Light modulated microwave measurements

Light and potential modulated microwave reflectivity measurements offer a novel approach to the study of the semiconductor electrolyte interface. Perturbation of the density of electrons and holes in a semiconductor influences the conductivity and hence the imaginary component of the dielectric constant at microwave frequencies. For small perturbations, the change ARm in microwave reflectivity depends linearly on the change in conductivity [27, 28, 75). The application of frequency response analysis to light modulated microwave reflectance is relatively new [30]. Although the technique is analogous to IMPS, it provides additional information. 

For the very small perturbations involved in the measurements, the light modulated microwave reflectivity change, ARm is a linear function of the ac component of the photogenerated charge that accumulates at the sem-iconductor/electrolyte interface 

The flux of minority carriers into the surface is linked to surface charging, electron transfer and recombination, so that 

Examination of equation (8.48) shows that the transient microwave response still contains information when there is no surface recombination. By contrast, if krcc = 0, the photocurrent simply follows the illumination step and contains no information about the rate of charge transfer at the interface. If krcc = 0, equation (8.48) becomes 

This time dependence of the microwave reflectivity predicted by equation 

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Figure 12.33 illustrates the set-up for LMMRS. The frequency response analyser replaces the single frequency lock-in amplifier used in the potential and light modulated microwave measurements described in Section 12.3. LMMRS detects the frequency-dependent modulation of the microwave reflectivity AR associated with the photogenerated minority carriers. This concentration decays by interfacial charge fransfer k d and recombination kKc)- The LMMRS response is therefore a semicircle with a characteristic frequency otam = + rec)- The low-frequency intercept of the... 

The frequency of the minimum in the semicircle is equal to the sum of the rate constants for charge transfer and recombination cum/n = k,r + krec- Light modulated microwave measurements therefore provide the sum of the two rate constants, but since it is possible to measure /c,r at high band bending where recombination is negligible, the rate constants can be separated if it is assumed that k,r is independent of potential (this assumption may not be valid for multi-electron transfer reactions as noted in section 4.2). 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

Light intensity and potential-modulated microwave measurements <5//. SDU—t Microwave impedance spectroscopy ... 

Schlichthorl et al. [177] have used light modulated microwave reflectivity to derive the rates of interfacial electron transfer processes at the n-Si/electrolyte interface. In these measurements, the modulation frequency was constant, and the rate constants for charge transfer were derived from the potential dependent ARm response. Schlichthorl et al. [73] have extended the technique considerably by introducing frequency response analysis. The technique is therefore analogous to IMPS, although, as shown below, it provides additional information. 

Fig. 21. Experimental set-up for light modulated microwave reflectance based on X-band microwave system [177]. The apparatus can also be used for IMPS measurements.

EPR spectra were recorded with a Varian E9 X-band spectrometer using field (100 kHz) and light (13 or 83 Hz) modulation with phase-sensitive detection at the modulation frequencies (19). Typically, the field modulation amplitude employed ranged from 20 to 40 gauss, the microwave power from 0.1 to 0.5 mW. Measurements were performed on frozen solutions of the porphyrins at about 100 K using the standard Varian variable temperature accessory or at about 10 R with an Oxford Instruments helium gas cryostat. Light sources used for photoexcitation were a 1000 W Xe arc source powered by a Photochemical Research Associates Supply with electronic modulation... 

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