Photocurrent relaxation

The fast relaxation in the case of BQ has been associated with an interfacial protonation reaction 

This reaction involves the transfer of a proton from the aqueous to the organic phase, which generates a positive current response. Taking into account the processes contributing to the photocurrent responses. Equations (11.35)-( 11.39) and (11.60), the differential equations associated with the concentrations of the intermediate species ([PQ]) and the semiquinone radical ([Q ]) are given by 

In this treatment, we have expressed the disappearance of the semiquinone radical from the interface as a first-order process (kdi) in order to simplify the analysis. A more rigorous treatment involves the computing of the concentration profiles of the products. However, considering that the steady-state photocurrents are rather small, this approximation has very little effect on the present analysis of the photocurrent transients. 

The resolution of the differential equations in order to obtain the time dependent photocurrent has been performed via the Laplace method. In this approach, the concentration of the intermediates and products can be expressed as  

As mention in section 3.3, the photocurrent responses are attenuated by the RC component of the cell at short times. This parameter can be introduced into expression (11.67) yielding - ,  

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Fig. 105. Plot of photocurrent relaxation time, x, following a ns light pulse vs. total load resistance flload (= Rm + Roul), where ROM = fJ,cries + /iL, showing linearity expected at small values of fl)Dad. Inset shows the plot at values of ftload approaching zero.

In claiming (i) that v E and (ii) that photocurrent relaxation sets in on a 10 ns time scale we also have to cope with the experiment of Baumann et al. (17) who report on photocurrent pulses excited by 25 ps laser flashes falling off with an instrument limited decay time ( 100 ps) and increasing linearly with field. A numerical estimate which will be presented elsewhere indicates that, contrary to earlier reasoning (18), these photocurrent pulses can be associated with the primary generation of geminate e...h pairs whose dipole moments will preferentially align parallel to the applied field as E increases (19 20). 

The photoinduced reduction of TCNQ by the porphyrin heterodimer ZnTPPS-ZnTMPyP provides a good illustration of these concepts [56,109]. Figure 12(a) displays photocurrent transients at the water DCE junction in the presence and absence of an equimolar ratio of Fe(CN)g /Fe(CN)g. The photocurrent relaxation in the absence of the aqueous redox couples is associated with the back electron transfer from TCNQ to the oxidized porphyrin complex. The substantial decrease in back electron transfer on addition of Fe(CN)g /Fe(CN)g is associated with the supersensitization phenomenon schematically depicted in Fig. 12(b). The back electron transfer from the radical TCNQ to the oxidized porphyrin complex is in competition with the regeneration of the dye by ferrocyanide. In the absence of back electron transfer, the overall reaction involves electron transfer from the redox species in the aqueous phase to TCNQ. In this case, the energetic balance is determined by the Galvani potential difference across the interface. 

Figure 11.25. Photocurrent dependence on the Gibbs free energy of electron transfer for the photo-oxidation of ferrocene derivatives (a) and photoreduction of quinone-type molecules (h) at the water/DCE interface. AG ( is evaluated from Equation (11.47), employing the formal redox potentials summarised in Table 11.1 and the applied Galvani potential difference. A deconvolution of the photocurrent relaxation in the presence of the electron acceptors was performed in order to estimate the flux of election injection g. The second-order rate constant for the photoninduced heterogeneous electron transfer is also calculated assuming values of 1 nm for dec and 5 x 10 s for A ,. The trends observed in both set of data were rationahsed in terms of a single solvent reorganisation energy and activation-less limit for the rate constant. Reprinted with permission from refs.[101] and [60]. Copyright (2002/2003) American Chemical Society.

Relaxations in photoprocesses, which may be due to surface recombination, minority carrier diffusion, or capacitive discharges, are typically measured as transients of photocurrents or photoprocesses. An analysis of such processes in the time domain encounters some inherent problems. 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

In the case of those noncrystalline solids that are of sufficiently high electrical condnctivity that dielectric relaxation proscribes the application of the transit time ontlined earlier, the experimental configuration displayed in Fig. 3.1(c) may be of the valne. Here, carriers of both species are excited in equal and uniform concentration across the active area of a specimen film fitted with coplanar electrodes. For step-function illumination, the rate of increase of photocurrent with time is linearly proportional to the carrier generation rate and the carrier drift velocity (and at times sufficiently short that recombination may be neglected). Thus, under the assumption that one species of carrier dominates the behavior, its mobility may be determined. 

We first survey in Section 4.2 the Kurizki-Shapiro-Brumer scheme [5-7] of phase-coherent photocurrent control and focus on its robustness to decoherence, relaxation, and quantum (Langevin) noise induced by the environment. We then... 

The time-resolved experiment clearly shows an instantaneous rise of the photocurrent as soon as the cell is exposed to light, the appearance of a peak of about 6 mA/cm2, followed by a relaxation to a steady regime within about 10 s. A constant photocurrent... 

In the presence of the spacer (Fig. 17.35a), an initially high photocurrent value ( 6 mA/cm2) is achieved, but, due to the larger spacing between the two electrodes, the diffusion of the electron mediator is not fast enough to supply new reduced mediator to the Ti02/dye interface from which, under irradiation, is constantly depleted. Thus, a steady photocurrent value, significantly lower than the initial spike, is attained after a few seconds. In Fig. 17.35b, the reduced diffusional path for the electron mediator allows for a more effective mass transport that accounts for the generation of a stable photocurrent without the observation of photoanodic relaxation processes. 

For positive lit electrodes one can register the drift of holes, and for negative ones- the drift of the electrons. The photosensitizer (for example Se) may be used for carrier photoinjection in the polymer materials if the polymer has poor photosensitivity itself. The analysis of the electrical pulse shape permits direct measurement of the effective drift mobility and photogeneration efficiency. The transit time is defined when the carriers reach the opposite electrode and the photocurrent becomes zero. The condition RC < tlr and tr > t,r should be obeyed for correct transit time measurement. Here R - the load resistance, Tr -dielectric relaxation time. Usually ttras 0, 1-100 ms, RC < 0.1 ms and rr > 1 s. Effective drift mobility may be calculated from Eq. (4). The quantum yield (photogenerated charge carriers per absorbed photon) may be obtained from the photocurrent pulse shape analysis. 

Electron-phonon interaction in a semiconductor is the main factor for relaxation of a transferred electron. There are two different relaxation processes that decrease the efficiency of light conversion in a solar system (1) relaxation of an electron from a semiconductor conduction band to a valence band and (2) a backward electron transfer reaction. The forward and backward electron transfer processes have been already included in the tunneling interaction, HSm-qd, described by Eq. (108). However, the effect of SM e-ph interaction is important for the correct description of electron transfer in the SM-QD solar cell system. In the previous section, we have gradually considered different types of interactions in the quantum dot and obtained the exact expression for the photocurrent (128) where the exact nonequilibrium QD Green s functions determined from Eq. (127) have been used. However, in... 

The standard method for measuring mobilities in materials with long dielectric relaxation times is the time-of-flight photocurrent technique, first described by Haynes and Shockley (1951) and Lawrance and Gibson (1952). This method was developed in considerable detail during the 1950s and 1960s by Brown... 

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