Abstract

The optical constants of p-type tin telluride at room temperature have been determined as functions of carrier concentration over the spectral range from 0.1 to 3.8 eV. The indices of refraction and absorption coefficients were obtained from analysis of normal reflectance and transmittance measurements on epitaxial films ranging in carrier concentration from 3.6×1019 to 6.8×1020 cm−3. At energies greater than approximately 1.0 eV the optical dispersion is found to arise primarily from bound carriers. In contrast, the dispersion at energies less than about 0.4 eV is in excellent agreement with that calculated on the basis of classical free-carrier dispersion. The fundamental absorption edge is characterized by a large, Burstein-type shift produced by changes of carrier concentration. Bound-carrier indices of refraction nBC are found to be unusually large and carrier-concentration dependent. A Kramers–Kronig analysis gives values of nBC in good agreement with experiment for energies less than 2 eV. Extrapolation of our experimental values of nBC to zero energy using the Kramers–Kronig relation yielded values of the optical dielectric constant . This quantity is found to be carrier-concentration dependent, ranging in value from 38 to 46 for the carrier concentrations studied here. It is shown that this variation in is primarily due to the Burstein shift of the fundamental absorption edge.

© 1968 Optical Society of America

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References

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  1. R. F. Brebrick, J. Phys. Chem. Solids 24, 27 (1963).
    [Crossref]
  2. J. Umeda, M. Jeong, and T. Okada, J. Appl. Phys. (Japan) 1, 277 (1962).
    [Crossref]
  3. R. Mazelsky and M. S. Lubell, Nonstoichiometric Compounds (American Chemical Society, Washington, D. C., 1963), Series 39, p. 210.
    [Crossref]
  4. J. A. Kafalas, R. F. Brebrick, and A. J. Strauss, Appl. Phys. Letters 4, 93 (1964).
    [Crossref]
  5. R. F. Brebrick and A. J. Strauss, J. Phys. Chem. Solids 41, 197 (1964).
  6. B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).
  7. A. Sager and R. C. Miller, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 653.
  8. R. S. Allgaier and B. B. Houston, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 172.
  9. R. F. Brebrick and A. J. Strauss, Phys. Rev. 131, 104 (1963).
    [Crossref]
  10. J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
    [Crossref]
  11. E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
    [Crossref]
  12. H. R. Riedl, R. B. Schoolar, and Bland Houston, Solid State Commun. 4, 399 (1966).
    [Crossref]
  13. R. B. Schoolar, H. R. Riedl, and J. R. Dixon, Solid State Commun. 4, 423 (1966).
    [Crossref]
  14. H. Finkenrath and H. Kohler, Phys. Letters 23, 437 (1966); Phys. Letters 24A, 261 (1967).
    [Crossref]
  15. J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).
    [Crossref]
  16. R. B. Schoolar and J. R. Dixon, Phys. Rev. 137, A667 (1965).
    [Crossref]
  17. Paul R. Wessel, Phys. Rev. 153, 836 (1967).
    [Crossref]
  18. H. R. Riedl, J. R. Dixon, and R. B. Schoolar, Solid State Commun. 2, 323 (1965); H. R. Riedl and R. B. Schoolar, Bull. Am. Phys. Soc. 11, 348 (1966); Phys. Rev. 162, 692 (1967).
    [Crossref]
  19. J. F. Hall and W. F. C. Ferguson, J. Opt. Soc. Am. 45, 714 (1955).
    [Crossref]
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    [Crossref]
  22. T. S. Moss, Optical Properties of Semi-Conductors (Academic Press Inc., New York, 1959), Ch. 1, p. 14.
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    [Crossref]
  24. W. W. Scanlon, Solid State Physics (Academic Press Inc., New York, 1959), Vol. IX, p. 115.
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    [Crossref]

1967 (1)

Paul R. Wessel, Phys. Rev. 153, 836 (1967).
[Crossref]

1966 (4)

Paul M. Grant and William Paul, J. Appl. Phys. 37, 3110 (1966); Paul M. Grant, Bull. Am. Phys. Soc. 10, 546 (1965).
[Crossref]

H. R. Riedl, R. B. Schoolar, and Bland Houston, Solid State Commun. 4, 399 (1966).
[Crossref]

R. B. Schoolar, H. R. Riedl, and J. R. Dixon, Solid State Commun. 4, 423 (1966).
[Crossref]

H. Finkenrath and H. Kohler, Phys. Letters 23, 437 (1966); Phys. Letters 24A, 261 (1967).
[Crossref]

1965 (5)

J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).
[Crossref]

R. B. Schoolar and J. R. Dixon, Phys. Rev. 137, A667 (1965).
[Crossref]

H. R. Riedl, J. R. Dixon, and R. B. Schoolar, Solid State Commun. 2, 323 (1965); H. R. Riedl and R. B. Schoolar, Bull. Am. Phys. Soc. 11, 348 (1966); Phys. Rev. 162, 692 (1967).
[Crossref]

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
[Crossref]

1964 (5)

J. A. Kafalas, R. F. Brebrick, and A. J. Strauss, Appl. Phys. Letters 4, 93 (1964).
[Crossref]

R. F. Brebrick and A. J. Strauss, J. Phys. Chem. Solids 41, 197 (1964).

B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).

Manuel Cardona and D. L. Greenaway, Phys. Rev. 133, A1685 (1964).
[Crossref]

Frank Stern, Phys. Rev. 133, A1653 (1964).
[Crossref]

1963 (2)

R. F. Brebrick and A. J. Strauss, Phys. Rev. 131, 104 (1963).
[Crossref]

R. F. Brebrick, J. Phys. Chem. Solids 24, 27 (1963).
[Crossref]

1962 (1)

J. Umeda, M. Jeong, and T. Okada, J. Appl. Phys. (Japan) 1, 277 (1962).
[Crossref]

1955 (1)

Allgaier, R. S.

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).

R. S. Allgaier and B. B. Houston, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 172.

Babiskin, J.

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).

Brebrick, R. F.

R. F. Brebrick and A. J. Strauss, J. Phys. Chem. Solids 41, 197 (1964).

J. A. Kafalas, R. F. Brebrick, and A. J. Strauss, Appl. Phys. Letters 4, 93 (1964).
[Crossref]

R. F. Brebrick, J. Phys. Chem. Solids 24, 27 (1963).
[Crossref]

R. F. Brebrick and A. J. Strauss, Phys. Rev. 131, 104 (1963).
[Crossref]

Bylander, E. G.

E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
[Crossref]

Cardona, Manuel

Manuel Cardona and D. L. Greenaway, Phys. Rev. 133, A1685 (1964).
[Crossref]

Dixon, J. R.

R. B. Schoolar, H. R. Riedl, and J. R. Dixon, Solid State Commun. 4, 423 (1966).
[Crossref]

R. B. Schoolar and J. R. Dixon, Phys. Rev. 137, A667 (1965).
[Crossref]

H. R. Riedl, J. R. Dixon, and R. B. Schoolar, Solid State Commun. 2, 323 (1965); H. R. Riedl and R. B. Schoolar, Bull. Am. Phys. Soc. 11, 348 (1966); Phys. Rev. 162, 692 (1967).
[Crossref]

E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
[Crossref]

Ferguson, W. F. C.

Finkenrath, H.

H. Finkenrath and H. Kohler, Phys. Letters 23, 437 (1966); Phys. Letters 24A, 261 (1967).
[Crossref]

Grant, Paul M.

Paul M. Grant and William Paul, J. Appl. Phys. 37, 3110 (1966); Paul M. Grant, Bull. Am. Phys. Soc. 10, 546 (1965).
[Crossref]

Greenaway, D. L.

Manuel Cardona and D. L. Greenaway, Phys. Rev. 133, A1685 (1964).
[Crossref]

Hall, J. F.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press Inc., New York, 1955), Ch. 4, p. 58.

Houston, B. B.

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).

R. S. Allgaier and B. B. Houston, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 172.

Houston, Bland

H. R. Riedl, R. B. Schoolar, and Bland Houston, Solid State Commun. 4, 399 (1966).
[Crossref]

Jensen, J. D.

J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).
[Crossref]

Jeong, M.

J. Umeda, M. Jeong, and T. Okada, J. Appl. Phys. (Japan) 1, 277 (1962).
[Crossref]

Kafalas, J. A.

J. A. Kafalas, R. F. Brebrick, and A. J. Strauss, Appl. Phys. Letters 4, 93 (1964).
[Crossref]

Kohler, H.

H. Finkenrath and H. Kohler, Phys. Letters 23, 437 (1966); Phys. Letters 24A, 261 (1967).
[Crossref]

Lubell, M. S.

R. Mazelsky and M. S. Lubell, Nonstoichiometric Compounds (American Chemical Society, Washington, D. C., 1963), Series 39, p. 210.
[Crossref]

Mazelsky, R.

R. Mazelsky and M. S. Lubell, Nonstoichiometric Compounds (American Chemical Society, Washington, D. C., 1963), Series 39, p. 210.
[Crossref]

Miller, R. C.

A. Sager and R. C. Miller, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 653.

Moss, T. S.

T. S. Moss, Optical Properties of Semi-Conductors (Academic Press Inc., New York, 1959), Ch. 1, p. 14.

Okada, T.

J. Umeda, M. Jeong, and T. Okada, J. Appl. Phys. (Japan) 1, 277 (1962).
[Crossref]

Paul, William

Paul M. Grant and William Paul, J. Appl. Phys. 37, 3110 (1966); Paul M. Grant, Bull. Am. Phys. Soc. 10, 546 (1965).
[Crossref]

Richard Burke, J.

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

Riedl, H. R.

R. B. Schoolar, H. R. Riedl, and J. R. Dixon, Solid State Commun. 4, 423 (1966).
[Crossref]

H. R. Riedl, R. B. Schoolar, and Bland Houston, Solid State Commun. 4, 399 (1966).
[Crossref]

E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
[Crossref]

H. R. Riedl, J. R. Dixon, and R. B. Schoolar, Solid State Commun. 2, 323 (1965); H. R. Riedl and R. B. Schoolar, Bull. Am. Phys. Soc. 11, 348 (1966); Phys. Rev. 162, 692 (1967).
[Crossref]

Sager, A.

A. Sager and R. C. Miller, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 653.

Scanlon, W. W.

W. W. Scanlon, Solid State Physics (Academic Press Inc., New York, 1959), Vol. IX, p. 115.

Schoolar, R. B.

H. R. Riedl, R. B. Schoolar, and Bland Houston, Solid State Commun. 4, 399 (1966).
[Crossref]

R. B. Schoolar, H. R. Riedl, and J. R. Dixon, Solid State Commun. 4, 423 (1966).
[Crossref]

E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
[Crossref]

H. R. Riedl, J. R. Dixon, and R. B. Schoolar, Solid State Commun. 2, 323 (1965); H. R. Riedl and R. B. Schoolar, Bull. Am. Phys. Soc. 11, 348 (1966); Phys. Rev. 162, 692 (1967).
[Crossref]

J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).
[Crossref]

R. B. Schoolar and J. R. Dixon, Phys. Rev. 137, A667 (1965).
[Crossref]

Siebenmann, P. G.

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).

Stern, Frank

Frank Stern, Phys. Rev. 133, A1653 (1964).
[Crossref]

Strauss, A. J.

R. F. Brebrick and A. J. Strauss, J. Phys. Chem. Solids 41, 197 (1964).

J. A. Kafalas, R. F. Brebrick, and A. J. Strauss, Appl. Phys. Letters 4, 93 (1964).
[Crossref]

R. F. Brebrick and A. J. Strauss, Phys. Rev. 131, 104 (1963).
[Crossref]

Umeda, J.

J. Umeda, M. Jeong, and T. Okada, J. Appl. Phys. (Japan) 1, 277 (1962).
[Crossref]

Wessel, Paul R.

Paul R. Wessel, Phys. Rev. 153, 836 (1967).
[Crossref]

Zemel, J. N.

J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).
[Crossref]

Appl. Phys. Letters (1)

J. A. Kafalas, R. F. Brebrick, and A. J. Strauss, Appl. Phys. Letters 4, 93 (1964).
[Crossref]

Bull. Am. Phys. Soc. (1)

B. B. Houston, R. S. Allgaier, J. Babiskin, and P. G. Siebenmann, Bull. Am. Phys. Soc. 9, 60 (1964).

J. Appl. Phys. (1)

Paul M. Grant and William Paul, J. Appl. Phys. 37, 3110 (1966); Paul M. Grant, Bull. Am. Phys. Soc. 10, 546 (1965).
[Crossref]

J. Appl. Phys. (Japan) (1)

J. Umeda, M. Jeong, and T. Okada, J. Appl. Phys. (Japan) 1, 277 (1962).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Chem. Solids (2)

R. F. Brebrick and A. J. Strauss, J. Phys. Chem. Solids 41, 197 (1964).

R. F. Brebrick, J. Phys. Chem. Solids 24, 27 (1963).
[Crossref]

Phys. Letters (1)

H. Finkenrath and H. Kohler, Phys. Letters 23, 437 (1966); Phys. Letters 24A, 261 (1967).
[Crossref]

Phys. Rev. (7)

J. N. Zemel, J. D. Jensen, and R. B. Schoolar, Phys. Rev. 140, A330 (1965).
[Crossref]

R. B. Schoolar and J. R. Dixon, Phys. Rev. 137, A667 (1965).
[Crossref]

Paul R. Wessel, Phys. Rev. 153, 836 (1967).
[Crossref]

E. G. Bylander, J. R. Dixon, H. R. Riedl, and R. B. Schoolar, Phys. Rev. 138, A864 (1965).
[Crossref]

R. F. Brebrick and A. J. Strauss, Phys. Rev. 131, 104 (1963).
[Crossref]

Frank Stern, Phys. Rev. 133, A1653 (1964).
[Crossref]

Manuel Cardona and D. L. Greenaway, Phys. Rev. 133, A1685 (1964).
[Crossref]

Phys. Rev. Letters (1)

J. Richard Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14, 360 (1965).
[Crossref]

Solid State Commun. (3)

H. R. Riedl, R. B. Schoolar, and Bland Houston, Solid State Commun. 4, 399 (1966).
[Crossref]

R. B. Schoolar, H. R. Riedl, and J. R. Dixon, Solid State Commun. 4, 423 (1966).
[Crossref]

H. R. Riedl, J. R. Dixon, and R. B. Schoolar, Solid State Commun. 2, 323 (1965); H. R. Riedl and R. B. Schoolar, Bull. Am. Phys. Soc. 11, 348 (1966); Phys. Rev. 162, 692 (1967).
[Crossref]

Other (6)

O. S. Heavens, Optical Properties of Thin Solid Films (Academic Press Inc., New York, 1955), Ch. 4, p. 58.

A. Sager and R. C. Miller, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 653.

R. S. Allgaier and B. B. Houston, in Proceedings of the International Conference on Semiconductor Physics, Exeter, 1962 (The Institute of Physics and the Physical Society, London, 1962), p. 172.

R. Mazelsky and M. S. Lubell, Nonstoichiometric Compounds (American Chemical Society, Washington, D. C., 1963), Series 39, p. 210.
[Crossref]

W. W. Scanlon, Solid State Physics (Academic Press Inc., New York, 1959), Vol. IX, p. 115.

T. S. Moss, Optical Properties of Semi-Conductors (Academic Press Inc., New York, 1959), Ch. 1, p. 14.

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Figures (6)

Fig. 1
Fig. 1

The reflectance and transmittance spectra of an as-grown SnTe epitaxial film (solid curves) and the reflectivity spectra obtained from a thick, chemically polished bulk sample (open circles). The plasma-reflectance minimum occurs at λR = 6.1 μ indicating a carrier concentration of 1.4×1020 cm−3. The bulk sample was chosen so as to have the same carrier concentration as the film.

Fig. 2
Fig. 2

The reflectance and transmittance spectra of two SnTe epitaxial films of different carrier concentrations. The wavelengths of the plasma reflectance minima λR are 2.9 and 10.1 μ, corresponding to carrier concentrations of 6.8×1020 and 3.6×1019 cm−3, respectively. The corresponding film thicknesses were 0.77 and 1.9 μ.

Fig. 3
Fig. 3

The index of refraction nf of SnTe having a carrier concentration of 1.4×1020 cm−3. The solid curve represents nf determined from bulk reflectivity or average film-reflectance data. The symbols indicate values of nf calculated from the positions of interference fringes as described in the text. They apply to three films of thicknesses 1.3 μ(□), 1.4 μ(♢), and 1.9 μ(△). The dashed curves were calculated from interference-fringe data of our thickest sample, assuming that the correct order of interference m was mistaken by plus or minus one fringe (m+2 or m−2).

Fig. 4
Fig. 4

The index of refraction nf applying to SnTe having carrier concentrations of 3.6×1019, 1.4×1020, 2.9×1020, and 6.8×1020 cm−3. These carrier concentrations apply in sequence from the highest to the lowest curves. The symbols represent values of nf determined from the interference-fringe patterns of six films as explained in the text. The thicknesses were 0.77 μ(tilted △), 1.2 μ(▽), 1.3 μ(○), 1.4 μ(♢), 1.4 μ(□), and 1.9 μ(△). The solid curves A, B, C, and D were calculated on the basis of the classical free-carrier model of optical dispersion and the bulk parameters listed in Table I. Curves A′, B′, and D′ represent bound-carrier dispersion. They were determined from a Kramers–Kronig analysis as explained in Sec. IIE.

Fig. 5
Fig. 5

The absorption coefficient applying to four carrier concentrations of SnTe given in Table I. The solid curves A, B, C, and D were calculated on the basis of a classical free-carrier model and the bulk parameters listed in Table I. The solid curve from 1.2 to 3.0 eV represents the results of Cardona and Greenaway (Ref. 23). The dashed curves represent the bound-carrier components of the total absorption determined as described in the text.

Fig. 6
Fig. 6

The bound-carrier indices of refraction nBC and extinction coefficients kBC for three carrier concentrations of SnTe. The carrier concentrations were 3.6×1019, 1.4×1020, and 6.8×1020 cm−3, and are represented by the triangles, circles, and squares, respectively. The filled symbols are values determined from analysis of R and T as explained in Sec. IIA. The unfilled symbols are experimental values corrected for free-carrier effects. The values of nBC for E<0.8 eV were determined from interference fringes and are uncertain to within ±3%. The error of their relative values is, however, considerably less than this. All other points have an estimated uncertainty of ±10%. The solid curves A′, B′, and D′ were calculated using the Kramers–Kronig relation, as explained in the text.

Tables (1)

Tables Icon

Table I Parameters used to calculate the classical free-carrier curves of Figs. 4 and 5.

Equations (14)

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

T = f ( n f , k f , n g , λ , t )
R = g ( n f , k f , n g , λ , t ) .
k f ( n f - 1 ) .
m λ m = 4 n f ( λ m ) t ,             m = 1 , 2 , 3 , ,
R af = ( n f - 1 ) 2 / ( n f + 1 ) 2
n f = ( 1 + R af 1 2 ) / ( 1 - R af 1 2 ) .
m / ( m + 2 ) = λ m + 2 n f ( λ m ) / λ m n f ( λ m + 2 ) .
˜ = ˜ BC + ˜ FC ,
˜ = - 4 π P e 2 m s 1 ω 2 + γ FC 2 ( 1 - i γ FC ω ) .
n 2 = [ 1 + ( 1 2 + 2 2 ) 1 2 ] / 2 ,
α = 4 π k / λ .
k 2 = [ - 1 + ( 1 2 + 2 2 ) 1 2 ] / 2.
˜ BC = ˜ - ˜ FC ,
n BC ( E ) - 1 = 2 π 0 k BC ( E ) [ E 2 - E 2 ] - 1 E d E ,