 16(12), 8814–8824 (2008).
    [Crossref] [PubMed]
  19. B. Johs and C. M. Herzinger, “Quantifying the accuracy of ellipsometer systems,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1031–1035 (2008).
    [Crossref]
  20. L. Broch and L. Johann, “Optimizing precision of rotating compensator ellipsometry,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1036–1040 (2008).
    [Crossref]
  21. L. Broch, A. En Naciri, and L. Johann, “Second-order systematic errors in Mueller matrix dual rotating compensator ellipsometry,” Appl. Opt. 49(17), 3250–3258 (2010).
    [Crossref] [PubMed]
  22. L. Broch, A. E. Naciri, and L. Johann, “Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators,” Thin Solid Films 519(9), 2601–2603 (2011).
    [Crossref]
  23. M. Losurdo, “Applications of ellipsometry in nanoscale science: Needs, status, achievements and future challenges,” Thin Solid Films 519(9), 2575–2583 (2011).
    [Crossref]
  24. Y. J. Cho, W. Chegal, J. P. Lee, and H. M. Cho, “Universal evaluations and expressions of measuring uncertainty for rotating-element spectroscopic ellipsometers,” Opt. Express 23(12), 16481–16491 (2015).
    [Crossref] [PubMed]
  25. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  26. H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (Williams Andrew Inc., 2005).
  27. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley and Sons, Ltd., 2007).
  28. M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons, and Polaritons (Springer, Berlin, 2010).
  29. M. Losurdo and K. Hingerl, Ellipsometry at the Nanoscale (Springer, 2013).
  30. Y. J. Cho, W. Chegal, and H. M. Cho, “Fourier analysis for rotating-element ellipsometers,” Opt. Lett. 36(2), 118–120 (2011).
    [Crossref] [PubMed]
  31. W. Chegal, J. P. Lee, H. M. Cho, S. W. Han, and Y. J. Cho, “Optimizing the precision of a multichannel three-polarizer spectroscopic ellipsometer,” J. Opt. Soc. Am. A 30(7), 1310–1319 (2013).
    [Crossref] [PubMed]
  32. G. E. Jellison, Jr., “Data analysis for spectroscopic ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, eds. (Williams Andrew Inc., 2005), Chap. 3.
  33. G. A. Candela, D. Chandler-Horowitz, J. F. Marchiando, D. B. Novotny, B. J. Belzer, and M. C. Croarkin, “Preparation and certification of SRM-2530: Ellipsometric parameters Delta and Psi and derived thickness and refractive index of a silicon dioxide layer on silicon,” NIST Special Publication 260–109 (1988).
  34. M.-A. Henn, H. Gross, F. Scholze, M. Wurm, C. Elster, and M. Bär, “A maximum likelihood approach to the inverse problem of scatterometry,” Opt. Express 20(12), 12771–12786 (2012).
    [Crossref] [PubMed]

2015 (1)

2014 (1)

D. E. Aspnes, “Spectroscopic ellipsometry – Past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

2013 (2)

2012 (1)

2011 (3)

Y. J. Cho, W. Chegal, and H. M. Cho, “Fourier analysis for rotating-element ellipsometers,” Opt. Lett. 36(2), 118–120 (2011).
[Crossref] [PubMed]

L. Broch, A. E. Naciri, and L. Johann, “Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators,” Thin Solid Films 519(9), 2601–2603 (2011).
[Crossref]

M. Losurdo, “Applications of ellipsometry in nanoscale science: Needs, status, achievements and future challenges,” Thin Solid Films 519(9), 2575–2583 (2011).
[Crossref]

2010 (1)

2008 (4)

K. M. Twietmeyer and R. A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16(15), 11589–11603 (2008).
[Crossref] [PubMed]

L. Broch, A. En Naciri, and L. Johann, “Systematic errors for a Mueller matrix dual rotating compensator ellipsometer,” Opt. Express 16(12), 8814–8824 (2008).
[Crossref] [PubMed]

B. Johs and C. M. Herzinger, “Quantifying the accuracy of ellipsometer systems,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1031–1035 (2008).
[Crossref]

L. Broch and L. Johann, “Optimizing precision of rotating compensator ellipsometry,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1036–1040 (2008).
[Crossref]

2004 (3)

D. E. Aspnes, “Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers,” J. Opt. Soc. Am. A 21(3), 403–410 (2004).
[Crossref] [PubMed]

B. Johs and C. M. Herzinger, “Precision in ellipsometrically determined sample parameters: simulation and experiment,” Thin Solid Films 455–456, 66–71 (2004).
[Crossref]

J. A. Zapien, A. S. Ferlauto, and R. W. Collins, “Application of spectral and temporal weighted error functions for data analysis in real-time spectroscopic ellipsometry,” Thin Solid Films 455–456, 106–111 (2004).
[Crossref]

2000 (1)

1994 (1)

1991 (2)

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: Applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[Crossref]

I. An and R. W. Collins, “Waveform analysis with optical multichannel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[Crossref]

1990 (1)

1988 (1)

1975 (1)

1970 (1)

An, I.

I. An and R. W. Collins, “Waveform analysis with optical multichannel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[Crossref]

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: Applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “Spectroscopic ellipsometry – Past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

D. E. Aspnes, “Spectroscopic ellipsometry – A perspective,” J. Vac. Sci. Technol. A 31(5), 058502 (2013).
[Crossref]

D. E. Aspnes, “Optimizing precision of rotating-analyzer and rotating-compensator ellipsometers,” J. Opt. Soc. Am. A 21(3), 403–410 (2004).
[Crossref] [PubMed]

D. E. Aspnes, “Precision bounds to ellipsometer systems,” Appl. Opt. 14(5), 1131–1136 (1975).
[Crossref] [PubMed]

Bär, M.

Broch, L.

L. Broch, A. E. Naciri, and L. Johann, “Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators,” Thin Solid Films 519(9), 2601–2603 (2011).
[Crossref]

L. Broch, A. En Naciri, and L. Johann, “Second-order systematic errors in Mueller matrix dual rotating compensator ellipsometry,” Appl. Opt. 49(17), 3250–3258 (2010).
[Crossref] [PubMed]

L. Broch, A. En Naciri, and L. Johann, “Systematic errors for a Mueller matrix dual rotating compensator ellipsometer,” Opt. Express 16(12), 8814–8824 (2008).
[Crossref] [PubMed]

L. Broch and L. Johann, “Optimizing precision of rotating compensator ellipsometry,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1036–1040 (2008).
[Crossref]

Chegal, W.

Chipman, R. A.

Cho, H. M.

Cho, Y. J.

Chu, J.

Collins, R. W.

J. A. Zapien, A. S. Ferlauto, and R. W. Collins, “Application of spectral and temporal weighted error functions for data analysis in real-time spectroscopic ellipsometry,” Thin Solid Films 455–456, 106–111 (2004).
[Crossref]

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry: Applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[Crossref]

I. An and R. W. Collins, “Waveform analysis with optical multichannel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[Crossref]

de Nijs, J. M. M.

El Ghemmaz, A.

Elster, C.

En Naciri, A.

Ferlauto, A. S.

J. A. Zapien, A. S. Ferlauto, and R. W. Collins, “Application of spectral and temporal weighted error functions for data analysis in real-time spectroscopic ellipsometry,” Thin Solid Films 455–456, 106–111 (2004).
[Crossref]

Goldstein, D. H.

Gross, H.

Han, S. W.

Henn, M.-A.

Herzinger, C. M.

B. Johs and C. M. Herzinger, “Quantifying the accuracy of ellipsometer systems,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1031–1035 (2008).
[Crossref]

B. Johs and C. M. Herzinger, “Precision in ellipsometrically determined sample parameters: simulation and experiment,” Thin Solid Films 455–456, 66–71 (2004).
[Crossref]

Huang, Z.

Johann, L.

L. Broch, A. E. Naciri, and L. Johann, “Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators,” Thin Solid Films 519(9), 2601–2603 (2011).
[Crossref]

L. Broch, A. En Naciri, and L. Johann, “Second-order systematic errors in Mueller matrix dual rotating compensator ellipsometry,” Appl. Opt. 49(17), 3250–3258 (2010).
[Crossref] [PubMed]

L. Broch and L. Johann, “Optimizing precision of rotating compensator ellipsometry,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1036–1040 (2008).
[Crossref]

L. Broch, A. En Naciri, and L. Johann, “Systematic errors for a Mueller matrix dual rotating compensator ellipsometer,” Opt. Express 16(12), 8814–8824 (2008).
[Crossref] [PubMed]

Johs, B.

B. Johs and C. M. Herzinger, “Quantifying the accuracy of ellipsometer systems,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1031–1035 (2008).
[Crossref]

B. Johs and C. M. Herzinger, “Precision in ellipsometrically determined sample parameters: simulation and experiment,” Thin Solid Films 455–456, 66–71 (2004).
[Crossref]

Kleim, R.

Kuntzler, L.

Lee, J. P.

Losurdo, M.

M. Losurdo, “Applications of ellipsometry in nanoscale science: Needs, status, achievements and future challenges,” Thin Solid Films 519(9), 2575–2583 (2011).
[Crossref]

Naciri, A. E.

L. Broch, A. E. Naciri, and L. Johann, “Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators,” Thin Solid Films 519(9), 2601–2603 (2011).
[Crossref]

Nguyen, N. V.

Pudliner, B. S.

Schmidt, E.

Scholze, F.

Silfhout, A. V.

Twietmeyer, K. M.

Wurm, M.

Zapien, J. A.

J. A. Zapien, A. S. Ferlauto, and R. W. Collins, “Application of spectral and temporal weighted error functions for data analysis in real-time spectroscopic ellipsometry,” Thin Solid Films 455–456, 106–111 (2004).
[Crossref]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

J. Vac. Sci. Technol. A (1)

D. E. Aspnes, “Spectroscopic ellipsometry – A perspective,” J. Vac. Sci. Technol. A 31(5), 058502 (2013).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Status Solidi., C Curr. Top. Solid State Phys. (2)

B. Johs and C. M. Herzinger, “Quantifying the accuracy of ellipsometer systems,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1031–1035 (2008).
[Crossref]

L. Broch and L. Johann, “Optimizing precision of rotating compensator ellipsometry,” Phys. Status Solidi., C Curr. Top. Solid State Phys. 5(5), 1036–1040 (2008).
[Crossref]

Rev. Sci. Instrum. (1)

I. An and R. W. Collins, “Waveform analysis with optical multichannel detectors: Applications for rapid-scan spectroscopic ellipsometry,” Rev. Sci. Instrum. 62(8), 1904–1911 (1991).
[Crossref]

Thin Solid Films (5)

B. Johs and C. M. Herzinger, “Precision in ellipsometrically determined sample parameters: simulation and experiment,” Thin Solid Films 455–456, 66–71 (2004).
[Crossref]

J. A. Zapien, A. S. Ferlauto, and R. W. Collins, “Application of spectral and temporal weighted error functions for data analysis in real-time spectroscopic ellipsometry,” Thin Solid Films 455–456, 106–111 (2004).
[Crossref]

L. Broch, A. E. Naciri, and L. Johann, “Analysis of systematic errors in Mueller matrix ellipsometry as a function of the retardance of the dual rotating compensators,” Thin Solid Films 519(9), 2601–2603 (2011).
[Crossref]

M. Losurdo, “Applications of ellipsometry in nanoscale science: Needs, status, achievements and future challenges,” Thin Solid Films 519(9), 2575–2583 (2011).
[Crossref]

D. E. Aspnes, “Spectroscopic ellipsometry – Past, present, and future,” Thin Solid Films 571, 334–344 (2014).
[Crossref]

Other (10)

G. E. Jellison, Jr., “Data analysis for spectroscopic ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, eds. (Williams Andrew Inc., 2005), Chap. 3.

G. A. Candela, D. Chandler-Horowitz, J. F. Marchiando, D. B. Novotny, B. J. Belzer, and M. C. Croarkin, “Preparation and certification of SRM-2530: Ellipsometric parameters Delta and Psi and derived thickness and refractive index of a silicon dioxide layer on silicon,” NIST Special Publication 260–109 (1988).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (Williams Andrew Inc., 2005).

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley and Sons, Ltd., 2007).

M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons, and Polaritons (Springer, Berlin, 2010).

M. Losurdo and K. Hingerl, Ellipsometry at the Nanoscale (Springer, 2013).

BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML, JCGM 100:2008, “Evaluation of measurement data - Guide to the expression of uncertainty in measurement,” (GUM 1995 with minor corrections) ( www.bipm.org ).

R. W. Collins, I. An, J. Lee, and J. A. Zapien, “Multichannel ellipsometry,” in Handbook of Ellipsometry, H. G. Tompkins and E. A. Irene, eds. (William Andrew Inc., 2005), Chap. 7.

S. Zollner, “Spectroscopic ellipsometry for inline process control in the semiconductor industry,” in Ellipsometry at the Nanoscale, M. Losurdo and K. Hingerl, eds. (Springer, Berlin, 2013), Chap. 18.

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Figures (1)

Fig. 1
Fig. 1 Schematic diagram of RE-SE.

Tables (1)

Tables Icon

Table 1 Vectors of the Fourier Coefficients and the Entries of the Sample Mueller Matrix. The PSG and PSA effective transmittances have different expressions depending on the optical configuration of the RE-SE used. For the index of the type (configuration) in question, P(Pr), A(Ar), and C(Cr) denote the fixed (constantly rotating) elements for the polarizer, analyzer, and compensator, respectively. S represents the sample.

Equations (44)

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

Q i = f i ( E 1 , E 2 ,, E J ).
Q ¯ i = 1 K k=1 K Q i,k = 1 K k=1 K f i ( E 1,k , E 2,k ,, E J,k ).
u A ( Q i )= 1 K( K1 ) k=1 K ( Q i,k Q ¯ i ) 2 .
u B ( Q i )= l=1 N Y ( f i Y l | Y ) 2 u 2 ( Y l ) ,
u c ( Q i )= u A 2 ( Q i )+ u B 2 ( Q i ) .
S (PDE) = T PSA T PSG M (DOS) M (PSA) M (SP) M (PSG) S (LS) .
I( θ r )= μ QE A PDE S 0 ( PDE ) = I 0 + n=1 N ho [ A n cos( n θ r )+ B n sin( n θ r ) ] ,
X= ( X j ) ( 2 N ho +1 )×1 =γ( P,A )Ω( P,A, δ c )V,
V= ( V j ) uv×1 = 1 γ( P,A ) Ω + ( P,A, δ c )X,
I(t)= I 0 + n=1 N ho [ A n cos(2nπt/T)+ B n sin(2nπt/T) ] +δI(t),
E j = (j1)T/J+ T d (j1)T/J+ T d + T i I(t) dt,
E= ( E j ) J×1 =Ξ( J,T, T i , T d ) X +δE,
X ¯ = ( X ¯ j ) ( 2 N ho +1 )×1 = Ξ + ( J,T, T i , T d ) E ¯ ,
H ¯ n c +i H ¯ n s = 2 J j=1 J E ¯ j exp( in θ j ) ,
I ¯ 0 = H ¯ 0 c /( 2 T i ),
( A ¯ n B ¯ n )=( C n c C n s C n s C n c )( H ¯ n c H ¯ n s ),(n1),
( Ξ + ) kj ={ 1 J T i ,(fork=1,andj=1,2,,J), 2 J [ C k/2 c cos( k 2 θ j ) C k/2 s sin( k 2 θ j ) ],(fork=2,4,,2 N ho ,andj=1,2,,J), 2 J [ C (k1)/2 c sin( k1 2 θ j )+ C (k1)/2 s cos( k1 2 θ j ) ],(fork=3,5,,2 N ho +1,andj=1,2,,J),
X ¯ j ={ X ¯ 1 ,( forj=1 ), X ¯ j cos[ ( j/2 ) θ r 0 ,j/2 ]+ X ¯ j+1 sin[ ( j/2 ) θ r 0 ,j/2 ],( forj=2,4,,2 N ho ), X ¯ j1 sin[ ( j1 ) θ r 0 ,(j1)/2 /2 ]+ X ¯ j cos[ ( j1 ) θ r 0, (j1)/2 /2 ],( forj=3,5,,2 N ho +1 ),
X ¯ =Λ( θ r 0 ) X ¯ ,
Λ jk ={ cos[ ( j/2 ) θ r 0 ,j/2 ],( forj=2,4,,2 N ho ,andk=j ), sin[ ( j/2 ) θ r 0 ,j/2 ],( forj=2,4,,2 N ho ,andk=j+1 ), sin[ ( j1 ) θ r 0 ,(j1)/2 /2 ],( forj=3,5,,2 N ho +1,andk=j1 ), cos[ ( j1 ) θ r 0 ,(j1)/2 /2 ],( forj=1,3,5,,2 N ho +1,andk=j ), 0,( fortheothers ),
V ¯ = ( V ¯ j ) uv×1 = 1 γ( P,A ) Ω + ( P,A, δ c )Λ( θ r 0 ) Ξ + ( J,T, T i , T d ) E ¯ ( ϕ,λ ),
N= M 12 M 11 ( or M 21 M 11 ),
C= M 33 M 11 ( or M 44 M 11 ),
S= M 34 M 11 ( or M 43 M 11 ).
u A ( Q j )= s( Q ¯ j , Q ¯ j ) = [ p,q=1 uv ( Q j V p | V )( Q j V q | V )s( V ¯ p , V ¯ q ) ] 1/2 ,
u A ( Q j )= 1 γ [ p,q=1 uv n,m=1 2 N ho +1 ( Q j V p | V )( Q j V q | V ) ( Ω + ) pn ( Ω + ) qm s( X ¯ n , X ¯ m ) ] 1/2 ,
u B ( Q j )= [ k=1 uv l=1 N Y ( Q j V k | V ) 2 ( V ¯ k Y l | Y ) 2 u 2 ( Y l ) ] 1/2 ,
( V ¯ Y l ) Y = ( Ω + Y l ) Y Ω V ¯ 1 γ ( γ Y l ) Y V ¯ .
( V ¯ Y l ) Y = ( Ω + Y l ) Y Ω V ¯ .
( V ¯ Y l ) Y = Ω + ( Λ Y l ) Y Λ 1 Ω V ¯ .
( V ¯ Y l ) Y = Ω + Λ ( Ξ + Y l ) Y Ξ Λ 1 Ω V ¯ .
( V ¯ Y l ) Y = 1 γ Ω + Λ Ξ + ( E ¯ Y l ) Y .
M (SP) =( M 11 M 12 0 0 M 12 M 11 0 0 0 0 M 33 M 34 0 0 M 34 M 33 ),
M ( LP ) = T P( A ) 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ).
M ( C ) = T C ( 1 0 0 0 0 1 0 0 0 0 cos δ c sin δ c 0 0 sin δ c cos δ c ),
R( θ )=( 1 0 0 0 0 cos2θ sin2θ 0 0 sin2θ cos2θ 0 0 0 0 1 )
γ={ κ( 1+ d 12 cos2A+ d 13 sin2A ), κ( 1+ d 12 cos2A+ d 13 sin2A )( 1+ l 1 cos2P+ l 2 sin2P ), (fortheRPEs), (fortheothers),
Ω (RPE) = 1 8 ( 2+ l 1 cos( 2A ) l 1 +2cos( 2A ) l 2 sin( 2A ) 2 l 1 +2cos( 2A ) 2+2 l 1 cos( 2A ) 0 2 l 2 2 l 2 cos( 2A ) 2sin( 2A ) l 1 cos( 2A ) l 1 l 2 sin( 2A ) l 2 cos( 2A ) l 2 l 1 sin( 2A ) ).
Ω (RCE-1) = 1 4 ( 1+cos( 2A )cos( 2P ) cos 2 ( δ c /2 ) cos( 2A )+cos( 2P ) cos 2 ( δ c /2 ) sin( 2A )sin( 2P ) cos 2 ( δ c /2 ) 0 0 0 0 sin( 2A )sin( 2P )sin δ c 0 0 0 sin( 2A )cos( 2P )sin δ c cos( 2A )cos( 2P ) sin 2 ( δ c /2 ) cos( 2P ) sin 2 ( δ c /2 ) sin( 2A )sin( 2P ) sin 2 ( δ c /2 ) 0 cos( 2A )sin( 2P ) sin 2 ( δ c /2 ) sin( 2P ) sin 2 ( δ c /2 ) sin( 2A )cos( 2P ) sin 2 ( δ c /2 ) 0 ).
Ω (RCE-2) = 1 4 ( 1+cos( 2A )cos( 2P ) cos 2 ( δ c /2 ) cos( 2P )+cos( 2A ) cos 2 ( δ c /2 ) sin( 2A )sin( 2P ) cos 2 ( δ c /2 ) 0 0 0 0 sin( 2A )sin( 2P )sin δ c 0 0 0 cos( 2A )sin( 2P )sin δ c cos( 2A )cos( 2P ) sin 2 ( δ c /2 ) cos( 2A ) sin 2 ( δ c /2 ) sin( 2A )sin( 2P ) sin 2 ( δ c /2 ) 0 sin( 2A )cos( 2P ) sin 2 ( δ c /2 ) sin( 2A ) sin 2 ( δ c /2 ) cos( 2A )sin( 2P ) sin 2 ( δ c /2 ) 0 ).
Ω (3PE-1) = 1 16 ( 2+cos( 2A )cos( 2P ) 2cos( 2A )+cos( 2P ) sin( 2A )sin( 2P ) 2cos( 2A )+2cos( 2P ) 2+2cos( 2A )cos( 2P ) 0 2sin( 2P ) 2cos( 2A )sin( 2P ) 2sin( 2A ) cos( 2A )cos( 2P ) cos( 2P ) sin( 2A )sin( 2P ) cos( 2A )sin( 2P ) sin( 2P ) sin( 2A )cos( 2P ) ).
Ω (3PE-2) = 1 16 ( 2+cos( 2A )cos( 2P ) cos( 2A )+2cos( 2P ) sin( 2A )sin( 2P ) 2cos( 2A )+2cos( 2P ) 2+2cos( 2A )cos( 2P ) 0 2sin( 2A ) 2sin( 2A )cos( 2P ) 2sin( 2P ) cos( 2A )cos( 2P ) cos( 2A ) sin( 2A )sin( 2P ) sin( 2A )cos( 2P ) sin( 2A ) cos( 2A )sin( 2P ) ).
u A ( Q j ) ε PH KJ T i μ QE 2 A PDE 2 T PSA T PSG L 0 .
Ζ( P,A,ϕ )= 1 N Q N λ j=1 N Q k=1 N λ u c 2 ( Q j ( λ k ) ) ,

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