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Theory of Charge Transport in the Illuminated Semiconductor/Liquid Junctions

Written By

Peter Cendula

Reviewed: February 4th, 2022 Published: March 12th, 2022

DOI: 10.5772/intechopen.103049

IntechOpen
New Advances in Semiconductors Edited by Alberto Adriano Cavalheiro

From the Edited Volume

New Advances in Semiconductors [Working Title]

Dr. Alberto Adriano Cavalheiro

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Abstract

The field of photoelectrochemical (PEC) cells for solar water splitting or CO2 reduction has attracted intense attention of many research groups in last 15 years. Nevertheless, a cost-effective and efficient PEC cell for hydrogen production in the large scale was not yet discovered. The core functionality of the PEC cell is provided by the semiconductor/liquid junction, creating the electrostatic field to separate the photogenerated charges. This work aims to be a starting point for a newcomer in the field providing a compact knowledge about the charge transport and electrochemistry fundamentals in semiconductor/liquid junctions in the steady state. We describe charge transport within the semiconductor and electron transfer between the semiconductor and electrolyte, followed by the effect of illumination and charge recombination on charge transport. Finally, we discuss the effects due to surface trap states and the relation of the theoretical expressions and experimental results.

Keywords

  • semiconductor
  • electrolyte
  • redox
  • solar energy
  • photoelectrochemical
  • hydrogen

1. Introduction

The transition to renewable energy sources is recognized as one of the greatest societal challenges of the twenty-first century, and it will have a major impact on climate, environment, and economy [1]. The major bottleneck for broader utilization of renewable energy is missing large-scale and long-term energy storage technologies [2, 3]. In this respect, fossil fuels make up 85% of the worldwide energy consumption, and they have an order of magnitude higher energy density than lithium-ion batteries [4]. Hence, to replace fossil fuels and also enable a low-carbon economy in the long term, an alternative route to produce fuels exclusively from the renewable resources is sought for.

In the last two decades, a lot of research effort was given to produce renewable fuels from solar energy and/or CO2 [5, 6, 7]. Hydrogen is one of the leading renewable fuels with important impact on a variety of industrial processes [8, 9], and European Union recognized its importance in 2020 and put an ambitious “Hydrogen Strategy for Climate-Neutral Europe” (https://ec.europa.eu/energy/sites/ener/files/hydrogen_strategy.pdf). From the variety of approaches for the renewable hydrogen production [6], great research activity is given to the photoelectrochemical (PEC) hydrogen production. For overview of the PEC water splitting principles, material requirements, characterization methods, and device architectures, we suggest the recent handbooks [10, 11, 12].

This chapter discusses theory related to the core functionality of the PEC hydrogen production or PEC CO2 reduction, which lies in the separation of the photogenerated charges by the electric field created by the semiconductor/electrolyte interface. The physical processes at the typical n-type photoanode/electrolyte junction in the alkaline electrolyte are shown in Figure 1a. When a semiconductor is immersed in a solution, a charge transfer occurs at the interface because of the difference in the electrochemical potential of the two phases, creating a built-in electrostatic field, which separates electronic charges. When the light is absorbed in the semiconductor, it excites electrons and holes to their respective bands, and these are separated by the built-in electrostatic field. Holes move to the electrolyte, consuming OH, and oxidize water to oxygen. Electrons move away from the electrolyte and are sent through the external wire to the metal counterelectrode with an additional bias voltage, where they reduce water to hydrogen and OH. The exchange of OH between the photoanode and the counterelectrode is completed by ion migration in the electrolyte. Although with intensive research efforts, a single semiconductor material being able to do overall PEC water splitting (two half-reactions) has not yet been identified.

Figure 1.

(a) Schematic diagram of processes in the photoanode during three-electrode investigation for water splitting in alkaline electrolyte. (b) Sketch of the tandem PEC cell with large-bandgap photoanode and small-bandgap photocathode connected via an ohmic contact.

Therefore, a natural strategy is to distribute the two half-reactions to two semiconductor photoelectrodes (similar to Z-scheme in natural photosynthesis) [13], where wider-bandgap n-type semiconductor photoanode (1.8–2.4 eV) drives oxygen evolution reaction, and a smaller-bandgap semiconductor photocathode (1.0–1.5 eV) placed behind it drives hydrogen evolution reaction, Figure 1b. Such tandem configuration makes optimum usage of the full solar spectrum, leading to higher efficiencies and a better ability to cope with the fluctuating illumination conditions.

The PEC hydrogen production is currently at the lab scale and has the potential to compete if solar-to-hydrogen (STH) efficiencies over 10–15% and stability for over 10 years are considered [14, 15]. The highest reported STH efficiencies for PEC water splitting, Figure 2, are 14–19% for III–V tandems [16, 17], 10–14% for silicon-based multijunctions [18], and 1–3% for oxide-based devices [13].

Figure 2.

Reported STH efficiencies as a function of year and sorted by the number of tandem photovoltaic junctions used (2 or 3). The fill color represents the semiconductor materials used in the photovoltaic portion of the device. All STH conversion efficiencies are as reported in the original publications. Reprinted with the permission from the Royal Society of Chemistry [13].

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2. Semiconductor/liquid junction

When semiconductor is immersed in liquid electrolyte containing a redox couple, electron transfer between occupied (empty) state in the semiconductor and empty (occupied) state of the ion species in the solution is possible, respectively. This charge transfer will continue until an equilibrium is reached when Fermi level of the semiconductor EFequals to the redox Fermi level in the electrolyte Eredox. Band edge positions of some semiconductors with respect to the redox potentials for water splitting are shown in Figure 3. Under equilibrium conditions, semiconductor region close to semiconductor/electrolyte interface (SEI) is depleted of the majority carriers, which is counterbalanced by the ions adsorbed at the semiconductor from the electrolyte side.

Figure 3.

Band edge positions of various semiconductors at pH = 0 (conduction band is shown in red, valence band in black). Voltage is reported with respect RHE and redox potentials of water splitting are shown as dashed lines. Bandgap energy is shown below the valence band position.

We start by describing the charge transfer in the semiconductor in the semiclassical approach. The resulting electrostatic potential ϕx, electron and hole concentrations nx,pxin the semiconductor can be calculated by solving the Poisson equation together with the carrier continuity equations

d2ϕdx2=ρxε0εr,E1
1qdjedx=GxRx,E2
1qdjhdx=GxRx,E3

where ρx=qNDnx+pxis the charge density, NDis the concentration of the ionized donors for n-type semiconductor (full ionization is assumed), and ε0,εrdenote permittivity of vacuum and relative permittivity of the semiconductor. The generation rate of the carriers is labeled Gxand the recombination rate Rx. The electron and hole currents are given by the drift and diffusion terms

je=qDednxdxqμenxdϕxdxE4

and

jh=qDhdpxdxqμhpxdϕxdx,E5

where electron and hole mobility are denoted μe,μh.

Usually, a space charge region (SCR) approximation is used to solve the stand-alone Poisson equation (without continuity equations), Figure 4, by assuming that a constant charge density exists in the SCR of width w

Figure 4.

(a) Energy diagram of stand-alone semiconductor and electrolyte, before contacting them. (b) Energy diagram of semiconductor and electrolyte after contact and application of voltageVawith respect to reversible hydrogen electrodeE0,RHE.

ρx=qND,0<x<wE6

and zero charge density exists outside of the SCR. The boundary condition of the vanishing electrostatic field at the edge of SCR gives dϕdxw=0, and furthermore, we choose arbitrary value ϕw=0. In this way, the Poisson equation is integrated to give ϕxinside SCR

ϕx=qND2ε0εrwx2.E7

The width of the SCR is given by

w=2ε0εrVscqND.E8

The potential drop in the SCR region can be altered by applying the voltage Vato the semiconductor back contact

Vsc=VaVfb,E9

where for the flatband voltage Va=Vfb, the bands of the semiconductor become flat and Vsc=0. The semiconductor energy bands remain usually pinned at the interface to the electrolyte (with or without redox couple) as measured by the impedance spectroscopy [19], and this is also valid for ϕx, Eq. (7). Therefore, position of the semiconductor band edges can be given on the traditional electrochemical energy scale, for example, relative to the reversible hydrogen electrode (RHE) [20]. Due to strong interaction of semiconductors with water in aqueous elecrolytes, applying the voltage bias to the semiconductor leads only to the change of the electrostatic potential across the space charge layer Vsc(the potential across the Helmholtz double layer remains constant). The energies of the conduction band and valence band Ecb,Evbare given by

Ecbx=χx,Evbx=EcbxEg,E10

and the quasi-Fermi level of electrons and holes EFn,EFp

EFn=Ecb+kTlnnNc,EFp=EvbkTlnpNv,E11

where the electron affinity is labeled χ, symbol kdenotes the Boltzmann constant, Tis the absolute temperature. We remark that in our discussion, no electronic states at the surface of the semiconductor are assumed for simplicity. The electron and hole concentrations at the SEI, nsand ps, are given by the Boltzmann distribution

ns=n0expqVsckTE12

and

ps=p0exp+qVsckT.E13

The equilibrium electron (hole) concentration is denoted as n0(p0). The equilibrium hole concentration p0is given by the expression

p0=NcNvexpEgkTND,E14

where the effective densities of states in the CB and VB are denoted Ncand Nvand the bandgap energy is Eg.

2.1 In the dark

Turning now our attention to the redox couple, the energy values of Red(Ox) species in the solution Ered,Eoxcan be described with the solvation state model introduced by Gerischer [21]. Redox couple is a pair of two ions (Redis the reduced species, Oxis the oxidized species), which can interchange electrons

Rede>OxE15

The Nernst equation describes the electrochemical potential of electrons in the redox couple, which is equivalent to the Fermi level of the redox couple Eredoxwhen the same reference is used for the semiconductor and redox system [22].

Eredox=Eredox0+kTlncoxcred,E16

where the reference redox level is denoted Eredox0, and cred,coxare the concentrations of the RedOxspecies. Herein, we assume weak interaction of the semiconductor with the redox couple and equal concentrations of Redand Oxspecies. The addition (removal) of an electron to (from) the Ox(Red) species is accompanied by the increase (decrease) of the energy equal to the reorganization energy λ(typically around 1 eV). Taking into account the rotation and motion of the solvent ions, probability distributions Wox,Wredof the energy states around the mean values Eox,Eredare obtained and shown in Figure 5

Figure 5.

N-type semiconductor in contact with a redox couple in the electrolyte withEredoxclose toEF. (a) Energy diagram along with distribution of the occupied states in the electrolyte (painted in green color). The conduction (valence) band energy is denotedEcb,Evb, and the Fermi energy is labeledEF. (b) The current-voltage curves in the logarithmic scale for parametersjv0=1mA/cm2andjc0=100mA/cm2. The negative currents were shown with a positive value in the logarithmic plot.

WoxE=W0expEEredox+λ24kTλ,E17
WredE=W0expEEredoxλ24kTλ,E18

where W0=4kTλ1/2is a constant to provide unit integrated probability over the whole energy spectrum. If Eredoxis closer to the conduction (valence) band edge of the semiconductor, electron exchange between the conduction (valence) band and redox couple is energetically preferred, which is a consequence of small loss of electron energy when both energy states have similar energy. The energy distribution functions are proportional to the concentration of the respective species and probability distribution

Dox=coxWox,E19
Dred=credWred.E20

The rate of electron transfer from the semiconductor to the electrolyte is given by the integral of the probability of the transition between these quantum states over all electron energies

EfEρEDoxEdE,E21

where fEdenotes the Fermi function in the semiconductor, ρEdenotes the energy distribution in the semiconductor, and WoxEis the distribution of empty states in the electrolyte. For the electron transfer from the conduction band to the electrolyte (cathodic current, superscript-), the latter expression becomes

jc=qcoxEcnsexpEEredox+λ24kTλ,E22

with the electron concentration at the semiconductor-electrolyte interface ns. Typically, by assuming a small overlap of the energy states in the semiconductor and electrolyte (within 1kTof the conduction band), the latter integral is simplified to

jc=qkcnscox,E23

with kcis the rate constant containing the exponential term (potential independent), and qis the electronic charge. The current jc+corresponding to the opposite process of the electron transfer from the electrolyte to the semiconductor (anodic current, superscript +) is calculated similarly

jc+=qkc+Nccred,E24

where we have used that the density of empty states in semiconductor equals NC, and the distribution of the occupied states is now proportional to cred.

In a similar way, the cathodic current from the valence band is potential-independent

jv=qkvNvcoxE25

whereas the anodic current from the valence band depends on the potential through ps

jv+=qkv+pscred.E26

Further simplification of the expressions for currents is derived by considering the balanced equilibrium charge transfer with the equilibrium conduction band current jc0

jc+=jc=jc0,E27

and equilibrium valence band current jv0

jv+=jv=jv0.E28

In equilibrium ns=ns0, ps=ps0. Henceforth, the net current through the conduction band from the semiconductor to the electrolyte is obtained by subtracting the cathodic current from the anodic current

jc=jc+jc=jc0nsns01=jc0expqVsckT1E29

and accordingly

jv=jv+jv=jv0psps01=jv0expqVsckT1E30

Our notation is compatible with the traditional electrochemical notation of the positive anodic current and the negative cathodic current, Figure 5c. We remark, however, that the conduction or valence band current is positive (negative) for the cathodic (anodic) bias voltage.

To illustrate the profile of the current-voltage curves, we have taken a small jv0and large jc0, which is expected for Eredoxpositioned close to the conduction band of n-type semiconductor. For a positive voltage (reverse bias voltage), the anodic current jc+of electrons from electrolyte to the conduction band is approximately constant. For the increasing negative voltage (forward bias voltage), more electrons (majority carriers) become available, and hence, the cathodic current jcof electrons from the conduction band to the electrolyte rises exponentially (rectification). The valence band currents are much smaller in magnitude and follow an exponential rise of jv+for the reverse bias and a constant value of jvfor the forward bias (opposite trend as compared with the conduction band current). Generally, a redox reaction at the semiconductor-eletrolyte interface can either receive electrons from the semiconductor or send electrons to the semiconductor. Electrons are majority (minority) carriers in the n-type (p-type) semiconductor, respectively, and hence, the situation with the relative magnitude of the currents across the interface becomes interesting when minority carriers are created by light excitation and can completely alter the current-voltage behavior. The total current at the semiconductor electrode with the Tafel slope 60 mV/dec

j=jc+jv=jc0expqVsckT1+jv0expqVsckT1.E31

partially resembles the Butler-Volmer equation for the current at the metal electrode with Tafel slope 120 mV/dec

j=j0expqV2kTexpqV2kT.E32

The difference between the metal and semiconductor current is caused by the potential drop falling over the Helmholtz layer in the metal, while the potential drops over SCR in the semiconductor. Furthermore, the exchange current density is much smaller for the semiconductor than for a metal since metals have much higher density of states near Fermi level than semiconductors.

For the n-type semiconductor and electrons (majority carriers) being transferred from the electrolyte to the semiconductor, it is usually described in the literature that holes (minority carriers) are transported from the semiconductor to the electrolyte and minority carrier reaction proceeds at the interface. In this situation, the anodic current is dominated by jv+since jcis essentially constant (due to a constant number of the empty states in the conduction band NC).

If electrons (majority carriers for n-type) are transferred from the n-type semiconductor to the electrolyte, it is usually termed majority carrier reaction, and hence, the cathodic current is dominated by jcsince jvis essentially constant (due to a constant number of occupied states in the valence band NV).

2.2 Upon illumination

In the preceding section, we presented anodic and cathodic current exchange with the electrolyte in the dark, and we neglected the carrier recombination. Magnitude of the first-order recombination is governed by the population of very few available minority carriers. Additionally, population of the minorites cannot be altered by the voltage bias, as only majority carriers can be injected by the voltage bias [23].

When a light of sufficient energy strikes the semiconductor, the generated electron-hole pairs contribute to the electron exchange with the redox couple or recombine. Due to carrier recombination, the currents calculated in the preceding section cannot be used without further considerations. Here we sketch the development due to Reichman [24], which is instructive but simple enough for tractability. The total current under illumination is composed of the conduction band and valence band currents

j=jc+jv.E33

The conduction band current, Eq. (30), remains the same under illumination as the electron population is not substantially altered upon illumination. The valence band current, Eq. (30), holds when the hole concentration at the surface psis calculated under illumination

jv=jv0psps01.E34

To obtain ps, it is assumed that quasi-equilibrium of holes is valid even under illumination

px=pwexp+qVsckTE35

and the stand-alone hole continuity equation, Eq. (3), is solved in the neutral region of the semiconductor, where electric field can be neglected. This simplification leads to the diffusion equation valid when hole diffusion length Lhis much smaller than the neutral region thickness

Dhd2pdx2pp0τh+I0αexpαx=0.E36

The hole diffusion constant is written as Dh, hole recombination lifetime τh(first-order recombination), absorption coefficient α, and incoming monochromatic photon flux from the electrolyte side I0(assuming Lambert-Beer conditions). The analytic solution with the boundary conditions p=p0and pw=pwis

p=p0+αI0τhexpαx1α2Lh2+Kexpx/Lh,E37

where Lh2=Dhτhand the constant K

K=expw/Lhpwp0αI0τhexpαw1α2Lh2.E38

The diffusion current at the edge of the neutral region x=wis

jdiff=j0pwp01+qI0αLhexpαw1+αLh,E39

with the saturation current density denoted j0=qp0DhLh.

In the space-charge region, we simply assume all photogenerated charges are separated by the electric field of the SEI, and there is no recombination, hence, the hole current to the electrolyte is

jsc=qI01expαw.E40

The valence band current is then sum of the currents in the neutral and the space-charge region for both anodic and cathodic bias voltage

jv=jdiff+jsc=jgj0expqVsckT1+j0jv0expqVsckT.E41

The term

jg=j0+qI01expαw1+αLhE42

represents the generation current. We remark that the Gartner photocurrent jGcorresponds to the second term in the last equation

jG=qI01expαw1+αLhE43

and was derived by assuming the ideal collection of holes within the SCR, no recombination in SCR and pw=0[25]. The photocurrent onset voltage for Gartner equation overlaps with the flatband voltage Vfbof the SEI, Figure 6b. There are two current constants j0,jv0in Reichman photocurrent Eq. (41), which govern the profile of JV curve.

Figure 6.

(a) Schematic of the illuminated SEI. (b)–(d) Current-voltageEq. (41)for baseline parameters inTable 1and several values ofjv0=1015,1012,109mA/cm2 (direction of arrow, placed at the corresponding critical voltageVc) in (b) linear plot and (c) semi-logarithmic plot and (d) in the dark (without illumination). For the cathodic (negative) bias voltage, sign of the current is reversed to enable plot in the semilogarithmic scale.

ParameterValueDescription
Eg(eV)1.2Bandgap energy
εr10Relative permittivity
ND(cm−3)1017Donor concentration
Nc(cm−3)1020Effective density of states in CB
Nv(cm−3)1020Effective density of states in CB
L(nm)100Semiconductor thickness
α(cm−1)103Absorption coefficient of the semiconductor
Lh(nm)10Hole diffusion length
τh(ps)1Hole recombination lifetime
I0(cm−2/s)51016Incoming monochromatic photon flux
Vfb(V vs. RHE)0Flatband voltage

Table 1.

Baseline material properties of the N-type semiconductor photoelectrode used in this chapter.

Without illumination (I0=0), the Reichman dark current includes recombination in neutral region and equals

jvdark=j0j0expqVsckT1+j0jv0expqVsckT.E44

Photocurrent jvhas onset delayed more anodic with respect to Gartner photocurrent jGfor decreasing (slower) rate of hole transfer to electrolyte jv0, see linear-scale current-voltage plot, Figure 6a. This is expected behavior as holes queue at SEI due to their slow transfer to electrolyte. For large anodic bias, Reichman photocurrent jvapproaches Gartner photocurrent jGas recombination becomes the limiting process. Under large anodic bias voltage (Vsc>0), the dark current approaches value j0and the photocurrent reaches jG, Figure 6. Under large cathodic bias voltage (Vsc<0), both dark current and photocurrent approach jv0.

For intermediate anodic bias voltage, both the dark current and photocurrent scale as expqVsckT(Tafel slope 60 mV/dec) and minority carrier recombination and transfer govern the kinetics similar to the pn-junction or semiconductor/metal contact. The range of the intermediate anodic bias (0<Vsc<Vc) with approximate slope 60 mV/dec increases with the decreasing value of jv0(rate of hole current transfer at the SEI). The critical voltage bias Vccan be derived from the condition that the terms in the denominator become equal and is given by [26, 27].

Vc=kTqlnj0jv0.E45

For baseline parameters and jv0=1015,1012,109mA/cm2, we get Vc=0.49,0.31,0.13V, and these correspond well with plots in Figure 6.

For completeness, we remark that SCR recombination can be easily incorporated in the treatment of Reichman, whereas we decided not to include this term in our plots [24]. The recombination current in the SCR is

jscR=Qpsps0,E46

where these expressions are used

Q=πkTniwexpqVsc2kT4τhVsc,E47
psps0=Q+Q2+4UW2U,E48
U=jv0+j0expqVsckT,E49
W=jv0+jG.E50

For very large jv0, the cathodic current can be diffusion-controlled, and we do not discuss this point here. Around the flatband voltage, the conduction band current, Eq. (30), might dominate the total current due to dark conduction band current, Figure 5b. The presence of bulk trap states in the semiconductor [23] or catalyst layer on the semiconductor [28, 29] was recently treated in model systems, while these are not considered herein.

The relation of the theoretical and measured photocurrent-voltage curves is discussed next. The conditions assumed for the Gartner photocurrent (fast electron transfer to the electrolyte, negligible recombination in the SCR or at the surface) are valid for high-quality semiconductors such as silicon, GaAs, GaP, Figure 7a, and the measured photocurrent onset voltage for GaP is 0.1 V larger than the flatband voltage (which marks the onset voltage of the Gartner photocurrent). This is not the case for most metal oxide photoelectrodes with short diffusion length of minority carriers and slow electron transfer to electrolyte. Taking iron oxide Fe2O3 as an example, measured photocurrent onset voltage is 0.4 V or more anodic of the flatband voltage, and the photocurrent rises slowly in the beginning (so called S-shape) in contrast to the steep rise predicted by the Gartner equation, Figure 7b. Some efforts lead to reproducing of the photocurrent S-shape by considering the surface recombination [32], but in general, spectroscopic methods are needed to provide an additional evidence for the correctness of the model and the extracted parameters from the photocurrent response.

Figure 7.

(a) Measured photocurrent-voltage curves (green color) for p-GaP in 0.5 mol H2SO4 recorded for the low-level monochromatic illumination at fixed wavelengths, the data were taken from [30]. We remark that voltage is measured against the saturated calomel electrode (SCE), and negative voltage is to the right. The Gartner photocurrent is shown in dashed black line. (b) Photocurrent-voltage curve for n-Fe2O3 (hematite) in NaOH solution and simulated AM1.5G illumination, the data were taken from [31]. The corresponding Gartner photocurrent is shown in dashed black line.

The complications that arise due to recombination in the surface states were treated by several studies [32, 33, 34, 35], and here we briefly outline theory by Peter [36, 37]. For the surface trap at the SEI with concentration Nslocated Esabove the Fermi level of the bulk semiconductor, the trap occupancy in the dark is

f0=11+expEsqVsckTE51

and the trap occupancy under illumination is

f=BB24AC2A,E52

where constants A,B,Care

A=knkpnsNs2,B=knNsjGA1+f0k0kpnsNsE53

and

C=knNsjG+Af0+k0kpnsf0.E54

Henceforth, the photocurrent voltage is described by the relation

js=jGqknnsNsff0.E55

For the increasing concentration of the surface states, the photocurrent rises steeply as the surface state occupation reaches unity when the Fermi level of the semiconductor moves through the surface state energy level, Figure 8a.

Figure 8.

(a) Photocurrent-voltage curves for surface recombination via surface state locatedEs=0.3 eV above the bulk Fermi level andNs=1011,1012,1014cm−2. (b) Potential drop in the Helmholtz layer for the sameNsas in (a).

The charging of the surface states influences the distribution of electrostatic potential in the semiconductor. The potential drop in the Helmholtz layer can be written as

δVH=qNs1f0CH,E56

when the vacant surface state is assumed to carry a positive charge, and CHis the capacitance of the Helmholtz layer. The increasing surface state concentration leads to more band-edge unpinning shown as flattening in Figure 8b.

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3. Conclusions

This chapter provided introduction to the topic of charge transport in the dark and illuminated semiconductor/liquid junction in order to understand behavior of the ideal SEI. The level to which real semiconductor electrodes mimic such ideal SEI can be very broad. First, we introduced basic considerations of the semiclassical charge transport equations in the semiconductor. Second, the interaction of the semiconductor with redox system in the electrolyte was described, along with the energetics of the electron transfer between semiconductor and redox system. Third, the importance of recombination kinetics in the semiconductor was considered upon illumination, and classical photocurrent formulas due to Gartner and Reichman were discussed. Finally, the effect of surface state occupancy on the photocurrent-voltage curves was described.

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Acknowledgments

Funding for this work was partially covered by grant of APVV-20-0528.

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Conflict of interest

The authors declare no conflict of interest.

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Written By

Peter Cendula

Reviewed: February 4th, 2022 Published: March 12th, 2022