Abstract

The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760–1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallo-graphic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. S. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
    [CrossRef]
  2. D. Y. Smith, "Dispersion theory, sum rules, and their application to the analysis of optical data," in: Handbook of optical constants of solids, E. D. Palik, ed., (Academic Press, Orlando, 1985), Vol. 1, p. 35.
  3. M. Born and M. Wolf, Principles of optics, 7th edition, (Cambridge University Press, Cambridge, 1999).
  4. Alternatively the indicatrix is used, which is a geometrical construction using the major refractive indices defined by nj = √(∑1) j, where (∑1) j are the diagonal elements of the dielectric tensor for non-absorbing and non-magnetic materials. For our description we assume a symmetric dielectric response which excludes spatial (optical activity) and temporal (e.g. Faraday effect) non-reciprocity.
  5. J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
    [CrossRef]
  6. A. B. Kuzmenko, E. A. Tishchenko, and V. G. Orlov, "Transverse optic modes in monoclinic α-Bi2O3," J. Phys.: Cond. Mat. 8, 6199-6122 (1996).
    [CrossRef]
  7. M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
    [CrossRef]
  8. D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
    [CrossRef]
  9. S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
    [CrossRef] [PubMed]
  10. C. D. Dimitrakopoulos and D. J. Mascaro, "Organic thin-film transistors: A review of recent advances," IBM J. Res. Dev. 45, 11-27 (2001).
    [CrossRef]
  11. G. Horowitz, "Organic thin film transistors: From theory to real devices," J. Mater. Res. 19, 1946-1962 (2004).
    [CrossRef]
  12. M. E. Gershenson, V. Pozorov, and A. F. Morpugo, "Colloquium: Electronic transport in single-crystal organic transistors," Rev. Mod. Phys. 78, 973-989 (2006).
    [CrossRef]
  13. M. L. Tiago, J. E. Northrup, and S. G. Louie, "Ab initio calculation of the electronic and optical properties of solid pentacene," Phys. Rev. B 67, 115212 (2003).
    [CrossRef]
  14. K. Hummer and C. Ambrosch-Draxl, "Electronic properties of oligoacenes from first principles," Phys. Rev. B 72, 205205 (2005).
    [CrossRef]
  15. K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
    [CrossRef]
  16. A. Troisi and G. Orlandi, "Band Structure of the four pentacene polymorphs and effect on the hole mobility at low temperature," J. Phys. Chem. B,  109, 1849-1856 (2005).
    [CrossRef]
  17. M. Schubert, "Another century of ellipsometry," Ann. Phys. 15, 480-497 (2006).
    [CrossRef]
  18. R. M. A. Azzam and R. M. A. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1984).
  19. M. Schubert and W. Dollase, "Generalized ellipsometry for biaxial absorbing materials: determination of crystal orientation and optical constants of Sb2S3," Opt. Lett. 27, 2073-2075 (2002).
    [CrossRef]
  20. M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons and Polaritons (Springer, Berlin, 2004).
  21. Without this additional projection T the obtained absolute ∑ (ω)-values are unrealistic and/or not Kramers-Kronig consistent. For the example of tetracene and pentacene, see [9] and [8]. A comparison of the so obtained results with the present data is given is the Appendix.
  22. I.-H. Suh, Y.-S. Park, and J.-G. Kim, "ORTHON: transformation from triclinic axes and atomic coordinates to orthonormal ones," J. Appl. Cryst. 33, 994 (2000).
    [CrossRef]
  23. E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
    [CrossRef]
  24. A. S. Davydov, Theory of Molecular Excitons (Plenum Press, New York-London, 1971).
  25. R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
    [CrossRef]
  26. R. B. Campbell, J. Trotter, and J. M. Robertson, "The crystal and molecular structure of pentacene," Acta Cryst. 14, 705-711 (1961).
    [CrossRef]
  27. C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
    [CrossRef]
  28. For comparison the parameters given in Ref. [26] and Ref. [27] are transformed into the parameters of the Niggli cell by using the matrices (-1 0 0 / 0 1 0 / -1 0 -1) and (0 1 0 / 1 0 0 / -12 0 -1), respectively.

2008

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

2007

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

2006

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

M. E. Gershenson, V. Pozorov, and A. F. Morpugo, "Colloquium: Electronic transport in single-crystal organic transistors," Rev. Mod. Phys. 78, 973-989 (2006).
[CrossRef]

M. Schubert, "Another century of ellipsometry," Ann. Phys. 15, 480-497 (2006).
[CrossRef]

2005

K. Hummer and C. Ambrosch-Draxl, "Electronic properties of oligoacenes from first principles," Phys. Rev. B 72, 205205 (2005).
[CrossRef]

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

A. Troisi and G. Orlandi, "Band Structure of the four pentacene polymorphs and effect on the hole mobility at low temperature," J. Phys. Chem. B,  109, 1849-1856 (2005).
[CrossRef]

2004

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

G. Horowitz, "Organic thin film transistors: From theory to real devices," J. Mater. Res. 19, 1946-1962 (2004).
[CrossRef]

2003

M. L. Tiago, J. E. Northrup, and S. G. Louie, "Ab initio calculation of the electronic and optical properties of solid pentacene," Phys. Rev. B 67, 115212 (2003).
[CrossRef]

2002

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

M. Schubert and W. Dollase, "Generalized ellipsometry for biaxial absorbing materials: determination of crystal orientation and optical constants of Sb2S3," Opt. Lett. 27, 2073-2075 (2002).
[CrossRef]

2001

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

C. D. Dimitrakopoulos and D. J. Mascaro, "Organic thin-film transistors: A review of recent advances," IBM J. Res. Dev. 45, 11-27 (2001).
[CrossRef]

2000

I.-H. Suh, Y.-S. Park, and J.-G. Kim, "ORTHON: transformation from triclinic axes and atomic coordinates to orthonormal ones," J. Appl. Cryst. 33, 994 (2000).
[CrossRef]

1998

E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
[CrossRef]

1996

A. B. Kuzmenko, E. A. Tishchenko, and V. G. Orlov, "Transverse optic modes in monoclinic α-Bi2O3," J. Phys.: Cond. Mat. 8, 6199-6122 (1996).
[CrossRef]

1961

R. B. Campbell, J. Trotter, and J. M. Robertson, "The crystal and molecular structure of pentacene," Acta Cryst. 14, 705-711 (1961).
[CrossRef]

1956

J. S. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Alonso, M. I.

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

Ambrosch-Draxl, C.

K. Hummer and C. Ambrosch-Draxl, "Electronic properties of oligoacenes from first principles," Phys. Rev. B 72, 205205 (2005).
[CrossRef]

Baas, J.

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

Campbell, R. B.

R. B. Campbell, J. Trotter, and J. M. Robertson, "The crystal and molecular structure of pentacene," Acta Cryst. 14, 705-711 (1961).
[CrossRef]

Chen, L.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Composeo, A.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

de Boer, J. L.

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

de Matos Gommes, E.

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

Dimitrakopoulos, C. D.

C. D. Dimitrakopoulos and D. J. Mascaro, "Organic thin-film transistors: A review of recent advances," IBM J. Res. Dev. 45, 11-27 (2001).
[CrossRef]

Doi, K.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Dollase, W.

Dressel, M.

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

Dros, A. B.

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

Dujovne, I.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Faltermeier, D.

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

Garriaga, M.

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

Gershenson, M. E.

M. E. Gershenson, V. Pozorov, and A. F. Morpugo, "Colloquium: Electronic transport in single-crystal organic transistors," Rev. Mod. Phys. 78, 973-989 (2006).
[CrossRef]

Gompf, B.

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

Hartmann, D.

E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
[CrossRef]

He, R.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Heineke, E.

E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
[CrossRef]

Hese, A.

E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
[CrossRef]

Hirjibehedin, C. F.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Horowitz, G.

G. Horowitz, "Organic thin film transistors: From theory to real devices," J. Mater. Res. 19, 1946-1962 (2004).
[CrossRef]

Hummer, K.

K. Hummer and C. Ambrosch-Draxl, "Electronic properties of oligoacenes from first principles," Phys. Rev. B 72, 205205 (2005).
[CrossRef]

Isakov, D.

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

Karl, N.

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

Kim, J.-G.

I.-H. Suh, Y.-S. Park, and J.-G. Kim, "ORTHON: transformation from triclinic axes and atomic coordinates to orthonormal ones," J. Appl. Cryst. 33, 994 (2000).
[CrossRef]

Kloc, C.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Kojima, Y.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Kuzmenko, A. B.

A. B. Kuzmenko, E. A. Tishchenko, and V. G. Orlov, "Transverse optic modes in monoclinic α-Bi2O3," J. Phys.: Cond. Mat. 8, 6199-6122 (1996).
[CrossRef]

Laimondo, L.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

Louie, S. G.

M. L. Tiago, J. E. Northrup, and S. G. Louie, "Ab initio calculation of the electronic and optical properties of solid pentacene," Phys. Rev. B 67, 115212 (2003).
[CrossRef]

Mascaro, D. J.

C. D. Dimitrakopoulos and D. J. Mascaro, "Organic thin-film transistors: A review of recent advances," IBM J. Res. Dev. 45, 11-27 (2001).
[CrossRef]

Mattheus, C. C.

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

Meetsma, A.

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

Miao, Q.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Morpugo, A. F.

M. E. Gershenson, V. Pozorov, and A. F. Morpugo, "Colloquium: Electronic transport in single-crystal organic transistors," Rev. Mod. Phys. 78, 973-989 (2006).
[CrossRef]

Muller, R.

E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
[CrossRef]

Nakano, H.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Northrup, J. E.

M. L. Tiago, J. E. Northrup, and S. G. Louie, "Ab initio calculation of the electronic and optical properties of solid pentacene," Phys. Rev. B 67, 115212 (2003).
[CrossRef]

Nuckolls, C.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Okazaki, K.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Orlandi, G.

A. Troisi and G. Orlandi, "Band Structure of the four pentacene polymorphs and effect on the hole mobility at low temperature," J. Phys. Chem. B,  109, 1849-1856 (2005).
[CrossRef]

Orlov, V. G.

A. B. Kuzmenko, E. A. Tishchenko, and V. G. Orlov, "Transverse optic modes in monoclinic α-Bi2O3," J. Phys.: Cond. Mat. 8, 6199-6122 (1996).
[CrossRef]

Osso, J. O.

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

Palstra, T. T. M.

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

Park, Y.-S.

I.-H. Suh, Y.-S. Park, and J.-G. Kim, "ORTHON: transformation from triclinic axes and atomic coordinates to orthonormal ones," J. Appl. Cryst. 33, 994 (2000).
[CrossRef]

Pflaum, J.

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

Pinczuk, A.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Pisignano, D.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

Polo, M.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

Pozorov, V.

M. E. Gershenson, V. Pozorov, and A. F. Morpugo, "Colloquium: Electronic transport in single-crystal organic transistors," Rev. Mod. Phys. 78, 973-989 (2006).
[CrossRef]

Ribeiro, J. L.

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

Robertson, J. M.

R. B. Campbell, J. Trotter, and J. M. Robertson, "The crystal and molecular structure of pentacene," Acta Cryst. 14, 705-711 (1961).
[CrossRef]

Ron, A.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

Schreiber, F.

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

Schubert, M.

Silvestri, L.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

Spearman, P.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

Suh, I.-H.

I.-H. Suh, Y.-S. Park, and J.-G. Kim, "ORTHON: transformation from triclinic axes and atomic coordinates to orthonormal ones," J. Appl. Cryst. 33, 994 (2000).
[CrossRef]

Tachibana, A.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Tanabe, T.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Tarroso Gomes, I.

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

Tavazzi, S.

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

Tiago, M. L.

M. L. Tiago, J. E. Northrup, and S. G. Louie, "Ab initio calculation of the electronic and optical properties of solid pentacene," Phys. Rev. B 67, 115212 (2003).
[CrossRef]

Tishchenko, E. A.

A. B. Kuzmenko, E. A. Tishchenko, and V. G. Orlov, "Transverse optic modes in monoclinic α-Bi2O3," J. Phys.: Cond. Mat. 8, 6199-6122 (1996).
[CrossRef]

Toll, J. S.

J. S. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Tripathi, A. K.

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

Troisi, A.

A. Troisi and G. Orlandi, "Band Structure of the four pentacene polymorphs and effect on the hole mobility at low temperature," J. Phys. Chem. B,  109, 1849-1856 (2005).
[CrossRef]

Trotter, J.

R. B. Campbell, J. Trotter, and J. M. Robertson, "The crystal and molecular structure of pentacene," Acta Cryst. 14, 705-711 (1961).
[CrossRef]

Vieira, L. G.

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

Yoshida, K.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

Acta Cryst.

R. B. Campbell, J. Trotter, and J. M. Robertson, "The crystal and molecular structure of pentacene," Acta Cryst. 14, 705-711 (1961).
[CrossRef]

Acta Cryst. C

C. C. Mattheus, A. B. Dros, J. Baas, A. Meetsma, J. L. de Boer, and T. T. M. Palstra, "Polymorphism in pentacene," Acta Cryst. C 57, 939-941 (2001).
[CrossRef]

Ann. Phys.

M. Schubert, "Another century of ellipsometry," Ann. Phys. 15, 480-497 (2006).
[CrossRef]

Appl. Phys. Lett.

R. He, I. Dujovne, L. Chen, Q. Miao, C. F. Hirjibehedin, A. Pinczuk, C. Nuckolls, C. Kloc, and A. Ron, "Resonant Raman scattering in nanoscale pentacene films," Appl. Phys. Lett. 84, 987-989 (2004).
[CrossRef]

IBM J. Res. Dev.

C. D. Dimitrakopoulos and D. J. Mascaro, "Organic thin-film transistors: A review of recent advances," IBM J. Res. Dev. 45, 11-27 (2001).
[CrossRef]

J. Appl. Cryst.

I.-H. Suh, Y.-S. Park, and J.-G. Kim, "ORTHON: transformation from triclinic axes and atomic coordinates to orthonormal ones," J. Appl. Cryst. 33, 994 (2000).
[CrossRef]

J. Appl. Phys.

K. Doi, K. Yoshida, H. Nakano, A. Tachibana, T. Tanabe, Y. Kojima, and K. Okazaki, "Ab initio calculation of electron effective masses in solid pentacene," J. Appl. Phys. 98, 113709 (2005).
[CrossRef]

J. Chem. Phys.

E. Heineke, D. Hartmann, R. Muller, and A. Hese, "Laser spectroscopy of free pentacene molecules (I): The rotational structure of the vibrationless S1 ←S0 transition," J. Chem. Phys. 109, 906-911 (1998).
[CrossRef]

S. Tavazzi, L. Laimondo, L. Silvestri, P. Spearman, A. Composeo, M. Polo, and D. Pisignano," Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra," J. Chem. Phys. 128, 154709 (2008).
[CrossRef] [PubMed]

J. Mater. Res.

G. Horowitz, "Organic thin film transistors: From theory to real devices," J. Mater. Res. 19, 1946-1962 (2004).
[CrossRef]

J. Phys. Chem. B

A. Troisi and G. Orlandi, "Band Structure of the four pentacene polymorphs and effect on the hole mobility at low temperature," J. Phys. Chem. B,  109, 1849-1856 (2005).
[CrossRef]

J. Phys.: Cond. Mat.

J. L. Ribeiro, L. G. Vieira, I. Tarroso Gomes, D. Isakov, and E. de Matos Gommes, "The infrared dielectric tensor and axial dispersion in caesium L-malate monohydrate," J. Phys.: Cond. Mat. 19, 176225 (2007).
[CrossRef]

A. B. Kuzmenko, E. A. Tishchenko, and V. G. Orlov, "Transverse optic modes in monoclinic α-Bi2O3," J. Phys.: Cond. Mat. 8, 6199-6122 (1996).
[CrossRef]

Opt. Lett.

Org. Electr.

M. I. Alonso, M. Garriaga, N. Karl, J. O. Osso, and F. Schreiber, "Anisotropic optical properties of single crystalline PTCDA studied by spectroscopic ellipsometry," Org. Electr. 3, 23-31 (2002).
[CrossRef]

Phys. Rev.

J. S. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Phys. Rev. B

D. Faltermeier, B. Gompf, M. Dressel, A. K. Tripathi, and J. Pflaum, "Optical properties of pentacene thin films and single crystals," Phys. Rev. B 74, 125416 (2006).
[CrossRef]

M. L. Tiago, J. E. Northrup, and S. G. Louie, "Ab initio calculation of the electronic and optical properties of solid pentacene," Phys. Rev. B 67, 115212 (2003).
[CrossRef]

K. Hummer and C. Ambrosch-Draxl, "Electronic properties of oligoacenes from first principles," Phys. Rev. B 72, 205205 (2005).
[CrossRef]

Rev. Mod. Phys.

M. E. Gershenson, V. Pozorov, and A. F. Morpugo, "Colloquium: Electronic transport in single-crystal organic transistors," Rev. Mod. Phys. 78, 973-989 (2006).
[CrossRef]

Other

R. M. A. Azzam and R. M. A. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1984).

M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons and Polaritons (Springer, Berlin, 2004).

Without this additional projection T the obtained absolute ∑ (ω)-values are unrealistic and/or not Kramers-Kronig consistent. For the example of tetracene and pentacene, see [9] and [8]. A comparison of the so obtained results with the present data is given is the Appendix.

D. Y. Smith, "Dispersion theory, sum rules, and their application to the analysis of optical data," in: Handbook of optical constants of solids, E. D. Palik, ed., (Academic Press, Orlando, 1985), Vol. 1, p. 35.

M. Born and M. Wolf, Principles of optics, 7th edition, (Cambridge University Press, Cambridge, 1999).

Alternatively the indicatrix is used, which is a geometrical construction using the major refractive indices defined by nj = √(∑1) j, where (∑1) j are the diagonal elements of the dielectric tensor for non-absorbing and non-magnetic materials. For our description we assume a symmetric dielectric response which excludes spatial (optical activity) and temporal (e.g. Faraday effect) non-reciprocity.

A. S. Davydov, Theory of Molecular Excitons (Plenum Press, New York-London, 1971).

For comparison the parameters given in Ref. [26] and Ref. [27] are transformed into the parameters of the Niggli cell by using the matrices (-1 0 0 / 0 1 0 / -1 0 -1) and (0 1 0 / 1 0 0 / -12 0 -1), respectively.

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 (5)

Fig. 1.
Fig. 1.

(a) Arrangement of the two pentacene molecules in the unit cell (a=6.14 Å, b=7.93 Å, c=14.90 Å). According to the triclinic symmetry the axes are not orthogonal but slightly tilted: α=92.8°, β=101.5° and γ=95.20. Band structure calculations yield the microscopic optical functions along the unit cell axes a, b, and c (cf. Fig. 4). (b) The microscopic polarization p along the unit cell axes a, b, and c is projected by T onto an orthogonal auxiliary frame (ξ,η,ζ). The orientation of this coordinate system with respect to the laboratory frame (x,y,z) is given by the Euler angles φ, θ, and ψ. (c) The macroscopic optical properties are described by the tensors of the real and imaginary parts of the dielectric function ε̄1 and ε̄2. The principal axes are different of each other and depend on frequency.

Fig. 2.
Fig. 2.

Setup of the rotating-compensator ellipsometer utilized to measure changes of the polarization state upon reflection off a single crystal surface as a function of angle of incidence Φ a and azimutal angle ϕ a .

Fig. 3.
Fig. 3.

Real and imaginary parts of the triclinic pentacene dielectric functions ε 1(ω) and ε 2(ω) along the crystallographic axes a, b, and c. From experimental data obtained on one crystal surface we could disentangle the intrinsic electronic excitations along the symmetry axes a,b,c. The ellipsometric experiment measures two components independently; the evaluation of ε 1 and ε 2 (solid lines) does not utilize the Kramers-Kronig relations. The simultaneous fit by the oscillator model (dotted lines) proves Kramers-Kronig consistency.

Fig. 4.
Fig. 4.

Bandstructure calculations of pentacene by Tiago et al. [13]. Solving the Bethe-Salpeter equation for electron-hole excitations, the density of states (DOS) and eventually the frequency dependent dielectric losses ε 2 along the three crystallographic directions a, b and c are evaluated.

Fig. 5.
Fig. 5.

Real and imaginary parts of the triclinic pentacene dielectric functions ε 1(ω) and ε 2(ω). (a) Spectral dependence of ε 1(ω) and ε 2(ω) along the three principal aces x, y, and z. Note that ε (z)(ω) correspond to the right scales (from [8]). (b) Dielectric functions along the crystallographic axes a, b, and c [reproduced from Fig. 3].

Tables (1)

Tables Icon

Table 1. Parameters to fit the electronic transitions of triclinic pentacene with Gaussian oscillators for the three polarizations Ea, b, and c,respectively. A n , E n and Δ n denote, respectively, amplitude, energy and broadening of the n-th oscillator function.

Equations (2)

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

p = ρ a a + ρ b b + ρ c c .
T = ( sin β cos γ cos β cos α sin β 0 0 sin 2 α ( cos γ cos β cos α sin β ) 2 0 cos β cos α 1 )

Metrics