The impact of boundary conditions on calculated photovoltages and photocurrents at photocatalytic interfaces


This work presents an in-depth study of how the choice of boundary conditions can impact upon the calculated photovoltage and photocurrent in photoelectrochemical (PEC) devices. Utilizing a floating boundary condition for the electrostatic potential and pseudo-Schottky boundary conditions for the interracial electron/hole currents, we show simultaneous calculation of photovoltage and photocurrent. We also explore the significance of capturing the photovoltage, with proper boundary conditions, to accurately replicate practical photocurrent along with the realistic band alignments. Finally, our results decouple the interracial hole transfer from the recombination at the interface/space-charged region and suggest possible methods to engineer the mesoscopic transfer process at PEC electrodes.

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

Figure 1
Figure 2
Figure 3
Figure 4


  1. 1.

    R. van de Krol: Principles of photoelectrochemical cells. In Photoelectrochemical Hydrogen Production (Springer, Berlin, 2012).

    Google Scholar 

  2. 2.

    L.M. Peter and K.G. Upul Wijayantha: Photoelectrochemical water splitting at semiconductor electrodes: fundamental problems and new perspectives. Chem. Phys. Chem. 15, 1983 (2014).

    CAS  Article  Google Scholar 

  3. 3.

    J. Su and L. Vayssieres: A place in the sun for artificial photosynthesis? ACS Energy Lett. 1, 121 (2016).

    CAS  Article  Google Scholar 

  4. 4.

    O. Zandi and T.W. Hamann: The potential versus current state of water splitting with hematite. Phys. Chem. Chem. Phys. 17, 22485 (2015).

    CAS  Article  Google Scholar 

  5. 5.

    D. Wang, A. Pierre, M.G. Kibria, K. Cui, X. Han, K.H. Bevan, H. Guo, S. Paradis, A.-R. Hakima, and Z. Mi: Wafer-level photocatalytic water splitting on GaN nanowire arrays grown by molecular beam epitaxy, Nano Lett 11, 2353 (2011).

    CAS  Article  Google Scholar 

  6. 6.

    C. Du, X. Yang, M.T. Mayer, H. Hoyt, J. Xie, G. McMahon, G. Bischoping, and D. Wang: Hematite-based water splitting with low turn-on voltages. Angew. Chem. Int. Ed. 52, 12692 (2013).

    CAS  Article  Google Scholar 

  7. 7.

    A. Iqbal, M.S. Hossain, and K.H. Bevan: The role of relative rate constants in determining surface state phenomena at semiconductor-liquid interfaces. Phys. Chem. Chem. Phys. 18, 29466 (2016).

    CAS  Article  Google Scholar 

  8. 8.

    D.R. Gamelin: Catalyst or spectator? Nat Chem. 4, 965 (2012).

    CAS  Article  Google Scholar 

  9. 9.

    J.E. Thorne, S. Li, C. Du, G. Qin, and D. Wang: Energetics atthe surface of photoelectrodes and its influence on the photoelectrochemical properties. J. Phys. Chem. Lett. 6, 4083 (2015).

    CAS  Article  Google Scholar 

  10. 10.

    B. Klahr, S. Gimenez, F. Fabregat-Santiago, T. Hamann, and J. Bisquert: Water oxidation at hematite photoelectrodes: the role of surface states. J. Am. Chem. Soc. 134, 4294 (2012).

    CAS  Article  Google Scholar 

  11. 11.

    M.R. Nellist, F.A.L. Laskowski, F. Lin, T.J. Mills, and S.W. Boettcher: Semiconductor-electrocatalyst interfaces: theory, experiment, and applications in photoelectrochemical water splitting. Acc. Chem. Res. 49, 733 (2016).

    CAS  Article  Google Scholar 

  12. 12.

    J. Reichman: The current-voltage characteristics of semiconductor-electrolyte junction photovoltaic cells. Appl. Phys. Lett. 36, 574 (1980).

    CAS  Article  Google Scholar 

  13. 13.

    S.J. Anz and N.S. Lewis: Simulations of the steady-state current density vs potential characteristics of semiconducting electrodes. J. Phys. Chem. 6103, 3908 (1999).

    Article  Google Scholar 

  14. 14.

    M.J. Cass, N.W. Duffy, L.M. Peter, S.R. Pennock, S. Ushiroda, and A. B. Walker: Microwave reflectance studies of photoelectrochemical kinetics at semiconductor electrodes. 1. steady-state, transient, and periodic responses. J. Phys. Chem. B 107, 5857 (2003).

    CAS  Article  Google Scholar 

  15. 15.

    P. Cendula, S.D. Tilley, S. Gimenez, J. Bisquert, M. Schmid, M. Gratzel, and J.O. Schumacher: calculation of the energy band diagram of a photoelectrochemical water splitting cell. J. Phys. Chem. C 118, 29599 (2014).

    CAS  Article  Google Scholar 

  16. 16.

    P.R.F. Barnes, A.Y. Anderson, J.R. Durrant, and B.C. O’Regan: Simulation and measurement of complete dye sensitised solar cells: including the influence of trapping, electrolyte, oxidised dyes and light intensity on steady state and transient device behaviour. Phys. Chem. Chem. Phys. 13, 5798 (2011).

    CAS  Article  Google Scholar 

  17. 17.

    A. Iqbal and K.H. Bevan: Simultaneously solving the photovoltage and photocurrent at semiconductor-liquid interfaces. J. Phys. Chem. C 122, 30 (2018).

    CAS  Article  Google Scholar 

  18. 18.

    T.J. Mills, F. Lin, and S.W. Boettcher: Theory and simulations of electrocatalyst-coated semiconductor electrodes for solar water splitting. Phys. Rev. Lett. 112, 148304 (2014).

    Article  Google Scholar 

  19. 19.

    H. Dotan, N. Mathews, T. Hisatomi, M. Gratzel, and A. Rothschild: On the solar to hydrogen conversion efficiency of photoelectrodes for water splitting. J. Phys. Chem. Lett. 5, 3330 (2014).

    CAS  Article  Google Scholar 

  20. 20.

    X. Shi, I. Herraiz-Cardona, L. Bertoluzzi, P. Lopez-Varo, J. Bisquert, J.H. Park, and S. Gimenez: Understanding the synergistic effect of WO3-BiV04 heterestructures by impedance spectroscopy. Phys. Chem. Chem. Phys. 18, 9255 (2016).

    CAS  Article  Google Scholar 

  21. 21.

    J.O. Bockris, A.K.N. Reddy, and M. E. Galboa-Aldeco: Modern Electrochemistry 2A, 2nd ed. (Springer: New York, 2000).

    Google Scholar 

  22. 22.

    R.F. Pierret: Semiconductor Device Fundamentals, (Addison-Wesley, Boston, MA, 1996).

    Google Scholar 

  23. 23.

    D.G. Vasileska, M. Stephen, and G. Klimeck: Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation (CRC Press, Boca Raton, 2010).

    Google Scholar 

  24. 24.

    S. Selberherr: Analysis and Simulation of Semiconductor Devices (Springer-Verlag GmbH, Vienna, 1984).

    Google Scholar 

  25. 25.

    D. Schroeder: Modelling of Interface Carrier Transport for Device Simulation (Springer-Verlag GmbH, Vienna, 1994).

    Google Scholar 

  26. 26.

    R. Memming: Semiconductor Electrochemistry (Wiley-CVH, Weinheim, Germany, 2000).

    Google Scholar 

  27. 27.

    N. Sato: Electrochemistry at Metal and Semiconductor Electrodes (Elsevier, Amsterdam, 1998).

    Google Scholar 

  28. 28.

    C.S. Crowell, S.M. Sze: Current transport in metal-semiconductor barriers. Solid State Electron. 9, 1035 (1966).

    CAS  Article  Google Scholar 

  29. 29.

    A. Kumar, P.G. Santangelo, and N.S. Lewis: Electrolysis of water at strontium titanate (SrTiO3) photoelectrodes: distinguishing between the statistical and stochastic formalisms for electron-transfer processes in fuel-forming photoelectrochemical systems. J. Phys. Chem. 96, 834 (1992).

    CAS  Article  Google Scholar 

  30. 30.

    F. Le Formal, E. Pastor, S.D. Tilley, C.A. Mesa, S.R. Pendlebury, M. Gratzel, and J.R. Durrant: Rate law analysis of water oxidation on a hematite surface. J. Am. Chem. Soc. 137, 6629 (2015).

    Article  Google Scholar 

  31. 31.

    F. Le Formal, S.R. Pendlebury, M. Cornuz, S.D. Tilley, M. Gratzel, and J.R. Durrant: Back electron-hole recombination in hematite photoanodes for water splitting. J. Am. Chem. Soc. 136, 2564 (2014).

    Article  Google Scholar 

  32. 32.

    M. Barroso, S.R. Pendlebury, A.J. Cowan, and J.R. Durrant: Charge carrier trapping, recombination and transfer in hematite (α-Fe2O3) water splitting photoanodes. Chem. Sci. 4, 2724 (2013).

    CAS  Article  Google Scholar 

  33. 33.

    S.D. Tilley, M. Cornuz, K. Sivula, and M. Gratzel: Light-induced water splitting with hematite: improved nanostructure and iridium oxide catalysis. Angew. Chem. Int. Ed. 49, 6405 (2010).

    CAS  Article  Google Scholar 

  34. 34.

    K. Sivula, F. Le Formal, and M. Gratzel: Solar water splitting: progress using hematite (α-Fe2O3) photoelectrodes. ChemSusChem 4, 432 (2011).

    CAS  Article  Google Scholar 

  35. 35.

    Z.D. Chen, H.N. Dinh, and E. Miller: Photoelectrochemical Water Splitting Standards, Experimental Methods, and Protocols (Springer, New York, NY, 2013).

    Google Scholar 

  36. 36.

    P. Salvador: Semiconductors’ photoelectrochemistry: a kinetic and thermodynamic analysis in the light of equilibrium and nonequilibrium models. J. Phys. Chem. 6105, 6128 (2001).

    Article  Google Scholar 

  37. 37.

    M. Rioult, H. Magnan, D. Stanescu, and A. Barbier: Single crystalline hematite films for solar water splitting: Ti-doping and thickness effects. J. Phys. Chem. C 118, 3007 (2014).

    CAS  Article  Google Scholar 

Download references

Author information



Corresponding authors

Correspondence to Asif Iqbal or Kirk H. Bevan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Iqbal, A., Bevan, K.H. The impact of boundary conditions on calculated photovoltages and photocurrents at photocatalytic interfaces. MRS Communications 8, 466–473 (2018).

Download citation