scholarly journals On some electron properties of tellurium and Wilson's mechanism of semi-conductivity

1935 ◽  
Vol 148 (865) ◽  
pp. 648-664 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Free Electron ◽  
Previous Investigation ◽  
Room Temperature ◽  
Specific Resistance ◽  
Mean Free Path ◽  
Free Electrons ◽  
Conduction Electrons ◽  
Classical Statistics ◽  
Limiting Case

In a previous investigation it was found that the unusually high value for the Wiedemann-Franz ratio of tellurium could be explained as being only a formal anomally. The amount of heat transferred by the bound atoms is the same in tellurium as in conducting metals; but, in tellurium, in contrast to good conductors, it is responsible for almost the entire heat conductivity because the heat transferred by the free electrons is especially small. This indicates that tellurium differs from true metals in that the density of free electrons is very small. Classical statistics is therefore applicable and the electrical conductivity is given by x = 4/3 e 2 ln (2 πmk T) -5/9 , (1) where n is the density of free (conduction) electrons and l is their mean free path. Taking the specific resistance of tellurium at room temperature as 0.3 ohm-cm and l as 5.2 X 10 -6 cm (Sommerfeld's value for silver, found by applying Fermi-Dirac statistics), n is 2.9 X 10 16 , or about one free electron per million tellurium atoms in contrast to good conductors in which there is approximately one free electron per atom. Even in the limiting case with l = 3.2 X 10 -3 cm (the distance between the tellurium atoms), n is 4.7 X 10 18 which is about one free electron for every 6000 tellurium atoms.

scholarly journals The theory of electronic semi-conductors

1931 ◽  
Vol 133 (822) ◽  
pp. 458-491 ◽  
Keyword(s):  
Classical Theory ◽  
Energy Levels ◽  
Electron Gas ◽  
Mean Free Path ◽  
Pauli Principle ◽  
Critical Energy ◽  
Free Electrons ◽  
Conduction Electrons ◽  
Metallic Conduction ◽  
Direct Proportionality

The application of quantum mechanics to the problem of metallic conduction has cleared up many of the difficulties which were so apparent in the free electron theories of Drude and Lorentz. Sommerfeld* assumed that the valency electrons of the metallic atoms formed an electron gas which obeyed the FermiDirac statistics, instead of Maxwellian statistics, and, using in the main classical ideas, showed how the difficulty of the specific heat would be removed. He was, however, unable to determine the temperature dependence of the resistance, as his formulae contained a mean free path about which little could be said. F. Bloch took up the question of the mechanics of electrons in a metallic lattice, and showed that if the lattice is perfect an electron can travel quite freely through it. Therefore so long as the lattice is perfect the conductivity is infinite, and it is only when we take into account the thermal motion and the impurities that we obtain a finite value for the conductivity. On this view all the electrons in a metal are free, and we cannot assume, as we do in the classical theory, that only the valency electrons are free. This does not give rise to any difficulty in the theory of metallic conduction, as the direct proportionality between the conductivity and the number of free electrons no longer holds when the Pauli principle is taken into account. If there is no external electric field, the number of electrons moving in any direction is equal to the number moving in the opposite direction. The action of a field is to accelerate or retard the electrons, causing them to make transitions from one set of energy levels to another. This can only happen if the final energy levels are already unoccupied, and therefore only those electrons whose energies are near the critical energy of the Fermi distribution can make transitions and take part in conduction, as it is only in the neighbourhood of the critical energy that the energy levels are partly filled and partly empty. These electrons are few in number compared with the valency electrons, and are what should be called the conduction electrons. On the classical theory alone are the valency electrons, the free electrons and the conduction electrons the same.

Quasi-Fermi Energy and Steady-State Recombination Demarcation Level in a-Si:H

1992 ◽  
Vol 258 ◽  
Author(s):  
J. Z. Liu
Keyword(s):  
Steady State ◽  
Fermi Energy ◽  
Free Electron ◽  
Room Temperature ◽  
Taylor Model ◽  
Apparent Discrepancy ◽  
Free Electrons ◽  
Recombination Lifetime ◽  
Quasi Fermi Level ◽  
The Rose

ABSTRACTA specially designed photoconductivity experiment directly shows that, above room temperature, the steady-state recombination lifetime of the free electrons in undoped amorphous silicon can be described by the free electron quasi-Fermi energy alone. The apparent discrepancy on recombination demarcation levels between the Rose model and the Simmons-Taylor model is resolved by including the effect of the occupation function. The significance of the free electron quasi-Fermi level is discussed.

scholarly journals The electrical conductivity of transition metals

1936 ◽  
Vol 153 (880) ◽  
pp. 699-717 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Transition Metals ◽  
Temperature Coefficient ◽  
Noble Metals ◽  
Formal Theory ◽  
Mean Free Path ◽  
Point Of View ◽  
Transition Elements ◽  
Conduction Electrons ◽  
The Mean

1— In a recent paper certain property of the transition metals Ni, Pd, and Pt and of their alloys with Cu, Ag, and Au have been discussed from the point of view of the electron theory of metals based on quantum mechanics. In particular, a qualitative explanation was given of the relatively high electrical resistance of the transition metals. It was shown from an examination of the experimental evidence that the conduction electrons in these metals have wave functions derived mainly from s states just as in Cu, Ag, and Au, and that the effective number of conduction electrons is not much less than in the noble metals. On the other hand, the mean free path is much smaller, because under the influence other the lattice vibrations the conduction electrons may make transitions to the unoccupied d states, and the probability of these transitions is several times greater than the probability of ordinary scattering. Since the unoccupied d states are responsible for the ferromagnetism or high paramagnetism of the transition elements, there is a direct connexion between the magnetic properties and the electrical conductivity. The purpose of this paper is as follows: in 2, 3, and 4 we develop a formal theory of conductivity for metals, such as the tradition metals, where two Brillouin zone are of importance for the conductivity; in 5 we apply the theory to show why, at high temperatures, the temperature coefficient of the paramagnetic metals Pd and Pt falls below the normal value; and in 6 we discuss the resistance of ferromagnetic metals, and show in 7 qualitatively why constantan (Cu-Ni) has zero temperature coefficient at room temperature.

The electrical conductivity of thin wires

1950 ◽  
Vol 201 (1067) ◽  
pp. 545-560 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Free Path ◽  
Mean Free Path ◽  
Fermi Velocity ◽  
Approximate Methods ◽  
Conduction Electrons ◽  
The Third ◽  
Thin Wires ◽  
Velocity Surface ◽  
The Mean

In the first part of this paper, simple approximate methods have been developed for evaluating the electrical conductivity of films and wires of a size comparable with the mean free path of the conduction electrons. In the second part, a rigorous theory has been given of the electrical conductivity of a thin wire, on the assumptions that the Fermi velocity surface is spherical and that the collisions of the electrons at the surface of the wire are inelastic. In the third part of the paper, this theory has been generalized to cover the case where the scattering is no longer inelastic. In the final part, Andrew’s recent experimental results for a thin mercury wire have been fitted to the theoretical curves obtained, and the mean free path evaluated.

The Measurement of Thermal Conductivity of Ag/Al Multilayered Films

1991 ◽  
Vol 229 ◽  
Author(s):  
Takeshi Kaizuka ◽  
We-Hyo Soe ◽  
Ryoichi Yamamoto ◽  
Masanori Ohyama
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Free Electron ◽  
Room Temperature ◽  
Electron Theory ◽  
Multilayered Films ◽  
Phonon Contribution ◽  
Ac Calorimetric Method ◽  
Lorentz Number ◽  
Modulation Wavelength

AbstractThe in-plane thermal conductivity of Ag/Al multilayered films was measured at room temperature by ac calorimetric method as a function of the modulation wavelength and was compared with the electrical conductivity. The electrical conductivity increases with wavelength, Λ, like other metallic multilayered films. The thermal conductivity also tends to increase with Λ, but the Λ dependence is not similar to that of electrical conductivity. Obtained Lorentz number value of the multilayers are almost 10–30% larger than that given by the free electron theory. The Wiedemann-Franz law did not hold in the Ag/Al films and the phonon contribution is not negligible.

scholarly journals Calculation of Electrical Conductivity and Giant Magnetoresistance within the Free Electron Model

1995 ◽  
Vol 384 ◽  
Author(s):  
X.-G. Zhang ◽  
W. H. Butler
Keyword(s):  
Electrical Conductivity ◽  
Free Electron ◽  
Giant Magnetoresistance ◽  
Magnetic Layer ◽  
Random Point ◽  
Free Electrons ◽  
Electron Model ◽  
Multilayer Systems ◽  
Free Electron Model ◽  
Experimental Values

ABSTRACTWe use the model of free electrons with random point scatterers (FERPS) to calculate the electrical conductivity and giant magnetoresistance (GMR) for FeCr multilayer systems and compare our results with the experimental values. Our analysis suggests that the primary cause of the GMR in FeCr systems is regions of interdiffusion near the interfaces. We find that in the samples analyzed, these regions of interdiffusion occupy about 8.5Å of the magnetic layer near each interface.

scholarly journals Formulation of heat conduction and thermal conductivity of metals

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 276-280 ◽  
Author(s):  
Rachid Chebbi
Keyword(s):  
Thermal Conductivity ◽  
Heat Capacity ◽  
Heat Conduction ◽  
Free Electron ◽  
Fermi Gas ◽  
Mean Free Path ◽  
Fermi Velocity ◽  
Boltzmann Transport ◽  
Free Electrons ◽  
Potential Applications

Abstract The well-known low-pressure monatomic gas thermal conductivity expression is based on the Maxwell-Boltzmann velocity distribution and involves the mean particle velocity, the gas heat capacity at constant volume and the particle mean free path. The extension of the formula to a free electron Fermi gas, using the Fermi velocity along with the Sommerfeld electronic heat capacity, was demonstrated in the literature using the Boltzmann transport equation. A different formulation of heat conduction in sufficiently pure metals, yielding the same formula for the thermal conductivity, is provided in the present investigation using the free electron Fermi gas energy distribution with the thermal conductivity determined from the net heat transfer occurring due to random motions of the free electrons in the presence of temperature gradient. Potential applications of this approach include extension of the present kinetic model incorporating quantum effects to cases in which electron scattering occurs such as in nanowires and hollow nanowires.

scholarly journals Shaping quantum photonic states using free electrons

2021 ◽  
Vol 7 (11) ◽  
pp. eabe4270 ◽  
Author(s):  
A. Ben Hayun ◽  
O. Reinhardt ◽  
J. Nemirovsky ◽  
A. Karnieli ◽  
N. Rivera ◽  
...  
Keyword(s):  
Free Electron ◽  
Degrees Of Freedom ◽  
Free Electrons ◽  
Complete Control ◽  
Fock State ◽  
Judicious Choice ◽  
Electron Microscopes ◽  
Photonic States ◽  
Photonic Cavities ◽  
Electron Interactions

It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.

Is Thermal and Light-Induced Annealing of Met Astable Defects in a-Si:H Driven by Electrons?

1995 ◽  
Vol 377 ◽  
Author(s):  
Helena Gleskova ◽  
S. Wagner
Keyword(s):  
Electrical Conductivity ◽  
Light Intensity ◽  
Defect Density ◽  
Hydrogenated Amorphous Silicon ◽  
Free Electrons ◽  
Free Electron Density ◽  
Independent Variables ◽  
The Third ◽  
Defect Annealing ◽  
Hydrogenated Amorphous

ABSTRACTWe report results of a search for a unifying rate law for the annealing of metastable defects in hydrogenated amorphous silicon (a-Si:H). We tested the hypothesis that defect-annealing by both heating or illumination is driven by the density of free electrons. This hypothesis is formulated via the rate equation - dN/dt = A nα N f (T), where N is the defect density, t the time, A a constant, n the free electron density, and f (T) a function of temperature derived from a distribution of annealing energies. The model fits two sets of data, with light-intensity and electrical conductivity as the independent variables, reasonably well, with a ranging from 0.39 to 0.76, but not the third set, where we varied the temperature.

Structure and Conductivity of Iodine-Doped C60 Thin Films

1994 ◽  
Vol 359 ◽  
Author(s):  
Jun Chen ◽  
Haiyan Zhang ◽  
Baoqiong Chen ◽  
Shaoqi Peng ◽  
Ning Ke ◽  
...  
Keyword(s):  
Thin Films ◽  
Electrical Conductivity ◽  
Room Temperature ◽  
Conductivity Measurements ◽  
X Ray Diffraction ◽  
Temperature Conductivity ◽  
Room Temperature Conductivity ◽  
X Ray ◽  
Thermally Activated ◽  
Order Of Magnitude

ABSTRACTWe report here the results of our study on the properties of iodine-doped C60 thin films by IR and optical absorption, X-ray diffraction, and electrical conductivity measurements. The results show that there is no apparent structural change in the iodine-doped samples at room temperature in comparison with that of the undoped films. However, in the electrical conductivity measurements, an increase of more that one order of magnitude in the room temperature conductivity has been observed in the iodine-doped samples. In addition, while the conductivity of the undoped films shows thermally activated temperature dependence, the conductivity of the iodine-doped films was found to be constant over a fairly wide temperature range (from 20°C to 70°C) exhibiting a metallic feature.

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