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Electric and magnetic characterization of impurity-induced states in diluted magnetic Pb1−yYbyTe semiconductors
Materials Science and Engineering B91– 92 (2002) 412– 415
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Electric and magnetic characterization of impurity-induced states in diluted magnetic Pb1 − y Yby Te semiconductors E.P. Skipetrov a,*, N.A. Chernova a, L.A. Skipetrova a, E.I. Slyn’ko b a
Physics Department, Moscow State Uni6ersity, 119899 Moscow, Russia b Institute of Material Science Problems, 274001 Cherni6tsi, Ukraine
Abstract In the present paper we report on results obtained by complex investigations of galvanomagnetic and magnetic properties of a diluted magnetic semiconductor Pb1 − y Yby Te. Ytterbium doping modifies the energy spectrum of charge carriers in lead telluride by formation of deep impurity levels, moving from valence to forbidden band with increase of ytterbium content. The paramagnetic Curie–Weiss response observed has revealed a small fraction of Yb ions in magnetically active Yb3 + charge state, while the majority of impurity ions are in non-magnetic Yb2 + state. We couple the magnetic and galvanomagnetic data in a model of charge carriers energy spectrum in Pb1 − y Yby Te, for which energy position and electron population of the ytterbium level are derived as a function of impurity concentration. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Lead telluride; Magnetic semiconductors; Doping effect; Electron states; Diamagnetism and paramagnetism
1. Introduction Doping of IV–VI semiconductors with mixed valence impurities (Group III elements Al, Ga, In, Tl; transition metals Ti, Cr, Eu, Gd, Yb…) leads to formation of deep localized states in the energy spectrum of charge carriers, that provides a set of new effects non-attainable in undoped alloys [1 – 3]. Impurity levels pin the Fermi level position due to a huge concentration of states, both empty and filled with electrons, corresponding to impurity ions being in the highest or lowest oxidation state, respectively. This results in unique spatial uniformity of charge carriers parameters and allows one to achieve a dielectric state in narrow-gap IV–VI semiconductors. In addition to energy spectrum modification, doping with transition (d- and f-) metals turns the materials considered into diluted magnetic semiconductors [4,5]. The special feature of mixed valence metal ions is that their magnetic activity, being correlated with the charge state, is determined by the position of the deep level in the energy spectrum of charge carriers. Thus, a number of effects arises due to the influence of * Corresponding author. Tel.: +7-95-939-4493; fax: + 7-95-9328876. E-mail address: [email protected] (E.P. Skipetrov).
energy spectrum parameters on magnetic properties of alloys, such as resonant enhancement of f–f exchange in Gd doped alloys with high carrier concentration [6] or change in magnetic activity of Cr under variation of composition in Pb1 − x Snx Te [7]. Ytterbium is a relatively new mixed-valence impurity, whose doping activity in IV–VI semiconductors has been studied. Since the first reports, outlining a similarity of ytterbium to the impurities mentioned above, much attention has been paid to Pb1 − x Gex TeYb alloys, as the deep Yb-induced level is situated in the energy gap, so that the alloys exhibit high resistance and anomalous high photosensitivity to infrared light [8–10]. A movement of the Yb level deep into the energy gap with increase of germanium content, as well as a significant energy width and a low electron population of the level have been claimed. Magnetization measurements performed for p-Pb1 − x Gex TeYb have revealed a paramagnetic behavior of the alloy due to the presence of the magnetically active Yb3 + (4f13) ions [11]. The same samples annealed become n-type and diamagnetic, that implies a transfer of all Yb ions to the non-magnetic Yb2 + (4f14) charge state. Thus, in Pb1 − x Gex TeYb one can study the electronic properties of the impurity level by applying magnetic methods as well.
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E.P. Skipetro6 et al. / Materials Science and Engineering B91–92 (2002) 412–415
413
Table 1 Parameters of Pb1−y Yby Te samples at 4.2 K Sample
Y
RH (cm3 C−1)
z (V cm)
1 2 3 4 5 6
0.0003 0.005 0.008 0.015 0.030 0.065
2.2×100 3.9×101 1.4×102 2.8×102 1.1×103 \5×106
2.3×10−4 1.2×10−3 3.2×10−3 1.1×10−3 4.1×10−2 5.1×102
In contrast to lead– germanium telluride, neither energy spectrum nor magnetic properties of Pb1 − y Yby Te have been investigated so far. However, the increase in Yb content widens the forbidden band of the alloys, which may result in a shift of the Yb impurity level from valence to forbidden band [12]. Redistribution of electrons between the bands during this transition may change the electron population of the impurity band that would lead to variation in magnetic activity of ytterbium ions. The scope of the present research is, therefore, a complete investigation of ytterbium impurity states in Pb1 − y Yby Te, involving both electric and magnetic characterization.
2. Experiment In this work we use Pb1 − y Yby Te single crystal boule grown by a modified Bridgman method [8]. Gradual distribution of ytterbium along the boule provides us a set of samples with Yb content ranging from 0.03 to 6.5 mol.%, that has been checked by an energy dispersive X-ray fluorescence analysis (Table 1). Samples in shape of bars 1 ×1×5 mm were used to measure the temperature dependence of resistivity z and the Hall constant RH (4.25 T5 300 K, B50.1 T). For magnetic investigations samples with typical dimensions of 3× 5× 8 mm were used. In each sample the temperature and magnetic field dependencies of magnetization were studied using a vibrating sample magnetometer equipped with a gas-flow cryostat over the temperature range 55T 5300 K in a magnetic field B up to 0.5 T. Temperature was controlled by a Cu– CuFe thermocouple and the magnetic field was determined by the Hall probes.
p (cm−3) 2.3×1018 1.3×1017 3.6×1016 1.8×1016 4.7×1015 B1012
NYb3+ (cm−3)
NYb (cm−3)
NYb3+/NYb
– 1.1×1019 1.7×1019 2.4×1019 6.6×1019 8.4×1019
4.4×1018 8.0×1019 1.2×1020 2.2×1020 4.6×1020 9.6×1020
– 0.14 0.13 0.11 0.14 0.09
hibits a metal-like behavior, while the Hall constant and resistivity at 4.2 K monotonously increase with Yb content. The Hall mobility also increases with impurity concentration, attaining a value of vH : 105 cm2 V − 1 s at y: 0.015 rather high for doped IV–VI semiconductors. The z(1/T) and RH(1/T) curves for Pb1 − y Yby Te(y : 0.065) differ a lot from those mentioned above due to a clearly observed low-temperature activation region, indicating the appearance of localized states in the energy gap. The obtained experimental results are used for determining the Fermi energy in metal-like alloys and the energy of localized states in alloys with activation behavior. The Fermi energy was computed in the frame of Kane’s energy-momentum relation using the free hole concentration at 4.2 K, obtained from the corresponding values of the Hall constant. The position of the localized states in the energy gap has been found from the slope of the z(1/T) curve in the activation region. The results of these calculations are summarized by Fig. 2.
3. Results and discussion A study of the galvanomagnetic effects in Pb1 − y Yby Te has revealed p-type conductivity and a strong dependence of the free hole concentration and mobility upon alloy composition. The temperature dependence of RH (Fig. 1) and z for Pb1 − y Yby Te (y 5 0.03) ex-
Fig. 1. Temperature dependence of the Hall constant in Pb1 − y Yby Te of various ytterbium content y. y: 1, 0.0003; 2, 0.005; 3, 0.008; 4, 0.015; 5, 0.030; 6, 0.065.
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Fig. 2. Fermi level position and activation energy of the impurity level as a function of ytterbium content in Pb1 − y Yby Te.
Fig. 3. Reverse magnetic susceptibility, corrected for the diamagnetic share, as a function of temperature for Pb1 − y Yby Te of various ytterbium content y. y: 1, 0.005; 2, 0.008; 3, 0.015; 4, 0.030; 5, 0.065.
In slightly doped PbTe the Fermi level appears at about 40 meV below the valence band edge. As Yb content increases, first, the Fermi level rapidly shifts toward the valence band edge, then there is a region of gradual slow increase of the Fermi energy, so that the Fermi level attains the valence band edge at y : 0.003.
Such impurity concentration dependence of the Fermi energy can be explained by the formation of a resonant impurity level, whose energy position depends upon ytterbium content, near the valence band edge. Thus, the initial shift-up of the Fermi level corresponds to the filling of the valence band with electrons, provided by donor activity of ytterbium, until the Fermi level becomes pinned by the impurity level. The latter slow movement is a result of the resonant level approaching the valence band edge due to the increase of the energy gap with ytterbium doping. It is rather clear that a further increase in ytterbium content should lead to a movement of the impurity level into the forbidden band. This effect was observed, indeed, in Pb1 − y Yby Te (y: 0.065), where the ytterbium level appears at about 20 meV above the valence band edge. Investigations of magnetic properties of Pb1 − y Yby Te have revealed the impurity paramagnetic contribution to the magnetic susceptibility of alloys: as temperature decreases the paramagnetic susceptibility grows in accordance with the Curie–Weiss law. The magnetization curves, measured at liquid helium temperature, are linear, illustrating a well-known linear magnetization of paramagnets at low field. In order to determine the Curie constants for the alloys of various Yb content we present the temperature dependence of inverse magnetic susceptibility, corrected by the matrix diamagnetic contribution 0 (Fig. 3), as follows from the Curie–Weiss law: C = 0 + (1) (T− U) where C and U are the Curie constant and temperature, respectively. The dependencies obtained are linear, and their extrapolation to lower temperature intersects the abscissa at U: − (1–3) K, indicating a weak antiferromagnetic interaction between magnetic centers. The Curie constants computed from the slopes of 1/(x − x0) lines were used to determine the concentration of magnetic Yb3 + ions (NYb3 + ) in alloys of various ytterbium content: 3k C NYb3 + = 2 2 B (2) g v BS(S+ 1) where kB is Boltzman constant and vB is Bohr magneton; the values of g-factor, g=2.52, and effective spin S= 1/2 we used were experimentally determined by electron paramagnetic resonance in [13]. The obtained concentrations of magnetic ions are presented in Table 1 together with the total ytterbium content in Pb1 − y Yby Te alloys computed from X-ray data. A trivial analysis of the two data sets reveals an increase of the magnetic ions concentration with ytterbium content. However, the fraction of magnetic ions to the total ytterbium concentration (NYb3 + /NYb) is rather low, about 10–15%, in all the investigated Pb1 − y Yby Te alloys.
E.P. Skipetro6 et al. / Materials Science and Engineering B91–92 (2002) 412–415
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4. Conclusions
Fig. 4. Variation of charge carriers energy diagram in Pb1 − y Yby Te with the increase of ytterbium content.
In terms of the energy spectrum of the impurity states in Pb1 − y Yby Te, the concentration of magnetic Yb3 + ions corresponds to the density of empty states in the ytterbium-induced band (Fig. 4). These empty states appear due to a transfer of electrons to the valence band empty states, originating from native acceptor defects. Let us discuss this process in more detail. In undoped PbTe the Fermi level is situated in the valence band, and the corresponding free hole concentration is determined by an effective number of native point defects Ni* (left part in Fig. 4). The Yb-induced level is formed above the Fermi level of PbTe either in the valence or forbidden band. This level exhibits donor properties, and provides electrons to the valence band until all empty states under the level become filled with electrons. At the same time a fraction of Yb ions transfer from Yb2 + to Yb3 + , providing a corresponding concentration of empty states in the impurity band (middle part in Fig. 4). A comparison between the free hole concentration in PbTe and the concentration of magnetic ions in Pb1 − y Yby Te (see Table 1) and also the increase of NYb3 + with doping observed in our experiments let us conclude that the growth of ytterbium content results in an increase of native defects concentration. Thus, in Pb1 − y Yby Te, as well as in some other doped IV– VI semiconductors [14], self-compensation occurs, i.e. a partial compensation of ytterbium donor activity by acceptor activity of native point defects. One can point out that the rate of the native defects formation is significantly less than the rate of increase in the Yb content with doping. Therefore, at high enough ytterbium content almost all the Yb ions are in non-magnetic Yb2 + state and the impurity band is almost filled with electrons (right part in Fig. 4).
The ytterbium level in Pb1 − y Yby Te alloys is situated in the vicinity of the valence band edge. At low ytterbium content this deep level is resonant with the valence band, however, by increasing the impurity concentration it approaches the valence band edge and shifts into the forbidden band. The ytterbium ions exist in Pb1 − y Yby Te in two charge states: magnetically active Yb3 + , whose concentration increases with Yb doping, being about 10–15% of total Yb content, and non-magnetic Yb2 + ions. A model of charge carriers energy spectrum in Pb1 − y Yby Te is introduced, that explains the results of electric and magnetic investigations. According to this model the magnetic Yb3 + ions correspond to empty electronic states. Their concentration increases with the ytterbium content due to the formation of native acceptor defects, pushing out electrons from the localized impurity states.
Acknowledgements This research was carried out under financial support from the Russian Foundation for Basic Research (Grants Nos 00-15-96784, 01-02-17446).
References [1] V.I. Kaidanov, Y.I. Ravich, Sov. Phys. Usp. 28 (1985) 31. [2] B.A. Akimov, A.V. Dmitriev, D.R. Khokhlov, L.I. Ryabova, Phys. Stat. Sol. (a) 137 (1993) 9. [3] T. Story, Acta Phys. Polon. A 94 (1998) 189. [4] J.K. Furdyna, J. Kossut (Eds.), Semiconductors and Semimetals, vol. 25, Academic Press, Boston, 1988. [5] T. Story, Acta Phys. Polon. A 92 (1997) 663. [6] T. Story, M. Gorska, A. Lusakowski, M. Arciszewska, W. Dobrowolski, E. Grodzicka, Z. Golacki, R.R. Galazka, Phys. Rev. Lett. 77 (1996) 3447. [7] T. Story, E. Grodzicka, B. Witkowska, J. Gorecka, W. Dobrowolski, Acta Phys. Polon. A 82 (1992) 879. [8] Y.K. Vygranenko, V.E. Slynko, E.I. Slynko, Inorg. Mater. 31 (1995) 1219. [9] E.P. Skipetrov, N.A. Chernova, E.I. Slynko, Y.K. Vygranenko, Phys. Rev. B 59 (1999) 12928. [10] E.P. Skipetrov, N.A. Chernova, E.I. Slyn’ko, J. Cryst. Growth 210 (2000) 288. [11] E. Grodzicka, W. Dobrowolski, T. Story, E.I. Slynko, Y.K. Vygranenko, M.M.H. Willekens, H.J.M. Swagten, W.J.M. De Jonge, Acta Phys. Pol. A 90 (1996) 801. [12] S.K. Das, R. Suryanarayanan, J. Appl. Phys. 66 (1989) 4843. [13] S. Isber, S. Charar, X. Gratens, C. Fau, M. Averous, S.K. Misra, Z. Golacki, Phys. Rev. B 54 (1996) 7634. [14] V.I. Kaidanov, S.A. Nemov, Y.I. Ravich, Semiconductors 28 (1994) 223.
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Electric and magnetic characterization of impurity-induced states in diluted magnetic Pb1 − y Yby Te semiconductors E.P. Skipetrov a,*, N.A. Chernova a, L.A. Skipetrova a, E.I. Slyn’ko b a
Physics Department, Moscow State Uni6ersity, 119899 Moscow, Russia b Institute of Material Science Problems, 274001 Cherni6tsi, Ukraine
Abstract In the present paper we report on results obtained by complex investigations of galvanomagnetic and magnetic properties of a diluted magnetic semiconductor Pb1 − y Yby Te. Ytterbium doping modifies the energy spectrum of charge carriers in lead telluride by formation of deep impurity levels, moving from valence to forbidden band with increase of ytterbium content. The paramagnetic Curie–Weiss response observed has revealed a small fraction of Yb ions in magnetically active Yb3 + charge state, while the majority of impurity ions are in non-magnetic Yb2 + state. We couple the magnetic and galvanomagnetic data in a model of charge carriers energy spectrum in Pb1 − y Yby Te, for which energy position and electron population of the ytterbium level are derived as a function of impurity concentration. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Lead telluride; Magnetic semiconductors; Doping effect; Electron states; Diamagnetism and paramagnetism
1. Introduction Doping of IV–VI semiconductors with mixed valence impurities (Group III elements Al, Ga, In, Tl; transition metals Ti, Cr, Eu, Gd, Yb…) leads to formation of deep localized states in the energy spectrum of charge carriers, that provides a set of new effects non-attainable in undoped alloys [1 – 3]. Impurity levels pin the Fermi level position due to a huge concentration of states, both empty and filled with electrons, corresponding to impurity ions being in the highest or lowest oxidation state, respectively. This results in unique spatial uniformity of charge carriers parameters and allows one to achieve a dielectric state in narrow-gap IV–VI semiconductors. In addition to energy spectrum modification, doping with transition (d- and f-) metals turns the materials considered into diluted magnetic semiconductors [4,5]. The special feature of mixed valence metal ions is that their magnetic activity, being correlated with the charge state, is determined by the position of the deep level in the energy spectrum of charge carriers. Thus, a number of effects arises due to the influence of * Corresponding author. Tel.: +7-95-939-4493; fax: + 7-95-9328876. E-mail address: [email protected] (E.P. Skipetrov).
energy spectrum parameters on magnetic properties of alloys, such as resonant enhancement of f–f exchange in Gd doped alloys with high carrier concentration [6] or change in magnetic activity of Cr under variation of composition in Pb1 − x Snx Te [7]. Ytterbium is a relatively new mixed-valence impurity, whose doping activity in IV–VI semiconductors has been studied. Since the first reports, outlining a similarity of ytterbium to the impurities mentioned above, much attention has been paid to Pb1 − x Gex TeYb alloys, as the deep Yb-induced level is situated in the energy gap, so that the alloys exhibit high resistance and anomalous high photosensitivity to infrared light [8–10]. A movement of the Yb level deep into the energy gap with increase of germanium content, as well as a significant energy width and a low electron population of the level have been claimed. Magnetization measurements performed for p-Pb1 − x Gex TeYb have revealed a paramagnetic behavior of the alloy due to the presence of the magnetically active Yb3 + (4f13) ions [11]. The same samples annealed become n-type and diamagnetic, that implies a transfer of all Yb ions to the non-magnetic Yb2 + (4f14) charge state. Thus, in Pb1 − x Gex TeYb one can study the electronic properties of the impurity level by applying magnetic methods as well.
0921-5107/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 1 0 7 ( 0 1 ) 0 1 0 4 1 - 8
E.P. Skipetro6 et al. / Materials Science and Engineering B91–92 (2002) 412–415
413
Table 1 Parameters of Pb1−y Yby Te samples at 4.2 K Sample
Y
RH (cm3 C−1)
z (V cm)
1 2 3 4 5 6
0.0003 0.005 0.008 0.015 0.030 0.065
2.2×100 3.9×101 1.4×102 2.8×102 1.1×103 \5×106
2.3×10−4 1.2×10−3 3.2×10−3 1.1×10−3 4.1×10−2 5.1×102
In contrast to lead– germanium telluride, neither energy spectrum nor magnetic properties of Pb1 − y Yby Te have been investigated so far. However, the increase in Yb content widens the forbidden band of the alloys, which may result in a shift of the Yb impurity level from valence to forbidden band [12]. Redistribution of electrons between the bands during this transition may change the electron population of the impurity band that would lead to variation in magnetic activity of ytterbium ions. The scope of the present research is, therefore, a complete investigation of ytterbium impurity states in Pb1 − y Yby Te, involving both electric and magnetic characterization.
2. Experiment In this work we use Pb1 − y Yby Te single crystal boule grown by a modified Bridgman method [8]. Gradual distribution of ytterbium along the boule provides us a set of samples with Yb content ranging from 0.03 to 6.5 mol.%, that has been checked by an energy dispersive X-ray fluorescence analysis (Table 1). Samples in shape of bars 1 ×1×5 mm were used to measure the temperature dependence of resistivity z and the Hall constant RH (4.25 T5 300 K, B50.1 T). For magnetic investigations samples with typical dimensions of 3× 5× 8 mm were used. In each sample the temperature and magnetic field dependencies of magnetization were studied using a vibrating sample magnetometer equipped with a gas-flow cryostat over the temperature range 55T 5300 K in a magnetic field B up to 0.5 T. Temperature was controlled by a Cu– CuFe thermocouple and the magnetic field was determined by the Hall probes.
p (cm−3) 2.3×1018 1.3×1017 3.6×1016 1.8×1016 4.7×1015 B1012
NYb3+ (cm−3)
NYb (cm−3)
NYb3+/NYb
– 1.1×1019 1.7×1019 2.4×1019 6.6×1019 8.4×1019
4.4×1018 8.0×1019 1.2×1020 2.2×1020 4.6×1020 9.6×1020
– 0.14 0.13 0.11 0.14 0.09
hibits a metal-like behavior, while the Hall constant and resistivity at 4.2 K monotonously increase with Yb content. The Hall mobility also increases with impurity concentration, attaining a value of vH : 105 cm2 V − 1 s at y: 0.015 rather high for doped IV–VI semiconductors. The z(1/T) and RH(1/T) curves for Pb1 − y Yby Te(y : 0.065) differ a lot from those mentioned above due to a clearly observed low-temperature activation region, indicating the appearance of localized states in the energy gap. The obtained experimental results are used for determining the Fermi energy in metal-like alloys and the energy of localized states in alloys with activation behavior. The Fermi energy was computed in the frame of Kane’s energy-momentum relation using the free hole concentration at 4.2 K, obtained from the corresponding values of the Hall constant. The position of the localized states in the energy gap has been found from the slope of the z(1/T) curve in the activation region. The results of these calculations are summarized by Fig. 2.
3. Results and discussion A study of the galvanomagnetic effects in Pb1 − y Yby Te has revealed p-type conductivity and a strong dependence of the free hole concentration and mobility upon alloy composition. The temperature dependence of RH (Fig. 1) and z for Pb1 − y Yby Te (y 5 0.03) ex-
Fig. 1. Temperature dependence of the Hall constant in Pb1 − y Yby Te of various ytterbium content y. y: 1, 0.0003; 2, 0.005; 3, 0.008; 4, 0.015; 5, 0.030; 6, 0.065.
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Fig. 2. Fermi level position and activation energy of the impurity level as a function of ytterbium content in Pb1 − y Yby Te.
Fig. 3. Reverse magnetic susceptibility, corrected for the diamagnetic share, as a function of temperature for Pb1 − y Yby Te of various ytterbium content y. y: 1, 0.005; 2, 0.008; 3, 0.015; 4, 0.030; 5, 0.065.
In slightly doped PbTe the Fermi level appears at about 40 meV below the valence band edge. As Yb content increases, first, the Fermi level rapidly shifts toward the valence band edge, then there is a region of gradual slow increase of the Fermi energy, so that the Fermi level attains the valence band edge at y : 0.003.
Such impurity concentration dependence of the Fermi energy can be explained by the formation of a resonant impurity level, whose energy position depends upon ytterbium content, near the valence band edge. Thus, the initial shift-up of the Fermi level corresponds to the filling of the valence band with electrons, provided by donor activity of ytterbium, until the Fermi level becomes pinned by the impurity level. The latter slow movement is a result of the resonant level approaching the valence band edge due to the increase of the energy gap with ytterbium doping. It is rather clear that a further increase in ytterbium content should lead to a movement of the impurity level into the forbidden band. This effect was observed, indeed, in Pb1 − y Yby Te (y: 0.065), where the ytterbium level appears at about 20 meV above the valence band edge. Investigations of magnetic properties of Pb1 − y Yby Te have revealed the impurity paramagnetic contribution to the magnetic susceptibility of alloys: as temperature decreases the paramagnetic susceptibility grows in accordance with the Curie–Weiss law. The magnetization curves, measured at liquid helium temperature, are linear, illustrating a well-known linear magnetization of paramagnets at low field. In order to determine the Curie constants for the alloys of various Yb content we present the temperature dependence of inverse magnetic susceptibility, corrected by the matrix diamagnetic contribution 0 (Fig. 3), as follows from the Curie–Weiss law: C = 0 + (1) (T− U) where C and U are the Curie constant and temperature, respectively. The dependencies obtained are linear, and their extrapolation to lower temperature intersects the abscissa at U: − (1–3) K, indicating a weak antiferromagnetic interaction between magnetic centers. The Curie constants computed from the slopes of 1/(x − x0) lines were used to determine the concentration of magnetic Yb3 + ions (NYb3 + ) in alloys of various ytterbium content: 3k C NYb3 + = 2 2 B (2) g v BS(S+ 1) where kB is Boltzman constant and vB is Bohr magneton; the values of g-factor, g=2.52, and effective spin S= 1/2 we used were experimentally determined by electron paramagnetic resonance in [13]. The obtained concentrations of magnetic ions are presented in Table 1 together with the total ytterbium content in Pb1 − y Yby Te alloys computed from X-ray data. A trivial analysis of the two data sets reveals an increase of the magnetic ions concentration with ytterbium content. However, the fraction of magnetic ions to the total ytterbium concentration (NYb3 + /NYb) is rather low, about 10–15%, in all the investigated Pb1 − y Yby Te alloys.
E.P. Skipetro6 et al. / Materials Science and Engineering B91–92 (2002) 412–415
415
4. Conclusions
Fig. 4. Variation of charge carriers energy diagram in Pb1 − y Yby Te with the increase of ytterbium content.
In terms of the energy spectrum of the impurity states in Pb1 − y Yby Te, the concentration of magnetic Yb3 + ions corresponds to the density of empty states in the ytterbium-induced band (Fig. 4). These empty states appear due to a transfer of electrons to the valence band empty states, originating from native acceptor defects. Let us discuss this process in more detail. In undoped PbTe the Fermi level is situated in the valence band, and the corresponding free hole concentration is determined by an effective number of native point defects Ni* (left part in Fig. 4). The Yb-induced level is formed above the Fermi level of PbTe either in the valence or forbidden band. This level exhibits donor properties, and provides electrons to the valence band until all empty states under the level become filled with electrons. At the same time a fraction of Yb ions transfer from Yb2 + to Yb3 + , providing a corresponding concentration of empty states in the impurity band (middle part in Fig. 4). A comparison between the free hole concentration in PbTe and the concentration of magnetic ions in Pb1 − y Yby Te (see Table 1) and also the increase of NYb3 + with doping observed in our experiments let us conclude that the growth of ytterbium content results in an increase of native defects concentration. Thus, in Pb1 − y Yby Te, as well as in some other doped IV– VI semiconductors [14], self-compensation occurs, i.e. a partial compensation of ytterbium donor activity by acceptor activity of native point defects. One can point out that the rate of the native defects formation is significantly less than the rate of increase in the Yb content with doping. Therefore, at high enough ytterbium content almost all the Yb ions are in non-magnetic Yb2 + state and the impurity band is almost filled with electrons (right part in Fig. 4).
The ytterbium level in Pb1 − y Yby Te alloys is situated in the vicinity of the valence band edge. At low ytterbium content this deep level is resonant with the valence band, however, by increasing the impurity concentration it approaches the valence band edge and shifts into the forbidden band. The ytterbium ions exist in Pb1 − y Yby Te in two charge states: magnetically active Yb3 + , whose concentration increases with Yb doping, being about 10–15% of total Yb content, and non-magnetic Yb2 + ions. A model of charge carriers energy spectrum in Pb1 − y Yby Te is introduced, that explains the results of electric and magnetic investigations. According to this model the magnetic Yb3 + ions correspond to empty electronic states. Their concentration increases with the ytterbium content due to the formation of native acceptor defects, pushing out electrons from the localized impurity states.
Acknowledgements This research was carried out under financial support from the Russian Foundation for Basic Research (Grants Nos 00-15-96784, 01-02-17446).
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