Transverse Nernst-Ettingshausen Research Articles

Transverse Nernst–Ettingshausen Effect in the Two–Dimensional Electron Gas of a Doubly Periodic Semiconductor Superlattice

Transverse Nernst–Ettingshausen Effect in the Two–Dimensional Electron Gas of a Doubly Periodic Semiconductor Superlattice

On the Band Structure of Bi2Te3

For p-Bi2Te3 crystals grown by the Czochralski method, the temperature dependences of the conductivity, Hall coefficient, thermoelectric power (α), and transverse Nernst–Ettingshausen coefficient are obtained experimentally in the temperature range 77–450 K. The transmittance spectrum in the range 400–5250 cm–1 is recorded at room temperature. It is shown that, to interpret the temperature dependences of the scattering parameter r and the ratio of the thermoelectric power to temperature (α/T), it is essential to take into account the complex valence-band structure and the contribution of heavy holes to transport phenomena. Estimations of the energy band parameters in the context of the two-band model give a hole effective mass close to the free electron mass and the energy gap between nonequivalent extrema at a level of several hundredths of eV. In the absorption spectrum derived from the transmittance spectrum, a sharp increase in absorption defined by indirect interband transitions with the band gap Eg ≈ 0.14 eV is observed in the region of frequencies ν ≥ 1000 cm–1. The absorption spectrum calculated from the reflectance data using the Kramers–Kronig relations is in agreement with the experimental absorption spectrum.

О зонной структуре Bi-=SUB=-2-=/SUB=-Te-=SUB=-3-=/SUB=-

AbstractFor p -Bi_2Te_3 crystals grown by the Czochralski method, the temperature dependences of the conductivity, Hall coefficient, thermoelectric power (α), and transverse Nernst–Ettingshausen coefficient are obtained experimentally in the temperature range 77–450 K. The transmittance spectrum in the range 400–5250 cm^–1 is recorded at room temperature. It is shown that, to interpret the temperature dependences of the scattering parameter r and the ratio of the thermoelectric power to temperature (α/ T ), it is essential to take into account the complex valence-band structure and the contribution of heavy holes to transport phenomena. Estimations of the energy band parameters in the context of the two-band model give a hole effective mass close to the free electron mass and the energy gap between nonequivalent extrema at a level of several hundredths of eV. In the absorption spectrum derived from the transmittance spectrum, a sharp increase in absorption defined by indirect interband transitions with the band gap E _ g ≈ 0.14 eV is observed in the region of frequencies ν ≥ 1000 cm^–1. The absorption spectrum calculated from the reflectance data using the Kramers–Kronig relations is in agreement with the experimental absorption spectrum.

Anisotropy of Nernst–Ettingshausen Effect in Superlattices During Scattering on Phonons

The paper focuses on anisotropy of the transverse Nernst–Ettingshausen effect in superlattices depending on the degree of mini-band filling and magnetic field direction during scattering on acoustic and polar optical phonons. The authors demonstrate that in the case of scattering on polar optical phonons one observes considerable anisotropy and, depending on the magnetic field direction, the Nernst–Ettingshausen coefficient may change its sign.

Nernst-Ettingshausen effect at the trivial-nontrivial band ordering in topological crystalline insulator Pb1−xSnxSe

The transverse Nernst-Ettingshausen (N-E) effect and electron mobility in Pb1−xSnxSe alloys are studied experimentally and theoretically as functions of temperature and chemical composition in the vicinity of vanishing energy gap Eg. The study is motivated by the recent discovery that, by lowering the temperature, one can change the band ordering from a trivial to nontrivial one in which the topological crystalline insulator states appear at the surface. Our work presents several new aspects. It is shown experimentally and theoretically that the bulk N-E effect has a maximum when the energy gap Eg of the mixed crystal goes through zero value. This result contradicts the claim made in the literature that the N-E effect changes sign when the gap vanishes. We successfully describe dc transport effects in the situation of extreme band’s nonparabolicity which, to the best of our knowledge, has never been tried before. A situation is reached in which both two-dimensional bands (topological surface states) and three-dimensional bands are linear in electron k vector. Various scattering modes and their contribution to transport phenomena in Pb1−xSnxSe are analyzed. As the energy gap goes through zero, some transport integrals have a singular (nonphysical) behaviour and we demonstrate how to deal with this problem by introducing damping.

Determination of parameters of a system of charge carriers in Y1–2x Ca x Pr x Ba2Cu3O y within a combined analysis of temperature dependences of thermoelectric power and Nernst–Ettingshausen coefficients

The temperature dependences of thermoelectric power S and transverse Nernst–Ettingshausen effect Q in high-temperature superconductors of the Y1–2xCaxPrxBa2Cu3Oy system with different concentrations of dopants have been investigated experimentally. It has been shown that all the specific features revealed in the behavior of the two kinetic coefficients under investigation can be described using the narrowband model with a single concept of the structure of an energy spectrum and a common set of model parameters that characterize the structure of the spectrum and properties of a system of charge carriers. Based on the quantitative analysis of the dependences S(T) and Q(T), the values of these parameters for samples of the studied composition have been determined and the character of their changes with an increase in the impurity content has been analyzed. It has been demonstrated that, for the explanation of the obtained results, it is necessary to take into account the interaction of calcium and praseodymium ions upon their simultaneous introduction into the lattice. It has been found that the mobility of charge carriers has extremely low values and almost does not depend on the level of doping, which is associated with the character of changes in the structure of the energy spectrum of Y1–2xCaxPrxBa2Cu3Oy upon doping. It has been concluded that the structure of the energy spectrum of high-temperature superconductors in the yttrium system is characterized by an asymmetry of the dispersion curve.

Effect of copper doping on kinetic coefficients and their anisotropy in PbSb2Te4

In anisotropic PbSb2Te4 and PbSb2Te4:Cu single crystals, nine main independent components of the Hall, electrical-conductivity, thermopower, and Nernst-Ettingshausen effects and their anisotropy in the range 77–450 K have been studied. PbSb2Te4 single crystals exhibit a high hole concentration (p ≈ 3 × 1020 cm−3). Copper exhibits a donor effect and significantly (approximately by a factor of 2) reduces the hole concentration in PbSb2Te4. The temperature dependences of the kinetic coefficients, except for the Hall effect, have a form typical of the one-band model. The significant anisotropy of the Hall coefficient R 123/R 321 ≈ 2 at low temperatures corresponds to the multi-ellipsoid model of the energy spectrum of holes in PbSb2Te4. An important feature of the data on transport phenomena is the high thermopower anisotropy (ΔS ≈ 60–75 μV/K) in the mixed conductivity region caused by the mixed scattering mechanism. Data on the anisotropy of the transverse Nernst-Ettingshausen effect confirm the mixed mechanism of hole scattering; in the cleavage plane, scattering at acoustic phonons dominates, while in the trigonal axis direction, impurity scattering appears significant. Doping with copper enhances the role of impurity scattering in the direction of the trigonal axis c 3; as a result, two components of the Nernst-Ettingshausen tensor Q 321 and Q 132 in the PbSb2Te4:Cu single crystal are positive at low temperatures, whereas, in the undoped crystal, only the Q 321 component is positive.

Simple apparatus for the multipurpose measurements of different thermoelectric parameters

A simple apparatus for the simultaneous measurement of Seebeck coefficient ( α) and electrical resistivity ( ρ) in the temperature range 100–600 K, Hall coefficient ( R H) and transverse Nernst–Ettingshausen coefficient ( N) in the temperature range 300–600 K of the bar shaped samples has been fabricated. The instrument has been designed so simply that the sample can be easily mounted for the fast measurements of different thermoelectric parameters. The sample holder assembly of the apparatus has been designed so cleverly that any part of that section can be replaced in case of any damage; and so it can be regarded as a modular based system. The apparatus is relatively cheaper in cost and also portable.

Magneto-thermoelectric effects in two-dimensional quantum well: role of short-range potential

We have studied transverse thermomagnetic effects in a quantum well (QW) with parabolic potential in the presence of a magnetic field parallel to the two-dimensional electron gas layer. The calculation was carried out for the case of elastic electron scattering on short-range potential for degenerate and non-degenerate electron gas. It is shown that the reviewed mechanism of charge carriers' relaxation is essential for the electroconductivity at low temperatures. In the quantum limit, the dependencies of the transverse Nernst–Ettingshausen coefficient and the thermopower on the magnetic field strength, the temperature and the carrier density are determined and analyzed. We have showed that the magnetothermopower is not determined by the entropy only, as is the case for bulk specimens.

Transverse Nernst-Ettingshausen effect, resonant scattering, and superconductivity in SnTe: In

The temperature dependences of the coefficient of the transverse Nernst-Ettingshausen effect in SnTe: In samples with different indium contents (1–16 at %) in the temperature range 100–300 K and the electrical resistivity at temperatures of 1.2–4.2 K and in magnetic fields of up to 10 kOe are investigated. The data obtained indicate the presence of resonant hole scattering into the band of quasi-local In impurity states in Sn1−xInxTe samples with In content x ≥ 0.05 and a superconducting transition with a critical temperature Tc ∼ 1.5–2.2 K. The SnTe: In samples with the degree of filling of impurity states by electrons, which is close to 1/2, and the Fermi level ɛF pinned in the vicinity of the minimum energy dependence of the relaxation time τ(ɛ) are characterized by inhomogeneities of a new type, i.e., inhomogeneities of the scattering parameter r = ϖlnτ/∂lnɛ|\( \varepsilon _F \), which are induced by fluctuations of the degree of filling of quasi-local states by electrons.

Thermoelectric and Thermomagnetic Transport in PbTe with Nanoscale Structures

ABSTRACTQuantum-dot superlattices (QDSLs) have demonstrated thermoelectric figure of merit (ZT) values double those of classical bulk materials, providing the proof that nanoscale materials can address this age-old limitation on thermoelectric technology. Since QDSL materials can only be obtained in thin-film form, the development of bulk materials with nanoscale inclusions would be useful for many large-scale applications. Nanometer-scale inclusions in lead chalcogenides are known to improve the thermoelectric figure of merit through a combination of two factors: a strong decrease in lattice thermal conductivity, and an increase in the Seebeck coefficient over that of bulk PbTe for a given carrier concentration. This paper focuses on experimental results obtained on two types of PbTe nanocomposites, namely samples prepared by sintering powders with nanometer-sized grains, and samples prepared with nanoprecipitates of metallic Pb. The results are analyzed using the “method of four coefficients.” At each measurement temperature there are four unknowns. These are the carrier concentration, the mobility, the carrier effective mass, and the energy dependence of the relaxation time Tau, which is modeled by a power law: Tau proportional to energy to power Lamda. Therefore, at each temperature, four measurements are taken: the electrical conductivity, and the Hall, Seebeck and transverse Nernst-Ettingshausen coefficients. This analysis concludes that the effect of the nanoscale inclusions on the power factor is due to an increase in the scattering parameter λ, and that the nanoscale inclusions affect the electron scattering in such a way as to increase the Seebeck coefficient.

Nernst–Ettingshausen and magnetoresistance effects in Hg1–xCdxSe single crystals in vicinity of phase transitions under hydrostatic pressure

AbstractIn the present paper the thermomagnetic longitudinal and transverse Nernst–Ettingshausen (N–E) effects were investigated in Hg1–xCdxSe (x = 0.03, 0.07) single crystals at hydrostatic pressure up to ∼2 GPa. Substitution of Cd atoms into cation sublattice increases strongly the stability of initial zinc blende lattice and shifts the phase transformation into cinnabar structure to higher pressures P ≥ 1.4 GPa. For ternary Hg1–xCdxSe compounds the values of mobility and scattering parameters of charge carriers have been obtained from the N–E and magnetoresistance (MR) effects up to phase transition points 1.4–1.7 GPa. The decreasing of mobility under pressure is consistent with opening of direct semiconductor gap. In vicinity of the structural phase transformations into cinnabar structure an anomaly of transverse N–E effect was observed connected probably with peculiarity of electronic band structure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of mutual drag of the carrier-phonon system on the thermopower and transverse Nernst-Ettingshausen effect

The thermopower and Nernst-Ettingshausen (NE) effect in degenerate semiconductors and semimetals placed in high electric and magnetic fields are calculated by taking into account the heating of both electrons and phonons as well as their thermal and mutual drags. The magnetic and electric field dependences of the thermoelectric power and the transverse NE voltage are found in analytical forms. It is shown that in weak and high transverse magnetic fields, the electronic and phonon parts of the NE coefficients change their sign for some scattering mechanisms.

Thermo- and galvanomagnetic technique for semiconductors testing at high pressure up to [formula omitted

The thermoelectric power ( S), magnetoresistance (MR) and thermomagnetic (TM) effects were measured at high pressure ( P) in the vicinity of semiconductor–metal phase transitions for Te, Se and S micro-samples. From longitudinal and transverse Nernst–Ettingshausen (N–E) effects for Te and Se, the scattering parameter ( r) of holes was estimated and under the closing of semiconductor gap ( E g) the decreasing of their effective mass ( m) was found. S of Sulphur also decreased with pressure up to 40 GPa and the negative MR effect observed indicates low mobility ( μ) of holes. The technique developed seems to be suitable for use in micro-device technology.

Thermoelectric and galvanomagnetic investigations of VI group semiconductors Se and Te at high pressure up to 30 GPa

At ultrahigh pressures up to 30 GPa the thermomagnetic Nernst–Ettingshausen effect was measured for Te and Se samples in the vicinity of semiconductor–metal phase boundary. The significant longitudinal and transverse Nernst–Ettingshausen effects observed for both semiconductors allowed one to estimate the scattering parameter for charge carriers. The increase in hole mobility obtained from longitudinal and transverse Nernst–Ettingshausen effects being consistent with the growth of magnetoresistance under pressure gave confirmation to the decrease in the effective mass of holes at the closure of direct semiconductor gap.

Effect of the mutual dragging of electrons and phonons on the thermomagnetic effects in HgSe

The longitudinal and transverse Nernst-Ettingshausen (NE) effects were measured in HgSe samples doped with various concentrations of gallium, 0.6×1018<N(Ga)<4.7×1018 cm−3. The NE measurements were performed for the classical interval of magnetic field strengths (0–40 kOe) in the temperature range from 20 to 60 K. It was established that the low-temperature NE coefficients change sign with increasing Ga concentration or the applied magnetic field strength. It is shown that all unusual features of the NE effects observed in HgSe crystals can be attributed to the effect of mutual dragging of electrons and phonons. This implies that the effect of mutual electron-phonon dragging can be experimentally detected in semiconductors with high concentration of conduction electrons.

Transverse Nernst-Ettingshausen effect in HgSe:Fe,Ga crystals containing mixed-valence iron impurities

The transverse Nernst-Ettingshausen effect is investigated experimentally and theoretically for HgSe:Fe,Ga samples with various iron and gallium impurity contents. It is shown that the unusual dependence of the magnitude and sign of the effect on the gallium impurity content are attributable to their influence on the degree of spatial ordering of the trivalent iron ions and, accordingly, on the nature of the scattering of conduction electrons. The results of the calculations agree qualitatively with the experimental data.

Effect of inhomogeneities of Bi2T3 crystals on the transverse Nernst-Ettingshausen effect

The effect of inhomogeneities in p-Bi2Te3 crystals, grown by different methods, on the coefficients of the transverse Nernst-Ettingshausen and Hall effects has been studied. The degree of homogeneity of the crystals was estimated on the basis of thermo-emf (Seebeck coefficient) data. It was established that the concentration dependences of the Nernst-Ettingshausen coefficient at T=300 K in homogeneous and inhomogeneous samples are different. This makes it possible to use the Nernst-Ettingshausen effect data for quality assessment of Bi2Te3 crystals. It is shown that the anomalous drop of the Hall coefficient with increasing temperature in a number of samples is due to inhomogeneities, and in Sn-doped Bi2Te3 crystals it is due to the existence of an impurity level against the background of the valence-band states.

Measurement of the Effective Mass of Transparent Conducting films of Cadmium Tin Oxide

ABSTRACTWe have prepared transparent conducting films of cadmium stannate (Cd2SnO4 with resistivity as low as 1.5×10-4 Ω cm. The resistivity of these films is low because of their surprisingly high mobility (60 cm2 V-1 sec-1) at high carrier concentration (7×1020cm-3). We conducted an investigation to determine whether the high mobility is due to unusually low carrier effective mass or to a long carrier relaxation time. The conductivity effective mass and relaxation time were estimated by Drude free-electron modeling of reflectance and transmittance spectroscopie measurements. The Drude model appears to represent the behavior of cadmium tin oxide very well. The optical effective mass of the electrons in cadmium stannate is about 0.35 mo, which is similar to that of other transparent conducting oxides. By varying the doping level, we were able to fabricate films with various levels of degeneracy, but these showed no significant difference in effective mass.We were also able to determine the carrier effective mass and the relaxation time by measuring four separate electron transport coefficients: conductivity, Hall, Seebeck, and transverse Nernst-Ettingshausen (Nernst). The Fermi level was found to vary from 0.31 to 0.83 eV above the conduction band minimum, and the conduction band was very close to parabolic in this range, with m* ∼ 0.33 mo, in good agreement with the optical result. We conclude that the effective mass of electrons in cadmium stannate is similar to electrons in other transparent conducting oxides and that high mobility results from a relatively long carrier relaxation time.

Magnetic field dependence of thermomagnetic effect of Bi88Sb12 alloy.

The magnetic field dependences of the thermoelectric effect, the magnetoresistance, the thermal conductivity and the transverse Nernst-Ettingshausen effect are investigated on Bi88Sb12 alloy single crystals. The Seebeck effect under the magnetic field along the temperature gradient is the longitudinal Nernst-Ettingshausen effect. The longitudinal and transverse Nernst-Ettingshausen effects (LNE and THE respectively) have been measured with the magnetic field up to 1.2T and at the temperature of 100K to 300K. Two configurations, Bz//c-axis and Bz⊥ c-axis, have been used. The Seebeck coefficient of the minus sign increases in the absolute value as the temperature is lowered. By the application of the magnetic field, the coefficient very much increases in the minus sense. The increase of the resistivity by the magnetic field is more drastic compared to the increase of Seebeck effect. The magnetic field dependence of the thermal conductivity κ is minor compared to the Seebeck effect S and the magnetoresistivity ρB. The figure of merit Z (=S2/ρBκ) is calculated by using the measured values of S, ρB and κ. Z value without the field changes from 5×10-4K-1 at 300K to 4×10-3K-1 at 110K. By applying the field of 1.2T, Z-value increase about 20-30% above about 160K, while decreases down to 5×10-4K-1 at 110K. The addition of an appropriate impurity such as Te should improve the Z under the magnetic field. The merit of the TNE effect for the thermomagnetic application is mentioned.