Measurements of the elastic constants and thermal expansion of PbTe have been made from 4.2° to 303.2°K. The extrapolated 0°K values for C44, (C11−C12)/2, and (C11+2C12)/3, respectively, are 1.514±0.009, 6.184±0.066, and 4.560±0.042×1011 dyn/cm2. At 303.2°K these values are 1.344±0.008, 5.016±0.057, and 4.107±0.037×1011 dyn/cm2. Intermediate values are presented graphically, as are the thermal-expansion data. The linear coefficient of thermal expansion is found to be 20.4±0.4×10−6/°C at room temperature. The 0°K Debye temperature is calculated to be 176.7°±0.5°K.
We have observed Shubnikov-de Haas oscillations in the longitudinal magnetoresistance of SnTe, a cubically symmetric, extrinsic ptype semiconductor. 1 " 5 The measurements were made in steady magnetic fields up to 155 kG. Oscillations were detected between 40 and 155 kG, and were seen in samples with carrier concentrations 6 /) between 5xl0 19 and 5xl0 20 cm" 3 . It is very unusual to have observed the Shubnikov-de Haas effect over such a wide range of carrier concentrations. Moreover, the upper limit is some 25 times larger than the highest concentration at which such oscillations have been detected previously in an extrinsic material. 7 It was possible to observe the oscillations at such large carrier concentrations because of the high magnetic field intensities available, and because of the extraordinarily weak "ionized impurity" scattering 8 in SnTe.The results presented here already suggest (1) the orientation of the Fermi surfaces, (2) the presence of a second, lower-lying valence band, and (3) an explanation for several puzzling electrical and elastic measurements obtained earlier. 2 ' 6 ' 9For our as-pulled single crystals, />«5xl0 20 cm"" 3 . We obtained lower p values by diffusion techniques to be described elsewhere. The crystallographic orientations studied included [001], [114], [112], [111], and [110] directions. Measurements were made at 4.2 and 1.4°K. The high, steady magnetic fields were produced in a li-inch inner diameter modified Bitter-type solenoid. 10
Measurements of the temperature dependence of the Hall coefficient are presented for samples of p-type PbTe having carrier concentrations between 3×1017 and 1×1020 cm−3. As the temperature increases, the Hall coefficient for any given carrier concentration at first remains at the constant value RL and then increases steadily at higher temperatures. As the carrier concentration increases from the lowest to the highest values studied, the Hall ratio R295°/RL increases smoothly from about 1.1 to 2.5. The data are analyzed in terms of a simple two-valence-band model. The results indicate that the energy separation between the two band edges is about 0.14 eV at 0°K, and that carriers in the second band have a heavy mass and low mobility relative to those in the first. The data also suggest that there are no carriers in the second band in the liquid-helium temperature range, even at the highest carrier concentration. This requires that the first valence band be strongly nonparabolic.
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