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Investigation of the Weak‐Field Charge Transport in Semiconducting V2−VI3 Compounds with Trigonal Symmetry II. Interpretation of the Weak‐Field Charge Transport in Sb2Te3 Single Crystals
Abstract
It is succeeded for the first time to interpret the thermoelectric and galvanomagnetic effects, in terms of a nonparabolic six-valley one-valence band model and anisotropic mixed scattering on acoustical phonons and ionized impurities and also the magnitude of thermomagnetic effects and the Lorenz numbers for Sb2Te3 single crystals in dependence on temperature between 100 to 300 K using physical relevant microscopic transport data. By a numerical analysis the effective main axis masses mHii, the tilt angle of Fermi ellipsoid ϑ, the masses m ⟂ c, m ‖ c, the density of state effective mass md, the mobilities u ⟂ c, u ‖ c, and the carrier density ptot are calculated. Also the Fermi level EF, the relaxation time factor τac0, the mixture parameters BHi and theparameter of nonparabolicity β are given. The calculated values are ingood agreement with the corresponding data found by using optical effects at 80 K and 300 K.Im Rahmen eines nichtparabolischen Sechstal-Ein-Valenzbandmodells und anisotrop-gemischter Streuung an akustischen Phononen und ionisierten Störstellen ist es erstmals gelungen, die Temperaturabhngigkeit zwischen 100 und 300 K der thermoelektrischen, galvanomagnetischen sowie der Größe der thermomagnetischen Effekte und der Lorenzzahlen von Sb2Te3−Einkristallen mit physikalisch relevanten mikroskopischen Transportdaten zu erklren. Mittels einer numerischen Analyse werden die effektiven Hauptachsenmassen mHii, der Neigungswinkel des Fermiellipsoids ϑ, die Massen m ⟂ c, m ‖ c, die effektive Zustandsdichtemasse md, die Beweglichkeiten u ⟂ c, u ‖ c und die Trgerdichte ptot berechnet. Außerdem werden das Ferminiveau EF, der Relaxationszeitfaktor τac0, die Mischungsparameter BHi und der Parameter der Nichtparabolizitt β angegeben. Die berechneten Werte sind in guter Übereinstimmung mit entsprechenden bei 80 und 300 K unter Nutzung von optischen Effekten gefolgerten Daten.
... It is evident that for all samples the ln(|R H /r|) vs. lnT dependence has a slope somewhat bigger than À 3 2 . This is probably connected with the fact that, in the crystal lattice of Bi 2 Se 3 , the transport phenomena can be described, according to Stordeur and Simon [12], by a mixed scattering mechanism of free carriers by acoustic phonons and ionized impurities. At room temperature, the scattering mechanism is governed mainly by the phonon scattering, whereas the scattering by the ionized impurities becomes gradually more important with decreasing temperature. ...
Single crystals of Bi2Se3 doped with Mn (cMn=0–3.0×1019atoms/cm3) were grown using a modified Bridgman method. The prepared samples were characterized by X-ray diffraction and chemical analysis, and subsequently investigated by measurements of the reflectivity in the plasma-resonance-frequency region and by measurements of the temperature and magnetic field dependencies of the magnetization, specific heat and transport properties. The results show that incorporation of Mn atoms in the crystal structure leads to an increase of the free-electron concentration, as well as to an increase of the mobility of the free electrons. The Mn2+ valence state of the Mn ions has been established by magnetic measurements, which show a different behavior than the scenario proposed by Choi et al. [J. Choi, H.-W. Lee, B.-S. Kim, S. Choi, J. Choi, J. H. Song and S. Cho, J. Appl. Phys. 97, 10D324 (2005)]. The observations are explained in terms of the point-defect model, which is based on the idea that the Mn impurities create substitutional defects of the Mn′Bi-type and reduce the concentration of antistructure Bi′Se defects.
... Such extraordinary states feature spin-momentum locked helical Dirac fermions [11], giving TIs great promise in spintronics [12] and fault-tolerant quantum computing [13]. Sb 2 Te 3 has been extensively studied in the context of thermoelectric material research [10,14,15] and the growth of Sb 2 Te 3 films by molecular beam epitaxy and other techniques has been investigated [16][17][18][19]. It is generally known that the surface states of TIs are robust against external perturbations because they are protected by time-reversal symmetry. ...
The effects of S atom surface adsorption and substitution on the helical surface states of Sb2Te3 are studied by the density-functional theory with spin-orbit coupling being taken into account self-consistently. It is found that S atoms play the role of surface passivation when adsorbed on both surfaces of a 6QL Sb2Te3 film in symmetrical configuration. For symmetrical surfaces with both the top and bottom surfaces of a thin film with adsorbed S atoms, the linear dispersion of the surface states is found to be preserved and the topological surface states survive. The spatial distribution of charge density of the surface state at the [Formula: see text] point is also symmetric. For a film with asymmetric S atom adsorption, i.e., only one of the surfaces has adsorbed S atoms, the surface band structure is found to be very different. The degeneracy of the surface states from the two sides of a film is broken. The gap opens slightly at [Formula: see text] and the spatial distribution of charge density of the surface state at the [Formula: see text] point is also modified greatly. The Fermi level is robust against S impurity adsorption on the surface of Sb2Te3. Compared with S substitution, the effect of single surface S adsorption on electron structures is more prominent. This supports the idea that the topological insulator surface electronic states are dominated by its structural symmetry and the effect of the asymmetric environment of topological insulator Sb2Te3 films should thus be considered.
... In these materials, doping had to be used to move the Fermi energy back to the bulk gap [13, 14, 16]. Sb 2 Te 3 has been extensively studied in the context of thermoelectric material research [30, 31] and the growth of Sb 2 Te 3 films by MBE and other techniques has been investigated323334. In fact, p-type Bi 2 Te 3 /Sb 2 Te 3 superlattices were found to possess the highest thermoelectric figure of merit (ZT) of about 2.4 at 300 K [35]. ...
The growth and characterization of single-crystalline thin films of topological insulators (TIs) is an important step towards
their possible applications. Using in situ scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), we show that moderately thick
Sb2Te3 films grown layer-by-layer by molecular beam epitaxy (MBE) on Si(111) are atomically smooth, single-crystalline, and intrinsically
insulating. Furthermore, these films were found to exhibit a robust TI electronic structure with their Fermi energy lying
within the energy gap of the bulk that intersects only the Dirac cone of the surface states. Depositing Cs in situ moves the Fermi energy of the Sb2Te3 films without changing the electronic band structure, as predicted by theory. We found that the TI behavior is preserved
in Sb2Te3 films down to five quintuple layers (QLs).
KeywordsTopological insulator-electronic structure-scanning tunneling microscopy-angle-resolved photoemission spectroscopy-molecular beam epitaxy
Defects and defect engineering are at the core of many regimes of material research, including the field of thermoelectric study. The 60-year history of V2VI3 thermoelectric materials is a prime example of how a class of semiconductor material, considered mature several times, can be rejuvenated by better understanding and manipulation of defects. This review aims to provide a systematic account of the underexplored intrinsic point defects in V2VI3 compounds, with regard to (i) their formation and control, and (ii) their interplay with other types of defects towards higher thermoelectric performance. We herein present a convincing case that intrinsic point defects can be actively controlled by extrinsic doping and also via compositional, mechanical, and thermal control at various stages of material synthesis. An up-to-date understanding of intrinsic point defects in V2VI3 compounds is summarized in a (χ, r)-model and applied to elucidating the donor-like effect. These new insights not only enable more innovative defect engineering in other thermoelectric materials but also, in a broad context, contribute to rational defect design in advanced functional materials at large.
Single crystals of Bi2Se3 doped with Cr (cCr = 0 - 3:2 × 1019 atoms/cm3) were grown using a modified Bridgman method. The prepared samples were characterized by X-ray diffraction and chemical analysis, and subsequently investigated by measurements of the temperature- and magnetic-field dependencies of the magnetization and transport properties. The results show that incorporation of Cr atoms into the crystal structure leads to an increase of the free-electron concentration as well as to an increase of the mobility of the free electrons. The Cr3+ valence state of the Cr ions has been established by magnetic measurements. The observations are explained in terms of the point-defect model, which is based on the idea that the Cr impurities create substitutional defects of the Cr ×Bi -type and reduce the concentration of antistructure Bi'Se defects; a similar behavior like in the case of single crystalline Bi2Se 3 doped with another transition metals.
Measurements of dc electrical conductivity and optical properties have been made on InSbTe3 thin films prepared by thermal evaporation having different thickness (25-150) nm range. The structure of InSbTe3 in its powder and thin film forms were investigated by X-ray diffraction (XRD). The electrical conductivity was measured in the temperature (303-392) K range. The obtained values of dc electrical conduction activation energy Delta E-sigma were found to be nearly independent on the film thickness and have the mean value of 0.173 eV in the range considered. The refractive index n and the absorption index k were determined in the spectral range 400-2500 nm. It is observed that n decreases with increasing film thickness at any wave length, while k is practically independent on film thickness in the range 25-150 nm. For films with thicknesses in the range 170-304 nm, the spectral distribution of transmittance T and reflectance R showed that T+R<1 in the whole spectrum which due to light scattering by surface roughness whose existence is confirmed by electron microscopy. Analysis of k indicated that the absorption mechanism refers to the existence of indirect transitions with an optical energy gap of 0.52 eV.
Single crystals of Sb2Te3doped with Ag (cAg=(0-9)×1019cm-3) were prepared from the melt Sb2-xAgxTe3(denoted by a) or the melt Sb2AgxTe3(denoted by b). The reflectivity in the IR region, electrical conductivity, and Hall coefficient were determined for these crystals. From the reflection spectra values of the high-frequency dielectric constant, optical relaxation time, and plasma resonance frequency were obtained for crystals with various Ag contents. The dependencies of the real (ε1) and imaginary (ε2) parts of the dielectric function and the imaginary part of the energy loss function (Im(-1/ε)) on the wavenumber were also determined. From theε2(ν) dependence at room temperature, it was concluded that in Sb2Te3(Ag) crystals the scattering mechanism of free carriers on the acoustical phonons prevails, but the participation of scattering on ionized impurities is also probable. The a- and b-type crystals of Sb2Te3(Ag) manifested practically the same values of transport coefficients and optical properties in the IR region. The determined values of the Hall coefficient showed that Ag atoms doping the Sb2Te3crystal structure behave as acceptors. The incorporation of 1Ag atom into the crystals prepared from Sb2-xAgxTe3and Sb2AgxTe3melts increases the hole concentration by about 1.7 holes. This result is interpreted as the incorporation of Ag atoms into the crystal structure in the form of substitutional defects of Ag″Sbwith two negative charges. Part of the Ag atoms can form defects of the type [Ag″Sb+h·], i.e., Ag′Sb, or be incorporated in the four-layer lamellae [Te-Ag0.5Sb0.5-Te-Sb0.5Ag0.5] as uncharged defects. The Ag atoms incorporated into the Bi2Te3structure always behave as donors. The formation of Agiinterstitials is proposed as well. The different behavior of Ag atoms in Sb2Te3and Bi2Te3crystals is probably associated with different parameters of the chemical bonds in these crystals, which is supported by the results of a semiempirical calculation.
Single crystals of Sb2Te3 doped with Cr (cCr=0–6×1020 cm-3) were prepared by the Bridgman method. The measurements of the Hall coefficient reveal a nonmonotonous dependence of hole concentrations on the Cr content in the crystal. The hole concentration decreases at low content of Cr, while at higher content of Cr it increases again. However, according to magnetic measurements, Cr atoms enter the structure and form uncharged substitutional defects CrSb×, which cannot affect the free carrier concentration directly. The observed dependence can be elucidated by means of a point defect model. The model is based on an assumption that defect structure of Sb2Te3 can be treated as hybrid Schottky and antisite defect disorder. Thus, we assume an interaction of CrSb× with the most populated native defects in the structure—antisite defects SbTe-1 and vacancies in the Te sublattice VTe+2.
Changes in the values of the plasma resonance frequency and some transport coefficients (electrical conductivity. Hall coefficient, Seebeck coefficient) of Sb 2− x In x Te 3 crystals show that an increase in the content of incorporated In atoms causes a decrease in the free carrier concentration. This result is interpreted in the following way. In atoms are incorporated in the Sb-sublattice and form uncharged substitutional defects In x Sb which, of the higher electropositivity of In than Sb, cause an increase in bond polarity and also in crystal ionicity. This effect leads to an increase in the energy of formation of antisite defects, such that the concentration of antisite defects is decreased with increasing values of x . The energy of formation of antisite defects in Sb 2− x In x Te 3 crystals has been determined for x = 0.0-0.4, these values lying in the range 0.35-0.44 eV. The conclusions about the bond polarity and the changes in the energy of formation of antisite defects are supported by quantum chemical calculations, which also provide an explanation of the changes in the lattice parameters of Sb 2− x In x Te 3 crystals with increasing values of x .
The lattice thermal conductivity of (Bi1−xSbx)2Te3 alloys, with and without spherical nanoparticle inclusions, has been computed using the Boltzmann transport equation with classical interatomic potentials within the relaxation time approximation. The experimental thermal conductivity of the pure alloys is fairly well reproduced as a function of concentration. We establish upper and lower limits for the thermal conductivities that could be obtained via seamlessly embedded spherical nanoparticles as a function of their size, density, and volume fraction. Large reductions in thermal conductivities (40–50%) can only be achieved with small nanoparticles with diameters below 10 nm.
Antimony telluride doped with small concentrations of vanadium was recently identified as a diluted magnetic semiconductor. We present a study of the heat transport in single crystals of Sb2-xVxTe3 with x=0, 0.01, 0.02, and 0.03. Thermopower and thermal conductivity were measured from 1.5 K to 300 K. The thermopower is positive for all samples investigated and has a modest dependence on vanadium content. At low temperatures, the lattice thermal conductivity has an approximate T2 dependence and the data up to 100 K can be fitted well assuming that phonons scatter on boundaries, point defects, charge carriers, and other phonons. Theoretical analysis reveals that the over-riding effect of vanadium impurity is the formation of point defects that suppress heat transport via both mass and elastic strain fluctuations.
The kinetic Hall R
ikl
, electrical-conduction σkk
, thermopower αkk
coefficients, and their anisotropy are investigated in the temperature range of 77–450 K for a series of copper-doped PbSb2Te4 crystals with various hole concentrations of (1.6–3.2) × 1020 cm−3. The thermopower anisotropy observed in all investigated crystals is indicative of a mixed hole-scattering mechanism. The main scattering mechanisms are scattering at acoustic phonons and at the Coulomb potential of impurities and defects. The experimental effective scattering parameters and partial mobilities are determined in the cleavage plane and along the trigonal axis. The theoretical estimates of mobility are in satisfactory agreement with the experiment. It is established that the character of the temperature dependence for the ratio αkk
/T = f(T) depends on the hole concentration. It is shown that the physical properties can be described within the framework of the one-band model for a crystal with p
min = 1.6 × 1020 cm−3; the value of the effective mass density of the hole state in the main-valence band extremum is estimated as m
d
≈ 0.5m
0. The energy gap between the valence-band extrema is estimated as ΔE
v ≈ 0.23 eV.
Improved ideas on point defects in the Sb2Te3−xSexcrystals are formulated in this paper. Measurements of the Hall coefficient for a series of Sb2Te3−xSex(x=0–1) crystals served to determine the concentration of holes as a function of the selenium content in the lattice of the mixed crystals. The obtained variations of the hole concentration, linked hitherto solely with the decrease in the concentration of antisite (AS) defects of the Sb′Tetype, are explained using a model describing the interaction of the Se atoms entering the lattice not only with AS defects but also with the vacancies in the tellurium sublattice. The original concentration of AS defects in undoped Sb2Te3crystals, approximately 11.3×1019, drops with increasingx, reaching for the Sb2Te2Se crystal a value of 3×1019cm−3; the concentration of vacancies in the anion sublattice drops slightly: from a value of 2.5×1019cm−3down to 0.7×1019cm−3. The calculated variations of the concentration of holes, AS defects, and V••Tevacancies are in agreement with the idea that the increase in the polarity of bonds gives rise to a decrease in the concentration of AS defects and in the concentration of anion vacancies.
Incorporation of the transition metal elements in the tetradymite structure of Sb2Te3 has a strong influence on electronic properties. Recent studies have indicated that Mn substitutes on the Sb sublattice increases the carrier concentration of holes. However, the doping efficiency of Mn appears rather low in comparison to what it should be based on the measurements of magnetization, structural analysis, and transport properties. In this paper we address this issue by making detailed studies of the Hall effect and electrical resistivity and we explain the results with the aid of a model that takes into account interactions of the Mn impurity with the native defects in antimony telluride. Specifically, we find that Mn atoms interact with antisite defects (antimony atoms located on the tellurium sublattice), a process that decreases the density of antisite centers and generates free electrons. These, in turn, recombine with holes and thus decrease their concentration and the apparent Mn doping efficiency.
The free carrier concentration of the Sb2−xInxTe3, Bi2−xInxTe3 and Bi2Te3−xSx crystals has been determined from the values of the Hall constants and the free carrier concentration of the Sb2−xTlxTe3 has been calculated from the plasma resonance frequency; with increasing value of x, the hole concentration decreases. As the incorporation of the elements In, Tl and S into the lattice Sb2Te3 or Bi2Te3, respectively, gives rise to the uncharged defects InxSb, TlxSb, InxBi and SxTe, the x causes the decrease of the antisite defects concentration. The proven effect is explained in the following way: the antisite defects can be created only in crystals whose atoms are bound by weakly polarized bonds. The incorporation of In, Tl and S atoms into the crystal lattice of Sb2Te3 or Bi2Te3 increases the bond polarity, the ionicity of ternary crystals increases. This unfavorably affects the increase of antisite defects whose concentration decreases. The change of the bond polarity is considered from the changes discovered in the formation energy of antisite defects of the above mentioned ternary crystals.
Single crystals of Sb{sub 2}Te{sub 3} doped with Pb atoms (c{sub Pb} = 0--2.1{times}10{sup 20} atoms/cm{sup 3}) were characterized by the measurements of the reflectivity in the plasma resonance frequency region, the Hall coefficient, the electrical conductivity, and the Seebeck coefficient. Measurements of the Hall coefficient for a series of Pb-doped Sb{sub 2}Te{sub 3} crystals served to determine the concentration of holes as a function of the Pb content in the lattice. The obtained variation of the hole concentration is ascribed to the formation of substitutional defects Pb{prime}{sub Sb} and to the interaction of the Pb atoms entering into the lattice with anti-site defects and vacancies in the tellurium sublattice. Improved ideas on point defects in the Pb-doped Sb{sub 2}Te{sub 3} single crystals are formulated in this paper. 18 refs., 6 figs., 3 tabs.
Decoupling of interdependent thermoelectric parameters was considered as a crucial strategy to enhance the thermoelectric performance of bulk materials. Here multi-scale microstructural effects have been introduced by a simple hot deformation process to obtain high-performance n-type bismuth telluride based alloys. Highly preferred orientation enables a significant improvement in in-plane electrical conductivity. The donor-like effect (an interaction of antisite defects and vacancies), which can be adjusted by varying hot deformation temperature, was also considered responsible for the remarkable enhancement in power factor. Besides, the in-plane lattice thermal conductivity was greatly reduced by in situ nanostructures and high-density lattice defects generated during the hot deformation process. The present study experimentally demonstrates a successful combination of microscale texture enhancement, atomic scale lattice defects and donor-like effect and recrystallization induced nanostructures as a new approach to improve thermoelectric properties. These effects led to a maximum ZT of 0.95 for the Bi2Te2Se1 sample hot deformed at 823 K, about 80% improvement over that without hot deformation.
Sb2Te3 and its solid solutions with group III elements such as In are materials of current interest for their potential thermoelectric applications. Single crystals of Sb2Te3 and In0.2Sb1.8Te3 have been grown by the Bridgman method and their powder X-ray diffractograms obtained and indexed. The transport properties, namely electrical conductivity, Seebeck coefficient and thermal conductivity, as well as the optical bandgap of the alloys have been measured and are compared. The ternary alloy containing In has a smaller optical bandgap and lower electrical and thermal conductivity than Sb2Te3, but a higher Seebeck coefficient.
Single crystals of Hf-doped Sb2Te3 (cHf = 0-2.4x1019cm-3) were prepared from the elements of Sb, Hf, and Te of the 5N purity by a modified Bridgman method. The obtained crystals were characterized by the measurements of the reflectance R in the plasma resonance frequency region. Values of the plasma resonance frequency, ωp, were determined by fitting the reflectance spectra using the relations for the real and imaginary parts of the complex dielectric function, following from the Drude-Zener theory. From the observed changes in the value ωp it was concluded that the doping of Hf atoms into the crystal structure of Sb2Te3 results in a decrease in the concentration of free current carriers - holes. This conclusion was confirmed by the measurement of temperature dependencies of the Hall coefficient RH, electrical conductivity σ, and the Seebeck coefficient α, within the temperature range of 100-400K. Moreover, temperature dependences of the power factor σα2 and mobility μ∼RH.σ of free carriers are discussed.
An analysis of the temperature dependence of several transport properties, particularly the Seebeck and Hall coefficients, of thermoelectrically optimized p-type (Bi1 − xSbx)2Te3 films is carried out in the interval from 80 to 350 K for x = 0.75 including a comparison with bulk material data. The model calculations are based on the solution of the homogeneous Boltzmann equation in a relaxation time approximation since the films exhibit an in some ways bulk-like behaviour, e.g. the Hall mobility is of the order of that of the bulk material. In the framework of a one-valence-band model, the analysis of both bulk and film data favours a non-parabolic dispersion relation for Bi0.5Sb1.5Te3. It is shown that acoustic intravalley scattering is the predominant scattering mechanism of the charge carriers in the thermoelectrically optimized films.
Thin films of Sb2−xVxTe3 with x=0, 0.15, 0.32 and 0.35 have been grown on sapphire (0001) substrates using molecular-beam epitaxy. With the increasing concentration of vanadium, the in-plane lattice constant of Sb2−xVxTe3 films decreases while the c-axis lattice constant shows a very small increase. The electrical resistivity of Sb2−xVxTe3 films decreases by an order of magnitude when V is substituted on the Sb sublattice. The Hall effect measurements show an increase in the concentration of holes as the content of vanadium increases.
Single crystals of Bi1.5Sb0.5Te3 doped with Ag atoms (cAg = 0 - 4.34x1019 atoms/cm3) were characterized by measurement of Hall coefficient, electrical conductivity, Seebeck coefficient and the figure of merit. It was found that Ag atoms in the crystal structure of Bi1.5Sb0.5Te3 behave like donors. It is necessary to add more than one Ag atom to the Bi1.5Sb0.5Te3 compound in order to suppress the hole concentration by one hole. Such a behaviour of the dopant is explained by the formation of various structural defects. Besides the dominant interstitial defects of Ag* silver atoms form also positively charged substitutional defects Ag″, Ag′, and a four-layer-lamellae of the type [Ag0.5Sb0.5]-Te-[Ag0.5Sb0.5]-Te. The incorporation of Ag atoms into the Bi1.5Sb0.5Te3 lattice, besides the suppression of the hole concentration, leads to a decrease in the figure of merit Z.
A single crystal of antimony telluride, grown from elements of semiconductor purity by means of the Bridgman method, is characterised by the departure from stoichiometry as determined from energy dispersive X-ray spectroscopy, by the concentration of free charge carriers p as obtained from the interpretation of the reflectivity spectra in the plasma resonance frequency range, by its density d, and by lattice parameters a and c. The investigated crystal of stoichiometry Sb2Te2.948 has the following values: p = 6.714 × 1019 cm−3, d = (6.50 ± 0.01) g cm−3, a = 0.42643(5) nm, c = 3.0427(4) nm. The departure from stoichiometry is explained using a model taking into account the existence of antisite Sb'Te defects as well as tellurium and antimony vacancies in the crystal lattice: this model in connection with the experimental data allows us to calculate the concentration of Sb'Te defects and to determine their formation energy EAS = (0.32 ± 0.01) eV.
Reflectance and transmittance in the IR spectral range are investigated on Sb2−xInxTe3 (x = 0.00 to 0.37) single crystal samples grown by a modified Bridgman method. By fitting the reflectance spectra the values of the plasma resonance frequency ωp, optical relaxation time τ, and high‐frequency dielectric constant ε∞are determined. With increasing indium concentration in the samples these quantities decrease from the values ωp = 1.88 × 10¹⁴ s⁻¹, τ = 2.4 × 10⁻¹⁴ s, and ε∞ = 55 for x = 0.00 down to the values ωp = 0.81 × 10¹⁴ s⁻¹, τ = 0.8 × 10⁻¹⁴ s, and ε∞ = 41 for x = 0.37. The observed variations are qualitatively accounted for by interaction of substitutional In Sbx defects arising on building of In atoms into the Sb2Te3 lattice with anti‐site Sb Te′ defects. The transmittance curves permit to determine the dependence of the absorption coefficient x on incident photon energy. The change in the width of the optical gap with increasing In concentration in the samples is discussed. The values of the exponent α in the relation x ∼ λα for the long‐wavelength absorption edge drop from 2.5 for Sb2Te3 to 1.2 for Sb1.63In0.37Te3.
Changes in the values of the plasma resonance frequency and some transport coefficients (electrical conductivity. Hall coefficient, Seebeck coefficient) of Sb2−xInxTe3 crystals show that an increase in the content of incorporated In atoms causes a decrease in the free carrier concentration. This result is interpreted in the following way. In atoms are incorporated in the Sb-sublattice and form uncharged substitutional defects InxSb which, of the higher electropositivity of In than Sb, cause an increase in bond polarity and also in crystal ionicity. This effect leads to an increase in the energy of formation of antisite defects, such that the concentration of antisite defects is decreased with increasing values of x. The energy of formation of antisite defects in Sb2−xInxTe3 crystals has been determined for x = 0.0-0.4, these values lying in the range 0.35-0.44 eV. The conclusions about the bond polarity and the changes in the energy of formation of antisite defects are supported by quantum chemical calculations, which also provide an explanation of the changes in the lattice parameters of Sb2−xInxTe3 crystals with increasing values of x.
Sb2Te3−xSex crystals were prepared from 5N purity elements and their crystal parameters a, c and Hall coefficients RH were measured as functions of the Se concentration up to x = 1. Well defined deviations of both crystal parameters from the linear Vegard's law are observed up to x = 0.4. At higher Se concentrations the linear Vegard's law is fulfilled. The main idea explaining this behaviour is the decrease of antisite defects of the type SbTe with increasing Se concentration. This process is complicated and its details are given in the paper.
The reflectance and the transmittance spectra in the IR region are measured on Ti-doped Sb2Te3 single crystal samples grown by a modified Bridgman technique. The plasma resonance frequency, the optical relaxation time, and the high-frequency dielectric constant are determined by fitting the Drude-Zener formulas to the reflectance spectra. It is found that Ti impurities in Sb2Te3 behave as donors. The transmittance spectra are used for the determination of the dependence of the absorption coefficient K on the energy of incident photons. The optical width of the energy gap is found to decrease with increasing Ti content. The values of the exponent α from the relation of K ∼ λα for the long-wavelength absorption edge range within the interval of 1.8 to 2.2, i.e. the dominant scattering mechanism of free current carriers in Sb2Te3 crystals doped with Ti atoms is the scattering by acoustic phonons.
An Sb2Te3-Einkristallen mit Beimengungen von Ti-Atomen, die nach der modifizierten Bridgman-Methode hergestellt wurden, werden Reflexionsvermögen und Transmission im IR-Bereich ermittelt. Mit einer numerischen Analyse der Reflexionsspektren werden die Werte der Plasma-Resonanzfrequenz, der optischen Relaxationszeit und der Hochfrequenz-Dielektrizitätskonstante bestimmt. Es wird gefunden, daß Ti-Beimengungen im Sb2Te3 Donatoren bilden. Die Transmissionsspektren werden benutzt, um die Abhängigkeit des Absorptionskoeffizienten K von der Energie der einfallenden Photonen zu bestimmen. Es wird gefunden, daß die optische Breite der Bandlücke mit wachsenden Beimengungen von Ti-Atomen abnimmt. Die Werte des Exponenten α in der Beziehung K ∼ λα für die langwellige Absorptionskante liegen im Interval 1,8 bis 2,2, d. h. der dominierende Streumechanismus für freie Ladungsträger in Sb2Te3 Kristallen mit Beimengungen von Ti-Atomen ist die Streuung an akustischen Phononen.
Bi2Se3 single crystals were prepared in the electron concentration range from 1.8 × 10¹⁹ to 5.6 × 10¹⁹ cm–3. At room temperature experimental values are given for the specific electrical resistivity, for the Hall and Seebeck coefficients, and the ir-plasma reflectivity spectra were measured in the wave number range from 300 to 4000 cm–1. For the first time it was found that not only the resistivity and the plasma reflectivity but also the thermopower show a distinct anisotropy perpendicular and parallel to the trigonal c-axis, whereas the Hall effect is isotropic. In terms of a one-carrier, one-valley conduction band model with elliptical isoenergy surfaces and a nonparabolic dispersion the anisotropy of the thermopower can be explained in the extrinsic range by an anisotropic mixed scattering mechanism on acoustic phonons and ionized impurities in the relaxation time approximation. In this frame a quantitative, consistent interpretation is reached for all experimental data. The calculated values for the high-frequency dielectric constant, the carrier density, the Fermi level, the parameter of nonparabolicity, the mean optical relaxation times, the effective masses and the drift mobilities are given.
Using combined optical-spectroscopic and transport investigations it is succeeded for the first time to determine all relevant valence band data for the whole series of mixed crystals (Bi1−xSbx)2Te3 (0 ≦ x ≦ 1). The reflectivity of polarized infrared light including its anisotropy is measured in the wave number range of 300 to 4000 cm⁻⁻¹. In addition to the spectra the Hall coefficients ϱ123 and ϱ312, the electrical conductivity σ ⟂ c, and the Seebeck coefficient S ⟂ c are also given. In term of a six-valley band model and scattering by acoustical phonons all experimental data are consistently described. The main axis masses m, the ellipsoid tilt angle ϑ, the effective density-of-states mass md, and the susceptibility masses m,∥c are calculated in dependence on composition, also the Fermi level EF, the carrier density p, the mobility μ ⟂ c, the high frequency dielectric constant ϵ∞⟂,∥c, and the relaxation time τopt. For the first time the structure factors in the Hall coefficients are given. In the plot m(x) the distinct maxima of m and md near x = 0.8 are evident and important for the application of these substances.
IR transmission spectra are measured at (Bi1−xSbx)2Te3 single crystals with x = 0.5, 0.7, 0.9 near the absorption edge at 84 and 300 K. For the determination of the optical constants also the reflectivity of polarized infrared light is recorded in the plasma range at 300 K. The dependence of the free carrier part of the dielectric function on the wave number ϵ(v̄) indicates that acoustic phonon scattering is the dominant mechanism. The interband contribution ϵ(v̄) is interpreted by indirect allowed band transitions. The energy gap and the phonon energies are calculated and lie in a physically reasonable range.
IR-Transmissionsspektren werden an (Bi1−xSbx)2Te3-Einkristallen mit x = 0,5; 0,7 und 0,9 nahe der Absorptionskante bei 84 und 300 K gemessen. Zur Bestimmung der optischen Konstanten wird bei 300 K auch das Reflexionsvermögen von polarisiertem Infrarotlicht im Plasmabereich aufgezeichnet. Die Abhängigkeit des freien Trägeranteils der dielektrischen Funktion von der Wellenzahl ϵ(v̄) zeigt, daß die Streuung an akustischen Phononen der dominante Mechanismus ist. Der Interbandbeitrag ϵ(v̄) wird durch indirekte erlaubte Bandübergänge erklärt. Die Energielücke und die Phononenenergien werden berechnet und liegen in einem physikalisch vernünftigen Gebiet.
Single crystals of Sb2Te3 doped with 0 to 1.0 at% Sn are prepared and the Hall coefficient, Seebeck coefficient, and plasma resonance frequency of the crystals are determined. The incorporation of one Sn atom into the Sb2Te3 crystal corresponds to an origin of ≈ 2.2 to 3.0 holes. Such an increase in the concentration of holes is explained in terms of a decrease in the bond polarization due to the incorporation of negatively-charged Sn'Sb defects into the Sb sublattice which is favourable for the formation of antisite defects in Sb2Te3. The observed increase in the hole concentration corresponds to the sum of created Sn'Sb defects and newly formed Sb'Te antisite defects in Sn-doped Sb2Te3.Die Hallkonstante, der Seebeckkoeffizient und die Plasmaresonanzfrequenz mit Zinn dotierter Sb2Te3-Kristalle (0 bis 1,0 At% Sn) werden ermittelt. Der Einbau eines Sn-Atoms in das Antimontelluridgitter hat die Bildung von 2,2 bis 3,0 Löchern zu Folge. Eine solche Zunahme der Landungsträgerkonzentration wird mit Hilfe des Effektes der Unterdrückung der Bindungs-Polarisation erklärt, die durch Bildung von negativ geladenen Störstellen, Sn'Sb verursacht wird Diese Störstellen im Sb-Untergitter unterstützen die Bildung der antistrukturellen Störstellen Sb'Te. Die ermittelte Zunahme entspricht also der Summe der Konzentration der Sn'Sb-Störstellen und der neu generierten antistrukturellen Störstellen Sb'Te im Sb2Te3-Gitter.
The influence of the starting powders’ morphology on the thermoelectric anisotropy of Bi–Te-based thermoelectric materials that are fabricated by spark plasma sintering has been investigated. Starting powders with three types of morphologies are prepared through a chemical reaction method (nano-sized particles with a spherical shape), a conventional pulverization method (flake-like shape) and a gas atomizing method (spherical shape). The thermoelectric anisotropy of each sintered body is determined by measuring the electrical resistivity and thermal conductivity in both the parallel and perpendicular directions to the spark plasma sintering pressing direction. The p-type Bi0.5Sb1.5Te3.0-sintered body that is composed of the spherically shaped powder has isotropic thermoelectric properties, while the same material composed of the flake-like powder shows anisotropic behavior. The n-type Bi2Te3 sintered body has a relatively small anisotropy when it is composed from the spherically shaped powder.
This paper reports on measurement of the temperature dependences of the following transport coefficients: electrical conductivity
in the σ11 cleavage plane, the Seebeck coefficients S
11 and S
33 (axis 3 is along the trigonal crystal axis), the Hall coefficients R
123 and R
321, and the Nernst-Ettingshausen constant Q
123; all measurements were made on high-quality Czochralski-grown Sb2Te3 single crystals. The results obtained are analyzed in terms of phenomenological theory. It is shown that the main features
of the experimental data, including the anisotropy of the Hall and Seebeck effects, can be explained within a two-band model
with notice-ably different anisotropy of the mobilities of holes of two types in the cleavage-plane and trigonal-axis directions.
Estimates are made of the band-gap width (ɛg≅0.3 eV), as well as of the energy gap between the main and additional valence-band extrema (Δɛv∼0.1 eV).
P-type thermoelectric material (Bi0.24Sb0.76)(2)Te-3 was sintered with pulse discharge sintering (PDS) process at temperatures of 345-495 degrees C. The microstructures of sintered materials were found to be well aligned along the basal planes on the transverse direction, particularly when sintered at lower sintering temperatures. The carrier concentration was found to be higher in the transverse direction than in the longitudinal, and to increase with sintering temperature, particularly when sintered at temperatures higher than 445 degrees C. On the other hand, the carrier mobility shows a peak value in the sintering temperature axis at a temperature of about 465 degrees C for the longitudinal and 445 degrees C in the transverse direction. Electrical and thermal conductivities were found to be higher in the transverse than the longitudinal direction, by a factor of about 2 when sintered at low temperature. Generally, both the electrical and thermal conductivity of the material increased with an increase in the sintering temperature. Seebeck coefficient was found to be higher in the longitudinal than in the transverse direction, and showed a general decreasing tendency with an increase in sintering temperature, particularly when the sintering temperature is higher than 445 degrees C. In terms of the figure of merit, the optimum sintering temperature was found to be 445 degrees C or 465 degrees C for a maximum Z value of around 3.1 x 10(-3)/K, in the longitudinal and transverse directions, respectively. (c) 2005 Elsevier B.V. All rights reserved.
Chromium-doped Sb2Te3 single crystals were prepared from elements of semiconductor purity using a modified Bridgman method. The samples of these crystals were characterized by means of X-ray diffraction analysis, measurements of the reflectivity in the plasma resonance frequency range ωp, of the Hall constant RH and electrical conductivity σ. It was found that the incorporation of Cr atoms into the Sb2Te3 crystal lattice reduces the volume of the unit cell, whereas the values of ωp and RH (i.e. the concentration of holes) remain unaltered and the values of σ decrease with increasing chromium content. This effect is qualitatively explained by an interaction of incorporated Cr atoms with antisite defects of Sb2Te3 crystal lattice. The In (RHσ) vs. In T dependences show that the dominant mechanism of scattering of free charge carriers in the studied crystals is the scattering by acoustic phonons; the presence of chromium atoms increases the scattering rate by ionized impurities.
Die mit Cr dotierten Sb2Te3-Einkristalle aus den Elementen mit Halbleiterreinheit wurden mit einer modifizierten Bridgman-Methode gezüchtet. Ihre Charakterisierung erfolgte mit Hilfe der Röntgenbeugungsmethode, der Hall-Konstanten RH, der elektrischen Leitfähigkeit σ und der Reflektivität im Gebiet der Plasma-Resonanzfrequenz ωp. Es wurde festgestellt, daß der Einbau der Cr-Atome im Sb2Te3 Kristallgitter die Volumenabnahme der Elementarzelle verursacht; die Werte von ωp und RH bleiben unverändert, die elektrische Leitfähigkeit nimmt mit zunehmendem Cr-Gehalt ab. Dieser Effekt wird mit Hilfe eines Modells erklärt, das die Existenz von Antistrukturdefekten im Sb2Te3 Kristallgitter annimmt. Die Abhängigkeiten In (RHσ) vs. In T zeigen, daß der überwiegende Streuungsmechanismus der freien Ladungsträger der Streuungsmechanismus der akustischen Phononen ist; die zunehmende Cr-Dotierung führt zu der Zunahme des Anteils des Streuungsmechanismus an ionisierten Störstellen.
The reflectance and the transmittance spectra in the IR region were measured on Pb-doped Bi2Te3 single crystal samples grown by a modified Bridgman technique. The plasma resonance frequency, the optical relaxation time, and the high-frequency permittivity were determined by fitting the Drude-Zener formulas to the reflectance spectra. It was found that Pb impurities in Bi2Te3 behave as acceptors. A part of incorporated Pb atoms behaves as electrically inactive. This effect is explained as due to the fact that electrically active Pb-atoms form substitutional defects, Pb′Bi, and the others form inactive two-dimensional defects — seven-layer lamellae Te—Bi—Te—Pb—Te—Bi—Te. The transmittance spectra were used for the determination of the dependence of the absorption coefficient K on the energy of incident photons. The optical width of the energy gap increases with increasing Pb content. The values of the exponent α from the relation of K ∼ λα for the long-wavelength absorption edge range within the interval of 1.6 to 2.8, i.e. the dominant scattering mechanism of free current carriers in Pb-doped Bi2Te3 crystals is the scattering by acoustic phonons. By comparison of the effect of doping atoms of the IV.B group of the periodic table on the concentration of holes in Bi2Te3 crystal lattice was concluded that the tendency to form substitutional defects Me′Bi (Me = Ge, Sn, Pb) in these crystals increases from Ge to Pb, whereas the tendency to the formation of seven-layer lamellae Te—Bi—Te—Me—Te—Bi—Te decreases.
In the series of trigonal V2—VI3 semiconductorsBi2Te3, Bi2Se3, and Sb2Te3 up to now it has not been succeeded to interpret the temperature dependence of the weak—field charge transport for Sb2Te3 single crystals in terms of a physical relevant model with reasonable semiconductor data. Therefore, an expanded transport model is presented takinginto account nonparabolic manyvalley band structure as well as the simultaneous action of anisotropic mixed charge carrier scattering by acoustical phonons and ionized impurities in the relaxation time approximation. Under these conditions the expressions for the thermoelectric, galvano- and thermomagnetic coefficients and the Lorenz numbers are given. These formulas are also valid for Bi2Te3 at pure acoustical mode scattering and for Bi2Se3 at single-valley band structure.
In der Reihe der trigonalen V2—VI3−Halbleiter Bi2Te3, Bi2Se3, und Sb2Te3 ist es bisher noch nicht gelungen, die Temperaturabhängigkeit des Schwachfeld-Ladungstransports in Sb2Te3−Einkristallen im Rahmen eines physikalisch relevanten Modells mit vernünftigen Halbleiterdaten zu erklären. Deshalb wird ein erweitertes Transportmodell vorgestellt, das sowohl die nichtparabolische Vieltalbandstruktur als auch das simultane Wirken einer anisotrop-gemischten Trägerstreuung an akustischen Phononen undd ionisierten Störstellen in der Relaxationszeitnäherung berücksichtigt. Unter dieser Voraussetzung werden die Ausdrücke für die thermoelektrischen, galvano- und thermomagnetischen Koeffizienten und die Lorenzzahlen angegeben. Bei reiner akustischer Gitterstreuung sind diese Formeln auch für Bi2Te3 und bei einer Eintalbandstruktur auch für Bi2Se3 gültig.
Incorporation of Ag in the crystal lattice of Sb2Te3 creates structural defects that have a strong influence on the transport properties. Single crystals of Sb2−xAgxTe3 (x=0.0; 0.014; 0.018 and 0.022) were characterized by measurements of the temperature dependence of the electrical resistivity, Hall coefficient, Seebeck coefficient and thermal conductivity in the temperature range of 5–300 K. With an increasing content of Ag the electrical resistance, the Hall coefficient and the Seebeck coefficient all decrease. This implies that the incorporation of Ag atoms in the Sb2Te3 crystal structure results in an increasing concentration of holes. However, the doping efficiency of Ag appears to be only about 50% of the expected value. We explain this discrepancy by a model based on the interaction of Ag impurity with the native defects in the Sb2−xAgxTe3 crystal lattice. Defects have a particularly strong influence on the thermal conductivity. We analyze the temperature dependence of the lattice thermal conductivity in the context of the Debye model. Of the various phonon scattering contributions, the dominant influence of Ag incorporation in the crystal lattice of Sb2Te3 is revealed to be point-defect scattering where both the mass defect and elastic strain play a pivotal role.
The effect of Sn atoms on the electrophysical properties and x-ray photoelectron spectra of Czochralski-grown Sb2Te3 single crystals is studied. The character of the temperature dependences of the kinetic coefficients is shown to depend noticeably
on the structure of the valence band, which consists of two valence subbands. Estimates of the effective density-of-states
masses of holes and of the gap between the valence-band extrema in Sb2Te3: Sn agree with the data available for the Sb2Te3 not doped with tin. X-ray photoelectron spectra of Sb2Te3: Sn single crystals do not exhibit noticeable core-level shifts and electron density redistribution in the valence band.
Sb2Te3−xSex (x = 0.00−1.25) single crystals were prepared using a modified Bridgman technique. The homogeneity of the crystals grown in this way was checked by means of an energy dispersion analyser and by reflectivity measurements. X-ray structure analysis revealed that the lattice parameters a and c decrease with increasing selenium content in the crystals. The crystals were characterized by measuring the infrared reflectivity spectra, electric conductivity and Hall constant. Experimental results showed that the incorporation of Se atoms into the crystal lattice of Sb2Te3 results in a suppression of the concentration of free carriers (holes).
This is the fourth ofseven volumes in a program of systematic reclassification of the Henry Draper stars on the MK system and contains all HD stars between delta = -26°.0 and -12°.0. The stars were classified visually on objective-prism plates taken with the Michigan Curtis Schmidttelescope at Cerro Tololo Inter-American Observatory. The 4°+6° prisms yield a dispersion at Hgamma of 108 Å/mm, and the resolution is about 2 Å/mm, comparable to that of the original MK system. The spectra were taken on IIaO plates and widened to 0.8 mm, with 20m, 4m, and 1m exposures being obtained. Of the 33,301 stars in the catalogue, 32,563 or 98% were classifiable. Previously published types are listed for the 2% not classifiable on the plates. Internal classification errors were obtained using the stars classified independently on more than one plate. Both the internal and external errors are similar to those usually obtained in the classification of slit spectra.
Coupled plasmon-LO-phonon modes have been studied in Sb2Te3 (bulk samples and epitaxial layers) by Raman scattering and IR-reflectivity. The high frequency plasmonlike mode (3: 300–2,000 cm–1) is observed, in contrast to the other two phonon-like plasmon-LO-phonon modes. The latter are expected to have negligible scattering intensities, since the IR-phonons in Sb2Te3 are not Raman-active. The 3-mode shows up with different frequencies since the effective masses, i.e. the plasmon is anisotropic. Dispersion measurements and their comparison with the results of a theoretical description (hydrodynamical theory) gives good agreement. From this values for the anisotropic effective masses are obtained.
Undoped Sb//2Te//3 and Ag-doped Sb//2Te//3 crystals are grown by a modified Bridgman method. Electrical conductivity, Seebeck coefficient, Hall constant, and reflectivity in the region of the plasma resonance frequency are measured. A quantitative analysis of the silver content in the prepared Sb//2Te//3 crystals is made by atomic absorption spectrometry. For the undoped Sb//2Te//3 crystals the free carrier concentration and the effective mass in the direction perpendicular to the c-axis, m// PERPEND , are calculated, using a simplified model. According to the results obtained the Ag atoms incorporated into Sb//2Te//3 crystals have the character of acceptors and the addition of one Ag atom corresponds to the increase in free carrier concentration by two holes.
A two-valence band model with a single-and six-valley structure is developed for the interpretation of galvanomagnetic effects in p-type mixed crystals of the system (BixSb1−x)2Te3(0 ≦ x ≦ 1), especially for x = 0 under the assumption of a purely anisotropic scattering in each band, neglecting interband and intervalley scattering. This model, refering to results from Shubnikov-de Haas investigations on Sb2Te3 at 4 K, is tested with galvanomagnetic data of undoped Sb2Te3 in the temperature region 100 K ≦ T ≦ 360 K. It is, however, not possible to fit such a two-valence band model to these data sufficiently well due, possibly, of a more complicated scattering process of charge carriers.
Es wird ein Zweivalenzbandmodell mit einer Eintal- bzw. Sechstalstruktur für die Interpretation galvanomagnetischer Effekte in p-Typ-Mischkristallen des Systems (BixSb1−x)2Te3 (0 ≦ x ≦ 1), insbesondere für x = 0 mit der Annahme reiner anisotroper Streuung in jedem Band unter Vernachlässigung von Interband- und Zwischentalstreuung entwickelt. Das Modell, das an Ergebnisse von Shubnikov-de Haas Untersuchungen an Sb2Te3 bei 4 K anknüpft, wird mit galvanomagnetischen Meßdaten von undotiertem Sb2Te3 im Temperaturbereich 100 K ≦ T ≦ 360 K getestet. Es ist jedoch nicht möglich, ein solches Zweivalenzbandmodell hinreichend gut an diese Daten anzupassen. Ein komplizierterer Streuprozeß der Ladungsträger scheint der Grund dafür zu sein.
For the first time the anisotropy of reflectivity of polarized infrared light of p-(Bi1–xSbx)2Te3 single crystals (0.5 ≦ x ≦ 1) is given in the wave number range of 300 to 4000 cm⁻¹. In addition to the excitation of free carriers in the reflection spectra of the mixed crystals also interband excitations are observed. For the mixed crystals the optical results are consistently described in terms of a six-valley band model and scattering on acoustical phonons together with the data for the dc conductivity, the Hall coefficients, and the thermopower. The main axis masses mii, the ellipsoid tilt angle θ, the effective density of states mass m, the cyclotron mass and the susceptibility masses are given in dependence on composition, also the Fermi level EF, the carrier density p, the mobility u⊥c, the high frequency dielectric constant ϵ′∞, and the relaxation time τ. The interband influence is interpreted by a simple band model and the energy gap Eg calculated.
Es werden erstmalig alle zwölf galvanomagnetischen Schwachfeldtransportkoeffizienten sowie die beiden Seebeck-Koeffizienten von Sb2Te3 im Temperaturbereich von 100 bis 360 K angegeben. Ferner wird die Änderung einiger dieser Effekte bei Pb-Dotierung beobachtet. Ausgehend von qualitativen Unterschieden im Transportverhalten von Sb2Te3 und der Analogiesubstanz Bi2Te3 werden Modelle zur konsistenten Beschreibung der Transporteigenschaften von Sb2Te3 diskutiert.
For the first time the temperature dependences are presented of all of the twelve galvanomagnetic low field transport coefficients and the two Seebeck coefficients of Sb2Te3 in the temperature range from 100 to 360 K. Furthermore the change of some of these effects by Pb doping is observed. Starting from qualitative differences in the transport behaviour of Sb2Te3 and the analogous substance Bi2Te3 some models for a consistent description of transport properties of Sb2Te3 are discussed.
On Sb2Te3 single crystals with conductivities between 3700 and 7000 Ω−1 cm−1 the anisotropy of the reflectivity of polarized infrared light, the anisotropy of conductivity and of the Seebeck and Hall coefficients are investigated. In addition to the excitation of free carriers in the reflection spectra of donor doped crystals also interband excitations are observed. In terms of a six-valley band model with anisotropic scattering the contribution of the free carriers to the susceptibility is calculated, and the anisotropy ratio of the effective susceptibility masses
is given. It is found that the anisotropy decreases with increasing conductivity. A comparison of
with the anisotropy of conductivity σ ⊥c/σ‖c shows that for Sb2Te3 single crystals with σ‖σ ⊥c < < 5000 Ω−1 cm−1 the carrier scattering is anisotropic.
An Sb2Te3-Einkristallen mit Leitfähigkeiten zwischen 3700 and 7000 Ω−1 cm−1 werden die Anisotropie des Reflexionsvermögens von polarisiertem infrarotem Licht, die Anisotropic der Leitfähigkeit, des Seebeck- und Hall-Koeffizienten untersucht. Für donatordotierte Kristalle werden in den Reflexionsspektren neben der Anregung der freien Träger auch Interbandanregungen beobachtet. Im Rahmen eines Sechs-Tal-Valenzbandmodells und anisotroper Streuung wird der Beitrag der freien Träger zur Suszeptibilität berechnet und das Anisotropieverhältnis der effektiven Suszeptibilitätsmassen
angegeben. Es wird gefunden, daß mit zunehmender Leitfähigkeit die Anisotropie abnimmt. Ein Vergleich von
mit der Anisotropie der Leitfähigkeit σ /σ σ ⊥c/σ‖c zeigt, daß für σ‖c < 5000 Ω−1 cm−1 die Trägerstreuung von Sb2Te3 Einkristallen anisotrop ist.
The pseudo-parabolic model (Heremans and Hansen, 1979) for the analysis of the thermoelectric power of bismuth in zero and weak magnetic fields is analysed further by calculation of the effect of intermediate and strong, non-quantising magnetic fields. The calculations are performed for elements of the thermoelectric power and of the electronic thermal conductivity. Comparison with experimental data in the range from 20K to room temperature shows that a variety of complicated field dependences in the intermediate field range, previously unexplained, follow from the present analysis. In strong fields a number of disagreements appear. The field values at which the disagreements set in are found to coincide quite well with the Landau quantisation limits.
The possibility of the commutational effect (CE) of thermo-e.m.f. at different orientations of the magnetic field and temperature gradient is investigated in the frames of the variational method of calculation of transport coefficients. It is found that for some of the components of the magnetothermo-e.m.f. tensor CE appears only in strong and intermediate fields. The importance of strict orientation of sample relative to external affects for the measurement of CE of magnetothermo-e.m.f. is pointed out.
[Russian Text Ignored]
Using a variational method, general formulae for the kinetic tensor components describing the galvanomagnetic phenomena in anisotropic semiconductors of the p-Te type are obtained in terms of matrix elements of different scattering mechanisms for the case of arbitrary magnitude and direction of the non-quantizing magnetic field. Theoretical and experimental results of the temperature and field dependences of the transverse and longitudinal Nernst-Ettingshausen effect in p-Te are compared and discussed.
Mit einer Variationsmethode werden allgemeine Formeln für die kinetischen Tensorkomponenten erhalten, die die galvanomagnetischen Phänomene in anisotropen Halbleitern vom p-Te-Typ beschreiben, wobei die Matrixelemente der verschiedenen Streumechanismen für beliebige Größe und Richtung des nicht quantisierenden Magnetfeldes benutzt werden. Theoretische und experimentelle Ergebnisse der Temperatur- und Feldabhängigkeiten des transversalen und longitudinalen Nernst-Ettingshausen-Effekts in p-Te werden verglichen und diskutiert.
The Nernst-Ettingshausen coefficient S132 and the magneto-Seebeck coefficient S3322 of pure perfect tellurium crystals can be explained within the temperature range 77 K ≦ T ≦ 200 K neither by pure scattering of the charge carriers at acoustical phonons, ionized impurities, and optical phonons, above and below the Debye temperature nor by mixed scattering at acoustical phonons and neutral impurities. The temperature dependence of the parameter refers to a scattering at optical phonons near the Debye temperature.Der Nernst-Ettingshausenkoeffizient S132 und der Magneto-Seebeck-Koeffizient S3322 reiner ungestörter Tellurkristalle lassen sich im Temperaturbereich 77 K ≦ T ≦ 200 K weder durch reine Streuung der Ladungstrger an akustischen Phononen, ionisierten Störstellen oder optischen Phononen oberhalb und unterhalb der Debye-Temperature noch durch Mischstreuung an akustischen Phononen und neutralen Störstellen erklrn. Die Temperaturabhngigkeit des Parameters deutet auf Streuung an optischen Phononen nahe der Debye-Temperatur hin.
In the series of trigonal V2—VI3 semiconductorsBi2Te3, Bi2Se3, and Sb2Te3 up to now it has not been succeeded to interpret the temperature dependence of the weak—field charge transport for Sb2Te3 single crystals in terms of a physical relevant model with reasonable semiconductor data. Therefore, an expanded transport model is presented takinginto account nonparabolic manyvalley band structure as well as the simultaneous action of anisotropic mixed charge carrier scattering by acoustical phonons and ionized impurities in the relaxation time approximation. Under these conditions the expressions for the thermoelectric, galvano- and thermomagnetic coefficients and the Lorenz numbers are given. These formulas are also valid for Bi2Te3 at pure acoustical mode scattering and for Bi2Se3 at single-valley band structure.
In der Reihe der trigonalen V2—VI3−Halbleiter Bi2Te3, Bi2Se3, und Sb2Te3 ist es bisher noch nicht gelungen, die Temperaturabhängigkeit des Schwachfeld-Ladungstransports in Sb2Te3−Einkristallen im Rahmen eines physikalisch relevanten Modells mit vernünftigen Halbleiterdaten zu erklären. Deshalb wird ein erweitertes Transportmodell vorgestellt, das sowohl die nichtparabolische Vieltalbandstruktur als auch das simultane Wirken einer anisotrop-gemischten Trägerstreuung an akustischen Phononen undd ionisierten Störstellen in der Relaxationszeitnäherung berücksichtigt. Unter dieser Voraussetzung werden die Ausdrücke für die thermoelektrischen, galvano- und thermomagnetischen Koeffizienten und die Lorenzzahlen angegeben. Bei reiner akustischer Gitterstreuung sind diese Formeln auch für Bi2Te3 und bei einer Eintalbandstruktur auch für Bi2Se3 gültig.
A comparison of the experimental and calculated data for the transport coefficients in bismuth obtained on the basis of the variational microscopic model is carried out. The assumption about the predomination of carrier scattering on acoustic phonons in bismuth is confirmed. The values of deformation potential constants are calculated for a wide range of temperatures. The temperature and magnetic field dependences of transport coefficients in the wide range of temperatures and magnetic fields determined by variational method, completely reproduce the experimental data.
[Russian Text Ignored]
A variational procedure for the solution of the Boltzmann equation with an arbitrary number of variational parameters is developed. In the frame of the method it is possible to carry out the optimization of trial function, as well as to check the convergence of the solution. It is shown that in semimetals the probability matrix of charge carrier scattering on acoustic phonons entering the expression for the collision operator has a non-diagonal form in the coordinate system of the effective mass tensor. General expressions are obtained for the transport coefficients allowing to determine their numerical values.
[Russian Text Ignored]
This paper is designed to supplement the existing extensive literature on the conductivity of a randomly inhomogeneous medium, by treating the effects of inhomogeneities on piezoelectric, galvanomagnetic, and thermoelectric measurements. The scale of the inhomogeneities is supposed small compared with the dimensions of the specimen being measured, but large compared with mean free path, Debye length, etc. Formulas for all the effects are derived which are asymptotically exact in the limit of small fractional fluctuations in the local conductivity, etc. Comparison with other approximations and application to various exactly soluble cases show that these formulas are often roughly valid for quite sizable fluctuations. For material which, if uniform, would show a high field saturation of transverse magnetoresistance, the presence of appreciable inhomogeneities in the Hall constant will cause the magnetoresistance to increase indefinitely with field. This effect is due to the current distortions arising from the large and fluctuating Hall fields. For the special case of an isolated inclusion, these distortions are shown to extend, at high fields, to distances in the direction of the magnetic field which are many times the diameter of the inclusion. Under some conditions it appears that even the random distribution of impurities in a semiconductor can give rise to perceptible fluctuations on a scale large enough for concepts of macroscopic conduction to be applicable. Since fluctuations of even smaller scale are still larger, the total effect of fluctuations cannot be properly treated by the present methods; however, when the macroscopic part of the fluctuations is large, conventional impurity‐scattering theories must be inadequate. Applications to polycrystalline metals and semiconductors are discussed briefly.