[modern aspects of electrochemistry] modern aspects of electrochemistry volume 33 || microwave...

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Microwave (Photo)electrochemistry

H. TributschDepartment of Solare Energetik, Hahn-Meitner Institute, Berlin, Germany

I. INTRODUCTION

1. Electrochemistry Combined with Microwave Measurements

Electrochemical techniques have been developed into very powerful toolsfor research and technology. However, decades ago, researchers started tounderstand that even more insight could be obtained if electrochemicaltechniques were combined with additional spectroscopic tools. Amongthese it is sufficient to mention infrared spectroscopy, Raman spectros-copy, luminescence techniques, electroreflection or ellipsometry.

Frequently, electrochemical information can be interpreted better inthe presence of additional nonelectrochemical information. Typically,however, there is one significant restriction: electrochemical and spectro-scopic techniques often do not detect exactly the same mechanisms. Withspectroscopic measurements (e.g., infrared spectroscopy), products thatare formed by electrochemical processes may be detected. In other cases(luminescence techniques) mechanisms may be found by which chargecarriers are trapped and recombine. Other techniques (electroreflectionstudies) allow the nature of electronic transitions to be determined andprovide information on the presence or absence of an electric field in thesurface of an electrode. With no traditional technique, however, is it

Modern Aspects of Electrochemistry, Number 33, edited by Ralph E. White et al.Kluwer Academic / Plenum Publishers, New York, 1999.

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possible to obtain the information on the behavior of photogeneratedelectronic charge carriers and electrochemically generated ions or dipolesthat would allow electrochemistry to be developed to a stage that could,for example, provide convenient access to absolute rate constants forinterfacial reactions. Such rate constants are typically poorly accessiblebecause of capacitive restraints and because the photoelectrochemicalsystem is underdcfined (there are more variables than equations). Electro-chemical kinetics only gives information on charge carriers leaving theelectrode; information on the charge carriers lost in recombination proc-esses is not accessible.

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

Figure 1. Drawing showing how static electrical fields andmicrowave fields interact with the same electronic or ioniccharge carriers and electrical dipoles.

Microwave (Photo)electrochemistry 437

electronic charge carriers, thereby losing energy or carrying out a reorien-tation interaction with a dipole. This means that both electrochemical andmicrowave conductivity processes display interactions with the samespecies in semiconductor/electrolyte interfaces. (The strength of interac-tion may, however, be different. In the case of interaction with dipoles, itwill be frequency dependent.) By combining electrochemical and micro-wave conductivity techniques, it is hoped that more complete informationon electrochemical processes can be gained.

Microwave measurements are typically performed at frequenciesbetween 8 and 40 Gc/s. The sensitivity with which photogenerated chargecarriers can be detected in materials by microwave conductivity measure-ments depends on the conductivity of the materials, but it can be very high.It has been estimated that electronic charge carriers per cubiccentimeter can be detected. Infrared radiation can, of course, also be usedto detect and measure free electronic charge carriers. The sensitivity forsuch measurements, however, is several orders of magnitude less and hasbeen estimated to be around electronic charge carriers per cubiccentimeter.1 Microwave techniques, therefore, promise much more sensi-tive access to electrochemical mechanisms.

The analogy between standard photoelectrochemical and microwaveconductivity measurements can be formulated in more precise terms:Microwave (photo)electrochemistry is a contact-free experimental tech-nique that is based on the measurement of the relative change of micro-wave power reflected from semiconductor liquid interfaces as aconsequence of changes in electrode potential, electrolyte composition,illumination, or time. It is a technique which, like (photo)electrochemistry,probes the behavior of charge carriers and dipoles in solid/liquid inter-faces, but via an independent circuit that does not involve the RC timeconstants of the electrochemical circuit (R = resistance, C = capacitance)and certain polarization effects that accompany direct-current measure-ments. A time resolution of at least 25 ps (which is required for the passageof a microwave in the detector during measurement) and a sensitivity thatpermits detection of to charge carriers are characteristic advan-tages as well as the possibility of monitoring photoactivated chargecarriers that do not reach the external circuit.

In (photo)electrochemistry, the expected photocurrent change, istypically dependent in a nonlinear way on the changes in the potentialapplied. The reciprocal complex impedance, is the variable. The realpart is proportional to the conductivity change across the elec-

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trode/electrolyte interface. The imaginary part is dependent on thedielectric constant and determines the phase shift. It can be used tomeasure the interfacial capacitance:

where V is the potential, is the photon energy, and t is the time.This relation for photoelectrochemistry is now compared with the

correlations for microwave conductivity measurements.

2. Electric Transport in Materials at Microwave Frequencies

Photoinduced microwave conductivity measurements in solid and liquidmaterials have a long history.2,3 Because of the much lower (ion) mobilityinvolved, it is much more difficult to measure photoinduced processes inliquids. However, reliable measurements have been made using thin liquidlayers and significant insight into molecular processes has been obtained.3

This suggests that microwave electrochemistry, which looks at processesgenerated by photoreactions in solid/liquid interfaces, has a good chanceof becoming a valuable technique for studying (photo)electrochemicallyinduced electrolyte processes (which, owing to a lack of experimentaldata, are not discussed here).

At microwave frequencies electric transport in materials (includ-ing interfaces) is determined by the dielectric function

The dielectric displacement is

where E(x) is the electric field with4

with

and


where is the dielectric constant, is induction (free charge carrierscannot follow), is the dielectric loss (absorption of energy), and isthe energy loss through free charge carriers.

The relative reflected microwave power is (S is a proportionalityfactor):

The relative microwave power reflected from an electrode/electro-lyte interface can thus be considered to be proportional to the change inthe imaginary propagation constant for microwaves caused by achange in potential, illumination, electrolyte, or time. It is proportional tothe induced change of conductivity in both charge carriers anddipoles is the concentration of charge carriers of type i; is theirmobility):

The real part describes the change in the phase factor which dependson the change in the dielectric constant responsible for the phase shift.The change in the reflected microwave power as a consequence of animposed potential change can therefore be written [by rewriting relation(6) with A´ as the proportionality constant]:

Although the conductivity change [relation (8)] of microwave conduc-tivity measurements and the of electrochemical measurements [rela-tion (1)] are typically not identical (owing to the theoretically accessiblefrequency dependence of the quantities involved), the analogy betweenrelations (1) and (8) shows that similar parameters are addressed by(photo)electrochemical and photoinduced microwave conductivity meas-urements. This includes the dynamics of charge carriers and dipoles,photoeffects, flat band and capacitive behavior, and the effect of surfacestates.

When two different experimental techniques are measuring the samevariables (electronic charge carriers, dipoles) it is hoped that the combined

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information provide a fuller description of the system. That this is actuallythe case will be shown in the course of this chapter by matching themathematical formalism for potential-dependent photocurrents of semi-conductor electrodes with that for potential-dependent microwave con-ductivity.

3. Historical Notes

The first microwave electrochemical measurements were performed in1971 at the University of California in Berkeley in the Laboratory ofChemical Biodynamics. The author was working as a postdoctoral fellowon dye sensitization of solar cells based on zinc oxide electrodes. Thedoctoral student R. A. Bogomolni was working nearby on the detectionof photogenerated charges in photosynthesis using microwave conductiv-ity techniques. They decided to put an electrochemical cell into a micro-wave resonator to find out whether the photogenerated charge carrierscould be detected in semiconductor electrodes during potential-dependentelectrochemical activity. The experiments succeeded and the results weresubmitted to the Journal of Physical Chemistry. The paper was acceptedbut in the mean-time the participants had drifted apart and the correctionsfor the revised manuscript were made only 10 years later.5

After starting his own laboratory in 1982, the author built microwavemeasurement facilities with his collaborators and resumed research onmicrowave electrochemical phenomena. While the potential of combiningphotoelectrochemistry with microwave conductivity techniques becameevident very soon,6,7 it was some time before microwave experimentscould be performed at semiconductor electrodes under better-definedmicrowave technical conditions.8

Many experimental results on microwave measurements were col-lected with layer-type materials (e.g., tungsten diselenide), but the micro-wave conductivity-potential curves, which were very different fromphotocurrent potential dependencies, could not be understood. A peak ofmicrowave absorption near the onset of the photocurrent in the depletionregion was especially puzzling. Classical photoelectrochemical theory didnot account for an accumulation and damming-up of minority carriersprior to interfacial charge transfer. In fact, no existing theory predicted thisphenomenon. The reason for the difficulty in calculating this effect wasthe complication encountered in solving the transport equations for chargecarriers in semiconductor interfaces in such a way as to be able to calculate


the potential-dependent integral microwave absorption in a semiconductorelectrode.

An important step toward the understanding and theoretical descrip-tion of microwave conductivity was made between 1989 and 1993, duringthe doctoral work of G. Schlichthörl, who used silicon wafers in contactwith solutions containing different concentrations of ammonium fluo-ride.9 The analytical formula obtained for potential-dependent, photoin-duced microwave conductivity (PMC) could explain the experimentalresults. The still puzzling and controversial observation of dammed-upcharge carriers in semiconductor surfaces motivated the collaboration witha researcher (L. Elstner) on silicon devices. A sophisticated computationprogram was used to calculate microwave conductivity from basic trans-port equations for a Schottky barrier. The experimental curves could bematched and it was confirmed for silicon interfaces that the analyticallyderived formulas for potential-dependent microwave conductivity wereidentical with the numerically derived nonsimplified functions within10%.10

After this step, the understanding of microwave electrochemicalmechanisms deepened rapidly. G. Schlichthörl went to the laboratory ofL. Peter to combine potential-modulated microwave measurements withimpedance measurements, while our efforts focused on laser pulse-inducedmicrowave transients under electrochemical conditions. It is hoped thatthe still relatively modest knowledge provided will stimulate other groupsto participate in the development of microwave photoelectrochemistry.

II. EXPERIMENTAL

1. Required Properties of Electrode Materials

A significant precondition for the measurement of excess photogeneratedcharge carriers in electrode materials is that the electrical components ofthe microwave field reach the site where conductivity variations aregenerated. A second condition is that the change in conductivity generatedbe large enough that the signal can be detected in the reflected microwavepower. The penetration depth, of high-frequency electromagnetic radia-tion in media with an electrical conductivity is well known:

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This shows that the penetration depth decreases dramatically with increas-ing conductivity of the medium to be penetrated. This has been plotted(Fig. 2) for different specific resistivities of the medium and the frequencyof 10–40 Gc/s11 at which microwave conductivity measurements aretypically performed. It can be seen that with a specific resistivity ofcm, a penetration depth of only 2 mm can be expected. Figure 2 further-more shows the doping densities at which the respective penetrationdepths can be expected for silicon. Whereas the lower frequency X-bandof microwaves (8–12.5 Gc/s) offers some advantages for materials withvery low resistance, the high-frequency microwave Ka-band (26.5–40

Figure 2. Penetration depth of microwave energy as a function of specific resis-tivity or conductivity of the semiconductor material for microwave radiation of 10and 40 Gc/s.11


Gc/s) offers the advantage that permanent dipoles will less easily followthe electrical field of the microwaves.

Before constructing an electrode for microwave electrochemical stud-ies, the question of microwave penetration in relation to the geometry ofthe sample has to be evaluated carefully. Typically only moderately dopedsemiconductors can be well investigated by microwave electrochemicaltechniques. On the other hand, if the microwaves are interacting with thinlayers of materials or liquids also highly doped or even metallic films canbe used, provided an appropriate geometry is selected to allow interactionof the microwaves with a thin oxide-, Helmholtz-, or space-charge layerof the materials.

2. Electrodes

The materials to be investigated have to be incorporated into electrochemi-cal cells in such a way as to permit the influx and the reflection ofmicrowaves. The electrodes have to be adjusted to the microwave tech-niques that will be used for the investigation. Basically three differentmeasurement approaches can be distinguished (Fig. 3). The simplesttechnique for microwave conductivity studies [Fig. 3(a)] is to place thesample directly at the exit of an ordinary waveguide. This setup has theadvantage of being very simple and relatively transparent with respect tothe 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) sampleabove dielectric microwave spiral. The electrical field E of the microwave is shownschematically.

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in a nearly ideal way. Thus it has to be considered that some microwavepower may also penetrate the sample to be reflected somewhere in theenvironment and it is advisable to shield the surrounding. This simpletechnique has been preferred in our laboratory. It has the advantage thaterrors can be avoided relatively easily, in contrast to the second geometry[Fig. 3(b)], which uses a microwave cavity. Microwave cavities, of course,allow a much more sensitive measurement. Typically the sensitivity isincreased by one order of magnitude compared with the geometry of Fig.3(a). However, the sample (and the entire electrochemical cell) has to beaccommodated within the resonator, which may cause a significant per-turbation of the electrical field distribution. Also, the electrical wires ofthe electrochemical cell may function as antenna in extracting microwaveenergy from the resonator. Therefore an optimized geometry has to besearched for, typically by trial and error.

Figure 3(c) shows an alternative geometry in which microwaveenergy is fed through an integrated circuit forming a spiral-shaped dielec-tric conduit above which a strong exponentially decaying electrical mi-crowave field will build up. This integrated microwave device has not yetbeen explored for microwave electrochemistry, but owing to its simplicity,it may turn out to be the most convenient way to provide microwave energyfor electrochemical studies.

Figure 4 shows a simplified schematic of an electrochemical cell formicrowave conductivity studies that is used directly above the exit of amicrowave conduit [Fig. 4(a)]. Since water dipoles strongly absorb micro-wave energy, the energy is conducted through a semiconducting slab thatforms the base and working electrode of an electrochemical cell. Theelectrolyte is placed so that it reflects microwave energy back into themicrowave guide, but also absorbs and transmits part of it. The referenceand counter-electrodes dip into this electrolyte. The connection of the backcontact to the working electrode is important. It cannot cover the entiresemiconductor surface since this would suppress penetration of micro-wave energy to the semiconductor/electrolyte interface. The electric con-tact must either be a ring contact that leaves the inside of thesemiconductor back contact open or it must be a small single or multiplecontact with thin wires that leaves enough space for the penetration ofmicrowaves.

Entirely different factors have to be considered when the electro-chemical cell is placed in a microwave cavity [Fig. 4(b)]. Only a very smallvolume of water can be introduced into the cavity without drastically


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

reducing its quality. The electrodes of the electrochemical cell have to bekept out of the resonator as much as possible. In the example shown, partof the electrochemical cell is accommodated within a cylindrical accesshole to the cavity. The electrical contact wire to the working electrode isbent in such a way as to follow a path of minimum microwave energy tothe outside in order to keep it from working as an antenna, extractingmicrowave energy from the cavity. The position of the electrochemicalcell has to be optimized to provide a cavity quality factor that is reasonablyfavorable for the measurement. Even though microwave electrochemicalmeasurements in cavities are more subject to possible errors, the resultsobtained with this geometry are qualitatively similar to those obtainedwith the simple geometry of Fig. 4(a) using zinc oxide electrodes.5,12

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Figure 4b. Cell in microwave cavity: (1) resonator,(2) waveguide, (3) cylindrical exit, (4) electro-chemical cell, (5) working electrode, (6) electrolyte,(7) counter-electrode, (8) contact wire to workingelectrode, (9) opical light guide.

3. Microwave Circuits

A classical setup for microwave conductivity measurements is based onthe utilization of the waveguides. A simple installation consists of amicrowave generator (typically a gun diode) which, when the Ka-band isused, can be operated in the frequency region of 28–40 Gc/s; this isprotected by an isolator against back-reflections from the rest of themicrowave circuit. The microwave power is conducted by an attenuatoracross a circulator into the microwave conductor branch at the end ofwhich the electrochemical cell is mounted. The microwave power re-flected from the electrochemical sample is conducted via the circulatorinto the microwave detector. It typically consists of a diode that acts as anantenna, receiving the electrical alternating field, rectifying it, and con-


verting it into a voltage signal. It increases proportionally with the ab-sorbed microwave power. Since the reflected microwave power is photo-modulated, a lock-in amplifier is needed for its measurement. Thephotomodulated current is measured simultaneously with a second lock-inamplifier and both the photocurrent and the reflected microwave powerare measured as a function of the potential applied to the working electrodein the electrochemical cell (Fig. 5). For the excitation of semiconductorelectrodes, conventional light sources, UV-lasers (for large gap oxides),or laser diodes can be used which can conveniently be modulated between10 and cps.

4. Stationary Measurements

Stationary microwave electrochemical measurements can be performedlike stationary photoelectrochemical measurements simultaneously withthe dynamic plot of photocurrents as a function of the voltage. Thereflected photoinduced microwave power is recorded. A simultaneous plotof both photocurrents and microwave conductivity makes sense becausethe technique allows, as we will see, the determination of interfacial rateconstants, flatband potential measurements, and the determination of avariety of interfacial and solid-state parameters. The accuracy increaseswhen the photocurrent and the microwave conductivity are simultane-ously determined for the same system. As in ordinary photoelectrochem-istry, many parameters (light intensity, concentration of redox systems,temperature, the rotation speed of an electrode, or the pretreatment of anelectrode) may be changed to obtain additional information.

Stationary potential-dependent measurements are not the only meas-urements that can be performed with microwaves. Figure 6 shows ascheme indicating the different techniques that can be used for microwavecharacterization of semiconductor electrodes.

5. Time-Resolved Measurements

Time-resolved microwave conductivity measurements with electrodes inelectrochemical 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 thepulse-induced microwave reflection. While transient microwave experi-ments with semiconducting crystals or powders have been performed

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frequently, the history of laser pulse-induced microwave transients inelectrodes of photoelectrochemical cells is relatively short. Since timeresolutions of up to 25 ps can be expected with this technique, which doesnot directly depend on the RC constant of an electrochemical circuit, thefuture potential for analysis of fast reactions at electrode/electrolyteinterfaces may be significant.

The use of a resonance cavity results, as mentioned, in a sensitivitythat is approximately one order of magnitude greater than that for a normalreflection cell. The consequence is, however, a sacrifice in time resolution,which is typically also of one order of magnitude.

6. Space-Resolved Measurements

By simply moving the sample on an XY table and allowing a laser spot toscan the entire surface, a basis for space-resolved measurements is pro-vided. This technique, developed in our laboratory13–15 is commerciallyavailable, but it has been used very little for the potential-dependentinvestigation of electrodes. The technique of producing photoinducedmicrowave conductivity images may now appear simple, but the spatialresolution of obtained with a microwave of a wavelength ofapproximately 1 cm was originally not evident. The high resolution ispossible only because the measurement occurs in the near field of micro-wave generation and not after the microwaves have reached the far field(radar applications). Space-resolved microwave conductivity images ofspace-resolved microwave transients provide significant insight into ma-terial properties and when potential-dependent measurements are in-cluded, permit the characterization of still more properties and adistinction between the quality of materials in different locations of theinvestigated sample. The really usable spatial resolution is typically lim-ited by the diffusion length of the materials (e.g., in technical siliconwafers), which means that photogenerated minority carriers diffuse thatdistance or are trapped within that distance, making higher resolutionimpossible. However, most semiconductor materials have a much smallerdiffusion length so that very high resolution can be obtained.

Figure 7 shows an example of a space-resolved microwave conduc-tivity measurement of the semiconducting surface of a natural pyrite

sample (from Murgul, Turkey). The overflow of the PMC signal(white color) was adjusted to a level that shows the patterns of distributionof low photoeffects (dark areas). Figure 8 shows a similar image in which,


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

however, the lifetimes of microwave conductivity transients are shown. Itgives insight into the patterns of surface recombination. The sample wasa -thick silicon wafer onto which 11 droplets of a zeolith suspensionwere deposited and dried. Although the dry zeolith layers are not sensitiveto visible light, they reduce the lifetime of electronic charge carriers insilicon by influencing surface recombination.

7. Microwave Phase Detection Experiments

As with alternating electrical currents, phase-sensitive measurements arealso possible with microwave radiation. The easiest method consists ofmeasuring phase-shifted microwave signals via a lock-in technique bymodulating the electrode potential. Such a technique, which measures thephase shift between the potential and the microwave signal, will givespecific (e.g., kinetic) information on the system (see later discussion).However, it should not be taken as the equivalent of impedance measure-ments with microwaves. As in electrochemical impedance measurements,

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Figure 8. Example of microwave conductivity transient map: PMC relaxation time maptaken from a thin silicon wafer onto which 11 droplets of zeolith suspension weredeposited and dried. Reduced lifetimes are clearly observed in the region of droplets. Forcolor version please see color plates opposite this page.

where the thermodynamic force (the electrical potential) is modulated tomeasure the phase shift with respect to the flux (the current), the micro-wave impedance measurement requires a modulation of the microwavepower (the thermodynamic force P) for a phase shift with respect to thereflected microwave power (the relative “flux” Since such tech-niques will become relevant in a more advanced stage of development ofmicrowave electrochemistry, Fig. 9(b) shows a circuit that can be used forphase-sensitive measurements of microwave conductivity. The microwavemeasurement system is basically split into two branches between whichthe phase and amplitude are tuned. A phase shift, for example, producedby the presence of a material, by illumination, or by electric polarization,can then be detected at the phase-sensitive microwave detector. A specialcase of a phase shift phenomenon is Faraday rotation. Electromagneticradiation passing through a magnetized transparent medium changes theplane of polarization. When microwaves are used, we speak of microwaveFaraday rotation. This phenomenon is equivalent to a Hall effect measuredwithout electrical contacts. Such measurements can be very useful forstudying material properties in powders and badly conducting samples.


Figure 9. (a) Electrode and representative circuit for phase-sensitiveelectrochemical measurements (impedance measurements) comparedwith (b) setup for phase-sensitive microwave (impedance) measure-ments.

Microwave Hall experiments have been performed in our labora-tory.16 They have shown that the mobility of charge carriers in semicon-ductors can be measured quite reliably even if the semiconductors are onlyavailable in the form of a powder. The measurement technique itself isrelatively complicated and involves, for example, rectangular waveguides,which can be rotated against each other on opposite sides of the sampleto monitor the phase rotation. In the “two-mode resonator,” two modes of

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the microwaves, and rotated against each other by interact insuch a way that at the entrance they couple to a field of while atthe exit the field is Coupling elements are used around thisresonator to adjust this situation, while a switched-on magnetic field willchange the phase and unbalance the constellation to allow a phase rotationmeasurement. The theory of such a measurement still needs furtherimprovement. Figure 10 shows the drawing of a “two-mode resonator”with its calibration elements for microwave Hall effect measurement,

Figure 10. (a) Two-mode cavity and (b) microwave circuit for Faraday rotation (microwaveHall effect) experiments.


together with the corresponding microwave circuit.16 This technique hasbeen applied to the measurement of charge carriers in photosyntheticmembranes. Its application to electrodes under variable potential has stillto be demonstrated. It will, for example, be interesting to find out how themobility of electronic charge carriers in sensitized nanocrystalline oxides(e.g., ZnO) depends on illumination intensity (number of mobileelectrons in nanocrystals) and applied (photo)potential, or how minoritycarriers react in the accumulation region of a semiconductor.

8. Potential Sweep or Potential Modulation Techniques

Instead of changing the light intensity to detect photoinduced microwaveconductivity changes, it is equally possible to change or modulate theelectrode potential to detect potential-dependent or potential-modulated(derived microwave conductivity) (MC) changes. If this leads to a changein the MC, it may provide information on electrode processes. However,the information obtained may be complicated to evaluate and may needsystematic research in individual cases. As an example we may mentionZnO in contact with an aqueous electrolyte (1 M KC1 at pH 2). TheMC-potential curves at different sweep velocities (Fig. 11) show pro-nounced features, which are not seen in an ordinary current voltagediagram. The interpretation of this electrochemical MC diagram for ZnOmust consider the cathodic reduction and formation of metallic zinc,which, as a thin surface layer may shield part of the electric microwavefield, thus decreasing the MC effect [by changing the sensitivity factor Sdefined in relation (6)]. Charge carriers may also be trapped and theeffective doping of the surface ZnO layer may be changed. During thepositive sweep, the metallic zinc atoms on the ZnO are dissolved andreleased into the electrolyte, which leads to a gradual corrosion of thesemiconducting oxide. With all these complications, the example showshow potential-dependent MC measurements can lead to new informationon electrochemical processes.

Another technique consists of MC measurements during potentialmodulation. In this case the MC change is measured synchronously withthe potential change at an electrode/electrolyte interface and recorded. Toa first approximation this information is equivalent to a first derivative ofthe just-explained MC-potential curve. However, the signals obtained willdepend on the frequency of modulation, since it will influence the chargecarrier profiles in the space charge layer of the semiconductor.

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


It is interesting that potential-modulated MC signals can also beobtained from metal electrodes (e.g., Pt in contact with an aqueouselectrolyte). Since the MC signal includes contributions from dipoleorientation [water, compare Eqs. (6) and (7)], it may be that potential-dependent changes of the water structure near the electrode surface willbe seen. This would mean that the oriented water structure makes differentcontributions to microwave absorption or reflection at different electrodepotentials. The potential-dependent formation of ultrathin oxide layerswith their possibly mobile charge carriers or an adsorption layer ofelectrochemical reaction products may also be seen. The fact that photoin-duced molecular charge separation has been clearly detected by micro-wave conductivity in liquid systems3 suggests that electrochemically orphotoelectrochemically generated products will also be seen with suffi-ciently sensitive PMC systems. When, during an electrochemical reaction,ions with the mobility are generated as well as species witha rotational charge mobility then a change in microwave conductivityof

can be expected.3 The rotational charge mobility can be calculated to beproportional to the square of the dipole moment and inversely proportionalto the rotational relaxation lifetime. It is frequency dependent and ap-proaches a limiting rotational charge mobility at high frequencies.

Up to now only qualitative data have been available on potential-dependent MC measurements of electrochemical interfaces. When metalsor other highly conducting materials are used, or when liquids are in play,special care has to be taken to allow access of microwave power to theactive electrode/electrolyte interface.

III. THEORETICAL CHALLENGE

1. A Fully Determined System

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

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ing electronic charge carriers. This is now discussed in more detail(compare Ref. 9).

While photoelectrochemical measurements allow the measurementof the photocurrent that is, the current of photogenerated chargecarriers, which can leave the semiconductor/electrolyte interface, thephotoinduced microwave conductivity signal provides integral informa-tion on the total amount of photogenerated charge carriers which, inequilibrium with recombination processes, are present in the semiconduc-tor electrode (among them are also those charge carriers that are finallylost through recombination). Figure 12 demonstrates via an energy dia-gram the situation in the semiconductor/electrolyte interface. Shown arethe minority carriers which are drifting toward the electrode inter-face, where a surface concentration of develops. This determinessurface recombination and the interfacial charge transfer, which are con-trolled by the rate constants and respectively. An n-type semiconduc-tor is given as an example [the following equations can be formulated inan analogous way for p-type semiconductors with electrons asminority carriers).

The photocurrent can be described by the following relation:

Figure 12. Energy diagram of a semiconductor/electrolyte in-terface showing photogeneration and loss mechanisms (viasurface recombination and interfacial charge transfer for minor-ity charge carriers). The surface concentration of minoritycarriers, is also indicated.


where q is the electric charge andThe photoinduced microwave conductivity signal, on the other hand,

can be described by the following integral over the excess minoritycarriers, to be taken over both the diffusion and the space charge region:

where S is the sensitivity factor to be calculated or calibrated, whichdepends on the geometry of the measurement cell; d is the thickness ofthe electrode; and W is the width of the space charge layer.

This means that the PMC signal will, apart from the generation rateof minority carriers and a proportionality constant, be determined by theinterfacial charge transfer rate constant and the interfacial chargerecombination rate

There is an additional simple relation between the surface concentra-tion of photogenerated minority carriers and the charge recombinationand charge transfer rates and to be considered:

where is the calculable minority carrier flux toward the semiconductorinterface,

These three equations (11), (12), and (13) contain three unknownvariables, and The rest are known quantities, provided thepotential-dependent photocurrent and the potential-dependent pho-toinduced microwave conductivity are measured simultaneously. Theproblem, which these equations describe, is therefore fully determined.This means that the interfacial rate constants and are accessible tocombined photocurrent–photoinduced microwave conductivity measure-ments. The precondition, however is that an analytical function for thepotential-dependent microwave conductivity (12) can be found. This is achallenge since the mathematical solution of the differential equationsdominating charge carrier behavior in semiconductor interfaces is quitecomplex, but it could be obtained,9,17 as will be outlined below. In thisway an important expectation with respect to microwave (photo)electro-chemistry, obtaining more insight into photoelectrochemical processes

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than that provided by classical photoelectrochemistry, can apparently befulfilled.

2. Measurement Opportunities and Prospects of MicrowaveElectrochemistry

Since photoelectrochemistry is not limited to photocurrent measurements,it may at this point be useful to think about some general new researchpossibilities to be expected from the combination of electrochemical andmicrowave measurements. Table 1 shows obvious combination possibili-ties between electrochemical and microwave measurements.

The combination of photocurrent measurements with photoinducedmicrowave conductivity measurements yields, as we have seen [Eqs. (11),(12), and (13)], the interfacial rate constants for minority carrier reactions

as well as the surface concentration of photoinduced minoritycarriers (and a series of solid-state parameters of the electrodematerial). Since light intensity modulation spectroscopy measurementsgive information on kinetic constants of electrode processes, a combina-tion of this technique with light intensity-modulated microwave measure-ments should lead to information on kinetic mechanisms, especially veryfast ones, which would not be accessible with conventional electrochemi-cal techniques owing to RC restraints. Also, more specific kinetic infor-mation may become accessible; for example, a distinction betweendifferent recombination processes. Potential-modulation MC techniquesmay, in parallel with potential-modulation electrochemical impedancemeasurements, provide more detailed information relevant for the inter-pretation and measurement of interfacial capacitance (see later discus-


sion). However, a general theory for the combination of electrochemicaland microwave potential modulation will have to be developed.

Electrochemical impedance spectroscopy leads to information onsurface states and representative circuits of electrode/electrolyte inter-faces. Here, the measurement technique involves potential modulation andthe detection of phase shifts with respect to the generated current. Thedriving force in a microwave measurement is the microwave power, whichis proportional to (E = electrical microwave field). Therefore, for amicrowave impedance measurement, the microwave power P has to bemodulated to observe a phase shift with respect to the flux, the transmittedor reflected microwave power Phase-sensitive microwave conduc-tivity (impedance) measurements, again provided that a reliable theory isavailable for combining them with an electrochemical impedance meas-urement, should lead to information on the kinetics of surface states anddefects and the polarizability of surface states, and may lead to morereliable information on real representative circuits of electrodes. Wesuspect that representative electrical circuits for electrode/electrolyte in-terfaces may become directly determinable by combining phase-sensitiveelectrical and microwave conductivity measurements. However, up tonow, 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, whichintegrates over all photogenerated charge carriers in the semiconductorinterface, is explained. This is a necessary requirement for the interpreta-tion of the PMC-potential curves.

3. Analytical Expression for Potential-Dependent MicrowaveConductivity

In order to calculate the integral (12) describing the microwave conduc-tivity signal, we have to obtain an analytical expression for the behaviorof charge carriers in the semiconductor interface. The Gärtner model,18

which assumes minority carrier collection by a potential-dependent spacecharge layer, is too simple for this purpose, since it does not considerinterfacial charge-transfer and surface recombination rate constants. Theformalisms of Reiss19 or Wilson20 do consider them, but provide expres-sions too complicated to be practical for calculating an analytical expres-sion for microwave conductivity. Starting from the basic equations

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[continuity equation (14)], the transport equation for electrons (15) andholes (16), and the Poisson equation (17)]

and considering the influx of additional charge carriers from the field-freeinterior of the semiconductor, a new effort had to be made to calculate thedistribution of the minority carrier concentration in a semiconductor/elec-trolyte junction.9 Among the simplifications introduced were a linearelectric field drop in the space charge layer,

= absorption coefficient), (L=diffusion length),and the condition that (d = thickness of the electrode). Under theserestrictions the integral over the excess minority carriers (12) can be solvedusing appropriate boundary conditions9:

where is the rate of interfacial charge transfer, is the surfacerecombination rate, is the electrode potential with respectto the flatband potential, is the light intensity, and (= space chargelayer width)

In this relation, is a relatively simple mathematical function, whichdepends on the electrode potential and has, as we will see,a significant meaning for microwave electrochemistry:


The surface concentration of minority carriers can be calculated onthe basis of the same formalism:

Relation (18) for the potential-dependent PMC signal is a reasonablygood approximation only for the depletion region, where the space chargelayer is controlled by the presence of fixed electron donors It wouldbecome even more complicated if bimolecular or even more complicatedkinetic reaction steps were considered.

In the accumulation region, the situation is much more complicated,so that a reliable analytical expression is difficult to obtain. However, itcan be shown17 that the PMC signals increase toward increased accumu-lation in a smooth, steplike function. The ratio between the PMC maxi-mum and the PMC minimum (at the flatband potential) can be calculatedand amounts to where is thebulk lifetime [compare relation (33)].

Relation (18) for the PMC signal in the depletion region is sufficientlycomplicated to require a more detailed analysis, but is already sufficientlysimple to allow the discussion of limiting cases.

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

Let us now investigate the case of a semiconductor with a relativelyslow interfacial charge transfer. In this case the surface concentration ofminority carriers is high and we can neglect the second term (which doesnot contain ). For higher values of electrode potential, the term Lexp can also be neglected.

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In the depletion region for a band bending wherea reasonably low surface recombination velocity is found, the PMC signalcan consequently be approached by

where is the surface concentration of minority carriers and since thephotocurrent is proportional to the surface concentration of minoritycarriers,

The interfacial charge-transfer rate constant can be determined whenthe PMC signal and the photocurrent are measured simultaneously. Whenthe interfacial charge transfer is, on the other hand, very large andnegligible, the PMC value becomes

4. Accuracy of Derived Analytical Formulas

(i) Numerical Solution of Basic Equations

It is possible to solve the fundamental transport equations for photo-generated charge carriers in a semiconductor junction (14)–(17) withoutany simplification. This has been done for a silicon Schottky barrier,10

which may serve as a reasonable model system for a semiconductor/elec-trolyte junction. The numerically computed potential-dependent PMCsignal showed a minimum in the flatband region of the semiconductor andsignificant peak structures in both the positive and negative potentialregion of a semiconductor electrode. These peaks are strongly influencedby surface recombination and charge-transfer rate constants, but also bythe bulk recombination lifetime. The influence of different values of rateconstants on the shape of these features is shown in Fig. 13. The PMCpeak in the depletion region is shown in Fig. 13(a) and in the accumulation


Figure 13. Numerically calculated PMC potential curves from transportequations (14)–(17) without simplifications for different interfacial reac-tion rate constants for minority carriers (holes in n-type semiconductor):(a) PMC peak in depletion region. Bulk lifetime s, combined inter-facial rate constants inserted in drawing. Dark points,calculation from analytical formula (18). (b) PMC peak in accumulationregion. Bulk lifetime: 10–5s. The combined interfacial charge-transfer andrecombination rate ranges from 10 (1), 100 (2), (3), 3 × 103 (4),(5), (6) to (7) The flatband potential is indicated.

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region in Fig. 13(b). The influence of interfacial rate constants is shownfor both PMC peaks.

These same features of the PMC signal can be reproduced by plottingthe calculated analytical formula for the depletion region [relation (18)].This is shown for the positive PMC peak in Fig. 14. By inserting the sameparameters into both the numerical and analytical computation procedures,it is found that the analytical solution coincides with the numerical one

interfacial rate constants for minority carriers minority carrier flux towardinterface:

(a) and different charge-transfer rates (inserted in the figures in (b) Constantcharge-transfer rate and different surface recombination rates (indicated in the figure).

α = 780 cm–1, D=11.65 cm2 s–1,

Figure 14. PMC potential dependence, calculated from analytical formula (18) for different


within 10% [the filled-in points in Fig. 13(a)]. This means that thesimplifications introduced for calculating the analytical relation (18) werereasonable. The stepwise increase in the PMC signal toward increasedaccumulation [Fig. 13(b)] cannot yet be simulated with a reliable analyti-cal formula because of complications with solving the intricate integralsfor the space charge layer under these conditions. However, as indicatedbefore, the ratio between and (at the flatband potential)amounts to and is therefore dependent on the bulk lifetimeof minority carriers Since we have succeeded in calculating the PMCcurve quantitatively, the derived PMC formula (18) can help us to under-stand and evaluate details of microwave electrochemical behavior ofsemiconductor electrodes.

(ii) Photocurrent Expression from Theory

Another interesting test which may give an idea of the use of thesimplifications introduced in deriving the analytical formula for photoin-duced microwave conductivity can be obtained from a comparisonbetween the simple Gärtner model for the potential-dependent photocur-rent18 and the theoretical photocurrent derived from the just-describedapproach.

The Gärtner model simulates charge collection by a potential-dependentspace charge layer and considers diffusion into the space charge layer ofcharge carriers generated deep inside the semiconductor. The well-knownGärtner formula for the photocurrent is

In our approximation we start with relation (20) for the surface concen-tration of minority charge carriers and derive via formula (11).

It follows that is (only photons leading to minority carriergeneration are considered)

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Assuming that there is no surface recombination and aninfinite interfacial charge-transfer rate as assumed in the Gärtnerapproach, the denominator of relation (27) becomes equal to one. Theexpression for the photocurrent then has the same structure as the Gärtnerformula. Formula (27) has the quality of showing the influence of thesurface recombination rate and the charge-transfer rate. When the (potential-dependent) surface recombination is large, the photocurrent becomes low.A high surface recombination rate near the flatband potential will displacethe photocurrent curve toward higher potentials (see Fig. 15). A low

Figure 15. Effect of interfacial rate constants on PMC behavior and on thephotocurrent (a) Fast interfacial charge-transfer rate, and (b) lowinterfacial charge-transfer rate.


charge-transfer rate will obviously decrease the photocurrent. The “diffu-sion” term in relation (27) is interesting. It increases withincreasing surface concentration of minority carriers in the presence of ahigh rate of interfacial charge transfer. It obviously considers an effectivediffusion loss into the field-free region (decreased diffusion into the spacecharge layer) when charge carriers are accumulating there. This shows thatthe compact photocurrent-voltage relation (27) is highly reasonable. Itmay serve to replace the Gärtner formula, which is not realistic forphotoelectrochemistry. We consider it support for the reliability of thederived formula (18).

In Fig. 15 the photocurrent voltage curves and the microwave con-ductivity potential curves are compared for two different cases. In Fig.15(a), a high interfacial charge-transfer rate was assumedand in Fig. 15(b) low charge-transfer rates Thesurface recombination was assumed to depend on the electrode potentialand was considered for different exponential parameters It can clearlybe seen that an inhibited charge transfer displaces the photocurrent voltagecurve towards higher positive electrode potentials. Simultaneously, asmoothly decreasing PMC signal [a high interfacial rate constant, Fig.15(a)] is giving way to a PMC peak the height of which depends on theinterfacial rate constant [Fig. 15(b)]. It is obvious that by measuring theintegral over the excess carriers in a semiconductor electrode, which is thebasis of the PMC measurement, minority charge carriers can be seen,which are dammed up toward the semiconductor interface owing to lowinterfacial charge-transfer rates and modest surface recombination rates.

IV. POTENTIAL-DEPENDENT STATIONARY MICROWAVECONDUCTIVITY MEASUREMENTS

1. n-Type Semiconductor/Electrolyte Junctions

As mentioned in the introduction, before an adequate theory was devel-oped, it was difficult to understand the experimentally determined pho-toinduced PMC signals, especially the minority carrier accumulation nearthe onset of photocurrents.The reason was that neither conventionalsolid-state semiconductor theory nor photoelectrochemical theory hadtaken such a phenomenon into account. But we have shown that it is realand microwave (photo)electrochemical experiments clearly confirm it.

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Figure 16 shows such PMC peaks in the depletion region for electrodesof Si,9 and They all appear near the onset of anodicphotocurrents. They have different shapes, which, however, can easily beexplained with the assumption of potential-dependent interfacial charge-transfer and charge recombination rates.

Figure 17(a) shows the PMC peak in the accumulation region (atnegative potentials) of silicon in contact with a propylene carbonate

Figured 16. PMC peaks in the depletionregion near the onset of anodic photocur-rents for and The clearlyreduced width of the ZnO peak can be seen.


Figure 17. PMC behavior in the accumulation region, (a) PMC potentialcurve and photocurrent-potential curve (dashed line) for silicon (dottedwith Pt particles) in contact with propylene carbonate electrolyte contain-ing ferrocene.21 (b) PMC potential curve and photocurrent-potentialcurve (dashed line) for a sputtered ZnO layer [resistivityon conducting glass (ITO)] in contact with an alkaline electrolyte

, measured against a saturated calomel electrode.22

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electrolyte21 as predicted by theory. Here photogenerated minority carriersare pulled into the interior of the negative space charge layer by theincreasing negative potential. In this way they increase their lifetime(through suppression of surface recombination). In the depletion regionof this electrode/electrolyte junction, two PMC shoulders are seen—aweak one near the onset of the photocurrent and a second high one whereoxide formation starts on Si owing to water traces in the electrolyte.21 Thisoxide formation reduces the charge-transfer rate for photoinduced minor-ity carriers and leads to a significant accumulation of charge carriers inthe space charge layer. Figure 17(b) shows that PMC peaks in the accu-mulation region can also be detected with a sputtered oxide layer in contactwith an alkaline electrolyte.22 Figure 18 shows the clearly pronouncedaccumulation-PMC peak for a silicon electrode in contact with a 50 mM

aqueous electrolyte and the depletion PMC peak at positiveelectrode potentials. The PMC-potential curves were measured for differ-ent light intensities.

2. Metal Oxide/Semiconductor Junctions

With respect to charge carrier dynamics, semiconductor/electrolyte junc-tions behave very similar to Schottky barriers, or, when a thin oxide layeris present in the interface, similar to metal oxide/semiconductor (MOS)junctions. Figure 19 shows a PMC model experiment with such an MOSdevice in which a 2 nm oxide layer separates the Si semiconductor fromthe metal contact.11,24 The comparison of photocurrent-voltage depend-encies with PMC-voltage curves clearly confirms the theory: where thephotocurrent appears in the depletion region, a PMC maxima appears.Such a peak also appears in the accumulation region. It can be seen thatthe PMC peaks do not increase proportionally with light intensity. It canalso be seen that the PMC signal in the accumulation region decreasesagain toward more negative potentials. This phenomenon is also recog-nized in the theoretical curves [Fig.l3(b)]. It turns out that at increasedforward potentials the dark current also increases, creating an ohmicvoltage drop. A field is created, along which the holes drift into the bulk.The concentration profile toward the electrode interface is thereby flat-tened10 and charge carriers are more easily lost at the back contact, whichdecreases the PMC signal.

It is interesting to note that PMC peaks depend on the frequency ofperiodic excess carrier generation. At higher frequencies, the PMC peak


Figure 18. (a) PMC potential curves and (b) photocurrentcurves for n-silicon in contact with a 50 mMaqueous electrolyte for different light intensities. Scan rate:20 mV. The light intensity is varied from (topcurves), to 50, 20, and (bottom curves).23

becomes smaller as if interfacial rate constants would increase. This isshown for an n-Si/Si-oxide/Au (100 Å) MOS junction (Fig. 20). At higherexcitation frequencies, passage of minority carriers through the oxidelayer in the MOS junction is apparently faster while the same number ofcarriers manage to cross the interface.

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Figure 19. PMC potential and photocurrent-potential curves for an Si-MOS device (2nm ) at different photon flux densities (indicated for photocurrents).

Figure 20. Influence of light pulsing frequency on PMC peaks of n-Si, incontact with a 10 nm Au at 20 mW cm–2 light intensity, compared withinfluence on photocurrcnt. Pulsing frequencies were 110, 1520, and 2930cps.


3. p-Type Semiconductor Electrodes

Up to now, relatively few experiments have been carried out using p-typesemiconductor electrodes. The theory predicts that the curves should bechanged in mirror image form from positive to negative potential at theflatband position. However, the PMC minimum between positive andnegative peak shifts in the positive direction by approximately 700 to 800mV, which is equivalent to the shift of the Fermi level when switchingfrom an n-type to a p-type material. Experiments with p-type silicon haveconfirmed this expectation (Fig. 21).9 An excess minority carrier peak(electrons) is found that coincides with the onset of cathodic photocurrentstoward negative potentials (entirely symmetrical to the correspondingPMC peak of n-type electrodes at positive potentials). The (potential-dependent) interfacial charge-transfer rate and the surface recombinationrate of photogenerated electrons will, for p-type electrodes, determine theamplitude and the shape of the PMC peak at negative electrode potentials.

4. Meaning of the Dammed-Up Charge Carriers

Why do minority carriers accumulate in the depletion region near the onsetof photocurrents? Theoretically, three factors are decisive for this phe-nomenon:

an increasing lifetime of charge carriers owing to the increasingelectrical field in the space charge layer, which causes a separationof charge carriersa surface recombination rate, sr, which decreases away from theflatband potential with increasing electrode potentialan interfacial charge transfer rate that may increase with theelectrode potential but should not become very fast

Any change in the constants and should of course be reflected ina change in the PMC peak.

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

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Figure 21. (a) PMC potential and (b) cathodic photocurrent-potential curves fora p-Si (111) electrode (resistivity, 10 cm). Electrolyte, 1 M lightintensity; 1 mW cm–2. Sweep toward negative potentials.

lifetime peak could, however, be clearly seen only with moderate laserpulse energies. Too high photon densities of laser pulses apparentlyinterfere with the electric field distribution and concentration profiles inthe semiconductor interface.

Since the magnitude and shape of this PMC peak depend on the rateconstants of minority charge carriers, the PMC peak provides access tokinetic measurements. It is interest that the height as well as the shape ofthe PMC peak change with the frequency of light pulsing. This is shown

Microwave(Photo)electrochemistry 477

Figure 22. (a) Comparison of stationary PMC peak atpositive potentials and (b) peak in PMC transientlifetime, measured for n-ZnO single crystals.25

in Fig. 23 for in contact with a 50-mM solution (5 mM). While the photocurrent-potential curve does not change signifi-

cantly when the pulsing frequency is varied between 11 and 110 cps, boththe height and the shape of the PMC peak do.26 This indicates that kineticconstants change, apparently because of pulsing frequency-dependentprofiles of the charge carrier distribution in the space charge layer.

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Figure 23. Influence of light pulsing frequency on peak height and peak positionof in contact with 50 mM Fe2+/3+ Pulsing frequenciesbetween 11 and 110 cps are compared for the PMC and photocurrent curves (lightintensity, 50 mW cm–2).

In microwave electrochemical measurements with unstable elec-trode/electrolyte interfaces, the PMC signals may change drastically intime. During a first sweep of a silicon electrode toward more positiveelectrode potentials, a pronounced PMC peak may be seen, which disap-pears during the return sweep toward negative potentials23 (Fig. 24). Thereason is that during the positive sweep the Si interface corroded to formsites for interfacial charge recombination (an increase in sr), which alsoleads to a decrease in anodic photocurrents. Figure (25) compares two


Figure 24. Degradation of n-Si/electrolyte ( pH 3) interface as seen fromthe hysteresis of the PMC signal and the photocurrent (dotted line).

experiments, one with n-Si (treated with Pt particles) in contact with a 5M HBr/0.05 M aqueous solution, and one with in contact withan aqueous 0.05 M solution. Silicon was allowed to degrade andWSe2 was cathodically polarized. In both cases, while the anodic pho-tocurrent decreases, the PMC peak shifts toward more positive potentials.The reason is an increased surface recombination near the flatband poten-tial.

In studies on Pt dotted silicon electrodes, PMC measurements re-vealed that tiny Pt dots increased the interfacial charge transfer comparedwith bare silicon surfaces in contact with aqueous electrolytes. However,during an aging effect, the thickness of the oxide layer between the siliconand the platinum dots gradually increased so that the kinetic advantageagain decreased with time.11

5. PMC Decay in the Depletion Region

Experimental evidence with very different semiconductors has shown thatat semiconductor interfaces where limited surface recombination and amodest interfacial charge-transfer rate for charge carriers generate a peak

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Figure 25. Effect of corrosion and prepolarization on (a) PMC voltage and (b) photocurrentvoltage dependence. Left: n-Si (covered with Pt particles) in contact with a 5 M HBr/0.05

aqueous solution. A comparison is made of the PMC peak during the first and thethird potential sweeps. Right: in contact with an aqueous 0.05 M solution.The effect of cathodic prepolarization on position and height of the PMC peak is shown.

of microwave conductivity, this conductivity signal decreases in the de-pletion region with increasing electrode potential (Figs. 16 and 19). Theexplanation of this phenomenon is not straightforward, since it occurs ina potential region where practically all charge carriers reach the semicon-ductor interface to react with the electrolyte. This is clearly indicated bythe presence of a limiting current in this potential region.

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


provide a reasonable explanation. In fact, it is found that the decay ofmicrowave conductivity in the depletion region is dominated by a mathe-matical function [relation (19)]. The dependence of this function onband bending in the semiconductor interface is shown in Fig. 26. Itdescribes the minority charge carrier concentration profile in the spacecharge layer and thus affects the PMC signal, even in the limiting pho-tocurrent region and in the presence of a constant interfacial chargetransfer by decreasing it toward larger band bending. Charge carrierprofiles have been calculated for polarized silicon interfaces10 and showthat with increasing electrode potentials photogenerated charge carriersconcentrate near the semiconductor/electrolyte interface (Fig. 27). Sincein the absence of electrostatic interaction the space charge region can becrossed with thermal velocity, it will be the increasing closeness ofminority carriers to the interface that will control the escape through aninterfacial reaction. While at lower positive electrode potentials reactingcharge carriers will be further away from the interfaces, they will beavailable closer to the interface at higher electrode potentials. With in-creasing electrode potential, their average stay in the space charge layerwill therefore decrease, thus decreasing microwave conductivity, which is

Figure 26. Dependence of function [relation (19)] and of on the electrodepotential (measured against the flatband potential)

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proportional to the concentration of mobile carriers. Since with increasingdepletion of the space charge region the photogenerated charge carriersare found to concentrate more toward the interface, they are thereforereacting more rapidly and spending less time in the space charge layer.[Since and increase and decrease complementaritywithin the limiting photocurrent range (compare Fig. 30]. The conse-quence is that the PMC signal decreases with increasing electrode poten-tial within the region of limiting photocurrent.

There is a simple example that can make this remarkablephenomenonintuitively more accessible (Fig. 28). Allowing the passage of photoin-duced minority carriers through the space charge layer at different elec-trode potentials in the limiting current region is equivalent to pressingwater at a constant rate through tubes with decreasing cross sections (theincreasing electrical field corresponds to the increasing pressure in themodel experiment with the water tubes). Measuring microwave conduc-tivity is equivalent to measuring the average number of water moleculesin tubes of different sizes. Even though the same amount of water per timeis pressed through the tubes, much less water is found in the thinner tubes,through which water is passing at a higher velocity.

The decrease of the PMC signal toward increasing depletion thereforereflects the increasing dynamics of minority carriers passing the spacecharge layer. No classical electrochemical technique has up to now per-mitted observation of this phenomenon with such clarity.

6. Determination of Flatband Potential

The theory locates the flatband potential between the PMC peak in theaccumulation and the PMC peak or the photocurrent shoulder in thedepletion region. If peaks or shoulder are sufficiently close to each other,the determination of the flatband potential is sufficiently accurate. A highsurface recombination rate, however, can move the peaks apart. In the caseof a high interfacial charge-transfer rate, the PMC peak in the depletionregion may completely disappear and give way to a gradually decreasingsignal. Under this condition of high charge-transfer rate, the formula forthe potential-dependent PMC signal (18) loses the term that contains thesurfaceconcentration of minority carriers (20), (which becomes verysmall). Formula (21) can be rewritten to give (W, the width of the spacecharge layer, is inserted and the thickness of the electrode is assumed tobe large):

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Figure 28. Semiconductor interfaces with increasing electricfields in the space charge layer (from top to bottom) comparedwith tubes of different diameters through which an equivalentamount of water is pressed per unit time (equivalent to limitingcurrent).

ln

with

and

When relation (28) is properly fitted, B,C, and the flatband potentialcan be determined. For a silicon electrode in contact with 0.6 M


Figure 29. PMC potential and photocurrent-potential curves for n-Si in contact with 0.6 MNH4F. The flatband potential is indicated.

solution, which dissolves the interfacial oxide layer the potential coin-cided with a flatband value determined using a conventional technique.9,17

The Debye length of the electrode material can be determined fromthe constant B, and the sensitivity factor S from C, provided the diffusionlength and the diffusion constant for minority carriers are known.

In the experiment discussed the flatband potential(0.8 V vs. a saturated Hg-sulfate electrode) would have been immediatelyrecognizable as the pronounced minimum between PMC and the pho-tocurrent curve (Fig. 29).

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

7. Determination of Interfacial Rate Constants

As outlined at the beginning of this chapter, combined photocurrent andmicrowave conductivity measurements supply the information needed todetermine three relevant potential-dependent quantities: the surface con-centration of excess minority carriers the interfacial recombinationrate and the interfacial charge-transfer rate By inserting the

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measuredphotocurrent and PMC values into the proper relations, thesequantities can be readily obtained, provided the remaining parameters ofthe system, including the sensitivity factor S are known or can be deter-mined. Such evaluations have been done with n-Si wafers in contact withammonium fluoride solutions of different concentrations.9 With a thin

Figure 30. (a)Measured PMC-potential and potential curves for n-Si in contact with asolution and (b) and values calculated as a function of electrode

potential.


interfacial oxide layer present on Si in contact with a solution,a pronounced PMC peak is identified near the onset of the photocurrentcurve in the depletion region [Fig. 30(a)]. In Fig. 30(b) the potential-dependent surface recombination rate and the interfacial charge transferrate as well as the potential-dependent surface concentration of minoritycarriers are shown. It should be pointed out that the indicated valuesare quantitative values, which could be measured because of the experi-mental determination of the sensitivity factor S. As expected, stronglydecays with increasing potential, while the surface concentration of holes,

stays nearly constant in the region of limiting photocurrent. However,it is not exactly constant. It decreases slightly while the charge-transferrate increases, so that their product yields a constant limiting photocurrentaccording to relation (11).

Following the same procedure, the kinetic constants have been deter-mined for very different electrochemical conditions. When elec-trodes are compared in contact with different redox systems it is, forexample, found9 that no PMC peak is measured in the presence of 0.1 MKI, but a clear peak occurs in presence of which isknown to be a less efficient electron donor for this electrode in liquidjunction solar cells. When is replaced by itsoxidized form, a large shoulder is found, indicating that minority carrierscannot react efficiently at the semiconductor/electrolyte junction (Fig. 31).

Interesting results have also been obtained with light-induced oscil-lations of silicon in contact with ammonium fluoride solutions. Thequantum efficiency was found to oscillate complementarity with the PMCsignal. The calculated surface recombination rate also oscillated comple-mentarily with the charge transfer rate.27,28 The explanation was a peri-odically oscillating silicon oxide surface layer. Because of a periodicallychanging space charge layer, the situation turned out to be neverthelessrelatively complicated.

These results clearly show that microwave electrochemical tech-niques are providing valuable new insights into the kinetics of relevantinterfacial mechanisms.

8. Accumulation Region

It is well known that photoelectrochemical measurements do not indicatephotocurrents in the accumulation region of an illuminated semiconduc-tor. The reason is that majority carriers control interfacial reactions, which

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Figure 31. PMC potential curves in depletion region compared foran electrode in contact with 0.1 M KI,

conductivity change (This condition is fulfilled when the microwavefield is not significantly attenuated within the illuminated layer.)

This means that the minority carriers are measured, however “formally,”with an effectively changed mobility, which also includes the mobility ofphotogenerated majority carriers.

The potential-dependent behavior of minority carriers in the accumu-lation region has up to now not been accessible to electrochemistry.

and

are so abundant that their concentration cannot be changed significantlythrough illumination. The excess minority carriers that are generated, onthe other hand, are pulled into the interior of the semiconductor electrode,where they are lost through recombination with majority carriers.

Photoinduced microwave conductivity measurements obviously al-low the measurement of minority carriers in the accumulation region (Fig.17). In fact, both charge carriers are measured simultaneously since thePMC signal can be assumed to be proportional to the photoinduced


Therefore, no experimental knowledge is available on interfacial reactionmechanisms under such conditions. These now become accessible viaPMC measurements. As theory shows [Fig. 13(b)], the PMC signals in theaccumulation region are controlled by potential-dependent surface recom-bination and charge-transfer rates, as well as by the bulk lifetime of chargecarriers.

It is not yet clear how useful information on minority carriers in theaccumulation region will become in practice. Two interesting applicationsmay be suggested here, where information on minority carriers in theaccumulation region may be of special interest. One is the mechanism ofphotoinduced insertion into and passage of protons through a pyrite layer(via cathodic insertion and diffusion as hydrogen). Photogenerated minor-ity carriers are found to support insertion of adsorbed hydrogen.29,30 Theother example is the separation of surface recombination from bulkrecombination through electropassivation of silicon (by applying a nega-tive potential to an n-type electrode). The field applied in the accumulationregion forces minority carriers to diffuse into the interior of the semicon-ductor, suppressing surface recombination.

An important aspect of the increase in the PMC signal toward negativepotentials of n-type semiconductor electrodes is that the surface recombi-nation process of charge carriers is gradually neutralized. The minoritycarriers increasingly drift into the interior of the electrode, where they aresubject to recombination with majority carriers. An increasingly effectivebulk lifetime of charge carriers therefore also increases the PMC signal,which has been confirmed by computer simulation (Fig. 13) and bysolving the transport equation by introducing simplifications. Towardincreasingly negative potentials, however, an additional potential dropmay also occur as a consequence of the passage of a high dark current.The result is that minority carriers will diffuse faster into the interior, thusflattening their concentration profile and transporting them (in the case ofthin layers or wafers) faster to the back contact, where they may be lostthrough recombination. Such a process is significant in the case of silicon,where large diffusion lengths prevail. The PMC peak in the accumulationregion is significantly lower for thin wavers than for thicker ones or onesin which the back surface has been passivated. When large dark currentsare not passing through the electrode in the accumulation region, otherphenomena may account for the decrease of the PMC signal toward highernegative potentials. For example, new tunneling possibilities may ariseowing to strong energy band bending and lead to recombination processes.

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It has been observed that the amplitude or presence of a PMC peakin the accumulation region is also dependent on the nature of the electro-lyte.12 ZnO in the presence of an aqueous electrolyte shows a photoin-duced PMC peak in the depletion region only at positive potentials. Noaccumulation peak is seen up to –2V (vs. a saturated sulfate electrode).When an organic electrolyte (propylene carbonate with ferrocene) is used,the PMC signal also appears in the accumulation region. Adding smallamounts of water to the propylene carbonate again causes the PMC signalto disappear. The reason for this behavior may be a drastically changinginterfacial charge-transfer rate constant. As shown in the numerical simu-lation in Fig. 13, the PMC peak in the accumulation region indeeddecreases with increasing interfacial recombination and charge-transferrate constants, which leads to a disappearance of minority carriers. Sinceminority carriers themselves do not react electrochemically at such nega-tive potentials, it must be the majority carriers that react. These react wellwith protons but not with (reduced) ferrocene. Since the measurement ofpositive and negative carriers is linked in the PMC measurement [comparerelation (30)], and the imposed electrode neutrality has to be maintained,the disappearance of an electron at the interface will lead to the extractionof a positive charge at the back contact. The total PMC signal will thereforedecrease. On the other hand, when the electron transfer is suppressed, bothexcess electrons and holes will stay in the electrode. The accumulation ofexcess electrons in the interface will, however, push excess holes into theinterior, thus keeping the PMC signal large. This may happen at a ZnO/in-terface in contact with propylene carbonate and ferrocene.

We conclude that the interfacial kinetics of excess majority carrierscontrol the PMC signal in the accumulation region, while it is the minoritycarriers, as we have seen, that control the PMC signal in the depletionregion.

9. Influence of Surface Recombination on the PMC Signal

Surface recombination processes of charge carriers are mechanisms thatcannot easily be separated from real semiconductor interfaces. Only a fewsemiconductor surfaces can be passivated to such an extent as to permitsuppression of surface recombination (e.g., Si with optimized oxide ornitride layers). A pronounced dip is typically seen between the potential-dependent PMC curve in the accumulation region and the photocurrentpotential curve (e.g., Fig. 29). This dip may be partially caused by a surface


Figure 32. Shapes of PMC curves and photocurrent curves in a junction formedfrom an n-type material by allowing in-diffusion of an acceptor (boron). The absenceof interface states generates a strong overlapping of the two curves.

recombination that is high at the flatband potential and that stronglydecays with increasing band bending. In order to visualize the effect ofsurface recombination, PMC and photocurrent curves are compared for a

junction30 (Fig. 32). This was a detector junction in which athick n-type Si layer was superficially highly dopedwith boron. It does not have a phase boundary coinciding with a realinterface and therefore has no interface recombination As a resulta very large effective charge-transfer rate It can be seenthat the PMC and photocurrent curves strongly overlap. The intersectionshould correspond to the potential where the energy bands of the n-typesilicon layer are flat.

10. Quantitative Data from PMC Measurements: The SensitivityFactor

The theoretically derived formula (21) relating PMC measurements to thesurface concentration of minority carriers and interfacial rate constantscontains a proportionality constant, S, the sensitivity factor. This factordepends on both the conductivity distribution in the semiconductor elec-

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trode and the geometry of the cell, as well as the experimental environ-ment. It is illusory to try to calculate it exactly. Therefore it must bedetermined experimentally. This can be done by making well-definedchanges in the PMC signal of the sample, measuring the correspondingPMC signals, and calculating the sensitivity factor by quantitativelyconsidering the imposed differences.

For an electrode with high interfacial rate constants, for example,relation (28) can be plotted, which yields the flatband potential. It allowsdetermination of the constant C, from which the sensitivity factor S canbe calculated when the diffusion constant D, the absorption coefficient α ,the diffusion length L, and the incident photon density (corrected forreflection) are known:

Another way to determine the sensitivity factor consists in determin-ing the difference between the PMC minimum (flatband potential) and thePMC maximum in the accumulation region (the infinite and negligiblesurface recombination rate). This difference can be calculated to be17

The diffusion length can thus be calculated since α is typically known,or since the bulk lifetime provided the diffusion coefficientD for minority carriers in the material is known. The sensitivity factor canbe determined from the maximum or minimum PMC signal. Using theminimum PMC signal at the flatband potential we derivefrom Equation (21).

it follows that


This is a relation in which the photoinduced microwave conduc-tivity signal at the flatband potential, is measured and the rest of theconstants are known.

Other situations may also occur that allow a simple determination ofthe sensitivity factor. When, for example, a sufficiently negative electrodepotential forces all minority carriers to drift into the interior of thesemiconductor electrode, where they recombine subject to the bulk life-time we will see a limiting PMC signal (given a sufficiently thickelectrode). Knowing the photon flux (corrected for reflection), we mayexpect the following formula to hold:

from which the sensitivity factor S can readily be determined whenmeasuring the limiting PMC signal and inserting the other solid-stateparameters.

Other ways to determine the sensitivity factor S are possible, forexample, by comparing microwave reflectance and admittance responsesin a potential region with ideal junction behavior.31

V. POTENTIAL-DEPENDENT TIME-RESOLVEDMEASUREMENTS

1. Experience with Time-Dependent Measurements

Time-resolved microwave conductivity measurements have a long historyand have, as a contact-free technique, successfully been applied to drysemiconducting crystals, layers, and powders. 2,32–35 It is well establishedthat both bulk properties (bulk lifetime, defects, deviations fromstoichiometry, carrier mobilities) and surface properties (surface states,adsorbed molecules, surface roughness) affect the kinetics of PMC tran-sients. More detailed information can be obtained by performing transientmeasurements under systematically varying conditions. Possibilities areexcitation at different wavelength, at differentexcitation density, at differ-ent temperatures, and underbias illumination (which may change the bandbending).36

Taking titanium dioxide as an example, we may mention that PMCtransients decay rapidly in the rutile phase and much slower in the(catalytically more active) anatase phase When a

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powder (Degussa P25) that contains both phases is illuminated with a20-ns laser flash (266 nm), a complicated PMC decay is seen on alogarithmic time scale, with 10% of the charge carriers living up tos.35 When the powder is moistened with 2-propanol, 30% of the chargecarriers live for 1 s. However, after treatment with tetranitromethane(which is able to act as an electron donor), the transients become signifi-cantly faster, with most charge carriers disappearing within s and fewsurviving to

Even though interesting qualitative information can be drawn fromsuch contact-free measurements, microwave photoelectrochemical stud-ies suggest that the interpretation of such transients is not straightforward.PMC signals depend on the bending of energy bands (that is, the effectivefield present in the space charge region of the interphase). Chemicalspecies, when adsorbing to the interphase, may affect the band bendingand this may also change during the recombination of charge carriers afterflash excitation of the samples (which, when strong, may temporarilyflatten the energy bands). Bias illumination of the semiconductor sampleto flatten energy bands may be of only qualitative help, since the bandbending of uncontacted samples is typically unknown as is the effect oflight intensity on the rebending of energy bands (which will depend oninterfacial recombination rates). It makes scientific sense to test theseconsiderations and to try well-defined potential-dependent PMC measure-ments with semiconductor electrodes.

The fact that a potential-dependent lifetime peak for PMC transientshas been found which coincides with the stationary PMC peak in thedepletion region near the onset of photocurrents (Fig. 22) is very relevantsince the stationary PMC peak is determined by the interfacial rateconstants of charge carriers (Figs. 13 and 14); this should also be the casefor the transient PMC peak. To demonstrate this correlation, the followingformalism can be developed10:

When a turnover of minority carriers is assumed to take place only atthe electrode/electrolyte interface (which is reasonable), the time-depend-ent change in the integral of minority carriers can be expressedas


which means that the integral over all minority carriers decreases propor-tionally to the surface concentration of minority carriers with the sum ofsurface recombination rate and interfacial charge transfer rate as a propor-tionality factor. Substituting for the integral over the charge carriers (21)the expression derived for slow interfacial charge turnover (22) andapproximately setting in volts, but dimension-less, since is a dimensionless function) (10)

and solving the resulting equation yields

which describes an exponentially decaying PMC signal with a decay timeof again introduced in volts but assumed dimensionless)

This lifetime for PMC transients results, as indicated, with moder-ately fast or slow interfacial charge turnover. It is determined not only bythe interfacial rate constants and which consume the minoritycarriers, but also by the electrical field in the space charge layer asdetermined by the bending of the energy bands and bysolid-state parameters as contained in the Debye length (such as and

This conclusion should equally be true for transient PMC measure-ments of semiconducting powders (the surface of which, in contact withair, is typically covered by a very thin water layer). Additional information(on the band-bending on and on the relative contribution of and

is necessary to interpret the transient PMC signal in terms of a specificrate constant. This may be obtained by changing the exciting or bias lightintensity (change of or changing the concentration of a redox species(affecting

With electrochemically studied semiconductor samples, the evalu-ation of [relation (39)] would be more straightforward. could beincreased in a well-defined way, so that the suppression of surface recom-bination could be expected. Provided the Debye length of the material isknown, the interfacial charge-transfer rate and the surface recombination

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rate could be determined, based on only two transient measurements atdifferent electrode potentials.

It is important to note that there may be at least two reasons forobtaining deviations from a purely exponential behavior for a PMCtransient. These are a too high excess carrier generation, which may causeinterfacial rate constants that are dependent on carrier concentration, andan interfacial band bending which changes during and after the flash.For fast charge transfer, a more complicated differential equation has tobe solved.

It is interesting to note that independent, direct calculations of thePMC transients by Ramakrishna and Rangarajan (the time-dependentgeneration term considered in the transport equation and solved byLaplace transformation) have yielded an analogous inverse root depend-ence of the PMC transient lifetime on the electrode potential.37 This showsthat our simple derivation from stationary equations is sufficiently reliable.It is interesting that these authors do not discuss a lifetime maximum fortheir formula, such as that observed near the onset of photocurrents (Fig.22). Their complicated formula may still contain this information forcertain parameter constellations, but it is applicable only for moderateflash intensities.

How can we demonstrate that microwave transients qualitativelyfollow the potential-dependent stationary PMC signals? We have seen thatthe PMC signal is dependent on the interfacial rate constantsAssuming a slow interfacial charge turnover [Eq. (18) with only the firstterm, multiplied by being relevant] and a potential sufficiently posi-tive from the flatband potential so that exp can be neglected, wecan substitute into the formula describing the transient lifetime(39) and obtain (for the depletion region)

This relation shows that the lifetime of PMC transients indeed followsthe potential dependence of the stationary PMC signal as found in theexperiment shown in Fig. 22. However, the lifetime decreases with in-creasingly positive electrode potential. This decrease with increasingpositive potentials may be understood intuitively: the higher the minoritycarrier extraction (via the photocurrent), the shorter the effective lifetime


measured. With increasing light intensity in the denominator of (40),the lifetime should also decrease. However, the measured PMC signalsimultaneously increases in the numerator according to (18), that is, it isproportional to If the charge-transfer or surface recombi-nation rate remain constant, should not change with light intensity. If thesurface recombination rate increases with light intensity, the PMC signalshould increase slower than proportionally with the light intensity (whichis typically observed). This may explain why the lifetime peak in thedepletion region of ZnO (Fig. 22) decreases with light intensity and is seenonly with the low light intensities of exciting laser pulses.

The real situation, however may be more complicated. A comparisonof the frequency dependence of photocurrents and PMC signals, measuredwith electrodes in contact with an aqueous electrolyte, showsthat the size and position of PMC peaks change with the pulsing frequencyof excess carrier generation (Fig. 23). Obviously, at higher light choppingfrequencies, the kinetics at the interface are effectively improved, sincefewer minority carriers are dammed up at the interface. This indicates thatthe kinetic constants entering into relation (18) may be frequency depend-ent. In other words, the minority carrier profiles in the space charge layershould be dependent on the frequency of periodic excitation of excesscharge carriers. Such behavior is not unusual for electrode/electrolyteinterfaces. Periodically excited currents often show a decreased interfacialresistance (which is not seen for the photocurrent in Fig. 23 because of thelimiting current behavior, which allows all minority charge carriers toreach and cross the interface).

2. Control of Interfacial Lifetime in Silicon withPolymer/Electrolyte Junction

Equation (40) relates the lifetime of potential-dependent PMC transientsto stationary PMC signals and thus interfacial rate constants [compare(18)]. In order to verify such a correlation and see whether the interfacialrecombination rates can be controlled in the accumulation region via theapplied electrode potentials, experiments with silicon/polymer junctionswere performed.38 The selected polymer, poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether, or technically (Hydrine-T), to whichlithium perchlorate or potassium iodide were added as salt, should notchemically interact with silicon, but can provide a solid electrolyte contactable to polarize the silicon/electrode interface.

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Figure 33. PMC lifetime map of n-type silicon wafer contacted with a polymer electrolyte(poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether) with lithium perchlorate) at 0V and at –5 V (cathodic polarization) measured against a copper counter-electrode (also incontact with the polymer electrolyte). The diagrams show (a) an average lifetime for chargecarriers of before (statistical distribution), and (b) a (white) overflow with an averagelifetime of after applying a negative potential of –5 V. It can be seen that the polymercontact is not homogeneous (the polymer shrinks during drying). For color versions pleasesee color plates opposite p. 453.


When an n-type silicon wafer is placed in contact with such aHydrine-T polymer layer containing lithium perchlorate in a cell forminga sandwich with a thin ITO layer on glass, a space-resolved microwavetransient measurement can be made with the technique described in Fig.6 and demonstrated with the example of Fig. 7. The spatial distribution oflifetime over an area of is shown in Fig. 33(a) for the case whenzero voltage is applied between silicon and the ITO contact layer, sepa-rated by a polymer electrolyte. In the plot of the statistical lifetimedistribution shown to the right, a peak lifetime of can be seen. Figure33(b) shows the situation when a potential of –5 V (accumulation) isapplied to the silicon electrode with respect to the ITO electrode. Thedistribution of lifetimes shows that the peak has broadened and reached amaximum of while a significant fraction of points (5%) havereached a lifetime near (white areas, lifetime measured inde-pendently). The fact that high PMC lifetimes of are reached onlywithin restricted areas [the white patches in Fig. 33(b)] may be due to atrivial problem, an inhomogeneous contact between the polymer and thesilicon wafer caused by the shrinking of the polymer during the dryingprocess.

The polymer layer of several tenths of a millimeter produces asignificant resistance loss for the passing current, so that only a smallfraction of the applied potential effectively drops at the silicon/polymerjunction. At a total potential of ions start reacting with thesilicon. The consequence is a significant drop in the PMC lifetime forphotogenerated charge carriers. As Fig. 34 shows, nearly 50% of thesilicon surface loses its photoconductivity, indicating that a solid-statechemical reaction has occurred in the semiconductor surface. This doesnot happen when Li perchlorate is replaced by the redox system Inthis case, only electrons can be transferred across the Si/electrolyte inter-face. When potential-dependent measurements are performed for a se-lected spot on the sample, a PMC lifetime–potential dependence isobtained, which is reproducible but during cycling shows a clear hysteresis(Fig. 35). A marked shoulder is seen in the negative potential region (theaccumulation region of n-Si), a minimum at the flatband potential of Si,and a pronounced peak in the depletion region. This peak is absent duringa sweep toward negative potentials, indicating that iodide oxidation affectsthe interface, increasing interfacial rate constants. With the exception ofthe larger potential range (owing to the significant potential drop in thepolymer layer), this PMC lifetime-potential curve has a shape similar to

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Figure 34. PMC lifetime map of n-type silicon/polymer (poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether plus iodide) junction at –10 V potential (mostly droppingacross the polymer layer), after insertion has changed the silicon interface. The statisticalevaluation shows the drastic drop in the PMC lifetime. For color version please see colorplates opposite p. 453.

Figure 35. Dynamic change of lifetime in an n-type silicon/poly-mer (poly(epichlorhydrine-co-elhylenoxide-co-allyl-glycyletherplus iodide) junction during a potential sweep. The arrows showthe direction of sweep A shoulder in the accumula-tion region and a peak in the depletion region of silicon are clearlyseen.


that of stationary theoretical and experimental PMC-potential curves(Figs. 13, 16, 17, 22, 30). This shows that potential-dependent PMCstructures are at least in part due to potential-dependent changes in thelifetimes of minority charge carriers. These results also demonstrate thatthe relation found between potential-dependent PMC transient lifetimesand the stationary potential-dependent PMC signal [relation (40)] isbasically correct.

Two transients, measured at 0 V and –5 V with a silicon/polymerjunction, are shown in Fig. 36. They clearly show the effect of a negativeelectrical field on recombination processes. Minority carriers are appar-ently pulled by the negative electrical field into the interior of the Sielectrode, where they recombine with an effectively longer lifetime. Sincesilicon has a very large diffusion length for charge carriers, they can diffusethrough the -thick Si wafer; most of them recombine at the backside, which thus limits their lifetime. Both silicon surfaces, the front andthe back side, must be electropassivated (polarized to accumulation) toforce charge carriers to survive to the bulk lifetime.

3. Potential-Dependent Measurements with OrganicElectrolytes

Time-resolved, potential-dependent PMC measurements have also beenperformed with silicon in contact with propylene carbonate containing 0.1M TBAP and 1 mM ferrocene.11,23 Both signal amplitudes and thelifetimes of transients excited by laser pulses (532 nm) are shown in Fig.37 in dependence on the electrode potential. Both curves show a clearminimum at the flatband potential. This indicates that surface recombina-tion plays a significant role under such conditions and that the appliedelectrical potential definitely controls the lifetime of charge carriers. Theseresults again confirm that the derived relation (40) between transientlifetime and the PMC signal (controlled by interfacial rate constants)indeed exists. The laser excitation (532 nm) occurred with a 10-ns flash,while the transients were measured in the 20–100-ns time region. ThePMC transients measured are much faster than the RC time constant ofthe electrode/electrolyte system and, since they are controlled by kineticconstants, will provide access to fast charge-transfer mechanisms at semi-conductor/electrolyte interfaces.

It is interesting that the flatband minimum of the amplitudes of PMCtransients [Fig. 37(a)] is much less pronounced when a longer excitation

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Figure 36. Microwave conductivity transients of an n-type silicon/polymer(poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether plus iodide) junction at 0 and–5V.

wavelength is used, which allows the light to penetrate muchdeeper into the semiconductor materials.11 Under such conditions, morecharge carriers are generated inside the semiconductor and surface recom-bination becomes less important.


Figure 37. Potential dependence of (a) amplitudes and (b) lifetimes of laser-induced PMCtransients (532 run) of silicon in contact with propylene carbonate containing 0.1 M TBAPand 1mM ferrocene (flatband at –0.5 V).

4. Access to Kinetic Constants via PMC Transients

The PMC transient-potential diagrams and the equations derived for PMCtransients clearly show that bending of an energy band significantlyinfluences the charge carrier lifetime in semiconductor/electrolyte junc-tions and that an accurate interpretation of the kinetic meaning of suchtransients is only possible when the band bending is known and controlled.

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Otherwise, the effect of electrode potential and kinetic parameters ascontained in the relevant expression for the PMC signal (21), whichcontrols the lifetime of PMC transients (40), may lead to an erroneousinterpretation of kinetic mechanisms. The fact that lifetime measurementsof PMC transients largely match the pattern of PMC-potential curves,showing peaks in accumulation and depletion of the semiconductor elec-trode and a minimum at the flatband potential [Figs. 13, 16–18, 34, and36(b)], demonstrates that kinetic constants are accessible via PMC tran-sient measurements, as indicated by the simplified relation (40) derivedfor the depletion layer of an n-type electrode.

The fastest reliable PMC transients recorded at electrodes (ZnOsingle crystals24) were limited by the lifetime of a 10-ns laser flash. It wasapparent from the nondeconvoluted signal at shorter time scales that muchfaster decay processes took place and would be accessible with faster laserpulses.

It is a significant challenge to study kinetic mechanisms of chargecarriers at electrodes with much faster time constants (ns- to ps-range),since such mechanisms are typically buried in RC-limited electrochemicaldecay processes. Only special experimental procedures (e.g., dischargingthe electrode via a very high resistance, measuring the developing pho-topotential, and modeling the transients39) gives partial access to fastelectrode processes (mostly recombination processes within the electrodematerial). Typically, individual interfacial rate constants are not obtainedsince they cannot be separated (being, for example, ratios of individualrate constants). As mentioned at the beginning of this chapter, the timeresolution for the measurement of PMC transients (28–40 Gc/ps) shouldbe expected to be in the range of 25 ps.

If we assume a picosecond flash of photons to generate charge carrierpairs in an electrochemically polarized n-type semiconductor/electrolytejunction, these charge carriers will start reacting, but only the contributionof minority carriers will significantly influence the kinetic equilibrium atthe semiconductor/electrolyte interface. The majority carriers will, via theexternal circuit, immediately start to recharge the interface. However, thisprocess will be much slower than the time needed for the (independentand contact-free) PMC transient measurement. The photogenerated mi-nority carriers will reach the electrode interface with a thermal velocity ofapproximately which is a picosecond process. Afterward,surface recombination and charge transfer kinetics will determine their


consumption. Such processes should therefore be measurable on a fasttime scale and in a potential-dependent manner.

Some precautions will be needed for successful measurements. Theshorter the time scale the higher the photon densities that will be required.This leads to very high generation of excess charge carriers and tononlinear phenomena of a complicated nature.

How can such problems be counterbalanced? Since a large capaci-tance of a semiconductor/electrolyte junction will not negatively affect thePMC transient measurement, a large area electrode (nanostructured ma-terials) should be selected to decrease the effective excess charge carrierconcentration (excess carriers per surface area) in the interface. PMCtransient measurements have been performed at a sensitized nanostruc-tured TiO2 liquid junction solar cell.40 With a 10-ns laser pulse excitation,only the slow decay processes can be studied. The very fast rise timecannot be resolved, but this should be the aim of picosecond studies. Suchexperiments are being prepared in our laboratory, but using nanostructured

Figure 38. Decay of PMC transients measured with a --based nanostructured sensitiza-tion solar cell (ruthenium complex as sensitizer in the presence of 0.1 M TBAP in propylenecarbonate). The transients are significantly affected by additions of iodide.40 (a) (b) 2

(c) (d)

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ZnO instead of because ZnO provides a 220 times higher mobilityfor photoinjected electrons, which would allow reduction of the excitinglaser intensity. The slow PMC decay of -based nanostructured sensi-tization solar cells (the Ru complex as sensitizer), which cannot bematched by a single exponential curve and is influenced by a bias illumi-nation, is strongly affected by the concentration of iodide in the electrolyte(Fig. 38). On the basis of PMC transients and their dependence on theiodide concentration, a kinetic mechanism for the reaction of photoin-jected electrons could be elaborated.40

On the basis of our theoretical considerations and preliminary experi-mental work, it is hoped that fast processes of charge carriers will becomedirectly measurable in functioning photoelectrochemical cells, Typicalsemiconductor electrodes are not the only systems accessible to potential-dependent microwave transient measurements. This technique may alsobe applied to the interfacial processes of semimetals (metals with energygaps) or thin oxide or sulfide layers on ordinary metal electrodes.

VI. POTENTIAL-DEPENDENT PERIODIC MEASUREMENTS

1. Potential Modulation-Induced Microwave Reflectivity

It was indicated earlier that microwave conductivity-potential curves canbe obtained not only during a dynamic potential scan (Fig. 11) but also inphase with periodic potential modulations. These potential modulationsgive rise to MC changes that reflect changes in electronic charges in thespace charge region of the semiconductor. Such potential-modulatedsignals can be obtained both in the dark and under illumination, as shownin Fig. 39, where such measurements are presented for in contactwith a redox electrolyte.25 A full theoretical analysis of this technique andits possibilities has still to be given.

An interesting special application has been proposed by Schlichthörland Peter.31,41 It aims at deconvolution of electrochemical impedance datato separate space charge and surface capacitance contributions. Themethod relies on detection of the conductivity change in the semiconduc-tor associated with the depletion of majority carriers in the space chargeregion via potential-modulated microwave reflectivity measurements. Theelectrode samples were n-Si(111) in contact with fluoride solution.


Figure 39. Potential-modulated (derived) microwave conductivity and potential-modulated current signals as a function of the electrode potential for a dark (a)and (b) illuminated electrode in contact with a 50 mMelectrolyte solution.

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Since under normal depletion conditions, conductivity changes aredominated by majority carriers, and interfacial electron transfer can beneglected in the dark, the carrier profile can be found by solving Poisson’sequation:

where d is the thickness of the electrode sample.A linear expansion of this equation for a small-amplitude potential

modulation, leads to the microwave reflectivity change

which, when the space charge capacitance is inserted, leads to

This formula shows a linear relation between the microwave conductivitychange and the space charge capacitance If energy band unpin-ning can be neglected, the potential-modulated MC signals follow thecapacitance of the space charge layer. Good Mott–Schottky behavior istherefore found for potential-modulated MC signals, even in presence ofsurface states.31,41 The flatband potential can thus be conveniently deter-mined and the energetic distribution of surface states deconvoluted usingboth MC and electrical capacitance measurements.

2. Combination of Intensity-Modulated Photocurrent andMicrowave Spectroscopy

Relaxations in photoprocesses, which may be due to surface recombina-tion, minority carrier diffusion, or capacitive discharges, are typicallymeasured as transients of photocurrents or photoprocesses. An analysis ofsuch processes in the time domain encounters some inherent problems.

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


used to generate a sinusoidally modulated light intensity. This techniqueis based upon transformation of both the perturbing function and thetransient response into the frequency domain. Such transformations canbe performed by both Fourier and Laplace transformations. A photocur-rent transient f(t) may, for example, be transformed into the Laplace space

where s is the Laplace frequency The real axis transform isobtained by substituting and the imaginary axis by substituting s =

Complex plane plots of the transformed data can be made and inter-preted. Surface recombination has been studied in such systems as GaPand GaAs under conditions of fixed-band bending. The frequency domainstudied was 1 Hz to 50 kHz. At higher frequencies, the relaxation of thespace charge-layer capacitance with the frequency at the imaginary mini-mum corresponding to is found is the series resistance and

is the space charge-layer capacitance).44

Intensity-modulated photocurrent spectroscopy has been used incombination with microwave reflectivity measurements to investigatehydrogen evolution at a p-type silicon45 and an n-type silicon.46 Themeasurement of amplitude and phase under harmonic generation of excesscarriers, performed by Otaredian47 on silicon wafers in an attempt toseparate bulk and surface recombination, should also be mentioned here.

In contrast to photocurrent measurements, photoinduced microwaveconductivity measurements are not limited by RC time constants. Usingsufficiently high-frequency excitation sources (laser diodes or optoacous-tic modulators), it should be possible to explore much faster time or higherfrequency domains. This is an interesting challenge since fast electrodeprocesses are typically obscured by the trivial RC time constant forcapacitive discharge (see, however, Ref. 39 for a strategy to overcome theRC problem). When intensity-modulated photocurrents and PMC signalsare evaluated in the time domain, and characteristic values (e.g., themaximum frequency) measured, the corresponding mathematical formula(containing kinetic parameters) can be solved, yielding more informationthan one technique alone.

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VII. OXIDES AND SENSITIZATION CELLS

1. Potential Dependence of Interfacial Rate Constants

ZnO was the first photoactive electrode in contact with an electrolyte tobe studied by PMC techniques.5 The PMC peak in the depletion regionnear the onset of the anodic photocurrent [originally measured in a cavity(Fig. 40)] has been perfectly reproduced with a geometrically muchsimpler setup for microwave measurements (Fig. 16). In these meas-urements the PMC peak turned out to be quite narrow, in contrast totheoretical PMC peaks or PMC peaks obtained with other semiconduc-tor/electrolyte junctions (Figs. 13,14,16,18). The most evident differencebetween a theoretical PMC peak and the PMC peak of a ZnO elec-trode/electrolyte junction is the much faster decay of the signal towardhigher positive electrode potentials. This decay is, as we learned, deter-mined by the function, which describes the potential-dependentprofile of the charge carrier distribution in the space charge layer. Thisprofile somehow changes with the electrode potential in a different waythan that calculated for constant interfacial charge-transfer rates. Thereason has recently been examined.12 Equation (24) relates (for an alreadysufficiently low surface recombination the PMC signal to the photocur-rent the charge-transfer rate constant, and It can be rewrittento yield

Since the potential-dependent photocurrent and the potential-dependentPMC signal were measured and is a known function, the poten-tial-dependent interfacial rate constant can be determined. It turns outthat it increases exponentially with the electrode potential applied

which accounts for the fast decay of the PMC signal toward an increas-ingly positive potential. The explanation of this surprising result is notstraightforward, but can be narrowed down on the basis of the experimentsperformed. ZnO is a large-gap semiconductor that duringUV excitation can photo-oxidize water to molecular oxygen but alsophotocorrodes during this process. Part of the oxygen released during the


photoreaction therefore comes from the ZnO-crystal lattice. When ZnO isanodically polarized in the presence of aqueous solutions containing

KCl, or NaCOOH, as was done in the experiments that led to thesharp PMC peak, a strong electrochemical interaction has to be assumedat the ZnO/electrolyte interface during anodic electron transfer. This maybe the reason why the classic Marcus–Gerischer theory on isoenergeticinterfacial electron transfer, which predicts a largely potential-independentcharge-transfer rate (no significant shift in the energy band position isexpected), is not applicable. When an organic redox electrolyte is selected(propylene carbonate with ferrocene), which is known to interact onlyweakly with an electrode, the potential-dependent decay of the PMCsignal of ZnO toward a higher electrode potential is clearly slower12 (eventhough it is not as slow as expected from the theory on the basis ofconst). It is interesting that in presence of an organic electrolyte, the PMCsignal also increases toward negative potentials (Fig. 41).12 A shoulder isseen immediately negative from the flatband potential, which indicatesthat charge carriers in the accumulation region can be measured more

Figure 40. PMC peak measured with a ZnO single-crystalelectrode in a microwave resonator near the onset of theanodic photocurrent.5

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Figure 41. PMC potential curves for a ZnO singlecrystal measured in contact with propylene carbon-ate (0.1 M TBAP) containing 10 mM ferrocene(curve 1), and with increasing concentrations (5,10,and 20%) of water (curves 2–4). Illumination withHe-Cd UV laser. 5 mW.

accurately than in the presence of an aqueous electrolyte. Apparently, inthe presence of an organic electrolyte and of only a reduced redox species(ferrocene), excess charge carriers have an increased lifetime in theelectrode. The fact that electrons cannot easily escape from the electrodemay help to build up a larger negative charge in the interface, which maydirect positive minority carriers toward the interior of the electrode,generating larger lifetimes. This experiment seems to show how the PMCsignal is influenced by the nature of the redox electrolyte.

The reason for the exponential increase in the electron transfer ratewith increasing electrode potential at the ZnO/electrolyte interface mustbe further explored. A possible explanation is provided in a recent studyon water photoelectrolysis which describes the mechanism of wateroxidation to molecular oxygen as one of strong molecular interaction withnonisoenergetic electron transfer subject to irreversible thermodynam-ics.48 Under such conditions, the rate of electron transfer will depend onthe thermodynamic force in the semiconductor/electrolyte interface to


which the applied electrode potential may contribute. However, moretrivial explanations should be considered first. The involvement of ahypothetical potential-dependent concentration of surface states in wateroxidation could also explain the phenomenon, as visualized in Fig. 42.

This discussion has shown how useful PMC measurements are foraddressing new questions in semiconductor electrochemistry.

Marcus-Gerischer model

Figure 42. Scheme comparing expected potential-independent charge-transfer ratesfrom Marcus–Gerischer theory of interfacia) electron transfer (left) with possiblemechanisms for explaining the experimental observation of potential-dependentelectron-transfer rates (right): a potential-dependent concentration of surface states,or a charge-transfer rate that depends on the thermodynamic force (electric potentialdifference) in the interface.

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2. Nanocrystalline Dye Sensitization Cell Studied by MicrowaveTransients

Up to now only preliminary PMC measurements have been performedwith nanocrystalline sensitization solar cells based on which has avery low electron mobility. In Fig. 38 we showed transient measurementsperformed with a 10-ns laser flash. A very fast rise time is observed which,as discussed earlier, may be resolved further only by picosecond excita-tion. The decay of the PMC signal is, on the other hand, sufficiently slowto be studied. It reflects the reverse reaction of injected conduction bandelectrons with the redox electrolyte. This can be clearly demonstrated byadding iodide to the electrolyte. This reducing species slows the reversereaction significantly, which has been explained by a kinetic model.40 Thisexperiment shows that transient PMC measurements are suitable for thestudy of dye sensitization cells and electrodes of nanocrystalline materials.However, high flash photon densities are needed to see these signalsbecause of the low mobility of electrons in Even thoughexperimentsmade under such conditions can be interpreted, they limit information onpotential-dependent behavior. One solution would be to use a much moresensitive resonator cavity for measurements on based nanostructuredsensitization solar cells. Another would be to concentrate research onnanostructured sensitization cells of ZnO-based substrates, which showan approximately 220 times higher electron mobility. Both strategies arebeing investigated in our laboratory.

Preliminary measurements with space-resolved PMC techniqueshave shown that PMC images can be obtained from nanostructured dyesensitization cells. They showed a chaotic distribution of PMC intensitiesthat indicate that local inhomogeneities in the preparation of the nanos-tructured layer affect photoinduced electron injection. A comparison ofphotocurrent maps taken at different electrode potentials with correspond-ing PMC maps promises new insight into the function of this unconven-tional solar cell type.

VIII. MICROWAVE PHASE MEASUREMENTS

As mentioned at the beginning of this chapter real phase-sensitive meas-urements of electrochemical systems have not yet been performed. Notonly is the experimental technique difficult, but a reliable theory of


microwave phase shift as a function of electrochemical parameters (elec-trical fields, surface states, photoeffects, electrolytes) is missing. In anal-ogy to electrochemical impedance measurements, where thethermodynamic force, the applied potential, is modulated to measurephase shifts, in microwave conductivity measurements the microwavepower, P, which provides the microwave electrical field, has to be modu-lated to obtain phase shifts. The dependence of these phase shifts on theelectrode potential and additional parameters (e.g., light intensity) canthen be determined.

The field of phase-sensitive microwave photoelectrochemical meas-urements will have to be explored very gradually. In our laboratory up tonow only a special case, phase rotation in a magnetic field (Faradayrotation), has been investigated. It allows us to perform contact-freemobility measurements of electronic charge carriers. This may serve todetermine the sign and mobility of photogenerated charge carriers or thedependence of the mobility of charge carriers in nanostructured materialson particle size or electrical polarization.

Measurements of a pyrite sample with a two mode resonator16 yieldedthe magnetic field dependence of microwave transmission (Fig. 43) from

Figure 43. Microwave transmission in a two-mode resonator as afunction of the magnetic field strength for measurement of themicrowave Hall effect in (two measurements with an offsetdifference).16

516 H.Tributsch

which electron mobilities of and (two measure-ments, one with offset) could be derived. An electrically contacted samplefrom the same batch using conventional Hall measurement gave a mobilityof

More experience has to be gained before phase-sensitive measure-ments can be performed on the potential-dependence of electrochemicalsystems, especially because of the presence of an electrolyte. Such meas-urements may, as already mentioned, provide new information on a varietyof questions relevant for electrochemical interfaces. The separation ofphotogenerated minority carriers and majority carriers, for example,which both contribute to the PMC signal, promises interesting new in-sights into the electrochemical kinetics of semiconducting interfaces. Inparticular, the understanding of the photoelectrochemical behavior in theaccumulation region, which is accessible to PMC techniques and stillunexplored, will require a separation of majority and minority carriermechanisms. This will be possible through phase-sensitive PMC and MCmeasurements.

IX. SUMMARY AND DISCUSSION

In this chapter we have attempted to summarize and evaluate scientificinformation available in the relatively young field of microwave pho-toelectrochemistry. This discipline combines photoelectrochemical tech-niques with potential-dependent microwave conductivity measurementsand succeeds in better characterizing the behavior of photoinduced chargecarrier reactions in photoelectrochemical mechanisms. By combiningphotoelectrochemical measurements with microwave conductivity meas-urements, it is possible to obtain direct access to the measurement ofinterfacial rate constants. This is new for photoelectrochemistry andpromises better insight into the mechanisms of photogenerated chargecarriers in semiconductor electrodes.

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


is intensive, minority carriers are depleted, causing a pronounced mini-mum of the PMC signal (Fig. 45). In the accumulation region of thesemiconductor at negative potentials, minority carriers tend to drift intothe interior of the electrode and are controlled by the bulk recombination

Figure 44. Energy scheme showing essential phenomena forphotoinduced microwave conductivitymechanisms: (a) Accumu-lation of minority carriers near the onset of photocurrents in thedepletion region, (b) Drift of minority carriers into the interior ofan accumulation region, thus escaping surface recombination.

518 H. Tributsch

Figure 45. (a) Schematic of PMC signal behavior in accumula-tion region (i), flatband region (ii), and depletion region (iii) with(b) visualization of energy band situation of an n-type semicon-ductor.

lifetime [Fig. 44(b)]. This produces a PMC shoulder, the height of whichis controlled by the bulk lifetime of minority carriers and the shape ofwhich is influenced by interfacial rate constants of the electronic chargecarriers and the electric field distribution as affected by current flow. Thiscomplementary information on charge carriers, as provided by PMCmeasurement, added to photoelectrochemical information, based on asuitable theoretical formalism, is the key advantage of microwave electro-chemistry.


At present, the microwave electrochemical technique is still in itsinfancy and only exploits a portion of the experimental research possibili-ties that are provided by microwave technology. Much experience still hasto be gained with the improvement of experimental cells for microwavestudies and in the adjustment of the parameters that determine the sensi-tivity and reliability of microwave measurements. Many research possi-bilities are still unexplored, especially in the field of transient PMCmeasurements at semiconductor electrodes and in the application ofphase-sensitive microwave conductivity measurements, which may besuccessfully combined with electrochemical impedance measurementsfor a more detailed exploration of surface states and representative elec-trical circuits of semiconductor liquid junctions.

In the more distant future, integrated microwave circuits generatingintensive microwave fields above a dielectric spiral may simply be at-tached as a thin slab to the back side of a semiconductor electrode for PMCmeasurements. By selecting the appropriate geometry and by choosingoptimized geometrical forms for electrodes (ultrathin layers, nanostruc-tured materials) many compounds that are not considered to be typicalsemiconductors may also become accessible for microwave conductivitystudies; these include oxide layers on metal surfaces as well as photogen-erated charge carriers in semimetals. Even the Helmholtz layer of liquidjunctions may become accessible to potential-dependent microwave con-ductivity studies (contributions of ions and dipoles). Instead of modulatingthe light, the electrode potential can also be modulated and in this wayphotoinactive electrode materials can be investigated with microwavetechniques. Since the time resolution for microwave experiments is on theorder of 25 ps with the microwave frequencies used, very fast electro-chemical processes will become accessible for investigation.

The fact that microwave conductivity measurements can be per-formed in a contact-free manner allows us to use them for quality controlduring the production of photoactive powders or thin layers, or forelectrochemical process technology. After the buildup of sufficient knowl-edge, microwave conductivity measurements themselves, independent ofclassic electrochemical information, may be used to obtain electrochemi-cal information in cases where conventional techniques are not convenientor accessible.

Such interesting prospects should not distract us from the fact that westill have to continue to build on the foundation of this research discipline.There is sufficient room for further improvement of electrochemical PMC

520 H. Tributsch

theory, and some applications (e.g., phase-sensitive measurements asapplied to electrochemical problems) still need a theoretical basis.

Although it is still in a rudimentary stage of development, microwaveelectrochemistry has contributed some significant knowledge to semicon-ductor electrochemistry. Among the most interesting results is the detec-tion of charge carrier accumulation in the depletion region near the onsetof photocurrents, access to a quantitative determination of interfacialcharge-transfer and recombination rates, the measurement of surfaceconcentrations of minority carriers, access to the measurement of minoritycarriers in the accumulation region of semiconductors (where typically nophotocurrents are observed), and access to ultrafast photoelectrochemicalmechanisms. Interesting information has also been obtained on the behav-ior of charge carriers within the space charge region as measured by thepotential dependent decay of the PMC signal in the limiting photocurrentrange. Microwave photoelectrochemistry has also provided a series oftechniques for the measurement of electrode parameters (e.g., flatbandpotentials, diffusion lengths, energetic distribution of surface states) andmay lead to reliable techniques for the separation of bulk and surfacerecombination lifetimes of minority carriers.

When more experience is gained on microwave electrochemicalphenomena, they could, for example, be used to characterize electro-chemical systems in a contact-free way. The PMC signal alone coulddescribe the system sufficiently for understanding its behavior. An inter-esting application would then be fast electrochemical sensors that, whileimplanted or separated by a glass diaphragm, could be scanned andevaluated without electrical contacts.

It is hoped that additional research groups will join in the developmentof microwave electrochemistry.

ACKNOWLEDGMENTS

The author would like to acknowledge the valuable experimental andtheoretical contributions of various collaborators during the developmentof the research technique described here. Among them are M. Kunst, D.Messer, G. Schlichthörl, D. Jokisch, F. Wünsch, A. M. Chaparro, and H.Schulenburg. Additional thanks are due to Mr. D. Jokisch for his help inpreparing the drawings and to Dr. F. Wünsch for proofreading and discuss-ing the manuscript.


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