Intensity modulated photocurrent spectroscopy

To define the above in more rigid mathematical expressions, we write for the modulated irradiation intensity 

When 6 is sufQciently small the photocurrent is a sinusoidal function of time and reads 

In this expression Jpk and tp are the amplimde and phase of the modulated photocurrent density. Both are frequency dependent. In a frequency response analyzer Jpk and (p are measured as a function of the modulation frequency. 

It is possible to use the conventional complex impedance, which is defined for impedance spectroscopy as 

It is good to realize that we have normalized the irradiation intensity and the photocurrent to particles per second per unit area. In this way the IMPS impedance and admittance are dimensionless. 

The accumulated surface charge Qs t) oscillates periodically, and the time dependent charging, transfer and recombination terms are replaced by the sums of their steady state and periodic equivalents. 

Equation (8.29) can be conveniently expressed in the dimensionless complex form 

The corresponding real and imaginary components of the IMPS response are 

The rate constants for electron transfer and recombination are readily separated because in the limit (w- 0), equation (8.31) tends to kir/(ktr + krec), and the maximum of the semicircle occurs when ca = 2ir f=kt + krec. In the absence of RC attenuation effects, the high frequency intercept of the IMPS plot t ( w — o°) is unity, so that the ac photocurrent can be used to determine gac, the Gartner flux of minority carriers. Measurements of gac as a function of potential (band bending) can be used to determine the minority carrier lifetime and absorption coefficient [46]. The main advantage of using the IMPS data rather than dc measurements of 

The time resolution of electrochemical measurements is usually limited by the RC time constant, rcen, of the electrochemical cell, which arises 

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Therefore intensity-modulated photocurrent Spectroscopy has been developed by Peter and co-workers as a tool for the analysis of photocurrent responses in the frequency domain.42,43 An optoacoustic coupler is... 

Intensity-modulated photocurrent spectroscopy has been used in combination with microwave reflectivity measurements to investigate hydrogen evolution at a p-type silicon45 and an n-type silicon.46 The measurement of amplitude and phase under harmonic generation of excess carriers, performed by Otaredian47 on silicon wafers in an attempt to separate bulk and surface recombination, should also be mentioned here. 

The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in amplifier and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148-156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-... 

FIG. 19 Block diagrams for photocurrent measurements with chopped light and lock-in detection (a) as well as for intensity-modulated photocurrent spectroscopy (b). (Adapted from Ref. 85.)... 

Figure 3.19 Intensity-modulated photocurrent spectroscopy, showing (a) the layout of a typical spectrometer, and (b) the response obtained AOM, acousto-optic modulator RE, reference electrode WE, working electrode CE, counter electrode FRA, frequency response analyzer...

Fig. 8.7. Experimental arrangement for intensity modulated photocurrent spectroscopy (IMPS). FRA frequency response analyser. LED light emitting diode.

G. Oskam, J. C. Schmidt, and P. C. Searson, Electrical properties of n-type (111) Si in aqueous K+FeCCNjs solution. II. Intensity modulated photocurrent spectroscopy, J. Electrochem. Soc. 143, 2538, 1996. 

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. 

Investigating electron migration in nanostructured anatase Ti02 films with intensity-modulated photocurrent spectroscopy [288], it was found that, upon illumination, a fraction of the electrons accumulated in the nanostructured film is stored in deep surface states, whereas another fraction resides in the conduction band and is free to move. These data indicate that the average concentration of the excess conduction band electrons equals about one electron per nanoparticle, irrespective of the type of electrode, the film thickness, or the irradiation intensity. 

Dloczik L., Ileperuma O., Lauermann I., Peter L. M., Ponomarev E. A., Redmond G., Shaw N. J. and Uhlendorf I. (1997), Dynamic response of dye-sensitized nanocrystalline solar cells characterization by intensity-modulated photocurrent spectroscopy , J. Phys. Chem. B 101, 10281-10289. 

Ponomarev E. A. and Peter L.M. (1995), A comparison of intensity-modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a... 

Vanmaekelbergh D., Marin F. 1. and van de Lagemaat J. (1996), Transport of photogenerated charge carriers through crystalline GaP networks investigated by intensity modulated photocurrent spectroscopy , Ber. Bunsenges Phys. Chem. 100, 616-626. 

The quasi-Fermi level concept makes it possible to quantitatively relate intensity-modulated photocurrent spectroscopy (IMPS) and impedance data as follows. 

Fig. 7.46 Illustration of intensity-modulated photocurrent spectroscopy (IMPS) in terms of current-potential curves (see text)...

Fig. 8.9 Comparison of experimental and calculated intensity-modulated photocurrent spectroscopy (IMPS) plots for the photodissolution of n-Si (111) in 6.5 M NH4F at low light intensities (photo quadrupling regime) The data used for the theoretical plot are k -2-10 s= 500 s ...

In their chapter on time- and frequency-resolved studies of photoelectrochemical kinetics, Peter and Vanmaekelbergh give an extensive survey of how modulation techniques such as photoelectrochemical impedance spectroscopy or intensity-modulated photocurrent spectroscopy can yield valuable information on the time dependence of reactions at semiconducting surfaces over a broad range of time scales. Kinetic studies with single crystals as well as porous or nanocrystalline material reveal the important role that is played by the bulk structure of semiconductor electrodes. 

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