We show that the line shape of resonant Raman spectra of CdTe can be reproduced using the spatial correlation model (SCM). Our results show that the resonant Raman spectrum for a surface with a RMS of 430 nm is characterized by the presence of two intense sharp peaks located at frequencies corresponding to LO and 2LOmodes. The resonant Raman spectrum for a surface with a RMS of 6 nm on the other hand, can be reproduced using the contribution of high frequency phonons related with the acoustic transverse harmonics. These results suggest that under resonance conditions, such acoustic transverse modes define the line shape for a small size correlation region diameter. This study provides a new application of SCM to estimate the size grain of a surface where this information is not available

Frausto-Reyes, C.

Medel-Ruíz, C.I.

Molina-Contreras, J.R.

Pérez Ladrón de Guevara, H.

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  
NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 4 No 1, 01PCSI01(3pp) (2015) 
 
 
2304-1862/2015/4(1)01PCSI01(3) 01PCSI01-1  2015 Sumy State University 
CdTe Raman Line Shape in Resonance: a Space Correlation Zone Study 
 
J.R. Molina-Contreras1,*, C. Frausto-Reyes2, C.I. Medel-Ruíz3, H. Pérez Ladrón de Guevara3 
 
1 Instituto Tecnológico de Aguascalientes, Av. A. López Mateos 1801 Oriente, 20256 Aguascalientes, Ags., México  
2 Centro de Investigaciones en Óptica, Unidad Aguascalientes,  
Prolongación Constitución 607, Apartado postal 507, 20200 Aguascalientes, Ags., México 
3 Centro Universitario de los Lagos, Universidad de Guadalajara,  
Av. Enrique Díaz de León s/n, 47460 Lagos de Moreno, Jalisco, México 
 
(Received 15 March 2015; published online 22 August 2015) 
 
We show that the line shape of resonant Raman spectra of CdTe can be reproduced using the spatial 
correlation model (SCM). Our results show that the resonant Raman spectrum for a surface with a RMS of 
430 nm is characterized by the presence of two intense sharp peaks located at frequencies corresponding to 
LO and 2LOmodes. The resonant Raman spectrum for a surface with a RMS of 6 nm on the other hand, 
can be reproduced using the contribution of high frequency phonons related with the acoustic transverse 
harmonics. These results suggest that under resonance conditions, such acoustic transverse modes define 
the line shape for a small size correlation region diameter. This study provides a new application of SCM to 
estimate the size grain of a surface where this information is not available.  
 
Keywords: Roughness, Raman Spectroscopy, Acoustic Transverse Phonons, Size Grain.  
 
 PACS numbers: 62.20. – e, 63.20.D-, 62.65. + k 
 
 
                                                          
*jrmolinacon@gmail.com  
1. INTRODUCTION 
 
From the perspective of applications, surface rough-
ness is of much interest as it is directly related to optical 
scattering and resistivity due to grain boundary and 
thickness. Surface roughness and grain size characteri-
zation due to this, are important components to improve 
the electrical performance of materials, but the im-
provements to surface quality depend upon how well the 
surface is understood and how efficiently the characteri-
zation technique is developed. Raman scattering (RS) is 
a powerful probe to obtain information on the vibrational 
states of a solid and it is sensitively influenced by the 
surface. As a fast and non-destructive technique, RS of 
crystalline semiconductors has been successfully em-
ployed to determine sample qualities such as surface 
conditions, homogeneity and microcrystallinity [1]. Ra-
man peaks broadness and shift, are effects that are not 
completely understood using excitation energy around 
the fundamental energy band gap E0 of materials. In 
semiconductors materials several phenomena may ap-
pear. For example, acoustic phonon, cascade effect, hy-
per-Raman and folded-phonon doublets of acoustic 
modes [2,3]. The appearance of these effects is normally 
attributed to structures generated by superlattices, layer 
thickness fluctuations, limited phonon confinement 
zones, surface roughness and imperfect samples [1,2]. 
These effects are commonly attached to a partial break-
down of crystal-momentum conservation laws (q ≠ 0) [4]. 
Knowing the phonon dispersion curves of the vibrating 
modes due the space correlation zone and the natural 
width of the peaks, the Space Correlation Model (SCM) 
[5-7] can be used to describe the Raman peak behav-
iours. The SCM assumes a Lorentzian peak line shape 
with a Gaussian attenuation factor that plays an im-
portant role as the crystal size or space correlation zone 
becomes smaller. The fittings achieved using the SCM in 
semiconductors materials are generally in good agree-
ment with the experimental measuring even when shifts 
and asymmetrical broadenings occur. This fact is due to 
the crystal size decrease, what suggests that a partial 
breakdown of the selection rules allows such behaviours. 
In a previous work it was shown that there is a direct 
correlation between the line shape of the Raman spectra 
and the surface roughness when it is used a laser with 
excitation energy around the fundamental energy band 
gap E0 of the analysed sample [8]. In this work we report 
results of the application of the SCM to the Raman spec-
tra obtained for CdTe with an excitation wavelength of 
830 nm in order to explain the effect of the grain size in 
the Raman spectra under resonance conditions. 
 
2. EXPERIMENTAL DETAILS 
 
CdTe is an II-VI cubic semiconducting compound 
with zinc blende-type symmetry and an energy gap of 
1.51 eV at room temperature. The bulk sample used in 
this experiment was a (001) oriented undoped commer-
cial wafer, single side polish from Bertram Laboratories. 
The sample surfaces were cleaned before the experiment 
with methanol and the experiment was done at room 
temperature. The Raman spectra was measured using a 
micro-Raman (Ranishaw system 1000B) with a 600 
lines/mm grating, a CCD camera (Rem Cam 1024×256 
pixels), which focus its 830 nm wavelength laser beam in 
a back scattering geometry [9], with a spot-size of about 
2 μm onto the sample, with a 50×objective of a Leica 
(DMLM) microscope. A Notch filter was allocated be-
tween the optical way of the laser and the microscope in 
order to suppress the Anti-Stokes contribution due the 
frequencies lower than 130 cm-1. The calibration of the 
instrument was done using the 520 cm−1 Raman line of a 
silicon wafer and for the data acquisition it was used the 
Grams software. The experimental set up used to study 
the surface morphology and to obtain the mean rough-
ness was an Atomic Force Microscope (Digital Instru-
ments, Dimension 3100). 
 J.R. MOLINA-CONTRERAS, ET. AL PROC. NAP 4, 01PCSI01 (2015) 
 
 
01PCSI01-2 
3. RESULTS AND DISCUSSION  
 
Figures 1(a) and 2(a) show that the Raman line 
shape of CdTe is sensitively influenced by the surface 
boundary conditions when it is measured under reso-
nance conditions. As the experimental Raman line 
shape for a surface with a 6 nm RMS roughness exhib-
its a strong asymmetric behaviour characterized by a 
significant line width of around 200 cm-1, the line shape 
for a surface with a 430 nm RMS roughness, is charac-
terized by the sharp peaks of the first and second LO 
phonon modes of CdTe. These experimental results 
clearly show that the first-order Raman peaks are in-
verse size-dependent asymmetric broadening due to   
the roughness when the excitation energy is around the 
fundamental energy band gap E0 of the material. That 
is, the greatest the roughness, the least the size-
dependent asymmetric broadening.  
Our results also show that as the size grain in-
creases, the Raman spectra are sharper, contrary to the 
expected behaviour for a crystalline sample. To gain 
further insight into the inverse size-dependent asym-
metric broadening due to the roughness; we carried out 
simulations of the Raman spectra using the SCM mod-
el. This model is based in the space confinement region 
of the phonon in the crystal, due to the decrease of 
volume, or the space correlation size. It can be consider 
that regarding the roughness, the phonon cannot pene-
trate beyond the rough surface surrounded by the bulk 
crystal, where phonon can be represented by a plane-
wake-like function; having a spatial extension over the 
whole crystal which can be considered infinite. This 
way, the confinement of the phonon, within the volume 
of the roughness, results in the relaxation of the con-
servation of crystal momentum. In the process of crea-
tion and decay of phonons, the relaxation of the q  0 
selection rule results in the appearance of additional 
contributions of phonons with q ≠ 0, which in turn, 
leads to asymmetric broadening. See the CdTe AFM 
images in Figure 3. 
The solid line in Figure 1(a) shows the result of the 
simulation of the Raman spectrum for the 6 nm RMS 
roughness. For the simulation, we considered that the 
propagation of a confined phonon, due to the rough-
ness, has a Gaussian weighting function as: 
 
   2 2exp 4q L   (1) 
 
And that the total Raman intensity at a frequency  is 
given by [7]:  
 
    
   

 

    

31
2 2
2
0
0
~ exp 4
0.5
d q
I q L
q
  (2) 
 
where L is the correlation region diameter (crystal size 
in Å), q is the wave vector expressed in 2/a units, a is 
the lattice constant (Å),Г0 is the full-width at half-
maxima (FWHM) (cm-1) of the unperturbed Raman  
peak and (q) is the phonon dispersion curve for CdTe. 
 
 
0.0
0.2
0.4
0.6
0.8
1.0
150 200 250 300 350
C
TA
11
C
TA
10
C
TA
9
C
TA
8
C
TA
7
 experimental
 calculated
(b)
 
N
o
rm
a
li
z
e
d
 I
n
te
n
s
it
y
Raman Shift (cm
-1
)
RMS: 6nm
L=5
(a)
C
TA
6
150 200 250 300 350
1.0
0.8
0.6
0.4
0.2
0.0
10TA9TA8TA7TA6TA
 
q
(2

/a
)
LO
2LO
TO
2TO
5TA
 
 
Fig. 1 – (a) Experimental Resonant Raman spectra of 6 nm 
RMS roughness CdTe surface (dots) and best fit calculated 
using SCM extended (continuous line). (b) Phonon dispersion 
curves used in the simulation of the experimental resonant 
Raman spectra. 
0.0
0.2
0.4
0.6
0.8
1.0
150 200 250 300 350
(b)
 experimental
 calculated
 
N
o
rm
a
li
z
e
d
 I
n
te
n
s
it
y
Raman Shift (cm
-1
)
LO
2LO
2TO
RMS: 430nm
L=100
(a)
150 200 250 300 350
1.0
0.8
0.6
0.4
0.2
0.0
 
 
q
(2

/a
)
LO 2LOTO 2TO
 
 
Fig. 2 – (a) Experimental Resonant Raman spectra of 430 nm 
RMS roughness CdTe surface (dots) and best fit calculated 
using SCM (continuous line). (b) LO and TO phonon 
dispersion curves used in the simulation of the experimental 
resonant Raman spectra. 
 CDTE RAMAN LINE SHAPE IN RESONANCE: A SPACE CORRELATION… PROC. NAP 4, 01PCSI01 (2015) 
 
 
01PCSI01-3 
 
 
 
Fig. 3 – (j) CdTe AFM image 6nm mean roughness (n) CdTe 
AFM image 430nm mean roughness (back of the sample). 
 
The asymmetrical broadening and the Raman 
shifts allowed by the phonon dispersion curves, even for 
the small space correlation size, do not contribute to 
the whole Raman spectra in the overlap wing zone. So, 
the whole spectrum is reproduced using the transversal 
acoustic (TA) mode and its harmonic mode contribu-
tion. These harmonics were included into the sum of 
the integrals. The phonon dispersion curves used were 
of the form: 
 
 35n + 98.38q – 63.81q2 (3) 
 
Where n is the harmonic of the TA mode. This consid-
eration was done because it is possible to observe the 
acoustic modes in the Raman spectra using an excita-
tion wavelength around the energy gap of the sample. 
The solid curve shown in Figure 1(a) is the fitted line 
shape for L = 5 (finite crystal) obtained by applying Eq. 
(2) and the phonon dispersion curves shown in Figure 
1(b). In Figure 1(a), it is evident that the inclusion of 
higher harmonic modes, improves the total fitting qual-
ity. The weight factor constants 𝐶𝑖
𝑇𝐴(for 𝑖 = 5 − 11) 
associated to the  intensities of each harmonic mode, 
obeys an exponential decreasing line shape as it is 
shown in Fig. 1(a) (dashed line). This is in accordance 
with the reported in [10]. 
The solid line in Figure 2(a) shows the result of the 
simulation of the Raman spectrum for a 430 nm RMS 
roughness. The continuous curve shown in Figure 2(a) 
is the best fitted line shape for L=100 (infinite crystal) 
obtained by applying Eq. (2) and using the phonon 
dispersion curves: (q) = 154.5 + 14.5cos(q) and 
(q) = 144 + 4cos(q) for the LO and TO in the →X 
transition branches respectively. For the second har-
monic peaks of the LO and TO in the →X transitions 
branches, the phonon dispersion curves used for CdTe 
ware (q) = 320 + 15.5cos(q) and (q) = 280 + 4cos(q)  
respectively. Figure 2(b) shows the shape of the disper-
sion curves used for the simulation. This simulation 
indicates a very good agreement but a very clear differ-
ence for the one obtained for a 6 nm RMS roughness. 
The modes which contribute in each case are clearly 
different. 
 
4. CONCLUSIONS  
 
The simulations of the Raman spectrum for a 6 nm 
RMS roughness; indicate that the TA harmonic modes 
strongly contribute to the Raman line shape. This is not 
the case for a surface with a RMS of 430 nm, which can 
be characterized just by the two intense sharp LO and 
2LO peaks of CdTe. In principle, this effect can be used 
to know the surface morphological state of a material. 
Besides to suggest that the Raman line shape is di-
rectly determined by the size of the grain on the surface 
of the material, our results indicate that the Space Cor-
relation Model has to include the TA harmonic modes. 
 
AKNOWLEDGEMENTS 
 
Authors are grateful to M. Rojas for information 
facilitated. 
 
 
REFERENCES 
 
1. M. Holtz, R. Zallen, Phys. Rev. B 38 9, 6097 (1988). 
2. V.F. Sapega, First International Workshop on Semiconduc-
tor Nanocrystals, SEMINANO 2005, September 10-12, 
2005, Budapest, Hungary, 213 (2005). 
3. R.M. Martin, C.M. Varma, Phys. Rev. Lett. 26 No20, 1241 
(1971).  
4. H. Ritchter, Z.P. Wang, L. Ley, Solid State Commun. 39, 
625 (1981). 
5. Md.N. Islam, Satyendra Kumar, Appl. Phys. Lett. 78 No6, 
715 (2001). 
6. Md. Nazrul Islam, Asima Pradhan, Satyendra Kumar, 
Appl. Phys. Lett. 98, 024309 (2005). 
7. K.K. Tiong, P.M. Amirtharaj, F. H. Pollak, D. E. Aspnes, 
Appl. Phys. Lett. 44, 1, 122 (1984). 
8. C. Frausto-Reyes, J. Rafael Molina-Contreras, C. Medina-
Gutiérrez, Sergio Calixto, Spectrochim. Acta Part A 65 51 
(2006). 
9. G. Turrel, M. Delhaye, P. Dhamelincourt, Raman Micros-
copy, Developments and Applications, (Eds. G. Turrel, J. 
Corset) (London: Academic Press: 1996). 
10. P.H. Tan, D. Bougeard, G. Abstreiter, and K. Brunner, 
Appl. Phys. Lett. 84 No14, 2632 (2004). 
 


CdTe Raman Line Shape in Resonance: a Space Correlation Zone Study

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 4 No 1, 01PCSI01(3pp) (2015)   2304-1862/2015/4(1)01PCSI01(3) 01PCSI01-1  2015 Sumy State University CdTe Raman Line Shape in Resonance: a Space Correlation Zone Study  J.R. Molina-Contreras1,*, C. Frausto-Reyes2, C.I. Medel-Ruíz3, H. Pérez Ladrón de Guevara3  1 Instituto Tecnológico de Aguascalientes, Av. A. López Mateos 1801 Oriente, 20256 Aguascalientes, Ags., México  2 Centro de Investigaciones en Óptica, Unidad Aguascalientes,  Prolongación Constitución 607, Apartado postal 507, 20200 Aguascalientes, Ags., México 3 Centro Universitario de los Lagos, Universidad de Guadalajara,  Av. Enrique Díaz de León s/n, 47460 Lagos de Moreno, Jalisco, México  (Received 15 March 2015; published online 22 August 2015)  We show that the line shape of resonant Raman spectra of CdTe can be reproduced using the spatial correlation model (SCM). Our results show that the resonant Raman spectrum for a surface with a RMS of 430 nm is characterized by the presence of two intense sharp peaks located at frequencies corresponding to LO and 2LOmodes. The resonant Raman spectrum for a surface with a RMS of 6 nm on the other hand, can be reproduced using the contribution of high frequency phonons related with the acoustic transverse harmonics. These results suggest that under resonance conditions, such acoustic transverse modes define the line shape for a small size correlation region diameter. This study provides a new application of SCM to estimate the size grain of a surface where this information is not available.   Keywords: Roughness, Raman Spectroscopy, Acoustic Transverse Phonons, Size Grain.    PACS numbers: 62.20. – e, 63.20.D-, 62.65. + k                                                             *jrmolinacon@gmail.com  1. INTRODUCTION  From the perspective of applications, surface rough-ness is of much interest as it is directly related to optical scattering and resistivity due to grain boundary and thickness. Surface roughness and grain size characteri-zation due to this, are important components to improve the electrical performance of materials, but the im-provements to surface quality depend upon how well the surface is understood and how efficiently the characteri-zation technique is developed. Raman scattering (RS) is a powerful probe to obtain information on the vibrational states of a solid and it is sensitively influenced by the surface. As a fast and non-destructive technique, RS of crystalline semiconductors has been successfully em-ployed to determine sample qualities such as surface conditions, homogeneity and microcrystallinity [1]. Ra-man peaks broadness and shift, are effects that are not completely understood using excitation energy around the fundamental energy band gap E0 of materials. In semiconductors materials several phenomena may ap-pear. For example, acoustic phonon, cascade effect, hy-per-Raman and folded-phonon doublets of acoustic modes [2,3]. The appearance of these effects is normally attributed to structures generated by superlattices, layer thickness fluctuations, limited phonon confinement zones, surface roughness and imperfect samples [1,2]. These effects are commonly attached to a partial break-down of crystal-momentum conservation laws (q ≠ 0) [4]. Knowing the phonon dispersion curves of the vibrating modes due the space correlation zone and the natural width of the peaks, the Space Correlation Model (SCM) [5-7] can be used to describe the Raman peak behav-iours. The SCM assumes a Lorentzian peak line shape with a Gaussian attenuation factor that plays an im-portant role as the crystal size or space correlation zone becomes smaller. The fittings achieved using the SCM in semiconductors materials are generally in good agree-ment with the experimental measuring even when shifts and asymmetrical broadenings occur. This fact is due to the crystal size decrease, what suggests that a partial breakdown of the selection rules allows such behaviours. In a previous work it was shown that there is a direct correlation between the line shape of the Raman spectra and the surface roughness when it is used a laser with excitation energy around the fundamental energy band gap E0 of the analysed sample [8]. In this work we report results of the application of the SCM to the Raman spec-tra obtained for CdTe with an excitation wavelength of 830 nm in order to explain the effect of the grain size in the Raman spectra under resonance conditions.  2. EXPERIMENTAL DETAILS  CdTe is an II-VI cubic semiconducting compound with zinc blende-type symmetry and an energy gap of 1.51 eV at room temperature. The bulk sample used in this experiment was a (001) oriented undoped commer-cial wafer, single side polish from Bertram Laboratories. The sample surfaces were cleaned before the experiment with methanol and the experiment was done at room temperature. The Raman spectra was measured using a micro-Raman (Ranishaw system 1000B) with a 600 lines/mm grating, a CCD camera (Rem Cam 1024×256 pixels), which focus its 830 nm wavelength laser beam in a back scattering geometry [9], with a spot-size of about 2 μm onto the sample, with a 50×objective of a Leica (DMLM) microscope. A Notch filter was allocated be-tween the optical way of the laser and the microscope in order to suppress the Anti-Stokes contribution due the frequencies lower than 130 cm-1. The calibration of the instrument was done using the 520 cm−1 Raman line of a silicon wafer and for the data acquisition it was used the Grams software. The experimental set up used to study the surface morphology and to obtain the mean rough-ness was an Atomic Force Microscope (Digital Instru-ments, Dimension 3100).  J.R. MOLINA-CONTRERAS, ET. AL PROC. NAP 4, 01PCSI01 (2015)   01PCSI01-2 3. RESULTS AND DISCUSSION   Figures 1(a) and 2(a) show that the Raman line shape of CdTe is sensitively influenced by the surface boundary conditions when it is measured under reso-nance conditions. As the experimental Raman line shape for a surface with a 6 nm RMS roughness exhib-its a strong asymmetric behaviour characterized by a significant line width of around 200 cm-1, the line shape for a surface with a 430 nm RMS roughness, is charac-terized by the sharp peaks of the first and second LO phonon modes of CdTe. These experimental results clearly show that the first-order Raman peaks are in-verse size-dependent asymmetric broadening due to   the roughness when the excitation energy is around the fundamental energy band gap E0 of the material. That is, the greatest the roughness, the least the size-dependent asymmetric broadening.  Our results also show that as the size grain in-creases, the Raman spectra are sharper, contrary to the expected behaviour for a crystalline sample. To gain further insight into the inverse size-dependent asym-metric broadening due to the roughness; we carried out simulations of the Raman spectra using the SCM mod-el. This model is based in the space confinement region of the phonon in the crystal, due to the decrease of volume, or the space correlation size. It can be consider that regarding the roughness, the phonon cannot pene-trate beyond the rough surface surrounded by the bulk crystal, where phonon can be represented by a plane-wake-like function; having a spatial extension over the whole crystal which can be considered infinite. This way, the confinement of the phonon, within the volume of the roughness, results in the relaxation of the con-servation of crystal momentum. In the process of crea-tion and decay of phonons, the relaxation of the q  0 selection rule results in the appearance of additional contributions of phonons with q ≠ 0, which in turn, leads to asymmetric broadening. See the CdTe AFM images in Figure 3. The solid line in Figure 1(a) shows the result of the simulation of the Raman spectrum for the 6 nm RMS roughness. For the simulation, we considered that the propagation of a confined phonon, due to the rough-ness, has a Gaussian weighting function as:     2 2exp 4q L   (1)  And that the total Raman intensity at a frequency  is given by [7]:               312 2200~ exp 40.5d qI q Lq  (2)  where L is the correlation region diameter (crystal size in Å), q is the wave vector expressed in 2/a units, a is the lattice constant (Å),Г0 is the full-width at half-maxima (FWHM) (cm-1) of the unperturbed Raman  peak and (q) is the phonon dispersion curve for CdTe.   0.00.20.40.60.81.0150 200 250 300 350CTA11CTA10CTA9CTA8CTA7 experimental calculated(b) Normalized IntensityRaman Shift (cm-1)RMS: 6nmL=5(a)CTA6150 200 250 300 3501.00.80.60.40.20.010TA9TA8TA7TA6TA q(2/a)LO2LOTO2TO5TA  Fig. 1 – (a) Experimental Resonant Raman spectra of 6 nm RMS roughness CdTe surface (dots) and best fit calculated using SCM extended (continuous line). (b) Phonon dispersion curves used in the simulation of the experimental resonant Raman spectra. 0.00.20.40.60.81.0150 200 250 300 350(b) experimental calculated Normalized IntensityRaman Shift (cm-1)LO2LO2TORMS: 430nmL=100(a)150 200 250 300 3501.00.80.60.40.20.0  q(2/a)LO 2LOTO 2TO  Fig. 2 – (a) Experimental Resonant Raman spectra of 430 nm RMS roughness CdTe surface (dots) and best fit calculated using SCM (continuous line). (b) LO and TO phonon dispersion curves used in the simulation of the experimental resonant Raman spectra.  CDTE RAMAN LINE SHAPE IN RESONANCE: A SPACE CORRELATION… PROC. NAP 4, 01PCSI01 (2015)   01PCSI01-3    Fig. 3 – (j) CdTe AFM image 6nm mean roughness (n) CdTe AFM image 430nm mean roughness (back of the sample).  The asymmetrical broadening and the Raman shifts allowed by the phonon dispersion curves, even for the small space correlation size, do not contribute to the whole Raman spectra in the overlap wing zone. So, the whole spectrum is reproduced using the transversal acoustic (TA) mode and its harmonic mode contribu-tion. These harmonics were included into the sum of the integrals. The phonon dispersion curves used were of the form:   35n + 98.38q – 63.81q2 (3)  Where n is the harmonic of the TA mode. This consid-eration was done because it is possible to observe the acoustic modes in the Raman spectra using an excita-tion wavelength around the energy gap of the sample. The solid curve shown in Figure 1(a) is the fitted line shape for L = 5 (finite crystal) obtained by applying Eq. (2) and the phonon dispersion curves shown in Figure 1(b). In Figure 1(a), it is evident that the inclusion of higher harmonic modes, improves the total fitting qual-ity. The weight factor constants 𝐶𝑖𝑇𝐴(for 𝑖 = 5 − 11) associated to the  intensities of each harmonic mode, obeys an exponential decreasing line shape as it is shown in Fig. 1(a) (dashed line). This is in accordance with the reported in [10]. The solid line in Figure 2(a) shows the result of the simulation of the Raman spectrum for a 430 nm RMS roughness. The continuous curve shown in Figure 2(a) is the best fitted line shape for L=100 (infinite crystal) obtained by applying Eq. (2) and using the phonon dispersion curves: (q) = 154.5 + 14.5cos(q) and (q) = 144 + 4cos(q) for the LO and TO in the →X transition branches respectively. For the second har-monic peaks of the LO and TO in the →X transitions branches, the phonon dispersion curves used for CdTe ware (q) = 320 + 15.5cos(q) and (q) = 280 + 4cos(q)  respectively. Figure 2(b) shows the shape of the disper-sion curves used for the simulation. This simulation indicates a very good agreement but a very clear differ-ence for the one obtained for a 6 nm RMS roughness. The modes which contribute in each case are clearly different.  4. CONCLUSIONS   The simulations of the Raman spectrum for a 6 nm RMS roughness; indicate that the TA harmonic modes strongly contribute to the Raman line shape. This is not the case for a surface with a RMS of 430 nm, which can be characterized just by the two intense sharp LO and 2LO peaks of CdTe. In principle, this effect can be used to know the surface morphological state of a material. Besides to suggest that the Raman line shape is di-rectly determined by the size of the grain on the surface of the material, our results indicate that the Space Cor-relation Model has to include the TA harmonic modes.  AKNOWLEDGEMENTS  Authors are grateful to M. Rojas for information facilitated.   REFERENCES  1. M. Holtz, R. Zallen, Phys. Rev. B 38 9, 6097 (1988). 2. V.F. Sapega, First International Workshop on Semiconduc-tor Nanocrystals, SEMINANO 2005, September 10-12, 2005, Budapest, Hungary, 213 (2005). 3. R.M. Martin, C.M. Varma, Phys. Rev. Lett. 26 No20, 1241 (1971).  4. H. Ritchter, Z.P. Wang, L. Ley, Solid State Commun. 39, 625 (1981). 5. Md.N. Islam, Satyendra Kumar, Appl. Phys. Lett. 78 No6, 715 (2001). 6. Md. Nazrul Islam, Asima Pradhan, Satyendra Kumar, Appl. Phys. Lett. 98, 024309 (2005). 7. K.K. Tiong, P.M. Amirtharaj, F. H. Pollak, D. E. Aspnes, Appl. Phys. Lett. 44, 1, 122 (1984). 8. C. Frausto-Reyes, J. Rafael Molina-Contreras, C. Medina-Gutiérrez, Sergio Calixto, Spectrochim. Acta Part A 65 51 (2006). 9. G. Turrel, M. Delhaye, P. Dhamelincourt, Raman Micros-copy, Developments and Applications, (Eds. G. Turrel, J. Corset) (London: Academic Press: 1996). 10. P.H. Tan, D. Bougeard, G. Abstreiter, and K. Brunner, Appl. Phys. Lett. 84 No14, 2632 (2004).  

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CdTe Raman Line Shape in Resonance: a Space Correlation Zone Study

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SocioEconomic Challenges Journal (Sumy State University)

Electronic Sumy State University Institutional Repository