Phonon Mediated Electron-Electron Scattering in Metals

Abstract

It is shown that the linear resistivity dependence on temperature for metals above the Debye's temperature mainly is caused by electron-electron scattering of randomly moving electrons. The electron mean free path in metals at this temperature range is in inverse proportion to the effective density of randomly moving electrons, i.e. it is in inverse proportion both to the temperature, and to the density-of-states at the Fermi surface. The general relationships for estimation of the average diffusion coefficient, the average velocity, mean free length and average relaxation time of randomly moving electrons at the Fermi surface at temperatures above the Debye's temperature are presented. The effective electron scattering cross-sections for different metals also are estimated. The calculation results of resistivity dependence on temperature in the range of temperature from 1 K to 900 K for Au, Cu, Mo, and Al also are presented and compared with the experimental data. Additionally in temperature range from 1 K to 900 K for copper, the temperature dependences of the mean free path, average diffusion coefficient, average drift mobility, average Hall mobility, average relaxation time of randomly moving electrons, and their resultant phonon mediated scattering cross-section are presented.

Analysis of Transport Properties of the Randomly Moving Electrons in Metals

“…where lF is in nm, and D(T0) is in cm 2 /s at T0 = 295 K. The calculation results obtained from Eq. 18 well agree to the data published in paper [16], and data estimated from the dimension effect [17]. The Eq.…”

“…In paper [16], it was shown that electron mean free path in the linear resistivity dependence on temperature range can be expressed by the diffusion coefficient for RM electrons of elemental metals as…”

“…The intensity of the scattering of electrons by electronic defects depends on the exchange of thermal energies between phonon and electron. Accounting that electron scattering by electronic defect is inelastic, and that electron energy fluctuations cause the excitation and annihilation of phonons, then the ratio of the exchange of the thermal energies between phonon and RM electron can be described as [4,16]:…”

Dinâmica ultrarrápida de nanopartículas metálicas

“…O tempo de termalização da energia dos elétrons em nanopartículas metálicas depende de características intrínsecas do sistema e tem forte dependência da localização espacial, nível de energia do elétron, densidade de estados, material, do tamanho da nanopartículas 56 e também depende de fatores externos como intensidade e frequência da energia fornecida aos elétrons. Fisicamente, o caminho livre médio dos elétrons em um metal é inversamente proporcional à densidade efetiva de elétrons se movimentando aleatoriamente, assim sendo, quanto mais elétrons se espalham mais elétrons serão espalhados e desta forma a taxa de espalhamento elétron-elétron em nanopartículas metálicas aumenta exponencialmente com o tempo após a interação com a fonte de energia 57 .…”