Tutorial 4

Photoelectrochemical Cells

31.03.2010

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Quasi Fermi Level Model

The advantage of quasi-Fermi level model:• Quasi-EF of majority carriers can be determined as it is identical to the

electrode potential; • Quasi-EF of minority carriers is also know for a given current.

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n-Fe2O3

http://pechouse.epfl.ch/page71222.html

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Tandem PEC Cell for Visible Light Water Splitting

The Holy Grail of Chemistry!

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Popular Killing Arguments Against PV and Why They Are Not Valid 1. Solar Modules Consume More Energy for Their Production Than

They Ever Generate 2. PV Produces More Greenhouse Gases Than It Saves 3. Grid-Connected PV Requires Lots of Back-Up Fossil Power Plants 4. PV Is Too Expensive 5. PV Is Not Ready for Marketing, More Research Is Required 6. PV Involves Toxic Materials 7. PV Consumes Valuable Land Area 8. PV Competes for Roof Space with

Thermal Collectors 9. A Feed-in Tariff Causes Unacceptably

High Electricity Cost

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

Nature 269, 316 - 318 (22 September 1977); doi:10.1038/269316a0Quasi-Fermi level measurement in an illuminated GaP photoelectrolysis cell

• There is no standard solution!• Only the quasi-Fermi levels which involve in a certain process and contribute

to the system will be considered.• Determination of quasi-Fermi level for majority carriers (Kelvin Probe,

Photoemission Spectroscopy)• Determination of quasi-Fermi level for minority carriers is not easy.

Assumptions need to be made. (split of quasi-Fermi levels)• Quasi-Fermi level may vary with position (junction vs bulk).

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Example 1: What is the maximum particle diameter for which a flatband situation prevails?

Poisson-Boltzmann:

Debye length:

Special case of dispersed semiconductors

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Poisson-Boltzmann equation solved for a spherical particle with radius of ro

Solution:

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The space charge is negligible when migration of charges due to the electrical field is weak compared to thermal diffusion:

no = 1017 cm–3

ε = 130TiO2 nanocrystalline particlese = 1.602×10–19 A sεo = 8.86×10–12 A s V–1 m–1

kB = 1.38×10–23 J K–1

Note that the injection of 1 electron into an undoped TiO2 particle of 40 nmdiameter (V = 3.4×10–17 cm3) corresponds to a doping density of no = 3×1016 cm–3.

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Example 2: Can Mott-Schottky plot be used to determine the flatband potential of nanocrystalline TiO2 when immersed in electrolyte?

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Mott-Schottky plot is not valid for mesoporous TiO2 as the semiconductor is completely depleted when immersed in high ionic strength electrolyte.

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Example 3: Construct at least 5 solar cells with the following materials.

Cu2STiO2AuSuitable electrolytesTCOCdS

TCO/Cu2S/Suitable electrolyte/AuTCO/CdS/Suitable electrolyte/AuTCO/TiO2/Cu2S QD/Suitable electrolyte/AuTCO/TiO2/CdS QD/Suitable electrolyte/AuTCO/TiO2/Au nanocrystal/Suitable electrolyte/AuTCO/CdS/Cu2S/Auetc....

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