Skip to main content
Log in

On injection in intrinsic single-carrier devices

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

A Correction to this article was published on 01 April 2024

This article has been updated

Abstract

By considering the changes in the interface charge-carrier densities of a single-carrier device as a function of injection barrier heights and comparing these to the equilibrium, background charge-carrier density of a device with Ohmic contacts, we calculate simple conditions for when these barriers are expected to limit injection and therefore significantly affect space-charge-limited currents in the device. We show that these conditions depend on the device temperature, semiconductor relative permittivity and effective density of states, but most importantly the thickness of the semiconducting film being probed. This is in accordance with previous observations and similar derived expressions for when defects influence single-carrier devices. The conditions described herein can be used to aid in the design of single-carrier devices for space-charge-limited current measurements that are not limited by injection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability

All simulated data is available from the corresponding author upon request.

Change history

References

  1. Poplavskyy, D., Nelson, J.: Nondispersive hole transport in amorphous films of methoxy-spirofluorene-arylamine organic compound. J. Appl. Phys. 93, 341 (2003)

    Article  Google Scholar 

  2. Katsouras, I., Najafi, A., Asadi, K., Kronemeijer, A.J., Oostra, A.J., Koster, L.J.A., de Leeuw, D.M., Blom, P.W.M.: Charge transport in poly(p-phenylene vinylene) at low temperature and high electric field. Org. Electron. 14, 1591–1596 (2013)

    Article  Google Scholar 

  3. Mackenzie, K.D., Le, C.P.G., Spear, W.E.: The density of states in amorphous silicon determined by space-charge-limited current measurements. Philos. Mag. Part B 46, 377–389 (1982)

    Article  Google Scholar 

  4. Ou, S.S., Stafsudd, O.M., Bason, B.M.: Space-charge-limited current measurement of traps in p-type electrochemically deposited CdTe thin films. Thin Solid Films 112, 301–308 (1984)

    Article  Google Scholar 

  5. SajediAlvar, M., Blom, P.W.M., Wetzelaer, G.J.A.H.: Space-charge-limited electron and hole currents in hybrid organic-inorganic perovskites. Nat. Commun. 11, 1–9 (2020)

    Google Scholar 

  6. Duijnstee, E.A., Le, C.V.M., Johnston, M.B., Koster, L.J.A., Lim, J., Snaith, H.J.: Understanding dark current-voltage characteristics in metal-halide perovskite single crystals. Phys. Rev. Appl. 10, 1 (2021)

    Google Scholar 

  7. Le Corre, V.M., Duijnstee, E., El Tambouli, O., Ball, J., Snaith, H., Lim, J., Koster, L.J.A.: Revealing charge carrier mobility and defect densities in metal halide perovskites via space-charge-limited current measurements. ACS Energy Lett. 6, 1087–1094 (2021)

    Article  Google Scholar 

  8. Mark, P., Helfrich, W.: Space-charge-limited currents in organic crystals. J. Appl. Phys. 33, 205–215 (1962)

    Article  Google Scholar 

  9. Röhr, J.A., Shi, X., Haque, S.A., Kirchartz, T., Nelson, J.: Charge transport in spiro-OMeTAD investigated through space-charge-limited current measurements. Phys. Rev. Appl. 9, 044017 (2018)

    Article  Google Scholar 

  10. Mott, N.F., Gurney, R.W.: Electronic Processes in Ionic Crystals. Oxford University Press, Oxford (1940)

    Google Scholar 

  11. Lampert, M., Mark, P.: Current Injections in Solids. Academic Press, Cambridge (1970)

    Google Scholar 

  12. De Bruyn, P., Van Rest, A.H.P., Wetzelaer, G.A.H., De Leeuw, D.M., Blom, P.W.M.: Diffusion-limited current in organic metal-insulator-metal diodes. Phys. Rev. Lett. 111, 1–5 (2013)

    Article  Google Scholar 

  13. Röhr, J.A., Mackenzie, R.C.I.: Analytical description of mixed ohmic and space-charge-limited conduction in single-carrier devices. J. Appl. Phys. 128, 165701 (2020)

    Article  Google Scholar 

  14. Röhr, J.A., Moia, D., Haque, S.A., Kirchartz, T., Nelson, J.: Exploring the validity and limitations of the Mott–Gurney law for charge-carrier mobility determination of semiconducting thin-films. J. Phys. Condens. Matter 30, 105901 (2018)

    Article  Google Scholar 

  15. Dacuña, J., Salleo, A.: Modeling space-charge-limited currents in organic semiconductors: Extracting trap density and mobility. Phys. Rev. B 84, 195209 (2011)

    Article  Google Scholar 

  16. Dacuña, J., Xie, W., Salleo, A.: Estimation of the spatial distribution of traps using space-charge-limited current measurements in an organic single crystal. Phys. Rev. B 86, 115202 (2012)

    Article  Google Scholar 

  17. Nicolai, H.T., Kuik, M., Wetzelaer, G.A.H., de Boer, B., Campbell, C., Risko, C., Brédas, J.L., Blom, P.W.M.: Unification of trap-limited electron transport in semiconducting polymers. Nat. Mater. 11, 882–887 (2012)

    Article  Google Scholar 

  18. Lee, H.K.H., Telford, A.M., Röhr, J.A., Wyatt, M.F., Rice, B., Wu, J., De Castro, M.A., Tuladhar, S.M., Speller, E., McGettrick, J., Searle, J.R., Pont, S., Watson, T., Kirchartz, T., Durrant, J.R., Tsoi, W.C., Nelson, J., Li, Z.: The role of fullerenes in the environmental stability of polymer: fullerene solar cells. Energy Environ. Sci. 11, 417–428 (2018)

    Article  Google Scholar 

  19. MacKenzie, R.C.I., Kirchartz, T., Dibb, G.F.A., Nelson, J.: Modeling nongeminate recombination in P3HT: PCBM solar cells. J. Phys. Chem. C 115, 9806–9813 (2011)

    Article  Google Scholar 

  20. Röhr, J.A., Kirchartz, T., Nelson, J.: On the correct interpretation of the low voltage regime in intrinsic single-carrier devices. J. Phys. Condens. Matter 29, 205901 (2017)

    Article  Google Scholar 

  21. de Levie, R., Seidah, N.G., Moreia, H.: Transport of ions of one kind through thin membranes. J. Membr. Biol. 10, 171–192 (1972)

    Article  Google Scholar 

  22. Grinberg, A.A., Luryi, S.: Space-charge-limited current and capacitance in double-junction diodes. J. Appl. Phys. 61, 1181–1189 (1987)

    Article  Google Scholar 

  23. Rose, A.: Space-charge-limited currents in solids. Phys. Rev. 97, 1538–1544 (1955)

    Article  Google Scholar 

  24. Simmons, J.G.: Richardson-Schottky effect in solids. Phys. Rev. Lett. 15, 967–968 (1965)

    Article  Google Scholar 

  25. Simmons, J.G.: J. Phys. Chem. Solids 32, 1987 (1971)

    Article  Google Scholar 

  26. van Mensfoort, S.L.M., Coehoorn, R.: Effect of Gaussian disorder on the voltage dependence of the current density in sandwich-type devices based on organic semiconductors. Phys. Rev. B 78, 085207 (2008)

    Article  Google Scholar 

Download references

Acknowledgements

J.A.R. would like to thank Prof. Roderick MacKenzie for his tireless efforts developing the OghmaNano software and Prof. André D. Taylor for his support.

Funding

The authors declare that no funds, grants or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jason A. Röhr.

Ethics declarations

Conflict of interest

The authors have no relevant financial nor non-financial interests to disclose.

Additional information

Publisher's Note

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

The original online version of this article was revised: “In this article, van Mensfoort and Coehoorn [S. L. M. van Mensfoort and R. Coehoorn, Phys. Rev. B 78, 085207 (2008)] should be cited before introducing Equation 10.”

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Röhr, J.A. On injection in intrinsic single-carrier devices. J Comput Electron 23, 224–232 (2024). https://doi.org/10.1007/s10825-024-02129-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-024-02129-w

Keywords

Navigation