Subscriber access provided by Kaohsiung Medical University
Communication
Anisotropic Photoluminescence from Isotropic Optical Transition Dipoles in Semiconductor Nanoplatelets Xuedan Ma, Benjamin T. Diroll, Wooje Cho, Igor Fedin, Richard D. Schaller, Dmitri V. Talapin, and Gary P. Wiederrecht Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00347 • Publication Date (Web): 09 Jul 2018 Downloaded from http://pubs.acs.org on July 13, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Anisotropic Photoluminescence from Isotropic Optical Transition Dipoles in Semiconductor Nanoplatelets ∗,†
Xuedan Ma,
Benjamin T. Diroll,
Schaller,
†Center
†,¶
†
‡
Wooje Cho,
Dmitri V. Talapin,
‡
‡
Igor Fedin,
Richard D.
†
and Gary P. Wiederrecht
for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States
‡Department
of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
¶Department
of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
E-mail:
[email protected] Abstract Many important light-matter coupling and energy-transfer processes depend critically on the dimensionality and orientation of optical transition dipoles in emitters. We investigate individual quasi-two-dimensional nanoplatelets (NPLs) using higher-order laser scanning microscopy and nd that absorption dipoles in NPLs are isotropic in three dimensions at the excitation wavelength. Correlated polarization studies of the NPLs reveal that their emission polarization is strongly dependent on the aspect ratio of the lateral dimensions. Our simulations reveal that this emission anisotropy can be readily explained by the electric eld renormalization eect caused by the dielectric 1
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 19
contrast between the NPLs and the surrounding medium, and we conclude that emission dipoles in NPLs are isotropic in the plane of the NPLs. Our study presents an approach for disentangling the eects of dipole degeneracy and electric eld renormalization on emission anisotropy and can be adapted for studying the intrinsic optical transition dipoles of various nanostructures.
Keywords CdSe/CdS core/shell nanoplatelets, optical transition dipole, higher-order Bessel-Gauss beam, emission anisotropy, electric eld renormalization eect Quasi-two-dimensional nanoplatelets (NPLs) possess extremely narrow spectral features due to their near-perfect monodispersity in the quantum-con ned thickness dimension.
1,2
Their extended plate geometry leads to large exciton coherence size and giant oscillator strength,
24
making NPL-based optoelectronic devices promising for highly e cient dipole
coupling and energy transfer processes.
5,6
NPLs are also potentially interesting candidates
for single photon sources in quantum information processing due to their lifetime-limited spectral line width stration
9
3,7
and lateral size-dependent biexciton quantum yield.
4,8
A recent demon-
of strong light-matter interaction between NPLs and planar microcavities at room
temperature advocates the promising application of NPLs in integrated quantum photonic devices. To leverage these exceptional properties of NPLs for high-performance optoelectronic and quantum photonic applications, knowledge of their transition dipole moment is essential for e cient dipole-dipole and dipole-cavity mode coupling. Optical transition dipoles of materials can vary signi cantly depending on their band structures and compositions. Many organic dye molecules exhibit linear absorption and emission dipoles
10,11
following the electric dipole
approximation. In some larger quantum con ned systems, the optical matrix elements and optical transition selection rules deviate from the simple electric dipole approximation. In the speci c case of wurtzite CdSe quantum dots (QDs), the lowest-lying emissive states are
2
ACS Paragon Plus Environment
Page 3 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
doubly degenerate in the plane perpendicular to the crystallographic c axis, giving rise to a twofold degenerate transition dipole.
1214
For most of these systems, single particle polariza-
tion spectroscopy has been utilized as an e cient tool in determining the dimensionality and orientation of the transition dipoles.
13,15
Compared to organic dye molecules and spherical
QDs, direct determination of transition dipoles in NPLs using polarization spectroscopy is nontrivial. This is because aside from the in uence of the intrinsic transition dipole properties, renormalization eect caused by the dielectric contrast between the NPLs and the surrounding medium can cause dierent degrees of internal electric eld attenuation for light polarized along dierent directions,
16
leading to polarization-dependent optical transition
probabilities of the NPLs. Moreover, since the transition dipoles are strongly related to the corresponding excitonic states among which the optical transitions happen, the absorption and emission transition dipoles of the NPLs could be substantially dierent.
13
In this Letter, we address these questions by studying the absorption and emission dipoles of core/shell CdSe/CdS NPLs using single particle spectroscopy.
The dimensionality and
orientation of the absorption dipoles are studied by using higher-order Bessel-Gauss laser beams, which when combined with confocal microscopy, are highly sensitive to surface eld gradients.
17
Comparing the experimentally obtained excitation patterns by raster scanning
individual NPLs through the higher-order laser beams with those from vector eld simulations, we nd that the absorption dipoles in NPLs are isotropic in three dimensions, disregarding their lateral dimensions. Further investigation of the emission dipoles of the NPLs using correlated polarization spectroscopy reveals that emission anisotropy of the NPLs is strongly dependent on the aspect ratio of the lateral dimensions. Numerical evaluation of the in uences of dipole degeneracy and renormalization eects on the emission anisotropy reveals that dielectric contrast-induced electric eld renormalization is the main reason for the observed emission anisotropy and the NPLs possess 2D degenerate emission dipoles. These ndings can provide new insights into the design of e cient optoelectronic and hybrid photonic devices based on NPLs.
3
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 19
Figure 1: (a) Coordinate system used in this study. (b) Representative scanning PL images of the NPLs. (c) PL intensity pro les from experiment (dots) and simulation (curve). (d), (e) Simulated excitation patterns of an emitter with a 2D (d) and 3D (e) degenerate absorption dipole at dierent tilt angles
α.
The 2D and 3D degenerate dipoles are simulated as two and
three superimposed perpendicular linear dipoles. Scale bars: 1
µm.
Four monolayer thick (∼1.2 nm) CdSe core NPLs with various lateral dimensions (∼70
2 nm to
∼440
2 nm ) were coated with 2 monolayer CdS conformal shells using a previously
published method.
18
PL spectra of the core/shell NPLs have a peak at
∼620
nm with no
apparent dependence on the lateral dimensions (Supporting Information S1). For single NPL optical measurements, diluted NPL suspensions were spin coated on glass cover slides and loaded onto a home-built confocal laser scanning microscope. To study the dimensionality and orientation of the absorption dipoles, individual NPLs were raster scanned at the speed of 10 ms/pixel through higher-order Bessel-Gauss laser beams to obtain the excitation patterns. A polarization converter was used to mode convert pulsed Gaussian laser beams (1 MHz) with a wavelength of 400 nm into higher-order azimuthally polarized beams. excitation power was kept below
∼5
The mean
nW, which is far below the multiexciton regime.
Excitation patterns of individual emitters obtained using higher-order laser beams are characteristic of the dimensionality and orientation of their absorption dipoles. proach has been applied to study absorption dipoles of molecules,
4
ACS Paragon Plus Environment
19
This ap-
SiO2 nanoparticles,
20
Page 5 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
and metallic nanoparticles.
21
Fig. 1(b) and its inset show representative doughnut-shaped
excitation patterns of NPLs by scanning them through the azimuthally polarized laser beams (see Supporting Information S2 for more examples). The NPLs experienced PL blinking during the scan, leading to a few dark pixels imposed on top of the excitation patterns. Change in the NPL lateral area has negligible in uence on the excitation patterns. To determine the dimensionality and orientation of the absorption dipoles from the experimentally obtained excitation patterns, we use a vector eld simulation method
22,23
implemented in a home-
written Matlab program to calculate the expected excitation patterns of dierent absorption dipoles (see Supporting Information S3 for a detail description of the simulation method). In the simulation, we assume that the laser beam propagates along the z-axis (Fig. 1(a)). Because azimuthally polarized laser beams do not create a longitudinal component and the total eld is transverse,
17
the excitation pattern of an emitter is determined by the projec-
tion of its absorption dipole in the xy-plane. This projection is dependent on the relative angle
α
between the transition dipole plane and xy-plane as well as the relative amplitudes
of the orthogonal composition dipole components. With the increase of angle
α,
the exci-
tation pattern of a 2D degenerate dipole undergoes a continuous change from the peculiar doughnut-shape to two bright o-axis lobes (Fig. 1(d)), whereas that of a 2D anisotropic dipole persistently presents two bright o-axis lobes (Supporting Information S4). The situation for an emitter with a 3D absorption dipole is fundamentally dierent.
For a 3D
degenerate dipole, its excitation pattern remains the same doughnut-shape regardless of its orientation (Fig. 1(e)). However, excitation patterns of an anisotropic 3D absorption dipole with unequal orthogonal dipole component amplitudes could either be doughnut-shaped or two o-axis lobes depending on its relative orientation (Fig. S5). These simulation results indicate that the experimentally observed excitation patterns of the NPLs result from absorption dipoles with isotropic projections in the xy-plane. These could either be isotropic 2D in-plane dipoles (Fig. 1(d)) or 3D dipoles with isotropic xy-plane projections (Fig. 1(e) and S5).
5
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 19
Figure 2: (a), (b) AFM images of a at glass cover slide and a glass cover slide after being drying etched with SF6 for 3 minutes. (c), (d) Cross-section height curves for the glass cover slides in (a) and (b).
Since the NPLs lie mostly face-down on at glass cover slides, determination of the exact 3D nature of their absorption dipoles based on these experimental results is not conclusive. We therefore introduce certain degrees of roughness to the glass cover slides by dry etching them with SF6 (Fig. 2(b) and 2(d)). The roughness is controlled by the etch time in such a way that it causes negligible laser beam distortion but various NPL orientations. quantitatively determine the surface roughness, we estimate the values of force microscopy measurements by assuming that
tan α = ∆y/∆x.
value shows that the etched substrates have an average
10%
of the surface having a corresponding
α
value
(see Supporting Information S5 for details).
> 450
α
value of
α
To
from atomic
Calculation of the
∼ 300 ,
and more than
α
with more than
23%
with
α > 300
Although the detailed orientations of each
individual NPLs remain unknown, statistically, this would lead to some of the NPLs lying with certain tilt angles with respect to the substrates. In this way, if the absorption dipoles of the NPLs are only 2D degenerate, various excitation patterns and unequal intensity pro les along dierent directions (Fig.
1(d) and Supporting Information S4) should be observed
from the NPLs dispersed on the etched substrates. However, scanning PL images of more than 150 NPLs from ve samples with dierent lateral dimensions show the same doughnutshaped excitation pattern with similar intensity pro les along dierent directions (Fig. 1(b),
6
ACS Paragon Plus Environment
Page 7 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
S3 and S4). Moreover, a reasonable agreement between the experimental intensity pro les and simulated pro les of a 3D degenerate dipole can be obtained (Fig. 1(c)). These ndings reveal that regardless of the NPL orientations, projections of their absorption dipoles in the xy-plane are always isotropic. To ful ll this condition, absorption dipoles of the NPLs at the excitation wavelength need to be 3D isotropic. This isotropic absorption dipole is most likely due to the relatively high density of electronic states at the excitation wavelength of 400 nm.
24
Figure 3: (a), (b) Projections of a linear (a) and 2D degenerate (b) transition dipole onto the sample plane. (c), (d) PL timetraces of a NPL (ρ
= 3.6) recorded by the detector behind
the rotating linear polarizer (c) and the detector without the linear polarizer (d). (e) Ratio of the intensity curves in (c) and (d). (f ), (g) PL timetraces of a NPL (ρ
= 1.5)
recorded by
the two detectors ((f ) with the linear polarizer; (g) without the linear polarizer). (h) Ratio of the curves in (f ) and (g). Marked areas indicate long "dark" periods of the NPLs.
7
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 19
Having determined the 3D isotropic nature of the absorption dipoles of the NPLs at the excitation wavelength, we further investigate their emission transition dipoles. To rst order, the optical transition strength of an emitter is proportional to transition dipole vector, and
E
is the electric eld vector of the absorbed or emitted light.
For a linear transition dipole oriented at a tilt angle dipole and xy-plane) and an in-plane angle the light electric eld) (Fig.
| µ · E |2 , where µ is the
ϕ
α
(the angle between the transition
(the angle between the transition dipole and
3(a)), its emission intensity is proportional to its projection
along the light electric eld direction, i.e.
cos2 α cos2 ϕ.
Rotating the polarization in the
collection beam path using a linear polarizer is equivalent to changes in the angle leads to a detected polarization degree, which is de ned as
Imin = 0,
respectively.
that here
ϕ
Imax =| µ |2 · | E |2 · cos2 α
If the emitter possesses a 2D emission dipole (Fig.
emission intensity is still dependent on the tilt angle
α
and it
P = (Imax − Imin )/(Imax + Imin ),
of 100% with the maximum and minimum intensities being and
ϕ,
and the in-plane angle
3(b)), its
ϕ,
except
refers to the angle between one of the transition dipole components and the
light electric eld. Recent ensemble studies
25,26
of CdSe NPL thin lms indicated that their
emission dipoles were oriented within the plane with no measurable out-of-plane component. Therefore, for a NPL with an in-plane 2D emission dipole lying on a at glass cover slide, the corresponding value of
α
is close to
00 .
Rotating a linear polarizer in the collection
beam path leads to maximum and minimum emission intensities of and
Imin =| µ⊥ |2 · | E⊥ |2 ,
with
µk , µ⊥
and
Ek , E⊥
Imax =| µk |2 · | Ek |2
being the transition dipole and light
electric eld components along the long and short axes, respectively. By de ning a dipole degeneracy factor
η =| µk |2 / | µ⊥ |2 ,
the polarization degree is given by
P = (η· | Ek |2 − | E⊥ |2 )/(η· | Ek |2 + | E⊥ |2 ).
(1)
Therefore, photoluminescence polarization is determined by both the dipole degeneracy factor
η
and electric eld intensities along the dierent axes with
8
ACS Paragon Plus Environment
P = 0
corresponding to
Page 9 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
isotropic emission. It is worth noting that because we excite the NPLs far above their emission energy with excitation intensities below saturation, in a rst approximation, we can treat the absorption and emission processes independently. The overall experimentally observed PL polarization i.e.
P = Pex · Pem ,
P
with
is hence the product of the absorption and emission polarizations,
Pex
Pem
and
being the polarization degrees of the absorption and
emission processes. Moreover, even though we have known from the above higher-order laser studies of the NPLs that their absorption dipoles are isotropic and the excitation dipole degeneracy factor
ηex = 1,
the emission dipole degeneracy factor
could be fundamentally dierent from
ηex
ηem
remains unknown and it
due to the very dierent excitonic states involved
in the two independent processes. For quantum emitters with negligible size eects (such as small molecules) or isotropic geometries (such as spherical quantum dots), PL polarization of individual emitters has been used as a direct indication of their intrinsic transition dipole degeneracy because correspondingly in Eq. (1)
| Ek |=| E⊥ |.
However, in the case of NPLs which have anisotropic
geometries, the dierence in the dielectric constants of the NPLs and their surrounding medium can lead to a renormalization of the electric eld inside the NPLs with respect to the homogeneous external electric eld in the surrounding medium
16,27
(i.e.
| Ek |6=| E⊥ |).
This renormalization eect itself can alter the probability of optical transitions along different directions and lead to a dependence of the absorption and emission on the incident light polarization.
Thus, experimentally observed PL polarization of NPLs is a combined
result of intrinsic optical transition dipole degeneracy and dielectric contrast-caused electric eld renormalization eect. In the following, we present a general approach for disentangling these two eects and extracting intrinsic emission dipole degeneracy of a quantum emitter with an anisotropic geometry based on PL polarization spectroscopy. Due to PL blinking and PL uctuation of the NPLs commonly attributed to charge carrier trapping at surface and/or core/shell interface states,
4,28
direct measurements of the
polarization-dependent PL intensity was nontrivial. We therefore split the collected PL from
9
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 10 of 19
the NPLs into two identical single photon avalanche diodes and place a linear polarizer in front of one of the diodes.
15
This technique enables simultaneous measurements of the PL
with the two detectors, and any PL intensity uctuation/blinking that is not caused by the linear polarizer can be compensated by comparing the signals from the two detectors. Fig.
3(c) and 3(d) show representative PL timetraces of a NPL from a sample with an
average length
L
of
∼15.9
nm and width
W
of
∼4.4
nm detected by the two diodes. The
timetrace in Fig. 3(c) was periodically modulated by a linear polarizer at an angular speed of
∼ 420 /s.
Despite the drastic PL uctuation, the ratio between the two timetraces (Fig. 3(e))
only re ects the polarization modulation and it can be tted with a single Calculation of the polarization degree
P
sin2 ϕ
function.
gives a value of 23.2%. Fig. 3(f ) - (h) present PL
timetraces of a NPL from a sample with an average length of
∼16.2
nm and width of
∼11.1
nm, and a polarization degree of 5.9% is obtained. We investigate polarization degrees of more than 180 NPLs from ve samples with dierent lateral dimensions (See Supporting Information S6 for distribution), and plot the average polarization degree values from each sample as a function of the corresponding aspect ratio (ρ
= L/W ) in Fig.
4(a). The emission
polarization degree increases with the NPL lateral aspect ratio. Similar polarization behavior is observed for NPLs dispersed on the etched substrates, although the average polarization degree is slightly larger than those of the NPLs on at substrates.
Without knowing the
detailed orientations of each individual NPL on the roughened substrates, we approximate their eective" aspect ratio to be
ρe = L/(W ·cos α).
From the dierence in the polarization
degrees of the NPLs dispersed on the two dierent types of substrates, we can estimate that the tilt angle
α of the NPLs on the etched substrates could vary between 00
average value of
210 ,
and
900
with an
consistent with the values determined from the AFM measurements.
However, local electromagnetic eld variation caused by the roughened surface may also contribute to the discrepancy.
Due to the lack of knowledge of the exact orientations of
each individual NPLs, the observed discrepancy may be caused by either of the two or both eects.
10
ACS Paragon Plus Environment
Page 11 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Figure 4: (a) Aspect ratio dependent polarization degrees of the NPL emission from experiment (red dots: NPLs on at glass cover slides; black dots: NPLs on dry-etched substrates) and simulation (dashed curve: FDTD simulation; solid curve: analytical calculation). (b) - (e) Local electric eld
|E|
distributions at the excitation wavelength for a normal inci-
dent plane wave polarized along the NPL width ((b) and (d)) and length ((c) and (e)). The 2 2 dimensions of the NPLs in (b), (c) and (d), (e) are 30×7.5 nm and 30×15 nm , respectively.
In principle, according to Eq. (1) the observed emission anisotropy (P attributed to:
(a) anisotropic emission dipoles (µem,k
6= µem,⊥ )
6= 0)
might be
determined by the band
structure of the NPLs which is related to their dimension, composition and crystal structure;
2932
(b) renormalization eect of the optical electric eld inside the NPLs caused by the
dierences in the dielectric constants of the NPLs and the surrounding environment.
3335
In
the second case, mismatch in the dielectric constants leads to dierent degrees of modulation to the optically-induced electric eld inside the emitter, with the internal electric eld for
E⊥ )
light polarized along the short axis (
Ek ). 34
(
attenuated stronger than that along the long axis
Because optical transition rate is proportional to the local electric eld inside the
NPLs, this in turn results in the probability of optical transitions for light polarized along the short axis being smaller. To determine the cause of the aspect ratio dependent PL polarization, we evaluate the in uences of the dielectric contrast and dipole degeneracy by calculating the attenuated electric eld intensities inside the NPLs using two approaches.
11
ACS Paragon Plus Environment
In the rst approach, we
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 19
simulate the electric eld intensity distributions inside the NPLs using the three-dimensional nite-dierence time-domain (FDTD) method. NPLs with aspect ratios
ρ = 4
Internal electric eld distributions of two
and 2 at the excitation wavelength are plotted in (Fig.
4(b) - (e)). For both NPLs, the internal electric eld is attenuated strongly when the light is polarized along the width, with the attenuation being even stronger for the one with the larger aspect ratio (Fig. 4(b)). To calculate the polarization degree using Eq. (1), we numerically calculate the overall internal electric eld intensities in NPLs for light polarized along the NPL length (|
Ek |2 )
and width (|
E⊥ |2 )
at both the excitation and emission
wavelengths. In the second approach, we calculate the internal electric eld analytically. For a dielectric ellipsoid with a dielectric constant
ε
embedded in a medium (εm ), the internal
Ek/⊥ ) with the light polarized parallel and perpendicular to the
electric eld of the ellipsoid ( axial direction is given by
Ek/⊥ = E0 · (εm /(εm + (ε − εm ) · nk/⊥ )), 27,36
with
nk/⊥
being the
depolarization factors that are de ned by the semimajor dimensions of the ellipsoid (a, c) as
nk = (1 − e2 ) · (ln((1 + e)/(1 − e)) − 2e)/(2e3 ), n⊥ = (1 − nk )/2,
where
e =
p
1 − a2 /c2 .
(2)
Because the depolarization factors of a dielectric ellipsoid and
rectangular plate are similar,
37
we apply this method to calculate the internal electric eld of
the NPLs. Since PL anisotropy is determined by both the absorption and emission processes, in principle from the simulated electric eld intensities we can calculate the polarization degrees
Pex
and
Pem
at both the excitation and emission wavelengths provided that the
corresponding dipole degeneracy factors polarization degree
ηex
and
ηem
are known, and as a result the overall
P = Pex · Pem .
Simulation results from both approaches are compared to the experimental values. Since we learn from the excitation patterns that the absorption dipole degeneracy factor only the value of the emission dipole degeneracy factor
12
ηem
ACS Paragon Plus Environment
ηex = 1,
is adjusted for tting. The best
Page 13 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
tting result is achieved with
ηem =
1 and the corresponding simulation results are plotted
in Fig. 4(a) (see Supporting Information S8 for other values of
ηem ).
These ndings reveal
that the dielectric contrast induced renormalization eect in the NPLs is the main reason for the observed PL anisotropy.
We also conclude that the 2D emission dipoles of NPLs
are isotropic irrespective of their extended plate geometries.
It is also worth mentioning
that the origin of PL anisotropy in NPLs and QDs is fundamentally dierent despite the similar isotropic 2D emission dipoles in both systems.
PL polarization of QDs is caused
by the random orientations of the 2D emission dipoles with respect to the sample planes, whereas for NPLs, it is mainly caused by the electric eld renormalization eect due to their anisotropic geometries. In conclusion, we have shown that despite their 2D in-plane emission dipoles, NPLs possess 3D isotropic absorption dipoles at the excitation energy.
This absorption isotropy is
because of the averaging over many electronic states at the excitation energy.
24
In contrast,
the isotropic in-plane emission dipoles of the NPLs might be due to the heavy hole level dominant valence band top which possesses mixed in-plane
px
and
py
symmetry.
26
Ultrafast
thermalization of charge carriers after absorption leads to their loss of memory of the initial absorption polarization, consequently leading to decoupled absorption and emission polarizations. We also present a general approach for disentangling the eects of dipole degeneracy and renormalized electric eld on PL anisotropy, which can be applied to a variety of systems for studying their intrinsic transition dipole properties. For NPLs, the aspect ratio dependent PL polarization indicates that their lateral dimensions and the dielectric constant of the surrounding medium can be designed to achieve the most e cient dipole coupling/light extraction for speci c applications.
This, for instance, in combination with the size tun-
able LO phonon bottleneck in CdSe NPLs,
7
can be applied towards highly polarized lasing
applications.
13
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 14 of 19
Acknowledgement We thank Ralu Divan for her assistance in the dry etching process. This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy O ce of Science User Facility, and supported by the U.S. Department of Energy, O ce of Science, under Contract No.
DE-AC02-06CH11357.
We also acknowledge support from NSF DMREF
Program under awards DMR-1629601 and DMR-1629383.
Supporting Information Available The following les are available free of charge. Ensemble characterization of CdSe/CdS core/shell NPLs; experimentally obtained excitation patterns of NPLs; numerical simulation of the excitation patterns; simulated excitation patterns of absorption dipoles with dierent orthogonal amplitudes and orientations; distribution of
α;
polarization degrees of NPLs on two dierent types of substrates; in uence
of CdS shell on the electric eld distribution; emission dipole degeneracy factor dependent polarization anisotropy.
References (1) Son, J. S.; Wen, X.-D.; Joo, J.; Chae, J.; Baek, S.; Park, K.; Kim, J. H.; An, K.; Yu, J. H.; Kwon, S. G. et al. Large-Scale Soft Colloidal Template Synthesis of 1.4 nm Thick CdSe Nanosheets. Angew. Chem. Int. Ed.
2009, 48, 68616864.
(2) Ithurria, S.; Tessier, M. D.; Mahler, B.; Lobo, R. P. S. M.; Dubertret, B.; Efros, A. L. Colloidal nanoplatelets with two-dimensional electronic structure. Nat. Mater.
2011,
10, 936941.
(3) Naeem, A.; Masia, F.; Christodoulou, S.; Moreels, I.; Borri, P.; Langbein, W. Giant ex-
14
ACS Paragon Plus Environment
Page 15 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
citon oscillator strength and radiatively limited dephasing in two-dimensional platelets. Phys. Rev. B
2015, 91, 121302(R).
(4) Ma, X.; Diroll, B. T.; Fedin, I.; Cho, W.; Schaller, R. D.; Talapin, D. V.; Gray, S. K.; Wiederrecht, G. P.; Gosztola, D. J. Size-Dependent Biexciton Quantum Yields and Carrier Dynamics of Quasi-Two-Dimensional Core/Shell Nanoplatelets. ACS Nano
2017,
11, 91199127.
(5) Rowland, C. E.; Fedin, I.; Zhang, H.; Gray, S. K.; Govorov, A. O.; Talapin, D. V.; Schaller, R. D. Picosecond energy transfer and multiexciton transfer outpaces Auger recombination in binary CdSe nanoplatelet solids. Nat. Mater.
2015, 14, 484489.
(6) Li, H.; Zhitomirsky, D.; Grossman, J. C. Tunable and Energetically Robust PbS Nanoplatelets for Optoelectronic Applications. Chem. Mater
2016, 28, 18881896.
(7) Achtstein, A. W.; Scott, R.; Kickhofel, S.; Jagsch, S. T.; Christodoulou, S.; Bertrand, G. H. V.; Prudnikau, A. V.; Antanovich, A.; Artemyev, M.; Moreels, I. et al. p-State Luminescence in CdSe Nanoplatelets: Role of Lateral Con nement and a Longitudinal Optical Phonon Bottleneck. Phys. Rev. Lett.
2016, 116, 116802.
(8) Tessier, M. D.; Spinicelli, P.; Dupont, D.; Patriarche, G.; Ithurria, S.; Dubertret, B. E cient Exciton Concentrators Built from Colloidal Core/Crown CdSe/CdS Semiconductor Nanoplatelets. Nano Lett.
2014, 14, 207213.
(9) Flatten, L. C.; Christodoulou, S.; Patel, R. K.; Buccheri, A.; Coles, D. M.; Reid, B. P. L.; Taylor, R. A.; Moreels, I.; Smith, J. M. Strong Exciton-Photon Coupling with Colloidal Nanoplatelets in an Open Microcavity. Nano Lett.
2016, 16, 71377141.
(10) Ha, T.; Enderle, T.; Chemla, D. S.; Selvin, P. R.; Weiss, S. Single Molecule Dynamics Studied by Polarization Modulation. Phys. Rev. Lett.
15
ACS Paragon Plus Environment
1996, 77, 39793982.
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 16 of 19
(11) Sick, B.; Hecht, B.; Novotny, L. Orientational Imaging of Single Molecules by Annular Illumination. Phys. Rev. Lett.
2000, 85, 44824485.
(12) Efros, A. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.; Bawendi, M. Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states. Phys. Rev. B
1996, 54, 48434856.
(13) Empedocles, S. A.; Neuhauser, R.; Bawendi, M. G. Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy. Nature
1999, 399, 126130. (14) Brokmann, X.; Coolen, L.; Dahan, M.; Hermie, J. P. Measurement of the Radiative and Nonradiative Decay Rates of Single CdSe Nanocrystals through a Controlled Modi cation of their Spontaneous Emission. Phys. Rev. Lett.
2004, 93, 107403.
(15) Koberling, F.; Kolb, U.; Philipp, G.; Potapova, I.; Basché, T.; Mews, A. Fluorescence Anisotropy and Crystal Structure of Individual Semiconductor Nanocrystals. J. Phys. Chem. B
2003, 107, 74637471.
(16) Rodina, A. V.; Efros, A. L. Eect of dielectric con nement on optical properties of colloidal nanostructures. J. Exp. Theor. Phys.
2016, 122, 554566.
(17) Youngworth, K. S.; Brown, T. G. Focusing of high numerical aperture cylindrical-vector beams. Opt. Exp.
2000, 7, 77.
(18) Ithurria, S.; Talapin, D. V. Colloidal Atomic Layer Deposition (c-ALD) using SelfLimiting Reactions at Nanocrystal Surface Coupled to Phase Transfer between Polar and Nonpolar Media. J. Am. Chem. Soc.
2012, 134, 1858518590.
(19) Novotny, L.; Beversluis, M. R.; Youngworth, K. S.; Brown, T. G. Longitudinal Field Modes Probed by Single Molecules. Phys. Rev. Lett.
16
2001, 86, 5251.
ACS Paragon Plus Environment
Page 17 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
(20) Chizhik, A. M.; Chizhik, A. I.; Gutbrod, R.; Meixner, A. J.; Schmidt, T.; Sommerfeld, J.; Huisken, F. Imaging and Spectroscopy of Defect Luminescence and ElectronPhonon Coupling in Single SiO2 Nanoparticles. Nano Lett.
2009, 9, 32393244.
(21) Failla, A. V.; Qian, H.; Qian, H.; Hartschuh, A.; Meixner, A. J. Orientational Imaging of Subwavelength Au Particles with Higher Order Laser Modes. Nano Lett.
2006,
6,
13741378.
(22) Richards, B.; Wolf, E. Electromagnetic diraction in optical systems II. Structure of the image eld in an aplanatic system. Proc. Roy. Soc. A
1959, 253, 358379.
(23) Lieb, M. A.; Meixner, A. J. A high numerical aperture parabolic mirror as imaging device for confocal microscopy. Opt. Express
2001, 8, 458474.
(24) Richter, M. Nanoplatelets as material system between strong con nement and weak con nemen. Phys. Rev. Mater.
2017, 1, 016001.
(25) Gao, Y.; Weidman, M. C.; Tisdale, W. A. CdSe Nanoplatelet Films with Controlled Orientation of their Transition Dipole Moment. Nano Lett.
(26) Scott,
R.;
Heckmann,
J.;
Prudnikau,
A.
V.;
2017, 17, 38373843.
Antanovich,
A.;
Mikhailov,
A.;
Owschimikow, N.; Artemyev, M.; Climente, J. I.; Woggon, U.; Grosse, N. B. et al. Directed emission of CdSe nanoplatelets originating from strongly anisotropic 2D electronic structure. Nat. Nanotechnol.
2017,
(27) Cunningham, P. D.; Boercker, J. E.; Placencia, D.; Tischler, J. G. Anisotropic Absorption in PbSe Nanorods. ACS Nano
2014, 8, 581590.
(28) Tessier, M. D.; Javaux, C.; Maksimovic, I.; Loriette, V.; Dubertret, B. Spectroscopy of Single CdSe Nanoplatelets. ACS Nano
2012, 6, 67516758.
(29) Bhattacharyya, J.; Ghosh, S.; Gokhale, M. R.; Arora, B. M. Polarized photoluminescence and absorption in A-plane InN lms. Appl. Phys. Lett.
17
ACS Paragon Plus Environment
2006, 89, 151910.
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 18 of 19
(30) Spirkoska, D.; Al.L.Efros,; Lambrecht, W. R. L.; Cheiwchanchamnangij, T.; i Morral, A. F.; Abstreiter, G. Valence band structure of polytypic zinc-blende/wurtzite GaAs nanowires probed by polarization-dependent photoluminescence. Phys. Rev. B
2012, 85, 045309. (31) Shirayama, M.; Kadowaki, H.; Miyadera, T.; Sugita, T.; Tamakoshi, M.; Kato, M.; Fujiseki, T.; Murata, D.; Hara, S.; Murakami, T. N. et al. Optical Transitions in Hybrid Perovskite Solar Cells: Ellipsometry, Density Functional Theory, and Quantum E ciency Analyses for CH3NH3PbI3. Phys. Rev. Appl
2016, 5, 014012.
(32) Andersen, M. L.; Stobbe, S.; Sørensen, A. S.; Lodahl, P. Strongly modi ed plasmonâmatter interaction with mesoscopic quantum emitters. Nat. Phys.
2011,
7,
215218.
(33) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Highly Polarized Photoluminescence and Photodetection from Single Indium Phosphide Nanowires. Science
2001, 293, 14551457. (34) Ruda, H. E.; Shik, A. Polarization-sensitive optical phenomena in semiconducting and metallic nanowires. Phys. Rev. B
2005, 72, 115308.
(35) Ruda, H. E.; Shik, A. Polarization-sensitive optical phenomena in thick semiconducting nanowires. J. Appl. Phys.
2006, 100, 024314.
(36) Kovalev, D.; Chorin, M. B.; Diener, J.; Koch, F.; Efros, A. L.; Rosen, M.; Gippius, N. A.; Tikhodeev, S. G. Porous Si anisotropy from photoluminescence polarization. Appl. Phys. Lett.
1995, 67, 1585.
(37) Mejdoubi, A.; Brosseau, C. Finite-Element Simulation of the Depolarization Factor of Arbitrarily Shaped Inclusions. Phys. Rev. E
2006, 74, 031405.
TOC 18
ACS Paragon Plus Environment
Page 19 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
19
ACS Paragon Plus Environment
