Analysis of Transport Properties of the Randomly Moving Electrons in Metals

Abstract

In this critical analysis on the base of randomly moving (RM) electrons, presented the resistivity dependence on temperature for elemental metals both above and below the Debye’s temperatures. There also are presented the general relationships for estimation of the average diffusion coefficient, the average velocity, mean free path and average relaxation time of RM electrons on the Fermi surface at mentioned temperature range. It is shown that the scattering of RM electrons mainly is due to electronic defects associated with distortion of the periodic potential distribution in the periodic lattice, and accounting the exchange of the thermal energies between phonon and RM electron. The calculation results of resistivity dependence on temperature in the temperature range from 1 K to 900 K are demonstrated for Au and W and compared with the experimental data. There also is presented the simple method for determination of the basic kinetic characteristic dependences on temperature only from the resistivity dependence on temperature. It is at first time determined for Au and W the temperature dependences of the mean free path, average diffusion coefficient, average relaxation time of RM electrons from 1 K to 900 K.

Gallium Arsenide‐Based Active Antennas for Optical Communication Photodetection with Robustness to Voltage and Temperature

“…Palenskis et al. [ 59 ] calculated the dependence of the resistivity of Au on the temperature in the range from 1 to 900 K and compared it with the experimental data, [ 60,61 ] determining that the electron inelastic mean free path of Au was 37 nm at 300 K and that the mean free path increased upon decreasing the temperature [it was inversely proportional to the Kelvin temperature (1/ T ) in the range from 100 to 1000 K]. In addition to the influence of the mean free path of Au on the change in photoresponsivity, the variation in the semiconductor resistivity with respect to temperature also played an important role in affecting the electron transport behavior.…”

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

“…On the other hand, 𝐅 eff = 𝐩/𝑡 = ħ𝐤/𝑡 (here p is the momentum, and k is the wave vector of the electron. If the average energy of the free electron during scattering change is about 1.64kT [14], the wave vector due to parameter   experiences a very large exchange of the direction. Thus, the free electron motion in material must be described by such general equation:…”

“…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.…”

“…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 .…”