Effect of Anisotropy of Elastic Energy and Shear Waves on Electron–Phonon Relaxation and Electrical Resistivity of Noble Metals. Review 4

The effect of anisotropy of elastic energy on electron–phonon relaxation and electrical resistivity of noble metals is studied within the framework of the Bloch–Grüneisen theory. The spectrum and polarization vectors of phonon are calculated, and the effect of phonon focusing on electron–phonon relaxation in noble metals is analyzed. By matching the calculated electrical resistivity to experimental data at high temperatures, much higher than the Debye temperature, where the resistivity is governed by a linear dependence, the constant E0t, characterizing the interaction of electrons with the shear components of vibrational modes, is determined. The contributions of phonons of various polarizations to the electrical resistivity of Au, Ag, and Cu crystals are analyzed. For scattering of electrons on the longitudinal components of quasi-transverse modes, the standard theory of deformation potential is used. It is shown that, at temperatures much lower than the Debye temperature, the contribution of quasi-transverse modes to the electrical resistivity of Au, Ag, and Cu is 99.5, 97, and 98%, respectively. At the same time, the contribution of longitudinal phonons, which was considered the main mechanism of electron–phonon relaxation in metals, turned out to be smaller than 3%. In this case, the dominant contribution to the electrical resistivity of Au, Ag, and Cu crystals at low temperatures is made by the relaxation of electrons on shear waves, which were not previously taken into account, amounting to 95, 91, and 95%, respectively. Calculation of the spectrum and polarization vectors of phonons, as well as taking into account the relaxation of electrons on the shear components of quasi-transverse modes, made it possible to quantitatively match the calculated temperature dependences of the electrical resistivity of noble metals to experimental data in a temperature range from 10 to 1000 K. Above the Debye temperature, the contribution to the electrical resistivity of noble metals from electron relaxation on the shear components of quasi-transverse modes also turned out to be significant and, at T = 1000 K, amounted to 72, 44, and 66% for Au, Ag, and Cu crystals, respectively. The results obtained show that, when analyzing the phenomena of electron transport in metals, it is necessary, firstly, to take into account the effect of elastic anisotropy on the spectrum and polarization vectors of phonons, and secondly, in the electron–phonon relaxation, it is necessary to take into account the electron scattering on shear components of quasi-transverse modes.