### Abstract

Fermi's Golden Rule has previously been used to formulate rate expressions for transfer of delocalized charge carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. If the charge-transfer rate constant is known experimentally, these rate expressions allow computation of the value of the electronic coupling matrix element between the semiconducting electrode and the redox species. This treatment also facilitates comparison between charge-transfer kinetic data at metallic and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been evaluated from experimental data for charge transfer from Au electrodes to various redox acceptors. Based on the experimental parameters determined for these systems, the maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10 17—10-16 cm4 s-1. These theoretical estimates are in accord with experimental results for rate constants at the Si/CH3OH interface. Differential capacitance vs. potential and current density vs. potential measurements have been used to characterize the interfacial energetics and kinetics of n-type Si electrodes in contact with a series of one-electron, outer-sphere redox couples. The differential capacitance data yielded values for the electron concentration at the surface of the semiconductor as well as values for the driving force of the electron-transfer event at Si/CH3OH-viologen2+/+ junctions. The slopes of C 2-E plots agreed with theory, and little frequency dispersion was observed in the x-intercepts of such plots. The conduction band edge of the n-type Si anodes was invariant to within ±40 mV as the redox potential of the solution was varied by >400 mV, indicating “ideal” interfacial energetic behavior in this system with no evidence for Fermi level pinning. From these measurements, the surface-state density of the Si/CH3OH contact can be estimated as <10^{11}cm^{-2}. The current density vs. potential plots exhibited a first-order kinetic dependence on the concentration of electrons at the semiconductor surface and a first-order kinetic dependence on the concentration of acceptors in the solution. Rate constants for transfer of charge from the semiconductor to the acceptor were determined as a function of the driving force for the interfacial charge-transfer event and were well fit to Marcustype behavior, with a reorganization energy of 0.7 eV and a maximum rate constant of 6X10 ^{17} cm^{4} s^{-1}.

Original language | English |
---|---|

Pages (from-to) | 149-160 |

Number of pages | 12 |

Journal | Zeitschrift fur Physikalische Chemie |

Volume | 1 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1998 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

**Rate Constants for Electron Transfer across Semiconductor/Liquid Interfaces : Theory and Experiment.** / Lewis, Nathan S.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Rate Constants for Electron Transfer across Semiconductor/Liquid Interfaces

T2 - Theory and Experiment

AU - Lewis, Nathan S

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Fermi's Golden Rule has previously been used to formulate rate expressions for transfer of delocalized charge carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. If the charge-transfer rate constant is known experimentally, these rate expressions allow computation of the value of the electronic coupling matrix element between the semiconducting electrode and the redox species. This treatment also facilitates comparison between charge-transfer kinetic data at metallic and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been evaluated from experimental data for charge transfer from Au electrodes to various redox acceptors. Based on the experimental parameters determined for these systems, the maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10 17—10-16 cm4 s-1. These theoretical estimates are in accord with experimental results for rate constants at the Si/CH3OH interface. Differential capacitance vs. potential and current density vs. potential measurements have been used to characterize the interfacial energetics and kinetics of n-type Si electrodes in contact with a series of one-electron, outer-sphere redox couples. The differential capacitance data yielded values for the electron concentration at the surface of the semiconductor as well as values for the driving force of the electron-transfer event at Si/CH3OH-viologen2+/+ junctions. The slopes of C 2-E plots agreed with theory, and little frequency dispersion was observed in the x-intercepts of such plots. The conduction band edge of the n-type Si anodes was invariant to within ±40 mV as the redox potential of the solution was varied by >400 mV, indicating “ideal” interfacial energetic behavior in this system with no evidence for Fermi level pinning. From these measurements, the surface-state density of the Si/CH3OH contact can be estimated as <1011cm-2. The current density vs. potential plots exhibited a first-order kinetic dependence on the concentration of electrons at the semiconductor surface and a first-order kinetic dependence on the concentration of acceptors in the solution. Rate constants for transfer of charge from the semiconductor to the acceptor were determined as a function of the driving force for the interfacial charge-transfer event and were well fit to Marcustype behavior, with a reorganization energy of 0.7 eV and a maximum rate constant of 6X10 17 cm4 s-1.

AB - Fermi's Golden Rule has previously been used to formulate rate expressions for transfer of delocalized charge carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. If the charge-transfer rate constant is known experimentally, these rate expressions allow computation of the value of the electronic coupling matrix element between the semiconducting electrode and the redox species. This treatment also facilitates comparison between charge-transfer kinetic data at metallic and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been evaluated from experimental data for charge transfer from Au electrodes to various redox acceptors. Based on the experimental parameters determined for these systems, the maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10 17—10-16 cm4 s-1. These theoretical estimates are in accord with experimental results for rate constants at the Si/CH3OH interface. Differential capacitance vs. potential and current density vs. potential measurements have been used to characterize the interfacial energetics and kinetics of n-type Si electrodes in contact with a series of one-electron, outer-sphere redox couples. The differential capacitance data yielded values for the electron concentration at the surface of the semiconductor as well as values for the driving force of the electron-transfer event at Si/CH3OH-viologen2+/+ junctions. The slopes of C 2-E plots agreed with theory, and little frequency dispersion was observed in the x-intercepts of such plots. The conduction band edge of the n-type Si anodes was invariant to within ±40 mV as the redox potential of the solution was varied by >400 mV, indicating “ideal” interfacial energetic behavior in this system with no evidence for Fermi level pinning. From these measurements, the surface-state density of the Si/CH3OH contact can be estimated as <1011cm-2. The current density vs. potential plots exhibited a first-order kinetic dependence on the concentration of electrons at the semiconductor surface and a first-order kinetic dependence on the concentration of acceptors in the solution. Rate constants for transfer of charge from the semiconductor to the acceptor were determined as a function of the driving force for the interfacial charge-transfer event and were well fit to Marcustype behavior, with a reorganization energy of 0.7 eV and a maximum rate constant of 6X10 17 cm4 s-1.

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U2 - 10.1524/zpch.1998.1.1.149

DO - 10.1524/zpch.1998.1.1.149

M3 - Article

VL - 1

SP - 149

EP - 160

JO - Zeitschrift fur Physikalische Chemie

JF - Zeitschrift fur Physikalische Chemie

SN - 0942-9352

IS - 1

ER -