Spin‐Magnetophonon Resonance in Semiconductors

Abstract

A theory is presented for spin‐magnetophonon resonance. The spin interaction of electrons with optical phonons is described by the introduction of vector and scalar potentials of the optical vibrational field. It is shown that the spin‐magnetophonon resonance should cause a minimum in the longitudinal magnetoresistance. The experimental data for n‐InSb and n‐InAs are discussed on the basis of this theory. Certain new magnetoresistance measurements are presented for the case of n‐InSb: 1) A maximum of the transverse magnetoresistance is observed at 82 kG corresponding to the spin‐magnetophonon resonance. The g‐factor for the conduction electrons, calculated from this maximum, is in good agreement with the theoretical value. 2) A minimum in the longitudinal magnetoresistance is observed at 24 kG, dur to the combined magnetophonon and spin‐magnetophonon resonance scattering.

On the deformation potential constant of the conduction band in InSb

“…Now when we have taken into account the effect of the conduction band nonparabolicity on the scattering probability, the effect of electron-phonon interaction on m, and eg, and the screening of the deformation and polarization potentials, the agreement was attained throughout the range of used pressures. The good agreement between calculation and experiment, obtained in [3] for the thermoelectric power at high pressures, is due to the fact the thermoelectric power depends more weakly on scattering than the mobility (the expression for the thermoelectric power does not contain t), and therefore the mentioned three factors, essentially affecting the value of the mobility, cause a very small change in the thermoelectric power. low temperatures.…”

“…In addition it is worth noting that our measurements of the dependence p ( P ) up to 15 kbar at 78 O K on samples with n = 8.3 x l O l 6 and 4.8 x 1018 cm-3 showed that the agreement between values of p experimental and calculated under assumption /ell = 40 eV is not affected by the change of the degree of nonparabolicity. Thus, one can conclude that the temperature corrections due to nonparabolicity do not introduce large errors into the value of el, for at pressures from 20 to 25 kbar the degree of nonparabolicity decreases appreciably : at 25 kbar 5 / E g is more than three times smaller than at atmospheric pressure.e) But whereas at high temperatures there are no obvious reasons, which could lead to appreciable errors, one can point out a weak spot in the calculations at eV/deg and -2.9 x a) It was noted in our paper [3] that the discrepancy between calculated and experimental values of the mobility for a sample with n = 2.4 x 10'8 om-3 at T = 290 O K is larger at smaller pressures. Now when we have taken into account the effect of the conduction band nonparabolicity on the scattering probability, the effect of electron-phonon interaction on m, and eg, and the screening of the deformation and polarization potentials, the agreement was attained throughout the range of used pressures.…”

“…(1) to (3) show that this error in t does not exceed a few per cent. The error in the value of el may be larger at low temperatures than a t high ones, since in most cases the contribution of the acoustic scattering is noticeably less than at high temperatures.…”

“…Buchy [7] measured the electron mobility in a sample with n = lo1* in the temperature range from 10 to 200 O K and determined = 30 eV. A similar analysis of the temperature dependence of the mobility in the interval 77 to 200 O K for various electron densities was made by us in 1963 (the data for 200 O K were quoted in [3]) and a satisfactory agreement between the calculated and experimental values was found also a t [Ell 2 30 eV.…”

“…Haga and Kimura [2] compared the theoretical and experimental values of the free carrier infrared absorption coefficients in samples with electron densities from 12 = 2 x l0ls to 1 x 1018 a t 300 O K and determined = 30 eV. A t the same value arrived Tsidilkovskii [3] analysing the measurements of the thermoelectric power in strong classical magnetic fields in pure crystals and the effect of hydrostatic pressure on the thermoelectric power in heavily doped crystals. On the other hand, the analysis of the effect of pressure on the mobility and transverse Nernst-Ettingshausen effect showed that the agreement between the values calculated for lell = 30 eV and the experimental ones improved as the pressure increased but a complete agreement was not attained even at 25 kbar.…”