Fundamentals of semiconductor electrochemistry and photoelectrochemistry, science
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//-->11Fundamentals of SemiconductorElectrochemistry andPhotoelectrochemistryKrishnan RajeshwarThe University of Texas at Arlington, Arlington, Texas1.11.21.31.3.11.3.21.3.31.3.41.41.4.11.4.21.4.31.51.5.11.5.21.5.31.5.41.5.51.61.71.7.11.7.21.7.31.7.41.7.5Introduction and Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Electron Energy Levels in Semiconductors and Energy Band Model.The Semiconductor–Electrolyte Interface at Equilibrium. . . . . . . .The Equilibration Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Depletion Layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mapping of the Semiconductor Band-edge Positions Relative toSolution Redox Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Surface States and Other Complications. . . . . . . . . . . . . . . . . . .Charge Transfer Processes in the Dark. . . . . . . . . . . . . . . . . . . .Current-potential Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . .Dark Processes Mediated by Surface States or by Space Charge LayerRecombination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Rate-limiting Steps in Charge Transfer Processes in the Dark. . . . .Light Absorption by the Semiconductor Electrode and CarrierCollection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Light Absorption and Carrier Generation. . . . . . . . . . . . . . . . . . .Carrier Collection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Photocurrent-potential Behavior. . . . . . . . . . . . . . . . . . . . . . . . .Dynamics of Photoinduced Charge Transfer. . . . . . . . . . . . . . . . .Hot Carrier Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multielectron Photoprocesses. . . . . . . . . . . . . . . . . . . . . . . . . .Nanocrystalline Semiconductor Films and Size Quantization. . . . .Introductory Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Nanocrystalline Film–Electrolyte Interface and Charge StorageBehavior in the Dark. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Photoexcitation and Carrier Collection: Steady State Behavior. . . . .Photoexcitation and Carrier Collection: Dynamic Behavior. . . . . . .Size Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .348891115161620232525252933343436363638404121 Fundamentals of Semiconductor Electrochemistry and Photoelectrochemistry1.81.8.11.8.21.91.10Chemically Modified Semiconductor–Electrolyte InterfacesSingle Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Nanocrystalline Semiconductor Films and Composites. . .Types of Photoelectrochemical Devices. . . . . . . . . . . . . .Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................................4141434446474731.1Introduction and ScopeThe study of semiconductor–electrolyteinterfaces has both fundamental and prac-tical incentives. These interfaces have in-teresting similarities and differences withtheir semiconductor–metal (or metal ox-ide) and metal–electrolyte counterparts.Thus, approaches to garnering a funda-mental understanding of these interfaceshave stemmed from both electrochem-istry and solid-state physics perspectivesand have proven to be equally fruit-ful. On the other hand, this knowl-edge base in turn impacts many tech-nologies, including microelectronics, en-vironmental remediation, sensors, so-lar cells, and energy storage. Some ofthese are discussed elsewhere in thisvolume.It is instructive to first examine thehistorical evolution of this field. Earlywork in the fifties and sixties undoubt-edly was motivated by application pos-sibilities in electronics and came onthe heels of discovery of the first tran-sistor. Electron transfer theories werealso rapidly evolving during this pe-riod, starting from homogeneous systemsto heterogeneous metal-electrolyte inter-faces leading, in turn, to semiconductor-electrolyte junctions. The 1973 oil embargoand the ensuing energy crisis causeda dramatic spurt in studies on semi-conductor–electrolyte interfaces once theenergy conversion possibilities of the lat-ter were realized. Subsequent progressat both fundamental and applied lev-els in the late eighties and nineties hasbeen more gradual and sustained. Muchof this later research has been spurredby technological applicability in envi-ronmental remediation scenarios. Veryrecently, however, renewed interest inclean energy sources that are nonfos-sil in origin, has provided new impetusto the study of semiconductor–electrolyteinterfaces. As we also learn to un-derstand and manipulate these inter-faces at an increasingly finer (atomic)level, new microelectronics applicationpossibilities may emerge, thus complet-ing the cycle that first began in the1950s.The ensuing discussion of the progressthat has been made in this field mainlyhinges on studies that have appeared sinceabout 1990. Several review articles andchapters have appeared since then thatdeal with semiconductor–electrolyte in-terfaces [1–10]; aspects related to electrontransfer are featured in several of these.This author is also aware of at least threebooks/monographs/proceedings volumesthat have appeared since 1990 [11–13]. The41 Fundamentals of Semiconductor Electrochemistry and Photoelectrochemistryreader is referred to the many authorita-tive accounts that exist before this timeframe for a thorough coverage of detailson semiconductor–electrolyte interfacesin general. Entry to this early literaturemay be found in the references citedearlier. In some instances, however, thediscussion that follows necessarily delvesinto research dating back to the 1970s and1980s.To facilitate a self-contained descrip-tion, we will start with well-establishedaspects related to the semiconductor en-ergy band model and the electrostat-ics at semiconductor–electrolyte inter-faces in the ‘‘dark’’. We shall thenexamine the processes of light ab-sorption, electron-hole generation, andcharge separation at these interfaces.The steady state and dynamic aspectsof charge transfer are then briefly con-sidered. Nanocrystalline semiconductorfilms and size quantization are thendiscussed as are issues related to elec-tron transfer across chemically modi-fied semiconductor–electrolyte interfaces.Finally, we shall introduce the vari-ous types of photoelectrochemical devicesranging from regenerative and photo-electrolysis cells to dye-sensitized solarcells.1.2electrons (e.g. Al with [Ne]3s23p1) will havea partially occupied frontier band in whichthe electrons are delocalized. On the otherhand, a solid with an even number of va-lence electrons (e.g. Si having an electronconfiguration of [Ne]3s22p2) will have afully occupied frontier band (termed a va-lence band, (VB)). The situation for Si isschematized in Fig. 1.As Fig. 2 illustrates, the distinctionbetween semiconductors and insulatorsis rather arbitrary and resides with themagnitude of the energy band gap (Eg)between the filled and vacant bands.Semiconductors typically haveEgin the1 eV–4 eV range (Table 1). The vacantfrontier band is termed a conduction band,(CB) (Fig. 2). We shall see later thatEghas an important bearing on the opticalresponse of a semiconductor.For high density electron ensemblessuch as valence electrons in metals, Fermistatistics is applicable. In a thermodynamicsense, the Fermi level,EF(defined at 0 KTab. 1Some elemental and compoundsemiconductors for photoelectrochemicalapplicationsConductivitytype(s)Opticalband gapenergy [eV]a1.111.422.261.352.421.701.503.00(rutile)3.2(anatase)3.35Semi-conductorElectron Energy Levels in Semiconductorsand Energy Band ModelUnlike in molecular systems, semiconduc-tor energy levels are so dense that theyform, instead of discrete molecular or-bital energy levels, broad energy bands.Consider a solid composed ofNatoms.Its frontier band will have 2N energyeigenstates, each with an occupancy oftwo electrons of paired spin. Thus, a solidhaving atoms with odd number of valenceSiGaAsGaPInPCdSCdSeCdTeTiO2ZnOaThen, pn, pn, pn, pnnn, pnnvalues quoted are for the bulksemiconductor. The gap energies increase in thesize quantization regime (see Sect. 7).1.2 Electron Energy Levels in Semiconductors and Energy Band Model4 N states0 electrons6 N electrons2 N states3p5Electron energyEg4 N states4 N electrons3s2 N states2 N electronsroDistanceFig. 1Schematic illustration of how energy bands insemiconductors evolve from discrete atomic states for the specificexample of silicon.Relative disposition ofthe CB and VB for a semi-conductor (a) and an insu-lator (b).Egis the optical bandgap energy.Fig. 2CBCBEgEgVB(a)(b)VBas the energy at which the probabilityof finding an electron is 1/2) can beregarded as the electrochemical potentialof the electron in a particular phase (inthis case, a solid). Thus, all electronicenergy levels belowEFare occupiedand those aboveEFare likely to beempty.Electrons in semiconductors may beregarded as low-density particle ensemblessuch that their occupancy in the valenceand CBs may beapproximatedby the
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