Abstract
The transport of photogenerated electrons in nanocrystalline semiconductor networks permeated with a conducting phase is studied, with a particular emphasis on dye-sensitized nanoporous TiO2 solar cells. We extend the classical approach to the trap-limited mobility according to specific features of the nanoporous configuration: electron transport by diffusion, the capacitive behavior of the nanoporous film and the possible bandshifts due to the charging of surface states. We show that the trap-limited diffusivity, as measured by small-signal techniques, is proportional to the ratio of the conduction-band capacitance and the trap capacitance. These capacitances are defined in terms of a pseudopotential related to the chemical energy of the free electrons, in order to account for possible band unpinning. Several specific distributions of bandgap states are investigated. The dependence of the trap capacitance on the number of free electrons takes the general form Ctrap=An1-a, where 0≤a≤1 depends on the distribution of the traps. The trap-limited diffusivity depends on the number of free electrons as Dn=Bna, and Dn also shows a power-law dependence with the light intensity. We describe the correlation of the electron conductivity with the photovoltage in the solar cell and the photon irradiation intensity.
Similar content being viewed by others
References
B. O’Regan, M. Grätzel: Nature 353, 737 (1991)
G. Hodes, I.D.J. Howell, L.M. Peter: J. Electrochem. Soc. 139, 3136 (1992)
H. Scher, M. Lax: Phys. Rev. B 7, 4491 (1973)
H. Scher, E.W. Montroll: Phys. Rev. B 12, 2455 (1975)
F.W. Schmidlin: Phys. Rev. B 16, 2362 (1978)
T. Tiedje, A. Rose: Solid State Commun. 37, 49 (1981)
G. Redmond, D. Fitzmaurice, M. Grätzel: J. Phys. Chem. 97, 6951 (1993)
G.K. Boschloo, A. Goossens: J. Phys. Chem. 100, 19489 (1996)
G. Boschloo, D. Fitzmaurice: J. Phys. Chem. B 103, 2228 (1999)
H. Wang, J. He, G. Boschloo, H. Lindström, A. Hagfeldt, S. Lindquist: J. Phys. Chem. B 105, 2529 (2001)
J. Nelson: Phys. Rev. B 59, 15374 (1999)
J. van de Lagemaat, A.J. Frank: J. Phys. Chem. B 104, 4292 (2000)
R. Könenkamp: Phys. Rev. B 61, 11057 (2000)
A.C. Fisher, L.M. Peter, E.A. Ponomarev, A.B. Walker, K.G.U. Wijayantha: J. Phys. Chem. B 104, 949 (2000)
M. Ben-Chorin, F. Möller, F. Koch, W. Schirmacher, M. Eberhard: Phys. Rev. B 51, 2199 (1995)
F. Cao, G. Oskam, G.J. Meyer, P.C. Searson: J. Phys. Chem. 100, 17021 (1996)
L. Dloczik, O. Ileperuma, I. Lauerman, L.M. Peter, E.A. Ponomarev, G. Redmond, N.J. Shaw, I. Uhlendorf: J. Phys. Chem. B 101, 10281 (1997)
P.E. de Jongh, D. Vanmaekelbergh: J. Phys. Chem. B 101, 2716 (1997)
L.M. Peter, K.G.U. Wijayantha: Electrochem. Commun. 1, 576 (1999)
N.W. Duffy, L.M. Peter, K.G.U. Wijayantha: Electrochem. Commun. 2, 262 (2000)
F. Cao, G. Oskam, P.C. Searson, J.M. Stipkala, T.A. Heimer, F. Farzad, G.J. Meyer: J. Phys. Chem. 99, 11974 (1995)
J. Bisquert, G. Garcia-Belmonte, F. Fabregat-Santiago, N.S. Ferriols, P. Bogdanoff, E.C. Pereira: J. Phys. Chem. B 104, 2287 (2000)
J. van de Lagemaat, N.G. Park, A.J. Frank: J. Phys. Chem. B 104, 2044 (2000)
J. Bisquert: J. Phys. Chem. B 106, 325 (2002)
F. Fabregat-Santiago, G. Garcia-Belmonte, J. Bisquert, A. Zaban, P. Salvador: J. Phys. Chem. B 106, 334 (2002)
P.E. de Jongh, D. Vanmaekelbergh: Phys. Rev. Lett. 77, 3427 (1996)
D. Vanmaekelbergh, F. Iranzo Marín, J. van de Lagemaat: Ber. Bunsenges. Phys. Chem. 100, 616 (1996)
D. Vanmaekelbergh, P.E. de Jongh: Phys. Rev. B 61, 4699 (2000)
G. Schlichthröl, S.Y. Huang, J. Sprague, A.J. Frank: J. Phys. Chem. B 101, 8141 (1997)
G. Franco, J. Gehring, L.M. Peter, E.A. Ponomarev, I. Uhlendorf: J. Phys. Chem. B 103, 692 (1999)
W.E. Spear: J. Non-Cryst. Solids 1, 197 (1969)
A. Zaban, A. Meier, B.A. Gregg: J. Phys. Chem. B 101, 7985 (1997)
J. Bisquert, G. Garcia-Belmonte, F. Fabregat Santiago: J. Solid State Electrochem. 3, 337 (1999)
S.R. Morrison: Electrochemistry at Semiconductor and Oxidized Metal Electrodes (Plenum Press, New York 1980)
J. van de Lagemaat, A.J. Frank: J. Phys. Chem. B 105, 11194 (2001)
R. Richert, L. Pautmeier, H. Bässler: Phys. Rev. Lett. 63, 547 (1989)
Q. Gu, E.A. Schiff, S. Grebner, F. Wang, R. Schwarz: Phys. Rev. Lett. 76, 3196 (1996)
T. Dittrich, E.A. Lebedev, J. Weidmann: Phys. Status Solidi A 167, R5 (1998)
E.A. Meulenkamp: J. Phys. Chem. B 103, 7831 (1999)
A. Rose: RCA Rev. 12, 362 (1951)
R.H. Bube: Photoelectronic Properties of Semiconductors (Cambridge University Press, Cambridge 1992)
P. Allongue, H. Cachet: J. Electroanal. Chem. 176, 369 (1984)
M. Pollak: Philos. Mag. 36, 1157 (1977)
S. Södergren, A. Hagfeldt, J. Olsson, S.E. Lindquist: J. Phys. Chem. 98, 5552 (1994)
S.Y. Huang, G. Schilchthörl, A.J. Nozik, M. Grätzel, A.J. Frank: J. Phys. Chem. B 101, 2576 (1997)
N.W. Duffy, L.M. Peter, R.M.G. Rajapakse, K.G.U. Wijayantha: J. Phys. Chem. B 104, 8916 (2000)
A. Solbrand, H. Lindström, H. Rensmo, A. Hagfeldt, S.E. Lindquist, S. Södergren: J. Phys. Chem. B 101, 2514 (1997)
J. Bisquert, A. Zaban, P. Salvador: J. Phys. Chem. B 106, 8774 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS
81.07.Bc; 73.30.+y
Rights and permissions
About this article
Cite this article
Bisquert , J., Zaban , A. The trap-limited diffusivity of electrons in nanoporous semiconductor networks permeated with a conductive phase. Appl Phys A 77, 507–514 (2003). https://doi.org/10.1007/s00339-002-1479-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00339-002-1479-4