Transcript Interfacial Charge Transfer in Solar Cells: A Single

Interfacial Charge Transfer in Solar
Cells: A Single Molecule Perspective
Derek J. Hollman
Undergraduate Physics Symposium
8 May 08
Dye-Sensitized Solar Cells (DSSC)
Interfacial Dynamics Essential to Device Performance!
Understanding the DSSC
• Understanding interfacial charge transfer in DSSC
complicated by heterogeneity
• Necessitates well-defined model system with
controlled interface
• Bulk properties do not reveal complete dynamics
in heterogeneous systems such as DSSC
• Must observe single molecules to address rates
and mechanisms of charge transfer
Experimental Realization
System:
• Perylene bisimide dye
• Gallium Nitride (GaN)
• Scandium Oxide (Sc2O3)
• Ultra-high vacuum
• Confocal Microscopy
We may observe:
• Electron transfer rates
• Distance dependence
• Influence of interband states
• Influence of surface states
• Orientation dependence
The Choice of Sc2O3/GaN
Chang Liu et al., APL 88 (2006), 222113
• Thickness from 5 Å-1000 Å to slow charge transfer
• Near-perfect, abrupt interface
• Sc2O3 (111) grown heteroepitaxially on GaN (0001)
Single Molecule CT Reporter
R = -C4H9 or -C13H27
•
•
•
•
Strong absorber (e = 75000 M-1cm-1) with unity quantum yield
Low intersystem crossing rates and short triplet lifetime
Perylene/TiO2 used in DSSC
Electronic properties tunable by bay-substitution
Towards Single Molecule Spectroscopy in UHV
27.57
Photobleaching
kcps
27.57
Photoblinking
0
-1.80
Photoblinking
• Distinct “on” and “off” states only seen at
single molecule level
Objective
Histograms/distributions: P(τ)
Autocorrelation function: g(2)(τ)
Mechanism!
• From these analyses, information about CT kinetics can be elucidated
• Simulate 2-state system, develop statistical analyses to recover rate information
Simulation: Signal Generation
1.2
With kf >> kex >> kfct, 3-state system effectively becomes a
2-state system
1
0.8
0.6
0.4
0.2
eff
fct
k , k bct
0
0
2
4
6
8
exp. deviate
repeat
ton, toff
on/off
counts
On/off Time Distributions
ln( #occurences)
6
4
2
0
0
20
40
Time (ms)
• On/off transitions may be Poissonian processes; on/off times are
exponentially distributed
• CT kinetics may also be power-law distributed
• Observing fluorescence intermittency provides information on CT kinetics
• Distribution contains information on mechanism
counts per time bin (1/1 ms)
counts per time bin (1/100 s)
counts per time bin (1/10 s)
Dependence on Bin Size
6
3
0
0
100000
200000
Time (s)
30
20
10
0
0
100000
200000
Time (s)
120
Ambiguity of on/off state
60
0
0
100000
Time (s)
200000
counts per time bin (1/1 ms)
Drawing the Line
140
120
100
80
60
40
20
0
0
500000
1000000
Time (s)
6
on-time histogram
200
krecovered = 97 ± 5 Hz
ln( #occurences)
kbct =clock;
100Hz measure
ktime
fct = 100Hz
• Start
molecule was
“on” or “off”
4
150
140
# Occurences
# Occurences
Analysis:
off-time histogram
• When a transition 100
occurs, record time,2 bin it, reset
50
clock
70
•0 Repeat
30
0
0
60
Time (ms)
90
0
10
20
30
Time (ms)
40
50
0
0
20
Time (ms)
40
Autocorrelation
( ) 
I (t ) I (t   )
I (t )
2
0.5
(2)
g
( 2)
g () - 1
1.0
0.0
1000
10000 1000001000000
Time (s)
• Determine correlation between pairs of
photons at arbitrarily long times
Conclusions
• CT kinetics of a DSSC can be understood by
analyzing single molecule fluorescence
intermittency trajectories
• Experimental design allows for a good model
and control of many parameters
• Simulation provides a framework for developing
analyses
• Analyses can recover rates for a 2-state system
Future Simulation Work
•
•
•
•
•
Fit autocorrelation functions
Power-law kinetics
Multiple dark states
Photon arrival times for additional information
Use analyses on real data!
University of Arizona
Dr. Oliver L. A. Monti
Dr. Brandon S. Tackett
Michael L. Blumenfeld
Laura K. Schirra
University of Florida
Dr. Brent P. Gila
Dr. Stephen J. Pearton
Mary P. Steele
Jason M. Tyler
Stefan Kreitmeier (TU München)
DSSC – A Complex Structure
SEM micrograph of titanium oxide films. M. Grätzel et al., J.
Am. Ceram. Soc. 80, 3157.
•
•
L. Kavan, M. Grätzel, S. E. Gilbert, C. Klemenz, H. J. Scheel, JACS 118,
6716
Charge transfer in heterogeneous environment
Crystal face- and structure-dependent device
performance
Kinetics in DSSC
T. Hannappel, B. Burfeindt, W. Storck, F. Willig, JPCB 101,
6799
Result:
Non-exponential charge
transfer kinetics
S.A. Haque, Y. Tachibana, D.L. Klug, J.R. Durrant, JPCB 102,
1745
Ideal Model System
• Donor: Single molecule to model excited state in solar
cell
• Acceptor: Single-crystalline wide bandgap
semiconductor
• Spacer Layer:
– Heteroepitaxial single crystalline surface
– Controllably vary donor-acceptor distance
– Slow down charge transfer kinetics
• Conditions: Growth and measurement in ultra-high
vacuum
Experimental Realization
System: Perylene bisimide
on Sc2O3 / GaN
We may observe:
• Forward and backward
electron transfer rates
• Distance dependence
• Influence of interband
states
• Influence of surface states
• Orientation dependence
… one molecule at a
time!
Single Molecule CT Reporter
R = -C4H9 or -C13H27
•
•
•
•
Strong absorber (e = 75000 M-1cm-1) with unity quantum yield
Low intersystem crossing rates and short triplet lifetime
Perylene/TiO2 used in DSSC
Electronic properties tunable by bay-substitution
PTCDI/Sc2O3/GaN so far
• ELUMO(PTCDI) =
0±100 meV vs.
Sc2O3/GaN CBM
Excitation/Emission GaN
3.0
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
(n
n
tio
500
ita
Em400
iss
ion
m
)
0.5
460
440
420
400
380
360
0.0
300
(n
m)
600
340
Ex
c
Fluores
cence (A
U)
3.0
340
360
380
400
Ex
420
ci
ta
440
t
io
n
(n
m
)
0.0
300
400
500
460
600
• There are states within the bandgap!
Fluorescence Intermittency
• Single molecules exhibit “blinking”
• On/Bright state: continual excitation,
fluorescence cycling
• Off/Dark state: non-fluorescing state resulting
from ISC or CT event
• ton, “on-time”: period of continual
excitation/fluorescing until a single molecule ISC
or CT event
• toff, “off-time”: period until a charge
recombination or reverse ISC event
Time Scales
• ISC events occur with low transition rate and
short lifetime, typically microsecond or
shorter
• CT events occur with much longer lifetimes,
millisecond to seconds, also tunable (insulator
layer)
• Data acquisition rate much slower than ISC
event rate
• ISC events only lower average cps
What it looks like
counts per time bin (1/1 ms)
ton
toff
120
60
0
0
500000
Time (s)
1000000
• Distinct visible states, on and off, only seen at
single molecule level
Model System
• With kf >> kex >> kfct, 3-state system effectively becomes a
2-state system
•
Experimental acquisition rate: 103 - 104 Hz
•
kf ~ 109 Hz, kex ~ 106 Hz, kfct ~ 103 Hz
Poissonian Processes
• On/off transitions are Poissonian processes
• On or off times may be characterized by Poisson
distribution
1.2
Exponential because
• Transfer of charge may be a tunneling
process
• Kinetics may follow well-defined rate
constant
probability density
1
0.8
ke-kt
0.6
0.4
0.2
0
0
1
2
3
4
Time
5
6
7
Power-law Kinetics
• CT kinetics may be powerlaw distributed: P(t )  At m
• Fluctuating rate constant;
molecule sampling
multiple surface sites
Basche, et. al
• Observing fluorescence
intermittency provides
information on CT kinetics
Motivation for a Simulation
• Shot-noise limited signals with low S/N, need
sophisticated methods of analyzing data
• Simulation provides framework for developing
various analyses
• Control of input rate parameters, want to
recover them
• Do not know experimental rates a priori, can
not verify analyses otherwise
Simulated Fluorescence Trajectory
counts per 0.1 ms
16
8
0
0
200000
400000
Time (s)
• Signal generated at rate much faster than
real acquisition rate, then re-binned
Re-binning Simulated Trace
15
counts per time bin (1/100 s)
counts per time bin (1/1 s)
2
1
0
10
5
0
0
500
Time (s)
1000
0
400
800
Time (s)
• Simulated data generated on 1µs time step
• Real data acquisition rate closer to 0.1-1ms
On/off Histograms
200
off times histogram
on times histogram
140
# Occurences
# Occurences
150
100
70
50
0
0
0
10
20
30
Time (ms)
40
50
0
30
60
Time (ms)
• Will investigate dependence on threshold,
bin size
90
Recovery
6
m = -0.097 ± 0.005
200
ln( #occurences)
off times histogram
# Occurences
150
kfct = 100Hz
100
4
krecovered = 97 ± 5 Hz
2
50
0
0
0
10
20
30
Time (ms)
40
50
0
20
40
Time (ms)
• Fit histograms to exponential; decay rate should be
input rate
• Recovery!
Autocorrelation
g ( ) 
( 2)
I (t ) I (t   )
I (t )
2
• Determine correlation between pairs of photons at
arbitrarily long times
• Shape of autocorrelation contains kinetics of system
• Algorithm implemented:
g ( 2) mt  
1 N m
I t I   m t 

N  m  1
1

N



I


t


 1

N
2
1