Homework

Group assignment: “Determine the quasi-Fermi levels of n-ZnO in a given system under conditions (1) in dark and (II) under illumination. Please use at least 3 different methods and justify them.”

Maximum 5 members in each group. Please submit your group report by next tutorial. We will have group discussion in the tutorial session.

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Photoelectrochemical Cell (I)

Lecture 9

References:1. Physics of Solar Cells. Jenny Nelson. Imperial College Press, 2003.2. Series on Photoconversion of Solar Energy, Volume 3: Nanostructured

and Photoelectrochemical Systems for Solar Photon Conversion. Mary D. Archer, Arthur J. Nozik. Imperial College Press, 2008.

3. Encyclopedia of Electrochemistry, Volume 6: Semiconductor Electrodes and Photoelectrochemistry. Allen J. Bard, Martin Stratmann, Stuart Licht. Wily-VCH, 2002.

4. Wikipedia (http://en.wikipedia.org/wiki/Main_Page).

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Historical Evolution of PEC Cell

In the 1950s and 1960s, early work was motivated by application possibilities in electronics. Electron transfer theories were also rapidly evolving during this period, starting from homogeneous systems to heterogeneous metal-electrolyte interfaces leading, in turn, to semiconductor-electrolyte junctions.

In the 1970s, the energy crisis caused a dramatic spurt in studies on PEC cell once its energy conversion possibilities were realized.In the late 1980s and 1990s, subsequent progress at both fundamental and applied levels has been more gradual and sustained.Very recently, renewed interest in clean energy sources has provided new impetus to the study of PEC cells.

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Semiconductor-Electrolyte Interface

χΦ + -

+-

4

(a) charge distribution, (b) charge-density distribution, (c) potential distribution, and (d) band bending at an n-type semiconductor–electrolyte interface under an ideal condition that neither surface charge nor surface dipole is present at the semiconductor.

Semiconductor-Electrolyte Interface

5

(a) charge distribution (b) charge-density distribution, (c) potential distribution, and (d) band bending at the semiconductor–electrolyte interface under a condition that negative surface charges are present.

Semiconductor-Electrolyte Interface

6

For a simple one-step redox couple, the electrochemical potential of electrons is given by the Nernst equation

€

µ e,redox = µ redoxo + kT ln aox

ared

⎛

⎝ ⎜

⎞

⎠ ⎟

At vacuum energy scale, the electrochemical potential of electrons in a redox system is equivalent to the Fermi level

€

µ e,redox = EF ,redox

UERef

Potential

SC

Φscr

ΦH

electrolyte

The absolute energy scale is related to the redox potential on the SHE scale by

€

EF ,redox = −4.44eV − qUredox

Energy Level of Redox Electrolyte

The total potential difference across the semi-conductor-electrolyte interface is

€

UE = φscr + φH + C (C is a constant determined by the reference.)

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Comparison of energy levels of redox electrolyte with that of semiconductor. (a) Band diagram of a semiconductor (in vacuum scale) and redox potential of electrolyte (in NHE). (b) Energy levels of redox electrolyte showing its distribution and variation in energy for oxidized and reduced levels.

Energy Level of Redox Electrolyte

8

Relative dispositions of various semiconductor band edge positions. These band edge positions are for an aqueous medium of pH ∼1.

Energy Level of Redox Electrolyte

9

Three situations for a n-type semiconductor–electrolyte interface. The size of the arrows denotes the magnitudes of the current in the two (i.e. anodic and cathodic) directions.

Semiconductor-Electrolyte Interface

equilibrium reverse bias forward bias

Flat band potential (Ufb) can be determined by Mott-Schottky equation:

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Interfacial Charge TransferAll electron-transfer processes must occur via one of the electronic bands or states of the semiconductor electrode. Depending on the relative position of the standard Fermi level (or standard redox potential) of the redox system, either the conduction or the valence band can be involved.

Gerischer model of n-sc with two different redox systems. In the first case, redox reaction occurs via CB while the second is a VB process.

h+

e-

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Interfacial Charge Transfer in DarkThe anodic current, arising from electron transfer from the redox system into the CB of the semiconductor, is given by

€

ic+ = qkc

+NccredNc is the DOS at the bottom of CB and cred the concentration of the reduced species of the redox couple. kc+ is the rate constant

λ is the reorganization energy. Since the CB edge remains fixed with respect to EF,redox during polarization, the rate constant and consequently the anodic current are independent of the potential. The cathodic current is given by

€

ic− = qkc

−nscoxcox is the concentration of the oxidized species of the redox couple and ns is the electron density at the surface defined by

€

kc+ = kc

o+ exp −Ec − EF ,redox

o − λ( )2

4kBTλ

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

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Interfacial Charge Transfer in Dark

€

ns = n0 exp −qφscrkBT

⎛

⎝ ⎜

⎞

⎠ ⎟

n0 is the electron concentration in the bulk. The rate constant kc- is

€

kc− = kc

o− exp −Ec − EF ,redox

o + λ( )2

4kBTλ

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

The cathodic current varies with the electrode potential because ns depends on ϕscr, and therefore on EF.So the total current corresponding to an electron transfer via the CB is

€

ic = ic+ − ic

− = −ico nsnso −1

⎛

⎝ ⎜

⎞

⎠ ⎟

where

€

ico = qkc

+Nccred

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Interfacial Charge Transfer under RadiationAs photogeneration is involved in the interfacial charge transfer, minority carrier generated by light excitation in the bulk can only diffusion to the surface, whereas those generated within the space charge region are driven towards the interface by the electric field. In the case of n-sc,

€

iv =

ig − io exp −qηkBT

⎛

⎝ ⎜

⎞

⎠ ⎟

1+ioivo

⎛

⎝ ⎜

⎞

⎠ ⎟ exp −

qηkBT

⎛

⎝ ⎜

⎞

⎠ ⎟

€

i0 =qni

2Dh

NDLh

where η is the overpotential, . If the recombination controls the current ( ), for a pure valance band process,

€

η =UE −Uredox

€

i0 << ivo

However, as the reduction of redox system is expected to occur via the CB,

€

iv = −i0 exp −qηkBT

⎛

⎝ ⎜

⎞

⎠ ⎟ −1

⎡

⎣ ⎢

⎤

⎦ ⎥ + iph

€

i = −ic0 exp − qη

kBT⎛

⎝ ⎜

⎞

⎠ ⎟ −1

⎡

⎣ ⎢

⎤

⎦ ⎥ + iph

i0 is the generation/recombination rate of minority carrier in the bulk sc.

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It is normally sufficient to consider only the Fermi level (majority) of sc if majority carriers are transferred across the interface. If no other reaction occurs, the minority carriers are still in equilibrium with the majority carriers. So the quasi Fermi level of electron and holes remain equal even during current flow.The situation is different if minority carriers are involved. Electrons and holes are not in equilibrium and their quasi-Fermi levels become different. Reactions at n- and p-sc can be analyzed quantitatively in terms of quasi-Fermi levels.

Take a VB process as an example, it is assumed the same reaction with identical rates takes place at the n- and p-sc of the same material if their EF,p are equal at the surface of the two electrodes.

Quasi Fermi Level Concept

Quasi Fermi Level Model

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• VB and CB at the surface of n- and p-sc have the same position at equilibrium;

• All electrode reactions can be described as a function of the surface hole density;

• The Fermi level of holes in the p-sc is constant within the electrode.

The quasi-Fermi level model is applicable if the following conditions are fulfilled (for the VB process of n-sc):

The advantage of quasi-Fermi level model:• Quasi-EF of majority carriers can be

determined as it is identical to the electrode potential; • Quasi-EF of minority carriers is also

known for a given current.

Quasi Fermi Level Model

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Quasi Fermi Level Model

Band bending in the dark and under illumination with (a) an n-type semiconductor-electrolyte and (b) a p-type semiconductor–electrolyte interface. Vacuum scale changes its shape to match the shape of band bending. Variation in Fermi level for minority carriers is shown by broken line (for illuminated semiconductor).

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Surface State Mediated Interfacial Charge Transfer

There are two principal charge transfer routes involving surface states. Considering an n-sc, the forward-bias current can either involve direct exchange of electrons between the semiconductor CB and Ox states in solution or can be mediated by surface states. The second route involves hole injection into the semiconductor VB from Ox states in solution. The recombination current is mediated either by surface states or via space charge layer recombination.

Ox

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Most contacts between aqueous electrolytes and small band gap semiconductors results in photocorrosion or photopassivation of the semiconductor surface.

Photocorrosion and Photopassivation

The electro-active species in the solution might scavenge the photogenerated carriers before they could induce decomposition of the semiconductor surface, thereby extending the operating lifetime of the electrode.

S

XX

X X

XXX

X

XX

X

+h+ +x-I P1 P2+h+ +x- +2h+ +2x-

y

S’

y

+e- +y+I’ P1’ P2’+e-

y- -

Mechanism of anodic and cathodic decomposition of semiconductor by bond breaking due to an accumulation of holes or electrons at the interface.

In the anodic decomposition process, often all reaction products are soluble in the electrolyte and therefore the reaction can go on continuously. In the cathodic process, however there is usually an insoluble product left on the surface which quickly blocks the decomposition.

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Materials and Electrolytes for PEC Cells

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Materials and Electrolytes for PEC Cells

Metal oxide semiconductor generally have band gaps being too large for optimal light absorption. Metal chalcogenides, phosphides are used with suitable electrolyte redox couples.

In the early 1980s, chemically modified semiconductor–electrolyte interfaces was directed toward protecting them from photocorrosion. And various non-aqueous solvents were used for the same purpose.

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Photoelectrochemical CellsA photoelectrochemical cell (PEC cell) consists of a photoactive semiconductor electrode (either n- or p-type) and a metal counter-electrode. Both these electrodes are immersed in a suitable redox electrolyte. In a regenerative PEC solar cell, the metal counter-electrode is expected to perform an electrochemical reaction that is the opposite of the process occurring at the semiconductor electrode.Classification of PEC Cell1) ΔG=0, Electrochemical photovoltaic cells: photo energy converted into

electric energy.2) ΔG≠0, Photoelectrosynthetic cells: photo energy used to affect chemical

reactions, with non-zero free energy change in the electrolyte.• ΔG>0, Photoelectrolytic cells: photo energy stored as chemical energy

in endorgic reactions. e.g. H2O → H2 + 1/2O2

• ΔG<0, Photocatalytic cells: photo energy provides activation energy for exorgic reactions. e.g. N2 + 3H2 → 2NH3

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Electrochemical Photovoltaic Cells

Electrochemical Photovoltaic Cell: Converts light to electric power leaving no net chemical change behind. Working Principle: For n-sc, photons of energy exceeding that of the band gap generate electron–hole pairs, which are separated by the electric field present in the space-charge layer. The negative charge carriers move through the bulk of the sc to the current collector and the external circuit. The positive holes are driven to the surface where they are scavenged by the reduced form of the redox relay (R). The oxidized form O is reduced back to R by the electrons that re-enter the cell from the external circuit.

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Photoelectrolytic Cells

Photosynthetic Cells: Operate on a similar principle except that there are two redox systems: one reacting with the holes at the surface of the n-sc electrode and the second reacting with the electrons entering the counter-electrode. The anodic and cathodic compartments need to be separated to prevent mixing of the two redox couplesAs an example of n-sc, water is oxidized to oxygen at the semiconductor photoanode and reduced to hydrogen at the cathode. The overall reaction is the cleavage of water by sunlight.

H2O → H2 + 1/2O2

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Photocatalytic Cells

Photocatalytic Cells: Light merely serves to accelerate the reaction rate in the case of ΔG<0. Thus these cells operate in the photocatalytic mode. Aqueous suspensions comprising irradiated semiconductor particles may be considered to be an assemblage of short-circuited micro-electrochemical cells operating in the photocatalytic mode, for instance the photooxidation of organic compounds, or reactions with high activation energy.

N2 + 3H2 → 2NH3

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Dye-sensitized Photoelectrochemical Cells

Dye-sensitized Photoelectrochemical Cells: Operates in a photovoltaic mode, or more appropriately, in a photogalvanic mode.Working Principle: The initial photo-excitation does not occur in sc, but occurs instead in a visible light-absorbing dye. Subsequent injection of an electron from the photoexcited dye into the semiconductor CB results in the flow of a current in the external circuit. Sustained conversion of light energy is facilitated by regeneration of the reduced form of the dye via a reversible redox couple.

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Chronological Improvements of PEC Cells

Efficiency Improvement of PEC Cells

Unfortunately none of these materials show a long-term stability to warrant making of a commercially viable PEC cell. The future of economically viable PEC cells depends entirely on the development of suitable low band gap, photoelectrochemically stable materials (interface), or novel work principles for PEC cells (e.g. dye-sensitized solar cells).

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Fujishima-Honda cell with n-TiO2 photoanode and Pt-cathode for UV light water splitting and the schematic energy level diagram of the cell.

PEC Cells for Water Splitting

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PEC cell utilizing n-sc and p-sc. The difference between the energy levels of VB edge of n-type and CB edge of p-type should be approximately equal to potential needed to electrolyze water.

PEC cell with one n-sc and one metal electrodes for photo-electrolysis of water.

PEC Cells for Water Splitting

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PEC Cells for CO2 Reduction

EC

EV

EF

p-InP

hν>1.35 eV

-

+

E(MV2+/MV+) FDH

CO2+2H+

HCOOH2MV+

2MV2+

SolutionSemiconductor

Photoelectrochemical enzymatic reduction of CO2. Photogenerated electrons from p-InP are supplied to formate dehydrogenase (FDH) in solution, which performs the 2e- reduction of CO2 to formic acid. The electron transfer between p-InP and the enzyme is mediated by methyl viologen (MV2+/+) in solution.

CO2 + 2H+ + 2e- → HCOOH

What would be the reaction at counter electrode?

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Summary

• Semiconductor-electrolyte interface• Interfacial charge transfer at semiconductor-electrolyte

interface• Quasi Fermi level model for semiconductor-electrolyte

system• Photo-stability of semiconductor-electrolyte system• Classification and status of photoelectrochemical cells

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