Frequency-resolved light modulation methods

The IMPS plots can be fitted using the following analytical solution of the continuity equation, which describes the generation, transport and back reaction of electrons 

The basic measurement technique for intensity-modulated photovoltage spectroscopy (IMVS) is the same as for IMPS. In principle, IMVS measurements can be made for any constant current condition, but in practice it is usual to make measurements under conditions where the net current is zero. In the case of a photoelectrochemical solar cell, this corresponds to the open-circuit condition, and a high impedance voltage amplifier is used to ensure that a negligible current is drawn from the illuminated device. The output of the voltage amplifier is fed to the FRA, and the remainder of the set up is the same as for IMPS (cf. Fig. 12.26). 

In a conventional solid-state photovoltaic cell or a semiconductor/electrolyte junction, the photovoltage is related to the densities of free electrons and holes. These in turn define the quasi-Fermi levels p and pE. The photovoltage is given by 

This behaviour contrasts with the IMPS response, where the high-frequency intercept is qjo and the low-frequency intercept is given by 

It follows that LMMRS still gives a semicircle when fcct 0 at high band bending. By contrast in the case of IMPS, the diameter of the semicircle contracts to zero at high band bending (in terms of the normalised IMPS response, iphoto/ o is unity). The contraction in the diameter of the IMPS semicircle can be seen in the data for p-InP shown in Fig. 12.30. This means that LMMRS be nsed to obtain kct over a wide potential range, whereas the IMPS analysis is restricted to the photocurrent onset region where appreciable recombination occnrs. 

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Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

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