Studies of photocurrent multiplication by IMPS

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]. 

The oxidation of formic acid to C02 is a two step reaction which involves the following steps 

Reaction (8.39d) is responsible for photocurrent doubling since it results in the two electron oxidation of formic acid to C02 for the absorption of only one photon. The electron injection step competes with the hole capture reaction, (8.39c), and as a result the photocurrent quantum efficiency depends on illumination intensity. At high intensities, the supply of photogenerated holes to the surface favours reaction (8.39c), and the quantum efficiency is I. At low light intensities, electron injection becomes predominant, and the quantum efficiency tends towards 2. 

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 

---

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]. 

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 . ... 

---