Chapter 4. Quantum Dot Solar Cells

Introduction to Chemical Convergence for Energy & Environment

Chapter 4. Quantum Dot Solar Cells

Spring Semester, 2010

Kookheon Char

What Are Quantum Dots, Rods, or Wells?

 Semiconductor nanostructures (nanocrystals) in several nanometer range (approx. 1,000 ~ 10,000 atoms)

 Unique physical & chemical properties:

- Large surface-to-volume ratio - Tunable bandgap

- Quantum behavior in electronic properties . .

.

Unique Optical & Electrical Properties

Tunable Band Gap

Quantum

Confinement Effect (QCE)

Wide Absorption Range

VIS IR

UV

A. J. Rogach et al., Adv. Func. Mater. (2002)

Multiple Exciton Generation (MEG) Unique Transport Phenomena

D. Vanmaekelbergh & P. Liljeroth, Chem. Soc. Rev. (2005)

Preparation Process: Wet vs Dry

Vacuum Deposition & Conventional Lithography (i.e., MOCVD, MBE, Photolithography, …)

InAs Quantum Dots

on GaAs Substrate GaAs/AlGaAs Quantum Wells Molecular Beam Epitaxy (MBE) Device

Wet Chemistry (Solution-Based Synthesis)

InAs Quantum Rods CdSe Quantum Dots

S. Kan et al., Nat. Mater. 2, 155 (2003) A. P. Alivisatos, Science 271, 933 (1996)

http://iop.ncl.ac.uk/research/dot.php B. Park, Nano Device, Lecture Note (2008)

QD Applications

Gao et al., Nature Biotech. (2004)

Light Emitting Diodes

Bio-Markers Solar Cells

Passive-Type Device (PL Device) Active-Type Device (EL Device)

Combined with Conventional PV Cells (w/ DSSC, OPV, Schottky type, …)

Bio-imaging

(IR emitter, low

photobleaching)

Part I:

Physical Aspects of Quantum Structures

From Atom to Bulk Materials

P⁺

Electron wave function

Cross-section of probability density

1s 2s 2p3s 3p

Energy States of Atomic Orbital (AO)

Atom Molecule

Energy States of Benzene Molecules (Molecular Orbital, MO)

Bulk

Valence & Conduction Band Formation of Diamond

Size Dependent Properties

 Size Dependent Physical Properties

 Optical Properties

- scattering, plasmonic effect, …

 Electronic Properties

- bandgap, electronic transition, carrier transport, …

 Melting Point (T

~ 1/r)

 Heat Capacity (C

> C

)

 Magnetic properties - Fe, Co, Ni, Fe

O

, …

 Reactivity

- Surface selective adsorption, reaction

Milk Gold ColloidSolution

Melting Point Depression

D(E)

Energy

D(E)

Energy

D(E)

Energy

Density of State (DOS) depending on dimensionality

dot rod well

 Effect of Ratio of Interfacial Volume to Particle Volume

K. I. Winey and R. A. Vaia, MRS BULLETIN, 32, 314. (2007) 2r

Sphere, r Aspect ratio = 1

δ = t / r 2r

l

Rod (Prolate), 2r < l Aspect ratio = l / 2r > 1

δ = t / r 2r

h

Plate (Oblate), 2r > h Aspect ratio = h / 2r < 1

δ = 2t / h

The ratio of interfacial volume to the particle volume (V_interface / V_particle) as a function of the particle aspect ratio and δ (ratio of the thickness of

the interface to the smallest dimension of particle) For the same volume fraction of NPs:

mean particle – particle separation ~ r total internal interfacial area ~ 1 / r number density of constituents ~ 1 / r

V

/ V

↑ as aspect ratio → 1

& δ → ∞

Reduced object size increases interfacial area dramatically !!

Calculated interfacial area per volume of particles (in nm^-1)

E. L. Thomas, Adv. Mater. 17, 1331. (2005)

Increased Surface to Volume Ratio (I)

 Example: Iron Nanocrystals

Nanoscale Materials in Chemistry, Wiley (2001)

Increased Surface-to-Volume Ratio (II)

Spherical Iron Nanocrystals

J. Phys. Chem. (1996)

Melting Point Depression

A. N. Goldstein et al., Science 256, 1425. (1992)

CdS NPs

T_b: bulk melting temperature

T_m: melting temperature for a particle of radius R L: molar latent heat

γ: surface tension ρ: density

Relationship between

lattice parameter (a) and surface tension of solid

(κ = 1.56 X 10^-11 m²N^-1)

γ_sol – γ_liq : 0.42 N m^-1 From the a – γ relation

γ_sol for bare nanocrystal : 2.50 N m^-1 γ for bulk crystal : 0.750 N m^-1

Increased Surface Tension

Melting Point Depression

Low Dimensional System: between Molecule & Bulk State

A. P. Alivisatos, Science, 271, 933 (1996)

 Change in Density of State (DOS) Corresponding to the Number of Atoms

Metals (i.e., Au NPs)

Semiconductors (i.e., Si NPs)

 E

centered in a band

 Infinitesimal energy spacing around the Fermi level

 Not drastic change in optical & electronic properties

 E

centered in a bandgap

 Drastic change in band edge as a function of size

 Large Variation of Optical & Electronic Properties in Size

Density of States Corresponding to Dimensionality

Density-of-State Shape Nano-Objects

0D

1D

2D

20 nm 5 nm

50 nm

D(E)

Energy

D(E)

Energy

D(E)

Energy

Quantum Dot

Quantum Rod

Quantum Well

Simple Description: Electron Gas in a Solid

 Ideal 3-D Electron Gas

Schrodinger equation for a free (V = 0) electron in 3-dimentional space

Periodic boundary condition for a cubic solid w/ side L

K. Barnham et al., “Low-Dimensional Semiconductor Structures”, Cambridge University Press (2001)

Solution:

Ideal 3-D Electron Gas (I)

For a cubic solid w/ side L, the allowed quantum states are evenly distributed in k- space with one state taking the volume, (2 π/L)

Number of states in a volume element d Ω

Volume for states with energy E ~ E+dE

Volume for states with energy E ~ E+dE

Ideal 3-D Electron Gas (II)

Two electrons (up spin, down spin) can be accommodated in each state

Density of State (DOS) per unit volume

Bulk Semiconductors

Ideal 2-D Electron Gas Ideal 1-D Electron Gas Ideal 0-D Electron Gas

Real Electron Gas in the Finite Dimension

Effective Mass Approximation

 Ignoring periodic potential by atoms in lattice…

 Limited at the conduction band minima &

the valence band maxima

E-k Diagram of Bulk Silicon

Φ

(r) ~ Φ(r)u(r)

Ideal Square Well (I)

Infinite square well:

Schrodinger equation for z-direction

Ideal Square Well (II)

Lowest energy of the system

Higher quantized energy levels

Density of States (DOS)

DOS of bulk

DOS of Quantum Wells

Students: Please try to calculate 1-D & 0-D systems!

Unique Properties of Quantum Structures

Quantum Dot as a Simple Model…

1.5 nm

<001>-oriented CdSe QD synthesized by Wet Chemistry

C. B. Murray et al., Annu. Rev. Mater. Sci. 30, 545 (2000)

increase in E_g

RT 10 K

Quantum Confinement Effect

Characteristic Length L

< Bohr Exciton Radius >

Controllable Bandgap by Tuning in Size

R e m

m R Bulk h

E QD E

h e g

g

0 2 2

2

4 8 . 1 1

1 ) 8

( )

( ^_^ 

 



 





Optical Transition in Quantum Dot (I)

O. I. Micic et al., J. Phys. Chem. B 101, 4904. (1997)

 Absorption Characteristics:

- Electronic transition from ground state to discrete valence states

- Discrete near-edge states & continuous far-edge states  transition probability - Large extinction coefficient

CdSe QDs

Al. L. Efros et al., Phys. Rev. B 15, 4843. (1996)

Size Dependent Electronic Transition of CdSe QDs

εX 105 cm-1 M-1 @ 1st exciton peak

Size (nm)

Molar Extinction Coefficient

Optical Transition in Quantum Dot (II)

Al. L. Efros et al., Annu. Rev. Mater. Sci. 30, 475. (2000)

 Emission Characteristics:

- Hot carriers are thermalized to the band-edge state.

- Large stokes shift (exciton-phonon interaction, carrier-carrier interactions, band- edge exciton fine structure due to anisotropy, …)

- Broadening caused by size inhomogeneity, exciton-phonon interactions, surface traps

Thermal Relaxation (coupled with phonons)

Excitation

hv' hv

Non-degenerated band edge state

Optically active state

Stokes Shift

Optical Transition from Surface State

B. O. Dabbousi et al., J. Phys. Chem. B 101, 9463. (1997)

hv hv’’

Photon w/ low energy Non-Radiative Process

Surface Passivation

hv hv'

Band-Edge Transition

emission from surface states

Undesired Electronic Transition

Transport Phenomena in Quantum Dot Solids

Interaction btw. Quantum Dots

Similar electronic structure compared w/ atom

Weak Coupling (hΓ << k_BT) Hopping (Coulomb Blockade)

Strong Coupling (hΓ >> k_BT) Conduction (thru Miniband)

Miniband Formation

Artificial Atom

Coulomb Blockade

σ (conductivity) ↑

as β (coupling btw. QDs) ↑ & Δα (Disorder) ↓

Dynamics of Carriers in Quantum Dots

Hot Carrier Extraction Solar Cells

Carrier Multiplication

(Multiple Exciton Generation: MEG) Solar Cells

Thermalization of Carriers thru Phonon Emission

Efficiency drop from the thermodynamic limit to

1 electron / 1 photon limitation (Schokley – Queisser Limit)

D. V. Talapin et al., Chem. Rev., 110, 389 (2010)

~ ps

Discrete DOS in CB ( Phonon Bottleneck)

Energy Transfer of e

to Hole States

vs.

Multiple Excitons by

Large Energy (hv > n E

)

Part II:

Synthesis of Quantum Structures

Based on Wet Chemistry

TEM Images of Various Nanocrystals Synthesized by Wet Chemistry

CdSe/CdS NRs CdSe/CdS Tetrapods

CdPt₃-Au Dumbbells

CdS-Au₂S Rods Au-CdSe-Au Rods

PbSe Nanowires Iron Oxide hollow

spheres PbSe Cubes CdTe Tetrapods

D. V. Talapin et al., Chem. Rev. (2010) Au/PbS Core/Shell

Candidate Materials for Semiconductor Nanocrystals

Bandgap (E

) of Various Semiconductor Materials

Vis. Range (for LED)

Solar Spectrum (for solar cells)

Requirements for Efficient Light Harvesting Materials

 Size & Shape

 1.1 eV < E

< 3 eV

 rods, tetrapods, dendritic shape

 Surface Treatment

 Efficiency & Stability



Wide Absorption Range (VIS ~ IR) Facilitated Charge Transfer

 Exciton Dissociation & Extraction

IR VIS

 Band Position



bandgap

 Decrease in R

& Oxidation

Conventional Synthetic Route

 Pyrolysis Method to Prepare High Quality CdSe QDs

Me₂Cd in TOP

 Nearly monodisperse in size

 Well-resolved optical transition at RT

 Wurzite, Zinc blende, or Rock salt crystals Hot injection

at high temp +

TOPSe, TOPTe TMS₂Se. TMS₂Te

or TOPO

Φ_PL~ 10 % at RT

~ 100 % at low T

C. B. Murray et al., J. Am. Chem. Soc. (1993)

Wurzitecrystal structure ^{1.2 nm}

11.5 nm

TOP: tri-n-octylphosphine

TOPO: tri-n-octylphosphine oxide

Surface Passivation

 Surface-State Passivation by Inorganic Shells

X. Peng et al., J. Am. Chem. Soc. (1997)

Core/Shell

Core

B. O. Dabbousi et al., J. Phys. Chem. B (1997)

CdSe/CdS QDs CdSe/ZnS QDs

470 480 520 560 594 620 nm

Epitaxial Growth of ZnS or CdS Shells with Several Monolayer Thickness (1 ~ 2 monolayers)

 Single-Step Synthesis for Cd

Zn

Se

S

Quantum Dots (Red/Green)

Synthesis of Highly Luminescent RGB Quantum Dots

 Low QY and photostability

 From violet (410 nm) to blue (460 nm)

 Narrow emission (fwhm < 30 nm)

 High QY (up to 80 %)

 Improved photostability

Cd_1-xZn_xSe_1-yS_y

Cd(OA)₂ Zn(OA)₂ TOPSe TOPS

core core

core

core

core

core

Cd_1-xZn_xSe_1-yS_y CdSe

ZnS

K. Char et al., Chem. Mater. (2008)

K. Char et al., Chem. Mater. (2008) abruptinterface

diffuseinterface

 Infusion-Assisted Synthesis for Cd

Zn

S@ZnS Quantum Dots (Blue)

CIE Indices of RGB QDs

Wavelength (nm)

350 400 450 500 550 600 650 700

Intensity (a. u.)

Core/Shell Structured RGB QDs

> 70 % > 70 % > 70 %

 Straightforward and efficient synthesis

 Wide absorption & high exctinction coefficients

 Narrow spectral bandwidth (FWHM < 35 nm)

 High QY (> 70 %) & photostability

 Scale-up capability (in gram scale)

G

B

R

3 g

RGB Quantum Dots for Light-Emitting Materials

Synthesis of Monodisperse Nanoparticles (I)

 “Burst” Nucleation and Slow Growth

LaMer Plot to separate nucleation and growth…

J. Park et al., Angew. Chem. Int. Ed. 46, 4630 (2007)

State I: Supersaturated

but no precipitation

State II: Burst nucleation

Large energetic barrier

Enough supersaturation

to overcome nucleation barrier

State III: Growth stage

Size focusing / defocusing

surface ( > 0) & volume (G_v < 0) component

Dissolution Growth

High S (supersaturation) for small critical radius

Please try to derive the critical radius

Thermodynamically & kinetically controlled growth

Synthesis of Monodisperse Nanoparticles (II)

 Surface Energy

Solvent (coordinating or non-coordinating) Surfactants (Surface binding)

 Temperature

 Supersaturation

Numerical Simulation on the Growth Behavior corresponding to:

Surface Energy Temperature Supersaturation

J. Park et al., Angew. Chem. Int. Ed. 46, 4630 (2007)

 Hot-Injection Method

Stabilization of Nanocrystals in Medium

 NO-NO Interactions

 Van der Waals interactions

 Related to Dimensionality, Relative Orientation, and Distance

Crossed Cylinders Parallel Cylinders Spheres



 





 ₂

1 2

1 1

~ R R

R R W D

2 / 1

2 1

2 1 2 /

~ 3 



 





R R

R R D W L

 _{1 2}^1/2

~ 1 RR W D

Three kinds of stabilizations are possible…

 Massive Aggregations possible!!

Steric Stabilization

w/ noninterpenetrating polymers (organic layers) adsorbed on

NP surfaces

Depletion Stabilization

w/ free polymer medium Electrostatic Stabilization w/ Coulombic repulsive force

δ⁺ δ⁺

δ⁺ δ⁺

δ⁺ δ⁺

δ⁺ δ⁺ δ⁺

δ⁺ - -

-

- - - - -

- - - - - - - -

-- -

- - -

- -

-

- -

+ +

+ +

+

+

+

Oligomeric / Polymeric Surfactants w/ amine, carboxylic acid, phosphonic acid, thiol functionalities

Shape Control of Colloidal Nanocrystals

Y-. W. Jun et al., Angew. Chem. Int. Ed. (2006)

 Main Factors for Shape Control

 Surface Energy

 Crystalline Phase

 Growth Rate

 Surfactant

 Growth Temperature

Seed-Mediated Solution-Liquid-Solid Growth Oriented Attachment

Kinetically Induced Anisotropic Growth

Seed-Mediated SLS Oriented Attachment Kinetic Shape Control

Seed-Mediated Solution-Liquid-Solid Growth

Phase Diagram of AuGe Alloys

Alloy formation  Supersaturation (similar to VLS growth in vapor phase)

Decomposition of Precursors

Ge Nanowire Grown from a Seed

Oriented Attachment

High Energy Facets

Large Surface Energy

minimizing ΔG by aggregation

Oriented Attachment

Octahedral Nanocrystal

(ex) PbSe Nanocrystals

Star-Shaped Nanocrystal Hexahedron Seed

K.-S. Cho et al., J. Am. Chem. Soc. (2005)

Kinetic Shape Control

G: Growth Rate S: Surface Energy

Reactivity Difference

along with each crystal facet

Shape Control of CdSe Nanocrystals

Control by Thermal Energy Control by Monomer Concentration

Y-. W. Jun et al., Angew. Chem. Int. Ed. (2006)