The interpretation of IMPS data relies on the competition between charge transfer and recombination to give a semicircle that can be analysed to obtain kct and krec. It follows that IMPS provides no information if recombination is absent. Surface recombination usually becomes negligible at potentials sufficiently far from the flatband potential, where a plateau is seen in the photocurrent-potential plot. IMPS plots measured in the plateau region do not exhibit a semicircle in the upper quadrant; only the lower RC semicircle is seen. Light-modulated microwave reflectance spectroscopy (LMMRS), on the other hand, can provide information about kct even when krec = 0 (Schlichthorl et al., 1995; Peter and Vanmaekelbergh, 1999). The reason for this is that microwave reflectivity detects the decay of photogenerated free charge carriers that are located at the surface, regardless of whether they are transferred across the interface or recombine with majority carriers. This is demonstrated by Fig. 12.32, which contrasts the calculated photocurrent and microwave responses for chopped illumination in the plateau photocurrent region.
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 ARM associated with the photogenerated minority carriers. This concentration decays by interfacial charge transfer (kct) and recombination (krec). The LMMRS response is therefore a semicircle with a characteristic frequency fifcm = (kct + krec). The low-frequency intercept of the LMMRS plot is given by (Schlichthorl et al., 1995)
Figure 12.32 Deconvolution of the currents at a semiconductor electrode for step-function illumination, showing the charging current ich, the recombination current irec and the charge-transfer current ict. Note that ict depends on the density of photogenerated carriers at the interface, which is detected by LMMR, i. e. the microwave signal follows the ict curve.
Re (Mm )= S4Jo (12.27)
kct + krec
where S is the sensitivity factor and jo is the absorbed photon flux. The high-frequency LMMRS intercept is zero. If S is known, kct and krec can be obtained using fthiin and the low-frequency intercept.
This behaviour contrasts with the IMPS response, where the high-frequency intercept is qjo and the low-frequency intercept is given by
Re (iphoto) = 7^4^ (12.28)
kct + krec
Figure 12.33 Experimental set-up for LMMRS.
It follows that LMMRS still gives a semicircle when kct ^ 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/qjo 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 used to obtain kct over a wide potential range, whereas the IMPS analysis is restricted to the photocurrent onset region where appreciable recombination occurs.
LMMRS has not been used extensively. This probably reflects the fact that few groups are actively using microwave techniques at present. The main limitations of the method are associated with the need to use low-doped samples in order to obtain sufficient sensitivity. Figure 12.34 shows LMMRS data obtained for p-Si in fluoride solution. The photoelectrochemical reaction in this case is hydrogen evolution, and analysis of the IMPS and LMMRS data for this system have confirmed that the two methods give consistent values for the electron-transfer rate constant, demonstrating the validity of the LMMRS approach. The important difference between LMMRS and IMPS is that LMMRS still provides information when there is no recombination. By contrast, IMPS provides no information in this region.
Reai[ARM(a)] / rel. units
Figure 12.34 LMMRS response of p-Si in HF, showing that the semicircular response persists at negative potentials that are in the photocurrent saturation region. Note that the high-frequency intercepts in the plots are at zero. For further details, see Schlichthorl et al. (1995).