6 The Role of Interface States in Electron-Transfer Processes at Photoexcited Semiconductor Electrodes
Downloaded by UNIV OF LEEDS on August 17, 2014 | http://pubs.acs.org Publication Date: March 2, 1981 | doi: 10.1021/bk-1981-0146.ch006
R. H . WILSON Corporate Research and Development, General Electric Company, P.O. Box 8, Schenectady, NY 12301
Electronic energy levels localized at the surface of a semiconductor have frequently been used to explain, experimentally observed currents at semiconductor-electrolyte junctions. These surface or interface states are invoked when the observations are inconsistent with direct electron transfer between the conduction or valence band of the semiconductor and electronic states of an electrolyte in contact with the semiconductor. Charge carriers in the semiconductor bands are transferred to surface states that have energies within the bandgap of the semiconductor. From these states electrons can move isoenergetically across the interface to or from electrolyte states in accordance with the widely accepted view of electron transfer. The process by which the semiconductor carriers reach the surface to react with surface states must be considered. The case of greatest importance under photoexcitation is with the semiconductor biased to depletion as shown in Figure 1. While it is possible for semiconductor carriers to reach the surface of the semiconductor through tunneling, or impurity conduction processes, these processes have not been shown to be important in most examples of photoexcited semiconductor electrodes. Consequently, these processes will be ignored here in favor of the normal transport of carriers in the semiconductor bands. Furthermore, only carriers within a few kT of the band edges will be considered, i.e., "hot" carriers will be ignored. Figure 1 illustrates different modes of electron transfer between electrolyte states and carriers in the bands at the semiconductor surface. If the overlap between the electrolyte levels and the semiconductor bands is insufficient to allow direct, isoenergetic electron transfer, then an inelastic, energy-dissipating process must be used to explain experi mentally observed electron transfer. Duke has argued that a complete theory for electron transfer includes terms that allow direct, inelastic processes. The probability of such processes, however, has not been treated quantitatively. On the other hand, inelastic transfer of carriers in the bands to surface states is well known and reaction rates sufficient to 1-9
10
11,12,13
0097-6156/81/0146-0103$05.00/0 © 1981 American Chemical Society In Photoeffects at Semiconductor-Electrolyte Interfaces; Nozik, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
Downloaded by UNIV OF LEEDS on August 17, 2014 | http://pubs.acs.org Publication Date: March 2, 1981 | doi: 10.1021/bk-1981-0146.ch006
104
PHOTOEFFECTS
AT
SEMICONDUCTOR-ELECTROLYTE
INTERFACES
Figure 1. Schematic of various electron transfer processes between semiconductor carriers at the surface and electrolyte and surface states
In Photoeffects at Semiconductor-Electrolyte Interfaces; Nozik, A.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.
Downloaded by UNIV OF LEEDS on August 17, 2014 | http://pubs.acs.org Publication Date: March 2, 1981 | doi: 10.1021/bk-1981-0146.ch006
6.
WILSON
105
Interface States in Electron-Transfer Processes
explain many of the experimental observations can be readily estimated. The objective of this paper is to focus on this reaction between carriers and surface states and to emphasize the reaction cross section as an important parameter in charge transfer as well as in surface recombin ation. The role of surface states in charge transfer at the semiconductorelectrolyte interface is contrasted with effects at semiconductor-vacuum, semiconductor-insulator and semiconductor-metal interfaces. Factors affecting the magnitude of the reaction cross section are discussed and the theoretical understanding of the capture process is briefly reviewed. Finally, some experimental observations are discussed in which charge transfer to surface states is important. The emphasis is on methods to be quantitative in describing the role of surface states by determining their density and reaction cross sections. Some previously published observations as well as preliminary new results are used to illustrate the role of surface bound species as charge transfer surface states. Quantitative Reaction Rates Localized states in the bulk of a semiconductor that have energies within the bandgap are known to capture mobile carriers from the conduction and valence bands.— The bulk reaction rate is determined by the product of the carrier density, density of empty states, the thermal velocity of the carriers and the cross-section for carrier capture. These same concepts are applied to reactions at semiconductor surfaces that have localized energy levels within the bandgap.— — In that case the electron flux to the surface, F , reacting with a surface state is given by 1
n
F
n
N
v
n= s eO"n n
where Ν is the density of electrons in the conduction band at the surface, Ν isthe area density of empty surface states, CT is the electron capture cross section of the surface states and ν is the thermal velocity of electrons. This is clearly an oversimplified description of the capture process which hides many of the complexities in the phenomenological parameter, CT. Nevertheless, this approach has been usefully applied in describing the kinetics of semiconductor surface states in a variety of circumstances. For holes near the edge of the valence band with density, ρ , at the surface the analogous expression for the hole flux to the surface, F , reacting with a filled surface state of area density, N , is s
p
r
F
r^ = P c f N
9 Z
Z
c
c
