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Preparation and some physical properties of tetradymite-type Sb2Te3 single crystals doped with CdS
Journal of Crystal Growth 222 (2001) 565–573
Preparation and some physical properties of tetradymite-type Sb2Te3 single crystals doped with CdS P. Losˇ t’a´ka,*, C˘. Drasˇ ara, A. Krejc˘ova´a, L. Benesˇ b, J.S. Dyckc, W. Chenc, C. Uherc Faculty of Chemical Technology, University of Pardubice, C˘s. Legiı´ Square 565, 532 10 Pardubice, Czech Republic Joint Laboratory of Solid State Chemistry, Czech Academy of Sciences and University of Pardubice, Studentska´ 64, 530 09 Pardubice, Czech Republic c Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
a b
Received 28 April 1999; accepted 22 October 2000 Communicated by J.B. Mullin
Abstract Single crystals of Sb2Te3 doped with CdS were prepared by a modified Bridgman method from the elements Sb and Te of 5 N purity and the CdS compound of 4.5 N purity. Samples were characterized by X-ray diffraction and by measurement of reflectance in the plasma resonance frequency region at room temperature. Furthermore, we made measurements of temperature dependence of the electrical resistivity, Hall and Seebeck coefficients, and thermal conductivity in the temperature range of 4.2–300 K. In the process of crystal growth, CdS dissociated and it was assumed that the Cd-atoms formed substitutional defects in the Sb-sublattice (Cd0Sb ) while the S-atoms formed ðÿdÞ substitutional defects in the Te-sublattice (STe ). # 2001 Elsevier Science B.V. All rights reserved. PACS: 72.80.Jc; 78.20.Ci; 61.72.Ji Keywords: Layered narrow-gap semiconductors; Reflectance; Electrical and thermal conductivities; Hall and Seebeck coefficients; Point defects
1. Introduction Antimony telluride (Sb2Te3) belongs to the family of layered-type semiconductors with tetradymite structure (space group D53d ) which are used in applications such as thermoelectric generators and coolers [1]. Therefore, an investigation of the effect of various dopants on the physical properties *Corresponding author. Tel.: +42-040-603-7168; fax: +42040-603-7068. E-mail address: [email protected] (P. Losˇ t’a´k).
of Sb2Te3 is interesting for both basic and applied research. Despite considerable attention devoted to the study of the changes in the properties of antimony telluride due to the presence of foreign atoms in its crystal structure, the available literature provides little insight into the influence of Cd or S impurities. It follows from the phase diagram of the Sb2Te3–CdTe system [2,3] that substitutional solid solutions based on the Sb2Te3 tetradymite structure exist in this system in the concentration range
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of 0–7 mol% CdTe. The authors of Ref. [3] also described the existence of a compound CdSb2Te4 which forms by peritectic reaction at 590 K. The transport coefficients (electrical resistivity, Hall constant, Seebeck coefficient and thermal conductivity) of polycrystalline Sb2Te3 doped with CdTe were studied previously [2]. Furthermore, it has been shown that the Cd impurity in Sb2Te3 gives rise to an increase in the free carrier density. This conclusion follows also from the results of the measurements of several transport parameters [4]. Cd atoms were also doped into single crystal forms of Sb2Te3 and the increased free carrier concentration was explained by the formation of substitutional defects Cd0Sb [5]. The phase diagram of the Sb2Te3–CdS system was determined by differential thermal analysis, microhardness, and by microstructural and X-ray phase analysis [6]. The data indicate that solid solutions based on Sb2Te3 occur for concentrations up to 12 mol% CdS. It was also shown that a new compound CdSb2Te3S forms by a peritectic reaction at 910 K. The effect of the CdS impurities or its constituents on the physical properties of antimony telluride single crystals has not yet been studied. In this communication we describe the method of preparation of single crystals of Sb2Te3 doped with CdS and we present a range of optical and transport measurements with which we characterize the structure and its physical properties. Our results are consistent with CdS dissociating upon melting and, rather than entering the structure as a compound, it breaks into its elemental constituents that incorporate themselves into the respective Sb and Te sublattices and form point defects in the tetradymite structure.
2. Experimental technique 2.1. Single-crystal growth and sample preparation The starting polycrystalline material, Sb2Te3+xmol% CdS (x=0–4) was synthesized from the elements Sb, and Te of 5 N purity and a CdS compound of 4.5N purity (Aldrich Chem. Co.) in evacuated conical silica ampoules at
1073 K for 48 h. The growth of the crystals was carried out in the same ampoule by means of a modified Bridgman method; the general approach and conditions for the growth of perfect single crystals of the tetradymite structure were described previously [7]. The resulting single crystals, 60 mm in length and 10 mm in diameter, could be easily cleaved. Their trigonal axis (the c-axis) was always perpendicular to the pulling direction, i.e., the (0 0 0 1) plane was parallel to the ampoule axis. The orientation of the cleavage faces was carried out using the Laue back-diffraction technique which confirmed that these mirror-like surfaces were always (0 0 0 1) planes. Samples were always prepared from the middle part of the single crystal. First we measured the reflectance on the cleavage faces and then we cut two samples from the same section using a spark erosion machine. The sample used for measurements of the electrical and thermal conductivity and for the Seebeck coefficient had dimensions 10 3 2 mm3; the smaller sample used to measure the Hall effect had dimensions 6 2 1 mm3. The actual concentrations of Cd and S incorporated in the crystal lattice of Sb2Te3 were determined using atomic absorption spectroscopy.
2.2. Determination of lattice parameters The lattice parameters of the single crystals were determined from powdered samples by X-ray diffraction analysis using an HZG-4B diffractometer (Freiberger Pra¨zisionmechanik, Germany). The diffraction maxima were measured by a step procedure using a step size of 0.018. The data were taken over the range of 2y =5–1008 with Cu Ka radiation in the range of 5 – 458 and with Ka1 radiation in the range of 45–1008; the Kb radiation was removed by a Ni filter. The calibration of the diffractometer was carried out with polycrystalline Si. The obtained diffraction lines were indexed according to Ref. [8] and the values of the lattice parameters a and c of the crystals were calculated by the least-squares method.
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2.3. Reflectance measurements
3. Results and discussion
Spectral dependences of the reflectance, R, in the plasma resonance frequency range were measured at room temperature in unpolarized light on natural (0 0 0 1) cleavage faces using a FT-IR spectrometer Bruker IFS 55. The light was at normal incidence to the (0 0 0 1) planes (the electric field vector E of the electromagnetic radiation was always perpendicular to the trigonal c-axis, i.e., E?c).
3.1. Lattice parameters The results of the X-ray diffraction analysis of Sb2Te3 crystals doped with CdS are given in Table 1 and the change in the lattice parameters as a function of the Cd and S content is plotted in Fig. 1. It is evident that with the increasing content of CdS, the lattice parameter a decreases while the
2.4. Thermal and electrical conductivity, and Seebeck and Hall coefficients Seebeck coefficient (thermopower) and thermal conductivity were determined using a longitudinal steady-state technique in a cryostat equipped with a radiation shield. Thermal gradients were measured with the aid of fine chromel–constantan differential thermocouples, and a miniature strain gauge served as a heater. For the Seebeck probes we used fine copper wires that have previously been calibrated, and their thermopower contribution subtracted from the measured sample thermopower. The Hall effect and electrical conductivity were studied using a Linear Research AC bridge with 16 Hz excitation in a magnet cryostat capable of fields up to 5 T. Measurements of these parameters were made over the temperature range of 4.2–300 K.
Fig. 1. Dependences of the lattice parameters on cadmium content cCd (+++) and sulphur content cS (&&&); a0 , c0 are lattice parameters of starting ‘‘pure’’ Sb2Te3.
Table 1 Lattice parameters of Sb2Te3 crystals doped with CdS Sample no.
cCd (1019 cmÿ3)
cS (1019 cmÿ3)
a (nm)
c (nm)
c=a
V (nm3)
D2Wa
1 2 3 4 5 6
0 2.57 6.69 9.75 17.60 20.03
0 4.15 5.02 9.68 15.33 18.14
0.42657(4) 0.42630(5) 0.42619(5) 0.42615(7) 0.42596(8) 0.42593(7)
3.0448(2) 3.0449(3) 3.0448(2) 3.0453(4) 3.0448(4) 3.0450(4)
7.138(3) 7.143(4) 7.144(3) 7.146(5) 7.148(6) 7.149(5)
0.4798(1) 0.4792(1) 0.4790(1) 0.4789(2) 0.4784(2) 0.4784(2)
0.0072 0.0113 0.0067 0.0139 0.0124 0.0107
P D2W ¼ N 1 2Wexp ÿ 2Wcalc =N, where 2Wexp is the experimental diffraction angle, 2Wcalc is the angle calculated from lattice parameters and N is number of investigated diffraction lines. a
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lattice parameter c changes very little. As a consequence, the unit cell of the structure is deformed and the ratio of the lattice parameters c=a increases. The reduction in the lattice parameter a also leads to a small reduction in the volume of the unit cell. The observed changes in the lattice parameters are taken as proof of incorporation of the Cd atoms in the Sb-sublattice and the S atoms in the sublattice of tellurium. This we surmise from a comparison of the sizes of atomic radii of Sb, Te, Cd, and S (rSb =0.159 nm, rTe =0.160 nm, rCd = 0.154 nm, and rS =0.129 nm). The major influence on the lattice parameter appears to be substitution of sulphur on the tellurium sites. The diffractograms of all samples showed only the lines corresponding to the tetradymite structure; the prepared crystals are thus classified under the D53d space group symmetry.
From the values of the plasma resonance frequency op and high-frequency relative permittivity e1 obtained in this way we calculated the values of the P=m? ratio using the relation valid for the presence of a single type of free charge carriers op ¼ ðPe2 =e0 e1 m? m0 Þ1=2 ;
ð1Þ
where P is the concentration of holes, e stands for the elementary charge, e0 is permittivity of free space, and m? m0 is the free carrier effective mass in the direction perpendicular to the trigonal axis (the c-axis). Making a simplifying approximation that the value of m? is constant in the investigated interval of the carrier densities, the ratii P=m? were used to calculate the charge carrier concentrations P. In this calculation we took the value of m? ¼ 0:109m0 , the value determined from mk ¼ 0:257m0 [10] and the ratio mk =m? ¼ 2:36 [11]. The results of this analysis are summarized in Table 2.
3.2. Interpretation of the reflectance spectra Reflectance spectra obtained on our samples are shown in Fig. 2. The reflectance curves R ¼ f ðnÞ reveal distinct minima which is evidence of good crystalline quality of the samples. The positions of the minima nmin are given in Table 2. With the increasing CdS content we observe a marked shift of the reflectance minima towards higher wavenumber values. In order to obtain information on the changes in the free carrier concentration associated with the incorporation of Cd and S into the Sb2Te3 lattice, the experimental R ¼ f ðnÞ curves were fitted using equations for the real and imaginary parts of the permittivity given by the Drude –Zener theory [9].
Fig. 2. Reflectance spectra of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
Table 2 Optical parameters of Sb2Te3 crystals doped with CdS Sample no.
umin (cmÿ1)
e1 (dimensionless)
t (10ÿ14 s)
op (1014 sÿ1)
P (1019 cmÿ3)
DP ¼ PÿP0 (1019 cmÿ3)
1 2 3 4 5 6
1080 1248 1444 1599 1772 1817
55 58 55 53 58 63
2.5 2.3 1.9 1.7 1.4 1.3
1.90 2.20 2.56 2.82 3.10 3.18
6.8 9.6 12.3 14.4 19.1 21.8
} 2.8 5.5 7.6 12.3 15.0
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Measurements of the Hall constant RH ðBkcÞ, Seebeck coefficient aðDT?cÞ and electrical resistivity r? are presented in Figs. 3 and 4. We note that both RH ðBkcÞ and aðDT?cÞ are positive and
that both decrease with the increasing content of CdS. This is a consequence of the increasing density of holes and the conclusion is in accord with the results obtained from the reflectance spectra measurements. From the temperature dependence of the electrical resistivity (see Fig. 4) we observe that at higher temperatures (T>100 K) the presence of CdS leads to a lower resistivity in comparison to the pure Sb2Te3. At temperatures below 100 K the trend is reversed. The crossover near 100 K arises due to a rapidly rising hole mobility in the pure Sb2Te3, while in the heavily doped structure the mobility of holes is a considerably weaker function of temperature. The general trend represented by a reduction in the hole mobility with the increasing content of CdS is due to the presence of the impurity in the crystal lattice; more specifically, due to the substitution of the Cd atoms on the Sb sublattice and the entry of the S atoms into the Te sublattice.
Fig. 3. Temperature dependences of the Hall coefficient RH ðBkcÞ and Seebeck coefficient aðDT?cÞ of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
Fig. 4. Temperature dependences of the electrical resistivity r?c and Hall mobility mH of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
It is evident that the values of P increase with the increasing content of CdS. According to the results of Ref. [12], the valence band structure of Sb2Te3 consists of two bands and therefore of two kinds of holes } those in the upper valence band (UVB), and those in the lower valence band (LVB). However, the two bands are not populated equally, the ratio of the LVB holes to that of the UVB holes is equal to 390. Therefore, we assume that for the analysis of the reflectance spectra we need to take into account only the existence of holes in the LVB, i.e., we assume that only one type of holes is present. 3.3. Hall constant, electrical resistivity and Seebeck coefficient
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3.4. Thermal conductivity Temperature dependence of the thermal conductivity is given in Fig. 5. An obvious feature here is a dramatic reduction of the conductivity below 100 K upon the presence of CdS in the Sb2Te3 lattice. We view this as a consequence of a strong point defect scattering arising from the incorporation of the Cd and S atoms in the respective sublattices of Sb and Te. At temperatures above 100 K we see very little difference between the thermal conductivities of the pure and doped Sb2Te3. It is known that thermal conductivity is, in general, the sum of two components. Thus, k ¼ kL þ ke , where k is the total thermal conductivity, kL is the lattice thermal conductivity, and ke is the electronic component of thermal conductivity. From the results of the reflectivity and the transport parameters if follows that the CdS impurity leads to an increase in the concentration of free charge carriers (holes). Thus, for the doped samples we expect a somewhat higher electronic contribution ke . Since for T>100 K we observe a practically T-independent total thermal conductivity, we would expect that the increasing ke compensates for the decreasing lattice contribution kL . It is therefore of interest to establish how large the respective thermal conductivity contributions ke and kL are.
The exact calculation of the electronic thermal conductivity is complicated by the presence of two valence bands [13] the parameters of which are not well established. However, making use of the Seebeck coefficient, we can estimate the value of the reduced Fermi energy Z and, assuming that the holes are scattered predominantly by acoustic phonons, we obtain Z > 4 for both doped samples. Consequently, we take both doped samples as degenerate and calculate ke using the following simple approach applicable for degenerate systems (this approach may not be suitable for the pure Sb2Te3). From the values of the electrical resistivity we calculate ke using the Wiedemann–Franz ratio, ke ¼ LT=r where L is the Lorenz number and T the absolute temperature. For a degenerate semiconductor we take L ¼ L0 ¼ p2 =3ðkB =eÞ2 , the socalled Sommerfeld value. Here kB is the Boltzmann constant. Subtracting ke from the total thermal conductivity we obtain the lattice component kL . The resulting thermal conductivity components plotted as a function of temperature are shown in Fig. 6. With the increasing CdS content we indeed observe higher electronic thermal conductivity while the lattice component is reduced. In the upper part of Fig. 6, we plot the temperature dependence of the lattice thermal resistivity WL ¼ 1=kL . As is well known, temperature dependence of WL for crystals containing impurities can be described by the equation WL ¼ AT þ B ¼ WL0 þ DW;
Fig. 5. Temperature dependences of the thermal conductivity k of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
ð2Þ
where WL0 is the thermal resistivity of a pure crystal and DW represents a contribution due to the presence of defects (impurities). The above equation is typically applicable at temperatures T > yD =3 where yD is the Debye temperature. From Fig. 6 it should be clear that, except at the highest temperatures, a straight line is a very good fit for the data above T 50 K. For Sb2Te3, the Debye temperature is about yD ’ 160 K. The departure of the data from the straight line observed for the sample #4 above 200 K and for the sample #3 above 250 K may be associated with the existence of two kinds of holes (light and heavy), the feature neglected in our analysis. Similar temperature dependence of WL was observed for Sb2Te3
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reasoned that DW was associated with the concentration of antisite defects of Bi atoms on the sites of Te atoms and that these defects carried a 0 negative charge ÿBiTe . In our opinion, with the increasing CdS content in Sb2Te3 we can likewise expect an increase in the concentration of charged point defects.
3.5. Point defects in Sb2Te3 crystals doped with CdS
Fig. 6. Temperature dependences of the total thermal conductivity k, lattice thermal conductivity kL , electronic contribution of the thermal conductivity ke and lattice thermal resistivity 1=kL of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
crystals [14] in which case the departure from the linear behavior was noted already at 200 K. The authors explained this behavior in terms of the presence of both types of holes. It should be noted, however, that such departures might arise on account of radiation losses that are difficult to eliminate completely for samples with very low thermal conductivity even in a well-designed experimental apparatus. In spite of an approximate nature of our estimate of ke and kL , from the functional dependence of WL it is clear that with the increasing content of CdS the impurity resistivity DW increases. We understand this in terms of the increasing density of point defects as the content of CdS increases. The effect is similar to that seen in the isostructural Bi2Te3 crystals where DW was observed to increase with the increasing (superstoichiometric) amount of Bi [15]. The authors
From the independent measurements of the reflectivity, Hall constant and thermopower described in the preceeding sections it follows that the incorporation of CdS in the crystal lattice of Sb2Te3 leads to a marked enhancement in the density of holes. This outcome is predicated by the character of point defects that arise in the Sb2Te3 lattice upon the intake of CdS. In this section, we present a model of point defects that, in our opinion, explains the origin of the enhanced free hole concentration in the CdSdoped Sb2Te3. The measured changes in the lattice parameter upon the incorporation of CdS in the Sb2Te3 lattice lead us to a conclusion that, when CdS is dissolved in the melt of Sb2Te3 during the growth of the crystals, CdS dissociates. Therefore, rather than entering into the tetradymite structure as a compound, it is the individual constituent atoms of Cd and S that get incorporated in the structure. Most likely, cadmium atoms enter substitutionally on the antimony sublattice while the atoms of sulphur are incorporated on the tellurium sublattice. This viewpoint is supported by the observed decrease in the lattice parameter a and the resulting reduction in the volume of the unit cell. According to the bonding picture developed by Krebs [16], Sb and Te atoms in the Sb2Te3 crystal are bonded by s-bonds formed by p-electrons of Sb (5p3) and p-electrons of Te (6p4). It follows that the substitutional defects such as Cd (5s2) on the Sb site must necessarily carry one negative charge, 0 . In this process, the two valence electrons of CdSb Cd are elevated into 5p orbitals and the formation of these defects can be schematically represented
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by the equation 2Cd þ 3Te ¼
Sb2 Te3 þ2Cd0Sb
þ 2 holes:
ð3Þ
The existence of the negatively charged substitutional defects Cd0Sb thus explains the experimentally observed enhancement in the concentration of holes. In contrast, assuming that the atoms of sulphur enter into the tellurium sublattice, we may expect them to give rise to the presence of uncharged substitutional defects on the sites of tellurium atoms, S Te . In order to ascertain whether the amount of incorporated Cd corresponds to the observed enhancement in the density of holes, we calculated the quantity DP ¼ P ÿ P0 , where P represents the concentration of holes in the CdS-doped Sb2Te3 while P0 is the concentration of holes in the pure Sb2Te3. The respective concentrations were obtained from the interpretation of the reflectivity data. Fig. 7 displays the data of DP as a function of concentration of the incorporated cadmium. It is clear that the functional dependence is a linear function with the slope of approximately 0.75. Therefore, only 75% of the incorporated Cd atoms form the Cd0Sb defects and thus increase the concentration of holes. If we consider, in addition to Cd, that S also is incorporated in the Sb2Te3 lattice, we can explain the less than perfect
Fig. 7. Dependence of the change in the free carrier concentration DP on the concentration of Cd atoms cCd for Sb2Te3 single crystals doped with CdS.
electrical activity of the Cd atoms. Our explanation is based on the previously observed [17–19] behavior of S in single crystals of Bi2 Te3ÿx Sx . In that specific case, changes in the optical properties and in selected transport coefficients suggested that the incorporation of sulphur into the Bi2Te3 lattice is accompanied by a reduction in the concentration of holes. The effect was explained in terms of an interaction between the uncharged substitutional defects S Te and the antisite defects of the type Bi0Te , the latter being present in the Bi2Te3 lattice as a result of the superstoichiometric amount of Bi. The atoms of sulphur located on the sites otherwise occupied by the tellurium atoms carry, as a result of the higher electronegativity of sulphur in comparison to tellurium, a partially ðÿdÞ negative charge, STe . For this reason, the bonds ðÿdÞ between STe and the atoms of Bi acquire a somewhat more polar character than the bonds between Te and Bi. The enhanced polar nature of the bonds leads to an increase in the energy of formation of the antistructural defects and, as a consequence, the density of these kinds of defects is much suppressed. The reduced concentration of Bi0Te then leads to a reduction in the concentration of holes. Based on this reasoning, we can likewise expect that when the atoms of sulphur enter the ðÿdÞ lattice of Sb2Te3, the formation of the STe defects will lead to a suppression in the concentration of the antistructural defects of the type Sb0Te , and thus to a reduction in the concentration of holes. The fact that during a simultaneous incorporation of both Cd and S atoms in the Sb2Te3 crystals there arise two kinds of defects } Cd0Sb which tends to increase the concentration of holes, and ðÿdÞ STe which causes a reduction in the hole density } is the main reason why only 75% of the incorporated cadmium atoms appear electrically active. Simply stated, a fraction of the holes (25%) generated as a result of the formation of the Cd0Sb defects is compensated by a reduced concentration of the Sb0Te antistructural defects that form as the sulphur atoms enter the lattice. We therefore conclude that the observed increase in the concentration of holes with the increasing content of CdS in the Sb2Te3 lattice is most likely associated with the formation of the Cd0Sb defects. We believe that such defects exert
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an overriding influence on the thermal resistivity of the crystalline lattice, i.e., they are the main contributing factor to DW, as discussed in Section 3.4. 4. Conclusions The analysis of the lattice parameters, reflectance in the plasma resonance frequency region, Hall and Seebeck coefficients, electrical resistivity and thermal conductivity of single crystalline samples of Sb2Te3 doped with CdS can be summarized as follows: The CdS compound dissociates in the process of crystal growth of the tetradymite structure and the Sb2Te3 lattice incorporates elemental Cd and S atoms. This leads to (a) a reduction in the lattice parameter a while the lattice constant c is essentially unchanged, (b) a marked increase in the concentration of holes. The increased concentration of holes is most likely the result of the formation of Cd0Sb defects as cadmium atoms are being incorporated on the antimony sublattice. In the process of formation of this kind of defect, apparently only 34 of the incorporated atoms of cadmium are active. The reduced electrical activity of cadmium in the Sb2Te3 lattice is associated with the simultaneous incorporation of sulphur on the tellurium sublattice that, via a reduced concentration of the Sb0Te antistructural defects, leads to a lower density of free hole carriers. Acknowledgements The authors gratefully acknowledge the NATO support provided under the grant HTECH.CRG 973186.
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Preparation and some physical properties of tetradymite-type Sb2Te3 single crystals doped with CdS P. Losˇ t’a´ka,*, C˘. Drasˇ ara, A. Krejc˘ova´a, L. Benesˇ b, J.S. Dyckc, W. Chenc, C. Uherc Faculty of Chemical Technology, University of Pardubice, C˘s. Legiı´ Square 565, 532 10 Pardubice, Czech Republic Joint Laboratory of Solid State Chemistry, Czech Academy of Sciences and University of Pardubice, Studentska´ 64, 530 09 Pardubice, Czech Republic c Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
a b
Received 28 April 1999; accepted 22 October 2000 Communicated by J.B. Mullin
Abstract Single crystals of Sb2Te3 doped with CdS were prepared by a modified Bridgman method from the elements Sb and Te of 5 N purity and the CdS compound of 4.5 N purity. Samples were characterized by X-ray diffraction and by measurement of reflectance in the plasma resonance frequency region at room temperature. Furthermore, we made measurements of temperature dependence of the electrical resistivity, Hall and Seebeck coefficients, and thermal conductivity in the temperature range of 4.2–300 K. In the process of crystal growth, CdS dissociated and it was assumed that the Cd-atoms formed substitutional defects in the Sb-sublattice (Cd0Sb ) while the S-atoms formed ðÿdÞ substitutional defects in the Te-sublattice (STe ). # 2001 Elsevier Science B.V. All rights reserved. PACS: 72.80.Jc; 78.20.Ci; 61.72.Ji Keywords: Layered narrow-gap semiconductors; Reflectance; Electrical and thermal conductivities; Hall and Seebeck coefficients; Point defects
1. Introduction Antimony telluride (Sb2Te3) belongs to the family of layered-type semiconductors with tetradymite structure (space group D53d ) which are used in applications such as thermoelectric generators and coolers [1]. Therefore, an investigation of the effect of various dopants on the physical properties *Corresponding author. Tel.: +42-040-603-7168; fax: +42040-603-7068. E-mail address: [email protected] (P. Losˇ t’a´k).
of Sb2Te3 is interesting for both basic and applied research. Despite considerable attention devoted to the study of the changes in the properties of antimony telluride due to the presence of foreign atoms in its crystal structure, the available literature provides little insight into the influence of Cd or S impurities. It follows from the phase diagram of the Sb2Te3–CdTe system [2,3] that substitutional solid solutions based on the Sb2Te3 tetradymite structure exist in this system in the concentration range
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of 0–7 mol% CdTe. The authors of Ref. [3] also described the existence of a compound CdSb2Te4 which forms by peritectic reaction at 590 K. The transport coefficients (electrical resistivity, Hall constant, Seebeck coefficient and thermal conductivity) of polycrystalline Sb2Te3 doped with CdTe were studied previously [2]. Furthermore, it has been shown that the Cd impurity in Sb2Te3 gives rise to an increase in the free carrier density. This conclusion follows also from the results of the measurements of several transport parameters [4]. Cd atoms were also doped into single crystal forms of Sb2Te3 and the increased free carrier concentration was explained by the formation of substitutional defects Cd0Sb [5]. The phase diagram of the Sb2Te3–CdS system was determined by differential thermal analysis, microhardness, and by microstructural and X-ray phase analysis [6]. The data indicate that solid solutions based on Sb2Te3 occur for concentrations up to 12 mol% CdS. It was also shown that a new compound CdSb2Te3S forms by a peritectic reaction at 910 K. The effect of the CdS impurities or its constituents on the physical properties of antimony telluride single crystals has not yet been studied. In this communication we describe the method of preparation of single crystals of Sb2Te3 doped with CdS and we present a range of optical and transport measurements with which we characterize the structure and its physical properties. Our results are consistent with CdS dissociating upon melting and, rather than entering the structure as a compound, it breaks into its elemental constituents that incorporate themselves into the respective Sb and Te sublattices and form point defects in the tetradymite structure.
2. Experimental technique 2.1. Single-crystal growth and sample preparation The starting polycrystalline material, Sb2Te3+xmol% CdS (x=0–4) was synthesized from the elements Sb, and Te of 5 N purity and a CdS compound of 4.5N purity (Aldrich Chem. Co.) in evacuated conical silica ampoules at
1073 K for 48 h. The growth of the crystals was carried out in the same ampoule by means of a modified Bridgman method; the general approach and conditions for the growth of perfect single crystals of the tetradymite structure were described previously [7]. The resulting single crystals, 60 mm in length and 10 mm in diameter, could be easily cleaved. Their trigonal axis (the c-axis) was always perpendicular to the pulling direction, i.e., the (0 0 0 1) plane was parallel to the ampoule axis. The orientation of the cleavage faces was carried out using the Laue back-diffraction technique which confirmed that these mirror-like surfaces were always (0 0 0 1) planes. Samples were always prepared from the middle part of the single crystal. First we measured the reflectance on the cleavage faces and then we cut two samples from the same section using a spark erosion machine. The sample used for measurements of the electrical and thermal conductivity and for the Seebeck coefficient had dimensions 10 3 2 mm3; the smaller sample used to measure the Hall effect had dimensions 6 2 1 mm3. The actual concentrations of Cd and S incorporated in the crystal lattice of Sb2Te3 were determined using atomic absorption spectroscopy.
2.2. Determination of lattice parameters The lattice parameters of the single crystals were determined from powdered samples by X-ray diffraction analysis using an HZG-4B diffractometer (Freiberger Pra¨zisionmechanik, Germany). The diffraction maxima were measured by a step procedure using a step size of 0.018. The data were taken over the range of 2y =5–1008 with Cu Ka radiation in the range of 5 – 458 and with Ka1 radiation in the range of 45–1008; the Kb radiation was removed by a Ni filter. The calibration of the diffractometer was carried out with polycrystalline Si. The obtained diffraction lines were indexed according to Ref. [8] and the values of the lattice parameters a and c of the crystals were calculated by the least-squares method.
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2.3. Reflectance measurements
3. Results and discussion
Spectral dependences of the reflectance, R, in the plasma resonance frequency range were measured at room temperature in unpolarized light on natural (0 0 0 1) cleavage faces using a FT-IR spectrometer Bruker IFS 55. The light was at normal incidence to the (0 0 0 1) planes (the electric field vector E of the electromagnetic radiation was always perpendicular to the trigonal c-axis, i.e., E?c).
3.1. Lattice parameters The results of the X-ray diffraction analysis of Sb2Te3 crystals doped with CdS are given in Table 1 and the change in the lattice parameters as a function of the Cd and S content is plotted in Fig. 1. It is evident that with the increasing content of CdS, the lattice parameter a decreases while the
2.4. Thermal and electrical conductivity, and Seebeck and Hall coefficients Seebeck coefficient (thermopower) and thermal conductivity were determined using a longitudinal steady-state technique in a cryostat equipped with a radiation shield. Thermal gradients were measured with the aid of fine chromel–constantan differential thermocouples, and a miniature strain gauge served as a heater. For the Seebeck probes we used fine copper wires that have previously been calibrated, and their thermopower contribution subtracted from the measured sample thermopower. The Hall effect and electrical conductivity were studied using a Linear Research AC bridge with 16 Hz excitation in a magnet cryostat capable of fields up to 5 T. Measurements of these parameters were made over the temperature range of 4.2–300 K.
Fig. 1. Dependences of the lattice parameters on cadmium content cCd (+++) and sulphur content cS (&&&); a0 , c0 are lattice parameters of starting ‘‘pure’’ Sb2Te3.
Table 1 Lattice parameters of Sb2Te3 crystals doped with CdS Sample no.
cCd (1019 cmÿ3)
cS (1019 cmÿ3)
a (nm)
c (nm)
c=a
V (nm3)
D2Wa
1 2 3 4 5 6
0 2.57 6.69 9.75 17.60 20.03
0 4.15 5.02 9.68 15.33 18.14
0.42657(4) 0.42630(5) 0.42619(5) 0.42615(7) 0.42596(8) 0.42593(7)
3.0448(2) 3.0449(3) 3.0448(2) 3.0453(4) 3.0448(4) 3.0450(4)
7.138(3) 7.143(4) 7.144(3) 7.146(5) 7.148(6) 7.149(5)
0.4798(1) 0.4792(1) 0.4790(1) 0.4789(2) 0.4784(2) 0.4784(2)
0.0072 0.0113 0.0067 0.0139 0.0124 0.0107
P D2W ¼ N 1 2Wexp ÿ 2Wcalc =N, where 2Wexp is the experimental diffraction angle, 2Wcalc is the angle calculated from lattice parameters and N is number of investigated diffraction lines. a
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lattice parameter c changes very little. As a consequence, the unit cell of the structure is deformed and the ratio of the lattice parameters c=a increases. The reduction in the lattice parameter a also leads to a small reduction in the volume of the unit cell. The observed changes in the lattice parameters are taken as proof of incorporation of the Cd atoms in the Sb-sublattice and the S atoms in the sublattice of tellurium. This we surmise from a comparison of the sizes of atomic radii of Sb, Te, Cd, and S (rSb =0.159 nm, rTe =0.160 nm, rCd = 0.154 nm, and rS =0.129 nm). The major influence on the lattice parameter appears to be substitution of sulphur on the tellurium sites. The diffractograms of all samples showed only the lines corresponding to the tetradymite structure; the prepared crystals are thus classified under the D53d space group symmetry.
From the values of the plasma resonance frequency op and high-frequency relative permittivity e1 obtained in this way we calculated the values of the P=m? ratio using the relation valid for the presence of a single type of free charge carriers op ¼ ðPe2 =e0 e1 m? m0 Þ1=2 ;
ð1Þ
where P is the concentration of holes, e stands for the elementary charge, e0 is permittivity of free space, and m? m0 is the free carrier effective mass in the direction perpendicular to the trigonal axis (the c-axis). Making a simplifying approximation that the value of m? is constant in the investigated interval of the carrier densities, the ratii P=m? were used to calculate the charge carrier concentrations P. In this calculation we took the value of m? ¼ 0:109m0 , the value determined from mk ¼ 0:257m0 [10] and the ratio mk =m? ¼ 2:36 [11]. The results of this analysis are summarized in Table 2.
3.2. Interpretation of the reflectance spectra Reflectance spectra obtained on our samples are shown in Fig. 2. The reflectance curves R ¼ f ðnÞ reveal distinct minima which is evidence of good crystalline quality of the samples. The positions of the minima nmin are given in Table 2. With the increasing CdS content we observe a marked shift of the reflectance minima towards higher wavenumber values. In order to obtain information on the changes in the free carrier concentration associated with the incorporation of Cd and S into the Sb2Te3 lattice, the experimental R ¼ f ðnÞ curves were fitted using equations for the real and imaginary parts of the permittivity given by the Drude –Zener theory [9].
Fig. 2. Reflectance spectra of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
Table 2 Optical parameters of Sb2Te3 crystals doped with CdS Sample no.
umin (cmÿ1)
e1 (dimensionless)
t (10ÿ14 s)
op (1014 sÿ1)
P (1019 cmÿ3)
DP ¼ PÿP0 (1019 cmÿ3)
1 2 3 4 5 6
1080 1248 1444 1599 1772 1817
55 58 55 53 58 63
2.5 2.3 1.9 1.7 1.4 1.3
1.90 2.20 2.56 2.82 3.10 3.18
6.8 9.6 12.3 14.4 19.1 21.8
} 2.8 5.5 7.6 12.3 15.0
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Measurements of the Hall constant RH ðBkcÞ, Seebeck coefficient aðDT?cÞ and electrical resistivity r? are presented in Figs. 3 and 4. We note that both RH ðBkcÞ and aðDT?cÞ are positive and
that both decrease with the increasing content of CdS. This is a consequence of the increasing density of holes and the conclusion is in accord with the results obtained from the reflectance spectra measurements. From the temperature dependence of the electrical resistivity (see Fig. 4) we observe that at higher temperatures (T>100 K) the presence of CdS leads to a lower resistivity in comparison to the pure Sb2Te3. At temperatures below 100 K the trend is reversed. The crossover near 100 K arises due to a rapidly rising hole mobility in the pure Sb2Te3, while in the heavily doped structure the mobility of holes is a considerably weaker function of temperature. The general trend represented by a reduction in the hole mobility with the increasing content of CdS is due to the presence of the impurity in the crystal lattice; more specifically, due to the substitution of the Cd atoms on the Sb sublattice and the entry of the S atoms into the Te sublattice.
Fig. 3. Temperature dependences of the Hall coefficient RH ðBkcÞ and Seebeck coefficient aðDT?cÞ of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
Fig. 4. Temperature dependences of the electrical resistivity r?c and Hall mobility mH of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
It is evident that the values of P increase with the increasing content of CdS. According to the results of Ref. [12], the valence band structure of Sb2Te3 consists of two bands and therefore of two kinds of holes } those in the upper valence band (UVB), and those in the lower valence band (LVB). However, the two bands are not populated equally, the ratio of the LVB holes to that of the UVB holes is equal to 390. Therefore, we assume that for the analysis of the reflectance spectra we need to take into account only the existence of holes in the LVB, i.e., we assume that only one type of holes is present. 3.3. Hall constant, electrical resistivity and Seebeck coefficient
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3.4. Thermal conductivity Temperature dependence of the thermal conductivity is given in Fig. 5. An obvious feature here is a dramatic reduction of the conductivity below 100 K upon the presence of CdS in the Sb2Te3 lattice. We view this as a consequence of a strong point defect scattering arising from the incorporation of the Cd and S atoms in the respective sublattices of Sb and Te. At temperatures above 100 K we see very little difference between the thermal conductivities of the pure and doped Sb2Te3. It is known that thermal conductivity is, in general, the sum of two components. Thus, k ¼ kL þ ke , where k is the total thermal conductivity, kL is the lattice thermal conductivity, and ke is the electronic component of thermal conductivity. From the results of the reflectivity and the transport parameters if follows that the CdS impurity leads to an increase in the concentration of free charge carriers (holes). Thus, for the doped samples we expect a somewhat higher electronic contribution ke . Since for T>100 K we observe a practically T-independent total thermal conductivity, we would expect that the increasing ke compensates for the decreasing lattice contribution kL . It is therefore of interest to establish how large the respective thermal conductivity contributions ke and kL are.
The exact calculation of the electronic thermal conductivity is complicated by the presence of two valence bands [13] the parameters of which are not well established. However, making use of the Seebeck coefficient, we can estimate the value of the reduced Fermi energy Z and, assuming that the holes are scattered predominantly by acoustic phonons, we obtain Z > 4 for both doped samples. Consequently, we take both doped samples as degenerate and calculate ke using the following simple approach applicable for degenerate systems (this approach may not be suitable for the pure Sb2Te3). From the values of the electrical resistivity we calculate ke using the Wiedemann–Franz ratio, ke ¼ LT=r where L is the Lorenz number and T the absolute temperature. For a degenerate semiconductor we take L ¼ L0 ¼ p2 =3ðkB =eÞ2 , the socalled Sommerfeld value. Here kB is the Boltzmann constant. Subtracting ke from the total thermal conductivity we obtain the lattice component kL . The resulting thermal conductivity components plotted as a function of temperature are shown in Fig. 6. With the increasing CdS content we indeed observe higher electronic thermal conductivity while the lattice component is reduced. In the upper part of Fig. 6, we plot the temperature dependence of the lattice thermal resistivity WL ¼ 1=kL . As is well known, temperature dependence of WL for crystals containing impurities can be described by the equation WL ¼ AT þ B ¼ WL0 þ DW;
Fig. 5. Temperature dependences of the thermal conductivity k of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
ð2Þ
where WL0 is the thermal resistivity of a pure crystal and DW represents a contribution due to the presence of defects (impurities). The above equation is typically applicable at temperatures T > yD =3 where yD is the Debye temperature. From Fig. 6 it should be clear that, except at the highest temperatures, a straight line is a very good fit for the data above T 50 K. For Sb2Te3, the Debye temperature is about yD ’ 160 K. The departure of the data from the straight line observed for the sample #4 above 200 K and for the sample #3 above 250 K may be associated with the existence of two kinds of holes (light and heavy), the feature neglected in our analysis. Similar temperature dependence of WL was observed for Sb2Te3
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reasoned that DW was associated with the concentration of antisite defects of Bi atoms on the sites of Te atoms and that these defects carried a 0 negative charge ÿBiTe . In our opinion, with the increasing CdS content in Sb2Te3 we can likewise expect an increase in the concentration of charged point defects.
3.5. Point defects in Sb2Te3 crystals doped with CdS
Fig. 6. Temperature dependences of the total thermal conductivity k, lattice thermal conductivity kL , electronic contribution of the thermal conductivity ke and lattice thermal resistivity 1=kL of Sb2Te3 single crystals doped with CdS (the samples are labelled according to Table 1).
crystals [14] in which case the departure from the linear behavior was noted already at 200 K. The authors explained this behavior in terms of the presence of both types of holes. It should be noted, however, that such departures might arise on account of radiation losses that are difficult to eliminate completely for samples with very low thermal conductivity even in a well-designed experimental apparatus. In spite of an approximate nature of our estimate of ke and kL , from the functional dependence of WL it is clear that with the increasing content of CdS the impurity resistivity DW increases. We understand this in terms of the increasing density of point defects as the content of CdS increases. The effect is similar to that seen in the isostructural Bi2Te3 crystals where DW was observed to increase with the increasing (superstoichiometric) amount of Bi [15]. The authors
From the independent measurements of the reflectivity, Hall constant and thermopower described in the preceeding sections it follows that the incorporation of CdS in the crystal lattice of Sb2Te3 leads to a marked enhancement in the density of holes. This outcome is predicated by the character of point defects that arise in the Sb2Te3 lattice upon the intake of CdS. In this section, we present a model of point defects that, in our opinion, explains the origin of the enhanced free hole concentration in the CdSdoped Sb2Te3. The measured changes in the lattice parameter upon the incorporation of CdS in the Sb2Te3 lattice lead us to a conclusion that, when CdS is dissolved in the melt of Sb2Te3 during the growth of the crystals, CdS dissociates. Therefore, rather than entering into the tetradymite structure as a compound, it is the individual constituent atoms of Cd and S that get incorporated in the structure. Most likely, cadmium atoms enter substitutionally on the antimony sublattice while the atoms of sulphur are incorporated on the tellurium sublattice. This viewpoint is supported by the observed decrease in the lattice parameter a and the resulting reduction in the volume of the unit cell. According to the bonding picture developed by Krebs [16], Sb and Te atoms in the Sb2Te3 crystal are bonded by s-bonds formed by p-electrons of Sb (5p3) and p-electrons of Te (6p4). It follows that the substitutional defects such as Cd (5s2) on the Sb site must necessarily carry one negative charge, 0 . In this process, the two valence electrons of CdSb Cd are elevated into 5p orbitals and the formation of these defects can be schematically represented
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by the equation 2Cd þ 3Te ¼
Sb2 Te3 þ2Cd0Sb
þ 2 holes:
ð3Þ
The existence of the negatively charged substitutional defects Cd0Sb thus explains the experimentally observed enhancement in the concentration of holes. In contrast, assuming that the atoms of sulphur enter into the tellurium sublattice, we may expect them to give rise to the presence of uncharged substitutional defects on the sites of tellurium atoms, S Te . In order to ascertain whether the amount of incorporated Cd corresponds to the observed enhancement in the density of holes, we calculated the quantity DP ¼ P ÿ P0 , where P represents the concentration of holes in the CdS-doped Sb2Te3 while P0 is the concentration of holes in the pure Sb2Te3. The respective concentrations were obtained from the interpretation of the reflectivity data. Fig. 7 displays the data of DP as a function of concentration of the incorporated cadmium. It is clear that the functional dependence is a linear function with the slope of approximately 0.75. Therefore, only 75% of the incorporated Cd atoms form the Cd0Sb defects and thus increase the concentration of holes. If we consider, in addition to Cd, that S also is incorporated in the Sb2Te3 lattice, we can explain the less than perfect
Fig. 7. Dependence of the change in the free carrier concentration DP on the concentration of Cd atoms cCd for Sb2Te3 single crystals doped with CdS.
electrical activity of the Cd atoms. Our explanation is based on the previously observed [17–19] behavior of S in single crystals of Bi2 Te3ÿx Sx . In that specific case, changes in the optical properties and in selected transport coefficients suggested that the incorporation of sulphur into the Bi2Te3 lattice is accompanied by a reduction in the concentration of holes. The effect was explained in terms of an interaction between the uncharged substitutional defects S Te and the antisite defects of the type Bi0Te , the latter being present in the Bi2Te3 lattice as a result of the superstoichiometric amount of Bi. The atoms of sulphur located on the sites otherwise occupied by the tellurium atoms carry, as a result of the higher electronegativity of sulphur in comparison to tellurium, a partially ðÿdÞ negative charge, STe . For this reason, the bonds ðÿdÞ between STe and the atoms of Bi acquire a somewhat more polar character than the bonds between Te and Bi. The enhanced polar nature of the bonds leads to an increase in the energy of formation of the antistructural defects and, as a consequence, the density of these kinds of defects is much suppressed. The reduced concentration of Bi0Te then leads to a reduction in the concentration of holes. Based on this reasoning, we can likewise expect that when the atoms of sulphur enter the ðÿdÞ lattice of Sb2Te3, the formation of the STe defects will lead to a suppression in the concentration of the antistructural defects of the type Sb0Te , and thus to a reduction in the concentration of holes. The fact that during a simultaneous incorporation of both Cd and S atoms in the Sb2Te3 crystals there arise two kinds of defects } Cd0Sb which tends to increase the concentration of holes, and ðÿdÞ STe which causes a reduction in the hole density } is the main reason why only 75% of the incorporated cadmium atoms appear electrically active. Simply stated, a fraction of the holes (25%) generated as a result of the formation of the Cd0Sb defects is compensated by a reduced concentration of the Sb0Te antistructural defects that form as the sulphur atoms enter the lattice. We therefore conclude that the observed increase in the concentration of holes with the increasing content of CdS in the Sb2Te3 lattice is most likely associated with the formation of the Cd0Sb defects. We believe that such defects exert
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an overriding influence on the thermal resistivity of the crystalline lattice, i.e., they are the main contributing factor to DW, as discussed in Section 3.4. 4. Conclusions The analysis of the lattice parameters, reflectance in the plasma resonance frequency region, Hall and Seebeck coefficients, electrical resistivity and thermal conductivity of single crystalline samples of Sb2Te3 doped with CdS can be summarized as follows: The CdS compound dissociates in the process of crystal growth of the tetradymite structure and the Sb2Te3 lattice incorporates elemental Cd and S atoms. This leads to (a) a reduction in the lattice parameter a while the lattice constant c is essentially unchanged, (b) a marked increase in the concentration of holes. The increased concentration of holes is most likely the result of the formation of Cd0Sb defects as cadmium atoms are being incorporated on the antimony sublattice. In the process of formation of this kind of defect, apparently only 34 of the incorporated atoms of cadmium are active. The reduced electrical activity of cadmium in the Sb2Te3 lattice is associated with the simultaneous incorporation of sulphur on the tellurium sublattice that, via a reduced concentration of the Sb0Te antistructural defects, leads to a lower density of free hole carriers. Acknowledgements The authors gratefully acknowledge the NATO support provided under the grant HTECH.CRG 973186.
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