Weak-field magnetoresistance and substrate-induced strain in (111)-oriented PbTe films

Rotational weak-field magnetoresistance (WFMR) measurements were carried out at 300, 77, and 4.2 K on four (111)-oriented n-type PbTe films, deposited by hot-wall epitaxy on BaF₂. The results were analyzed in terms of a four-coefficient generalization of the Seitz-Pearson-Suhl formulation of WFMR which can detect symmetry-lowering effects. Film thicknesses ranged from 4 to 16 {μ}m, carrier densities from 6×{}10¹⁶ to 1×{}10¹⁷ cm^-3, and carrier mobilities from about 1400 at room temperature to as high as 500 000 cm²/V sec at 4.2 K. For each of 48 runs, WFMR data were obtained as the magnetic field B{→} was rotated in the (111) film plane and in a plane perpendicular to the film. The expected sinusoidal behavior is skewed in the second case (the extrema do not occur at special orientations of B{→} imposed by crystal symmetry), so that all four coefficients of the generalized theory, b, c, d, and d', were determined in each case from measurements on the same sample. For cubic symmetry, d'=d, but it was generally found that d'all three temperatures and decreases with decreasing temperature. This increasing film distortion (an in-plane extension) was ascribed to the thermal-expansion-coefficient difference between the PbTe film and its BaF₂ substrate. The deviations from d'/d=1 are smaller in one sample which had been repeatedly cycled between 300 and 4.2 K during an earlier study. For the other three samples at 4.2 K, the measurements yielded d'/d{}10^-2 and a longitudinal WFMR that is an order of magnitude smaller than that found in bulk PbTe. These unique characteristics suggest that all, or essentially all, of the carriers from the four 〈111〉-oriented valleys of the PbTe conduction band had been transferred to the single valley normal to the film plane. The sets of four WFMR coefficients from each run conform closely to the symmetry constraint imposed by a trigonally distorted, three-parameter version of the magneto-transport model for the cubic 〈111〉 multivalley band structure. Values of the carrier transfer parameter F in this model provide more quantitative information about the shift of carriers into the single valley. The other two parameters---the valley mobility anisotropy K and scattering factor G---are generally similar to values found in bulk crystals at 300 and 77 K, but for two of the four films exhibit unreasonable increases at 4.2 K. Ultimately, these were attributed to the enhancement of the WFMR when the magnetic field is perpendicular to the film plane, an effect which is probably associated with stress relaxation across the film thickness. Finally, the values of F were used to deduce that the intervalley energy shifts increase from about 3 meV at 300 K to 12 meV or more at 4.2 K, corresponding to calculated tensile strains in the film plane of 0.4 and 1.6×{}10^-3. Smaller tensile strains at 4.2 K, and zero or even compressive strains at 300 K, have been deduced from other kinds of measurements. A complete explanation for these substantial differences is lacking, but it seems evident that two important factors are the preparation conditions and the thermal history of each sample.