Far infrared properties of PbTe doped with cerium

Journal of Alloys and Compounds 433 (2007) 292–295

Far infrared properties of PbTe doped with cerium P.M. Nikoli´c a,∗ , W. K¨onig b , S.S. Vujatovi´c a , V. Blagojevi´c c , D. Lukovi´c a , S. Savi´c a , K. Radulovi´c a , D. Uroˇsevi´c d , M.V. Nikoli´c e a Institute of Technical Sciences SASA, Knez Mihailova 35/IV, 11000 Belgrade, Serbia Max Planck Institut f¨ur Festk¨orperforschung, Heisenbergstrasse 1, 7000 Stuttgart 80, Germany c Faculty of Electronic Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia d Mathematical Institute SASA, Knez Mihailova 35/I, 11000 Belgrade, Serbia e Center for Multidisciplinary Studies of the University of Belgrade, Kneza Viseslava 1, Belgrade, Serbia b

Received 22 December 2005; accepted 17 June 2006 Available online 8 August 2006

Abstract Single crystal samples of lead telluride doped with cerium were made using the Bridgman method. Far infrared reflectivity spectra in the temperature range from 10 to 300 K are presented. The experimental data were numerically analyzed using a fitting procedure based on the plasmon–phonon interaction model and optical parameters were determined. Two additional local modes were observed at about 138 and 337 cm−1 . The origin of these local vibrational impurity modes was discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Semiconductors; Chalcogenides; Infrared spectroscopy

1. Introduction Since the giant negative magnetoresistance effect in PbTe doped simultaneously with Yb and Mn was discovered [1,2], more attention has been paid to PbTe doped with rare earth elements. Donor-like behavior of La, Pr, Sm and Gd in PbTe was investigated [3] and also X-ray characterization of precipitates in cerium doped PbTe crystals [4], lead chalcogenides are well-known materials used for the production of optoelectronic devices [5,6]. Doping of these materials; especially lead telluride and lead–tin telluride; with various impurities has been studied a lot in the last 20 years [7–9]. The strong influence of small concentrations of impurities (usually less than 1 at.%) on lead chalcogenides is connected with deep energy levels that appear as a result of doping. For instance; lead telluride doped with some group III impurities; such as In; Ga or B, exhibits certain unusual properties such as Fermi level pinning; persistent photoconductivity, etc. [10–13]. Similar impurity states were observed when PbTe was doped with the rare earth element Yb [14,15]. An important difference was registered here because the position of the pinned Fermi level depends on the concentra-

tion of ytterbium [1] while it does not depend on the amount of indium. The Hall coefficient; thermoelectric power and electric conductivity in PbTe doped with: La, Pr, Sm and Gd were also investigated [3]. As far as we know only room temperature far infrared optical reflectivity was measured [16] for PbTe with Ce and also PbTe doped with Sm in the temperature range between 10 and 300 K [17]. In this work far infrared optical properties of single crystal PbTe doped with Ce were measured in the temperature range between 10 and 300 K, and the experimental results were numerically analyzed. 2. Experimental Single crystal ingots of PbTe doped with the starting composition of 3 at.% Ce were synthesized using the standard Bridgman method [18]. The composition of cerium decreased from the top to the end along the length of the ingot, so at least, half a dozen samples with different contents of cerium could be cut and prepared for measurements. Highly polished PbTe(Ce) samples were used for optical measurements. Far infrared reflectivity measurements were made at temperatures from 10 to 300 K using a Brucker IFS-113 V spectrometer equipped with an Oxford Instruments cryostat.

3. Experimental results and discussion ∗

Corresponding author. Tel.: +381 11 3342400x140; fax: +381 11 185263. E-mail address: [email protected] (P.M. Nikoli´c).

0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.06.066

Far infrared reflectivity spectra of a single crystal PbTe doped with 0.5 at.% Ce are shown in Fig. 1. A sharp dip is observed at the wave number of about

P.M. Nikoli´c et al. / Journal of Alloys and Compounds 433 (2007) 292–295

Fig. 1. FIR reflectivity spectra of PbTe doped with 0.5 at.% Ce at temperatures: 1–300, 2–200, 3–130, 4–110, 5–50 and 6–10 K. 225 cm−1 for the temperatures between 10 and 110 K, which cannot be seen at room temperature. Low temperature measurements proved that these dips are due to the fact that evacuation of the cryostat chamber was insufficiently high so water was frozen at the sample surface. This is in agreement with Warren’s experimental results [19] of optical mode of ice. At low temperatures smaller dips were observed on all reflectivity diagrams at about 380 and 440 cm−1 . They belong to the effect of a thin layer of TeO2 also formed on the surface of the sample. It is interesting to notice that the reflectivity decreases in the range above 500 cm−1 for the sample temperature below 110 K, while for the temperatures of 130, 200 and 300 K reflectivity is practically unchanged in that temperature range. This decrease is better expressed at temperatures approaching 10 K. The observed decrease of the reflectivity intensity below 110 K is, by our opinion, associated with a phase transition produced by the impurity, i.e. cerium. All experimental diagrams were numerically analyzed using the following four-parameter model introduced by Gervais and Piriou [20]:

2 ε(ω) = ε∞

×

j=1

(ω2 + iγlj ωx − ωlj2 )

ω(ω + iγp )(ω2 + iγt ω − ωt2 )

q  ω2 + iγLOk ω − ω2

p  ω2 + iγLn ω − ω2

Ln

n=1

2 ω2 + iγon ω − ωon

LOk

k=1

(1)

2 ω2 + iγTOk ω − ωTOk

293

Fig. 2. Far infrared spectrum of PbTe doped with 0.5% Ce as a function of the wave number, measured at T = 50 K.

where ωlj and γ lj are parameters of the first numerator representing the eigenfrequencies and damping factors of coupled plasmon-longitudinal phonon waves, respectively. Parameters of the first denominator correspond to transversal (TO) vibrations, while γ p is the damping factor of plasma. The second term in Eq. (1) represents the Ce impurity local modes where ω01 and ␻02 are characteristic impurity mode frequencies. Frequencies ωL1 and ωL2 are parameters connected with the oscillator strength and γ 01 , γ 02 , γ L1 , and γ L2 are their damping factors, respectively. Finally, ωLOk and ωTOk are the longitudinal and transversal frequencies, and γ LOk and γ TOk stand for the damping factors of uncoupled modes of the host crystal. Best-fit values of these parameters were calculated. The oscillators denoted by j = 1, 2 in Eq. (1) are dominant structures in the far infrared reflection spectra and represent the position of the coupled plasmonLO–phonon modes. The frequency of mode ωl1 [21] is marked by an arrow in Fig. 2 for the temperature of 50 K. The points show the experimental data while the solid line shows the results of numerical optimization of the parameters using Eq. (1). The reflectivity spectra were observed down to 50 cm−1 , so the value of 32 cm−1 for the transversal phonon frequency ωt is taken from literatures [8,10]. Oscillators with weak intensities at about 50 and 70 cm−1 are modes from the edge of the Brillouin zone because the phonon density of PbTe has a maximum at these frequencies [22], while the mode at 105 cm−1 represents the LO mode

Table 1 The values of the optical parameters calculated using Eqs. (1) and (2) Parameters (cm−1 )

ωp ωl1 γ l1 ωl2 γ l2 ωt ωL1 γ L1 ω01 γ 01 ωL2 γ L2 ω02 γ 02 ωLO (PbTe) γ LO (PbTe) ε∞

T (K) 10

30

50

90

110

130

200

300

264.2 297.2 69 16 0.11 × 10−1 18 187 93 138.8 117 370.6 397 337 70 105 132 39.7

262.4 296.7 74.7 18 1.5 20.35 184.8 94.6 138.7 113.4 370.6 366 337.4 68.6 104 150.8 37.1

259.3 290.2 86 20 1.2 22.4 187.7 91.8 138.8 125 370.6 250.7 337.7 75 105.4 155 36.7

246.7 272.7 98 22 0.5 × 10−1 24.4 170.5 89 138.8 84 370.9 343 337 90.4 105 175 35.4

232.9 256.4 106 24 0.9 × 10−1 26.4 170.8 105.4 138.5 87.5 370.5 243.8 337.8 93.7 105 180.3 33.4

224 244.8 75.6 26 0.2 28.4 160.2 99.2 138.8 81.5 370 204 337.8 103 105 336 33.3

202.8 220.1 64.8 28 0.1 × 10−1 30.4 144 63 138.1 60 370.5 188 337.8 137 104 200 31.4

174.2 185.8 73.3 30 0.2 × 10−1 32 136.9 87.7 138.2 81 370 203 337.8 198 105 132.4 30.9

294

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of PbTe (the third term in Eq. (1)).The values for ωp were determined using the following equation: ωp =

ωl1 ωl2 ωt

(2)

The calculated values of the plasma frequencies versus temperature are given in Fig. 3a. The calculated values of dielectric permittivity as a function of temperature are given in Fig. 3b. The values of all parameters calculated using Eqs. (1)

and (2) are given in Table 1. They were deduced from a least squares computer fit to the experimental reflectivity data. The fitting program was developed in the programming language FORTRAN 95, which enables the user to select the values of parameters existing in the mathematical model. Separately or together, all the parameters used can be fitted, and the user can select the magnitude of the change of each parameter. The starting values of all transversal and longitudinal modes (parameters) used in the fitting procedure were obtained from a Kramers Kr¨onig analysis done previously [23]. The fitting error can be estimated using one of the following criteria: the sum of absolute differences between the experimental and calculated values; the sum of square differences between the calculated and the experimental values; the sum of relative errors; the sum of the square of relative errors. Therefore the experimental curves can be compared with the theoretical ones obtained using the mathematical model for the given parameters and their values can be determined during the fitting procedure. The plasma frequency ωp increased as the temperature decreased. This is a consequence of the change in the concentration of free carriers of PbTe doped with Ce when the Fermi level is pinned. High frequency dielectric permittivity ε∞ also increased when the temperature decreased as seen in Fig. 3b. In both cases, for ε∞ and ωp an unexpected discontinuity occurred in the range between 90 and 110 K, which could be connected with a phase transition. Looking at the reflectivity diagrams in Fig. 1 where reflectivity is practically constant at frequencies above 450 cm−1 for the temperature above 130 K, one can see that reflectivity decreased for temperatures at and below 110 K. This is very well expressed in the reflectivity diagram measured at 10 K. This behavior is usually associated with a phase transition as a product of the impurity i.e. Ce. We also determined two local modes (ω01 ≈ 138 cm−1 and ω02 ≈ 337 cm−1 ) and their damping factors (γ 01 and γ 02 ). For ωl1 ≥ ω01 this mode is shielded with the coupled plasmon–phonon mode, but for ωl1 ≤ ω02 an additional mode is exposed. These results can be compared with literature data for PbTe doped with another rare earth element—ytterbium (Yb) that also has two electrons in 5s and 6s shells and six electrons in the 5p shell. However, Yb has the maximum number of electrons (14) in the 4f shell while cerium has only two electrons. All other shells are identical for both elements. In Ce and Yb the source of ionization of electrons are not 5s and 5p orbits. The sources of ionization are at the 4f2 6s2 (3 H4 ) levels in Ce and 4f14 6s2 (1 S0 ) levels in Yb. It shows that 5s and 5p shells are above the 4f one and the 4f shell is first. For one-fold ionization of the Ce atom it is 4f2 6s (2 H1/2 ); for two-fold it is 4f2 (3 H4 ) and for threefold ionization it will be 4f1 (2 F5/2 ). For Yb it is similar for one-fold ionization 4f14 6s (2 S1/2 ) for two-fold 4f14 (1 S0 ) and for three-fold ionization it should be 4f13 (2 F1/2 ). Now we could consider which state the observed two local Ce modes belong to: Ce+ , Ce2+ or Ce3+ . For PbTe doped with Yb the position of the pinned Fermi level is defined by the balance between Yb+ and Yb3+ charge states of the dopant [2]. Electron paramagnetic resonance data show that in the case of Yb doping, Fermi-level pinning is provided by switching the impurity valence by one: Yb2+ –Yb3+ . In the case of PbTe doped with Ce we believe that the metastable Ce2+ state transfers to more stable forms as follows: 2Ce2+ → Ce+ + Ce3+

(3)

and that the electron from the Ce+ state may transfer to the conduction band as follows: Ce+ → Ce3+ + 2e−

(4)

Then usually the Fermi level is pinned near the top of the valence band and the sample is of the p-type.

4. Conclusion

Fig. 3. Plasma frequencies (a) and dielectric permittivity (b) vs. the temperature.

In this work far infrared reflection spectra of a cerium doped PbTe single crystal at temperatures between 10 and 300 K have been shown. Besides a strong plasmon-LO–phonon interaction, two additional modes at temperatures below 200 K were observed. The first local mode was at about 138 cm−1 while

P.M. Nikoli´c et al. / Journal of Alloys and Compounds 433 (2007) 292–295

the second one was at about 337 cm−1 . The lower frequency mode can be assumed to be a local cerium mode representing the population of a metastable state. The other mode at about 337 cm−1 could be the result of electron transfer from the stable two-electron state to the conduction band. Acknowledgements We wish to thank Dr. Ð. Bugarinovi´c for very useful discussions. This work was performed as part of project B 6150 financed by the Ministry for Science and Environmental Protection of the Republic of Serbia. References [1] I.I. Ivanchik, Proceedings of the 24th International Conference on Physics of Semiconductors, Jerusalem, Israel, 1998, World Scientific, Singapore, 1998 (PART VIII B) paper 8. [2] I.I. Ivanchik, D.R. Khokhlov, A.V. Morozov, A.A. Terekhov, E.I. Slynko, V.I. Slinko, A. de Vissa, W.D. Dobrowolski, Phys. Rev. B 61 (22) (2000) R14889–R14892. [3] G.T. Alekseeva, M.V. Vedernikov, E.A. Gurieva, P.P. Konstantinov, L.V. Prokofeva, Yn.I. Ravich, Semiconductors 32 (7) (1998) 716–719. [4] P. Fita, K. Smolinski, Z. Golecki, K. Lowniczak-Jablanska, Appl. Phys. A 68 (1999) 681–685. [5] A. Lambrecht, H. Bottner, M. Agne, R. Kurbel, A. Fach, B. Halford, U. Schiessl, M. Tacker, Semicond. Sci. Technol. 8 (1993) S334–S336. [6] B.A. Akimov, A.V. Dmitriev, D.R. Khokhlov, R.I. Ryabova, Phys. Stat. Sol. (A) 137 (1993) 9–55. [7] B.A. Akimov, V.P. Zlomanov, L.I. Ryabova, S.M. Chudinov, O.B. Yatsenko, Sov. Phys. Semicond. 13 (1979) 759–763.

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