Single crystal samples of PbTe doped with PbI2 were made using the Bridgman technique. Far infrared reflectivity diagrams of PbTe doped with 0.4 at% and 0.6 at% Iodine were measured and numerically analyzed. A plasma resonance at about 650 cm(-1) with the reflectivity minima very close to zero was observed for both samples. Thermal diffusivity was determined for the same samples using the photoacoustic method with a transmission detection configuration and the values of the minority free carrier (holes) mobility were calculated

Aleksić, Obrad S.

Blagojevic, V.

Nikolic, N.

Nikolic, P. M.

Nikolić, Maria Vesna

Paraskevopoulos, Konstantinos M.

Radovanović, M.

Vasiljević-Radović, Dana

Vujatovic, S. S.

Zorba, T. T.

Paraskevopoulos, K. M.

 CER - Central Repository of the Institute of Chemistry;  Technology and Metallurgy

OPTOELECTRONICS AND ADVANCED MATERIALS – RAPID COMMUNICATIONS                  Vol. 6, No. 3-4, March - April 2012, p. 352 - 356 
 
Far infrared and photoacoustic characterization of iodine 
doped PbTe 
 
P. M. NIKOLIĆ*, K. M. PARASKEVOPOULOSa, O. S. ALEKSIĆb, S. S. VUJATOVIĆ, D. VASILJEVIĆ-RADOVIĆc, 
T. T. ZORBA
a, V. BLAGOJEVIĆd,  N. NIKOLICb, M. RADOVANOVIĆe, M. V. NIKOLIĆb 
Institute of Technical Science of SASA, Knez Mihailova 35, Belgrade, Serbia 
a
Physics Department, Solid State Section, Aristotle University, Thessaloniki, Greece 
b
Institute for Multidiciplinary Research, University of Belgrade, Kneza Višeslava 1, Belgrade, Serbia 
c
ICTM-Centre of Microelectronic Technologies and Single Crystals, University of Belgrade, Njegoševa 12,  
Belgrade, Serbia 
d
Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia 
e
Faculty of Technical Sciences,University of Novi Sad, Novi Sad, Serbia 
 
 
 
Single crystal samples of PbTe doped with PbI2 were made using the Bridgman technique. Far infrared reflectivity diagrams 
of PbTe doped with 0.4 at% and 0.6 at% Iodine were measured and numerically analyzed. A plasma resonance at about 
650 cm
-1
 with the reflectivity minima very close to zero was observed for both samples. Thermal diffusivity was determined 
for the same samples using the photoacoustic method with a transmission detection configuration and the values of the 
minority free carrier (holes) mobility were calculated. 
 
(Received December 29, 2011; accepted April 11, 2012) 
 
Keywords: Doped Semiconductors, Far Infrared Reflectivity, Photoacoustic Characterization. 
 
 
 
1. Introduction 
 
Recent publications have focused on revaluation of 
PbTe1-xIx as a high performance thermoelectric material 
[1]. A large figure of merit (ZT) of 1.4 in the temperature 
range between 700 K and 850 K was confirmed, which is 
much larger than the value usually referenced for this 
material. One should say also that a higher value of the 
thermoelectric figure of merit, above 2, was recently 
reported for PbTe doped with both chromium and iodine 
[2]. 
The solubility of Iodine in lead telluride is rather high. 
Halogen solubility in PbTe1-xHalx increases similarly to the 
atomic weight of Cl, Br and I e.g. Xcl0.03, XBr0.07 and 
XI0.09 [3]. 
Doping PbTe with PbI2, Al or Zr in order to optimize 
the carrier concentration of functional gradient materials 
was also investigated [4]. Far infrared properties of PbTe 
doped with Hg were investigated in [5]. 
In literature, as far as we know, there is no published 
infrared optical reflectivity data on PbTe doped with 
Iodine. So, in this work we have studied far and mid 
infrared optical reflectivity properties of PbTe doped with 
PbI2. We also investigated thermal and electronic transport 
properties of the same PbTe + I samples using a 
photoacoustic (PA) method with the transmission 
detection configuration [6]. 
 
 
 
 
2. Experimental 
 
Single crystal samples of PbTe1-xIx were prepared 
from elementary tellurium of 99.999% purity, lead metal 
of 99.999% and PbI2 of 99.998% purity. Since  La Londe 
et al [1] showed that the Seebeck coefficient fot PbTe1-xIx  
has the highest values for x between 0.01 and 0.0055 we 
made a sample starting with x = 0.01 using the standard 
Bridgman method [7]. The produced ingot was a single 
crystal with a sharp beginning of about 2 mm and useful 
ingot with a diameter of about 8 mm where the 
composition was about 0.6 at.% I that gradually decreased 
approaching the upper end to 0.4 at.% I. Samples were 
cleaved or cut from the ingot and then highly polished 
before they were used for structural, optical and 
photoacoustic measurements. X-ray diffraction of samples 
was used to prove that each sample was single crystal. 
EDS analysis (INCA Penta EDS system attached to a 
TESCAN VEGA TS 5130MM Electron Microscope) was 
used to determine the content of Pb, Te and I in each 
sample. It was proved that the concentration of Iodine 
slightly decreased from the top to the end of the ingot. 
Microstructural characterization was done by AFM 
(Thermo Microscopes, Autoprobe CP Research). All 
measurements were performed in the non-contact mode 
using a rectangular silicon cantilever (resonant frequency 
in the range 250-300 kHz, spring constant in the range 30-
80 N/m). Far infrared reflectivity spectra of the PbTe 
samples doped with 0.6 at% - 0.4 at% of I were measured 
at room temperature using a Bruker IFS -113 V 
spectrometer. Photoacoustic (PA) amplitude and phase 
Far infrared and photoacoustic characterization of iodine doped PbTe                                               353                                                 
 
spectra of the same samples were measured using a 
photoacoustic cell protected against the surrounding 
influence [8] and the experimental setup was described 
elsewhere [9]. 
 
 
3. Results and discussion 
 
AFM images of the analyzed PbTe samples doped 
with Iodine are given in Fig. 1. One can see that the 
surface has relatively homogenous grains. 
 
 
(a) 
 
(b) 
 
Fig. 1. AFM image of a PbTe sample doped with 0.4 at%  
I (a) 3D surface view; (b) 2D planar view. 
 
Room temperature FIR reflectivity diagrams for two 
PbTe+I samples, one from the beginning and the other 
near the end of the ingot are given in Fig. 2a and Fig. 2b. 
For these samples a reflectivity minimum was observed at 
about 640 cm
-1 
and 650 cm
-1
, respectively. Reflectivity 
minima (Rmin) for both cases were approaching zero e.g. 
they were at about 0.01 and 0.02 respectively. The 
frequency marked by an arrow in Fig. 2a and Fig. 2b 
represents the position of the coupled Plasmon – 
longitudinal phonon (LO) modes. These experimental 
diagrams were numerically analyzed using the four 
parameter model introduced by Gervais and Piriou [10] 
and the optical parameters (plasma frequency - p and its 
damping factor - ) were determined. Their values for the 
mentioned two samples are given in Table 1. The values of 
their error bars were less than 1 cm
-1
. The optical mobility 
(opt) of the free carriers was calculated using the method 
of Moss et al. [11] and is also given in Table 1. 
 
 
(a) 
 
 
(b) 
 
Fig. 2. Room temperature IR reflectivity diagrams for  
PbTe doped with 0.6 at.% I (a) and 0.4 at.% I (b). 
 
 
Table 1. Optical parameters determined for PbTe+I 
samples (Rmin – reflectivity minima; p – plasma 
frequency;  - damping factor for plasma frequency; opt  
                – optical mobility of free carriers). 
 
PbTe +I at% I Rmin p 
[cm
-1
] 
  
[cm
-1
] 
µopt         
[ cm
2
/Vs] 
Pb5 
beginning 
0.6 0.01 637 72.1 600 
Pb6 end 0.4 0.02 638 57 633 
 
The values of free carrier mobility were also 
calculated by fitting photoacoustic measurements. The 
amplitude and phase spectra of these samples were 
measured using a specially constructed PA cell which had 
an optimized acoustic protection from the surrounding 
influence [12]. The optical source was a red laser (80 
mW), which was modulated by a mechanical chopper. The 
354                      P. M. Nikolić, K. M. Paraskevopoulos, O. S. Aleksić, S. S. Vujatović, D. Vasiljević-Radović, T. T. Zorba ...            
 
sample was irradiated by a spot 3 mm in diameter and it 
was mounted directly on the front of the electrets 
microphone. Both amplitude and phase spectra of the PA 
signals for both samples were measured for two different 
plate thicknesses. The initial thickness of sample 1 was 
1.265 mm and then it was made thinner to 0.93 mm. The 
sample 2 was measured when it was 1.14 mm thick and 
after it was made thinner to 0.835 mm, and measured 
again. The different thicknesses were obtained by 
polishing one side of the thick plate with diamond paste 
and the other side was at first only flattened with silicon 
carbide with 1 µm grade and then made thinner. That 
surface was always illuminated with the modulated laser 
beam, while the side which was polished with diamond 
paste was always put on the front of the electrets’ 
microphone. The measured amplitude and phase PA 
signals, versus the modulation frequency, for both samples 
are given in Fig. 3a and Fig. 3b, respectively. These 
measurements for two samples thicknesses were necessary 
for normalization of the PA amplitude and phase spectra 
as the sensitivity of the electrets’ microphone decreases in 
the frequency range below 100 Hz, so we used the signal 
ratio for two different thicknesses of each measured 
sample. Beginning with the Rosencwaig-Gersho thermal 
piston model [13] the PA signal S(-l, ) can be given with 
the following equation: 
 
 
 
blo
o
lkT
lP
lS


,
,

                          (1) 
 
where  is the adiabatic constant; Po and To are the ambient 
pressure and temperature, respectively; kl=(1+j)/µb, where 
µb is the thermal diffusion length of the backing gas and lb 
is the distance between the sample and the microphone. 
Finally  (-l, ) is the periodic temperature variation of 
the rear sample surface. The PA signal for two 
measurements and two different sample thicknesses can be 
normalized taking the signal ratio using the equation: 
 


  







 jm
llj
eAe
l
l
S
S )]()(([
2
1
2
1 2211
)(
)(
)(
)(
   (2) 
 
where  (-l)  is the temperature distribution on the surface 
of the sample put in contact with the electrets microphone; 
Am is the amplitude ratio and  is the phase difference of 
the measured PA signals for two different sample 
thicknesses of the same sample. 
 
 
 
            
(a)                                                                                                (b) 
 
Fig. 3. PA amplitude (a) and phase spectra (b) for PbTe  doped with 0.6 at.% I for two different sample thicknesses. 
 
 
The amplitude ratio and phase difference of fitted 
diagrams for sample 2 and its two different thicknesses are 
given in Fig. 4a and Fig. 4b respectively. Values of the 
fitted parameters obtained during the fitting procedure for 
both sample 1 and sample 2 and their two normalized PA 
spectra are given in Table 2. The values of the following 
parameters were calculated: thermal diffusion coefficient 
(DT), excess carrier life time (), the hole diffusion 
coefficient (D) and optical absorption coefficient () the 
calculated mobility of hole carriers (µh). 
 
Far infrared and photoacoustic characterization of iodine doped PbTe                                               355                                                 
 
                        
(a)                                                                                          (b) 
Fig. 4. Experimental (points) and theoretically calculated (full line) PA amplitude (a) and phase difference (b) spectra of  
PbTe doped with 0.4 at.% I. 
 
 
Table 2. Thermal parameters determined for PbTe+I samples. 
 
Sample I [at%] DT [m
2/s]  [µs] D[m2/s]  [m-1] µh[cm
2/Vs] 
Sample 1 
1.26mm/0.93 mm 
0.6 0.204 10-5 0.041 0.26610-2 8647 1030 
Sample 2 
1.14mm/0.835 mm 
0.4 0.19 10-5 0.106 0.42310-2 30604 1640 
 
The calculated values of the hole mobility are higher 
than for pure PbTe, and they are in agreement with the 
diagrams of room temperature carrier concentration 
dependence of Hall mobility for PbTe1-xIx given by La 
Londe et al. [1]. They determined maximum hole mobility 
of about 2000 cm
2
/Vs responding to carrier concentrations 
of free holes of about 10
19 
cm
-3
. Since the thermal 
diffusivity coefficient (DT) decreases when the atomic 
percentage of Iodine in PbTe decreases from 0.6 at% to 
0.4 at% we can conclude that it is also in agreement with 
the change of the figure of merit (ZT) given in [1] where 
the best content of I is about 0.12 at%. The above 
conclusion is obvious if we mention that DT=K/dCp, where 
K is the thermal conductivity, Cp is the specific heat and d 
is density. But also having in mind that  
 
)(
2
LE KK
TS
ZT



          (3) 
 
where S, ,KE and Kh are the Seebeck coefficient, 
resistivity and electric and lattice components of thermal 
conductivity, respectively. 
It is obvious that sample 2, doped with 0.4 at% I is 
slightly better than sample 1 doped with 0.6% having the 
hole mobility 1640 cm
2
/Vs. The same sample also has a 
smaller thermal diffusivity coefficient (DT) and thus a 
lower thermal conductivity K. The final result is that, for 
the sample of PbTe doped with 0.4 at% I, the figure of 
merit (ZT) is higher, that is in agreement with the results 
of La Londe [1]. A similar conclusion could be made 
using reference [14]. 
The effect of Iodine content (percentage) in PbTe is 
obviously very important because even the lattice 
parameter of PbTe1-xIx has a non-monotonic function 
having a sharp minimum for a specific value of iodine 
content [15]. It is interesting that the thermoelectric 
properties of a double doped PbTe with Cd and Iodine was 
recently studied by Kyunghan et al [16] investigating 
possible increase of the Seebeck coefficient and they 
found that the optimal PbI2 doping of the PbTe+1 at% 
CdTe for the best ZT was 0.055 mol%. 
Iodine as a dopant in PbTe is mainly considered from 
the aspect of improving thermoelectric properties of PbTe. 
Furthermore, PbTe-Ge [17] and PbTe-Si [18] eutectic 
composites can be doped with PbI2 with a precisely 
controlled carrier concentration. In this work we have 
shown that using optical reflection measurements in the 
plasma frequency resonance range one can get information 
on the concentration and mobility of free carriers. For 
higher free carrier concentrations the plasma minimum 
occurs at higher wave numbers and vice versa. The plasma 
frequency becomes narrower when the free charge carrier 
relaxation time decreases. The high frequency dielectric 
permeability can also be determined from the short wave 
part of the reflection spectrum. Similar properties can be 
obtained using photoacoustic measurements of the same 
samples.  
 
 
4. Conclusion 
 
In this work, as far as we know, far infrared optical 
reflectivity and photoacoustic properties of single crystal 
PbTe samples doped with PbI2 between 0.4 at% I and 0.6 
at% I were measured for the first time. We obtained the 
results which confirm literature data that a small 
percentage of Iodine, much less than 1 at% can 
356                      P. M. Nikolić, K. M. Paraskevopoulos, O. S. Aleksić, S. S. Vujatović, D. Vasiljević-Radović, T. T. Zorba ...            
 
significantly improve thermoelectric and electrical 
properties of this doped semiconductor. From 
photoacosutic spectra we calculated the thermal diffusivity 
and hole diffusion coefficient and finally free hole 
mobility values. For PbTe doped with 0.4 at% I the free 
hole mobility was 1640 cm
2
/Vs. Further decrease of the 
iodine content until an optimal concentration would result 
in further improved thermoelectric and electrical 
properties and possible application as a high performance 
thermoelectric material. 
 
 
Acknowledgements 
 
This work was performed within projects III45007 
and III45014 financed by the Ministry for Science and 
Education of the Republic of Serbia. 
 
 
References 
 
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______________________ 
*Corresponding author: Pantelija.Nikolic@sanu.ac.rs 
 


English

Far infrared and photoacoustic characterization of iodine doped PbTe

Nikolić, Pantelija M.

Paraskevopoulos, K.M.

Aleksić, Obrad

Vujatović, Stevan S

Zorba, T.T.

Blagojević, V.

RIMSI

Central Repository of the Institute of Chemistry, Technology and Metallurgy (CER)

OPTOELECTRONICS AND ADVANCED MATERIALS – RAPID COMMUNICATIONS                  Vol. 6, No. 3-4, March - April 2012, p. 352 - 356  Far infrared and photoacoustic characterization of iodine doped PbTe  P. M. NIKOLIĆ*, K. M. PARASKEVOPOULOSa, O. S. ALEKSIĆb, S. S. VUJATOVIĆ, D. VASILJEVIĆ-RADOVIĆc, T. T. ZORBAa, V. BLAGOJEVIĆd,  N. NIKOLICb, M. RADOVANOVIĆe, M. V. NIKOLIĆb Institute of Technical Science of SASA, Knez Mihailova 35, Belgrade, Serbia aPhysics Department, Solid State Section, Aristotle University, Thessaloniki, Greece bInstitute for Multidiciplinary Research, University of Belgrade, Kneza Višeslava 1, Belgrade, Serbia cICTM-Centre of Microelectronic Technologies and Single Crystals, University of Belgrade, Njegoševa 12,  Belgrade, Serbia dFaculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia eFaculty of Technical Sciences,University of Novi Sad, Novi Sad, Serbia    Single crystal samples of PbTe doped with PbI2 were made using the Bridgman technique. Far infrared reflectivity diagrams of PbTe doped with 0.4 at% and 0.6 at% Iodine were measured and numerically analyzed. A plasma resonance at about 650 cm-1 with the reflectivity minima very close to zero was observed for both samples. Thermal diffusivity was determined for the same samples using the photoacoustic method with a transmission detection configuration and the values of the minority free carrier (holes) mobility were calculated.  (Received December 29, 2011; accepted April 11, 2012)  Keywords: Doped Semiconductors, Far Infrared Reflectivity, Photoacoustic Characterization.    1. Introduction  Recent publications have focused on revaluation of PbTe1-xIx as a high performance thermoelectric material [1]. A large figure of merit (ZT) of 1.4 in the temperature range between 700 K and 850 K was confirmed, which is much larger than the value usually referenced for this material. One should say also that a higher value of the thermoelectric figure of merit, above 2, was recently reported for PbTe doped with both chromium and iodine [2]. The solubility of Iodine in lead telluride is rather high. Halogen solubility in PbTe1-xHalx increases similarly to the atomic weight of Cl, Br and I e.g. Xcl0.03, XBr0.07 and XI0.09 [3]. Doping PbTe with PbI2, Al or Zr in order to optimize the carrier concentration of functional gradient materials was also investigated [4]. Far infrared properties of PbTe doped with Hg were investigated in [5]. In literature, as far as we know, there is no published infrared optical reflectivity data on PbTe doped with Iodine. So, in this work we have studied far and mid infrared optical reflectivity properties of PbTe doped with PbI2. We also investigated thermal and electronic transport properties of the same PbTe + I samples using a photoacoustic (PA) method with the transmission detection configuration [6].     2. Experimental  Single crystal samples of PbTe1-xIx were prepared from elementary tellurium of 99.999% purity, lead metal of 99.999% and PbI2 of 99.998% purity. Since  La Londe et al [1] showed that the Seebeck coefficient fot PbTe1-xIx  has the highest values for x between 0.01 and 0.0055 we made a sample starting with x = 0.01 using the standard Bridgman method [7]. The produced ingot was a single crystal with a sharp beginning of about 2 mm and useful ingot with a diameter of about 8 mm where the composition was about 0.6 at.% I that gradually decreased approaching the upper end to 0.4 at.% I. Samples were cleaved or cut from the ingot and then highly polished before they were used for structural, optical and photoacoustic measurements. X-ray diffraction of samples was used to prove that each sample was single crystal. EDS analysis (INCA Penta EDS system attached to a TESCAN VEGA TS 5130MM Electron Microscope) was used to determine the content of Pb, Te and I in each sample. It was proved that the concentration of Iodine slightly decreased from the top to the end of the ingot. Microstructural characterization was done by AFM (Thermo Microscopes, Autoprobe CP Research). All measurements were performed in the non-contact mode using a rectangular silicon cantilever (resonant frequency in the range 250-300 kHz, spring constant in the range 30-80 N/m). Far infrared reflectivity spectra of the PbTe samples doped with 0.6 at% - 0.4 at% of I were measured at room temperature using a Bruker IFS -113 V spectrometer. Photoacoustic (PA) amplitude and phase Far infrared and photoacoustic characterization of iodine doped PbTe                                               353                                                  spectra of the same samples were measured using a photoacoustic cell protected against the surrounding influence [8] and the experimental setup was described elsewhere [9].   3. Results and discussion  AFM images of the analyzed PbTe samples doped with Iodine are given in Fig. 1. One can see that the surface has relatively homogenous grains.   (a)  (b)  Fig. 1. AFM image of a PbTe sample doped with 0.4 at%  I (a) 3D surface view; (b) 2D planar view.  Room temperature FIR reflectivity diagrams for two PbTe+I samples, one from the beginning and the other near the end of the ingot are given in Fig. 2a and Fig. 2b. For these samples a reflectivity minimum was observed at about 640 cm-1 and 650 cm-1, respectively. Reflectivity minima (Rmin) for both cases were approaching zero e.g. they were at about 0.01 and 0.02 respectively. The frequency marked by an arrow in Fig. 2a and Fig. 2b represents the position of the coupled Plasmon – longitudinal phonon (LO) modes. These experimental diagrams were numerically analyzed using the four parameter model introduced by Gervais and Piriou [10] and the optical parameters (plasma frequency - p and its damping factor - ) were determined. Their values for the mentioned two samples are given in Table 1. The values of their error bars were less than 1 cm-1. The optical mobility (opt) of the free carriers was calculated using the method of Moss et al. [11] and is also given in Table 1.   (a)   (b)  Fig. 2. Room temperature IR reflectivity diagrams for  PbTe doped with 0.6 at.% I (a) and 0.4 at.% I (b).   Table 1. Optical parameters determined for PbTe+I samples (Rmin – reflectivity minima; p – plasma frequency;  - damping factor for plasma frequency; opt                  – optical mobility of free carriers).  PbTe +I at% I Rmin p [cm-1]   [cm-1] µopt         [ cm2/Vs] Pb5 beginning 0.6 0.01 637 72.1 600 Pb6 end 0.4 0.02 638 57 633  The values of free carrier mobility were also calculated by fitting photoacoustic measurements. The amplitude and phase spectra of these samples were measured using a specially constructed PA cell which had an optimized acoustic protection from the surrounding influence [12]. The optical source was a red laser (80 mW), which was modulated by a mechanical chopper. The 354                      P. M. Nikolić, K. M. Paraskevopoulos, O. S. Aleksić, S. S. Vujatović, D. Vasiljević-Radović, T. T. Zorba ...             sample was irradiated by a spot 3 mm in diameter and it was mounted directly on the front of the electrets microphone. Both amplitude and phase spectra of the PA signals for both samples were measured for two different plate thicknesses. The initial thickness of sample 1 was 1.265 mm and then it was made thinner to 0.93 mm. The sample 2 was measured when it was 1.14 mm thick and after it was made thinner to 0.835 mm, and measured again. The different thicknesses were obtained by polishing one side of the thick plate with diamond paste and the other side was at first only flattened with silicon carbide with 1 µm grade and then made thinner. That surface was always illuminated with the modulated laser beam, while the side which was polished with diamond paste was always put on the front of the electrets’ microphone. The measured amplitude and phase PA signals, versus the modulation frequency, for both samples are given in Fig. 3a and Fig. 3b, respectively. These measurements for two samples thicknesses were necessary for normalization of the PA amplitude and phase spectra as the sensitivity of the electrets’ microphone decreases in the frequency range below 100 Hz, so we used the signal ratio for two different thicknesses of each measured sample. Beginning with the Rosencwaig-Gersho thermal piston model [13] the PA signal S(-l, ) can be given with the following equation:    bloolkTlPlS,,                          (1)  where  is the adiabatic constant; Po and To are the ambient pressure and temperature, respectively; kl=(1+j)/µb, where µb is the thermal diffusion length of the backing gas and lb is the distance between the sample and the microphone. Finally  (-l, ) is the periodic temperature variation of the rear sample surface. The PA signal for two measurements and two different sample thicknesses can be normalized taking the signal ratio using the equation:     jmlljeAellSS )]()(([2121 2211)()()()(   (2)  where  (-l)  is the temperature distribution on the surface of the sample put in contact with the electrets microphone; Am is the amplitude ratio and  is the phase difference of the measured PA signals for two different sample thicknesses of the same sample.                (a)                                                                                                (b)  Fig. 3. PA amplitude (a) and phase spectra (b) for PbTe  doped with 0.6 at.% I for two different sample thicknesses.   The amplitude ratio and phase difference of fitted diagrams for sample 2 and its two different thicknesses are given in Fig. 4a and Fig. 4b respectively. Values of the fitted parameters obtained during the fitting procedure for both sample 1 and sample 2 and their two normalized PA spectra are given in Table 2. The values of the following parameters were calculated: thermal diffusion coefficient (DT), excess carrier life time (), the hole diffusion coefficient (D) and optical absorption coefficient () the calculated mobility of hole carriers (µh).  Far infrared and photoacoustic characterization of iodine doped PbTe                                               355                                                                          (a)                                                                                          (b) Fig. 4. Experimental (points) and theoretically calculated (full line) PA amplitude (a) and phase difference (b) spectra of  PbTe doped with 0.4 at.% I.   Table 2. Thermal parameters determined for PbTe+I samples.  Sample I [at%] DT [m2/s]  [µs] D[m2/s]  [m-1] µh[cm2/Vs] Sample 1 1.26mm/0.93 mm 0.6 0.204 10-5 0.041 0.26610-2 8647 1030 Sample 2 1.14mm/0.835 mm 0.4 0.19 10-5 0.106 0.42310-2 30604 1640  The calculated values of the hole mobility are higher than for pure PbTe, and they are in agreement with the diagrams of room temperature carrier concentration dependence of Hall mobility for PbTe1-xIx given by La Londe et al. [1]. They determined maximum hole mobility of about 2000 cm2/Vs responding to carrier concentrations of free holes of about 1019 cm-3. Since the thermal diffusivity coefficient (DT) decreases when the atomic percentage of Iodine in PbTe decreases from 0.6 at% to 0.4 at% we can conclude that it is also in agreement with the change of the figure of merit (ZT) given in [1] where the best content of I is about 0.12 at%. The above conclusion is obvious if we mention that DT=K/dCp, where K is the thermal conductivity, Cp is the specific heat and d is density. But also having in mind that   )(2LE KKTSZT          (3)  where S, ,KE and Kh are the Seebeck coefficient, resistivity and electric and lattice components of thermal conductivity, respectively. It is obvious that sample 2, doped with 0.4 at% I is slightly better than sample 1 doped with 0.6% having the hole mobility 1640 cm2/Vs. The same sample also has a smaller thermal diffusivity coefficient (DT) and thus a lower thermal conductivity K. The final result is that, for the sample of PbTe doped with 0.4 at% I, the figure of merit (ZT) is higher, that is in agreement with the results of La Londe [1]. A similar conclusion could be made using reference [14]. The effect of Iodine content (percentage) in PbTe is obviously very important because even the lattice parameter of PbTe1-xIx has a non-monotonic function having a sharp minimum for a specific value of iodine content [15]. It is interesting that the thermoelectric properties of a double doped PbTe with Cd and Iodine was recently studied by Kyunghan et al [16] investigating possible increase of the Seebeck coefficient and they found that the optimal PbI2 doping of the PbTe+1 at% CdTe for the best ZT was 0.055 mol%. Iodine as a dopant in PbTe is mainly considered from the aspect of improving thermoelectric properties of PbTe. Furthermore, PbTe-Ge [17] and PbTe-Si [18] eutectic composites can be doped with PbI2 with a precisely controlled carrier concentration. In this work we have shown that using optical reflection measurements in the plasma frequency resonance range one can get information on the concentration and mobility of free carriers. For higher free carrier concentrations the plasma minimum occurs at higher wave numbers and vice versa. The plasma frequency becomes narrower when the free charge carrier relaxation time decreases. The high frequency dielectric permeability can also be determined from the short wave part of the reflection spectrum. Similar properties can be obtained using photoacoustic measurements of the same samples.    4. Conclusion  In this work, as far as we know, far infrared optical reflectivity and photoacoustic properties of single crystal PbTe samples doped with PbI2 between 0.4 at% I and 0.6 at% I were measured for the first time. We obtained the results which confirm literature data that a small percentage of Iodine, much less than 1 at% can 356                      P. M. Nikolić, K. M. Paraskevopoulos, O. S. Aleksić, S. S. Vujatović, D. Vasiljević-Radović, T. T. Zorba ...             significantly improve thermoelectric and electrical properties of this doped semiconductor. From photoacosutic spectra we calculated the thermal diffusivity and hole diffusion coefficient and finally free hole mobility values. For PbTe doped with 0.4 at% I the free hole mobility was 1640 cm2/Vs. Further decrease of the iodine content until an optimal concentration would result in further improved thermoelectric and electrical properties and possible application as a high performance thermoelectric material.   Acknowledgements  This work was performed within projects III45007 and III45014 financed by the Ministry for Science and Education of the Republic of Serbia.   References    [1] A. D. La Londe, Y. Z. Pei, G. 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Phys., 105,         083718 (2009). [18] J. R. Sootsman, J. He, V. P. Dravid, S. Ballikaya, D.         Vermeulen, C. Uher, M. G. Kanatzidis, Chem. Mater.,         22, 869 (2010).    ______________________ *Corresponding author: Pantelija.Nikolic@sanu.ac.rs  

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Far infrared and photoacoustic characterization of iodine doped PbTe

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