Photocurrent multiplication

In the above analysis we always assumed that the photocurrent was entirely due to minority carriers. In a number of cases, however, the measured photocurrent appears to exceed the current of minority carriers at the electrode surface. This effect, called the photocurrent multiplication, was observed, in particular, in photooxidation of various organic substances at ZnO electrodes (Cardon and Gomes, 1971 Freund, 1972), CdSe electrodes (Van den Berghe et al., 1971), and 2 electrodes (Miyake et al., 1977). 

Photocurrent multiplication at an -type electrode can be explained by participation in the electrode reaction of conduction-band electrons, in addition to photoholes. For example, an organic compound R can be oxidized at a photoanode in two stages ... 

To take into account all the above-mentioned effects, it is convenient to introduce into formulas (31) and (34) an empirical factor M, called the photocurrent multiplication coefficient. It reflects the fact that a single lightgenerated carrier can, by virtue of secondary reactions, initiate the transition of several elementary charges across the interface. 

Examples of photocurrent multiplication [1] include the photo-oxidation of formic acid and of secondary alcohols at /i-type semiconductors, and the photoreduction of oxygen at p-type semiconductors. The mechanisms involve majority carrier injection by a photogenerated intermediate, and IMPS has been used to determine the rate constant for these processes. 

The first system exhibiting photocurrent multiplication to be studied by IMPS was the photoreduction of oxygen to H202 at p-GaP [36, 37]. The oxidation of formic acid at /i-CdS was then characterised by the same method [35]. Further examples of current doubling that have been studied by IMPS include the photo-oxidation of formic acid at Ti02 [31] and the photoanodic oxidation of /i-Si [33, 34]. 

IMPS is a powerful technique for the study of photocurrent multiplication because it allows deconvolution of the minority and majority carrier contributions to the total photocurrent. The component of the photocurrent flux due to injection of majority carriers lags behind the in-phase component associated with the flux of photogenerated minority carriers. The time delay corresponds to the first order lifetime of the injecting intermediate, and the injection component is attenuated progressively as... 

Another interesting characteristic of many multi-equivalent redox systems is the phenomenon of photocurrent multiplication. This phenomenon may be illustrated for two systems utilizing illuminated n-type and p-type semiconductors ... 

Thus, the key feature of photocurrent multiplication is a majority carrier injection step (reaction 34b or 34d) from a reaction intermediate (usually a free radical) into the semiconductor CB or VB, respectively. Thus, in the examples above, each photon generates two carriers in the external circuit, affording a quantum yield (in the ideal case) of 2. This is the current-doubling process. 

Photocurrent multiplication has been observed for a variety of semiconductors including Ge [269], Si [268-271], ZnO [272-278], Ti02 [279-282], CdS [283, 284], GaP [285], InP [286] and GaAs [287-289]. These studies have included both n- and p-type semiconductors, and have spanned a range of substrates, both organic and inorganic. As in the Si case, this phenomenon can also be caused by photodissolution reactions involving the semiconductor itself. The earlier studies have mainly employed voltammetry, particularly hydrodynamic voltammetry (see, e.g.. Ref. [282]). 

As more recent examples (see Refs. [2], [9] and [10] for reviews) reveal, IMPS is a powerful technique for the study of photocurrent multiplication. Unlike in the cases discussed earlier (Figure 27), majority carrier injection leads to a component of the... 

The frequency windows for the study of photocurrent multiplication by IMPS is set by the dynamic response of the potentiostat (at high frequencies) and by the RC time constant attenuation. The injection rate constant, (first-order), can be calculated from the minimum of the arc, Wmin the upper limit to /cjnj appears to be ca. 10 s [9]. For example, k a for formic acid oxidation on n-CdS has been estimated to be 6 x 10 s [284]. 

L. M. Peter, A. M. Borazio, H. J. Lewerenz, and J. Stumper, Photocurrent multiplication during photodissolution of n-Si in NH4F. Deconvolution of electron injection steps by intensity modulated photocurrent spectroscopy, J. Electroanal. Chem. 290, 229, 1990. 

Before photocurrent excitation spectra can be normalised to allow for the wavelength dependence of the illumination intensity, it is essential to establish the relation between the photocurrent response and the incident photon flux. This can be done using calibrated neutral density fdters. The relationship is generally not linear for photoconductive systems or for systems in which processes such as surface recombination or photocurrent multiplication occur (Peter, 1990). The incident photon flux can be measured using a UV-enhanced silicon photodiode with known sensitivity. 

In the absence of surface recombination, all minority carriers that are collected by diffusion and migration in the semiconductor/electrolyte junction will eventually either transfer to redox species in the solution or react with the semiconductor itself leading to anodic or cathodic photodecomposition. Slow interfacial kinetics will result in the build up of photogenerated carriers at the interface, but unless photocurrent multiplication occurs, the saturation photocurrent will simply be determined by the light intensity, and the quantum efficiency will be unity. This means that the photocurrent contains no information about interfacial kinetics. In reality, most semiconductor/electrolyte interfaces are non-ideal, and a substantial fraction of the photogenerated electrons or holes do not take part in interfacial redox reactions because they recombine via surface states (see section 2.3.3). It is this competition between interfacial electron transfer and surface recombination that opens the way to obtain information about the rates of interfacial processes. 

Fig. 30. Transient photocurrent response to illumination step measured at low light intensity for n-Si in 1.0 M NH4F at pH 4.5 [49]. The slow rise and fall are attributed to the slowest step in the photocurrent multiplication scheme. The semilogarithmic plot can be used to derive the value of k. Compare with Fig. 29 which demonstrates the superior resolution of IMPS.

Another example of photocurrent multiplication that have been studied by IMPS is the photo-anodic dissolution of n-InP in HCl [65], which is a six electron process. The IMPS analysis is an extension of the 4 electron case for silicon, and analysis of the experimental IMPS results show that in three out of the six steps, electron injection can compete with hole capture. The rate constants for the three consecutive electron injection steps were found to be ka > 6 x 10 s , kb = 6 x 10 s and kc = 6 X 10 s . ... 

At higher light intensity, the quantum efficiency drops indicating that reaction steps involving valence-band holes take over from electron injection steps. A quantum efficiency of two for InP means that three of the six oxidation steps require minority carriers and thus photons. As for silicon, the quantum efficiency decreases (from 2 to 1) as the light intensity is increased. As described in the previous section, IMPS can be used very effectively to study the mechanisms of photocurrent multiplication reactions. The method has proved particularly successful for the silicon and... 

Hiramoto, M., Imahigashi, T, and Yokoyama, M., Photocurrent multiplication in organic pigment films, Appl. Phys. Lett., 64, 187, 1994. 

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