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\def\rmfcornisa{RESEARCH \hfill\rmf\ {\bf 64} (2018) 61--66
\hfill JANUARY-FEBRUARY 2018}
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\def\rmfcintilla{{\it Rev.\ Mex.\ Fis.\/} {\bf 64} (2018) 61--66}
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\markboth{E.\ Campos-Gonz\'{a}lez \lowercase{\textit{et al}}.,}
{Optical characterization of cdte nanoparticles embedded in a
nanoparticulate SnO$_{2}$ matrix}
\begin{document}
\title{Optical characterization of CdTe nanoparticles embedded in a \\
nanoparticulate SnO$_{2}$ matrix
\vspace{-4pt}}
\author{E.\ Campos-Gonz\'{a}lez$^{a,b}$, M.\ Becerril$^{b}$, J.\ Santoyo-Salazar$^{b}$,
 H.\ Silva-L\'{o}pez$^{b}$,  F.\ de Moure Flores$^{a}$, \\ and   O.\ Zelaya-\'{A}ngel$^{b,*}$}
\address{$^{a}$Facultad de Qu\'{i}mica, Materiales, Universidad Aut\'{o}noma de
Quer\'{e}taro,\\ Quer\'{e}taro, 76010, M\'{e}xico. \\
$^{b}$Departamento de F\'{\i}sica, Centro de Investigaci\'{o}n y de Estudios
Avanzados del I.P.N.\\  Apartado Postal 14-740, M\'{e}xico D.F.\ 07360, M\'{e}xico.
\\
$^*$e-mail: ozelaya@fis.cinvestav.mx}
\maketitle
\recibido{14 August 2017}{2 October 2017
\vspace{-10pt}}
\begin{abstract}
Cadmium telluride (CdTe) nanoparticles were grown in the interior of a SnO$_{2}$ 
transparent matrix by means of the r.f. sputtering technique. X-ray diffraction 
(XRD) patterns reveal that the CdTe quantum dots (QD) grow in the hexagonal 
wurtzite (W) phase. Diffraction data show that SnO$_{2}$ is constituted by 
nanoparticles also, with size of the same order of the W-CdTe QD. The broad bands 
of the XRD patterns and the Scherrer formula allowed, by assuming a spherical 
shape, the W-CdTe QD size calculation, which have average diameters in the range 
4.8 - 14.0 nm. These data were confirmed by electron microscopy images. Optical 
absorbance gives information to calculate the energy of the two lowest excitonic 
states (band gap). The Raman spectra show several broad bands in the range 100 - 200 
cm$^{-1}$, on which deconvolution allows separate five modes in the 100 - 200 cm$^{-1}$ 
interval. The bands correspond to CdTe and tetragonal Te. The transversal optic (TO) 
and longitudinal optic (LO) modes of CdTe at the $\Gamma$ point of the first Brillouin zone, 
for phonons in nanoparticles, follow the expected behavior if the radius of crystal 
decreases, taking into account that the selection rules for momentum conservation are relaxed.
\end{abstract}
\keys{ Semiconductors;\ quantum dots;\ Raman;\ II-VI. \vspace{0pt}}
\pacs{81.07.-b; 81.07.Ta; 78.30.-j; 81.05.Dz \vspace{-2pt}}
\begin{multicols}{2}



\section{Introduction}


CdTe semiconductor nanoparticles immersed in transparent matrices have currently many important 
applications in electrochemistry \cite{key:bae}, photoelectricity \cite{key:seabold}, solar cells 
fabrication~\cite{key:verma}, chemical sensors \cite{key:frasco}, bio-labelling \cite{key:green} 
etc. The achievement of desired particle sizes over the largest possible range, controlled particular 
sizes, and good crystallinity are some of the properties expected in nanocrystal growing methods. 
The transparent matrices can be solid or liquid and organic or inorganic, depending on their use and 
the growth method employed. Thus, hard matrices for CdTe such as silica \cite{key:mota} and soft ones 
like hydrogels \cite{key:kharla} have been employed, which allow a large variety of applications. 
SnO$_{2}$ is a transparent oxide with the property of possessing high electric conductivity that places
the oxide in a special position as matrix for electronic devices design, as instance. At present, CdS 
nanoparticles embedded in SnO$_{2}$ have been successfully utilized in photocurrent generation 
\cite{key:nasr}, and in solar cells based on CdTe nanoparticles immersed in SnO$_{2}$ matrix have been 
already studied with good results \cite{key:pehnt}. Nowadays, a lot of growing techniques exist, physical 
or chemical, to prepare semiconducting nanoparticles, which have found a great acceptance among the 
researches of wide-world. In the last four years several works have been publishe about CdTe nanoparticles 
immersed in SiO$_{2}$, in which the good photoluminescent properties at energies larger than that of bulk 
CdTe have been reported \cite{key:szhang,key:tang,key:morales}.


In this work the preparation of CdTe nanoparticles by means of r.f. sputtering with radius in the range 
2.4 - 7.0 nm is reported. Actually, a CdTe-SnO$_{2}$ nanocomposite was grown on glass substrates. Within 
the framework of II-VI semiconductor quantum dots (QD) the sputtering growth technique offers controlled 
size distribution, also the preparation of CdTe crystallized in the metastable hexagonal wurtzite 
phase~\cite{key:farias}. Structural and optical studies include X-ray diffraction, transmission electron 
spectroscopy, optical absorption and Raman analysis to characterize the quantum confinement in the CdTe 
nanoparticles  immersed in the  also  nanoparticulate SnO$_{2}$ matrix, both undoped. The variation at 
room temperature (RT) of the main vibrational modes of wurtzite CdTe nanoparticles, when their size goes 
to small values, is studied. The main contribution of this the analysis of the optical properties of 
hexagonal CdTe, since there are few reports in this crystalline phase of this important semiconductor.

\section{Experimental Details}

The CdTe + SnO$_{2}$ thin films were prepared on 7059 Corning glass substrates by means of the r.f. 
sputtering technique in an Ar ambient at 20 mTorr and at RT. The time for deposition was 180 min. 
The target was 5 cm$^{2}$ of diameter and was prepared with mixed 99.999 \% purity SnO$_{2}$ and CdTe 
powders. The CdTe weight percentage in the target varied from 2\% to 20\% to get different nanoparticles 
size.  After\hspace{1pt} the\hspace{1pt} growth\hspace{1pt} the 




\begin{center}
\includegraphics*[82mm,152.69mm]{fig01.jpg}
\end {center}

\lilahf{{\sc Figure 1.} (a) Typical X ray diffraction (XRD) pattern of the W-CdTe embedded in SnO$_{2}$ matrix. 
Reflections labeled with H indicates CdTe in hexagonal wurtzite crystalline phase. XRD peaks 
corresponding to the tetragonal phase of the SnO$_{2}$ matrix can be observed. Insets illustrate 
the deconvolution fitting process followed to calculate the nanoparticle  radius.  (b)  Deconvolution  
of  hexagonal  CdTe  and  SnO$_{2}$   broad  X-ray diffraction bands. In this picture it can be 
appreciated that both types of nanoparticles have approximated the same average size.}
% ********************

\vspace{10pt}



\noindent 
 samples were annealed at 300$^\circ$C in air during one hour. 
A variety of different crystallite size in the 4.8 - 14 nm range was obtained. Films have thickness of 
200 $\pm{}$ 20 nm, as measured by using a Dektak II profilometer. For the crystalline structure analysis 
an X-ray Diffractometer Siemens D5000 (Cu- K$\alpha $ radiation) was utilized. The size of 
nanoparticles was determined by employing the Scherrer formula and transmission electron microscopy (TEM) 
images. TEM apparatus employed was a Jeol 2010 working at 200 KeV. The CdTe + SnO$_{2}$ layers were 
detached from the substrate and attached 



\begin{center}
\includegraphics*[82mm,124.5mm]{fig02.jpg}
\end {center}

\lilahf{{\sc Figure 2.} (a)TEM image of CdTe distribution of nanoparticles immersed in the SnO$_{2}$ matrix for 
an average diameter of $\sim 12$ nm. The inset illustrates the TEM image of a detail of CdTe QD prepared 
with average size of $\sim 4$ nm, the bar scale is 10 nm. (b) Electron diffraction pattern of 
nanoparticulate W-CdTe and SnO$_{2}$ matrix.}
% ********************

\vspace{10pt}

\noindent 
onto the TEM-grills. Indexation was computed by the relation 
d$_{t}  = \lambda_{t}$L$_{t}$/r$_{t}$ where 
$\lambda_{t} = 0.0027$ nm is the electron wavelength 
at 200 keV, the steady camera for diffraction with L$_{t}$ = 30 cm, and where r$_{t}$ (mm) is the radius
measured from the transmitted electron beam to the diffracted rings (Fig.~2b). Data were taken, from 
selected area of electron diffraction (SAED) and x-ray diffraction (XRD) patterns, to define the structure 
by Diamond 3.0 software. The band gap and higher electronic transitions were measured from optical absorption 
spectra (OA). OA spectra were measured by means of a UNICAM 8700 spectrophotometer. The Raman spectra of 
the samples were measured at room temperature with the LabRaman II Dilor spectrometer with excitation light 
of 514 nm wavelength. All the characterization was performed at RT.


\section{Results and Discussion}

The crystalline structure of the CdTe nanoparticles immersed in SnO$_{2}$\hspace{2pt} is\hspace{1pt} the\hspace{2pt} hexagonal\hspace{1pt} wurtzite\hspace{2pt}  
(W-CdTe)\hspace{2pt} phase\hspace{2pt} as\hspace{1pt} ob-

\begin{center}
\includegraphics*[82mm,56.42mm]{fig03.jpg}
\end {center}

\lilahf{{\sc Figure 3.} (a)Calculation of the first exited energy of electrons in the nanoparticle with 
$R= 4.5$ nm employing both the first derivative of absorbance spectra and the 
$(\alpha h \nu ) ^{2}  =  A ( E _{g-\textrm{nano}} - h\nu$) formula. 
(b) First derivative of absorbance of two samples, the first maximum indicates the position of the
 first quantized energy level. Arrows with asterisks as superindex indicate the energy of the second 
quantized energy level.}
% ********************

\vspace{10pt}


\noindent served  in Fig. 1(a), where a typical XRD pattern of the CdTe + SnO$_{2}$ nanocomposite, 
in the range 20 $\leq{}$ 2$\theta{}$ $\leq{}$ 50 degrees, is exhibited. XRD peaks which correspond to 
the tetragonal crystalline phase of SnO$_{2}$, the matrix, are also observed in Fig. 1(a). In the two 
insets of this figure are displayed in detail, in the interval $2 \theta = 22 - 25$ degrees, W-CdTe 
diffractograms with three reflections. These nearby three XRD signals can be considered as the finger 
print of the wurtzite phase of many materials which crystallize in hexagonal packing. Wurtzite is a 
metastable phase for CdTe, however, Farias \textit{et al}. have demonstrated that, from the thermodynamic point 
of view, wurtzite phase should be more stable than the zinc blende for very small radius nanoparticles 
\cite{key:becerril}. The samples studied here were deposited at $\sim 1.1$ nm/min, which can be 
considered as a very slow growing rate, in such a way that it enables the nanoparticles to grow, 
practically, in equilibrium conditions at RT. The XRD reflections of the SnO$_{2}$ do not always appear in
the low $2\theta $ values region, probably there the reflections are so weak because the existence of 
preferred orientation in other crystallographic directions. In Fig. 1(b), an XRD reflection of SnO$_{2}$ 
can be observed together with the triplet of W-CdTe. This diffractogram indicates that the size of SnO$_{2}$ 
nanoparticles is of the same order of the size of the CdTe ones. In order to calculate the average radius 
$R$ of the nanoparticles, a deconvolution process with Gaussian profiles was carried out to 
determine the full width at half maximun (FWHM) of the XRD bands. This step allows obtain the center of 
each band also. The average radius of the particles, obtained from the Scherrer's formula and from FWHM 
values of the bands in XRD patterns of a set of ten CdTe nanoparticles, lies in the 2.4 - 7.0 nm range. 
The TEM image of the CdTe-QD distribution grown with ${R} = 6.0 \pm  0.7$ nm into the SnO$_{2}$ 
matrix is displayed in Fig. 2(a), the inset illustrates the TEM image nanoparticles with 
$R = 4.0 \pm $ 0.5~nm. In Fig.~2(b) the electron diffraction   pattern of the CdTe nanoparticles
 plus the SnO$_{2}$ nanoparticulate matrix is exhibited, where the pattern clearly evidences that CdTe
 nanoparticles have grown  with the hexagonal symmetry.


From the UV-Vis optical absorption spectra of the CdTe + SnO$_{2}$ films and the relation 
($\alpha$\textit{h}$\nu$)$^{2} =  A$($E_{g-\textrm{nano}}- h\nu$) the first electronic
 transition, \textit{i.e.}, the direct energy band gap ($E_{g-\textrm{nano}}$) was obtained for the samples. Here,
 $\alpha$ is the optical absorption coefficient, $h$ the Plank's constant, $\nu$ the photon frequency,
 $h \nu$ the photon energy, and \textit{A} a constant. In Fig. 3(a) is shown the calculation of
$E_{g-\textrm{nano}}$ for the sample prepared with ${R} = 4.6 \pm  0.4$ nm, where the extrapolation 
of the linear part of the curve until the \textit{h}$\nu$ axis indicates that  $E_{g-\textrm{nano}} = 1.64$ eV.
 In this same panel the first derivative with respect to ${h}\nu$ of the absorbance 
[$d$(OA)/$d$(${h}\nu$)] as a function of \textit{h}$\nu$ is outlined (thin line). The 
position of the maximum of \textit{d}(OA)/\textit{d}(\textit{h}$\nu$) on the \textit{h}$\nu$ axis coincides 
with the value of E$_{g }$ formerly calculated. Thus, the first derivative of OA will be used to estimate with 
good approximation all the electronic transition data, as has been used for other authors \cite{key:rastogi}. 
Furthermore, the $d$(OA)/\textit{d}(\textit{h}$\nu$) lineshape allows observe other transitions with 
better resolution. In Fig. 3(b) \textit{d}(OA)/\textit{d}(\textit{h}$\nu$) of two samples is displayed, the 
position of the first electronic transition is indicated with\hspace{1pt} the\hspace{1pt} first\hspace{1pt} maximum. 


\vspace{10pt}

\begin{center}
\includegraphics*[82mm,119.13mm]{fig04.jpg}
\end {center}

\lilahf{{\sc Figure 4.} First two electronic transitions of W-CdTe versus the square inverse of nanoparticle radius. }
% ********************




\noindent The second electronic transition
 due to the next discrete level has been identified with the second band and was indicated with other small arrow accompanied by an asterisk. The third transition observed in Fig. 3(b) is a well pronounced maximum around 2.5~eV, 
which has been identified by us that is originated from CdO formed at the interface 
CdTe-SnO$_{2}$~\cite{key:yzhang}, 
since the direct band gap of CdO is $\sim{} 2.5$~eV \cite{key:santos}. Other possible phases formed in the CdTe 
surface \cite{key:becerril} as product of oxidation are TeO$_{2}$ and CdTeO$_{3}$ \cite{key:yzhang,key:babu}, 
however these oxides have band gap values of $\sim{}$3.8 and $\sim 3.9$ eV, respectively 
[19-22]. Then, in our case, that a CdO layer has been formed in the 
CdTe/SnO$_{2}$ interface is highly probable. A small feature in the bottom spectrum in Fig. 3(b), which was 
indicated by the ``\textit{hh}'' label, is due to first electronic transition from the heavy-holes in the valence 
band \cite{key:esch}. In this same spectrum a shoulder is observed at around 2.44 eV which is due to the 
spin- orbit plus the crystal field unfolding 
($\Delta_{so} + \Delta_{cf}$). The values 
$\Delta_{so} = 93$ meV and $\Delta_{cf} = 3$ meV have been reported for 
W-CdTe \cite{key:lefe,key:dayal}. The last unfolding arises because here CdTe has hexagonal symmetry 
\cite{key:portillo}. For high energy values ($E_{g-\textrm{nano}}\geq 1.64$ eV) a deconvolution process 
was applied to have a better definition of the position of the second electronic transition. 




The first ($E_{g-\textrm{nano}}$) and the second electronic transitions as a function of the inverse square 
radius of QD are displayed in Fig. 4. Despite the scattering of the experimental points, it can be concluded 
that both electronic transitions satisfy the well known $E_{g}$ versus $R^{-2}$ dependence. The solid lines on the experimental data have been drawn according with the relation $E_{n,l}$(R) = E$_{g} + (\nabla^{2}/2R^{2}$)[(\textit{x{\tiny n}
$_{e,le}$})$^{2}$/\textit{m$_{e}$ + }(\textit{x{\tiny
n}$_{h lh}$})$^{2}/ m_{h}$], where \textit{n},  \textit{l} are the electron or hole eigenstates as 1s, 1p, 1d, etc.  $E_{g} = 1.43$ eV is the band gap energy of the bulk CdTe at RT, $m_{e}$ and $m_{h}$  are the effective masses of electron and holes, respectively.
$x_{n_{e},l_{e}}$,  $x_{n_{h},l_{h}  }$   
are the roots of the spherical Bessel functions [27,28]. The Bohr Radius of CdTe is 7.3 nm, which means that our analysis has been totally developed in the strong quantum confinement regime. The optical properties of absorbance and photoluminescence of the CdTe nanoparticles do not overlap with those of SnO$_{2}$ because the difference in the band gap values 
($E_{g} = 3.8$ eV for bulk SnO$_{2}$). 




High resolution of CdTe Raman spectra was carried out in the set of samples. The Raman spectra of two CdTe 
representative samples (samples with $ R = 5.4 \pm{} 0.4$ and $2.4 \pm{} 0.5$ nm) in the range 
100-400 cm$^{-1}$ are depicted in Figs. 5(a) and~5(b), respectively. In both cases the deconvolution 
process with Lorentzian curves of the spectrum is also illustrated. Five modes are observed in the Raman 
spectra of CdTe in the 100 - 170 cm$^{-1}$ range. The modes which practically coincide are those of $E_{2}$-Te 
and TO-CdTe, both at
$\sim 140$ cm$^{-1}$. However, in past we have found that the TO-CdTe mode lies slightly at low energies of
 $E_{2}$-Te [29]. A lower vibrational band observed at slightly low energy than $\sim 140 $ cm in 
CdTe nanocrystals, has been associated to DALA mode (disorder activated longitudinal acoustic) by other authors
 \cite{key:devki}. In Figs. 5(a) and 5(b) the mode E$_{2}$-Te has been fitted at lower energy than that of 
TO-CdTe. The mode at The Raman spectrum of CdTe has been The modes centered at 
$\sim 140$ and $\sim 160$ cm$^{-1}$ correspond to the transversal optic (TO) and to the longitudinal optic 
(LO) vibrational modes of cubic and hexagonal CdTe, respectively \cite{key:huerta,key:fiedler,key:dzhagan}, 
and the mode located at about 120 cm$^{-1}$ has been associated to with the A$_{1}$(TO) of hexagonal Te 
\cite{key:dzhagan,key:ochoa}. The positions of the centers of both the TO and the LO modes of CdTe as a function 
of \textit{R} are shown in Fig. 6(a). The most important modes in nanometric SnO$_{2}$ are observed at 
wavenumbers above the 450 cm$^{-1}$ \cite{key:dieguez}. Even with the large scattering of experimental points, 
a tendency of the LO mode to soften and the TO mode to harden can be ensured. In Fig. 6(b) the dispersion 
curves of cubic zincblende CdTe in the 160-180 cm$^{-1}$ interval are shown \cite{key:ochoa,key:dieguez}. 
No specific information exists in the literature about the dispersion curves of the hexagonal wurtzite CdTe, 
nevertheless, given the similarities 

\vspace{5pt}

\begin{center}
\includegraphics*[79mm,142.54mm]{fig05.jpg}
\end {center}

\lilahf{{\sc Figure 5.} Raman spectra of two CdTe nanoparticles. (a) Deconvolution to separate
the positions of the modes of Te and of the TO and LO modes of the CdTe nanoparticle
with $R = 5.4$ 0.4 nm. (b) Of sample with $R = 2.4$ 0.5 nm.}
% ********************



\begin{center}
\includegraphics*[82mm,161.17mm]{fig06.jpg}
\end {center}

\lilahf{{\sc Figure 6.} (a) Section of the dispersion curves of cubic- zincblende CdTe found in the
literature. (b) Positions of the LO and TO modes of the W-CdTe nanoparticles as a
function of the particle radius.}
% ********************

\vspace{10pt}

\noindent existent between hexagonal-Wurtzite (HW) and cubic-Zinc blende (CZB) 
crystalline phases, the unit cell length of HW along the (0001) axis is double with respect to CZB along the 
(111) direction ($\Gamma  \rightarrow  $ L) \cite{key:zardo}. The dispersion curves of CZB along the 
$\Gamma{}$-X and $\Gamma{}$-L, high symmetry directions, of the 1$^{st}$ Brillouin zone can be used to analyze the
 variation of the TO and LO modes around the $\Gamma{}$ point when \textit{R} decreases. The very low 
dimensional character of nanoparticles breaks the translational periodicity, then, the selection rules of 
crystal momentum conservation are relaxed when \textit{R}$\rightarrow{}$0, the momentum conservation is less 
and less preserved. Then, transitions out the $\Gamma{}$ point are allowed, as outlined by the dashed arrow in
 Fig. 6(b). In this way, as \textit{R} goes to lower values, the dashed arrow can move away the $\Gamma{}$ point
 more and more. This fact indicates that when \textit{R} decreases LO decreases, and on the contrary, TO increases.
 The shift to lower frequency values of the LO mode of CdTe when \textit{R} decreases has been observed by Rolo \textit{et al} 
\cite{key:brus}. This behavior is consequence of quantum confinement effects.  Theoretically, Trallero-Giner \textit{et al}. 
have developed a model for the LO mode of CdS for nanocrystals, in which the mode is softens when nanoparticles 
size decreases \cite{key:trallero}.


\section{Conclusions}

Wurtzite CdTe nanoparticles embedded in SnO$_{2}$ matrix in the radius range 2.4-7.0 nm were 
succesfully prepared by means of the r.f. sputtering technique. X-ray diffraction shows that 
W-CdTe and Tetragonal SnO$_{2}$ nanocrystals have sizes of the same order. W-CdTe is the metastable 
phase of bulk CdTe, however for nanoparticles is a stable phase. The quantum confinement occurs 
in the strong regime as the Bohr radius for CdTe is 7.3 nm. From optical absorbance the first and 
second electronic transition were determined. In Raman spectra the LO and TO modes of W-CdTe were 
measured where, as expected from dispersion curves, the LO mode hardens and the TO softens when the 
radius of nanoparticles tends to lower values.



\section*{Acknowledgements}


The authors thank to M. Guerrero and A. Garc\'{\i}a for their technical assistance. The authors 
acknowledge financial support for this work from FONDO SECTORIAL CONACYT-SENER-SUSTENTABILIDAD 
ENERG\'ETICA through CeMIE-sol, within of the strategic project number 37; ``Development of new 
photovoltaic devices and semi-superconductor materials''.
 E. Campos-Gonz\'{a}les also acknowledges 
CONACyT-M\'{e}xico for support underprogram ``Estancias Posdoctorales Nacionales''.














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