Conductivity microwave

The method uses the proportionality between the relative change of reflected microwave power and the conductivity induced by a light pulse in a solid embedded in a waveguide system (93). Time resolution of nanoseconds was reported. 

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Shock-modified rutile is found to exhibit two characteristic resonances, which can be confidently identified as (1) an isotropic resonance characteristic of an electron trapped at a vacancy, and (2) an isotropic resonance characteristic of a Ti" interstitial. The data indicate a concentration of 2 X 10 cm , which is an order of magnitude greater than observed in hydrogen- or vacuum-induced defect studies. At higher pressures the concentration of interstitials is the same as at lower pressure, but more dispersion is observed in the wave shape, indicating higher microwave conductivity. 

This situation appears to be different when microwave conductivity measurements are used in parallel with electrochemical measurements. As Fig. 1 shows, there is a marked parallelism between electrochemical processes and microwave conductivity mechanisms. In both cases electrical fields interact with electronic or ionic charge carriers as well as dipoles. In electrochemical processes, it is a static or low-frequency electrical field that is moving electrical charge carriers or orienting dipoles. In a micro-wave measurement, the electric field of the microwave interacts with... 

Microwave measurements are typically performed at frequencies between 8 and 40 Gc/s. The sensitivity with which photogenerated charge carriers can be detected in materials by microwave conductivity measurements depends on the conductivity of the materials, but it can be very high. It has been estimated that 109-1010 electronic charge carriers per cubic centimeter can be detected. Infrared radiation can, of course, also be used to detect and measure free electronic charge carriers. The sensitivity for such measurements, however, is several orders of magnitude less and has been estimated to be around 1015 electronic charge carriers per cubic centimeter.1 Microwave techniques, therefore, promise much more sensitive access to electrochemical mechanisms. 

This relation for photoelectrochemistry is now compared with the correlations for microwave conductivity measurements. 

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

After starting his own laboratory in 1982, the author built microwave measurement facilities with his collaborators and resumed research on microwave electrochemical phenomena. While the potential of combining photoelectrochemistry with microwave conductivity techniques became evident very soon,6,7 it was some time before microwave experiments could be performed at semiconductor electrodes under better-defined microwave technical conditions.8... 

An important step toward the understanding and theoretical description of microwave conductivity was made between 1989 and 1993, during the doctoral work of G. Schlichthorl, who used silicon wafers in contact with solutions containing different concentrations of ammonium fluoride.9 The analytical formula obtained for potential-dependent, photoin-duced microwave conductivity (PMC) could explain the experimental results. The still puzzling and controversial observation of dammed-up charge carriers in semiconductor surfaces motivated the collaboration with a researcher (L. Elstner) on silicon devices. A sophisticated computation program was used to calculate microwave conductivity from basic transport equations for a Schottky barrier. The experimental curves could be matched and it was confirmed for silicon interfaces that the analytically derived formulas for potential-dependent microwave conductivity were identical with the numerically derived nonsimplified functions within 10%.10... 

This shows that the penetration depth decreases dramatically with increasing conductivity of the medium to be penetrated. This has been plotted (Fig. 2) for different specific resistivities of the medium and the frequency of 10-40 Gc/s11 at which microwave conductivity measurements are typically performed. It can be seen that with a specific resistivity of 10 Q cm, a penetration depth of only 2 mm can be expected. Figure 2 furthermore shows the doping densities at which the respective penetration depths can be expected for silicon. Whereas the lower frequency X-band of microwaves (8-12.5 Gc/s) offers some advantages for materials with very low resistance, the high-frequency microwave Ka-band (26.5 10... 

The materials to be investigated have to be incorporated into electrochemical cells in such a way as to permit the influx and the reflection of microwaves. The electrodes have to be adjusted to the microwave techniques that will be used for the investigation. Basically three different measurement approaches can be distinguished (Fig. 3). The simplest technique for microwave conductivity studies [Fig. 3(a)] is to place the sample directly at the exit of an ordinary waveguide. This setup has the advantage of being very simple and relatively transparent with respect to the phenomena occurring. Microwave power is reflected from the sample... 

Figure 3. Different geometries for microwave conductivity measurements, (a) Sample (black square) at end of microwave guide, (b) sample in microwave resonator, and (c) sample above dielectric microwave spiral. The electrical field E of the microwave is shown schematically.

Figure 4a. Electrochemical cells for microwave conductivity measurements. Cell above microwave conduit (1) electrochemical cell (plastic tube, placed on working electrode material), (2) counter-electrode, (3) reference electrode, (4) electrolyte, (5) space charge layer, (6) diffusion layer, (7) contact to working electrode, (8) waveguide.

A classical setup for microwave conductivity measurements is based on the utilization of the waveguides. A simple installation consists of a microwave generator (typically a gun diode) which, when the Ka-band is used, can be operated in the frequency region of 28-40 Gc/s this is protected by an isolator against back-reflections from the rest of the microwave circuit. The microwave power is conducted by an attenuator across a circulator into the microwave conductor branch at the end of which the electrochemical cell is mounted. The microwave power reflected from the electrochemical sample is conducted via the circulator into the microwave detector. It typically consists of a diode that acts as an antenna, receiving the electrical alternating field, rectifying it, and con-... 

Stationary microwave electrochemical measurements can be performed like stationary photoelectrochemical measurements simultaneously with the dynamic plot of photocurrents as a function of the voltage. The reflected photoinduced microwave power is recorded. A simultaneous plot of both photocurrents and microwave conductivity makes sense because the technique allows, as we will see, the determination of interfacial rate constants, flatband potential measurements, and the determination of a variety of interfacial and solid-state parameters. The accuracy increases when the photocurrent and the microwave conductivity are simultaneously determined for the same system. As in ordinary photoelectrochemistry, many parameters (light intensity, concentration of redox systems, temperature, the rotation speed of an electrode, or the pretreatment of an electrode) may be changed to obtain additional information. 

Time-resolved microwave conductivity measurements with electrodes in electrochemical cells can conveniently be made with pulsed lasers (e.g., an Nd-YAG laser) using either normal or frequency-doubled radiation. Instead of a lock-in amplifier, a transient recorder is used to detect the pulse-induced microwave reflection. While transient microwave experiments with semiconducting crystals or powders have been performed... 

Figure 7 shows an example of a space-resolved microwave conductivity measurement of the semiconducting surface of a natural pyrite (FeS2) sample (from Murgul, Turkey). The overflow of the PMC signal (white color) was adjusted to a level that shows the patterns of distribution of low photoeffects (dark areas). Figure 8 shows a similar image in which,... 

Figure 7. Example of space-resolved photoinduced microwave conductivity mapping of semiconductor interface distribution of photoconductivity in natural pyrite (from Murgul, Turkey, surface etched in acid solution). The overflow was adjusted to show patterns of low photoactivity. For color version please see color plates opposite p. 452.

Figure 8. Example of microwave conductivity transient map PMC relaxation time map taken from a 20- m thin silicon wafer onto which 11 droplets of zeolith suspension were deposited and dried. Reduced lifetimes are clearly observed in the region of droplets. For color version please see color plates opposite this page.

Figure 11. Dynamic microwave conductivity-potential curves taken with a ZnO single crystal and shown for two potential sweep velocities (a) and (b) and a corresponding dynamic (photo)current-potential curve (bottom). The dark effects and photoeffects are indicated for the two cases. Curves 1 and 2 correspond to (a) and (b) respectively.

At the beginning of this chapter we presented evidence that a combination of (photo)electrochemistry with photoinduced microwave conductivity measurements promises more direct access to kinetic parameters involv-... 

The photoinduced microwave conductivity signal, on the other hand, can be described by the following integral over the excess minority carriers, to be taken over both the diffusion and the space charge region ... 

These three equations (11), (12), and (13) contain three unknown variables, ApJt kn and sr The rest are known quantities, provided the potential-dependent photocurrent (/ph) and the potential-dependent photoinduced microwave conductivity are measured simultaneously. The problem, which these equations describe, is therefore fully determined. This means that the interfacial rate constants kr and sr are accessible to combined photocurrent-photoinduced microwave conductivity measurements. The precondition, however is that an analytical function for the potential-dependent microwave conductivity (12) can be found. This is a challenge since the mathematical solution of the differential equations dominating charge carrier behavior in semiconductor interfaces is quite complex, but it could be obtained,9 17 as will be outlined below. In this way an important expectation with respect to microwave (photo)electro-chemistry, obtaining more insight into photoelectrochemical processes... 

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-... 

Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E2 (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe a phase shift with respect to the flux, the transmitted or reflected microwave power APIP. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. 

In the following section the mathematical derivation of the stationary, potential-dependent, photoinduced microwave conductivity signal, which integrates over all photogenerated charge carriers in the semiconductor interface, is explained. This is a necessary requirement for the interpretation of the PMC-potential curves. 

Analytical Expression for Potential-Dependent Microwave Conductivity... 

The surface concentration of minority carriers (20) is obviously contained in the expression for the photoinduced microwave conductivity (18) so that we can write... 

Another interesting test which may give an idea of the use of the simplifications introduced in deriving the analytical formula for photoin-duced microwave conductivity can be obtained from a comparison between the simple Gartner model for the potential-dependent photocurrent18 and the theoretical photocurrent derived from the just-described approach. 

IV. POTENTIAL-DEPENDENT STATIONARY MICROWAVE CONDUCTIVITY MEASUREMENTS... 

The increased lifetime of photogenerated minority carriers can be measured experimentally. This is shown for a single-crystal ZnO-electrode (Fig. 22). Both the stationary PMC peak and the potential-dependent lifetime in the depletion region, measured with transient microwave conductivity techniques are plotted.25 It is seen that the stationary PMC peak coincides with a peak in the lifetime of minority carriers. This... 

The numerical calculation of the potential-dependent microwave conductivity clearly describes this decay of the microwave signal toward higher potentials (Fig. 13). The simplified analytical calculation describes the phenomenon within 10% accuracy, at least for the case of silicon Schottky barriers, which serve as a good approximation for semiconduc-tor/electrolyte interfaces. The fact that the analytical expression derived for the potential-dependent microwave conductivity describes this phenomenon means that analysis of the mathematical formalism should... 

Another technique for flatband determination is based on the measurement of potential-modulated microwave conductivity signals and is described further in the next section. 

As outlined at the beginning of this chapter, combined photocurrent and microwave conductivity measurements supply the information needed to determine three relevant potential-dependent quantities the surface concentration of excess minority carriers (Aps), the interfacial recombination rate (sr), and the interfacial charge-transfer rate ( r). By inserting the... 

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