"Electron Transfer in Chemistry" (Ed.: V. Balzani) Vol. 5, Part 3 “Energy and the Environment” (Ed.: I. Gould) Wiley-VCH, Weiheim, 2001; pp. 589-644. _________________________________________________________

Solar Energy Conversion

Michael Grätzel and Jacques-E. Moser *

Laboratory for Photonics and Interfaces Institute of Physical Chemistry

Ecole Polytechnique Fédérale de Lausanne CH-1015 Lausanne

Switzerland

– 2 –

Table of Contents

1. Introduction and Scope

2. Thermodynamic Efficiency Limitations in Photochemical Conversion

2.1 Maximum power extraction

2.2 Limitations due to the entropy of light

2.3 Further increase of entropy on absorption and scattering

2.4 Efficiency of energy conversion under polychromatic radiation

3. Status of Photochemical Energy Conversion Systems

4. Molecular Photovoltaics

4.1 Mimicking photosynthesis

4.2 Mesoscopic oxide semiconductor films

4.2.1 Light harvesting by monomolecular layers

4.2.2 Preparation and morphology of mesoscopic semiconductor films

4.3 Photoinduced charge separation at the solid/electrolyte interface

4.3.1 Molecular engineering of sensitizers

4.3.2 Dynamics of charge injection in wide bandgap semiconductors

4.3.3 Recapture of the injected electron

4.4 Charge separation in molecular photovoltaic devices

4.4.1 Interception of dye cations by a redox mediator

4.4.2 Charge carrier percolation through mesoporous solid films

4.4.3 Charge separation across a solid-state heterojunction

4.5 Charge separation and recombination in nanocrystalline heterotriads

4.6 Photovoltaic performances of dye-sensitized nanocrystalline solar cells

– 3 –

5. Water Cleavage by Visible Light

5.1 Analogues of photosystem II of green plants

5.2 Colloidal semiconductors systems

5.3 Tandem systems for water cleavage by visible light

6. Future Outlook and Concluding Remarks

Acknowledgements

References

– 4 –

1. Introduction and Scope

There can be no question that the quality of human life is intimately associated with the

ready availability of energy resources. At present, the worlds’ energy consumption rate

exceeds already the stunning figure of 6000 Gigawatt. This is expected to grow rapidly

in the next decades due to the increase in demand from the developing countries. The

overwhelming part of our energy supply arises from the chemical energy stored in the

fossil fuels. These reserves are being rapidly depleted and their combustion has led to

unacceptable levels of pollution of our environment. Further acceleration of this process

would lead to disastrous climatic consequences. It is evident that the well being of

mankind is threatened unless renewable energy resources can be developed in the near

future. Photochemistry is expected to make decisive contributions to identify

environmentally friendly solutions to the energy problem. One attractive strategy

discussed below is the development of systems that mimic natural photosynthesis in the

conversion and storage of solar energy. Electron transfer reactions play a vital role in

the light induced charge separation that forms the basis of this process. Our review will

treat such redox processes that lead to the conversion of light to electric power and the

storage of solar energy in the form of chemical fuels such as hydrogen. We shall focus

our discussion on heterogeneous electron transfer reactions that occur on solid–liquid

interfaces that are of particular interest in this connection. To start with we shall briefly

analyze the thermodynamic limitations of light energy conversion processes.

– 5 –

2. Efficiency Restrictions in Photochemical Conversion

The primary concern of photochemists and chemists when they run a reaction is the

mass yield of product. In chemical reactions whose aim is to convert chemicals into

fuels, in electrochemical reactions which convert electricity to chemical potential, or

vice versa, and in photochemical reactions which convert light into chemical potential

or work, the free energy yield is of equal importance. The laws of thermodynamics

impose limitations on the efficiency of the conversion of light energy into chemical

potential. Free energy losses in the sequence of steps during a photochemical process

have several origins that will be considered in the following order [1]: (1) non-

equilibrium conditions at maximum power, (2) entropy of the radiation source, (3)

entropy increase on scattering or absorption of the original radiation, (4) inefficiency of

polychromatic radiation. Further limitations associated to the storage of the chemical

potential will not be discussed here.

2.1 Maximum power extraction

General to all reactions, whether photochemical or not, is the loss of free energy caused

by non-equilibrium conditions due to finite power extraction. Consider a chemical

reaction in which a reactant A at chemical potential µA is converted into a product B at

chemical potential µB.

A B

i ijf

jb!A !B

(1)

– 6 –

The rate of storage of chemical potential in the product B per unit of volume is J⋅µB,

where the flux J = – d[A]/dt = d[B]/dt. If A and B are in equilibrium, the rates of the

forward and back reactions are equal and the net flux to the product J = jf – jb = 0.

Under non-equilibrium conditions where the forward reaction takes place with J > 0,

there is a net overall entropy increase and µB < µA. If K is the equilibrium constant for

reaction A B in ideal conditions, the change in chemical potential is given by

the van’t Hoff isotherm :

Δµ = µB – µA = – RT ln K + RT ln ([B]/[A]) (2)

By putting K = kf / kb, where kf and kb are the rate constants of reactions A→B and

B→Α , respectively, and by substituting the fluxes defined by jf = kf [A] and jb = kb [B],

one obtains the expression of the free energy loss in a spontaneous reaction :

Δµ = RT ln ( 1 – ϕ ) (3)

where ϕ = J / jf. The conversion power P of the reaction is given by the rate of

production of chemical potential in the form of the product B at the potential µB :

P = J⋅µB = J⋅(µA + Δµ). At maximum power, the reaction flux J is given by :

!

1 – ! – ln (1 – !) =

µA

RT (4)

and the free energy transfer efficiency :

!p = µA + "µ

µA (5)

– 7 –

The amount of chemical potential converted in a photochemical reaction is typically of

the order of 1–2 eV. If µA = 1 eV, one calculates from the latter equations ϕ = 0.972,

Δµ = – 0.093 eV, and ηp = 0.91.

If the product B is involved in a leakage reaction to yield an undesired product C with a

rate constant kl, Equation (4) can be re-written :

! – "

1 – ! – ln (1 – !) =

µA

RT (6)

with κ = kl / (kb + kl),, and the free energy conversion efficiency at maximum power :

!p = [ 1 – kl" (# – 1)

kb

] " µA + $µ

µA (7)

Assuming a leakage reaction with kl = kb, and µA = 1 eV, one obtains κ = 0.5,

ϕ = 0.986, Δµ = – 0.110 eV, and ηp = 0.89. If kl is increased by a factor of ten, the

efficiency decreases slightly to ηp = 0.85.

2.2 Limitations due to the entropy of light

The fact that radiation possess entropy imposes additional constraints on the possible

changes in a material system interacting with light. These constraints determine, in

particular, the efficiency of processes involving the utilization of radiant energy.

Let consider a photochemical reaction without leakage, where the only fates of the

product A* are reaction to give the final product (with flux i) and reverse reaction (with

flux jb). The potential of the reactants is composed of the chemical potential µA of A

and the potential µR of the radiation or, by analogy with chemical potentials, the partial

molar free energy of the absorbed light quanta.

– 8 –

A + h! A*

i ijf

jb!A !R !A*

(8)

The change in potential during the light absorption process is given by:

!µ = µA* - µA - µR = RT ln (1 – ") (9)

If the radiation is monochromatic at wavelength λ, its total energy is QR [J⋅Einstein–

1] = NA⋅hc / λ , where NA is Avogadro’s number, and the entropy associated with it

ΔSR = ΔQR / TR. The effective temperature TR of the monochromatic radiation of

wavelength λ and of a given spectral irradiance Iλ is expressed by the formula :

TR = hc

kB ! " 1

ln ( 1 + 2 hc2 #

!5

I!

)

(10)

where Ω is the solid angle subtended by the source at the receiver (including any optical

concentrator). The spectral irradiance Iλ is the energy of the radiation incident on a unit

area per unit time and unit wavelength interval at a given wavelength λ. Thus, we may

write the dimension of Iλ as, for example, [Iλ] = W m–2 nm–1. Expression (10) for TR

is the same as the Planck formula for a black-body giving the same spectral irradiance

Iλ at the same wavelength λ for unit wavelength interval and unit solid angle. Thus rays

of light propagating in a specified direction and delivering at the receiver a spectral

irradiance Iλ possess a temperature equal to that of a black-body emitting radiation and

giving rise to the same irradiance.

The entropy of the radiation ΔSR is lost when the light disappears in the absorption

process. An equivalent amount of entropy must then be created in the absorber at

– 9 –

ambient temperature TA. Therefore, the maximum energy available to do work at

temperature TA is given by:

µR = QR (TR - TA)

TR (11)

The maximum possible conversion efficiency is then expressed by what appears to be

simply the Carnot formula applied to radiation:

!r = µR

QR =

TR - TA

TR (12)

Figure 1. Spectral irradiance of the sun at mean earth-sun separation.

– 10 –

The sun delivers a spectral irradiance at the earth surface at AM1.0 (air mass), without

concentrator, of 1.16 W⋅m–2⋅nm–1 at λ = 700 nm.[2] The solid angle represented by the

sun seen from the earth is Ω = 6.8×10–5 steradian. From Equation (10), one calculates

in this case TR = 5500 K, and from Equation (12) with TA = 298 K one obtains

ηr = 0.946. If the solar spectrum were that of a black-body, all wavelengths would lead

to the same values of TR and ηr. Figure 1 shows that this condition is fulfilled only if

the receiver were outside the atmosphere. At the earth surface, absorption by

atmospheric oxygen, ozone, water and carbon dioxide makes the structured solar

irradiance spectrum deviate significantly from the ideal black-body spectrum and

requires TR(λ) is calculated for each wavelength.

2.3 Further increase of entropy on absorption or scattering

Apart from the entropy of the original radiation, a second source of entropy must be

taken into account that causes losses of free energy in the course of the photochemical

reaction. Upon absorption, the directionality of the radiation beam is indeed completely

lost. The entropy thus increases, while the radiation temperature decreases. An

equivalent effect is obtained when the original directional radiation concentrated in a

small solid angle is scattered in all directions. The temperature of the scattered light is

obtained by replacing in Equation (10) the solid angle Ω by the value 4π corresponding

to isotropic radiation at the receiver:

TRs = hc

kB ! " 1

ln ( 1 + 8# hc2

!5

I!

)

(13)

– 11 –

With the same numerical figures as above for the irradiance of the sun at 700 nm, the

scattering of the radiation over 4π or (what is strictly equivalent) its absorption in a

photochemical reaction cause its effective temperature to decrease from TR = 5500 K to

TRs = 1297 K. The maximum efficiency calculated from Equations (11) and (12) then

drops from ηr = 0.95 to ηrs = 0.77. The solid angle does not appear anymore in

Equation (13). It should be kept in memory, however, that if the solid angle of

collection is increased at the absorber by use of an optical concentrator, the measured

irradiance increases in proportion and hence the temperature, potential and efficiency.

In the same conditions as in the example above, concentration of the incident radiation

by a factor of 10, for instance, translates into a rise of the radiation temperature from

1297 K to 1517 K and an augmentation of the maximum conversion efficiency from

0.77 to 0.80.

Under optimum conditions of maximum power, the extraction flux J = Jmax is given by

Equation (4), or more generally, if there are leakage processes, by Equation (6). The

global efficiency ηg of conversion of light into chemical potential at maximum power

can be expressed by:

!g = " # (µA* – µA)

NA# hc = 1 –

TA

TR –

RTA# "

NA# hc # ln (4$ / %) +

RTA# "

NA# hc # ln (1 – &)

(14)

The last three terms represent the fractional losses due to (1) the entropy of the original

radiation, (2) the entropy increase due to absorption or scattering of light, and (3) the

minimum loss caused by non-equilibrium conditions at power extraction. For

λ = 700 nm and AM1.0 solar radiation, µRs = 1.36 eV. By substitution of µ/RT = 52.9

in Equation (4), one obtains ϕ = 0.97. The maximum global efficiency being finally

estimated as ηg = 1 – 0.055 – 0.180 – 0.058 = 0.71.

If there are leakages from the excited state due to radiationless deactivation processes,

Equation (6) must be used with κ = 1 – Φf, where Φf is the fluorescence quantum yield

– 12 –

of A in the absence of reaction. These leakages will increase the last term of the

summation in Equation (14) and hence lower the global conversion efficiency. In the

above example, if Φf = 0.5 (κ = 0.5), the flux ratio ϕ is increased from 0.98 to 0.99 and

the global conversion efficiency at maximum power slightly reduced from 0.71 to 0.70.

2.4 Efficiency of energy conversion under polychromatic radiation

So far, calculations have assumed that the energy of the excited state is equal to that of

the absorbed photon. This is not the case for polychromatic radiation when a single

absorber is used. Losses due to non-absorption or the degradation of energy in excess of

the excitation energy of A* are generally not avoidable. The simplest and most

important case with which we are concerned is that of an absorber with a threshold

excitation wavelength λt. In a somewhat idealized form, the properties of a threshold

converter are the following : (1) the absorptance of the system is 0 for light with

wavelength λ superior to the threshold wavelength λt ; (2) all absorbed quanta produce

the same excited state with an excitation energy hc/λt ; (3) the excess energy hc/λ –

hc/λt is transferred to the medium as radiation or heat.

Scheme 1

– 13 –

Assuming that no reaction can take place from hot excited state levels, all absorbed

photons, after degradation of excess energy, give rise to the same excitation energy

hc/λt. The fraction θ of the energy absorbed from a polychromatic source which is

available in the photochemical conversion process is given by :

! =

F"#"

"t

d"

0

"t

F" d"

0

$

(15)

where Fλ is the spectral radiation flux incident on the converter from an external source.

For a threshold wavelength of 700 nm and AM1.0 solar radiation (Figure 1), the

fraction θ = 0.38.[3]

Obviously, the value of θ, and thus that of ηo, depends on the value of the threshold

wavelength λt. For a given spectral distribution of the incident radiation energy, an

optimal threshold wavelength exists which yields a maximum θ. The optimal threshold

wavelength for a given spectrum of the incident radiation may be determined from

Equation (15). The calculation shows, for example, that for Planckian radiation (which

spectral distribution matches that of a black-body at the same temperature) with a

temperature TR = 5200 K (direct solar light at AM1.5) the optimal wavelength is

λtopt = 1273 nm, and accordingly θopt = 0.44. This wavelength is near the absorption

threshold of silicon solar cells. Therefore, at λ = 700 nm, TA = 25 °C, and for AM1.5

radiation, the maximum thermodynamic overall energy conversion efficiency of these

photovoltaic cells is ηo = ηg × θ = 0.70 × 0.44 = 0.31. For green plants, the threshold

wavelength determined by the optical properties of chlorophyll is 700 nm. In this case,

for AM1.5 irradiation θ = 0.34, giving an overall conversion efficiency ηo = 0.24.

Molecular photovoltaic devices that will be discussed in section 4 are based on dye-

– 14 –

sensitizers whose absorption threshold, for the most efficient ones, is typically

λt = 800–900 nm. The thermodynamic limiting energy conversion efficiency for these

photoconverters is thus somewhat lower than that of silicon cells and does not exceed

0.27 at any wavelength under AM1.5 solar irradiation.

– 15 –

3. Status of Photochemical Energy Conversion Systems

Photovoltaic devices are based on the concept of charge separation at an interface of

two materials of different conduction mechanism, normally between solid-state

materials, either n- and p-type regions with electron and hole majority carriers in a

single semiconductor material, heterojunctions between different semiconductors or

semiconductor-metal (Schottky) junctions. In photo-electrochemical cells, the junctions

are semiconductor-electrolyte interfaces. In recent years, despite prolonged effort, a

disillusion has grown about the prospects of electrochemical photo-effects at these

interfaces giving rise to competitive photovoltaic devices, since those semiconductors

with band gaps sufficiently narrow for efficient optical absorption of visible-light

photons are necessarily insufficiently stable against photo-corrosion. The width of the

bandgap is a measure of the chemical bond strength. The semiconductors stable under

illumination, typically the ceramic oxides of reactive metals such as titanium, therefore

have a wide band gap, an absorption edge towards the ultraviolet and a consequent

insensitivity to the visible spectrum. Hence the breakthrough represented by the

separation of the optical absorption and the charge separation processes in photo-

electrochemistry, realized by the association of a redox dye as light-absorbing material

with the wide band gap semiconductor. These sensitized semiconductor systems will be

discussed further below.

The main thrust of the research in photoelectrochemistry during the three decades

during the seventies and eighties has been to develop systems for the splitting of water

into hydrogen and oxygen. The main obstacle to direct photoelectrolysis of water are

the lack of efficient light absorption (for reasonable solar efficiencies, the band gap

must be less than 2.0 eV), corrosion of the semiconductor (thermodynamically, most

useful semiconductors are photochemically unstable in water), and energetics i.e. the

– 16 –

difficulty of matching the semiconductor band-edge energies with the H2 and O2

evolution reactions). The most photochemically stable semiconductors in aqueous

solution are oxides, but their band gaps are either too large for efficient light absorption

or their semiconductor characteristics are poor. Semiconductors with better solid-state

characteristics are typically thermodynamically unstable with respect to oxidation.

However, p-type semiconductors generally offer some protection against

photocorrosion, because under illumination the surface is cathodically protected. p-type

indium phosphide is stable in strong acid under illumination and H2 evolution but

requires an external bias for water splitting. This earlier work on the photoelectrolyis of

water has been reviewed.[4]

– 17 –

4. Molecular Photovoltaics

In a conventional p-n junction photovoltaic cell made, for example, of silicon, the

semiconductor assumes two roles simultaneously: It harvests the incident sunlight and

conducts the charge carriers produced under light excitation. In order to function with a

good efficiency, the photons have to be absorbed in the vicinity of the p-n interface.

Electron-hole pairs produced away from the junction must diffuse to the p-n contact

where the local electrical field separates the charges. To avoid charge carrier

recombination during the diffusion, the concentration of defects in the solid must be

small. This imposes severe requirements on the purity of the semiconductor material,

rendering solid state devices of the conventional type quite expensive. Molecular

photovoltaic systems separate the functions of light absorption and carrier transport.

Light harvesting is carried out by a dye-sensitizer which initiates electron transfer

events leading to charge separation. This renders unnecessary the use of expensive solid

state components in the system. While being simple from the conceptual point of view,

the practical implementation of such devices must overcome several serious obstacles if

the aim is to develop molecular systems which convert sunlight to electricity at an

efficiency comparable to that of silicon cells, and meet the stability criteria for practical

applications.

4.1 Mimicking Natural Photosynthesis

Natural photosynthesis is the most important of the many interesting photochemical

processes known in biology. Not only was the evolution of the Earth’s atmosphere

dependent on it, but also it is the main route by which the free energy of the

– 18 –

environment is made available to the living world. Green plants, algae and

cyanobacteria make use of sunlight to drive a thermodynamically uphill reaction, the

reduction of carbon dioxide to carbohydrates by water.

CO2 + H2O → 1/6 C6H12O6 + O2 (16)

The input chemicals are carbon dioxide and water, while the output is oxygen and

carbohydrates. The latter serve as a feed stock for other organic products such as wood,

coal, oil and gas constituting the world’s fossil fuel reserves. It is estimated that about

1011 tons of carbon dioxide are assimilated annually by plants on Earth, whereby the

amount of solar energy harvested by natural photosynthesis is 3×1018 kJ, corresponding

to the continuous generation of 90 000 gigawatt of electrical power.

Most of the key features of how photosynthetic energy conversion operates are known

by now. Light induced charge separation is achieved through judicious spatial

arrangement of the pigments and elements of the electron transport chain in the tylakoid

membrane. Co-operative interaction between these components allows the electron

transfer to proceed in a vectorial fashion. Although strategies to design artificial

photoconversion devices should not attempt to blindly imitate all the intricate of natural

photosynthesis, it is inconceivable to accomplish the challenging task of converting

visible light into electrical work or chemical potential without suitable engineering on

the molecular level. Efficient molecular photovoltaic devices described in section 4 and

tandem systems for water cleavage by visible light presented in section 5 use similar

concepts as green plants to harvest and convert solar energy. It is therefore useful to

review the salient features of their natural analogue.

The essence of natural photosynthesis is the use of photochemical energy to split water

and reduce CO2. Molecular oxygen is evolved in the reaction, although it appears at an

earlier stage in the sequence of reactions than the reduction of carbon dioxide.

– 19 –

Photochemical processes produce compounds of high chemical potential, which can

drive a multi-step synthetic sequence from CO2 to carbohydrate in a cyclic way.

Reaction (16) is quite endoergic and thus thermodynamically very improbable in the

dark (ΔG° = 522 kJ per mole of CO2 converted). Production of one molecule of oxygen

and concomitant conversion of one molecule of carbon dioxide require the transfer of

four electrons:

2H2O → O2 + 4e– + 4H+ (17)

4e– + 4H+ + CO2 → 1/6 C6H12O6 + H2O (18)

Reaction (16) is the sum of reactions (17) and (18). Clearly, if each photon harvested by

the system can lead to the transfer of one electron, then a minimum of four photons are

required for the conversion of each CO2 molecule. Experimental measurements of the

quantum yield indicate that eight photons are actually needed, suggesting that two

photons are used for each electron transfer and that a two-step process is taking place

with long-lived intermediates coupling the steps.

Photosynthesis comprises a light-induced and a dark reaction. The first, called

photophosphorylation, involves the two-electron reduction of nicotinamide adenine

dinucleotide phosphate (NADP+) by water, to produce NADPH and oxygen. The redox

reaction is coupled to the generation of adenosine triphosphate (ATP) from adenosine

diphosphate (ADP):

2H2O + 2NADP+ + 3ADP + 3P → 2NADPH + H+ + 3ATP + O2 (19)

where P stands for the phosphate PO43– anion. This light-driven reaction takes place in

the tylakoid membranes located in the interior of the chloroplasts of plant cells.

– 20 –

Figure 2. Functional organization of photosystem II in protein-complexes

contained in the thylakoid membrane. Excitation energy is harvested by chlorophyll

(Chl) and carotenoids (Car) molecules and transfered to the special pair (Chl2).

Vectorial electron transfer across the membrane takes place from excited Chl2* to

plastoquinone (pQ) via pheophitine (Ph) and quinone (Q) electron mediators.

The photosynthetic unit assembled in these membranes is composed of antenna

pigments for light energy harvesting, i.e. chlorophyll and carotenoids, as well as a

reaction center consisting of two photosystems. The photons absorbed by the antenna

pigments are first transferred to a chlorophyll dimer that is part of the reaction center.

The electronic excitation causes electrons to be ejected from the chlorophyll dimer and

then passed on to various electron-transferring mediators. The judicious spatial

arrangement of these components allows the electrons to be transferred in a vectorial

fashion from the inner to the outer part of the membrane (Figure 3). The positive

– 21 –

charges left behind produce oxygen and protons from water while the electrons reduce

NADP+ to NADPH. The latter is nothing else but a hydride, i.e. a stored form of

hydrogen. The pH gradient generated across the membrane is used to store additional

energy via the phosphorylation of ADP to ATP. There are two light absorbing

photosystems, PS I and PS II, each containing chlorophyll, that operate in series.

Photoexcitation of PS II initiates a series of redox steps resulting in the transfer of

electrons from water to plastoquinone (pQ). This product is the electron donor for PS I

which under illumination performs the reduction of NADP+ to NADPH (Figure 3).

Figure 3. The Z-scheme of green plants photosynthesis: coupling of the two

pigment systems, I and II. P680 and P700 = chlorophyll; pQ = plastoquinone;

Cyt = cytochrome; pC = plastocyanine; Fd = ferrodoxine.

– 22 –

The dark reaction, known as Calvin cycle, uses the reducing power of NADPH as well

as the free energy stored in the ATP to assimilate carbon dioxide in the form of

carbohydrates. The way by which Nature achieves carbon fixation is via the reaction of

CO2 with ribulosebiphosphate (RuBP) to give two molecules of 3-phosphoglycerate, a

process which is catalyzed by the enzyme RuBP-carboxylase. The phosphogylcerate is

converted further to fructose 6-phosphate, the final product of the Calvin cycle. The

overall reaction, despite its complex mechanism corresponds to the simple

Equation (16) above.

Most green plants operate with photosynthesis efficiencies of a few percent. Eucalyptus

trees are particularly efficient in this respect and reach as high as 5 %, one fifth of the

thermodynamic maximum energy conversion efficiency discussed in section 2. In plant

leaves, sunlight is only weakly absorbed by chlorophyll and carotenoids molecules.

These dyes, however, are contained in the membrane of stacked pancake-shaped

vesicles, the thylakoids, that are grouped in the chloroplast cells. Efficient harvesting of

sunlight is eventually achieved by absorption through numerous pigment layers.

Furthermore, light harvesting and charge separation functions are carried out separately

in the natural photosynthetic system, and end up in the transport of opposite charges on

both sides of the thylakoid membrane.

In molecular photovoltaic devices discussed hereafter, the incident photons excite a

dye-sensitizer that injects an electron into the conduction band of a wide bandgap

semiconductor. Positive holes left in the dye are then carried away by an electrolyte

mediator or conducted through a hole-transporting medium (Figure 4). Mimicking the

key features of natural photosynthesis, these devices rely on a mesoporous film

structure to ensure efficient harvesting of sunlight using a molecular absorber. As well,

light absorption and electron collection functions are separated in such systems.

Electron injection into semiconducting nanoparticles which achieves charge separation

– 23 –

across the solid/electrolyte interface is analogous to charge separation in the

photosynthetic membrane.

Figure 4. Schematic representation of the principle of the nanocrystalline

injection photovoltaic cell showing the electron energy level in the different phases. The

cell voltage ΔV obtained under illumination corresponds to the difference in the quasi-

Fermi level of TiO2 under illumination and the electrochemical potential of the redox

couple (M+/M) used to mediate charge transfer between the electrodes.

– 24 –

4.2 Mesoscopic oxide semiconductor films

4.2.1 Light harvesting by monomolecular dye layers

Absorption of incident radiation by a molecular sensitizer adsorbed as a monolayer to

the surface of a solid come up against the fundamental problem of limited light capture

cross section of the dye molecules. The absorption cross section σ [cm2] is related to

the decadic molar extinction coefficient ε [l⋅mol–1⋅cm–1] by the expression (20):

σ = ε × 1000 × ln(10) / NA (20)

where NA is Avogadro’s number. Since ε characterizes molecules in solution which

spatial orientation is random, favorable orientation of the chromophores upon

adsorption on a surface can lead to an increase of the effective cross section by at most a

factor of 2. Typical ε values for dyes lie between 104 and 2×105 l⋅mol–1⋅cm–1 yielding

for the light capture cross section values between 0.0038 and 0.15 nm2. The area the

sensitizer molecules occupies on the surface of the supporting solid is much larger, e.g.

about 1–2 nm2. Hence, at most a few percent of the incident light can be absorbed.

Deposition of a multilayer of dye on the surface in order to increase its light absorption

is generally a mistaken tactic, since energy transfer between sensitizer molecules rarely

gives rise to efficient antenna effects and outer dye layers act only as a light filter, with

no contribution to photocatalysis.

A successful strategy to solve the problem of light absorption through such molecular

layers is found in the application of high internal surface area films consisting of

nanocrystalline oxide particles with a diameter of 10–20 nm. The mesoporous

morphology of the layer plays a crucial role in the harvesting of sunlight. Depending on

– 25 –

film thickness, their real exposed surface area can easily be made 1000 times larger than

the apparent geometric one. When light penetrates the dye-covered solid “sponge”, it

travels through hundreds of adsorbed dye monolayers and is efficiently captured.

Consider the case of a 3 µm thick mesoporous film whose effective surface area is 300

times larger than that of a compact solid and that the film is covered by a monolayer of

dye molecules each of which occupies an area of 1 nm. On the geometric projection of

such a rough surface a dye coverage of Γ = 3×1016 cm–2 is reached. Its absorbance A

[–] is given by the equation:

A = Γ × σ (21)

where Γ is the chromophore surface concentration and σ its absorption cross section.

Suppose that the dye molecule at the wavelength of its absorption maximum has a light

capture cross section of 5×10–17 cm–2 (ε = 1.3×104 l⋅mol–1⋅cm–1). As a result the

absorbance of the film would be A = 1.5. Neglecting light scattering by the film, its light

harvesting efficiency (LHE), namely the absorptance, is given by Equation (22),

implying that 97 % of the incident photons are absorbed.

LHE = 1 – 10–A (22)

4.2.2 Preparation and morphology of mesoscopic oxide semiconductor films

Over the recent years, nanocrystalline materials have attracted increasing attention from

the scientific community because of their extraordinary physical and chemical

properties. These result from the ultra-fine structure (i.e. grain size < 50 nm) of the

materials. Nanocrystalline electronic junctions are constituted by a network of

– 26 –

mesoscopic oxide or chalcogenide particles, such as TiO2, ZnO, Fe2O3, Nb2O5, WO3,

Ta2O5 or CdS and CdSe, which are sintered together to constitute transparent

mesoporous films, typically a few microns thick. As electrons can rapidly percolate

between interconnected particles through the film, the entire surface-adsorbed

molecular layer can be electronically addressed. Charge transfer events involving

adsorbed molecule can thus be induced through the nanocrystalline support and

recorded as electrical current. Optical monitoring is also facile as the signals arising

from the grafted molecules are greatly enhanced due to the huge internal surface area of

the junction.

Since fifteen years titanium dioxide has become the semiconductor of choice. The

material has many advantages for sensitized photo-electrochemistry: As most wide

bandgap oxides, it is stable and does not tend to corrode in liquid electrolytes. The

Lewis acidity of its surface affords a convenient handle for attachment of dye molecules

by way of electron-rich anchoring groups. Moreover, TiO2 is a low cost, widely

available, non-toxic, and even biocompatible, substance that is widely used in domestic

applications.

Mesoporous oxide films are commonly produced via a sol-gel type process involving a

hydrothermal step. The procedure is illustrated for TiO2 in Figure 5. The initial

precipitation of the oxide involves controlled hydrolysis of a Ti(IV) compound, usually

an alkoxide such as titanium tetraisopropoxide or TiCl4, followed by peptization.

Autoclaving of the obtained sols (heating at 200–250 °C for 12 h) allows for controlled

growth of the primary particles and improves their crystallinity. During this

hydrothermal growth, smaller particles dissolve and fuse to large particles by a process

known as “Ostwald ripening”. After partial removal of solvent and addition of a binder,

the sol is ready for deposition on the substrate. For the latter, a conducting glass (sheet

resistance = 8–10 Ω/square) is often used. The sol is deposited by doctor blading or

screen printing and briefly fired in air. During the firing, the binder and possible organic

– 27 –

contaminants are burned out, thus producing a clean, mostly dehydroxylated, oxide

surface. The film thickness is typically 5–10 µm and the film mass about 1–2 mg⋅cm–2.

Figure 5. Outline of the steps involved in the preparation of mesoporous TiO2

film electrodes.

– 28 –

The electronic contact between particles is produced by sintering during the firing

treatment at about 450 °C. A mesoporous structure with a very high effective surface

area is thereby formed. Analysis of the layers shows their porosity to be about 60 % and

the average pore size 12 nm.

Figure 6. Scanning electron micrograph of a mesoporous TiO2 film supported

on conducting glass. The predominant facets of the anatase crystals have the (101)

orientation.

Figure 6 displays the morphology of such a nanocrystalline TiO2 (anatase) layer

deposited on a transparent conducting oxide (TCO) glass. A large fraction of the

particles has a bipyramidal shape, which is typical for anatase crystalline form. The

exposed surface faces are mostly oriented in the (101) direction.[5] The mean particle

– 29 –

diameter is 20 nm in this case. Their size and morphology can be adjusted by varying

the conditions of the sol-gel process used for film preparation. Films of self-assembled

rod-like particles have been obtained when the hydrothermal treatment of the TiO2

colloid is done in the presence of tetramethylammonium hydroxide at 190–230 °C. The

rod-like particles were observed to have (100) faces terminated from the (001) side. The

pores diameter of the film in this case is 4 nm with a very narrow size distribution.[6]

4.3 Photoinduced charge separation at the solid/electrolyte interface

The use of mesoporous oxide films as a substrate to anchor the dye molecules allow

sunlight to be harvested over a broad spectral range in the visible region. Similarly to

chlorophyll in the green leaf, the dye acts as an electron transfer sensitizer. Upon

excitation by light, it injects an electron into the conduction band of the oxide, resulting

in the separation of positive and negative charges. Charge transfer from photo-excited

dyes into semiconductors was discovered more than a century ago in a famous

experiment by J. Moser.[7] He observed that the photoelectric effect reported earlier by

E. Becquerel on silver plates [8] was enhanced in the presence of erythrosine dye. The

one-page publication describing his observations is shown in Figure 7. A few years

before, H. Vogel in Berlin had associated dyes with the halide semiconductor grains to

make them sensitive to visible light.[9] This led to the first panchromatic film, able to

render the image of a scene realistically in black and white.[10] However, the clear

recognition of the parallelism between the two procedures, a realization that the same

dyes in principle can function in both systems [11] and a verification that their operating

mechanism is by injection of electrons from photo-excited dye molecules into the

conduction band of the n-type semiconductor substrates [12] date to the 1960’s.

– 30 –

Figure 7. A copy of the 1887 publication by J. Moser on the amplification of

photoelectric currents by optical sensitization of silver halides by erythrosin.[7] The

system described in this paper is indeed the first dye-sensitized photovoltaic solar cell.

In subsequent years the idea developed that the dye could function most efficiently if

chemisorbed on the surface of the semiconductor.[13,14] The concept emerged to use

dispersed particles to provide a sufficient interface,[15] then photo-electrodes were

– 31 –

employed.[16,39] Finally, the use of nanocrystalline TiO2 films sensitized by a suitable

molecular dye provided an important technological breakthrough.[17] These

mesoporous membranes have allowed in effect for the first time the development of a

regenerative photoelectrochemical cell based on a simple molecular light absorber,

which attains a conversion efficiency commensurate with that of silicon based

photovoltaic devices, but at a much lower cost.

4.3.1 Molecular engineering of dye sensitizers

Many studies based on the observed bulk photoelectrochemical effects and on direct

probing of the processes occurring at the solid surface have provided firm evidences

that the sensitizing mechanism involves as a primary step electron or hole injection by

the electronically excited sensitizer molecule (S*) into the semiconductor (SC).

S | SC + hν → S* | SC → S+ | (e–)cb SC (23)

S | SC + hν → S* | SC → S– | (h+)vb SC (24)

Alternatively, charge injection into the semiconductor can involve the reductive or

oxidative quenching of the dye excited state by a redox active species (a

supersensitizer) followed by thermal interfacial electron transfer.[18]

S* | SC + D → S– | SC + D+ → S | (e–)cb SC + D+ (25)

S* | SC + A → S+ | SC + A– → S | (h+)vb SC + A– (26)

– 32 –

In the case of the injection of an electron from the excited state of a molecular sensitizer

into the conduction band of a semiconductor [Equation (23)], the thermodynamics of

the photoredox reaction requires the oxidation potential of the dye excited state

φο(S+/S*) to be more negative than the conduction band flatband potential of the

semiconductor, and thus :

φο(S+/S) < φC + ΔE0,0 / F (27)

where φο(S+/S) is the oxidation standard potential of the dye, ΔE0,0 its excitation

energy, φC (SC) the conduction band flatband potential, and F the Faraday constant.

The redox potential for the dye can shift upon adsorption from solution due to

Coulombic or stronger covalent interactions with the solid substrate. This potential

change can amount to several hundreds of millivolts. While n-type semiconductors

cannot be used generally to measure oxidation potentials of adsorbed dye sensitizers by

conventional cyclic voltammetry, reduction potential φο(S/S–) is often more accessible.

Assuming oxidation and reduction potentials of the dye ground state on the surface are

linked by a constant relation :

φο(S/S–) = φο(S+/S) – ΔE0,0 / F + x, (28)

the energetic threshold for charge injection from the dye excited state into the

conduction band of the solid would require the reduction potential of the adsorbed dye

to be φο(S/S–) < φCB + x, where the last term has been found for a large number of

various organic sensitizer molecules to be x = 0.35 V.[19]

The ideal sensitizer for a single junction photovoltaic cell should absorb all light below

a threshold wavelength of at least 900 nm. In addition, it should be anchored to the

semiconductor oxide surface and inject electrons to the conduction band with a quantum

– 33 –

yield of unity. Its redox potential should also be sufficiently high that it can be

regenerated rapidly via electron donation from an electrolyte or a hole conductor.

Finally, it should be stable enough to sustain at least 108 redox turnovers under

illumination, corresponding to approximately 20 years of functioning under natural light

in day-night cycles. The best photovoltaic performance in terms of both conversion

yield and long-term stability has so far been achieved with polypyridyl complexes of

ruthenium and osmium.[20–23] Sensitizers having the general structure ML2X2, where

L stands for 2,2’-bipyridyl-4,4’-dicarboxylic acid (dcbpy), M for Ru(II) or Os(II), and X

for halide, cyanide, thiocyanate, or water,[20–22] are particularly promising. In recent

years, the ruthenium complex dye cis-[RuII(dcbpy)2(NCS)2] has emerged as the model

of a heterogeneous charge-transfer sensitizer for molecular photovoltaic cells. Reported

for the first time in 1993,[20] its performances has been unmatched since then. Only

recently, a credible challenger has been found with the black dye tri(thiocyanato)-

(2,2’:6’,2”-terpyridyl-4,4’,4”-tricarboxylate)ruthenium(II) [≡ RuII(tctpy)(NCS)3] that

exhibits better near-IR photo-response.[23]

N !

N !

COOH !

COOH !

N !

N !

COOH !

COOH !

Ru !

N !

S !C !

N !C !

S !

N !

N !

N !

COO- !

COO- !

COO- !

Ru !

N !

C !

S !

N !

C !

S !

N !C !

S !

cis-[RuII(dcbpy)2(NCS)2] ! RuII(tctpy)(NCS)3 !

Scheme 2

– 34 –

The efficiency of cis-[RuII(dcbpy)2(NCS)2] complex as a redox sensitizer of titanium

dioxide is conferred by several important features of the molecule. Carboxylic groups

carried by the ligands provide a good anchoring of the dye on the acidic surface of

TiO2. Surface derivatization of the mesoporous oxide film is normally performed by

dipping it into a solution of the dye in a 50:50 (v/v) solvent mixture of acetonitrile and

tert-butanol. A monolayer of the sensitizer is formed spontaneously. The adsorption

follows a Langmuir isotherm with a binding constant K = 5×104 l⋅mol–1. The area

occupied by one molecule at the anatase surface at full monolayer coverage is

1.65 nm2. The interaction between the carboxylic group and the oxide is of fundamental

importance in determining the geometrical structure of the adsorbed dye state and

influencing the electronic coupling with the Ti(3d) conduction band orbital manifold.

The most likely configuration supported by IR analysis [24] involves the attachment of

the dye via two of its four carboxylate groups. The carboxylate either bridges two

adjacent rows of titanium ions through bidentate coordination or interacts with surface

hydroxyl groups through hydrogen bonds. Of the two remaining carboxylate groups,

one is ionized while the other remains in the protonated form. Model studies, using the

dcbpy ligand adsorbed onto single-crystal TiO2 (110) rutile, investigated by means of

X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, and quantum

chemical calculations,[25] are in favor of the bridging bidentate configuration illustrated

by Figure 8. The ligand is oriented at an angle of about 40 degrees with respect to the

(001) crystallographic direction. In addition to this linkage mode, calculations suggest

the monodentate ester bond is also thermodynamically stable. The bidentate bonding,

however, is stronger and thus would be the preferred anchoring configuration for the

cis-[RuII(dcbpy)2(NCS)2] dye on titanium dioxide.

The interfacial electron transfer events will be strongly affected by the electronic

structure of the dye in the adsorbed state and the energy level matching between its

excited state and the conduction band of the semiconductor. Generally, the optical

– 35 –

transition of Ru complexes has metal-to-ligand charge-transfer (MLCT) character.

Excitation of the dye involves transfer of an electron from a metal ion d-orbital to the

π* orbital of the ligand. cis-[RuII(dcbpy)2(NCS)2] exhibits two such transitions in the

visible domain. The absorption maxima in ethanolic solution are located at 518 and

380 nm, the extinction coefficients being 1.33×104 and 1.3×104 mol–1⋅l⋅cm–1,

respectively. The complex emits at 750 nm, the excited state lifetime being 60 ns.[20]

Results from ab initio calculation [26] of a decarboxylated cis-[RuII(dcbpy)2(NCS)2]

complex show that the highest occupied molecular orbital (HOMO) level is shared by

both the Ru(II) metal ion and the –N=C=S ligands. Application of photoelectron

spectroscopy have confirmed that both Ru-4d and atomic orbitals centered on the –NCS

groups, in particular S-3p, contribute to the HOMO of the complex.[27] In a

photovoltaic cell, the oxidized dye, after electron injection to the conduction band of the

oxide, should quickly be reduced by a redox species in the surrounding electrolyte. The

observation that the frontier molecular orbital contains a substantial amount of 3p

character from the sulfur atom of the –NCS ligand may play an important role in this

process. The thiocyanate groups point in the direction of the electrolyte, which may

facilitate reduction by mediators, making it particularly suitable for highly efficient

solar cells.

Ab initio calculations also show that the lowest unoccupied molecular orbital (LUMO)

of the cis-[RuII(dcbpy)2(NCS)2] complex is concentrated on the π* structure of the

dcbpy ligands. Hence, absorption of visible light by the compound can be assigned to a

RuNCS-bpy(π*) charge transfer transition. Preliminary calculations also indicate that

the dcbpy rings share their LUMO with the carboxylate groups, thus enhancing

electronic coupling between the dye excited state and the acceptor levels manifold of

the solid.

The oxidation potential and excitation energy of the fully protonated form of the dye in

solution being φ0(S+/S) = +1.10 V/NHE and ΔE0,0 = 1.65 eV, respectively, the

– 36 –

oxidation potential of the MLCT excited state of the sensitizer establishes at

φ0(S+/S*) = –0.55 V/NHE.[20] The flatband potential of TiO2 in dry aprotic solvents

can be as negative as φC = –1.25 V/NHE.[28,29] In such conditions, the conduction

band of the solid would in principle be out of reach of the dye excited state and only

deep localized sub-bandgap states could potentially act as acceptor levels in the

injection process. Surface protonation via adsorption of the carboxylic groups results

however in a positive shift of the flatband potential that can amount to several hundred

millivolts. Moreover, complete deprotonation of the four carboxylic groups of

cis-[RuII(dcbpy)2(NCS)2] was demonstrated recently to cause its oxidation potential to

shift negatively by ca 300 mV.[30] Both effects combined together with the presence of

traces of H2O render the interfacial electron transfer from the dye excited state to the

conduction band of titanium dioxide thermodynamically favorable.

4.3.2 Dynamics of charge injection in wide-bandgap semiconductors

Photoinduced charge injection from an electronically excited molecular state into a wide

continuum of acceptor levels, including the conduction band of a semiconductor, is one

of the simplest photochemical surface reaction [Equation (23)]. This process is however

rather special, in the sense that there are many channels available for the electron

transfer. The reaction can choose its energetic path to yield an electron within the band

of the solid that is characterized by a variable amount of kinetic energy. The energy

excess should also be carried by the dye cation S+, produced concomitantly, in the form

of vibrational excitation. As a consequence, provided the driving force is sufficiently

large compared to the nuclear reorganization energy, the system can find an

activationless path, optimizing in this way the electron transfer rate (Figure 9).

– 37 –

Figure 9. Energetics and dynamics of electron injection from the electronic

excited state S* of a dye to the conduction band of a semiconductor. Charge transfer

from a specific vibronic state v’ of S* can lead to any vibrational state v’’ of the product

S+, provided there is a sufficient density of acceptor levels covering a wide enough

energy range in the solid. Energy conservation requires that a lower lying electronic

state in the conduction band (kinetic energy of the carrier in the conduction band Ek)

corresponds to a higher vibrational state v’’ of S+ (vibrational excitation energy Ev).

This conditions implies that acceptor levels are quantified by the energy spacing hω of

the oxidized state oscillator. In terms of the Marcus model, the interfacial electron

transfer process would be kinetically optimum when its free energy ΔG is equal to the

reorganization energy Λ of the system. This ideal path is available as long as the excess

energy Ex of the excited state of the dye to the lowest acceptor state in the

semiconductor Ex is larger than Λ.

– 38 –

In terms of semiclassical electron transfer theory, the simplest kinetic model describing

the charge injection as a non-adiabatic radiationless process is derived from Fermi’s

Golden Rule. The rate constant for the reaction can be expressed as the product of a

thermally averaged Franck-Condon factor FC, which depends on the driving force ΔGo

as well as the nuclear reorganization energy Λ accompanying the electron transfer, and

an electronic factor which is proportional to the square of the electronic coupling

element |H| :

ket = 4!2

h |H|2 FC

(29)

For a large number of accessible acceptor levels, the summation over all the terms of

the Franck-Condon factor reduces to the unweighted density of final states.[31,32]

ki = 4!2

h |H|2 1

h" na

(30)

In Equation (30), the actual density of final states is approximated by the reciprocal

energy level spacing 1/hω of the dye cation oscillator, multiplied by a factor 0 ≤ na ≤ 1

accounting for the density of empty electronic states available in the solid. Above the

flatband energy level, the density of acceptor states in the conduction band of a

semiconductor is usually very large and the density of final states solely determined by

the density of energy levels of the dye cation (na ≅ 1). Below the band edge, empty trap

states are present, whose density decreases gradually at lower energies (na → 0).

The density of accepting states NC(E) in the conduction band of a semiconductor is

given by Equation (31) :[33]

NC (E) = 4 ! 2 m

de

*

h 2

3/2

E – EC 1/2

(31)

– 39 –

where EC is the energy of the conduction band edge, and m*de the density-of-state

effective mass for electrons. The latter parameter depends strongly on the material. In

TiO2, for instance, assuming m*de ≅ m*e ≥ 6 me, the calculated density of states would

be at least two orders of magnitude larger than that in ZnO, for example, where

m*de ≅ 0.24 me.[34,35] The density of states is also expected to be dependant upon the

size of the semiconductor nanocrystallites. Strong quantum confinement indeed results

in widely spaced electronic levels and therefore in a very low density of states.

Although this size quantization effect would be negligible for TiO2 where the exciton

binding energy is very small, it is expected, for example, to play a significant role for

ZnO particles whose diameter is smaller than ~10 nm.

Equation (30) can only be used when the electron transfer process takes place from a

single prepared excited state of the sensitizer. In the general case, absorption of photons,

whose energy hν is larger than the electronic excitation energy ΔE0,0 of the dye, leads

to the population of higher vibronic levels of the molecule [Equation (32)]. Relaxation

of these vibrationally excited intramolecular states (Equation (33)] and of the whole

system along the classical reaction coordinate is expected to compete with the electron

transfer process [Equation (34)].[36] In these conditions, the electronic coupling |H|

between the donor and the acceptor states becomes a time- and excitation wavelength-

dependent function and cannot be readily accessed anymore.[32]

S | SC + hν (> ΔE0,0) → S* (v’>0) | SC (32)

S*( v’>0) | SC → S*( v’=0) | SC + ∇ kr (33)

S*( v’>0) | SC → S+ | (e–)SC + ∇ ki’ (34)

S*( v’=0) | SC → S+ | (e–)SC + ∇ ki (35)

– 40 –

S*( v’=0) | SC → S | SC + hν’ + ∇ Σkd (36)

Two limiting cases could be considered that would, however, let us treat in a simple

way the interfacial electron transfer process as involving a single prepared excited state

of the sensitizer: (1) Charge injection is slow enough compared to the vibrational

relaxation of the dye excited state ( ki’ << kr ). In this event, electron transfer would be

able to take place only from the lowest excited state (v’=0) [Equation (35)], and the

injection quantum yield Φi would be simply controlled by the kinetic competition

between the electron injection [Equation (35)] and the decay of the excited state

[Equation (36)] :

Φi = ki / ( ki + Σkd ) = ki / ( ki + 1 / τf ) (37)

where τf is the excited state lifetime of the sensitizer. (2) Charge injection is fast

compared to nuclear relaxation of the excited state ( ki’ >> kr ). In this case, interfacial

charge transfer would take place from the prepared hot vibronic level [Equation (34)]

and the quantum yield for the primary injection process would be close to unity Φi ≅ 1.

For both limiting cases, ki’ << kr and ki’ >> kr, relation (30) would be relevant,

provided electron transfer is non-adiabatic.

When the electronic coupling of the donor and acceptor becomes sufficiently large

(typically |H| > 150 cm–1 ≅ 0.7 kT), the electron transfer will be increasingly adiabatic

and, in the absence of solvent dynamics control, the rate constant will eventually be

proportional to a nuclear vibration frequency factor νn. In this case the electronic

coupling element is not contained in the rate expression. For other cases, where |H| is

small enough, the value of the coupling element is needed for a quantitative description

of the electron transfer rate. There is obviously a considerable interest in the role of the

– 41 –

electronic coupling factor, as the separation distance and anchoring geometry of the

sensitizer on the surface will determine its magnitude. The Gamov expression (38) is

frequently used to estimate the changes in |H| with separation distance in photoinduced

electron transfer where the electron donor and acceptor are fixed relative to one

another :

|H| = |H|0 exp [ – β ( r – r0 ) ] (38)

where the damping factor β has values ranging from 0.85 to 2.5 Å–1. Provided that

other factors beside distance do not influence the electron transfer rate, Equation (39)

can be used to estimate the rate at a known separation distance r :

ket = ket0 exp [ – β ( r – r0 ) ] (39)

where ket0 ≅ 1013 s–1. Other parameters, such as spin changes, symmetry factors, and

the relative orientation of both reactant may influence the magnitude of the electronic

coupling element.[37]

In favorable thermodynamic conditions, where the lowest electronic excited state

energy level of the sensitizer lies above the bottom edge of the conduction band, charge

injection competes kinetically with the decay of the sensitizer’s excited state [Equation

(36)]. Hence, for dyes that are characterized by emission lifetimes τf of the order of one

nanosecond, interfacial electron transfer rate constants of the order of ki = 1011 s–1

suffice to ensure high injection quantum yields. Most of the previous knowledge on

bulk semiconductor-electrolyte interfacial charge transfer is derived from steady-state

photocurrent measurements achieved in photo-electrochemical cells. Obtaining electron

transfer rate constants from such an indirect method, however, is difficult because

photocurrent depends on many other interfacial and bulk processes.

– 42 –

The rapid dynamics of electron injection can be investigated by application of transient

laser spectroscopy to colloidal dispersions or nanocrystalline semiconductor films. Such

materials are particularly amenable to time resolved optical studies, as they display a

good transparency throughout all the visible and NIR spectral domains. Moreover, they

are characterized by a high solid surface area exposed to the solution, yielding high

sensitizer absorbance for only monolayer dye coverage. Most presently studied oxide

semiconductor systems, namely TiO2, SnO2 and ZnO, are also of particular interest for

the development of artificial photosynthetic and photovoltaic devices.[99]

Earlier studies on dye sensitized TiO2 reported nanosecond time constants for the

injection kinetics.[38–41] These results were obtained indirectly from the measurement

of the injection quantum yield and implicitly assumed that the interfacial electron

transfer reaction was competing only with the decay of the dye excited state. Other

works were based on the same assumption but used measurements of the dye

fluorescence lifetime, which provided ps-fs time resolution.[42–44] Direct time

resolved observation of the build up of the optical absorption due to the oxidized dye

species S+ has been employed in more recent studies.[45–50] This appears as a more

reliable way of monitoring the charge injection process as it does not require any initial

assumption on the sensitizing mechanism.

Figure 10a shows the transient difference spectra obtained upon nanosecond laser

excitation of cis-[RuII(dcbpy)2(NCS)2] in ethanolic solution and of nanocrystalline

titanium dioxide transparent films onto which the sensitizer was adsorbed. The dye is

excited with 605 nm output of a laser system and the absorbance change observed

immediately after the laser excitation is plotted as a function of the detection

wavelength.[51] Luminescence quenching and photocurrent experiments have

confirmed that 600 nm excitation of the sensitizer resulted in the formation of the

charge separated state S+|(e–)SC.

– 43 –

Figure 10. (a) Transient absorption spectra obtained upon ns pulsed laser

excitation of cis-[RuII(dcbpy)2(NCS)2] dye in ethanolic solution (1), and of a sensitized

TiO2 transparent film (2). Spectra were recorded 50 ns (1a, 2a) and 0.5 µs (1b, 2b)

after the laser excitation pulse (λ = 605 nm, 5 ns pulse duration). (b) Transient

absorption spectra recorded 6 ps after ultrafast laser excitation (λ = 605 nm, 150 fs

pulse duration) of cis-[RuII(dcbpy)2(NCS)2] dye in ethanol (1), and of a fresh sensitized

titanium dioxide film (2). Insert shows the temporal behavior of the absorbance of the

latter system, measured at λ = 750 nm with sub-picosecond time-resolution.

– 44 –

The spectrum obtained upon irradiation of dye sensitized TiO2 displays a broad

absorption feature peaking around 800 nm which half lifetime exceeds 0.5 µs. Such a

lifetime is more than one order of magnitude longer than that of the isolated dye excited

state in solution. The recorded spectrum is comparable to that of the one-electron

oxidation product [RuIII(dcbpy)2(NCS)2]+ of the complex produced by oxidative

quenching of the excited state in an alcoholic solution containing methylviologen as an

acceptor,[46] or generated by pulse radiolysis.[52] It can be readily distinguished from

the spectrum of the dye excited state obtained in solution, whose band maximum is

located at 710 nm.[51] These observations demonstrate unambiguously that the

transient spectral feature observed upon excitation of the sensitized semiconductor

cannot be assigned to an excited state of the dye but must be attributed to the charge

separated state S+|(e–)cb resulting from interfacial charge injection, where both a

LMCT transition of the –NCS ligands to the Ru(III) metal ion center in S+ and

absorption by conduction band and/or trapped electrons contribute to the spectrum.

Further sub-picosecond data were collected.[46] Transient data measured for dye-

sensitized TiO2 films were compared with those obtained for control dye-coated ZrO2

films, as the high conduction band edge of the latter material should prevent electron

injection. Figure 10b shows the absorption difference spectra obtained at a time delay of

5 ps after 605 nm pulsed laser excitation. The spectrum obtained for the dye-sensitized

zirconia films exhibits a maximum at 710 nm as observed for cis-[RuII(dcbpy)2(NCS)2]

dye in ethanolic solution and is therefore assigned to the dye MLCT excited state. On

the other hand, the transient spectrum recorded for sensitized TiO2 displays a maximum

at 800 nm that is characteristic of the dye cation S+. In contrast to the data obtained for

dye-coated ZrO2 films, the difference spectra measured with sensitized TiO2 exhibited

some temporal evolution for time delays less than 5 ps. Typical transient absorption

data at a probe wavelength of 750 nm is shown in the insert of Figure 10b. The data

show a fast ~100 fs instrument response limited signal growth followed by a slower

– 45 –

kinetic phase extending on several picoseconds. A detailed multi-exponential analysis

of the traces obtained revealed at least three kinetic components with lifetimes of

<100 fs (35%), 1.3 ps (22%) and 13 ps (43%).[29,53]

In a recent experiment,[35] mid-IR spectroscopy was used to probe directly the buildup

of electron concentration inside the semiconductor. Careful examination at different

wavelengths and time scales yielded a complex kinetics which could be described by

two exponentials with rise times of 50 ± 25 fs (> 84 %) and 1.7 ± 0.5 ps (< 16 %), the

slower component being very sensitive to the sample condition.

The origin of such complex electron transfer kinetics is not clear yet. The participation

of various electronic excited states of the Ru(II) dye sensitizer to the reaction was ruled

out as one failed to observe any effect of the excitation wavelength. Nor was a

significant difference observed in the results obtained for dyed TiO2 films exposed to

air and in propylene carbonate, thus excluding possible effects due to the solvation

dynamics.[53] Direct interfacial electron transfer to various localized defect states could

be associated to different electronic coupling elements and could therefore result in a

wide distribution of rate constants. The occupancy of these trap states can be modulated

by sweeping the Fermi level below the flatband energy upon applying an external

electrical bias. Modulation of the applied potential, does not appear, however, to result

in any noticeable change in the injection yield and kinetics.[29] On the other hand,

adsorption of potential determining cations, such as Li+, that causes the flatband

potential of the semiconductor to shift positively, apparently also affects the electron

injection rate.[54] An acceleration factor of 8 fold was observed in particular for

cis-[RuII(dcbpy)2(NCS)2]-sensitized nanocrystalline titanium dioxide in pure propylene

carbonate upon addition of 0.1 M Li+.[29] These observations suggest that the multiple

time constants result from heterogeneities in the energetics of the nanocrystalline TiO2

films. In addition, adsorption of dye molecules on different surface sites and with

various anchoring geometries could also cause an intricate kinetic outcome.[55]

– 46 –

Figure 11. Energy scheme for cis-[RuII(dcbpy)2(NCS)2] dye sensitizer adsorbed

on various oxide semiconductors. Molecular levels are based on the values of the

oxidation potential of the complex: φo(S+/S) = +0.86 V/SCE and excitation energy

ΔE0,0 = 1.85 eV.[20] The flatband potentials φfb(SC) of the different solid oxides were

estimated by monitoring the optical absorption at 750 nm of transparent

nanocrystalline electrodes in propylene carbonate as a function of applied

potential.[60]

The fastest kinetic phase of electron injection in cis-[RuII(dcbpy)2(NCS)2]-sensitized

nanocrystalline titanium dioxide films apparently takes place in the femtosecond

regime. Besides, the vibrational relaxation of the dye excited state is expected to occur

typically within 0.4–1 ps (kr ≅ 1012 s–1).[56,57] Observed injection rate constants of

the order of 1013 s–1 certainly preclude complete thermalization of the dye excited state

S* to the v’ = 0 level prior to the reaction, and suggest that charge transfer can occur

– 47 –

directly from hot (v’ > 0) excited sensitizer molecules. In systems where the v’=0

energy level of the electronically excited state of the dye lies below the bottom of the

conduction band of the semiconductor (na→0), charge injection from vibrationally

relaxed excited molecules of the sensitizer is either slow or unfeasible. However, if

electron injection from a hot vibronic state of the dye is able to compete successfully

with its nuclear relaxation (ki’ > kr), charge injection should become possible for higher

excitation photon energy, and an excitation wavelength dependence of the quantum

yield Φi = ki’ / ( ki’ + kr ) would be expected.

Figure 11 schematizes the energetics of the cis-[RuII(dcbpy)2(NCS)2] dye sensitizer

adsorbed on various oxide semiconductors. This dye was chosen because of its broad

spectrum that should allow the excitation of hot vibronic states upon excitation by

photons of energy hν > ΔE0,0. Picosecond resonance Raman studies have indicated that

vibrational relaxation of Ru(bpy)32+ analogous complex dye is complete within ca

6 ps.[58,59] The presence of –N=C=S ligands, that are characterized by a high

frequency stretching mode (ϖ ≅ 2139 cm–1),[51] is expected, however, to reduce this

relaxation time to 1–2 ps.

In dry propylene carbonate, the flatband energy of amorphous (a-Nb2O5) and

crystalline niobia (c-Nb2O5), tantalum pentoxide (Ta2O5) and zirconia (ZrO2) was

found to be 0.2, 0.4, 0.7 and 1.1 eV respectively higher than that of TiO2.[60] As a

consequence, the v’=0 level of the MLCT excited state of the adsorbed dye lies below

the bottom edge of the conduction band of these materials. Monitoring of the

sensitizer’s ground state bleaching signal upon nanosecond laser flash photolysis of the

Ru(II) complex clearly exhibited a biphasic kinetic behavior. Excited dye molecules

that do not inject into the solid produce a recovery of the ground-state absorption within

15 ns. On the other hand, the dye cation S+, generated by the photoinduced electron

transfer process, recaptures the injected electron much slower in the microsecond time

domain.[51] Both kinetic steps, whose rate constants are two orders of magnitude apart

– 48 –

from each other, can be easily separated. Quantitative evaluation of their respective

amplitudes allows then the evaluation of the absolute injection quantum yield Φi at any

excitation wavelength, independently of the absorption spectrum of the dye.[60] Results

obtained for various RuII(dcbpy)2(NCS)2-sensitized semiconductors show a strong

excitation energy dependence of Φi. For c-Nb2O5 a clear wavelength dependence of the

injection efficiency is observed between λ = 650 nm, the onset of injection, and

λ = 500 nm, where the charge transfer quantum yield reaches a plateau value at ~0.75

(Figure 12).

Figure 12. Dependence upon excitation photon energy hν of electron injection

quantum yield Φi obtained for various oxide semiconductors sensitized by

cis-[RuII(dcbpy)2(NCS)2].

– 49 –

Measurements carried out in identical conditions with dye-sensitized TiO2 gave an

injection quantum yield close to unity that was independent of the excitation

wavelength. On amorphous niobia, whose flatband potential is intermediate between

those of TiO2 and c-Nb2O5, the injection onset is shifted to the red by approximately

0.2 eV compared to the crystalline material. On tantalum pentoxide, the injection onset

is found in the blue at λ = 480 nm. The shift of the electron injection threshold by

+0.6 eV for Ta2O5 compared to c-Nb2O5 is larger than the energy difference measured

between the positions of the respective conduction band edges of both materials

(0.3 eV) and should probably be related to a lower density of trap states in tantalum

oxide. Finally, in accordance to the energy scheme, no charge injection was observed

for cis-[RuII(dcbpy)2(NCS)2] adsorbed on ZrO2 up to an excitation energy of 2.7 eV.

The dependence of the photosensitization efficiency upon the excitation wavelength has

also been observed in a photo-electrochemical cell based on TiO2 sensitized by

FeII(dcbpy)2(CN)2 complex.[61] The absorption band selective photon-to-current

conversion efficiency measured in this case suggested that charge injection into the

semiconductor is occurring via an ultra-short-lived, upper excited state of the dye.

These observations of an excitation wavelength dependence of the charge injection

process show that photoinduced interfacial electron transfer from a molecular excited

state to a continuum of acceptor levels can take place in competition with the relaxation

from upper excited levels. The rather slow growth of the injection quantum yield above

the energy onset suggests it actually reflects the density of acceptor states in the solid

that are present below the conduction band edge. In conditions where the injection

quantum yield is unity (ki’ >> kr) and electron transfer takes place to the conduction

band of the semiconductor (na ≅ 1), the occurrence of the electron transfer process from

a single prepared state S*(v’ > 0) validates the simple model of Equation (30) and

allows to estimate the electronic coupling matrix element |H|. Assuming a frequency of

the dye cation oscillator ϖ ≤ 1500 cm–1, a value of |H| ≤ 113 cm–1 (≅ 1/2 kT) would be

– 50 –

calculated from the rate constant ki = 1013 s–1 measured typically for

[RuII(dcbpy)2(NCS)2]-sensitized nanocrystalline TiO2. Although the value used for the

cation vibration wavenumber ϖ, and therefore that determined for |H|, are here probably

over-estimated, this figure corresponds to a rather strong electronic coupling and

suggests the electron injection rate could have reached the adiabatic limit.

Modulation of the injection efficiency between excited Ru(II) complexes and

nanocrystalline TiO2 and SnO2 transparent films was observed upon biasing the Fermi

level of the oxide electrodes.[62,63] Applying a negative bias voltage to the film

impaired the photosensitized charge injection, turning on the photoluminescence of the

adsorbed dye. Basing on this results it has been suggested the rate of heterogeneous

electron transfer depends directly upon the driving force of the reaction,[63] and follows

a normal Marcus-type of behavior. Alternatively, such an effect could also be

rationalized by the reduction of the density of acceptor states, which are gradually

populated upon raising the Fermi level of the solid. The Franck-Condon factor, that

comprises parameters such as the reaction free energy ΔG0, the nuclear reorganization

energy Λ and the temperature T, is expected to play only a negligible role in systems

that are kinetically near optimum in terms of the Marcus theory and that are

characterized by a large number of acceptor states. According to Equation (30), the rate

of interfacial electron transfer for a given sensitizer is controlled only by the electronic

coupling matrix element |H| and the acceptor states density. The activationless nature of

the charge transfer process has been experimentally confirmed by the observation of

temperature independent injection kinetics.[47] Other reported data show that, in

energetically favorable conditions, the rate of electron injection is not controlled by the

energetics of the sensitizer’s excited state, nor by the medium reorganization, but rather

by the density and occupancy of electronic states in the solid.[29]

– 51 –

Table 1. Electron injection rate constants ki, reported for various dye sensitizers

adsorbed on nanocrystalline TiO2.

Dye-sensitizers Medium ki [s–1] [a] |H| [cm–1] [d] References

RuII(bpy)3 [b] H2O, pH10 2×105 2×10–2 [16]

RuII(dcbpy)3 H2O, pH3 3×107 2×10–1 [16]

RuII(bpy)2(dcbpy) air 2×108 4×10–1 [41]

Eosin-Y H2O, pH3 9×108 1 [38,45]

[RuII(dcbpy)2(CN)2]3 EtOH 6×109 3 [64]

Fluorescein 27 H2O, pH3 3×1012 [a] 6×101 [49]

RuII(dcbpy)3 EtOH 4×1012 7×101 [42]

Coumarin-343 CH3OH 5×1012 [a] 8×101 [43,50,65]

Perylene vacuum 5×1012 8×101 [47]

RuII(dcbpy)2(NCS)2 EtOH 1013 [a] 102 [46]

H2TCPP PC 1013[a] 102 [29]

ZnTCPP PC 1013 [a] 102 [29]

FeII(CN)64– [c] D2O, pH2 >2×1013 >1.6×102 [66]

Alizarin [c] EtOH >2×1013 >1.6×102 [67]

[a] Only the fastest kinetic component is taken into account when multiexponential

kinetics were reported. [b] Linkage of most of the dye molecules onto the surface is

ensured by a carboxylic or phosphonic anchoring group. In case such a group is

lacking, adsorption occurs through purely electrostatic interactions. [c] Fe(CN)64–

and alizarin form charge transfer (CT) surface complexes on TiO2 that are the relevant

chromophores in the photosensitization process. [d] Electronic matrix elements |H|

coupling dye excited states with the acceptor states of the semiconductor were

calculated with Equation (30), assuming for all systems na = 1 and ϖ = 1500 cm–1.

– 52 –

On titanium dioxide, the photoinduced charge injection process were reported to take

place on time scales ranging from less than 100 fs to several microseconds, depending

on the sensitizer used (Table 1). Such a variation of eight orders of magnitude can be

accounted for only by very different values of the electronic coupling between the dye

excited state and the acceptor orbitals at the surface of the semiconductor. Using

Equation (30), and assuming for all systems na = 1 and a collective vibrational mode

frequency of the dye oxidized state ϖ = 1500 cm–1, the electronic coupling matrix

element can be calculated for each sensitizer. Obtained values of |H| vary from

0.02 cm–1 to > 160 cm–1. Considering relation (38), and assuming a damping factor

β = 1.2 Å–1, this range of figures implies a difference in the electron transfer reaction

distance of the order of 8 Å between the slowest and the fastest system. Various types

of association of the sensitizer with the oxide surface could explain such a difference.

Adsorption through electrostatic interaction is clearly insufficient. In aqueous medium,

adsorbed water molecules on TiO2 can act as spacers and force the dye sensitizer to stay

several angstroms apart from the solid. Moreover, in the case of the symmetric

Ru(bpy)32+ complex, the LUMO of the dye is delocalized over all three ligands, thus

considerably increasing the average separation distance for interfacial electron transfer.

Strong electronic coupling between the π* molecular orbital of the dye excited state and

the empty TiIV–3d orbital manifold of the semiconductor is achieved by directly linking

the sensitizer’s moiety that carries the lowest energy π* orbital to the surface.

Carboxylic and phosphonic anchoring groups are quite good in coupling dye sensitizers

onto the surface of TiO2. Charge injection rate constants obtained with such systems

appear to be hardly dependent on the type of chromophore used, as they all establish at

ca ki = 1013 s–1, which value is probably close to the adiabatic limit.

– 53 –

4.3.3 Recapture of the injected electron

Figure 13 schematizes the energetics and dynamics of processes that take place after

charge injection from a molecular excited state to the acceptor levels of a

semiconductor. Thermalization and trapping of hot injected carriers is known to occur

typically with a rate constant kth ≅ 1013 s–1.[68–70] Reverse transfer of a hot electron

(k–i) is therefore generally prevented. The kinetics of back-electron transfer from the

conduction band to the oxidized dye follow a multiexponential time law, occurring on a

microsecond to millisecond time scale. Two reasons are suggested for the relatively

slow rate of the recapture of the injected electron : (1) While electron injection is

kinetically near optimum, the high exoergicity of the back electron transfer can make

the system lie deep in the inverted Marcus region, where the rate of the charge transfer

process is expected to decease with increasing driving force. (2) Alternatively, the

dynamics of trapping and detrapping of electrons localized in intraband-gap states can

control the overall reaction kinetics that would not depend upon the sole interfacial

electron transfer rate.

Efficient dye sensitizers of oxide semiconductors are generally characterized by an

oxidation potential of their excited state φo(S+/S*) that is close to the conduction band

flatband potential φfb of the solid. As a consequence, the free energy ΔGbo of the back

electron transfer can be as negative as –1 to –2 eV, depending on the potential assumed

for free and/or trapped electrons involved in the reaction. The total reorganization

energy associated with the heterogeneous charge transfer process is typically of the

order of 0.5 eV, and is therefore smaller than the reaction driving force Λ < –ΔGbo. In

terms of current electron transfer theory, this situation, depicted by Figure 13,

corresponds to an inverted kinetic region.

– 54 –

Figure 13. Energetics of the charge recombination following electron injection

(ki) from a dye excited state S* into the conduction band of a semiconductor.

Thermalization and/or trapping of injected electrons (kth) takes place prior to the

interfacial electron back transfer to the dye oxidized state S+. The reaction free energy

associated to the latter process depends upon the population of the electronic states in

the solid and can be distributed over a broad range of values. Numerical potential data

shown in the Figure are those of the cis-[RuII(dcbpy)2(NCS)2] | TiO2 system.

For a non-adiabatic process the ET rate constant is generally expressed by

Equation (29). Within the classical limit where the energy of the vibrational modes

associated with the activated complex formation is small (hν << kT):

FC = 2! " kT exp ( –#G‡ / kT ) (40)

– 55 –

and

ΔG‡ = (ΔGo + Λ)2 / 4Λ, (41)

where ΔG‡ is the reaction activation energy. However, this classical expression is not

generally adequate to describe the kinetics of electron transfer within the inverted

region. Introducing a quantum modification of the Franck-Condon factor by assuming a

single collective high frequency vibrational mode (hν > kT) yields :

FC = 2! "o kT exp – "i

h# 1

w ! !w=0

"

"i

h#

w

exp – ($Go + w h# + "o)

2

4 "o kT (42)

where Λi and Λo are the high frequency mode (inner sphere) and low frequency modes

(inner- and outer-sphere) terms of the reorganization energy, respectively. The quantum

treatment of high frequency vibrational modes has a marked effect in the inverted

Marcus region. The large Franck-Condon coupling that characterizes generally the

inverted region renders nuclear tunneling a dominant process. The first consequence of

this effect is a drastic decrease of the dependence of the electron transfer rate upon its

energetics. Nuclear tunneling underneath the nuclear reorganization barrier also means

the electron transfer process in these conditions becomes activationless. As a second

consequence, it is therefore expected that the temperature dependence of the electron

transfer kinetics vanishes.

In accord with the experimental findings that the charge recombination process exhibits

inverted region kinetic behavior [71–73] and the predictions of the semiclassical model

above, pseudo-activationless kinetics were indeed observed. The dynamics of the

electron back transfer from the conduction band of TiO2 nanoparticles to the cations of

various organic sensitizers was shown to be essentially insensitive to temperature.[74]

The temperature and medium dependence of the kinetics of the back electron transfer

– 56 –

process taking place from the conduction band of mesoporous TiO2 to the oxidized

form of the adsorbed cis-[RuII(dcbpy)2(NCS)2�] dye sensitizer was also

investigated.[75,76] As expected from the thermodynamics of the process (ΔGo ≅ –

1.75 eV in ethanol), that should make the reaction lie deep in the inverted region, the

effect of the temperature on the reaction rate was very weak. A decrease of the rate

constant by less than a factor of 2 was observed when the temperature was varied from

300 K down to 100 K. This and the fact that hardly any medium dependence of the

electron transfer rate could be observed suggested that the Franck-Condon barrier to

electron transfer is dominated by high frequency modes which make its rate of crossing

mainly controlled by nuclear tunneling.

The insignificant role played by the Franck-Condon factor implies the electronic

coupling dictates to a large extent the kinetics of the charge transfer process. Fitting of

experimental temperature dependence data by Equations (29) and (42) yielded values of

the electronic coupling matrix element |H| of the order of only a few cm–1.[74] This

electronic coupling is fairly weak compared to that of the charge injection, where |H|

was found for the same sensitizer to be one or two orders of magnitude larger. This

difference could be explained by the configuration of the sensitizer molecules in the

adsorbed state. In efficient systems, forward electron transfer is favored by directly

anchoring the sensitizer’s moiety that carries the LUMO of the dye to the surface. In

molecules that possess a large transient dipole moment, charge recombination requires

the electron must be transferred from the semiconductor to the oxidized center over a

longer distance. This effect is particularly evident for Ru(II) complexes such as

cis-[RuII(dcbpy)2(NCS)2]. Electron injection into TiO2 takes place from the

carboxylated bipyridyl ligands that are linked to the oxide surface and carries the lowest

π* orbital. The distance separating the center of the π* system in the sensitizer’s excited

state and the first layer of Ti(IV) ions in the solid is approximately 5.5 Å. The reverse

reaction, however, involves an electron transfer from the semiconductor to the Ru(III)

– 57 –

center of the oxidized state, about 8 Å apart. According to the Gamov expression

[Equation (38)], and assuming β = 1.2 Å–1, a difference of 2.5 Å in the ET distance

would imply a variation of the value of the electronic coupling by a factor of 20, in

good agreement with experimental data. For systems that do not apparently benefit from

this favorable effect, charge recombination was reported to occur in the subnanosecond

time scale.[48,49,77] Logically, the value of the electronic coupling in these cases was

estimated to be of the same order of magnitude (|H| ≅ 50–100 cm–1) than that of the

electron injection process.[49,78]

Whether charge transfer occurring through the solid/liquid interface proceeds directly

from free electrons in the conduction band or is mediated by surface states is an

important clue in the understanding of the mechanism and kinetics of the back electron

transfer reaction. In principle, a distribution of energetically different traps for electrons

could be responsible for a non-single-exponential recombination rate. Multiexponential

kinetics of back electron transfer processes were indeed reported in several recent

publications. Durrant and co-workers have presented some new data on this issue,

showing the reaction to be strongly dependent on applied potential and electrolyte

composition.[79] In agreement with the conclusions reached by Lian and co-

workers,[65,80] these observations show that kinetics of charge recombination between

electrons injected into nanocrystalline TiO2 films and adsorbed dye cations are strongly

dependent upon occupancy and energetics of the electronic states in the solid. They also

suggest the back-electron transfer dynamics is controlled by electron transport between

energetically distributed trap sites within the oxide nanoparticles.[81] This may be of

relevance for the performance of the cell and should be considered in the modeling of

the electrical performance together with the reaction between the electrolyte mediator

and conduction band electrons.[82]

– 58 –

4.4 Charge separation in molecular photovoltaic devices

Upon irradiation, redox dye photosensitizers adsorbed on the surface of wide bandgap

metal oxide semiconductors readily inject an electron in the conduction band of the

solid. While charge injection has been found for numerous efficient systems to occur in

the femtosecond time frame, the electron back transfer takes place much more slowly,

typically in the microsecond-millisecond domain. This charge recombination process

can be intercepted by reaction of a reducing mediator M with the oxidized dye

[Equation (43)]. The overall efficiency of the light-induced charge separation then

depends upon the kinetic competition between back electron transfer and dye

regeneration processes.

S+ | e– (SC) + M → e– (SC) + S | SC + M+ (43)

Photovoltaic cells based on the sensitization of mesoporous titanium dioxide by Ru(II)

complex dyes in conjunction with the I3–/ I– redox couple as a mediator have proved

very efficient at exploiting this principle. In such systems, the ionic mediator travels

back and forth by diffusion from the working- to the counter-electrode to shuttle to the

sensitizer the electrons that have gone through the electrical circuit.[17,20,83] Recently,

solid-state devices have been described where the liquid electrolyte present in the pores

of the nanocrystalline oxide film is replaced by a large bandgap p-type semiconductor

acting as a hole-transport medium.[84–87]

– 59 –

4.4.1 Interception of dye cations by a redox mediator

The interception of the oxidized dye by the electron donor in the electrolyte, i.e., iodide,

is crucial for obtaining good conversion yields and high cycle lifetime of the sensitizer.

For cis-[RuII(dcbpy)2(NCS)2] dye, time-resolved laser experiments have shown the

interception to take place within about 10 ns under the conditions applied in the solar

cell. The S+/S couple shows reversible behavior in different organic solvents, the

standard redox potential in acetonitrile being φo = 0.83 V/SCE. The lower limit of 1 s

can be derived for the lifetime of the oxidized dye from cyclic voltammetry. This means

that interception is 108 times faster than intrinsic degradation of the oxidized sensitizer,

explaining the fact that cis-[RuII(dcbpy)2(NCS)2] can sustain 100 million turnovers in

continuous solar cell operation without loss of performance. Lack of adequate

conditions for rapid regeneration of the dye leads to dye degradation.

The I3–/I– redox couple has been found to be particularly suited fore dye-sensitized

photo-electrochemical solar cells based on nanocrystalline TiO2, as it rapidly

regenerates the sensitizer [Equation (44)] and ferries charges between the two

electrodes. In these devices no other known redox couple works nearly as well.

Although in solution I– is capable of quenching reductively the excited state of many

dyes [Equation (25)], on a semiconductor surface such as SnO2 and TiO2, the iodide

quenching is not able to compete kinetically with the ultrafast charge injection.[88]

S+ | TiO2 + 3/2 I– → S | TiO2 + 1/2 I3– (44)

The detailed mechanism of the two-electron transfer dye regeneration reaction

[Equation (44)] has not been fully elucidated and many factors appear to influence its

rate.[22,83] The following one-electron transfer reactions can in principle take place on

– 60 –

the surface of the oxide and account globally for the oxidation of iodide to

triiodide :[22,89]

S+ | TiO2 + I– → S | TiO2 + I• (45)

I• + I– → I2–• (46)

S+ | TiO2 + 2 I– → S | TiO2 + I2–• (47)

2 I2–• → I– + I3– (48)

Oxidation of iodide to I2–• radical is thermodynamically more favorable than the

reaction leading to the iodine atom.[90] Thus, reaction (47) is favored over

reaction (45), provided that (I–, I–) or (S+, I–) ion pairs are present in significant

amount.[22,89]

The kinetics of the oxidation of iodide by the oxidized state of

cis-[RuII(dcbpy)2(NCS)2] sensitizer adsorbed on nanocrystalline TiO2 films was

measured by transient laser spectroscopy.[91] Figure 14 shows the transient absorption

kinetics recorded in propylene carbonate with various electrolytes added. In all cases,

the recovery of the ground-state absorption of the dye, after the fast electron injection

into the solid, does not follow a simple kinetic law. In the absence of any electrolyte

(trace a), the time needed to reach half of the initial absorbance (t1/2) through back

electron transfer is 2 µs. Total recovery of the initial absorption, however, requires

several hundreds of microseconds to milliseconds. Traces b, c, and d were recorded

after addition of a common concentration of 0.1 M of iodide in the form of

tetrabutylammonium (TBA+), Li+, and Mg2+ salts, respectively. Addition of the

– 61 –

electrolyte in all three cases lead to a considerable acceleration of the dye regeneration

with t1/2 < 200 ns and complete suppression of the slow kinetic tail.

Figure 14. Time course of the transient absorbance changes measured upon

laser excitation of cis-[RuII(dcbpy)2(NCS)2] dye adsorbed on nanocrystalline TiO2

films. Bleaching signals were measured at λ = 520 nm in anhydrous propylene

carbonate, without electrolyte (a), and in the presence of TBAI 0.1 M (b), LiI 0.1 M (c),

and MgI2 0.05 M (d). The insert displays the dependence of the half lifetime t1/2 of the

dye ground-state absorbance recovery upon the concentration of Li+ cations.

Concentration of iodide [I–] = 0.1 M was kept constant while pLi+ ≡ –log[Li+] was

varied.

The rate of the reaction leading to the regeneration of the dye ground-state was found to

depend strongly on the nature and concentration of cations present in the solution. Small

– 62 –

cations able to specifically adsorb onto the oxide surface, such as Li+ and Mg2+, were

found to favor the fast oxidation of iodide by the sensitizer’s oxidized state. A sudden

acceleration of the electron transfer process was observed at a critical cation

concentration (see insert of Figure F4.4/1). Electrophoretic measurements showed that

this concentration corresponds to the reversal of the titanium dioxide particle surface

charge from negative to positive upon adsorption of ζ-potential-determining species.

This observation was interpreted in terms of a change in the reaction mechanism

characterized by different rate constants. The slower reaction path, that does not require

the iodide anions to be adsorbed onto the surface, was attributed to the

thermodynamically unfavorable oxidation of I– to iodine atom [Equation (45)].

Alternatively, the encounter of a (S+, I–) complex with a second iodide anion could

yield I2–• radicals directly as a product of the electron transfer process [Equation (49)].

(S+, I–) + I– → S + I2–• (49)

These reactions should be prevalent as long as the solid surface is negatively charged.

When the surface charge is reversed to positive upon adsorption of the cations, a faster

mechanism becomes predominant. Because it requires high local concentration of I– on

the surface of TiO2, the latter was suggested to be due to the thermodynamically more

favorable oxidation of I– to I2–•, that involves prior formation of (I–, I–) ions pairs on

the surface [Equation (50)].

S+ + (I–, I–) | TiO2 → S + I2–• (50)

Apart from recapture of the injected electrons by the oxidized dye, there is an additional

loss channel in the nanocrystalline dye-sensitized cell which involves reduction of

triiodide ions in the electrolyte present within the mesoporous network :

– 63 –

I3– + 2 ecb–(TiO2) → 3 I– (51)

The back electron transfer reaction between conduction band electrons and I3–

[Equation (51)] is the ultimate fate of photoinjected carriers. This reaction can be

directly followed by measuring the dark current of the photovoltaic cell. The latter

should be kept at a minimal level as it determines the photovoltage and, hence, the

overall conversion efficiency of the device.[92–94] On mesoporous TiO2 electrodes

sensitized by cis-RuII(dcbpy)2(NCS)2, the rate of the back reaction of injected electrons

with I3– was measured from intensity modulated experiments and was observed to be

second order in the electron density, with k = 8.4×103 M–1 s–1.[94] As for the direct

recombination processes discussed above that also imply the reaction of conduction

band and trapped electrons with acceptor molecules at the surface, the rate of charge

transfer is expected to depend strongly on the distribution and occupancy of intra-

bandgap states in the semiconductor, and therefore upon the light intensity, the applied

potential bias, and the nature and concentration of adsorbates.

4.4.2 Charge carrier percolation through mesoporous solid films

The migration of electrons within the TiO2 conduction band to the current collector

involves charge carrier percolation over the mesoscopic particle network. This

important process which leads to nearly quantitative collection of injected electrons is

presently attracting a great deal of attention.[81,95–98] The mesoporous electrode is

very different compared to a compact semiconducting layer because (1) the

nanocrystalline film possess only a very low inherent conductivity, (2) a space charge

layer is unable to establish within minute-size individual particles that are smaller than

– 64 –

the Debye’s length, and (3) the oxide particles and the pores filled by the electrolyte

form interpenetrating networks whose phase boundaries produce a junction of huge

contact area. In an approach to rationalizing the transport phenomena, mesoporous films

may be viewed as an ensemble of individual nanoparticles through which electrons can

percolate by hopping from one crystallite to the next, rather than regarding them as

perforated compact electrodes.[99]

A first attempt to model carrier transport in nanocrystalline TiO2 films suggested

diffusion to be the operative mechanism.[95] It turned out, however, to be erroneous to

describe the electron motion by a single value of the diffusion coefficient. The transport

phenomenon is complex as it involves trapping and detrapping of charges. The traps

have various depths, leading to a distribution of trapping and detrapping times. Which

type of trap the electron experiences during its random walk through the oxide film

depends on its quasi-Fermi level under illumination, i.e., on the light intensity.[96] At

low light levels, deep traps participate in the electron motion with a correspondingly

low diffusion coefficient De– and slow motion is expected. Increasing light intensity

ends up in the filling of deeper trap states under steady-state conditions. The transport in

this case is faster since it involves only shallow traps, resulting in a higher value for De–

. The central importance of trap states in these systems has recently been discussed by

Nelson,[81] who applied a dispersive transport model based on the continuous-time

random-walk theory of Scher and Montroll.[100]

Another currently debated issue concerns space charge control of the photocurrent. It is

generally assumed that the negative charge of the moving electron is efficiently

screened by cations in the electrical double layer surrounding the semiconductor

nanoparticles, making it move with its image charge as an essentially neutral species.

There is evidence, however, that the charge compensation on the electrolyte side of the

junction can lag behind the electron movement in the solid network. This effect is

particularly important in ion-paired organic electrolytes when high photocurrents are

– 65 –

drawn. Therefore, it was observed in photocurrent transient measurements that the

photocurrent response times became longer with decreasing electrolyte

concentration.[101] As well, the calculated value of the effective diffusion coefficient of

carriers in the oxide semiconductor De– = 1.5×10–5 cm2 s–1 is several orders of

magnitude smaller than that in the bulk crystalline material and strikingly similar to the

diffusion coefficient of ions in the solution. A description of the coupled electron-ion

motion [82] and a quantitative model of the mass transport by the electrolyte in

mesoporous systems [102] have been proposed, albeit employing a constant value for

the electron diffusion coefficient.

Simple calculation shows that the steady-state carrier concentration in full sunlight

corresponds to approximately one electron per TiO2 particle.[103] However, using this

value together with De– = 1.5×10–5 cm2 s–1 ends up in a resistance for the illuminated

nanocrystalline film which is at least a thousand times higher than the experimentally

measured value. This discrepancy may be explained by a Mott transition occurring

during the photodoping of the anatase particles that results in a large increase of their

conductivity.[104] Clearly, a central question remains, which is how, in the dye-

sensitized liquid-junction solar cell, an initially very poorly conducting network of TiO2

nanoparticles can attain the excellent photocurrent-voltage characteristics presented

below in section 4.6.

4.4.3 Charge separation across a solid-state heterojunction

In dye-sensitized photovoltaic cells, practical advantages may be gained by the

replacement of the liquid electrolyte with a solid charge-transport medium. Inorganic

p-type semiconductors such as CuI [85] and CuSCN,[87] and organic hole

conductors [84,105,106] have been proposed in this regard. Recently, the use of

– 66 –

2,2’,7,7’-tetrakis(N,N-di-p-methoxyphenyl-amine)9,9’-spirobifluorene (spiro-

MeOTAD) to constitute an amorphous hole transmitting material, in conjunction with a

mesoporous TiO2 film sensitized by cis-[RuII(dcbpy)2(NCS)2], allowed to build a

solid-state dye-sensitized solar cell with high photon-to-electron conversion

efficiencies.[84]

Figure 15. Energetic scheme of electron transfer processes taking place in a

dye-sensitized heterojunction photovoltaic cell. Also shown is the structure of the spiro-

MeOTAD molecule that constitutes an efficient organic hole transport material (HTM).

– 67 –

Figure 15 shows an energetic scheme for the electron transfer processes taking place at

the dye-sensitized heterojunction of such a device. Electron injection from the

sensitizer’s excited state into the conduction band of TiO2 is followed by regeneration

of the dye by hole injection into the hole transport material (HTM). Conduction band

electrons in the metal oxide, as well as holes in the organic medium are then transported

by electronic conduction to the anode and the cathode, respectively. Pulsed picosecond

laser photolysis has shown that the hole injection from the oxidized dye-sensitizer

[RuIII(dcbpy)2(NCS)2]+ into the spiro-MeOTAD hole conductor proceeds over a broad

time ranging from < 3 ps to > 1 ns.[107] This wide time-scale was attributed to a

statistical distribution of the dye-hole conductor distances, and suggested that the dye

was not perfectly and uniformly contacted by spiro-MeOTAD molecules.

4.5 Charge separation in nanocrystalline heterotriads

Charge separation resulting from light absorption by molecular chromophores has been

extensively studied along two parallel routes: On the one hand, numerous molecular

assemblies of donors (D), chromophores (S) and acceptors (A) in many variations have

been synthesized, forming dyads, triads, tetrads or even pentads, to achieve charge

separation in solution or in monolayers. On the other hand, charge separation at

chromophore-semiconductor interfaces (heterodyad S–A) exploited on films of

nanocrystalline metal oxides has allowed the development of dye-sensitized

nanocrystalline solar cells. Combining the intramolecular with the interfacial light-

induced charge separation strategies is expected to increase the light-to-electricity

conversion yield of the photovoltaic systems.

The maximum voltage delivered by the dye-sensitized solar cell corresponds to the

difference between the potential corresponding to the quasi Fermi energy level of the

– 68 –

electrons in the semiconductor φF = E*F,n / F and the redox potential φ(M+/M) of the

mediator in solution. A higher cell voltage can hence be obtained by lowering the quasi

Fermi potential which depends on the electron concentration in the conduction band of

the illuminated sensitized semiconductor. This concentration relaxes to a steady state

where the electron injection Iinj flux equals the electron escape flux (Figure 16). The

escape flux is composed of two contributions: the electron-sensitizer recombination flux

Ib [Equation (52)] and the electron leak to the mediator in the contacting electrolyte IM

[Equation (53)].

S+ | (e–cb)TiO2 → S | TiO2 (52)

M+ + e–cb → M (53)

D–S* | TiO2 → D–S+|(e–cb)TiO2 → D+–S|(e–cb)TiO2 (54)

D+–S|(e–cb)TiO2 → D–S|TiO2 (55)

Lowering the quasi Fermi potential by reducing the former flux requires a lengthening

of the lifetime of the charge-separated state S+ | (e–cb)TiO2, a goal which can be reached

by removing the hole on S+ away from the semiconductor surface. This was achieved

by replacing the simple chromophoric sensitizer S by a dyad sensitizer S–D in which D

is an electron donor possessing a redox potential lower than that of the sensitizer but

higher than that of the redox mediator. Consequently, after electron injection, the hole

will be transferred from S+ to D [reaction (54)]. The recombination after Equation (55)

is expected to be slower than the direct recombination [Equation (52)], because of the

exponential decay of the electron transfer rate ket(r) with the distance r, according to

– 69 –

Gamov’s expression (39) The whole system D–S|TiO2 constituted by the dyad adsorbed

on the semiconductor, considered as an acceptor, will be referred to as heterotriad.

The quantitative influence the different rates of electron transfers on the photopotential

φF of the illuminated electrode was established according to the following model. In a

heterodyad S|TiO2 in open circuit (Figure 16, top), the electrons injected into the TiO2

conduction band at the flux Iinj can either recombine with the oxidized sensitizer with

the pseudo first-order rate constant kb or reduce the oxidized redox mediator M+ in

solution with the second-order rate constant kM. The steady-state electron density n in

the semiconductor is thus given by Equation (56). The quasi Fermi level E*F,n of the

semiconductor is varying with the electron density according to Equation (57), where EC

is the conduction band level and Nc is the effective density of states in the conduction

band, a constant value for a given material at a given temperature.[108] The

corresponding photopotential φF of the electrode is obtained by division by the Faraday

constant F [Equation (58)]. Combining Equations (57) and (58) affords the

photopotential as a function of the kinetic parameters [Equation (59)]. In a heterotriad

D–S|TiO2 (Figure 16, bottom), the quenching of the oxidized dye by the linked donor is

by far the fastest process (kq >> k'b see examples below). Ib is therefore negligible and

the relevant fluxes for the determination of Δφ'F are IM which is independent of the

sensitizer, I'inj and the recombination flux I'b with the oxidized donor. The open-circuit

photopotential difference ΔφF between the two systems is then expressed by Equation

(60), that can be further simplified if I'inj = Iinj, which can be considered true if the

chromophore is the same in the heterodyad and in the heterotriad.

n = Iinj / (kb + kM [M+]) (56)

E*F,n = Ec – kT ln (Nc /n) (57)

– 70 –

φF = φc – (kT/F ) ln (Nc /n) (58)

φF = φc – (kT/F ) ln (Nc – (kb + kM [M+]) /Iinj ) (59)

ΔφF = (kT/F ) ln (kb I'inj / k'b Iinj) (60)

Figure 16. Electron fluxes for charge separation and recombination processes

in a heterodyad (top) and heterotriad (bottom), in the presence of a redox mediator in

solution, under open-circuit conditions. In the heterodyad, the injected electrons can

either recombine with the oxidized sensitizer S+ (Ib) or reduce the oxidized mediator

M+ (IM). S+ is reduced either by the conduction band electrons or by the redox

mediator M (Ii). In the heterotriad, the electron transfer from the linked donor D to S+

is much faster than the recombination. The new recombination process occurs at

k'b < kb due to the larger distance.

– 71 –

An improved solar cell voltage can also be achieved by raising the redox potential of the

mediator. The substitution of the heterotriad to the heterodyad is for that case an

advantage too. In fact, the higher redox potential of the (M+/M) couple results in a

reduced driving force for the regeneration of the dye (S+ + M → S + M+) which will be

accompanied, in the normal Marcus region, by a reduced rate. If this rate decreases, the

competitive recombination flux increases, unless, again, the lifetime of the charge-

separated state is prolonged by fast transfer of the hole to a linked donor.

Argazzi et al. followed that strategy to elaborate a nanocrystalline solar cell which

incorporates a molecular dyad based on ruthenium bipyridine as a sensitizer and

phenothiazine as a donor (Scheme 3).[109]

Scheme 3

In compound H0, the respective redox potentials of the S (RuIII/II) and D (PTZ+/0)

moieties are 1.33 and 0.97 V/NHE, giving a 0.36 V driving force for the charge transfer.

In the model compound where the donor is absent, charge recombination was

determined by transient laser spectroscopy to follow a biexponential process, with the

kinetic components kb1 = 8.5×106 s–1 (77%) and kb2 = 5.1×105 s–1 (23%).

– 72 –

NRu

NNPO

N

N

N

P

O

O

OCH3

N

OCH3

OCH3

OCH3

O

O

NN

N

N

O N

N

N

RuO

S*/S+ -0.55 V

X

S/S+ 1.5 V

D / D+

0.85 V

TiO2

h!

16.4 Å24.4 Å

10 ns

0.0

1.0

-0.6

TiO2300 µs

H3|TiO2

fast

O NPOO

O

30 µs

S*/S+ -0.55 V

h!

TiO2

TiO2

S/S+ 1.5 V

D / D+

0.95 V

fast

<5 ns

(3 µs)

10.1 Å18.1 Å

-0.6

1.0

0.0

E / VNHE

H2|TiO2

TiO2

12.2 Å OCH3

3 µs

OCH3

S*/S+ -0.55 V

P

O

ON

N

N

ON

N

N

Ru

1.0

h!

0.0

X

D / D+

0.80 V

-0.6 fast

<5 ns

H5+A1|TiO2

S/S+ 1.36 V

TiO2

A1

H5

N

N

NN

N

NRu PO3

CS

H4

– 73 –

Figure 17. Distances, energy levels and electron transfer half-lives in the

heterotriads H2|TiO2, H3|TiO2 and H5+A1|TiO2. The distances were calculated by

molecular mechanics using CAChe software, assuming a perpendicular arrangement of

the molecules on the surface. The energy levels are those obtained and calculated by

electrochemistry as well as absorption and emission spectroscopy. The half-lifetime

reported for the electron transfer processes were obtained by laser flash photolysis. The

value of 3 µs for the S+ | (e–cb)TiO2 → S|TiO2 recombination was obtained with the

heterodyad H5|TiO2.

In heterotriad H0|TiO2, electron transfer from the phenotiazine moiety to the oxidized

sensitizer took place within the laser pulse (< 30 ns) while the charge recombination

occurred at the rate k'b = 3.6×103 s–1, which means a decrease by a factor of 2000

compared to the heterodyad, and a half-lifetime of the charge-separated state of 300 µs.

According to Equation (60), the photopotential of the heterotriad should be 200 mV

higher than for the heterodyad. A difference of 175 mV was measured in the absence of

redox mediator. The former system still afforded a 100 mV higher open-circuit voltage

than the latter in a cell where the I3–/I– couple was present.

Bonhôte et al. investigated three systems based on ruthenium-terpyridine-phosphonate

as sensitizer and triarylamines as donors.[110] The excited form of the considered

sensitizer was reported to efficiently inject electrons into TiO2 [111,112] while

triarylamines are known to form very stable cation radicals.[113] In the two heterotriads

H1|TiO2 and H2|TiO2 (Figure 17), the donor and the sensitizer are covalently linked at

different distances while the co-adsorbed phosphonated triarylamine A1 and ruthenium-

terpyridine sensitizer H3, or H4 constitute bimolecular heterotriads. The redox

potentials of the different constituents of the heterotriads are given in Figure 17. The

– 74 –

driving forces for the D → S+ charge transfer were 0.55 V for H1, 0.65 V for H2, and

0.56 V for A1 + H4.

Resonance Raman spectroscopy indicated that in the excited assemblies H2* | TiO2 and

(A1 + S*) | TiO2, one electron is promoted from the metal center to the terpyridine

ligand linked to the semiconductor, whereas in the system H1* | TiO2 the excited

electron is located on the ligand linked to the donor. The quantum yield of the charge

separation reaction (54) was found to be close to unity for the two former assemblies,

but only 60 % for the latter one. In all three cases, the electron injection was very fast

(< 1ns) and the hole transfer to the donor was fast (10–20 ns). The half-lifetime of the

charge separated state was 3 µs for (A1+ + H4) | (e–cb)TiO2, as in the model system

H4+ | (e–cb)TiO2; it was 30 µs in H1+ | (e–

cb)TiO2 and 300 µs in H2+ | (e–cb)TiO2, as

with H0+ |(e–cb)TiO2.

The differences in the recombination rates of the different heterotriads can be correlated

with the mean distance separating the amine from the surface of the oxide.

Perpendicular attachment of the molecules on the surface would imply D – TiO2

distances of 12, 18 and 24 Å for the heterotriads (A1+ + H4) | TiO2, H1 | TiO2, and

H2 | TiO2, respectively (Figure 17). Assuming a typical damping factor β = 1.2 Å–1 for

“through-space” electronic coupling between conduction band electrons and D+, a

decrease of the recombination rate by one order of magnitude is expected to correspond

to an increase of the mean electron transfer distance by 1.9 Å. The discrepancy between

that value and the 6 Å distance difference expected from perpendicular anchoring can

be explained by the fact that, very likely, a large portion of adsorbed molecules adopt a

tilted conformation on the surface, leading to a broad distribution of distances for the

charge recombination, and hence to a complex kinetic behavior. In fact, attempts to fit

the observed temporal curves demonstrated that they are multiphasic, certainly because

the adsorption geometry of the molecules is not fixed. This geometry is likely to be

dependent on the surface coverage. In a compact monolayer, perpendicular anchoring

– 75 –

should be favored, whereas molecules widely dispersed on the surface should be freer to

lean over. It was indeed observed for all three heterotriads that the rate of the

recombination depends drastically on the surface concentration. At 50 % surface

coverage, upon irradiation by a laser pulse of fixed energy, a 50 % reduction of the

number of charge separated pairs is expected. Considering a second-order kinetic law,

the rate of recombination is expected to decrease accordingly. It was observed on the

contrary that the slowest kinetic components measured for H2 | TiO2 at surface

saturation disappeared under partial coverage conditions, while the half-lifetime of the

charge separated state τ1/2 was reduced by more than one order of magnitude. An effect

of the same amplitude was observed with heterotriads H1 | TiO2 and (A1 + H4) | TiO2.

Heterotriad H2 | TiO2 represents obviously the most promising system of the series for

long-lived charge separation. In an attempt to further increase the lifetime of H2+ | (e–

cb)TiO2 state, the photodynamics was studied in the ambient temperature liquid salt 1-

ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)-imide [114] which was shown

to behave at the molecular scale like a solvent of low dielectric constant (∈ ≈ 10), where

the medium reorganization energy should be minimized. The charge recombination was

indeed slowed down significantly, with a twice as long τ1/2 as in propylene carbonate. A

very long tail in the kinetic curve, accounting for a few percents of the initial

absorbance, was even found to extend up to several hundreds of milliseconds

(τ1/4 = 5 ms, τ1/8 = 120 ms). Careful degassing the molten salt did not affect this long

time kinetic phase, indicating that removal of the conduction band electrons by

molecular oxygen was not competing with the charge recombination.

Under full sun illumination (AM1.5) in propylene carbonate, heterotriad H1 | TiO2

gave a 82 mV higher photopotential than H4 | TiO2 of which only 58 mV can be

accounted for by the 10 fold reduced recombination rate. Another contribution of

10 mV is expected from the 50 % higher injection flux Iinj of the former system, due to

the wider absorption spectrum. In spite of a 100 fold lower recombination rate

– 76 –

compared with H4 | TiO2, expected to yield a 116 mV gain, the heterotriad H2 | TiO2

gave the lowest photopotential of the series. This observation must be related to a

supplementary contribution to Ib represented by the short-circuiting pathway constituted

by the lateral charge percolation from triarylamine to triarylamine and finally to the

SnO2, as shown by the electrochromism of H2 | TiO2. This was confirmed by the

observation that the quantum yield of the whole charge separation process increased

when H2 was diluted on the surface by non-electroactive molecules.

In a regenerative solar cell, with the I3–/I– redox couple, the open circuit photovoltage

of H1 | TiO2 was now 139 mV higher than that of H4 | TiO2. This increased difference

can be attributed to a reduced electron-triiodide reaction rate (kM), shown by the

measurement of IM in the dark, under 550 mV reverse bias, probably as a result of a

restricted access of the triiodide ions to the semiconductor caused by the presence of the

bulky triarylamine groups. Heterotriad H2 | TiO2, which photopotential was 31 mV

lower than H4 | TiO2 affords in the regenerative cell a 59 mV higher photovoltage, very

likely because, in addition to a lower IM , the reduction of H2+ | TiO2 by iodide

competes with the lateral electron transfer. Despite of the limitations caused by lateral

charge percolation, the development of heterotriads as efficient charge-separation

systems appears promising.

4.6 Photovoltaic performances of dye-sensitized nanocrystalline solar cells

A scheme of the photovoltaic device used in the generation of electric power from light

is shown in Figure 4. The mesoporous semiconductor oxide film is sandwiched between

two conducting glass plates, its pore space being filled with a redox electrolyte or a hole

conductor. We have shown above how the molecular properties of the sensitizer are

chemically engineered to ascertain efficient electron injection from the dye excited state

– 77 –

(S*) into the conduction band of titanium dioxide. We also discussed how the recapture

of the electrons by the oxidized dye (S+) is intercepted by transferring the positive

charge to a redox mediator M+/M, i.e. the triiodide/iodide couple, present in the

electrolyte and hence to the counter-electrode. Via this last charge transfer, in which the

mediator is returned to its reduced state, the circuit is closed. The system converts light

into electricity in a catalytic fashion, i.e. without permanent chemical transformation.

Figure 18. Typical spectral response curve of the incident photon-to-current

conversion efficiency (IPCE) for a mesoporous TiO2 electrode sensitized by “N3“ and

the “black dye”. A normalized solar irradiance spectrum under AM1.5 conditions is

superimposed for direct comparison.

– 78 –

The maximum voltage ΔV that such a device could deliver corresponds to the difference

between the Fermi potentials in both conducting electrodes, and thus to the difference

between the redox potential of the M+/M mediator couple and the conduction band

edge potential of the semiconductor. Figure 18 compares the spectral dependence of the

conversion efficiency of incident monochromatic light in electric current (IPCE) for

cis-[RuII(dcbpy)2(NCS)2] (≡ “N3”) and RuII(tctpy)(NCS)3 (≡ “black dye”) sensitizers.

Very high efficiencies of current generation approaching 0.8 were obtained. When

corrected for the inevitable reflection and absorption losses in the conducting glass

serving to support the nanocrystalline film the yields are practically quantitative in the

plateau region of the curves. However, the response of the “black dye” extends 100 nm

further into the infrared than that of “N3”. The photocurrent onset is close to 920 nm,

i.e., near the optimal threshold for single junction converters. The overall conversion

efficiency η of the photovoltaic cell can easily be calculated from the integral

photocurrent density measured at short-circuit isc, the open-circuit photovoltage Voc, the

fill-factor of the cell f, and the intensity of the incident light IR :

η = isc × Voc × f / IR (61)

Figure 19 gives an example for the current-voltage characteristics of a nanocrystalline

injection solar cell based on the cis-[RuII(dcbpy)2(NCS)2] dye. The overall solar to

electric conversion efficiency under standard AM1.5 sunlight conditions, i.e.

1000 W m–2 incident intensity, is η = 0.10, which is commensurate with the

performance of silicon-based conventional photovoltaic devices. Nanocrystalline

injection solar cells based on the RuII(tctpy)(NCS)3 sensitizer displayed similar results

with confirmed overall energy conversion efficiency as high as 10.4 %. Comparison of

the latter value with the maximum thermodynamic conversion efficiency ηo = 0.27,

earlier discussed in section 2, shows that theoretically avoidable losses amount to ca

– 79 –

63 % of the available free energy. As inferred from the very high current yields

obtained in such molecular photovoltaic devices, losses are essentially due to the waste

of potential in electron transfer processes and to the dark current of the cell. The driving

force of the charge injection process is minimal in the case of N3-sensitized TiO2 in dry

nitrile solvents. While partial degradation of the injected electron energy through

trapping in the solid network cannot be neglected, it is apparent that the potential

mismatch between the redox couples of the sensitizer S+/S and the complex mediator

I3–/I– is responsible for a major part of losses.

Figure 19. Photocurrent-voltage characteristic of a nanocrystalline

photoelectrochemical cell sensitized with cis-[RuII(dcbpy)2(NCS)2]. i(sc) is the

maximum (short circuit) current density, and V(oc) the maximum (open circuit) voltage

delivered by the cell. The conversion efficiency is calculated by use of Equation (61).

– 80 –

5. Water Cleavage by Visible Light

As pointed out by Allen Bard and Marye Anne Fox in a recent review,[115] the photo

driven conversion of liquid water to gaseous hydrogen and oxygen:

H2O → H2 + 1/2 O2 ΔGo = 237.7 kJ/mole (62)

is the “Holy Grail” of all photo-catalytic reactions. Is has been a long standing challenge

of practical artificial photosynthetic systems. The hydrogen produced from sunlight and

water can be subsequently employed in the catalytic reduction of carbon dioxide to

produce fuels such as methane or methanol. The latter could also be used as feed stock

for the production of organic chemicals. Alternatively, hydrogen could serve directly as

a fuel for transportation purposes or for the production of electricity in fuel cells,

without producing pollutants and green house gases upon combustion. For a practical

system, a conversion efficiency of at least 10 % is required, implying that the hydrogen

and oxygen produced have a fuel value of at least 10 % of the solar energy incident on

the system. As the peak solar power incident on earth is about 1 kW m–2 a panel of one

square meter collector surface should produce hydrogen at a rate of about 36 liter (at

standard temperature and pressure) per hour when exposed to direct sunlight.

As water is transparent to sunlight, a sensitizer or semiconductor is required in order to

absorb the solar photons and transform their radiant energy to generate the chemical

potential required to split the H2O molecules. The optimal absorption threshold for a

single photoconverter has been calculated to be at an energy of 1.6 eV,[116] implying

that all solar photons below 770 nm should be absorbed. Such a system could split

water with an efficiency of up to 30 %. Higher efficiencies of up to 42 % can be

obtained by using a tandem device where two photosystems operate in series.

– 81 –

The “brute force” approach to achieve this goal is to employ a solid state photovoltaic

cell to generate electricity that is subsequently passed into a commercial-type water

electrolyzer. Although efficiencies obtained are relatively high, i.e. close to 8 %, these

devices are very expensive. Hence the price of hydrogen produced this way can not

compete with conventional sources. The long-term outlook is better for systems that

borrow their principles from natural photosynthesis (see section 4.1 above).

5.1 Analogues of photosystem II of green plants

Researchers have long attempted to prepare catalysts capable of oxidizing water to

oxygen [Equation (17)], as the reaction constitutes the most difficult part in a complete

water cleavage system. However, despite considerable efforts there are few man-made

catalysts of any kind available and none have made an impact on industrial

chemistry.[117,118] The difficulty of promoting this seemingly simple reaction has

both thermodynamic and mechanistic origins. The catalyst must break the strong OH

bonds on two water molecules (enthalpy 500 kJoules mole–1) in a concerted fashion.

This has to be coupled to the removal of 4 protons and 4 electrons. The chemical

intermediates formed during the process are so reactive that self-destruction of the

catalyst often occurs. Nature solved this problem through evolution of a unique metallo-

enzyme required for oxygenic photosynthesis in all plants and cyanobacteria. This

enzyme is called the Photosystem II water oxidizing complex, or WOC. Its active site is

comprised of an oxo-bridged tetra-manganese cluster one Ca2+ ion and one or more

Cl– ion. In association with tyrosyl this core catalyzes reaction (4.4.2) using a

chlorophyll cation radical as terminal electron acceptor.

The most intensively studied molecular systems mimicking the action of the WOC are

based on the µ-oxo bridged ruthenium dimer [cis-(bpy)2Ru(OH2)]2O4+ where each

– 82 –

ruthenium is associated with two bipyridyl ligands and one water molecule. The

catalytic water oxidation cycle involves abstraction of 2 electrons from each of the

Ru(II) centers forming two dioxo-ruthenium(IV) moieties which convert back to the

starting state under oxygen release and subsequent re-aquation of the ruthenium metal

centers.[119]

5.2 Colloidal semiconductor systems

Photocatalytic water cleavage systems based on aqueous dispersions of semiconductor

particles has been extensively studied in the eighties and this work has been

reviewed.[120] They have the advantage of being cheap but their efficiency is generally

below 1 %. The additional drawback is that hydrogen and oxygen are generated

simultaneously. Apart from the problem of gas separation, this produces a slow down of

the photoreaction as the two gases accumulate and back react with each other. A way to

avoid the latter problem is to seperate the hydrogen and oxygen generating half

reactions as reported recently by Arakawa and co-workers.[121] However the efficiency

of the process remains low.

5.3 Tandem systems for water cleavage by visible light

The most promising approach to reach the goal of water cleavage by visible light is by

way of a tandem system. The main reason for this is that the constraints imposed by

thermodynamics are relaxed when 8 photons of light are used instead of four to

accomplish the production of two molecules of hydrogen and one molecule of oxygen

from water. A tandem system is particularly favorable when complementary parts of the

– 83 –

solar spectrum are exploited by the two photosystems that operate in series. The

maximum thermodynamic efficiency of such device is 42 %.

Khaselev and Turner [122] reported on a direct water electrolysis system based on a

novel, integrated, monolithic photoelectrochemical cell. This was patterned after the

GaInP2 / GaAs p/n, p/n tandem cell device grown at the National Renewable Energy

Laboratory in Golden Colorado. The solid-state tandem cell consists of a GaAs bottom

cell connected to a GaInP2 top cell through a tunnel diode interconnect. The top p/n

GaInP2 junction, with a band gap of 1.83 eV, is designed to absorb the visible portion of

the solar spectrum; and the bottom p/n GaAs junction, with a band gap of 1.42 eV,

absorbs the near-infrared portion of the spectrum transmitted through the top junction.

The conversion efficiency achieved was 12 %.

A tandem device that achieves the direct cleavage of water into hydrogen and oxygen

by visible light was developed in collaboration with two partner groups from the

Universities of Geneva and Bern.[123] This is based on the in-series connection of two

photosystems. A thin transparent film of nanocrystalline tungsten trioxide or ferric

oxide absorbs the blue part of the solar spectrum.

WO3 + hν → WO3 (e–, h+) (63)

The valence band holes (h+) created by band gap excitation of the WO3 or Fe2O3 serve

to oxidize water to oxygen:

4 h+ + H2O → O2 + 4 H+ , (64)

while the conduction band electrons are fed into the second photosystem. The latter

consists of the dye sensitized nanocrystalline TiO2 film. It is placed directly behind the

WO3 film capturing the green and red part of the solar spectrum that is transmitted

– 84 –

through the top electrode. The photovoltage generated by the second photosystem

enables the generation of hydrogen by the conduction band electrons.

4 H+ + 4 e– → 2 H2 (65)

The overall reaction corresponds to the splitting of water by visible light.

Figure 20. The Z-scheme of biphotonic water photolysis.

There is close analogy to the Z-scheme operative in the light reaction of photosynthesis

in green plants (Figure 2). This is illustrated by the electron flow diagram shown in

Figure 20. In green plants, there are also two photosystems connected in series, one

affording water oxidation to oxygen and the other generating the NADPH used in

carbon dioxide fixation. As discussed above, the advantage of the tandem approach is

– 85 –

that higher efficiencies than with single junction cells can be reached if the two

photosystems absorb complimentary parts of the solar spectrum. At present, the overall

AM1.5 solar light to chemical conversion efficiency achieved with this device stands at

4.5 %. Figure 21 shows a photograph of a such a cell producing hydrogen and oxygen

bubbles vigorously under visible light illumination. Present endeavors aim at further

improving the efficiency of the device.

Figure 21. Photograph showing the decomposition of water by visible light in a

tandem cell consisting of a mesoporous WO3 film and a mesoporous dye sensitzed TiO2

which are superimposed.

– 86 –

6. Future Outlook and Concluding Remarks

Intensive research is presently carried out around the world focusing on the following

issues:

i) the molecular design and synthesis of new sensitizers having enhanced near- infrared

light response, examples being phthalocyanines or the black dye discussed above.

ii) a better understanding of the interface, including experimental and theoretical work

on dye adsorption processes.

iii) the analysis of the dynamics of interfacial electron transfer processes down to the

femtosecond time domain.

iv) the unraveling of the factors that control electron transport in nanocrystalline oxide

semiconductor films.

v) the replacement of the liquid electrolyte by solid materials that serve as a hole

conductor.

A great advantage of dye sensitized cells is that they can be used to produce directly

high-energy chemicals from sunlight. Such “photosynthetic” devices solve the principle

problem of conventional photovoltaic cells that is the lack of capacity for energy

storage. The “Holy Grail” of all photoconversion processes is the splitting of water into

hydrogen and oxygen by sunlight and the improvement of the tandem devices described

above will be one of the primary targets of future research. Rapid progress is expected

in these areas as an impressive number of competent teams around the world are

actively pursuing this research. These systems will undoubtedly promote the acceptance

of renewable energy technologies, not least by setting new standards of convenience

and economy.

– 87 –

Acknowledgements

Recognition is due to the members of the electrochemical photovoltaics development

team of the Swiss Federal Institute of Technology (EPFL), some of whose work is

referenced below; to those industrial organizations whose interest in the molecular

photovoltaic system has induced them to license the concept and thereby support our

research; to EPFL; and to OFEN (Swiss Federal Office of Energy) for past

encouragement and support. Thanks are also due to Dr Pierre Bonhôte for valuable help

in the writing of section 4.5.

– 88 –

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