Galvanomagnetic Tensors of Bismuth Single Crystals at Low Temperatures

A measurement of the galvanomagnetic tensors of bismuth at the liquid helium temperature and in the magnetic field up to 10 kilo Oersted is reported of three single crystals with different crystallographic orientations. All non-vanishing tensor components (except one) predicted by the crystal symmetry and Onsager\u27s reciprocal relation are measured. The dependency of the symmetric tensor components on the direction of the magnetic field is studied somewhat in detail. The experimental results are analysed semi-phenomenologically on the basis of the Boltzmann equation. Our experimental results of the absolute values and the field dependencies for the symmetric and antisymmetric tensor components respectively are such as expected theoretically in chemically pure samples. The anisotropy of the tensor components of typical type is, however, fairly small compared with that expected from the known energy surface anisotropy. This shows the importance of the anisotropic scattering or a failure of usual approximate theory, but unfortunately we could not obtain quantitative conclusion because a part of each anisotropy should have been attributed to undesirable boundary effect and other effects

The Effect of Thermally Produced Lattice Defects on the Electrical Properties of Tellurium

The electrical properties of tellurium crystals are re-investigated under the assumption of excess holes in the valence band owing to the trapping of electrons by the lattice defects generated by the thermal excitation of lattice atoms. From the observed data of the electrical conductivity and the Hall effect, and by applying the treatment of composite semiconductor in which the extrinsic acceptors and the thermally produced acceptors both generate holes other than the intrinsic pair excitations of electrons and holes, the width of the forbidden energy band ΔE, the effective masses of electrons and holes m_e and m_h, and the carrier mobilities due to the lattice scattering μ_eL and μ_hL are determined as ΔE = 0.32+1.9×10^TeV, m_e = 0.68m, m_h=0.91m and μ_eL = 2.1μ_hL = 6.1 × 10^6Tcm^2/volt・sec. The sign reversals of Hall effect and thermoelectric power from minus at lower temperatures to plus at higher ones found in the pure intrinsic region are explained by the predominance of holes released from the lattice defects the concentration of which increases with the rise of temperature, and the optimum fit of the calculated characteristics to the observed one is obtained by assuming the activation energy to produce one lattice defect as 0.52 eV

Transverse Galvanomagnetic Effect of Bismuth Single Crystal in a Strong Magnetic Field

Transverse galvanomagnetic effects of bismuth single crystal are measured in a strong magnetic field up to about 100 kilo Oersted at 4.2, 3.0 and 1.8K. And the twelve components of the galvanomagnetic tensor are obtained with respect to the magnetic field dependence. Furthermore the behaviors of the galvanomagnetic tensor components near the quantum limit of the magnetic quantization are studied, expecting that they can lend themselves to analyse the energy band structure. In a strong magnetic field, the amplitudes of the oscillatory part of the galvanomagnetic tensors are nearly temperature independent, and the behaviors of Hall effect appear to be different from the expected one from the classical theory of the two bands model

On the Electromagnetic Properties of Single Crystals of Tellurium. II : Ettingshausen-Nernst Effect

The Ettingshausen-Nernst effect of a single crystal of highly purified tellurium has been measured over the temperatures ranging from -160 to +300℃. In the intrinsic semiconductor range of temperature, it was found that the value of coefficient of this effect is roughly in agreement with that evaluated theoretically from the values of the electron and hole mobilities and the width of the forbidden region, which were deduced by analysing the experimental values of the conductivity, the Hall coefficient and the magneto-resistance coefficient measured on the same specimen

Thermoelectric Power of the Non-Polar Semiconductor, That of Tellurium Crystals as an Example

In order to explicate the experimental results on the thermoelectric power of the crystals of pure tellurium and those alloyed with antimony less than 5 per cent, the thermoelectric power of the non-polar composite semiconductor in general has been derived as follows, Chemical formula, where φ is the height of the electrochemical potential above the valence band, ΔE(T) =ΔE(0)+βT is the width of forbidden band, m_e and m_h are effective masses of electrons and holes, b is the ratio of electron and hole mobilities and χ is the energy required to extract the electron at the top of the valence band to rest outside of the crystal. Numerical calculations carried out for tellurium crystals have shown that the measured characteristics can well be accounted for throughout the temperature range being studied. The quantitative discordance observed at higher temperatures has been explained by a more or less elaborated theory in which a dual band structure which consists of two overlapped energy bands is assumed for the conduction band, the same band scheme being compatible with other electric properties of tellurium

Paramagnetism of Tin Observed at the Superconducting Transition

Measurements have been made of the paramagnetism of tin cylinders in the presence of an external magnetic field and with an externally supplied current at the superconducting transition. It has been ascertained that the paramagnetic effect is not such an apparent one as once supposed, but an intrinsic one without hysteresis. The current minimum I_0, required for the appearance of a paramagnetic effect is represented in the (I-H-T) space by the simultaneous equations I_0=ξd(T_c-T) and H_0=ξT_c-T)-I_g/γd. Here I_g, γ, T_c and ξare characteristic constants of the superconductor and have values 1.2 amp, 0.23, 3.73°K and 1.1×10^2 oersted/deg respectively for the case of tin. H_0 and d are the external magnetic field in cersted and the specimen diameter in mm respectively. It is shown that the formula, I_0 = I_g + γdH obtained by earlier investigators for the minimum current requirement is the one for the orthogonal projection on the. (I-H) plane of the critical line in the (I-H-T) space. The paramagnetic region is shown schematically in the (I-H-T) space. Finally some remarks concerning the theory of the paramagnetic effect are given

Electrical Properties of Antimony-Doped Tellurium Crystals

Electrical resistivity, Hall effect and thermoelectric power of tellurium crystals alloyed with antimony of quantities between 0.002 and 5 atomic per cent have been measured in the temperature range from liquid air temperature to 300℃, and the data are compared with the properties of pure tellurium crystals with a view to clarifying the change of electrical properties accompanying the increase of acceptor impurities. The Values of resistivity and Hall coefficient at about 15℃ distribute from 4.2×10^ to 1.7×10^ ohm-cm and from -3.6×10^3 to +3.25 emu respectively as observed for twelve specimens containing antimony up to 5 per cent ; and the density and mobility of holes calculated from the above data range from 2.3×10^ to 2.3×10^ per cm^3 and from more than 4.9× 10^2 to 1.6×10^2 cm^2/volt-sec respectively. Tenth or hundredth parts of added antimony atoms are deemed to yield the acceptor levels having little or no excitation energy in the temperature range under study. The decrease in hole mobilities with the increase of antimony addition are concluded to be due to the predominance of acceptor ion scattering. Thermoelectric power shows a temperature dependence having a maximum at low temperatures and a minimum at intermediate temperatures in the pure specimens, while it tends to show monotonous characteristics having a roughly linear increase with temperature rise in accordance with the increase of antimony concentration

On the Electromagnetic Properties of Single Crystals of Tellurium. III : Adiabatic and Isothermal Hall Effect, and Ettingshausen Effect

A study has been made of the comparison of the adiabatic and the isothermal Hall effects of a tellurium crystal from -180°to +350℃. An ordinary d. c. method was used for the adiabatic effect and a potentiometric nil-method utilizing a 1000 cycles a. c. was employed for the isothermal one. The difference of two kinds of Hall coefficients was found to be less than 10 per cent below 230℃, but above 240℃ the adiabatic coefficient has a value as low as 85~50 per cent of the isothermal coefficient. This notwithstanding, the remarkable sign reversal is observed at 240℃ also in the isothermal Hall coefficient, which fact evinces itself to be one of the essential properties of tellurium

Electric Resistance, Hall Effect, Magneto-Resistance and Seebeck Effect in a Pure Tellurium Film

The electric resistance, the Hall effect, the magneto-resistance and the Seebeck effect are investigated with regard to pure tellurium films, deposited by evaporation on glass plates, over the temperatures ranging from -195°to +60℃ ; the substrates in concern have been baked out in the same high vacuum prior to the metal deposition. The electric resistance and the weight of the deposits are compared for various thicknesses of the films and a certain regular correlation is found between them. The Hall coefficient at room temperature increases almost in proportion to the thickness of the film defined from its electric conduction. The Hall coefficient and the thermoelectric power against aluminium are both positive throughout the whole range of temperature which facts show that the current carriers predominantly have a positive sign