# Electron-phonon, electron-electron and electron-surface scattering in metals from ballistic effects

TL;DR: In this paper, a detailed comparison of experimental scattering rates obtained by different measuring techniques and of experimental and theoretical scattering rates in various metals was made. But the experimental results were not considered.

Abstract: Ballistic effects are reviewed which allow the determination of scattering rates of local groups of electrons on the Fermi surface of metals. Significant progress in our understanding of scattering mechanisms has been made in the last decade through the improved capabilities of high frequency size effects. The anisotropy of electron phonon scattering has been shown to be a general rule; the electron-electron scattering rate has been measured not only in transition metals, but also in simple metals; new effects have been observed from scattering at the sample surface, supporting theoretical calculations of the electric field distribution near the surface. A detailed comparison is made of experimental scattering rates obtained by different measuring techniques and of experimental and theoretical scattering rates in various metals.

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^{1}TL;DR: Femtosecond time-resolved two-photon photoemission has attracted particularly strong interest because it incorporates many of the surface analytical capabilities of photo-emission and inverse photo emission, with time-resolution approaching the fundamental response of electrons to optical excitation as mentioned in this paper.

591 citations

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TL;DR: In this article, the Norskov-Newns-Lundqvist model was used to detect chemically induced e−h pairs with thin metal film Si Schottky diodes.

307 citations

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TL;DR: In this article, complete Boltzmann collision integrals were applied to describe the transient electron distribution due to excitation, thermalization, and relaxation, and the electron-phonon coupling strength was analyzed under nonequilibrium conditions.

Abstract: When an ultrashort laser pulse irradiates a metal, energy is absorbed by the electron system which is driven out of thermal equilibrium on a femtosecond time scale. Due to electron-electron collisions, a new thermodynamical equilibrium state within the electron system is established in a characteristic time, the so-called thermalization time. The absorbed energy of the electrons will be further transferred to the phononic system. The thermalization time as well as the electron-phonon coupling strength both strongly depend on the material properties and the excitation type. Furthermore, a nonthermalized electron gas couples differently to the phononic system as a thermalized one. In order to follow the relevant microscopic dynamics without the need to assume thermalized electrons, we apply complete Boltzmann collision integrals to describe the transient electron distribution due to excitation, thermalization, and relaxation. We implement the density of states of real materials in our approach. As a result of our simulations, we extract the electron thermalization time and the electron-phonon coupling under nonequilibrium conditions. Examples are given for aluminum, gold, and nickel.

240 citations

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TL;DR: In this paper, the conduction electron energy exchanges were investigated in gold and silver nanoparticles with average size ranging from 2 to 26 nm, embedded in different matrices, and the experimental studies were performed by following the internal thermalization dynamics of photoexcited nonequilibrium electrons with a femtosecond pump-probe technique.

Abstract: The conduction electron energy exchanges are investigated in gold and silver nanoparticles with average size ranging from 2 to 26 nm, embedded in different matrices. The experimental studies were performed by following the internal thermalization dynamics of photoexcited nonequilibrium electrons with a femtosecond pump-probe technique. The probe wavelength dependent measurements are in qualitative agreement with the results of a theoretical model based on bulk metal electron kinetics and band-structure modeling. In both metals, the measured electron thermalization times are close to the bulk ones for nanoparticles larger than 10 nm and sharply decrease for smaller ones. The results are independent of the nanoparticle environment and synthesis technique showing that the observed size behavior reflects an increase of the efficiency of the electron-electron energy exchanges in small nanoparticles. It is in agreement with a simple model based on a bulk metal approach of the electron kinetics modified to introduce surface effects. The observed increase of the electron-electron interaction with size reduction is ascribed to reduction of the screening of the Coulomb interaction by the conduction and core electrons close to the nanoparticle surface.

157 citations

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TL;DR: In this article, the synthesis and electron transport properties of polycrystalline samples of diborides (AB2) with different transition metals atoms (A=Zr, Nb, Ta) were reported.

Abstract: We report on syntheses and electron transport properties of polycrystalline samples of diborides (AB2) with different transition metals atoms (A=Zr, Nb, Ta). The temperature dependence of resistivity, ρ(T), and ac susceptibility of these samples reveal a superconducting transition of ZrB2 with T c =5.5 K, while NbB2 and TaB2 have been observed to be nonsuperconducting up to 0.37K. Hc2(T) is linear in temperature below T c , leading to a rather low Hc2(0)=0.1 T. At T close to T c , Hc2(T) demonstrates a downward curvature. We conclude that these diborides, as well as MgB2 samples, behave like simple metals in the normal state with usual Bloch-Gruneisen temperature dependence of resistivity and with Debye temperatures 280, 460, and 440 K for ZrB2, NbB2, and MgB2, respectively, rather than T2 and T3, as previously reported for MgB2.

98 citations

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01 Jan 1938TL;DR: In this paper, the conductivity of thin films of the alkali metals has been measured in the H. W. Wills Physical Laboratory, Bristol and the experimental results were compared with a formula derived on the basis of this hypothesis.

Abstract: The conductivity of thin films of the alkali metals has recently been measured in the H. W. Wills Physical Laboratory, Bristol*. It was found that as the thickness of the film is decreased to that of a few atomic layers the conductivity drops below that of the bulk metal. In the papers quoted the hypothesis was put forward that this effect is due to the shortening of the mean free paths of the conduction electrons of the metal by collisions with the boundaries of the film. The experimental results were compared with a formula derived on the basis of this hypothesis. This formula was, however, obtained subject to a number of simplifying assumptions, and it is the first purpose of this paper to obtain a more accurate formula. I also compare this formula with experiment, and make certain deductions about the surfaces of thin films.

1,812 citations

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Abstract: The problem of metallic conduction at high frequencies and low temperatures, recently discussed by Pippard, is reformulated using the general methods of the theory of metals, and exact solutions are obtained which are valid for all frequencies and temperatures. It is shown that, for large values of the free path of the conduction electrons, the electric field is propagated through the metal as a ‘surface wave’ which differs considerably from the classical exponential solution. The temperature variation of the surface impedance in the microwave region is considered in detail. Pippard’s simplified theory is shown to be qualitatively correct, and a quantitative discussion of his experimental results is given. The frequency variation of the surface impedance at low temperatures is also discussed, and it is shown that relaxation effects are negligible in the microwave region but become important in the infra-red and eventually restore the validity of the classical theory. The theory predicts that, as the frequency is increased, the reflexion coefficient of metals passes through a minimum in the far infra-red.

461 citations

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TL;DR: A review of recent theoretical investigations toward unified understanding of magnetism in narrow-band electron systems is given in this article, where the classical controversy between the itinerant and localized models have been resolved into a more general and well-defined problem of spin density fluctuations in a general sense.

453 citations

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TL;DR: In this paper, a new semiclassical model for the boundary condition for the distribution function of the size effect in the electrical conductivity was proposed, which satisfies the requirement of flux conservation.

Abstract: A statistical model for the reflection of scalar plane waves from a rough surface leads to a plane wave in the direction of specular reflection and to a contribution with a finite angular spread about that direction, depending on the tangential correlation of the surface asperities. Based upon on this result, a new semiclassical model, which satisfies the requirement of flux conservation, is proposed for the boundary condition for the distribution function of the size effect in the electrical conductivity. In the absence of correlation, the resultant expression replaces the constant specularity parameter p of Fuchs by the function exp[−(4π(h/λ) cosθ0)2] with θ0 the angle of the electron wave vector with the surface normal. Correlation produces an additional forward component within the diffuse contribution. Numerical results of the size effect for zero correlation are compared to the Fuchs model as well as a more recent model, and show a different thickness dependence for thin samples. The effect of correlation is to add to the conductivity, as a result of the diffuse contribution whose velocity has a finite expectation value in the direction of the current.

399 citations