Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Conduction band structure of high-mobility organic semiconductors and partially dressed polaron formation

Nature Materials volume 21, pages 910–916 (2022)Cite this article

Subjects

Abstract

The energy band structure provides crucial information on charge transport behaviour in organic semiconductors, such as effective mass, transfer integrals and electron–phonon coupling. Despite the discovery of the valence (the highest occupied molecular orbital (HOMO)) band structure in the 1990s, the conduction band (the lowest unoccupied molecular orbital (LUMO)) has not been experimentally observed. Here we employ angle-resolved low-energy inverse photoelectron spectroscopy to reveal the LUMO band structure of pentacene, a prototypical high-mobility organic semiconductor. The derived transfer integrals and bandwidths from the LUMO are substantially smaller than those predicted by density functional theory calculations. To reproduce this bandwidth reduction, we propose an improved (partially dressed) polaron model that accounts for the electron–intramolecular vibrational interaction with frequency-dependent coupling constants based on Debye relaxation. This model quantitatively reproduces not only the transfer integrals, but also the temperature-dependent HOMO and LUMO bandwidths, and the hole and electron mobilities. The present results demonstrate that electron mobility in high-mobility organic semiconductors is indeed limited by polaron formation.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: AR-LEIPS spectra of pentacene thin-film phase on SiO2.
Fig. 2: LUMO band structures of pentacene.
Fig. 3: Results of theoretical calculations.
Fig. 4: Temperature-dependent UPS and LEIPS spectra.
Fig. 5: Theoretical temperature-dependent electron and hole mobilities.

Similar content being viewed by others

Data availability

All the data supporting the findings of this study are available within the article, its Supplementary Information files or from the corresponding authors upon request.

Code availability

The electronic-state-calculation codes used in this paper are Quantum ESPRESSO, Wannier90 and GAMESS. Detailed information related to the license and user guide for these codes are available at https://www.quantum-espresso.org/, http://www.wannier.org/ and https://www.msg.chem.iastate.edu/gamess/.

References

  1. Karl, N. Charge carrier transport in organic semiconductors. Synth. Met. 133–134, 649–657 (2003).

    Article  CAS  Google Scholar 

  2. Podzorov, V., Menard, E., Rogers, J. A. & Gershenson, M. E. Hall effect in the accumulation layers on the surface of organic semiconductors. Phys. Rev. Lett. 95, 226601 (2005).

    Article  CAS  Google Scholar 

  3. Hasegawa, T. & Takeya, J. Organic field-effect transistors using single crystals. Sci. Technol. Adv. Mater. 10, 024314 (2009).

    Article  CAS  Google Scholar 

  4. Lin, Y. J., Tsao, H. Y. & Liu, D. S. Hall-effect mobility of pentacene films prepared by the thermal evaporating method with different substrate temperature. Appl. Phys. Lett. 101, 013302 (2012).

    Article  CAS  Google Scholar 

  5. Marumoto, K., Kuroda, S. I., Takenobu, T. & Iwasa, Y. Spatial extent of wave functions of gate-induced hole carriers in pentacene field-effect devices as investigated by electron spin resonance. Phys. Rev. Lett. 97, 256603 (2006).

    Article  CAS  Google Scholar 

  6. Ueno, N. & Kera, S. Electron spectroscopy of functional organic thin films: deep insights into valence electronic structure in relation to charge transport property. Prog. Surf. Sci. 83, 490–557 (2008).

    Article  CAS  Google Scholar 

  7. Martinelli, N. G. et al. Influence of intermolecular vibrations on the electronic coupling in organic semiconductors: the case of anthracene and perfluoropentacene. ChemPhysChem 10, 2265–2273 (2009).

    Article  CAS  Google Scholar 

  8. Gershenson, M. E., Podzorov, V. & Morpurgo, A. F. Colloquium: Electronic transport in single-crystal organic transistors. Rev. Mod. Phys. 78, 973–989 (2006).

    Article  CAS  Google Scholar 

  9. Nematiaram, T. & Troisi, A. Modeling charge transport in high-mobility molecular semiconductors: balancing electronic structure and quantum dynamics methods with the help of experiments. J. Chem. Phys. 152, 190902 (2020).

    Article  CAS  Google Scholar 

  10. Schweicher, G. et al. Molecular semiconductors for logic operations: dead-end or bright future? Adv. Mater. 32, 1905909 (2020).

    Article  CAS  Google Scholar 

  11. Schweicher, G., Olivier, Y., Lemaur, V. & Geerts, Y. H. What currently limits charge carrier mobility in crystals of molecular semiconductors? Isr. J. Chem. 54, 595–620 (2014).

    Article  CAS  Google Scholar 

  12. Fratini, S., Mayou, D. & Ciuchi, S. The transient localization scenario for charge transport in crystalline organic materials. Adv. Funct. Mater. 26, 2292–2315 (2016).

    Article  CAS  Google Scholar 

  13. Liu, C. et al. A unified understanding of charge transport in organic semiconductors: the importance of attenuated delocalization for the carriers. Mater. Horiz. 4, 608–618 (2017).

    Article  CAS  Google Scholar 

  14. Oberhofer, H., Reuter, K. & Blumberger, J. Charge transport in molecular materials: an assessment of computational methods. Chem. Rev. 117, 10319–10357 (2017).

    Article  CAS  Google Scholar 

  15. Troisi, A. & Orlandi, G. Charge-transport regime of crystalline organic semiconductors: diffusion limited by thermal off-diagonal electronic disorder. Phys. Rev. Lett. 96, 086601 (2006).

    Article  CAS  Google Scholar 

  16. Holstein, T. Studies of polaron motion. Part II. The ‘small’ polaron. Ann. Phys. (N Y) 8, 343–389 (1959).

    Article  CAS  Google Scholar 

  17. Hannewald, K. et al. Theory of polaron bandwidth narrowing in organic molecular crystals. Phys. Rev. B 69, 075211 (2004).

    Article  CAS  Google Scholar 

  18. Ciuchi, S. & Fratini, S. Band dispersion and electronic lifetimes in crystalline organic semiconductors. Phys. Rev. Lett. 106, 166403 (2011).

    Article  CAS  Google Scholar 

  19. Koch, N. et al. Evidence for temperature-dependent electron band dispersion in pentacene. Phys. Rev. Lett. 96, 156803 (2006).

    Article  CAS  Google Scholar 

  20. Hatch, R. C., Huber, D. L. & Höchst, H. Electron–phonon coupling in crystalline pentacene films. Phys. Rev. Lett. 104, 047601 (2010).

    Article  CAS  Google Scholar 

  21. Nakayama, Y. et al. Single-crystal pentacene valence-band dispersion and its temperature dependence. J. Phys. Chem. Lett. 8, 1259–1264 (2017).

    Article  CAS  Google Scholar 

  22. Li, Y., Coropceanu, V. & Brédas, J. L. Thermal narrowing of the electronic bandwidths in organic molecular semiconductors: impact of the crystal thermal expansion. J. Phys. Chem. Lett. 3, 3325–3329 (2012).

    Article  CAS  Google Scholar 

  23. Coropceanu, V. et al. Charge transport in organic semiconductors. Chem. Rev. 107, 926–952 (2007).

    Article  CAS  Google Scholar 

  24. Frank, K. H., Yannoulis, P., Dudde, R. & Koch, E. E. Unoccupied molecular orbitals of aromatic hydrocarbons adsorbed on Ag(111). J. Chem. Phys. 89, 7569–7576 (1988).

    Article  CAS  Google Scholar 

  25. Hill, I. G. et al. Occupied and unoccupied electronic levels in organic π-conjugated molecules: Comparison between experiment and theory. Chem. Phys. Lett. 317, 444–450 (2000).

    Article  CAS  Google Scholar 

  26. Yoshida, H., Tsutsumi, K. & Sato, N. Unoccupied electronic states of 3d-transition metal phthalocyanines (MPc: M = Mn, Fe, Co, Ni, Cu and Zn) studied by inverse photoemission spectroscopy. J. Electron Spectros. Relat. Phenomena 121, 83–91 (2001).

    Article  CAS  Google Scholar 

  27. Zahn, D. R. T., Gavrila, G. N. & Gorgoi, M. The transport gap of organic semiconductors studied using the combination of direct and inverse photoemission. Chem. Phys. 325, 99–112 (2006).

    Article  CAS  Google Scholar 

  28. Krause, S., Casu, M. B., Schöll, A. & Umbach, E. Determination of transport levels of organic semiconductors by UPS and IPS. New J. Phys. 10, 085001 (2008).

    Article  CAS  Google Scholar 

  29. Kanai, K. et al. Determination of electron affinity of electron accepting molecules. Appl. Phys. A 95, 309–313 (2009).

    Article  CAS  Google Scholar 

  30. Dose, V. Momentum-resolved inverse photoemission. Surf. Sci. Rep. 5, 337–378 (1985).

    Article  CAS  Google Scholar 

  31. Yoshida, H. Near-ultraviolet inverse photoemission spectroscopy using ultra-low energy electrons. Chem. Phys. Lett. 539–540, 180–185 (2012).

    Article  CAS  Google Scholar 

  32. Yoshida, H. Principle and application of low energy inverse photoemission spectroscopy: a new method for measuring unoccupied states of organic semiconductors. J. Electron Spectros. Relat. Phenom. 204, 116–124 (2015).

    Article  CAS  Google Scholar 

  33. Yoshida, H., Inaba, K. & Sato, N. X-ray diffraction reciprocal space mapping study of the thin film phase of pentacene. Appl. Phys. Lett. 90, 181930 (2007).

    Article  CAS  Google Scholar 

  34. Yoshida, H. & Sato, N. Crystallographic and electronic structures of three different polymorphs of pentacene. Phys. Rev. B 77, 235205 (2008).

    Article  CAS  Google Scholar 

  35. Zhou, S. Y. et al. Coexistence of sharp quasiparticle dispersions and disorder features in graphite. Phys. Rev. B 71, 161403 (2005).

    Article  CAS  Google Scholar 

  36. Park, S. et al. Electronic band dispersion determination in azimuthally disordered transition-metal dichalcogenide monolayers. Commun. Phys. 2, 68 (2019).

    Article  CAS  Google Scholar 

  37. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  38. Berland, K. et al. van der Waals forces in density functional theory: a review of the vdW-DF method. Rep. Prog. Phys. 78, 066501 (2015).

    Article  CAS  Google Scholar 

  39. Mostofi, A. A. et al. wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).

    Article  CAS  Google Scholar 

  40. Tiago, M. L. et al. Ab initio calculation of the electronic and optical properties of solid pentacene. Phys. Rev. B 67, 115212 (2003).

    Article  CAS  Google Scholar 

  41. Yanagisawa, S. & Hamada, I. Determination of geometric and electronic structures of organic crystals from first principles: role of the molecular configuration on the electronic structure. J. Appl. Phys. 121, 45501 (2017).

    Article  CAS  Google Scholar 

  42. Ortmann, F., Bechstedt, F. & Hannewald, K. Theory of charge transport in organic crystals: beyond Holstein’s small-polaron model. Phys. Rev. B 79, 235206 (2009).

    Article  CAS  Google Scholar 

  43. Fratini, S. & Ciuchi, S. Dynamical localization corrections to band transport. Phys. Rev. Res. 2, 13001 (2020).

    Article  CAS  Google Scholar 

  44. Houili, H., Picon, J. D., Zuppiroli, L. & Bussac, M. N. Polarization effects in the channel of an organic field-effect transistor. J. Appl. Phys. 100, 23702 (2006).

    Article  CAS  Google Scholar 

  45. Von Helden, L., Breuer, T. & Witte, G. Anisotropic thermal expansion in pentacene and perfluoropentacene: effects of molecular packing motif and fixation at the interface. Appl. Phys. Lett. 110, 141904 (2017).

    Article  CAS  Google Scholar 

  46. Lukas, S., Söhnchen, S., Witte, G. & Wöll, C. Epitaxial growth of pentacene films on metal surfaces. ChemPhysChem 5, 266–270 (2004).

    Article  CAS  Google Scholar 

  47. Yasuda, T., Goto, T., Fujita, K. & Tsutsui, T. Ambipolar pentacene field-effect transistors with calcium source-drain electrodes. Appl. Phys. Lett. 85, 2098–2100 (2004).

    Article  CAS  Google Scholar 

  48. Chua, L. L. et al. General observation of n-type field-effect behaviour in organic semiconductors. Nature 434, 194–199 (2005).

    Article  CAS  Google Scholar 

  49. Chiu, L. Y. et al. Manipulating the ambipolar characteristics of pentacene-based field-effect transistors. J. Mater. Chem. C 2, 1823–1829 (2014).

    Article  CAS  Google Scholar 

  50. Saudari, S. R. & Kagan, C. R. Electron and hole transport in ambipolar, thin film pentacene transistors. J. Appl. Phys. 117, 035501 (2015).

    Article  CAS  Google Scholar 

  51. Ishii, H., Inoue, J. I., Kobayashi, N. & Hirose, K. Quantitative mobility evaluation of organic semiconductors using quantum dynamics based on density functional theory. Phys. Rev. B 98, 235422 (2018).

    Article  CAS  Google Scholar 

  52. Ishii, H., Kobayashi, N. & Hirose, K. Order-N electron transport calculations from ballistic to diffusive regimes by a time-dependent wave-packet diffusion method: application to transport properties of carbon nanotubes. Phys. Rev. B 82, 085435 (2010).

    Article  CAS  Google Scholar 

  53. Fratini, S. et al. A map of high-mobility molecular semiconductors. Nat. Mater. 16, 998–1002 (2017).

    Article  CAS  Google Scholar 

  54. Yoshida, H. Note: Low energy inverse photoemission spectroscopy apparatus. Rev. Sci. Instrum. 85, 016101 (2014).

    Article  CAS  Google Scholar 

  55. Schmidt, M. W. et al. General atomic and molecular electronic structure system. J. Comput. Chem. 14, 1347–1363 (1993).

    Article  CAS  Google Scholar 

  56. Yamane, H. et al. Hole-vibration coupling of the highest occupied state in pentacene thin films. Phys. Rev. B 72, 153412 (2005).

    Article  CAS  Google Scholar 

  57. Computational Chemistry Comparison and Benchmark DataBase. Precomputed Vibrational Scaling Factors (National Institute of Standards and Technology, 2015); https://cccbdb.nist.gov/vibscalejust.asp

  58. Ishii, H., Kobayashi, N. & Hirose, K. Charge transport calculations by a wave-packet dynamical approach using maximally localized Wannier functions based on density functional theory: application to high-mobility organic semiconductors. Phys. Rev. B 95, 035433 (2017).

    Article  Google Scholar 

  59. Goto, H., Obata, S., Nakayama, N. & Ohta, K. CONFLEX 8 (Conflex, 2017).

Download references

Acknowledgements

The authors thank N. Ueno for stimulating and helpful discussion on the electron–phonon coupling of organic semiconductors. This work was supported by JSPS KAKENHI (JP26288007, JP18H01856, JP21H01902 and JP21H05472), JST PRESTO, CREST (JPMJCR21Q1), and the Futaba Research Grant Program of the Futaba Foundation. H.S. thanks the JST SPRING grant (JPMJSP2109) for financial support. H.I. acknowledges financial support from the University of Tsukuba, Pre-Strategic Initiatives ‘Development Center for High-Function and High-Performance Organic–Inorganic Spin Electronics’.

Author information

Author notes

  1. These authors contributed equally: Haruki Sato, Syed A. Abd. Rahman.

Authors and Affiliations

  1. Graduate School of Science and Engineering, Chiba University, Chiba, Japan

    Haruki Sato, Syed A. Abd. Rahman & Yota Yamada

  2. Department of Applied Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan

    Hiroyuki Ishii

  3. Graduate School of Engineering, Chiba University, Chiba, Japan

    Hiroyuki Yoshida

  4. Molecular Chirality Research Center, Chiba University, Chiba, Japan

    Hiroyuki Yoshida

Authors
  1. Haruki Sato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Syed A. Abd. Rahman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yota Yamada
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hiroyuki Ishii
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hiroyuki Yoshida
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

H.Y. created the concept of this work. H.S., S.A.A.R. and Y.Y. acquired and analysed the experimental data. H.I. and H.Y. performed the theoretical analysis. H.S. and H.Y. wrote the manuscript.

Corresponding authors

Correspondence to Hiroyuki Ishii or Hiroyuki Yoshida.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Antoine Kahn, Peter Puschnig and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. S1–S9, Tables S1–S9 and sections S1–S12.

Supplementary Data CIF1

Crystallographic data (CIF file) of pentacene thin-film phase at 300 K of temperature based on the lattice constants given in Yoshida et al [Ref. 33].

Supplementary Data CIF2

Crystallographic data (CIF file) of pentacene thin-film phase at 300 K of temperature based on the lattice constants given in Nabok et al [Ref. S6].

Supplementary Data CIF3

Crystallographic data (CIF file) of pentacene thin-film phase at 120 K of temperature based on the lattice constants given in Yoshida et al [Ref. 33].

Supplementary Data CIF4

Crystallographic data (CIF file) of pentacene thin-film phase at 220 K of temperature based on the lattice constants given in Yoshida et al [Ref. 33].

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sato, H., Abd. Rahman, S.A., Yamada, Y. et al. Conduction band structure of high-mobility organic semiconductors and partially dressed polaron formation. Nat. Mater. 21, 910–916 (2022). https://doi.org/10.1038/s41563-022-01308-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-022-01308-z

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing