Photocurrent theory

As mentioned in the introduction, before an adequate theory was developed, it was difficult to understand the experimentally determined pho-toinduced PMC signals, especially the minority carrier accumulation near the onset of photocurrents.The reason was that neither conventional solid-state semiconductor theory nor photoelectrochemical theory had taken such a phenomenon into account. But we have shown that it is real and microwave (photo)electrochemical experiments clearly confirm it. 

Typical photocurrent transients are shown in Fig. 6 for electrons and in Fig. 7 for holes. The shape of these curves is representative for all transients observed in the study and is characteristic of dispersive transport [64-68]. The carrier mobility p was determined from the inflection point in the double logarithmic plots (cf. Fig. 6b and Fig. 7b) [74]. TOF measurements were performed as a function of carrier type, applied field, and film thickness (Fig. 8). As can be seen from Fig. 8, the drift mobility is independent of L, demonstrating that the photocurrents are not range-limited but indeed reflect the drift of the carrier sheet across the entire sample. Both the independence of the mobility from L, and the fact that the slopes of the tangents used to determine the mobility (Fig. 6 and Fig. 7) do not add to -2 as predicted by the Scher-Montroll theory, indicate that the Scher-Montroll picture of dispersive transients does not adequately describe the transport in amorphous EHO-OPPE [69]. The dispersive nature of the transient is due to the high degree of disorder in the sample and its impact on car-... 

An increase of the photocurrent at energies less than 2 eV was observed [151,152] unlike the previous result. This was attributed to the localized impurity ionization up to 0.8 eV below the conduction band. The crystals are considered as model systems for the one and three-dimensional versions of Onsager s theory of germinate recombination. 

The resemblance of the photocurrent to the optical adsorption spectrum has suggested the involvement of molecular excited states in the creation of charge carriers. While this resemblance is by no means universally observed, the concept of carrier creation via exciton interactions at or very near the illuminated electrode has become increasingly favored. Many of the data leading to these conclusions have been obtained by the use of pulsed light techniques (6, 7,3). These methods are virtually independent of electrode effects and the subsequent analysis of the transient current has led to considerable advances in the theory of charge transfer in molecular crystals. 

The conclusion that the photocurrents are limited by recombination has been verified recently by Karl and Sommer (1971) who also determined the value of the bimolecular electron-hole recombination constant. The shapes of the transients observed in these experiments are similar to those which are characteristic of damaged surface layers (see p. 181). In a similar way many workers have observed non-linear field dependences of the collected charge. In their study of durene, Burshtein and Williams (1977) show that a consideration in terms of Onsager s (1938) theory of geminate surface recombination appears to be unsatisfactory the results are best explained in terms of efficient deep trapping and/or recombination in a narrow region near the illuminated surface. 

A Theory of the Photocurrent for Semiconductors of Low Surface State Concentration Near the Limiting Current... 

Two assumptions were made in the first theory of the photocurrent at irradiated semiconductor electrodes (Butler,51977). The first of these was that mentioned in the... 

The mathematical evolution of the theory is involved, and struggling with its algebra does little to increase our understanding of photoelectrochemistry. The result for a photocurrent provoked by a light with a monochromatic frequency is... 

There are three clear divisions in the photoelectrochemical field. In the first, one shines light upon a metal electrode. Here, the theory is well worked out (Barker, 1974 Khan and Uosaki, 1976), but metals absorb light very poorly compared with semiconductors, and this makes the photocurrents obtained by irradiating them extremely small. The second division concerns the absorption of light by molecules in solution and electron transfer from or to these photoactivated species and to or from a conveniently placed electrode (Albery, 1989). Such phenomena are of interest to photochemists, but here the electrode is the handmaiden of the photochemistry and so we regretfully forgo a description of the material. 

M. A. Butler, /. Appl. Phys. 44 1914 (1977). Theory of photocurrents in terms of energy gap and flatband potential transport in rate control. 

In I/E curves the onset of photocurrent is expected from classical theories to occur near the Hatband potential as measured in the dark (Efb (d)), i.e. where the majority carrier current starts too. However, a large shift of the onset potential is seen especially if no additional redox couple is present in the aqueous electrolyte, in cathodic direction for p-, in anodic direction for n-type materials (Fig. 1). This shift depends on the light intensity but saturates already at relatively low intensities (Memming, 1987). If minority carrier acceptors (oxidants for p- and reductants for n-type semiconductors) are added to the solution, the onset can be shifted back to Efb (d) if they have the appropiate redox potential. In principal two types of redox couples can be found those which lead to a shift of the photocurrent onset potential and those which don t. The transition between the two classes occurs at a specific redox potential. 

Theory of the transient photocurrent behaviour at the ORDE. The stationary optical disc electrode is assumed to be uniformly illuminated by parallel light which is switched on at time t = 0, and which produces a measurable concentration of photogenerated electrons on the particles denoted by c. The differential equation for the generation and transport of these electrons to the electrode surface, with concurrent homogeneous back reaction is set up with the following assumptions. 

Figure 94 (a) The SCL transient currents for various normalized trapping times (R = Ttrap/t0) as calculated from theory (see Ref. 26) R = oo denotes the trap-free case is the steady-state current without trapping, (b) t trap-free SCL transient current injected from ITO under a positive step voltage applied to an IT0/PPV/TPD PC/A1 device jScl corresponds to in part (a). Bottom TOF photocurrent transient for holes generated by a light pulse at the A1/(TPD PC) interface (the negative polarity applied to ITO). (From Ref. 428). 

Internal photoemission of charge carriers from metal electrodes takes place when a metal, placed in contact with an insulator, absorbs light so that it promotes electrons from its Fermi level to the conduction band of the insulator. This happens only if the incident photon energy is equal to or greater than the barrier height between the insulator and the metal electrode. On the basis of Fowler s theory [9], the measured photocurrent is given by the expression... 

Within the framework of the Schottky junction theory, many models have been developed to explain the photovoltaic spectral response of organic materials. Assuming a direct formation of carriers, without diffusion of exciton to the surface but taking into account the charge diffusion length Ln p, the photocurrent density Jsc for light incident on the junction side is [64]... 

Harten s method [140] has now become the commonest electrochemical technique as will be shown below, very reliable solutions are now available for the behaviour of the photocurrent over a wide variety of materials and direct methods are also available for verifying the central assumption in the theory, that the potential distribution remains classical, at least over the potential range sampled. 

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