Phonon Confinement and Related Effects in Three-Dimensional Assemblies of Cubic Cadmium Selenide Quantum Dots Synthesized by Conventional Chemical and Sonochemical Routes

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Article

Phonon Confinement and Related Effects in 3D Assembliesof Cubic Cadmium Selenide Quantum Dots Synthesized

by Conventional Chemical and Sonochemical RoutesBiljana Pejova

J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp405823f • Publication Date (Web): 23 Aug 2013

Downloaded from http://pubs.acs.org on September 7, 2013

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Phonon Confinement and Related Effects in 3D Assemblies of Cubic Cadmium

Selenide Quantum Dots Synthesized by Conventional Chemical and Sonochemical

Routes

Biljana Pejova*

Institute of Chemistry, Faculty of Natural Sciences and Mathematics,

Sts. Cyril and Methodius University, POB 162, 1001 Skopje, Macedonia,

e-mail: [email protected]

*corresponding author

Tel: +389-2-3117-055

Fax: +389-2-3226-865

Suggested running head: Phonon confinement in cubic CdSe QD solids

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Abstract

The effects of phonon confinement and exciton-phonon coupling (EPC) in 3D assemblies of CdSe quantum dots with zincblende structure, synthesized by colloidal chemical and sono-chemical routes as well as in post-deposition thermally treated samples were studied by resonant Raman scattering (RRS) technique. Combining RRS results with those from structural analysis based on X-Ray diffraction and optical spectroscopy, insights into the factors determining the intricate trends in the positions of bands due to first- and higher-order vibrational transitions upon crystal size reduction were gained. The band shifts with respect to the bulk material were found to result from subtle balance between phonon confinement effects and lattice contraction due to internal strain. Accurate assignments of the surface optical (SO) phonon modes were made on the basis of dielectric continuum model of Ruppin and Englman. The magnitude of EPC (measured, e.g. through the Huang-Rhys parameter) and its size-dependence in the synthesized 3D QD as-semblies was studied as well. It was found that the EPC in the studied low-dimensional material appears to be much weaker than in the case of corresponding bulk specimen, but a decreasing trend was observed upon post-deposition thermal annealing treatment, which is accompanied by average crystal size increase. In strongly confined nanocrystal assemblies, it is larger than in those with weaker confinement effects. The relative importance of the two EPC mechanisms: the long-range (Fröhlich interaction) vs. the short range one (due to the optical deformation potential – ODP) was discussed and related to the appearance of bands due to transverse optical (TO) pho-non modes in the studied material. Combination modes involving acoustic phonons and the 1LO mode were observed for the first time in 3D QD assembly deposited in thin film form.

Key words: cadmium selenide, zincblende, phonon confinement, exciton-phonon coupling, reso-nant Raman spectra, Huang-Rhys parameter, semiconductors, quantum dot assemblies, thin films.

1. Introduction

In the last decade, a notable amount of the research focus within virtually all physical sci-

ences has been put on a thorough understanding of the evolution of materials’ properties upon

entrance of the nano-size region.1-3 Numerous studies have been devoted to size-quantization of

charge carrier states in semiconductor nanocrystals, as typical systems in which the charge carrier

motion can be confined in up to three spatial dimensions.2,3 Transformation of the corresponding

density of states from continuum (for bulk specimen) to discrete ones (for nanosized samples)

upon confinement of the charge-carriers’ motion results in one of the most quoted effects, the

blue-shift of optical absorption onset (i.e. the corresponding band gap energy) of the system in

question.4 This, on the other hand, has opened the fascinating possibility for band gap tuning, and

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a realistic possibility for experimental design of materials’ optoelectronic properties. Size-

quantization effects in semiconductors also affect the oscillator strength of the corresponding op-

tical transitions.5 A direct consequence of this is the possibility for large optical nonlinearities in

nanocrystalline materials.4,5 However, actual realization of such large nonlinearities depends on

the spectral distribution of the oscillator strength. The wider the spectral region over which the

oscillator strength is distributed, the smaller the superiority of nanocrystals in comparison to oth-

er low-dimensional systems (such as, e.g. quantum wells). This distribution, on the other hand,

depends on the magnitude of exciton-phonon coupling (EPC), which is also responsible for the

mechanism of relaxation of the excited charge carriers. In general, the vibrational-electronic cou-

pling in semiconductor nanoctructures is a key factor determining their optoelectronic and

transport processes.6-12 The effects of size-quantization on the vibrational motions within semi-

conductor nanocrystals with linear dimensions comparable to the Bohr excitonic radius of the

corresponding material (i.e. quantum dots – QDs) have also been studied in the last period, albeit

to a much smaller extent than the corresponding effects on electronic properties.6-10,13-19 Howev-

er, consensus does not seem to have been reached, in the case of numerous issues. Such issues

range from pretty “basic” questions, such as the very direction of the shift of a particular nano-

crystal vibrational mode with the change in the QD size, up to the question of evolution of the

exciton-phonon coupling strength with QD size.6-18 In the latest period, however, it seems that the

interest in issues related to phonon spectra of ultrasmall semiconductor nanocrystals has been re-

newed, due to the apparent “phonon bottleneck” problem6,7,13,15 of the mechanism of charge car-

rier relaxation in these low-dimensional systems. Most of the studies within this research area

have been devoted either to colloidal nanocrystals dispersed in liquids,20-24 and references therein nano-

crystals embedded in glass or other (usually isolating) matrices,25-43 and references therein nanocrystal-

line powders etc.44-48 and references therein Much less attention has been paid to 3D assemblies of QDs

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deposited in the form of thin films.49-59 As in numerous other cases, cadmium selenide (CdSe) has

emerged as a quite prototypical system to study all the mentioned effects. The reason for this is

two-fold. On one hand, the intrinsic relevance of this material to various fields of contemporary

high technology (QD-based solar cells and other photovoltaic devices, nanotransistors, charge-

coupling devices etc.) has been well recognized. On the other hand, the physico-chemical proper-

ties of this particular material have been studied a lot, especially for its bulk-phase counterparts.60

We have recently developed a highly-controllable colloidal chemical deposition method for syn-

thesis of the less-exploited phase of CdSe (the cubic one, with zincblende structure), with high

crystallographic purity, practically completely avoiding the presence of wurtzite and ox-

ide/hydroxide phases.61-63 The method enables deposition of 3D assemblies of close-packed cubic

CdSe QDs in thin film form, in high size-quantization regime. Post-deposition thermal annealing

treatments could be used to tune the opto-electronic properties of the synthesized material, simi-

larly as in other cases studied by our group.64-70 Two other literature studies relevant to synthesis

and opto-electronic properties of CdSe with the less-common structural type have recently been

published by Hens et al71 and Chergui et al.72 In the present study, we focus on the phonon-

confinement and related effects in 3D assemblies of close-packed cubic CdSe QDs in thin film

form, with tunable variable size. For the purpose of the present study, we have also developed a

sonochemical route to the title system, allowing further reduction of the average crystal size of

the synthesized material. Combining the structural analysis by X-ray diffraction methods with

optical and Raman scattering spectroscopic techniques, we aim to get a deep physical insight into

numerous issues related to phonon-confinement effects, as well as the exciton-phonon coupling

(EPC) in the synthesized low-dimensional semiconductors. These include: the factors determin-

ing the intricate trends in the positions of bands due to first- and higher-order vibrational transi-

tions upon size-reduction; the issues related to the very appearance of bands due to certain modes

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in the Raman spectra of the studied 3D QD assemblies, as compared to the corresponding bulk

counterparts (including both the transitions that exist in bulk samples, too, but also the ones

emerging in low-dimensional solids, e.g. surface i.e. zone-edge modes); the magnitude of exci-

ton-phonon coupling and its size dependence in the investigated QD solids. We also discuss the

relative importance of the two EPC mechanisms: the long range one (Fröhlich interaction) and

the short range one (due to the optical deformation potential – ODP) in the presently studied ma-

terial, on the basis of appearance and position of a weak TO-type feature in the Raman spec-

tra.12,22,32 The overall experimentally observed trends in the EPC strength (measured, e.g. through

the Huang-Rhys parameter)73 in the present study, were related to our recent conclusions derived

on the basis of the temperature dependencies of sub-band gap absorption tails,67 enlightening the

relevance of coupling to higher-energy phonons in the case of processes of light absorption and

scattering from QD solids.

2. Experimental

2. 1. Colloidal Chemical and Sonochemical Synthesis of 3D Assemblies of CdSe QDs

The studied thin films composed by close packed cadmium selenide QDs with sphalerite

(zincblende) structure were synthesized by the colloidal chemical route developed by our

group.61,62 This conventional colloidal chemical method is based on controlled precipitation reac-

tion taking place in aqueous medium with controlled pH value. Sodium selenosulfate was used as

precursor of selenide anions, while the concentration of cadmium(II) ions was controlled by am-

monia, which was introduced in the reaction system as a component of ammonia buffer solution.

Ammonia had therefore a double role: a ligand for Cd2+ ions and a component of the buffer sys-

tem, controlling the pH value of the reactor. Though the overall deposition is a resultant of a

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number of sequential processes, controlled by several equilibria,61,62 it can be formally represent-

ed by the following overall equation:

[Cd(NH3)4]2+ + SeSO3

2- + 2OH- = CdSe(s) + 4NH3 + SO42- + H2O (1)

A more in-depth analysis of the reaction kinetics and mechanism has been presented in our previ-

ous publications,61,62 devoted to the developed conventional colloidal chemical route to

zincblende CdSe QDs deposited in thin film form.

For the purpose of the present study, however, besides applying the conventional chemi-

cal method, we have also developed a sonochemical route to nanostructured CdSe films. Sono-

chemical synthesis was carried out irradiating the reaction system with high-intensity ultrasonic

probe. This was done by direct immersion of ultrasonic horn in the solution used for thin film

growth. The ultrasound intensity was 100 W·cm-2 and the corresponding frequency was 20 kHz.

2. 2. XRD characterization

To identify the synthesized material (in thin film form and as bulk precipitate), as well as

to gain certain insights into the average crystal size and some of its basic structural properties, the

X-ray powder diffraction method was used. X-ray diffraction patterns were recorded on a Philips

PW 1710 diffractometer, using monochromatic Cu-Kα radiation. Average nanocrystal size in the

synthesized CdSe 3D QD assemblies was calculated on the basis of the intrinsic broadening of

the diffraction peaks, within the Debye-Scherrer approach.74 The following equation was used:

θββ

λ

cos

9.0

3

422sm

d−

= (2)

In (2), βm is the raw value of the full width at half maximum intensity (FWHMI) of the peak

(which includes both instrumental and intrinsic broadening factors), while βs is a standard

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FWHMI value referring to a correspondent peak in the case of macrocrystalline and strain-free

sample. XRD peak positions and FWHMI values were obtained by least-squares interpolation of

the experimental XRD patterns with linear combinations of Gaussian and Cauchy (Lorentzian)

functions. For the purpose of the present study, refinement of the lattice constant values was car-

ried out with linear regression analysis, on the basis of the following expression:

)(sin 2222 lkhAhkl ++=θ (3)

where 22 4/ aA λ= , a being the lattice constant value.75 Average isotropic lattice strain was cal-

culated as:

bulka

a∆=ε (4)

where abulk is the bulk specimen lattice constant. Dislocation density (δ) was computed as δ =

1/D2, where D is the average crystal diameter.

2. 3. Optical Spectroscopy and Raman Scattering Measurements

In the present study, we have employed UV-VIS spectroscopy to probe the band structure

of the synthesized 3D QD assemblies deposited in thin film form. Electronic spectra of the films

were recorded by a Cary 50 UV-visible spectrophotometer, in the spectral range from 190 to

1100 nm. Spectral data were further processed and subjected to certain numerical analyses. Band

gap energies were calculated on the basis of semiconductor absorption functions constructed as-

suming bands with spherical symmetry, employing parabolic approximation for the dispersion

relation in the expressions arising from Fermi’s golden rule for interband electronic transi-

tions.76,77 A combined interpolation-extrapolation procedure was implemented for that purpose,

as explained in our previous works.61-70

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Raman spectra of the films were recorded in situ, using Horiba Jobin-Yvon LabRam 300

micro-Raman spectrometer, equipped with two lasers: frequency-doubled Nd:YAG laser operat-

ing at 532 nm with the excitation power of 6.7 mW on the sample and the He-Ne laser operating

at 632.8 nm (with excitation power of approximately 6 mW power on the sample). Olympus

MPlan microscope with objective magnification of 100 × and 50 × was used to focus the laser

beam. Dispersion of the backscattered light was achieved using a grating of 1800 lines/mm, and it

was detected on a multi-channel air-cooled CCD detector. Sufficient number of scans was accu-

mulated for each measurement, with sufficiently long exposure times, to achieve good signal-to-

noise ratio. Raman scattering from each of the investigated samples was measured from several

points from films’ surfaces. In order to minimize the luminescence in the studied QD solids, laser

excitation power was appropriately controlled (reduced). In the presently studied case, however,

considering the particular experimental conditions, the emission quantum yields are additionally

reduced due to the non-strict resonance conditions and the possibility for quenching in the close

packed QD solids. Due to all this, to minimize the emission influence on the resonance Raman

spectra, often only modest mathematical corrections were required.

3. Results and Discussion

XRD patterns of as-deposited CdSe QDs close packed in thin film form and as bulk pre-

cipitates, as well as of the post-deposition thermally annealed samples have been presented and

discussed in details in our previous papers.61-63,67 As the focus of the present study is on the pho-

non-confinement and related effects, in Table I the most relevant structural parameters for as-

deposited samples by conventional chemical and sonochemical routes, as well as of the annealed

ones are summarized. These include: the average crystal size, lattice constant values, average iso-

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tropic strain and dislocation density. Fig. 1 shows the XRD pattern of the newly synthesized

CdSe 3D QD assemblies by sonochemical route, together with the standard. As can be seen from

Fig. 1 and Table I, sonification of the reactor during the synthesis leads to QD assemblies with

somewhat smaller average crystal size as compared to those synthesized by the conventional col-

loidal chemical route. This trend may be attributed to heterogeneous sonochemical effects.78

As the excitation wavelength used in the Raman scattering study is nearly resonant with

the lowest electronic transition of the studied semiconductor nanocrystals (1Se – 1Sh), we have

actually observed resonant Raman scattering from our samples. The recorded resonant Raman

spectra of the as-deposited 3D QD assemblies in thin film form by the conventional chemical ap-

proach as well as by the sonochemical route are shown in Fig. 2. A series of most notable 4 peaks

is clearly observable in both cases, which are actually replicas of the longitudinal optical mode

(LO) in CdSe (i.e. the fundamental transition and its overtones).79,80 The near resonance condi-

tions enabled us to make an in-depth analysis of both first- and higher-order scattering regions,

due to the enhancement of intensity of the corresponding bands. One of the straightforwardly no-

ticeable features of our resonance Raman spectra are the notable low-frequency asymmetry of

both 1LO band and its replicas, and somewhat less pronounced high-frequency asymmetry. The

low-frequency asymmetry of the 1LO band is a feature that has been discussed in the litera-

ture,38,43,54,52,55 and the most plausible physical explanation for its appearance has been offered

within the so-called phonon-confinement model, initially developed by Richter et al,81 and fur-

ther generalized by Campbell et al.82 Despite its physical exactness, the phonon confinement

model has often been replaced by a more pictorial concept of surface modes, or zone-edge

modes.4,43,76,77 Even in a bulk crystal, in the case of which the phonon is represented by a plane

wave propagating through the crystal described by a spatio-temporal factor ( )[ ]trki ω−rr

exp , with

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the wave vector given by ( ) ( )ωεω ck /= (where ε is the dielectric constant of the crystal), in the

frequency range between the LO and TO frequencies ( ) 0<ωε and thus the wave vector becomes

imaginary. This physically means that the wave decays exponentially in the medium, and in this

particular frequency range the wave cannot propagate through the bulk crystal. Instead, only the

surface modes with spatially decaying fields exist. Such surface modes, of course, can be much

more easily observed in nanocrystals, due to the enhanced surface-to-volume ratio in these sys-

tems. Therefore, instead of using the perhaps more exact phonon confinement model, we will rely

on the more pictorial concept of surface modes existing in the studied QDs, interacting with the

electronic subsystem and other phonons. We will therefore base our analysis of the resonant Ra-

man spectra mostly on non-linear fitting of the studied spectral regions (a procedure which is

sometimes imprecisely referred to as “spectral deconvolution”). In other words, the model in-

volving zone edge phonons actually implies appearance of in a sense new modes in the case of

low-dimensional structures, as compared to the macrocrystalline (bulk) analogues. As it will be

seen from the discussion later in the manuscript, the crystal size decrease and entrance into the

size-quantization region affects not only the low-frequency wings of the LO bands, but also the

higher-frequency ones. Appearance of high-frequency asymmetry,22 however, could not be ex-

plained at all within the original variant of the phonon confinement model.

3.1. The longitudinal optical (LO) mode

The most intensive band in the spectral region corresponding to first-order Raman scatter-

ing (the first-order Raman spectrum) corresponds to the longitudinal optical mode (LO) of sphal-

erite-type CdSe.80,83 As already implied, the overall spectral appearance in the region where this

band appears is actually much more complex and, as we discuss further in the manuscript, several

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other bands, due to other modes, also appear there. To derive quantitative conclusions about the

spectral appearances in this region, which would further allow us to get a much deeper physical

insight into the processes of light scattering from close-packed QDs constituting the thin films,

we have carried out a careful curve-fitting analysis of the overall spectra in all regions relevant to

the present study, as explained before. All the quantitative values referring to band positions or

their half-widths and intensities have thus been derived by the curve-fitting procedure. Regardless

on the initial choice of the type of function representing a particular component band, which was

usually a linear combination of Gaussian and Lorentzian functions (a good approximation to per-

haps more realistic Voigt function – which is a convolution between Gaussian and Lorentzian

ones), the final form of all the bands appeared to be Lorentzian (i.e. the Lorentzian contribution

tend to be 1 during the fitting procedure). Even when an alternative solution to the fitting problem

was possible (with component bands which are not necessarily “purely” Lorentzian), the parame-

ters of the component bands were essentially identical to those obtained for purely Lorentzian

profiles.

The position of the 1LO band in the case of as-deposited nanostructured CdSe films by

the colloidal chemical deposition method (CCD) at 206.2 cm-1 (Fig. 3) is red-shifted by 3.8 cm-1

with respect to the bulk value of 210 cm-1 (denoted by a solid line with an arrow in Fig. 3). A fur-

ther red shift of this mode by about 2 cm-1 (204.9 cm-1) is observed in the case of sonochemically

deposited (SCD) samples in comparison to the ones synthesized by CCD method (Fig. 3). This

additional red shift of the 1LO band in the SCD films is accompanied by half-width increase

(from 9.6 to 14.1 cm-1 in the case of CCD and SCD ones respectively). As the observed Lorentzi-

an line shapes of the 1LO bands are indicative of homogeneous broadening, such trend in the

half-widths may be attributed to more frequent collisions between phonons in smaller QDs fol-

lowed by relaxation at QD-QD interfaces. In the case of one-phonon peaks, the widths of corre-

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sponding spectral bands are a measure of the coupling between the k = 0 phonon and the other

sets of phonons determining its decay process.84 Upon inherent disorder increase as a conse-

quence of the QD size decrease, there is an extra contribution to the linewidth due to the break-

down of the k = 0 rule, appearing as a superposition to the “intrinsic” band shape.81,82 Therefore,

the present data are consistent with the model implying more frequent phonon-phonon collisions

upon QD size decrease. However, in order to determine a particular functional form of the de-

pendence of the half-widths on the crystal size, much more samples with varying sizes in a wider

interval would be required. Post-deposition annealing treatment of the as-deposited films by the

sonochemical method leads to a small blue shift of the frequency of 1LO mode. A typical trend in

the case of post-deposition thermally annealed sonochemically deposited sample is shown in Fig.

4. The blue shift of the 1LO mode with respect to the as-deposited film was detected already up-

on annealing of the samples at 200 ºC. Further annealing at 300 ºC does not result in additional

changes of the position of this band. Post-deposition annealing of the films deposited by conven-

tional colloidal chemical approach, on the other hand, does not result in any changes of the posi-

tion of the 1LO band. We rationalize the observed trends as follows. The “absolute” value of

phonon frequency in a QD is determined both by the phonon dispersion (including phonon con-

finement effects in a nanostructure) and by the lattice contraction effects.30,31,39,40,84 The previous

statement may be expressed in a quantitative manner by the following equation:

( ) ( ) ( )RRR CDL ωωωω ∆+∆+= (5)

where ωL is the LO phonon frequency corresponding to a bulk CdSe specimen, ∆ωD(R) is the

frequency shift due to phonon dispersion, while ∆ωC(R) is the frequency shift induced by lattice

contraction. Following Cardona et al., the component ∆ωD(R) is given by:84

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( )2

L

2L

L

2

2L

2LD 2

−≈−

−=∆

RRR

npnp µ

ωβ

ωµ

βωω (6)

In (6), the phenomenological parameter βL characterizes the phonon dispersion, while µnp is the

np-th root of the equation:

µµ =tan (7)

where:

RL

22L

βωω

µ−

= (8)

The lattice contraction contribution to ∆ω(R) is, on the other hand, given by:30,31,39,40,84

( ) ( )a

aR

a

aR

∆−≈

−

∆+=∆

−

LLC 3131 γωωωγ

(9)

where γ is the Grüneisen parameter, while ∆a/a is the relative strain (∆a defined as ananocrystal –

abulk). In the case of materials with negative phonon dispersion (as in our presently studied case),

the phonon dispersion – induced frequency shift is negative (i.e. a red shift), while a compressive

strain (∆a < 0) induces frequency blue shift due to negative sign in (9). Physically, the compres-

sive strain actually arises from crystal surface reconstruction effects induced by surface tension.

The overall effect in the sense of a LO phonon shift with crystal size is thus a compromise be-

tween these two opposite trends. In order to attempt to make a quantitative prediction of the mag-

nitude of the two effects, we have estimated the ∆ωC and ∆ωD contributions to the actual ω(R)

value, on the basis of data derived by our structural investigations of the samples. Taking the lit-

erature value of the Grüneisen parameter of CdSe as 1.1,30,31,39,40,84 and a value of 210 cm-1 for ωL

in the case of bulk material, and also having in mind that the lower bound value for the relative

strain in the case of as-deposited films by the conventional chemical approach is – 0.00311, the

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∆ωC appears to be about 2.2 cm-1, which is rather significant, considering the fact that the shifts

of the band positions are of the order of several cm-1. Such finding implies that ∆ωD contribution

to the overall frequency shift should be about – 6.0 cm-1 (so that the overall red shift equals 3.8

cm-1). The observed blue shift of the LO frequency upon thermal annealing of the SCD films, in

the context of previous discussion, may thus be mainly attributed to the fact that phonon con-

finement effects diminish upon annealing. Moreover, the size-dependence of ∆ωD appears to be

more pronounced than the size-dependence of ∆ωC. Such change of the phonon confinement is in

line with diminishing of electronic size-quantization effects in the annealed films, observed as

red-shifts of the absorption onsets in the UV-VIS absorption spectra (Fig. 5). This leads to dimin-

ishing of the red-shift contribution to ω(R). While the ∆ωC contribution is also expected to de-

crease upon thermal annealing (though maybe not to completely disappear, due to the yet small

crystal size), its contribution remains positive (i.e. blue shift), smaller than the corresponding

contribution in as-deposited films, and also smaller than ∆ωD. In other words, ∆ωC changes less

upon annealing than the ∆ωD does. The opposite contributions of ∆ωD and ∆ωC to overall ∆ω,

illustrating typical trends with size – reducing as compared to a bulk specimen, as well as anneal-

ing-induced changes, even up to cancellation of both effects at certain crystal size are schemati-

cally shown in Fig. 6. In the case of CCD films, on the other hand, the compressive strain is

smaller even in the as-deposited samples (as compared to the SCD ones), while it diminishes sig-

nificantly upon thermal annealing. This allows the phonon dispersion effects to effectively cancel

the lattice contraction ones upon post-deposition annealing of the samples, resulting in a net null

shift.

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3.2. The transverse optical (TO) and surface optical (SO) modes

To determine the positions of bands due to other modes in the studied nanostructured

films, we have carried out a curve-fitting procedure of the relevant regions in the Raman spectra.

We hereby refer to the region around the 1LO band. This spectral region could be best fitted with

5 functions, each of which was found to be Lorentzian. Experimental Raman spectroscopic data

showing the region around 1LO mode in the case of sonochemically deposited CdSe films, to-

gether with the reconstructed curve and the component peaks obtained by the least-squares curve

fitting procedure are shown in Fig. 7. To aid the assignment of component bands, we have used

the relations between the frequencies of the longitudinal optical (LO) and transverse optical (TO)

modes, as well as between the transverse optical and the surface optical (SO) modes. Using the

Lyddane-Sachs-Teller equation,4,76,77 the following relation is obtained between the frequencies

of the TO and LO modes:

LO0

TO ωεε

ω ∞= (10)

On the other hand, the relation between the SO phonon energies and the energies of the TO pho-

nons in the case of spherical nanocrystals, on the basis of the dielectric continuum model of Rup-

pin and Englman, is given by:85

( )( ) ll

ll

/1

/1

M

M02TO

2SO ++

++=

∞ εεεε

ωω (11)

where εM = 1 is the surrounding medium dielectric constant, ε∞ and ε0 are high frequency and

static dielectric constant of the corresponding bulk material, and l = 1, 2, 3,… is the angular mo-

mentum quantum number (i.e. the order of the spherical harmonic). To make the description

more clear, we will first refer to the bands appearing at lower frequencies than the LO mode, dis-

cussed previously. In the case of chemically deposited CdSe nanostructured films, two bands ap-

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pear below 206.2 cm-1 (the frequency of the 1 LO mode), at 193.0 cm-1 and 176.2 cm-1. Using the

bulk CdSe values for ε∞ and ε0 in the Lyddane-Sachs-Teller equation, however, in combination

with the value of 206.2 cm-1 for the LO mode predicts the TO mode band position at about 168.4

cm-1. If bulk value of 210 cm-1 is used, on the other hand, the TO mode is predicted to appear at

about 171.5 cm-1. The lowest-frequency band in the first-order Raman spectrum of the studied

nanoctructured CdSe films could thus be attributed to a TO-like mode. Appearance of bands due

to the TO modes in nanostructured II-VI semiconductors has until recently been considered to be

quite “atypical”. In recent thorough studies by Vasilevskiy and collaborators,32,86-88 however, the

relative role of different exciton-phonon coupling mechanisms in the appearance of Raman spec-

tra of QDs has been discussed in quantitative details. On the basis of their treatment, our results

may be discussed as follows. In a polar semiconductor, two main mechanisms of exciton-phonon

coupling exist: the long range one (known as Fröhlich interaction) and the short-range one, which

is due to the optical deformation potential (ODP).32,86-88 In the case of a bulk crystal, due to con-

servation of momentum, the Fröhlich modes are dipole-forbidden in the first-order Raman spec-

tra, in contrast to the ODP-ones. In a QD, on the other hand, as the translational symmetry is bro-

ken, both mechanisms could be important. The initial success in modeling the Raman scattering

in CdSe and CdS nanocrystals taking into account only the Fröhlich interaction has led to neglect

of the ODP mechanism in low-dimensional systems of this type. It has been recently found, how-

ever, that in the case of e.g. CdTe QDs,87 ODP mechanism seems to be of some importance, and

weak TO-type feature is present in the Raman spectra thereof. The model proposed by Va-

silevskiy and collaborators predicts an appearance of a TO-type mode in the Raman spectra of

CdTe,32,86-88 somewhat blue-shifted in comparison to the bulk value, accounting for the ODP-type

interaction. This is in line with our experimental observations in the case of QD solids built up by

CdSe QDs, close-packed in thin film form, having in mind the literature data according to which

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the TO mode in bulk CdSe appears at 169.8 cm-1. Our experimental data are also in line with the

surface enhanced Raman scattering (SERS) results for single CdSe nanobelts.55 This indicates the

significance of the ODP interaction in this II-VI semiconductor as well, though it is still of much

less importance than in the case of III-V semiconductors. In the case of sonochemically deposited

CdSe films, the TO-type band appears at 169.7 cm-1, while it shifts up to 171.8 cm-1 upon thermal

annealing of the films. Such trend of small frequency upshift upon crystal size increase is in line

with previous experimental findings in similar systems.32,86-88

The band appearing at 193.0 cm-1 in the case of chemically and at 194.2 cm-1 in the case

of sonochemically deposited films is attributed to the surface mode (SO). According to the die-

lectric continuum model (eq. (13)),85 using the observed TO-type mode frequency, the SO mode

is predicted to give rise to a band in the range from about 197 to 201 cm-1, depending on the actu-

al value of the quantum number l (Fig. 8). This approach, which is actually based on the concept

of quantized optical vibrations of a spherical nanoparticle (vibrons), allows one to assign the

mentioned low-frequency shoulder as contribution of vibrons with l > 1 (see eq. (13)). The SO

mode is expected to appear between the TO and LO modes (as observed in our case, too). In the

frequency range between TO and LO modes, electromagnetic wave can not propagate in the bulk

crystal and only surface modes with spatially decaying fields may exist. As implied before, it is

self-understood that the SO modes can be observed much easier in nanoparticles than in bulk ma-

terials, due to the enhanced surface-to-volume ratio.

The frequency of the SO mode in CCD CdSe QD solids exhibits a slight increase upon

thermal annealing of the films. In the case of SCD films, on the other hand, a relatively larger

frequency decrease of about 10 cm-1 was observed upon post-deposition thermal annealing.

Though it would be expected that the overall trends in the case of SO modes should be deter-

mined by the same factors as those discussed in the context of LO modes: phonon dispersion vs.

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lattice contraction effects, the lattice contraction effects are currently thought to be of primary

importance in the case of SO modes. In the absence of size-contraction effects, actually, if one

additionally neglects the small positive TO phonon dispersion, the Frölich mode frequencies are

expected to be independent on the crystal size. However, on the contrary, size-dependent lattice

contraction effects are not offset by the phonon dispersion effects in the case of the surface pho-

non modes so that the Fröhlich frequency exhibits a more rapid increase upon decrease of the QD

size. This is exactly what we have observed in the present study. It could be assumed that it is this

effect that causes a relatively large shift in SCD films upon thermal annealing. The size-

dependence of the SO mode frequencies is much more pronounced than in the case of LO mode.

The small shift, which actually occurs in an opposite direction in the case of CCD films could not

be attributed to a compromise between the two effects in the case of this mode, if a positive pho-

non dispersion is assumed. However, it is worth noting at this point that all of the previously out-

lined reasoning has been derived on the basis of physical modeling of spherical nanoparticles. It

has been shown, however, that deviations from ideal spherical shape of the QDs affect mostly the

interface phonon modes. Within the quantitative quantum theoretical model proposed by Comas

et al,41 it has been concluded that deviations from the perfect spherical shape of nanocrystals

could be responsible for measurable both red- and blue-shifts of SO mode frequencies. Therefore,

the physical effects observed in our experimental Raman spectra in the region of surface optical

modes, in the sense of both their position and electron-phonon interaction could be attributed to

the effects due to deviations from spherical symmetry of QDs.

3.3. The combination bands in the first- and second-order Raman spectra

The remaining two bands in the spectral region of 1LO band, appearing above the band

due to this mode, following Ref.,55 could be assigned as combinations LO + TA (the band ap-

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pearing about 210 cm-1), and LO + LA (the band at about 248 cm-1). Such assignment is also in

line with the results outlined in Ref. 56 referring to CdSe nanoparticles capped with bifunctional

molecules, containing both thiol and carboxylate functional groups.56 The first observation of

combination between LO and acoustic modes in the case of colloidal CdSe QDs has been report-

ed in Ref. 55. Before that study, no literature data existed for such combined modes in the case of

II-VI semiconductor compounds. The clear appearance of these combination bands in the case of

our QD solids, may be attributed to a significantly enhanced coupling to the short wavelength

phonons in the case of enhanced confinement in ultrasmall QDs. Actually, the presently offered

explanation for the high-frequency asymmetry of the 1LO mode is to account for sequential scat-

tering on optical and acoustic phonon, despite their non-observance in the case of bulk II-VI

compounds. Nanostructures characterized by strong confinement of charge carriers and phonons,

however, may be characterized by quite different scattering probabilities than those characteristic

for a bulk crystal.

The spectral region around 400 cm-1 in the resonant Raman spectrum of CdSe thin film

obtained by conventional chemical deposition is shown in Fig. 9. As can be seen, the most prom-

inent feature in this region is the two-phonon LO transition (2LO), with notable lower-frequency

asymmetry. This region could be successfully fitted with four component bands, with positions

closely matching the corresponding ones found in the case of resonant Raman spectra of CdSe

nanobelts (Fig. 9).55 According to the approach in Ref. 55, we attribute these bands to the follow-

ing combination modes (in the order of increasing wavenumber): 2TO (361.6 cm-1), TO + LO

(374.8 cm-1), SO + LO (385.6 cm-1) and 2LO (414.8 cm-1).

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3.4. The exciton-phonon coupling and the Huang-Rhys parameter

In Raman scattering spectra, the coupling between phonons and excited charge carriers re-

flects in the ratio of intensities of phonon replicas to the fundamental Raman band. In the case of

n-th order phonon scattering process, the Raman scattering cross-section is given by:9

( )2

0 LO

42 0∑

∞

= +−−=

m ij

n

inE

mmnR

Γωωµω

hhh (12)

In (12), ωh denotes the incident photon energy, Eij is the excited state energy, µ is the electronic

transition dipole moment, Γ the homogeneous linewidth, while m denotes the intermediate state.

mn is the Franck-Condon overlap, given by:9

( )222/1

2

1exp

!

!∆∆∆ mn

m

mn Lm

nmn −−

−

= (13)

where L denotes Laguerre polynomial. The exciton-phonon coupling strength is best quantified

by the Huang-Rhys factor S, defined as:6-9

2

2

1∆=S (14)

Combining equations (12) and (13), using the ratio of two different Raman cross-sections, one

can in principle numerically estimate S and ∆. By combination of equations (12) and (14), on the

other hand, one arrives at the following expression relating the Huang-Rhys factor with the over-

tone:fundamental intensity ratio:6-9

( )( ) 22

0

220

1

2

22 Γωω

Γωω

+−+

+−+=

hh

hh

LOex

LOex

LO

LO

E

ES

I

I (15)

Rigorously speaking, the Huang-Rhys factor actually determines the intensities of the vibronic

component bands of an electronic transition (in a vibrationally resolved absorption or emission

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spectrum at 0 K). Specifically, S equals the ratio of single-quantum vibronic transition to the elec-

tronic origin, as can be see from the general equation:6-9

!00

02

2

00

0

v

Sv

I

I vv ==

→

→ (16)

Direct determination of S, however, from photoluminescence and excitation spectra has been

shown to be quite a challenging task, especially in the case of QD assemblies.6-9 On the other

hand, Resonant Raman scattering has been shown to be an experimentally much more easily ac-

cessible variant to measure vibronic intensities. It has often been assumed in interpretation of res-

onant Raman measurements that the I2LO/I1LO intensity ratio is either equal or at least proportional

to S, analogously as in the case of one-phonon absorption or emission processes.6-9 One should,

however, keep in mind that resonance Raman scattering is much more complex, coherent two-

photon process. Numerous arguments have been discussed in the literature as to whether the ratio

of the intensities of the first overtone to the fundamental Raman band equals or is proportional to

the Huang-Rhys factor. Recent simulation results by Kelley6,7 have clearly demonstrated that in a

general case, the simple relations that connect the I2LO/I1LO intensity ratio and the Huang-Rhys

parameter are not straightforwardly applicable. In the same study,7 even a simple exact formula

has been proposed that relates the overtone to fundamental Raman intensity ratio to the Huang-

Rhys factor in the case of nanocrystals, and it has been pointed out which conditions (prerequi-

sites) have to be satisfied so that a direct estimation of S is possible from the intensity ratios.

The measured intensity ratios I2LO/I1LO in the case of presently studied 3D assemblies of

CdSe QDs deposited in thin film form by conventional chemical and sonochemical routes, as

well as for the post-deposition treated samples are given in Table II. As can be seen, while the

I2LO/I1LO ratio is similar in the case of chemically and sonochemically deposited QD solids, both

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values decrease almost twice upon post-deposition thermal annealing. Note that the presently re-

ported values of the I2LO/I1LO ratio fall within the interval of values that has been reported for oth-

er similar samples.6-15 In the case of a bulk CdSe sample, this intensity ratio is much larger than

unity.6-9 Therefore, the exciton-phonon coupling in the case of presently studied 3D QD assem-

blies built up by close packed CdSe QDs appears to be much weaker than in the case of bulk

specimen of this material. Similar conclusions have been also derived in the case of other CdSe-

based nanostructures.6,7 and references therein A further definite conclusion that could be derived on the

basis of our experimental data is that the exciton-phonon coupling in the case of our presently

studied CdSe QD solids deposited as thin films decreases upon post-deposition thermal annealing

treatment, which is accompanied by average crystal size increase. In other words, in strongly con-

fined SC NCs, it is larger than in those with weaker confinement effects. Our results are similar

to those reported for e.g. CdSxSe1-x nanocrystals embedded in a glass slab,89 CdSe/ZnS core/shell

nanorods,54 and colloidal CdSe nanorods.43 Taking these trends altogether with the observations

in the case of bulk CdSe, it appears that the overall trend in the magnitude of exciton-phonon

coupling is more complex. Going from bulk (macrocrystalline) specimen, it first decreases upon

crystal size decrease, but under the conditions of strong size-quantization, it increases again. Sim-

ilar conclusions could be derived on the basis of our experimental data when the Huang-Rhys

factor was estimated, either using eq. (15) or the formula given in:7

2

1

2 15.195.1 SSI

I

LO

LO −= (17)

As can be seen from Table II, these values are much lower than the S value characteristic for bulk

CdSe (~ 10).

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4. Conclusions

In the present paper, we have studied the phonon confinement and related effects as well as the exciton-phonon coupling in 3D assemblies of cubic cadmium selenide QDs synthesized by conventional colloidal chemical (CCD) and sonochemical routes (SCD), as well as in post-deposition thermally annealed samples, employing resonant Raman scattering (RRS), X-ray dif-fraction and optical spectroscopic techniques. Notable low-frequency asymmetry of both 1LO band and its replicas in the resonant Raman spectra of thin films composed by 3D assemblies of CdSe QDs, and somewhat less pronounced high-frequency asymmetry was clearly observed. The position of the 1LO band in the case of as-deposited films by the CCD method is red-shifted by about 4 cm-1 with respect to the bulk value. A further red shift of this mode by about 2 cm-1 is observed in the case of SCD samples, which is accompanied by about 40 % increase of half-width. Post-deposition annealing of the as-deposited films by the sonochemical method leads to a small blue shift of the frequency of 1LO mode. The observed band shifts were found to result from subtle balance between phonon confinement effects and lattice contraction due to internal strain, which were quantitatively modeled. Using the Lyddane-Sachs-Teller equation and the die-lectric continuum model, the low-frequency asymmetry of the 1LO band was attributed to the appearance of surface optical (SO) and transverse optical (TO) modes, which were accurately as-signed. On the basis of these data, it was concluded that in the present ultrasmall CdSe QDs close packed in thin film form, the short range mechanism of exciton-phonon coupling (EPC), due to the optical deformation potential (ODP), becomes of comparable importance with the long-range one (Fröhlich interaction). Concerning the higher-frequency asymmetry of the fundamental LO band in the case of 3D QD assemblies, this is the first study in which it is addressed and ana-lyzed. This asymmetry was attributed to appearance of bands due to combinations of LO mode with the longitudinal acoustic and transverse acoustic modes, which occurs due to the significant-ly enhanced coupling to short-wavelength phonons as a results of enhanced confinement in ul-trasmall QDs. Such trends in the EPC vs. R dependence were attributed to the changes in relative significance of Coulomb interaction vs. confinement effects.

5. Acknowledgements

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Figure captions:

Fig. 1. XRD pattern of the newly synthesized CdSe 3D QD assemblies by sonochemical route, to-

gether with the standard.

Fig. 2. The recorded resonant Raman spectra of the as-deposited 3D QD assemblies in thin film

form by the conventional chemical approach (a) as well as by the sonochemical route (b). Insets

emphasize the regions of appearance of the 1LO phonon replicas.

Fig. 3. The region of appearance of the 1LO band in the resonant Raman spectra of as-deposited

nanostructured CdSe films by the colloidal chemical deposition method (CCD) and by the sono-

chemical route. The position of the corresponding band in a bulk specimen of cubic CdSe is denot-

ed by a solid line with an arrow.

Fig. 4. A typical trend in the shift of the position of the 1LO band in the case of sonochemically

deposited sample of nanostructured CdSe film upon post-deposition thermal annealing.

Fig. 5. Diminishing of electronic size-quantization effects in the annealed films, observed as red-

shifts of the absorption onsets in the UV-VIS absorption spectra: plot of the spectral dependence of

absorption coefficient in the case of a) as-deposited and b) thermally annealed CdSe film.

Fig. 6. Schematic presentation of the opposite contributions of ∆ωD and ∆ωC to overall ∆ω, illus-

trating typical trends with size – reducing as compared to a bulk specimen (a), as well as annealing-

induced changes (b), even up to cancellation of both effects at certain crystal size (c); (ωL denotes

the LO phonon frequency of a bulk specimen of CdSe with zinc blende structure; see text for de-

tails).

Fig. 7. Experimental Raman spectroscopic data in the region around 1LO mode in the case of sono-

chemically deposited CdSe films, together with the reconstructed curve and the component peaks

obtained by the least-squares curve fitting procedure.

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Fig. 8. Position of the surface optical mode (SO) as a function of the quantum number l, predicted

by the dielectric continuum model of Ruppin and Englman. (l = 1, 2, 3,… is the angular momentum

quantum number, i.e. the order of the spherical harmonic).

Fig. 9. The spectral region around 400 cm-1 in the resonant Raman spectrum of CdSe thin film ob-

tained by conventional chemical deposition, together with the reconstructed curve and the compo-

nent peaks obtained by the least-squares curve fitting procedure.

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Table I. The basic structural parameters of as-deposited and thermally annealed CdSe thin films derived on the basis of XRD data (see text for details).

<a> / Å <R> / nm <ε> δ / nm-2

As-deposited (SCD) 6.0708 ± 0.0121 2.0 ± 0.02 0.0034 0.063

As-deposited (CCD) 6.0746 ± 0.0163 2.7 ± 0.01 0.0028 0.034

Annealed at 300 ºC 6.0842 ± 0.0046 12.0 ± 0.03 0.0012 0.002

Table II. The measured I2LO/I1LO intensity ratios for the studied 3D assemblies of CdSe QDs depos-ited in thin film form by conventional chemical and sonochemical routes, and for the post-

deposition treated samples (see text for details).

I2LO/I1LO S

As-deposited (SCD) 0.583 0.39

SCD Annealed at 300 ºC 0.343 0.20

As-deposited (CCD) 0.596 0.40

CCD Annealed at 300 ºC 0.384 0.23

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Fig. 1.

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500

1000

1500

2000

2500

3000

3500

4000

4500

5000

100 300 500 700 900 1100

Raman shift / cm-1

Raman intensity

1LO

2LO

3LO4LO

500

700

900

1100

1300

1500

300 500 700 900

2LO

3LO4LO

a)

9000

11000

13000

15000

17000

19000

21000

23000

25000

100 300 500 700 900 1100

Raman shift / cm-1

Raman intensity

1LO

2LO

3LO4LO

9000

10000

11000

12000

13000

300 500 700 900

2LO

3LO4LO

b)

Fig. 2.

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150 170 190 210 230 250

Raman shift / cm-1

Raman intensity / arb. units

chemically deposited

sonochemically

deposited

bulk LO

Fig. 3.

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Raman shift / cm-1

Fig. 4.

-1


170 180 190 200 210 220 230 240 250

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0

1

2

3

4

5

6

7

8

9

10

1.5 1.7 1.9 2.1 2.3 2.5 2.7

hv /eV

α/(

104 cm

-1)

ab

Fig. 5.

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a)

b)

c)

Fig. 6.

∆ω(R)

ωL ω(R)

∆ωD(R) ∆ωC(R)

bulk

as-deposited

annealed

∆ω(R) ≈ 0

ω(R) ≈ ωL

∆ωD(R) ∆ωC(R)

∆ω(R)

ωL ω(R)

∆ωD(R) ∆ωC(R)

bulk

as-deposited

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0

100

200

300

400

500

600

700

800

900

70 120 170 220 270 320 370

Raman shift / cm-1

Raman intensity

Fig. 7.

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197.0

197.5

198.0

198.5

199.0

199.5

200.0

200.5

201.0

201.5

202.0

0 20 40 60 80 100

l

v(S

O)

/ cm

-1

Fig. 8.

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0

100

200

300

400

500

600

700

800

320 340 360 380 400 420 440 460 480

Raman shift / cm-1


Fig. 9.

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TOC Graphics

150 170 190 210 230 250

Raman shift / cm-1


chemically deposited

sonochemically

deposited

bulk LO

∆ω(R)

ωL ω(R)

∆ωD(R) ∆ωC(R)

bulk

as-deposited

annealed

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Documents

Phonon Confinement and Related Effects in Three-Dimensional Assemblies of Cubic Cadmium Selenide Quantum Dots Synthesized by Conventional Chemical and Sonochemical Routes