Summary of New Insight into Electron Transport in Metals

Abstract

This paper gives a summary of a new insight into basic electron transport characteristics in crystalline elemental metals. The general expressions based on the Fermi-Dirac distribution of the effective density of the randomly moving electrons, their diffusion coefficient, drift mobility, and other characteristics, including the Einstein relation between diffusion coefficient and drift mobility, are presented. It is shown that the creation of the randomly moving electrons due to lattice atom vibrations produces the same number of electronic defects, which cause scattering of the randomly moving electrons and related transport characteristics.

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

“…The rest part N -Neff of atoms which have the valence electrons with energy lower than the Fermi level energy does not have sufficient thermal vibration energy to excite their valence electrons. As it is pointed in [13], the rest part n -neff of the valence electrons, which energy is lower by a few kT than Fermi level energy, due to the Pauli exclusion principle and Fermi-Dirac statistics can not change their energy, and they cannot scatter the free RM electrons.…”

“…In [13,14], it has been shown that the lattice atom vibrations produce not only the effective density of free randomly moving electrons 𝑛 eff = 𝑔(𝐸 F )𝑘𝑇 (here 𝑔(𝐸 F ) is the density of states at the Fermi level energy), but also the same density of electronic defects (not completely screened ions) is produced 𝑁 eff = 𝑛 eff . In Figure 2, there are demonstrated the electronic defect dependence on temperature for aluminum, and for transition group metal tungsten.…”

“…As can be seen, the effective density of the electronic defects even at temperature 1 K is higher than 10 18 cm -3 , and these electronic defects cannot be, in principle, decreased as it can be done with the residual defects. As it is shown in [13,14], the resistivity of the elemental metals dependence on temperature can be described as (𝑇) =  0 + (𝑇 0 )(𝑇/𝑇 0 ) ph (𝑇/), (13) where  is the Debye temperature,  ph (𝑇/) is the phonon mediation factor accounting the free RM electron scattering by electronic defects:…”

“…Though the valence electron wave functions overlap with that of neighbor atoms [6][7][8], they remain associated with native ion cores. Only valence electrons, which have energies close to the Fermi level energy due to lattice atom vibrations can be released, and can randomly move in metal [13,14]. The effective density neff of the free randomly moving (RM) electrons in metals and other materials has been defined in [15] as…”

“…The resistivity of metals linear increase with a temperature above Debye's temperature was usually explained by charge carriers scattering due to lattice atom vibrations: due to an increase of the electron scattering cross-section [6,9−12,19−22]. As shown in [13,14], the electron scattering crosssection at a temperature above the Debye temperature does not depend on temperature, and the lattice vibrations play another role: they produce the free RM electrons, and at the same time they produce the electronic defects (weakly screened ions, which lost valence electrons). The effective density of the electronic defects 𝑁 eff = 𝑛 eff .…”