0581.5271 Electrochemistry for Engineers

LECTURE 11

Lecturer: Dr. Brian Rosen Office: 128 Wolfson

Office Hours: Sun 16:00

Photoelectrochemical Cells (PECs)

Energy Balance

Figures of Merit for PEC’s

Photoelectrochemical Cell (PEC)

Molecular Orbital Theory

MO Theory Applied to Semiconductors

e-

h+

“Electron-hole pair”

Bandgaps for Common Semiconductors

* eV = 0 is vs. the energy of a single electron in a vacuum

Covalent vs. Ionic Semiconductors

• Covalent (Eg represents energy gap between bonding and antibonding orbitals of same symmetry)– Silicon

• VB made up of bonding π orbitals • CB made up of antibonding π* orbitals

• Ionic (Eg represents energy gap between completely different orbitals)– Titanium dioxide (TiO2)

• VB made up of filled 2p orbitals of O2-

• CV made up of empty 2d orbitals of Ti+4

– More stable towards corrosion since ionic band gaps are generally larger and material is less reactive

Sunlight under AM 1.5

Bandgap Size Optimization

If hv > Eg, the extra energy will readily thermalize and the electron will drop down to the conduction band edge, Ecb

If hv = Eg, the electron will excite to the conduction band edge, Ecb

Optimal range for solar energyadsorption is therefore between 1.1 and 1.7eV

Beer’s Law Applied to Semiconductors

Si

I0

I

z)exp(

ln

zI

IT

zI

IA

O

O

Io = Incident light intensityI = Transmitted light intensityz = optical path length (not thickness!)A = AbsorbanceT = Transmittance Α = absorption coefficient (function of wavelength!!)

Direct vs. Indirect Gap • Direct Gap – fully allowed (optical, spin) transition (GaAs,

CdTe)• Indirect Gap- optically forbidden transitions near the band are

only made possible by coupling with photon momentum and molecular vibrations (Si, TiO2)

Carriers in Intrinsic Semiconductors• Thermal energy will always excite valence

electrons into the conduction band (except at 0K)

• Hole moving towards a contact is equivalent to an electron moving away

e-

h+

kT

EApn g

ii exp

Eg = bandgap in eVk = boltzman constantT = absolute temperatureni = electron concentration in intrinsic material [cm-3]pi = hole concentration in intrinsic material [cm-3]

e-

h+

kT

EApn g

ii exp

An electron in the conduction band MUST create a hole in the valence band, therefore the carrier concentration is

kT

EAn g

i exp2

Carriers in Intrinsic Semiconductors

n2 at room temperature for Si (relatively low band gap) comes to a carrier concentration less than 1 part per billion;Therefore, we must utilize doping to increase the conductance

Semiconductor Doping

• Ability to change the Fermi Level of the electrode

• Increasing the conductivity such that photo- generated electrons and holes can travel larger distances without resistive losses

Semiconductor Doping • n-type doping replaces native atoms with an atom containing

an extra electron than itself– Electrons are majority carrier, holes are minority carrier

• p-type doping replaces native atoms with an atom containing one less electron than itself – Holes are majority carrier, electrons are minority carrier

n-type p-type

Shallow Donors and Acceptors

Shallow n-typeDonor energy level is near the conduction

band edge of the native material

p-typeAcceptor energy level is near the valence band

edge of the native material

Shallow donors and acceptors are generally fully ionized at room temperature!

Si1.

12 e

V

Semiconductor-Liquid Junction and Depletion Depth, W

Electric field generation at the interface allows forcharge separation!

The number of states in solution far exceeds thatin the semiconductor,therefore, the energy of the solution will notchange appreciably

W

Electric Field inside the Depletion LayerIn the bulk, a negative test change does not feel the interface because the

positive charges in the depletion layer screen the negative charge in the liquid

As the test charge moves through the depletion layer, the effect of screening is lessened and the electric potential becomes more negative

Band Bending

Built in Voltage, Vbi

Maximum electric field within the semiconductor after equilibration with the electrolyteDependent on both semiconductor and electrolyte!

Barrier Height Energy, qφb

XXXXX

Φb = barrier height in voltsq Φb = barrier height in eV

For Experiment Preparation

d

bi

qN

VW

2

Vbi = built in voltageNd = number of dopant atomsq = charge of carrier ε = static dielectric constant of semiconductorV(x) = electric potential as a function of depth

W

2)( dqNxV

Surface Concentration of Carriers• In and n-type semiconductor, electrons (the

majority carrier) are depleted within ‘W’, because of less shielding from positive nuclei.

• electron concentration, n(x):

kT

xqVnxn b

)(exp)(

nb = bulk concentration of electrons (per cm3)q = charge of an electronV(x) = electric potentialk = Boltzman constantT = Absolute temperature (kelvin)

Accumulation (and Bending)

Accumulation

• Depletion region in n-type semiconductor is limited by the density of dopant atoms since these atoms are the source of the electrons

• In accumulation, the extra electron can be in the vicinity of both a dopant atom or a native atom. Accumulation limit is by overall atom density

Semiconductor-Electrolyte Interface(n-type, at Equilibrium)

AeA

AeA

Semiconductor-Electrolyte Interface(n-type, Oxidizing bias)

AeA

AeA

Semiconductor-Electrolyte Interface(n-type, Reducing bias)

AeA

AeA

Semiconductor-Electrolyte Interface(n-type, Illumination)

Electrons and holes separate in the electric field, creating an additional fieldwhich counteracts and “unbends” the bands

-

+

-

+

Electrons and holes separate in the electric field, creating an additional fieldwhich counteracts and “unbends” the bands

Semiconductor-Electrolyte Interface(p-type, Illumination)

Photoelectrochemical Cell (PEC)

Photoelectrochemistry

Hydrogen Photocathode(Photoelectrochemical Cell)

Minority carrier (here, electrons) are driven TOWARDS the interface

p-type semiconductor

Oxygen Photocathode (Photoelectrochemical Cell)

Minority carrier (here, holes) are driven TOWARDS the interface

n-type semiconductor

Oxygen Photocathode (PhotoASSISTED Cell)

Minority carrier (here, holes) are driven TOWARDS the interface

n-type semiconductor

Photochemical Cell

Dye Sensitized Solar Cell

1. Photon excites electron to conduction band of dye

2. Electron exits the dye (deactivating it) and travels through TiO2 network to anode

3. Electron powers external load4. Electron reduces triiodine to

iodide at cathode 5. Iodide oxidizes at dye

(connected to TiO2 connected to anode) reactivating the dye

Photo-assisted CO2 Reduction

-2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0.0-6

-5

-4

-3

-2

-1

0 dark-current

Cu

rren

t D

ensi

ty (

mA

/cm

2 )

Potential (mV vs. Ag/AgCl)

photo-current

Photocarriers generated by exposure to light produces up to 450 mV of photovolage

Photocurrent is 20x greater than dark current at low over-potentials

Data by BAR, CR, and ASK

-2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0.0-6

-5

-4

-3

-2

-1

0

Cu

rren

t D

ensi

ty (

mA

/cm

2 )

Potential (V vs. Ag/AgCl)

n+ Silicon p Silicon

approx. photovoltage

Shottky Barrier (Metal – Semiconductor Interface)

-

+