Download Multiple Exciton Generation in Semiconductor Nanocrystals: Applications to Third Generation Solar Photon Conversion

Carrier Dynamics and Multiple Exciton Generation in Nanocrystals:
Applications to 3rd Generation Solar Photon Conversion
A.J. Nozik
National Renewable Energy Laboratory
University of Colorado, Boulder
Randy Ellingson
Matt Beard
Justin Johnson(PD)
Kelly Knutsen (PD)
Joseph Luther (GS)
Jim Murphy (GS)
Pingrong Yu
Mark Hanna
Sasha Efros (NRL)
Andrew Shabaev (NRL)
Josef Michl (UCB)
Mark Ratner (NWU)
Exciton dynamics, MEG
THz spectroscopy, MEG
SF,Exciton dynamics,MEG
Exciton dynamics, MEG (Si)
MEG photocurrent, QD arrays
THz Spectroscopy, QD arrays
MEG Solar Cells
Thermodynamic Efficiencies
Theory of MEG
Theory of MEG
Singlet Fission (SF)
Singlet Fission (Theory)
Funding: U.S. DOE Office of Science, Div Basic Energy Sciences, Division of Chemical
Sciences
Consequences of Size Quantization
ƒ Large blue shift of absorption
edge
ƒ Discrete energy
levels/structured absorption
and photoluminescence
spectra
ƒ Dramatic variation of optical
and electronic properties
ƒ Enhanced photoredox
properties for photogenerated
electrons and holes
ƒ Greatly enhanced exciton
absorption at 300 K
ƒ Conversion of indirect
semiconductors to direct
semiconductors or vice versa
ƒ Greatly enhanced oscillator
strength per unit volume
(absorption coefficient
■ Greatly modified pressure
dependence of phase changes and
direct to indirect transitions
■ Greatly enhanced non-linear
optical properties
ƒ Efficient anti-Stokes luminescence
Effects on Dynamics:
ƒ Slowed relaxation and cooling
(~10X) of photogenerated hot
electrons and holes (excitons)
ƒ Conservation of crystal
momentum relaxed
ƒ Enhanced Auger processes
(invoked to explain PL blinking,
breaking phonon bottleneck, and
multiple exciton generation )
QUANTIZATION EFFECTS
● Auger processes enhanced
● Hot exciton cooling slowed (compared to MEG)
● Crystal momentum not a good quantum number
e–
e–
ne = 4
τ QW
therm
ne = 3
τ bulk
therm
ne = 2
ne = 1
E gbarrier
hh = 1
hh = 2
hh = 3
hh = 4
Ec
hν
Bulk band gap
hν
Ev
h+
h+
Quantum Well
QW
τ therm
>> τ bulk
therm
Bulk
P84IIB-G0933203
Enhanced Photovoltaic Efficiency in Quantum Dot Solar
Cells by Multiple Exciton Generation
MEG is an inverse Auger
process; Auger processes
are enhanced in QDs:
<2Pe|ν(r1,r2)|1Se1Se1Sh>
● crystal momentum need
not be conserved (not a
good quantum number)
● Carrier thermalization
is
suppressed (phonon
bottleneck)
ez
ez
z
impact ionization (now called Multiple
Exciton Generation (MEG)
Egap
hν
O
h+
______________1Pe
hω = 20 meV 100 meV
_______________1Se
e-
One photon yields
two e-–h+ pairs
O
(MEG can compete successfully
with phonon emission and forward
Auger processes)
h+
Quantum Dot
A.J. Nozik, Ann. Rev. Phys. Chem. 52, 193, 2001; Physica E14,115, 2002;
and in “Next Generation Photovoltaics”, Marti& Luque, Eds, AIP, 2003;
Efficiency of Solar Photon Conversion
Main Process Limiting Conversion Efficiency
(> 50% loss)
Hot eRelaxation
SOLAR ELECTRICITY
Conventional PV Cell
eheat loss
Energy
e-
ηmax = 32%
hν
p-type
n-type
heat loss
1 e- - h+ pair/photon
usable photovoltage (qV)
Photovoltaic Cells
I.
1st Generation
•
•
Single crystal Si
Poly-grain Si
II. 2nd Generation (Polycrystalline Thin Film)
•
•
•
•
•
Amorphous Si
Thin film Si
CuInSe2
CdTe
Dye-sensitized Photochemical Cell
III. 3rd Generation (ntheor>32% Queisser-Shockley limit and low cost)
•
•
•
•
•
•
•
•
(High efficiency multi-gap tandem cells(here now but expensive))
Multiple Exciton Generation (MEG) solar cells
Quantum Dot Solar Cells
Singlet Fission Solar Cells
Hot electron converters
Intermediate Band PV
Photon management (upconversion and down conversion)
Thermophotovoltaics/thermophotonics
See: M. Green, “Third Generation Photovoltaics”. Springer, 2003, and
Marti and A. Luque, “Next Generaton Photovoltaics”, Inst. Of Physics Series in
Optics and Optoelectronics, 2002
Another Way
Photocurrent Multiplication by Impact Ionization (I.I.)
e
e
e
e
e
h+
h+
h+
hν ≥ 2 Eg
Eg
h+
h+
1 photon yields 2 (or more) e- - h+ pairs
(I.I. previously observed in bulk Si, Ge, InSb, PbS, and PbSe
> 30 years ago—mainly with applied electric field (avalanche
photodiodes)—BUT NOT USEFUL FOR PV BULK MATERIALS
Detailed Balance Efficiency Calculations
QY for carrier generation:
QY=0
E<Eg
QY = M
MxEg<E<(M+1)Eg for M <Mmax,
where Mmax=4/Eg
Photogenerated current:
Jg =q C∫QY(E)Γ(E)dE
Recombination current:
60
8
50
7
6
5
M=3
3
0
1
2
3
4
hν (eV)
QY for a tandem MEG cell
2
1
Mtop=2
J(V)=Jg – JR(V)
Series connected Tandem Cell:
and
J(V) = J1(V1) = J2(V2)
Eg1
2
1
V = V1+V2.
10
M=1
1
∞
IV curve:
20
M=2
2
Eg=0.75 eV
QY (E )E 2
J R (V , E g ) = qg ∫
dE
(
)
E
qQY
E
V
−
E g exp(
) −1
kT
30
M=4
4
0
40
Mmax=5
2Eg1
Mbottom=2
Eg2 2Eg2
5
0
2
AM1.5G
9
Solar Photon Current (mA/cm eV)
-All photons above the bandgap are absorbed.
-Photons less than the bandgap not absorbed.
-Only loss if radiative recombination.
-All photogenerated carriers are collected.
70
10
Optical Generation Quantum Yield
Detailed balance model
Limiting Efficiency for Unconcentrated AM1.5G Spectrum
(Single Bandgap)
45
AM1.5 Efficiency (%)
40
QD
Mmax
35
30
25
M=3
20
SF
15
10
5
0
0.0
M=2
M=1
0.5
1.0
Bandgap (eV)
Hanna and Nozik, JAP 100, 74510 (2006)
1.5
2.0
RATE
OF EFFICIENCY
INCREASE
WITH SOLAR
Maixmum
Efficiency
at Optimum
Band CONCENTRATION
Gap
Maximum Efficiency (%)
90
Maximum
multiplication
80
70
M=3
60
M=2
50
M=1
40
30
1
10
100
1000
Concentration
10000
Single gap MEG cell efficiency increases at a faster rate under solar concentration
than a normal semiconductor cell with no carrier multiplication (M=1).
Bulk Si
Queisser,
et al. 1994
Conservation of energy E and momentum hk/(2π) is
fulfilled if the two dash-dotted arrows add vectorially to
zero.
QDs: Requirement for conservation of momentum is
relaxed. Threshold should be lower.
Quantum yield & IQE
measurements
Because of the need to conserve
momentum, and because the rate of
impact ionization is much slower than
the rate of phonon emission at low
electron energies, impact ionization
is an inefficient process in bulk
semiconductors in the visible and
near IR, and for Si requires UV
photons.
Si
Transmission
Electron Micrograph (TEM) of
PbSe Quantum
Dots (also called
(Nanocrystals)
5 nanometers
5 x 10-9 m
0.000005 mm
20 rows of atoms,
~ 6000 atoms, in
these QDs
TEM From Andrew
Norman
PbTe Arrays in HCP Configuration
PbTe NCs
•New Synthetic Routes
•First optical characterization
-absorption spectra
-Photoluminescence
-multiple exciton generation
•Sphere to Cube Transition
•Comparison of Lead Salt
Properties
Murphy, J. E. et al. “PbTe Colloidal Nanocrystals: Synthesis, Characterization,
and Multiple Exciton Generation.” J. Am. Chem. Soc. 128, 3241–3247 (2006).
TEM: Andrew Norman
Arrays of Cubic-shaped Lead Salt
NCs PbTe
PbSe
TEM: Andrew Norman
MEG DYNAMICS
Determine the photogenerated carrier density (QY) and thus MEG
dynamics by: (a) measuring the free carrier absorption (IR probe)
and exciton bleach (HOMO-LUMO probe); (b) measuring dynamics
of multi-exciton decay vs single exciton decay, and the rise time
of exciton bleaching and induced exciton absorption
-
∆α α e-h pair (exciton)
Pump hν > nEg
IR Probe: λ~5000nm
HOMO-LUMO Probe:
λ ~ 1300-1700 nm
+
--
CB
+
VB
density; 1S bleach decay
dynamics = f(multiexciton
density); 1S bleach
dynamics and induced
exciton absorption
determine carrier cooling
rate and carrier
multiplication rate
Transient absorption experimental setup
SRS
Boxcar
Quantronix
Ti:Sapphire
Amplifier
PC
Monochromator
Delay
1.5 ns
KML
Ti:S
Oscillator
805 nm
Vis/IR probe
290 nm-10 µm
Topas OPA
Sample
Delay
1.5 ns White Light probe
440-1070 nm
Al2O3
Chopper
Pump
290-2200 nm
Topas OPA
●
Experimental Verification of Greatly
Enhanced e--h+ multiplication (we term
Multiple Exciton Generation (MEG)) in
Quantum Dots
R.D. Schaller and V.I. Klimov, Phys. Rev. Letts, 92,
186601 (May), 2004 (PbSe QDs)
● R.J. Ellingson, M. Beard, J. Johnson, P. Yu, O.Micic, A.
Shabaev, A. Efros, A.J. Nozik, Nano Letters 5, 865, 2005
(PbSe and PbS QDs; 300% QY (3 e-/photon) at 4 times
Eg)
● Recently, MEG also found in PbTe (NREL, JACS, 128,
3241, 2006) and CdSe (LANL, APL, 2005); 7 e-/photon in
PbSe! (LANL, NanoLetts, 6, 424, 2006); InAs (Van
Maekelbergh, Banin, et. Al., J. Phys. Chem. C (2007)); and
Si (NREL, 2007)
Exciton dynamics for different pump energies with
mid-IR intraband probe (5 µ)
0.6
(a)
Ehν/Eg = 5.00
Ehν/Eg = 4.66
Ehν/Eg = 4.25
Ehν/Eg = 4.05
Ehν/Eg = 3.60
Ehν/Eg = 3.25
Ehν/Eg = 1.90
∆α(normalized at tail)
0.5
0.4
0.3
0.2
0.1
0.0
0
100
200
300
Time delay (ps)
400
MEG in PbX; X = Se, S, Te
(QY > 200% means 3 e-/photon are created; QY = 300% means all
dots have 3 e- )
Quantum
(%)
QuantumYield
Yield
300
Eg(HOMO - LUMO) -0.91 eV
0.91 eV
0.91 eV
0.91 eV
0.82 eV
0.73 eV
0.73
0.73
PbTe - 0.91 eV
PbS - 0.8 eV
250
200
150
100
1
2
3
Ehν/Eg
4
5
Silicon Nanocrystals
• Particles 3-10 nm diameter
• Bulk bandgap 1.12 eV (~1100 nm);
• Si NC bandgaps 1.22-1.6 eV (1016 –
775 nm)
TEM image courtesy of
Innovalight, Inc.
Amine soak properties
oleate
aniline
ethylenediamine
Murphy, Beard, Nozik, JPC B 2006
PROPOSED NEW PHYSICS BASED ON MODEL INVOLVING:
COHERENT SUPERPOSITION OF MULTI-EXCITON
STATES IN SEMICONDUCTOR NANOCRYSTALS
Shabaev, Efros, Nozik, Nano Lett. 6, 2856 (2006)
Other proposed models to explain MEG:
R.D. Schaller, V.M. Agranovich, and V.I.
Klimov, Nature Phys. 1 (2005) p. 189.
A. Franceschetti, J.M. An, and A. Zunger,
Nano Lett. 6 (2006) p. 2191.
Multi-Exciton Generation by One Photon
Efficient Multi-Exciton Generation in PbSe
0.6
Ehν/Eg = 5.00
Ehν/Eg = 4.66
Ehν/Eg = 4.25
Ehν/Eg = 4.05
Ehν/Eg = 3.60
Ehν/Eg = 3.25
Ehν/Eg = 1.90
∆α(normalized at tail)
0.5
0.4
0.3
0.2
Quantum Yield (%)
300
(a)
(b)
250
200
Eg (Homo - Lumo)
0.72 eV
0.72 eV
0.72 eV
0.82 eV
0.91 eV
0.91 eV
0.91 eV
0.91 eV
PbS - 0.85 eV
150
0.1
100
0.0
0
100
200
300
Time delay (ps)
400
2
•Rise time ~ < 2-3 ps (Inverse Auger process)
Instantaneous creation of a coherent superposition
of several electron-hole pairs by a single photon
5
R.Ellingson, et.al. NanoLetters TBP
1.0
(a)
(c)
∆T/T (Norm alized)
•Decay time ~100 ps (Auger process)
4
Ehν/Eg
What is the reason of such high efficiency? Impact Ionization?
Puzzle:
3
0.8
Excitation Energy -1 x Eg
2 x Eg
3 x Eg
4 x Eg
Instrument Response
0.6
0.4
0.2
0.0
0
1
2
3
Time delay (ps)
4
5
NEW MODEL FOR MEG
Coherent Superposition of Multi-Excitonic States in PbSe QDs
2Pe
2Pe
2Pe
2Pe
1Se
1Se
1Se
1Se
1Sh
1Sh
1Sh
1Sh
2Ph
2Ph
2Ph
2Ph
States with Energy Larger than Energy
Gap
Electron in NC occupying 2P state:
d (nm)
e
7.07
2Pe
2Pe
2
WC
1Se
Eg ≈ ∆2P
Eg
1Sh
1Sh
2Ph
2Ph
e2/| r1- r2|
r1 r2
1SeE
1Se
Eg
0
1Sh
1Ph
-1
2Fh
0.03
0.04
2
0.05
0.06
-2
1/d (nm )
degenerate and coupled:
g
Ÿ0
r2
1Dh
2Sh
1Fh
1Ph
1Gh
2Dh
3Sh 1Hh
WC= <2Pe|v(r1,r2)| 1Se 1Se 1Sh>
Eg
1Sh
e
Two states are
2Pe
1Se
3Se 1H
∆2P
Kang&Wise (1997)
WC
4.08
2De
1Ge
2Pe
1Fe
2Se
1De
1Pe
-2
d
r1
4.47
PbSe
0.02
2Pe
5.00
2Fe
1
Energy (eV)
∆2P
1Se
5.77
1Sh
Coherent Superposition of Multi-Exciton States
Optical excitation of
2Pe
“2Pe”-”2Ph” transitions:
1Se
Eg
2Pe
light h ω
1Se
∆2P
1Sh
∆2P
2Pe
1Se
2Ph
Eg
Eg
1Sh
∆2P
2Ph
2Pe
1Se
1Sh
∆2P
2Ph
Eg
1Sh
3 e-h pairs
1 e-h pair
2Ph
2 e-h pairs
The efficiency of the multi-exciton generation depends on the relaxation
mechanism.
There is high probability that the state relaxes to the two e-h pair state.
Density matrix
Theoretical description
requires:
time dependent density
matrix for:
• Short pulse excitation
•Different relaxation
mechanisms
∂ρ i
= [ρ H ]
∂t h
2Pe
(Shabaev, Efros, Nozik,
Nano Lett. 6, 2856 (2006)
W
Eg
f21
1Sh
2Ph
2Ph
f00
1Se
1Se
1Sh
1Sh
2Ph
2Ph
2Pe
1Se
1Se
1Sh
1Sh
g11
1Sh
2Pe
2Pe
1/τA
2Ph
1Se
2Pe
γ2
γ1
2Pe
Dynamics for times: ∆t << τA<< τr
f12
1Se
f10
f01 V
f22
fast component
f11
2Ph
1/τex
1/τbi
g22
Time Resolved THz
Spectroscopy
Sample
Nonphotoexcited
or reference scan
= “pump off”
Off
ETHz (t)
τ
Pump Scan
= “pump on”
On
ETHz(t, τ)
∆Φ
∆ETHz (t ,τ )
Off
ETHz
(t )
−σ (τ ) x
≅
2cnε o
•Measure transient THz frequency average conductivity
•Subpicosecond resolution
•Mechanistic information
•No electrical contacts
Film Treatments
d(nm)
εS
nave
µ
FW HM = 49 meV
1.4
Oleic Acid
Aniline
Butlyamine
ethylenediamine
hydrazine
NaOH
1.8
0.8
0.4
0.4
0.25
0.1
2
2
5.4
16
52
1
1.57
2.2
2.46
2.62
2.69
2.4
-----
7.4
47.0
29.4
35.0
Ethylenediamine
H2NCH2CH2NH2
CH3(CH2)7HC=CH(CH2)7COOH
D ∼ 1.8 nm
D ∼ 0.8 nm
1.0
3Eg
↓
0.8
↔
0.10
0.05
0.6
0.4
0.15
2E g
↓
800
1200
D = < 0.4 nm
1600
2000
Wavelength (nm)
0.2
0.0
400
800
1200
1600
W avelength (nm)
Aniline Cap
Oleate Cap
Absorbance (O.D.)
1.2
0.20
Absorbance (O.D.)
Treatment
1.6
(cm2V-1s-1)
2000
Quantum Dot Solar Cells
Potential Major Advantages of
Using Quantum Dots
• Enhanced photocurrent multiplication
by MEG (Inverse Auger Process
• Hot electron transport through
minibands in QD arrays
• Slowed Cooling of High Energy (Hot)
Electrons (phonon bottleneck)
Enhanced Photovoltaic
Efficiency in Quantum Dot
Solar Cells by Inverse Auger
Effect (Impact Ionization)
Quantum Dot
Solar Cells
e●
e-
●
E gap
hν
e-
●
One photon yields
two e-–h+ pairs
Impact ionization
O
h+
QD-Sensitized
Nanocrystalline
TiO2 Solar Cell
A.J. Nozik, Physica
E 14, 115 (2002);
O
h+
QD-Conducting
Polymer Blend
Solar Cell
p-i-n QD Array
Solar Cell
2e–/photon
InAs QD
0.4-1.0 eV
> 2Eg
Quantum Dot Sensitized TiO2
Solar Cell
ee-
e-
300 Å TiO2
e-
hν
Vph
eI3-/I3.2 eV
TiO2
Transparent
TCO
Electrode
e-
TCO
electrode
MEG
QDs ,
30-60 Å
h+
QD
electrolyte
Pt
Counter
Electrode
-Analogous to dye-sensitized TiO2 solar cells
-10 to 20 µm film of NC TiO2 (10-30 nm)
-Ru dyes ⇒ Efficiency ~ 11%
-Advantages of QD’s as sensitizers:
-possibility of slowed hot e- cooling
-possibility of impact ionization
-tunable absorption
InAs QD Solar Cell Based on NC TiO2
Vacuum
eV
-3
TiO2
e-
-4
hν
-5
InAs
h+
-6
QD1 QD2 bulk
-7
-8
TiO2
InAs
J-V Characteristic for 3.4 nm InAs QD Sensitized Solar Cell
Miniband Formation in 1-D Confined
Quantum Films
QD Array in p-i-n Photon Conversion Cell
e– minibands
e–
e–
e–
<8 Å
h+ minibands
e–
–
e
MEG
e–
e–
hν
MEG
h+
hν
h+
Eg
h+
h+
h+
h+
n
i
p
PV Cell Based on QDs Dispersed in n-and p-type
Organic Conducting Polymers
Summary/Conclusions
●
Size quantization in semiconductors may greatly affect the relaxation dynamics of
photoinduced carriers. These include:
- slowed hot electron relaxation (partial phonon bottleneck)
- enhanced Auger process (MEG)
●
The theoretical and measured energy threshold for impact ionization in bulk
semiconductors (e.g. Si, InAs, GaAs) is 4-5 times the band gap. Much lower thresholds are
predicted for QDs because of the relaxation of the need to conserve momentum. The rate of
exciton multiplication is also expected to be much faster in QDs (Auger processes α 1/d6 )
●
Very efficient exciton multiplication experimentally observed in PbSe, PbTe, PbS,
InAs, and Si QDs; the threshold photon energy is 2Eg. Up to 3 electrons per photon (300%
QY) have been observed at sufficiently high photon energies (≥ 4Eg ). A new model based on
coherent superposition of multiexcitonic states is introduced to explain these results. Two
excitons/photon yield over 90% of the efficiency benefit of carrier multiplication.
●
Singlet fission is the molecular analog of MEG and also could yield enhanced solar
photon conversion efficiencies. It had been observed in dimeric diphenylisobenzofurane.
Single gap cells with carrier multiplication with MEG yield the same improvement for PV as
2-gap tandem PV cells. A tandem cell with SF and/or MEG is required to improve maximum
efficiency for H2O splitting. Higher efficiency in SF cells for PV require a tandem cell
configuration.
Summary/Conclusions - Continued
• Various configurations of Quantum Dot Solar Cells are
suggested that could yield high conversion efficiencies:
1. Nanocrystalline TiO2 sensitized with QDs
2. QD arrays exhibiting 3-D miniband formation
3. QDs embedded in a polymeric blend of electron- and
hole-conducting polymers.
4. SF molecular chromophores in a tandem cell for PV
and photoelectrolysis
● THE DYNAMICS OF HOT ELECTRON and
EXCITED MOLECULE COOLING, FORWARD
AND INVERSE AUGER RECOMBINATION
(MEG), AND ELECTRON TRANSFER CAN BE
MODIFIED IN QD AND SF SYSTEMS TO
POTENTIALLY ALLOW VERY EFFICIENT
SOLAR PHOTON CONVERSION VIA
EFFICIENT MULTIPLE EXCITON
GENERATION