Antibunching and excitation lifetimes in CdSe nanocrystals

Antibunching and excitation lifetimes in CdSe
nanocrystals
Margaret Cosgriff
March 19, 2009
2
1
Abstract
Using a beam-splitter and two photon detectors, we measured the cross-correlation
function of a series of single nanocrystals, and found that the nanocrystals exhibit
antibunching (zero correlation at zero time delay) as expected, indicating that the
nanocrystals were indeed emitting only one photon at a time. Modeling the nanocrystals as a three-level energy system (ground, excited, and "dark"), we measured the
characteristic time delay between photons emitted by a nanocrystal, which corresponds to the inverse of the transition rate from the excited state and the ground
state. We performed this measurement using 532nm and 405nm wavelength light to
excite the nanocrystals. Nanocrystals excited by 532nm wavelength light had a mean
time constant of 22.7
± 5.3ns,
and those excited by 405nm wavelength light had a
mean time constant of 22.4 ± 6.3ns.
3
4
2
Introduction
Colloidally synthesized nanocrystals can be manufactured to fluoresce at many different frequencies within a wide range, making them very useful in a variety of experiments. As semiconductor crystals, they have applications in the manufacture of
electronics.15 ,16 N anocrystals are also useful as a replacement for organic dyes in studies of cell biology: they are non-toxic, last longer than organic dyes, and, unlike many
organic dyes, nanocrystals that fluoresce at different wavelengths can be excited by
a single wavelength. This property allows researchers to observe multiple structures
simultaneously, by tagging them with different colors of nanocrystals and exciting
them with a single laserY Nanocrystals are also good candidates to be single-photon
emitters, and could therefore be used in quantum computing, as well as in the classic
single-photon interference physics experiment, and other fundamental tests of quantum mechanics. However, nanocrystals also "blink" (stop emitting for varying periods
of time), complicating such applications. is
overlap
Candut:tian
bmd
Fermi level
metal
s ernie onduet or
Bandgap
insulator
Figure 1: Electron band structure of metals, semiconductors, and insulators.13
The optical properties of a bulk semiconductor depend on its electron band struc-
5
ture. An incoming photon can excite an electron from the valence band of the semiconductor into the conduction band, leaving a "hole" in the valence band. This electron
is generally excited well into the conduction band and "relaxes," losing energy nonradiatively while staying in the conduction band. The hole and the excited electron
can move freely within their respective bands, until they eventually recombine, emitting a photon. The characteristic time it takes the electron-hole pair to recombine
determines the semiconductors fluorescence rate. The energy of the emitted photon is
very close to the energy bandgap between the conduction band and the valence band,
and is always lower than the energy of the exciting photon due to this relaxation
process, a fact that is crucial to the design of fluorescence microscopy experiments.
v=:::o
v=oo
V=oo
V=oo
v=o
o
L
x
Figure 2: Diagram of a one-dimensional infinite potential well. 8
These energy bands, however, only exist in bulk semiconductors. In nanocrystals,
which are semiconductor clusters a few nanometers across, the energy bands are split
into discrete energy levels. Nanocrystals behave essentially as quantum wells, as the
surface of the crystal acts as a (near-) infinite potential barrier. Because the size of
a potential well determines the allowed energy levels, the diameter of a nanocrystal
controls the wavelength of light at which it fluoresces.
And, because the diame-
ter of nanocrystals can be controlled during their creation, the relationship between
nanocrystal size and fluorescence frequency means that nanocrystals can be manufac-
6
tured to fluoresce at many different frequencies.
Unfortunately, nanocrystals, also called quantum dots, generally do not fluoresce
continuously. Whereas in an ideal fluorescent material, a steady illumination will
produce a steady fluorescence at a rate dependent on illumination intensity, absorption
cross-section of the material, and exciton (electron-hole) decay rate, nanocrystals
exhibit digital "blinking" behavior, switching between an on-state where the dot emits
light, and an off-state where it does not. IS Excitation still occurs in this off-state, but
the resulting additional electron-hole pair recombines nonradiatively.6
The statistics of this blinking behavior has recently become the subject of significant study, which has shown that the distributions of on- and off- times follows
a power law, in contrast to the generally exponential distribution of these times in
dye molecules and other blinking systems. 14 ,IS Several models exist that attempt to
explain this power law time distribution. The models all start with a relatively simple
three-level system, in which electrons transition directly between a ground and an excited state, as in normal fluorescence, and also from the excited state to a dark state,
and then back to the ground state, which does not result in photon emission. The dot
stops fluorescing when either an electron or a hole escapes the dot or is trapped in a
surface state, leaving the dot with an overall charge. In a charged dot, excitons can
recombine via a nonradiative Auger process, which occurs on a much faster timescale
than radiative processes, making the dot much less likely to fluoresce. 6 The models
then differ on the source of the power law statistics.
Traditional rate-limited behavior is characterized by exponential distributions of
lifetimes. These rates are related to transitions between quantum levels by Fermi's
Golden Rule, and even complex distributions of rates result in exponential distributions. Power law behavior, in contrast, is characteristic of "random walk" processes.
7
Models of nanocrystal blinking try to address the question of what is occurring physically that can be described as a random walk. One model holds that an excited
nanocrystal ejects an electron that performs a physical random walk before returning
to the nanocrystal. While the nanocrystal is charged, it is dark, and the coulomb force
keeps the ejected electron from escaping to infinity. Another model has an electron
tunneling to one of many surface trap states, which are distributed such that the offtime distributions follow a power law. A third model has an excited electron making
the transition to and from a trap state of varying energy only when the two states
are in a very narrow resonance range, with the energy levels themselves performing a
"random walk." 10,18
Another feature of quantum dots is that they exhibit anti bunching, which we
observe through a measurement of the correlation function
g(2)
(T). Our measure-
ments use a Hanbury-Brown/Twiss (HBT) configuration, where light is emitted from
a source is split and directed to two detectors, and those two detectors (in the case
of antibunching) never register photons at the same time. Antibunching in quantum
dots is strong evidence that they are single photon emitters. If the two detectors
never, or almost never, detect photons from a quantum dot at the same time, it is
highly unlikely that the dot ever emits two photons at once. Beyond the qualitative
observation of the resulting dip at time T = 0, measurement of the
g(2)
(T) function can
also be used to determine the distribution of excited state lifetimes among nanocrystals, and the wavelength dependence of this distribution. Antibunching behavior has
been experimentally confirmed in CdSe, ZnS, and InAr nanocrystals. 2 ,15 Most such
experiments make use of pulsed excitation, but antibunching has also been observed
from quantum dots under continuous-wave excitation. 12
I studied the antibunching behavior of CdSe nanocrystals at two laser wavelengths,
8
one at 532nm and the other at 405 nm. I measured the second order correlation
function
g(2)
(T) from the fluorescence of these nanocrystals to derive the transition
rates between the I -exciton excited state and the ground state of these quantum dots.
9
10
3
Theory
A common test that a fluorescent emitter is a single dot is to check for anti bunching.
A standard method for measuring anti bunching, and also state lifetimes, is to measure
the second order correlation function
(2)(T)
g
=
g(2)
(T), given by the equation
J I(t)I(t + T)dt
J 12(t)dt
(1)
We did not measure this function directly, because given the time-scale of fluorescence ('"'-'IOns), we would need to be able to measure I(t) with sub-nanosecond
precision, which was not possible with our equipment, or without increasing fluorescence rates so high that we would have damaged our samples. Instead, we used an
HBT setup (explained in Section 4) to split the fluorescence from the sample into
two channels, and measured the time delay between a detection in one channel and
the next detection in the other channel. This type of measurement is a very good
approximation of the cross-correlation function assuming the count rate is low over
the time interval being observed (which in this experiment it was: typical count rates
were '"'-'50kHz, and the full time interval over which we observed
g(2) (T)
was 500ns).
Under that assumption it is very unlikely that two photons would be detected in the
second channel during that interval; to have multiple photon counts contribute to the
correlation function, the count rates would have to be at least 2MHz.9
We model a nanocrystal as a three level system, with transition rates from the
ground to excited state (k 12 ), from the excited state to the ground state (k2d, from
the excited state to a dark state (k 23 ), and from the dark state to the ground state
(k3d. The behavior of the dark state that generates power law blinking does imply
11
Channell
.Een
~
OJ
E
H
Figure 3: Model graph of intensity vs.
Channel 2
time for our two detectors.
Assuming a
low count rate (so that each "count" only represents one photon), g(2)(7) is just the
distribution of
~t's.
Our experimental setup, which only records the
~t's
between a
detection in the "first" channel and the next detection in the "second," would miss
~t3
in this example, but since the count rate is assumed to be low,
~t3
and similar
intervals are unlikely to be within the range of ~t's (±250ns) that we are considering.
that the form of
k3I
is more complicated than the constant value we assume it to be
here, but the time-scale on which blinking occurs is too slow to affect the correlation
function on the time scale of our experiment. The correlation data can therefore be
fit to a function derived from rate equations for the purpose of extracting lifetime
information during an on-time cycle.
When the nanocrystal transitions from the excited state to the ground state, it
emits a photon; all other transitions do not produce light. N I , N 2 , and N3 are the
probabilities of the the nanocrystal being in the ground state, excited state, and
..
.
dark state, respectively, and N I , N 2 , and N3 are the corresponding time derivatives.
12
Excited state
Dark state
k12
Ground state
Figure 4: Diagram of a three level system, the energy model we used to describe a
nanocrystal. The k ij parameters are transition rates between the energy levels i and
J.
Assuming constant transition rates, this implies the following relations:
(2)
(3)
(4)
(5)
We expect solutions of the form
13
(6)
Plugging in, we find an equation for A:
Of the four transition rates,
is
k12'
k21
is the largest , on the order of 10 7 8 -
1.
Next largest
which is proportional to the intensity of the exciting light and the absorption
scattering cross-section, on the order of 10 58-1, with
order of 10° to 103 . 6 This relationship,
k21
»
k12
»
k23
and
k 23 , k31 '
k31
much smaller, on the
allows several simplifying
approximations to be made, giving the following expression for the three possible
values of A.
Thus the equations for
N1
(t) , N2 (t) , and
N3 (t)
(after some algebra) are
(8)
(9)
(10)
14
where
The intensity of the light emitted by a nanocrystal is proportional to k 12 N 2 (t) , the
number of electrons in the excited state times the rate at which they transition to the
ground state. Since A3t
«
1 for the range of time we are considering, this rate is
(11)
The cross-correlation function
g(2) ( T)
should be proportional to this expression.
15
16
4
Experimental Methods
In a traditional optical microscope the sample material is illuminated by a lamp. The
light reflected or scattered from the sample is magnified by an objective lens, generating an image that is observed by a camera or human eye through an eyepiece.
Although it allows for direct visual examination of the sample, the presence of diffuse, broad-spectrum lamplight makes measurements of light emitted by a fluorescent
sample almost impossible. A solution to this problem is to excite the fluorescent sample with a light from a narrow band of wavelengths, often using filtered light from
a mercury lamp. This method is called fluorescence microscopy. The wavelength of
light emitted by a fluorescent material is always longer than the exciting wavelength,
a difference known as the Stokes shift.
Not all materials fluoresce; some only scatter incident light. In order to examine
these materials using fluorescence microscopy, the material can be stained with a
fluorescent dye, or labeled with a semiconductor nanocrystal.
Since nanocrystals
generally do not react with proteins, they are therefore useful in studying biological
systems. The Stokes shift allows the signal from the fluorescing sample to be separated
from the exciting wavelength with the use of a dichroic mirror or filter that transmits
one wavelength but reflects or absorbs the other.
In epifluorescence microscopy, the signal from the sample passes through the same
optic that focused the exciting light onto the sample, reducing the number of optical
elements required, and ensuring that the detection system is focused on the sample
region that is being illuminated.
The image resolution can be improved still further if a laser instead of a lamp
is used to excite the sample. Light from a lamp is incoherent, and can at best be
17
Radius:
2' A
HIA
9A
1.5
2.5
2
3
Photon Energy (eV)
Figure 5: "Absorption (thick lines) and fluorescence spectra (thin lines) for CdSe
nanocrystals at T=77K." 11 Note that the absorption peak is always at a higher energy
than the fluorescence peak.
focused down to a lOOj..lm diameter spot on the sample plane. In order to focus on a
smaller area, a coherent light source, such as a laser, must be used to illuminate the
sample. Laser light, which is also wavelength-specific, can in fact be focused down
to the diffraction limit, a spot on the order of lOO-300nm for the 532nm wavelength
light used in this experiment. This thousand-fold improvement in spatial resolution
allows for the creation of scanning microscopes, in which either the exciting light or
the stage on which the sample is mounted move, so that different parts of the sample
18
barrier
filter
dichroic
beam
spUtter
exciUtUon
fUter
exciting
light
objective
emitted
fluorescence
light
Figure 6: Fluorescence mIcroscopy diagram.
The high-energy (in this case blue)
exciting light reflects off the dichroic mirror, is focused by the objective, and absorbed
by the specimen. The specimen then emits lower energy (in this case green) light,
which passes through the dichroic mirror. 7
are excited, and fluoresce, at different times. Both the intensity of the signal and the
relative position of the exciting light and the sample are known at all times during
the scan, creating a map of the sample.
The dichroic mirror effectively removes most of the exciting light noise from the
signal, but it cannot stop light from other parts of the sample from interfering with
19
the measurement. To reduce this problem, confocal microscopes have the light from
the sample pass through a pinhole. Light from points to the side or even (for threedimensional samples) above and below the desired point on the sample will not focus
at the pinhole, and will therefore be largely blocked. This component helps increase
the signal-to-noise ratio of the sample data at the cost of decreased overall signal.
Taken together, the laser light source for tight focusing and the confocal geometry
for blocking background noise allow the performance of single-photon-counting experiments, which are crucial for detecting antibunching.
I
I
Figure 7: Confocal microscopy.19 In the upper image, light from outside the focal
plane does not focus onto the pinhole, and is blocked. In the lower image, the pinhole
is wider, allowing more light through, including light from outside the focal plane.
In our experiment, we used a 532nm Nd:YAG laser and a 405nm diode laser to
illuminate our sample. The laser light reflects off two mirrors, which were adjusted
to send the beam through two irises, defining the light path. We placed several easily
removable optical density filters in the path of the beam to adjust the power reaching
20
NdYAG Laser
~
HeNe Laser
~
Diode Laser 405 n m
Piezo
Sample
Nano
Stag e ='""'-7"----"~_T_"""'""'=
Microscope
Objective
i!
Flip Mirrors
To PC
Optical Density
Filters
Beam
Expander
+-.
Dichroic
Mirror
t
~L.
Beam
Splitter
Adjustable
Aperture
I'- - - - - -'
Filter
Lens
Figure 8: Optical layout for the microscope when it is in confocal mode.
the sample. We used a power of 5-10mW to illuminate the sample in wide-field imaging
mode (described below), and O.5j.JW while in confocal mode, when the beam is much
more focused at the sample plane. We estimate that the light intensity at the sample
is the same for both modes, approximately 200W /cm 2 . The beam then passes through
an expanding lens and is raised to the microscope entrance height by a periscope. The
beam is expanded by a lens before it enters the microscope objective so that it can
be more tightly focused onto the sample by the objective lens, a process known as
"filling the back aperture." The microscope we used is an Olympus microscope with
a 60x 1.42NA oil immersion objective. It has a removable lens where the laser enters
the microscope (not shown) that allowed us to switch easily between wide-field mode
21
(with the lens) and confocal mode (without). After this lens is a dichroic mirror,
which reflects almost all (>99%) of the laser light, and similarly passes almost all of
the emitted red-orange light from the sample. In confocal mode, the light beam, still
expanded, reflects off the dichroic mirror and enters the microscope objective, focusing
to the diffraction limit of 1.22)..1 /d
~
153nm after passing through index-matching oil
to increase the light collecting parameter (the numeric aperture). In wide-field mode
the light beam is no longer expanded when it enters the objective, having passed
through the removable lens, and so illuminates a much wider area on the sample.
The sample stage has two positioning drives: one coarse stage with centimeter
travel, and a piezoelectric driven 3-axis stage with
f"V
10nm positioning accuracy. Ap-
proximately 30% of the fluorescence from the sample is collected by the objective, as
in epifluorescence microscopy, and passes through the dichroic mirror and another lens
that focuses the signal light onto the plane of the aperture, 100f-lm diameter pinhole.
At this point approximately 20% of the photons emitted by the sample remain in the
output signal. After the aperture, another lens re-collimates the output signal. The
signal is then split by a 50-50 beamsplitter, and reaches the two avalanche photodiodes
(APDs).
Avalanche photodiodes use a semiconductor to detect photons. A photon entering
the APD is absorbed by the semiconductor, which creates an electron-hole pair. By
itself, the charge of a single such electron is not easily measured, but the APD applies
a voltage to the semiconductor that separates the charges. The voltage accelerates
the electron to the point that it excites other electrons in the semiconductor to the
conduction band, a phenomenon known as the avalanche effect. This process creates
enough charge to be measured, and the APD sends out a voltage pulse, indicating it
has detected a photon. APDs are very sensitive; exposure to the ambient light in a
22
room lit by ordinary lamps will effectively destroy the detectors. To limit this risk,
and the likelihood of detecting light not from the sample,we kept both detectors in an
opaque box to further reduce the risk of false detections and damage to the devices
(only light exiting the 100p,m pinhole can reach the detectors).
The signal from the two APDs went to a time-to-amplitude converter (TAC)
to measure the cross-correlation function of the sample fluorescence.
The cross-
correlation function g(2) ( T) can be approximated, for sparse data, by the time intervals
between consecutive pulses from the two APDs. The signal from one detector goes to
the TACs "start" channel, while the other, after passing through a length of delaying
wire, goes to the "stop" channel. The TAC, as its name suggests, converts the time
between a pulse in the start channel and a pulse in the stop channel, if less than a
certain maximum time , to an output voltage pulse, with an adjustable conversion factor which we set to 10V per 500ns. The signal from the TAC goes to a multichannel
analyzer, which uses a program called Gamma to plot the distribution of incoming
voltages. This distribution, after accounting for the conversion factor and the delay in
the stop signal, approximates the autocorrelation function of the fluorescence emitted
by the sample.
Procedure
Our samples consisted of CdSe nanocrystals on a quartz slide. The nanocrystals
come in a toluene solution, which we diluted in toluene three times: the first two times
at a ratio of 1:100, and the third time at a ratio of 1:10. We flame-cleaned a quartz
slide to remove surface contaminants and water, and spin-coated it with 8-12p,L of
the diluted nanocrystal solution. We then mounted the slide on a custom-made slide
holder, and placed the slide in a sealed container to dry it , by pumping the air from the
23
container and waiting for several minutes. The nanocrystals are protected by a shell
of carbon chain molecules, but this protective coating dissolves in a dilute solution,
so it is important to minimize the time between diluting the nanocrystal solution and
drying the sample. This also means that samples degrade over time, and are generally
useless after a day or two.
We had previously used glass slides instead of quartz, which we cleaned by bathing
them in a mixture of 70% sulfuric acid and 30% hydrogen peroxide, which we dubbed
a "piranha clean." This method was effective, but it was also time-consuming, so we
experimented with flame cleaning, which seemed to be just as effective. Unfortunately,
when we tried to flame-clean glass slides, they tended to warp and break, so we had
to switch to quartz slides. We also experimented with using a coating of polymethylmethacrylate (PMMA) to protect the dots from bleaching (signal degradation over
time due to laser damage to the surface of the dot), but our sample of PMMA itself
fluoresced, and may have scattered signal from the dots, creating a signal-to-noise
issue that we could not resolve. Because of these problems, we stopped using PMMA.
After the sample dried, we refreshed the index-matching oil on the objective,
cleaning off any remaining oil and adding a new drop. We then mounted the slide
holder on the microscope stage, and carefully raised the objective until the bead of oil
touched the bottom of the slide. Once the oil and the slide were in contact, we put the
microscope in wide-field mode, and, using the microscope lamp, tried to focus on a bit
of dust on the upper surface of the slide, as an approximation of the vertical position
of the nanocrystals. After finding and focusing on a piece of dust, we turned off the
lamp and the room lights, turned on (or unblocked) the Nd: YAG laser, checking to
make sure that about 5mW of power was getting through, and switched the output
light from the eyepiece to a CCD camera mounted above the eyepiece arm of the
24
mIcroscope. Since the nanocrystal solution we used was so dilute, it was very unlikely
that a dot would be in our confocal scanning range, but in wide-field mode we could
use the camera to center a dot at a position we had previously determined to be in our
confocal scanning region. The camera focal plane was very close to the focal plane
in confocal mode which allowed us to position the dots in camera mode. Without
the wide-field mode and the CCD camera, it would be very difficult to align a single
quantum dot with the confocal detection system.
Once we had found and focused on a group of dots in camera mode, we blocked
the laser light and added more optical density filters, so that the power entering the
microscope was approximately .5/-lW. With an approximately diffraction-limited spot,
this corresponded to approximately 200W/cm 2 . We then removed the wide-field lens,
and turned on the power to the APDs. Using a LabView program, we scanned the
largest area possible (25/-lm by 25/-lm) , looking for a region of high emission, which
would indicate the presence of a dot. If the area was uniformly dark, we moved the
microscope stage and repeated the scan, until we found a bright spot. We then did
a narrow scan of the bright spot, adjusting the the vertical position of the piezostage
to refine the focus further. If the bright spot appeared to be a dot (the emission
intensity switched back and forth between a high "on" state and a low "off" state,
with no intermediate level of intensity), we then turned on the TAC and dwelled on
the center of the bright spot, gathering data.
25
26
5
Results
We collected data from 13 emitters (either single dots or clusters of two or three)
illuminated by the 532nm laser, and 17 emitters illuminated by the 405nm laser. The
intensity vs time data was collected as a series of timestamps, which we converted to
intensity by re-binning: summing the number of counts in each 10ms interval.
350
300
'2
:E 250
'"
S
0
,....,
200
....
<l.l
,3<
'"
~
150
::l
0
u 100
50
0
0
50
100
150
200
250
300
Time (sec.)
Figure 9: Intensity vs time graph of a single dot (8_06_08_16). This dot exhibits
blinking, and the overall downward trend in the 'on' intensity indicates that the dot
was also bleaching.
The correlation data is a list of bin counts from the multi-channel analyzer (MCA),
with each bin corresponding to a specific TAC voltage. The TAC settings and MCA
resolution (1024 channels over a range of 0-10V) allow conversion of the signal to
time correlation data. The raw data, therefore has a time-bin resolution of ~g~:c~
=
0.488ns/ch. With typical lifetimes of 20-30ns (and visible curvature out to ±100ns), a
27
lower resolution ('"'-'5ns/ch) would improve the signal-to-noise ratio while still allowing
a valid fit. We therefore also re-binned the correlation data, condensing 10 channels
into one point. We plotted the intensity vs time and correlation vs time delay data
for each emitter using Igor, a data analysis software package, and fit the correlation
data to a curve of the form
C(T)
=
A(l- e-blt-tol)
+ c,
(12)
80
60
~
p
'-'
u
40
20
0
-200
-100
0
100
200
't (ns)
Figure 10: Cross-correlation function of a single dot (8_06_08_16) illuminated by
532nm wavelength light, with a fitted curve.
A
=
61.5
± 5.8, b =
0.0393
± .0061 , c =
The parameters for the curve are
14.4 ± 6.0, and to = -.1
± 1.7.
where b is the inverse of the time constant. The constant c can correspond to the
background count, but a high enough value (approximately half of the maximum
function value) indicates the presence of two dots, rather than one. "A" corresponds
28
to the intensity of the emitted light, and to
IS
an offset from zero, accounting for
possible delays in the electronics.
The correlation plot in Fig. 10 shows clearly that the sample was a single quantum
0, an offset of 14.4 ± 6 counts is far less than half of the 61.5 count
emitter: At
T =
amplitude.
A Poissonian source would generate a constant correlation amplitude
given by rlr 2i:ltT where
rl
and r2 are the detector count rates, i:lt is the bin size (in
seconds) and T is the total data collection time. 3 For the data in Fig. 9,
rl =
7433
Hz, r2 = 4266 Hz , i:lt = 4.89 x 1O- 9 s, and T = 300 s, resulting in a Poissonian count
of 46.5. The fact that the correlation is super-Poissonian for times greater than 100
ns is a consequence of long-time photon bunching. 1 Ten of the emitters illuminated
by the 532nm laser, and 14 from the 405nm proved to be single dots with sufficient
fluorescence output to produce a high enough signal-to-noise ratio. Of the remainder,
one data set proved to be the product of two dots, and the rest were from dots too
weak to produce a useful cross-correlation function.
29
200
150
~
p
u 100
'-'
50
0
-200
-100
100
0
200
't(ns)
Figure 11: Cross-corrleation function of what is probably two dots (8_06_08_8), illuminated by 532nm wavelength light.
The parameters for the curve are A
112.0 ± 5.8, b = 0.0615 ± 0.0095, c = 55.2 ± 11.5, and to = -3.6 ± 1.1. Note both the
higher "A" value, indicating a higher overall intensity, and the 'c' value (corresponding
to background emission), which is comparable to the 'A' value of the previous graph.
That the intensity at zero time-delay of this emitter is of comparable magnitude to
the maximum intensity of the emitter in figure 8 suggests that this emitter consists
of two dots.
30
Time constants (ns)
The correlation data in all of the single
532 nm
405 nm
dots measurements rises from the anti-
14.9±4.4
23.7±2.8
26.8±4.3
32.1±7.2
26.2±2.8
14.6±2.1
20.8±2.6
16.6±5.5
12.8±4.9
34.8±9.7
23.4±5.5
29.2±5.1
22.8±5.2
19.4±2.6
24.4±3.6
22.4±4.0
29.7±3.5
22.7±3.1
24.4±3.9
14.9±4.4
15.4±4.8
22.8±10.4
21.2±4.5
bunching minimum at
T =
0 to the super-
Poissonian level with a time constant "\2 ;:::::;
k21 . Thus, from a data curve fitting pro-
cedure in Igor , we can extract the single
dot fluorescence rate k 21 . For each excitation wavelength, the result of the data
analysis is accumulated in the histogram
plots of Fig 12. These two distributions
are centered around the same average value
(22.4ns vs 22.7ns) but the 405nm data
seem to be more broadly distributed. However, given the small number of measurements, it is difficult to draw a meaningful conclusion from the data about a re-
24.0±2.9
Fluorescence
lationship between excitation wavelength
lifetime data from single
and the time constant of a fluorescing dot
NCs
or the shape of its distribution.
Table 1:
31
4-
(a) 405 nm
-
--..
~ 3II
62
......
-r-
=
§ 1-
r-
-
U
o
10 15 20 25 30 35
Time Constant (ns)
4-
(b) 532 nm
-
--..
8 3II
62
......
=
§ 1-
U
r-
r-
r-
o
f-
I
10 15 20 25 30 35
Time Constant (ns)
Figure 12: Histogram of time constants of (a) dots illuminated by 405nm light (mean
time constant 22.4 ± 6.3ns), and (b) dots illuminated by 532nm light (mean time
constant 22.7 ± 5.3ns).
32
6
Discussion
As a means of identifying single emitters, the fluorescence, two detector correlation
(RBT) experiment is very useful. While it is possible to make a qualitative observation
of the fluorescence intensity variability, the anti-bunching signal at T = 0 is a definitive,
quantitative measure. The vast majority of fluorescence emitters that we measured
using the ND600/quartz substrate were single NC's with only one measurement being
from a two- N C source.
The simple three-state model is valid for very short time scales, on the order of a
few hundred nanoseconds after emission. At longer times, however, a spectral diffusion trap-state model is more useful to describe the distribution of on- and off-times of
a fluorescing nanocrystal. The lifetime measurements did not show a quantifiable difference with excitation energy (see figure 12). The excitation with 532nm wavelength
light is at an energy (2.33eV) near the absorption edge of the dots we were using,
and excites the dots to the lS e delocalized energy level, while 405nm wavelength light
is well above the absorption edge and excites the dot to the 1P3 level.lO The dots
excited by the 405nm laser should exhibit a broader distribution of time constants
due to the larger effects of spectral diffusion at higher energy levels. l l The distribution
of on-times has been found to follow a power law for times up to 3s, followed by an
exponential cutoff when the nanocrystal is excited with 532nm and 488nm light, but
the on time distribution drops off earlier when the nanocrystal is excited with 405nm
light (see figures 14 and 15). This narrower distribution of on-times implies a wider
distribution of high or excited energy states in nanocrystals excited with 405nm light,
which would allow the nanocrystals to more rapidly excite and de-excite when they
are "on," leading to the broader lifetime distribution our data tentatively displays.
33
Our data suggests a slightly larger standard deviation for the 405nm time constants than the 532nm time constants (6.3ns vs 5.3ns), but it would require data from
upwards of 100 more dots to draw a meaningful conclusion from that difference. At
both excitation energies there was a significant amount of variation from dot to dot in
the measured time constant. Some of the time constant variation between dots may
be due to variation in the size of the dots we used, or in the surface environment of
the slides, which could create large variations in the local electric fields experienced
by the dots. The time constant of a dot is also the time signature of the width of
its emission line. 4 Variations in dot size and slide surface environment could therefore
cause inhomogeneous broadening of this line.
In considering future directions for this research, the variation of fluorescence
decay rate with time could serve as an independent measure of spectral diffusion,
complimenting spectral measurements. 5 Currently, we have to use an entire data set
to fit a
g(2)
(T) function because only approximately 10% of the photons emitted by the
dots reach the detectors, and the TAC only registered a count if two of these photons
arrived within 500ns of each other. Although this sparseness in our data makes the
data we recorded a good approximation of the cross-correlation function, it also makes
it impossible, with our current setup, to observe possible time variation in the time
constants of individual dots. A pulsed laser excitation source for this purpose has
been proposed for funding.
34
Figure 13: "Experimental fluorescence spectra for CdSe-nanocrystals[oo.] for various
excitation energies at 77 K" 11. Note the broadening of the fluorescence peak as the
excitation energy increases. Spectral diffusion could thus affect the width as well as
the frequency of the nanocrystals' emission spectrum peaks.
35
1 ~---r----~--~----~----r---~
NC600
0
~
~
(a)
>.
~ -1
c
Q)
"0
>-
-2
.1:
:g -3
.J:l
... 488 nm, 175 W/cm 2
e0. .4
-
c
o
mon
= 1.42, 'Ton = 9 s
•
532 nm, 300 Wlcm 2
- - - mon = 1.44, 'Ton = 9 s
0> -5
.2
·6 ~_--L-_--'--<:--_-'--_-:-'::_ _- ' - - _ " " ' "
-1.0
0.0
2.0
log(on t im~ (s))
Figure 14: Log-log graph of on time probability density vs. on time for NC600 dots
excited by 488nm and 532nm wavelength light
5.
,--.
,--.
";'
'I)
-
~
0
:>.
'I)
c:
oD
"0
:>.
-1
-2
.0
-3
.0
0
I...
-4
ro
CL
c:
0
~
-5
0\
0
-6
-1.0
0.0
1.0
2.0
Figure 15: Log-log graph of on time probability density vs. on time for NC600 dots
excited by 405nm and 532nm wavelength light 5 . Note the earlier drop off for 405nm
wavelength exciting light.
36
7
Conclusion
We used a two-detector RBT setup to examine the fluorescence of CdSe nanocrystals.
Much of the optical arrangement we used had been assembled previously for another
nanocrystal experiment, but we assembled the post-microscope setup, aligning the
confocal pinhole, beamsplitter, and APDs, and building an opaque box to protect the
APDs from ambient light. We coated flame-cleaned slides with a diluted solution of
nanocrystals, and dried them, before mounting them on the microscope. We excited
the nanocrystals with 532nm and 405nm light, and measured the cross-correlation
function
g(2)
(T) of individual emitters using two avalanche photodiodes and a time-
to-amplitude converter, using Igor to transform the raw TAC data to a useable form,
and to fit the predicted form of g(2) (T) to our data.
We confirmed that CdSe nanocrystals exhibit antibunching, and are therefore single photon emitters. Of the 25 emitters we observed that produced a strong enough
signal to meaningfully analyze, one proved to be a cluster of two nanocrystals, whose
g(2) (
T) function dropped to half-maximum at T = 0, and the rest had cross-correlation
functions that clearly exhibited antibunching, dropping to a small fraction of the maximum
g(2)
(T) value at zero time delay.
The excitation lifetimes we extracted from our cross-correlation data did not seem
to vary between excitation wavelengths. Nanocrystals excited by 532nm light had a
mean time constant of 22.4ns, while those excited by 405nm light had a mean time
constant of 22.7ns. There was a suggestive difference in the distribution of these time
constants (standard deviation of 5.3ns for the 532nm light, vs 6.3 for 405nm light),
but this would have to be confirmed in a much larger study.
37
38
8
Acknowledgements
I would like to thank Professor Catherine Crouch for her advice and assistance, and
the use of her lab, Robert Mohr for his help and moral support, Orion Sauter for his
work creating the programs that recorded and processed our data, and of course my
advisor Professor Carl Grossman for his constant help and support throughout this
endeavor.
39
40
9
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