Two-Phonon Deformation Potential in InSb

Abstract

The nonpolar optic two-phonon deformation potential is shown to have observable effects on the electronic spectrum. Its value is deduced for InSb.The nonpolar interaction Hamiltonian between carriers and phonons can be expanded in powers of the lattice displacement,The first-order term u* VU (=# e/) (1) ) gives rise to the familiar one-phonon scattering. The higher-order terms correspond to multiphonon scattering in which two or more phonons are created and/or destroyed. It has been suggested 1 * 2 that the term bilinear in the acoustic phonon amplitudes, # e / 2 \ may account for the temperature dependence of mobility in nonpolar semiconductors. However, two-phonon scattering can also arise from the second-order matrix element of H ep (1 \ As described by Herring, 3 most of the acoustic scattering matrix element of # e/>(2) will be canceled by the second-order matrix elements oiH eP^\ This cancelation of terms in the transport formulation has made it difficult to draw any conclusions from transport data concerning the importance of the bilinear acoustic term, H eP^2 \ 3 Similarly, both contributions must be considered simultaneously in lattice dynamical calculations. There one must include H eP (2) in the electronic contribution to the force constants in order to preserve the translational invariance of the free energy. Only then will all acoustic-mode frequencies vanish at long wavelengths. 4In contrast, the effect of # e / 2) for nonpolar optical (NPO) phonons can be isolated for the following reasons: (1) Optical phonons have finite frequencies as q-~0; (2) for electrons in a band of s-like symmetry, the first-order NPO matrix element ofH eP (l) vanishes; and (3) experiments involving resonant electron-phonon(s) interaction can be used. Each of these factors will prohibit interference between matrix elements oiH eP^ and H eP i2 \ In this Letter we report some magneto-optical observations of the effects ofH eP (2) for NPO phonons and present the first determination of the two-phonon deformation potential in InSb. Our magneto-optical studies oiH eP {2) are not hampered by the complications involved in the analysis oiH eP {2) (acoustic) in transport data.Magnetotransmission measurements were made on a 1.87-mm-thick Te-doped InSb sample (n = 1.4xl0 15 cm" 3 , |U=3xl0 15 cm/V sec at 77°K). Most samples were oriented with the magnetic field B in the (110) direction and the light propagation vector perpendicular to B. The sample temperature was 6°K and in the magnetic fields of interest, carriers freeze out so that impurity transitions predominate. The infrared energy range covered was from 33 to 55 meV, the twooptical-phonon region. Part of the two-phonon absorption spectrum for B = 0 is shown in Fig. 1. The present data show more structure than similar data which was reported previously. 5 In the presence of a magnetic field, induced absorption appeared which corresponds to a 10-15% modification of zero-field data. The induced absorption was isolated and the structure in the resulting spectrum was attributed to...