Microwave surface conductivity

The frequency response of a DR coupled to a microwave circuit is shown in Fig. 5.34. The selectivity Q of the resonator is given by /r/A/ and, under conditions where the energy losses are confined to the dielectric and not to effects such as radiation loss or surface conduction Q (tan (5)-1 where tan 3 is the loss factor for the dielectric. 

When a dielectric resonator is coupled with microwave circuits, the dielectric material responds to the frequency. The frequency selectivity of the microwave device depends on the loss quality of the materials. The selectivity Q ) of the dielectric materials is defined as the ratio of/ to A/, and the Q approximates the reciprocals of the loss factor (tan 5). The loss in DR (l/2 ) is the sum of the loss of dielectric materials (I/Qm). surface conduction HQ, and radiation loss (1/2,) ... 

The behavior of electromagnetic waves in normal metals at ordinary temperatures and microwave frequencies is quite adequately described by the classical treatment based on MaxwelPs equations and Ohm s law. At low temperatures this is no longer true even though MaxwelPs equations are still valid, Ohm s law is inadequate to describe the relation between high frequency electric currents and fields in metals. According to classical theory, the surface resistance R is inversely proportional to the square root of the dc conductivity cr. Consequently, as the temperature is lowered and o- increases, the classical theory predicts that R cc. This is not borne out in practice, as will be seen by referring to Fig, 1. The ordinate is IR the observed surface conductance, and the abscissa is proportional to c T. Initially the behavior is classical and as the temperature is lowered. As the dc conductivity becomes larger, however, I does not increase proportionately and in the low temperature limit it becomes independent of a (and temperature). This phenomenon is known as the anomalous skin effect. The experimental data shown are due to Chambers [1]. The solid curve is the curve predicted from the theory of Reuter and Sondheimer [2],... 

As already described in Section 4.4.3, information on the potential distribution across the interface can also be obtained by microwave reflection measurements. The reflection depends on the conductivity. The most sensitive method is the measurement of the small-amplitude potential modulated microwave response AR which is proportional to the corresponding modulation of the surface conductivity A(Aff). We have then for an n-type semiconductor... 

Commercial dryers differ fundamentally by the methods of heat transfer employed (see classification of diyers, Fig. 12-45). These industrial-diyer operations may utihze heat transfer by convection, conduction, radiation, or a combination of these. In each case, however, heat must flow to the outer surface and then into the interior of the solid. The single exception is dielectric and microwave diying, in which high-frequency electricity generates heat internally and produces a high temperature within the material and on its surface. 

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. 

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... 

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.

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. 

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

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... 

An interesting special application has been proposed by Schlichthorl and Peter.31,41 It aims at deconvolution of electrochemical impedance data to separate space charge and surface capacitance contributions. The method relies on detection of the conductivity change in the semiconductor associated with the depletion of majority carriers in the space charge region via potential-modulated microwave reflectivity measurements. The electrode samples were n-Si(lll) in contact with fluoride solution. 

The schemes in Figs. 44 and 45 may serve to summarize the main results on photoinduced microwave conductivity in a semiconductor electrode (an n-type material is used as an example). Before a limiting photocurrent at positive potentials is reached, minority carriers tend to accumulate in the space charge layer [Fig. 44(a)], producing a PMC peak [Fig. 45(a)], the shape and height of which are controlled by interfacial rate constants. Near the flatband potential, where surface recombination... 

Figure 44. Energy scheme showing essential phenomena for photoinduced microwave conductivity mechanisms (a) Accumulation of minority carriers near the onset of photocurrents in the depletion region, (b) Drift of minority carriers into the interior of an accumulation region, thus escaping surface recombination.

At present, the microwave electrochemical technique is still in its infancy and only exploits a portion of the experimental research possibilities that are provided by microwave technology. Much experience still has to be gained with the improvement of experimental cells for microwave studies and in the adjustment of the parameters that determine the sensitivity and reliability of microwave measurements. Many research possibilities are still unexplored, especially in the field of transient PMC measurements at semiconductor electrodes and in the application of phase-sensitive microwave conductivity measurements, which may be successfully combined with electrochemical impedance measurements for a more detailed exploration of surface states and representative electrical circuits of semiconductor liquid junctions. 

During the first period of drying, the liquid that covers the particle external surface and is present in the macropores evaporates. The material structure does not affect the rate of evaporation. The liquid evaporates with the rate at which heat is supplied to the surface. The rate of drying is thus limited by heat transfer between the particles and their surroundings. The temperature at the particle surface remains constant. If heat is delivered by convection this temperature is the wet-bulb gas temperature. In case of radiation (e.g. microwave driers) or conduction (e.g. indirect contact driers) the surface temperature ranges between the wet-bulb gas temperature and the boiling point of the liquid. The moisture content at the end of the constant rate of drying period is called the critical moisture content. 

Flash photolysis with microwave detection of charge carriers could become an additional technique in the future. The method has not yet been applied to colloids but has been used with small suspended particles. Immediately after the laser flash a conductivity signal was observed which decayed in the 0.1 to 1 microsecond range. The signal was longer-lived for a suspension of TiOj in para-dioxane than in Decalin. Such an effect of the surrounding medium on the decay kinetics of the conductivity indicates that surface states are involved... 

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