Band bending flatband

The photocurrent density (/ph) is proportional to the light intensity, but almost independent of the electrode potential, provided that the band bending is sufficiently large to prevent recombination. At potentials close to the flatband potential, the photocurrent density again drops to zero. A typical current density-voltage characteristics of an n-semiconductor electrode in the dark and upon illumination is shown in Fig. 5.61. If the electrode reactions are slow, and/or if the e /h+ recombination via impurities or surface states takes place, more complicated curves for /light result. 

The photocurrent onset potential is often taken as the flatband potential, since the measurement of the flatband potential is typically only good to 100 mV and the onset of photocurrent is often observed with less than 100 mV of band bending. This practice is dangerous, however, since the onset potential is actually the potential at which the dark cathodic current and the photoanodic current are equal. Even though in the case of the p-GaP illustration, the observation of an anodic current and a photocathodic current are separated by several hundred millivolts, in many systems these two currents overlap. In those cases, the relationship between the flatband potential and the onset potential becomes unclear. 

Fig. 10.2. The semiconductor/solution interface in the flatband state. There is no band bending and no excess negative or positive charge on the semiconductor in the interfacial region in a solution-negligible surface state.

At higher pH values a smaller slope is observed possibly due to the potential drop across an oxide layer of increasing thickness. No specific effect of the various anions (Cf, SO 4 , CjO ") was observed. For n-Si in NH4F solutions, OCP increases with pH with a slope of about 45 mV/decade from pH 4 to 13 which is similar to the pH dependence of the flatband potential.This indicates that the band bending of the electrode is essentially constant at different pH values. 

Hfb is called the flatband potential. In the above discnssion, we assumed the energy bands to be pinned at the snrface so any variation of the electrode potential leads to a change of the band bending, as illnstrated in Fig. 2.16. Investigations of many semicondnctor electrodes have shown that the position of the energy bands is independent of the doping, i.e. the energy bands of n- and p-type electrodes have the same position at the snrface. In aqneous solutions, the potential across the Helmholtz layer is entirely determined by the interaction of the semiconductor and the solvent. 

Figure 4.24 Band bending at an /7-type semiconductor electrode at (a) equilibrium (b) a negative overpotential U- (c) the flatband potential U. ...

In a system with band-edge pinning, the flatband potentials are to the potentials at which there is no band bending. 

The position of the band edges with respect to the redox potentials in the electrolyte is conveniently expressed by the so-called flatband potential , fb- As the word suggests, this is the potential that needs to be applied to the semiconductor to reduce the band bending to zero. The flatband situation is illustrated in the right-hand panel of Fig. 2.17. It is important to realize that the flatband potential denotes the position of the Fermi level of the semiconductor with respect to the potential of the reference electrode. This means that fb is slightly below the conduction band edges shown in Fig. 2.18, and that it accurately reflects the thermodynamic ability of an n-type semiconductor to reduce water to hydrogen. 

There are other examples in the literature where the photocurrent does not rise near the flatband potential and then considerable band bending is required before any photocurrent can be detected. This inhibition is due to surface recombination, which will be treated in Section 5.2.3. 

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