Lifetime Of Excited Electrons Research Articles

Publisher’s Note: Lifetimes of Excited Electrons in Fe and Ni: First-Principles GW and theT-Matrix Theory [Phys. Rev. Lett.93, 096401 (2004)

We present the results of an ab initio calculation of excited electron lifetimes in ferromagnetic materials which incorporates non-spin-flip and spin-flip processes within GW and T-matrix approaches. The method we develop is applied to low-energy electron excitations in Fe and Ni. It is found that the spin-wave generation in Fe essentially reduces the lifetimes of the spin-minority d states whereas the free-electron-like spin-minority states and all the spin-majority states are affected much less. The influence of spin-flip scattering on the lifetimes in Ni appears to be weak. The T-matrix non-spin-flip processes are important for the lifetimes of excited spin-minority states.

The lifetime of electronic excitations in metal clusters

Density functional theory and the self-energy formalism are used to evaluate the lifetime ofelectronic excitations in metal clusters of nanometre size. The electronic structure of thecluster is obtained in the jellium model and spherical symmetry is assumed. Twoeffects that depend on the size of the clusters are discussed: the change in thenumber of final states to which the excitation can decay, and the modification inthe screened interaction between electrons. For clusters with density parameterrs = 4 and diameter a few nanometres, a lifetime value of fs is reached for electronic excitations of eV. This value is of the same order of magnitude of that obtained in the bulk limit at thesame level of approximation. For smaller clusters, a distinct non-monotonic behaviour ofthe lifetime as a function of the cluster size is found and the lifetime of excitations of eV can vary between 4 and 30 fs.

Lifetimes of excited electrons in Ta: Experimental time-resolved photoemission data and first-principlesGW+Ttheory

Time-resolved two-photon photoemission spectroscopy and first-principles GW and $\mathrm{GW}+\mathrm{T}$ theories have been used to study excited electron lifetimes in tantalum. The $\mathrm{GW}+\mathrm{T}$ approach includes evaluation of the lowest self-energy term of the many-body perturbation theory in the GW approximation and higher terms in the $T$-matrix approximation. The $\mathrm{GW}+\mathrm{T}$ calculated lifetimes are in good agreement with the measured lifetimes at excitation energies above $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. At lower energies, a slightly worse agreement between theoretical and experimental data is obtained which we refer to as the influence of cascade processes.

Collective and single-particle dynamics in time-resolved two-photon photoemission

A general model for time-resolved two-photon photoemission from solids is presented comprising both collective and single-electron dynamics. In combination with interferometric time-resolved two-photon photoemission, this allows one to determine the shape of the collective response function across the excitation spectrum and the single-particle lifetime of excited electrons. Ag nanoparticles supported on graphite exhibit a strong collective resonance and serve as model system to demonstrate experimentally this separation of collective and single-particle dynamics in two-photon photoemission.

Ultrafast Electron Dynamics in Metals

During the last decade, significant progress has been achieved in the rapidly growing field of the dynamics of hot carriers in metals. Here we present an overview of the recent achievements in the theoretical understanding of electron dynamics in metals, and focus on the theoretical description of the inelastic lifetime of excited hot electrons. We outline theoretical formulations of the hot-electron lifetime that originates in the inelastic scattering of the excited quasiparticle with occupied states below the Fermi level of the solid. First-principles many-body calculations are reviewed. Related work and future directions are also addressed.

Publisher's Note: Lifetimes of Excited Electrons in Fe and Ni: First-Principles GW and theT-Matrix Theory [Phys. Rev. Lett.93, 096401 (2004)

Publisher's Note: Lifetimes of Excited Electrons in Fe and Ni: First-Principles GW and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>-Matrix Theory [Phys. Rev. Lett.<b>93</b>, 096401 (2004)

Lifetimes of excited electrons in Fe and Ni: first-principles GW and the T-matrix theory.

We present the results of an ab initio calculation of excited electron lifetimes in ferromagnetic materials which incorporates non-spin-flip and spin-flip processes within GW and T-matrix approaches. The method we develop is applied to low-energy electron excitations in Fe and Ni. It is found that the spin-wave generation in Fe essentially reduces the lifetimes of the spin-minority d states whereas the free-electron-like spin-minority states and all the spin-majority states are affected much less. The influence of spin-flip scattering on the lifetimes in Ni appears to be weak. The T-matrix non-spin-flip processes are important for the lifetimes of excited spin-minority states.

Gain and transient photoresponse of quantum well infrared photodetectors: a detailed ensemble Monte Carlo study

We investigate different gain characteristics observed on quantum well infrared photodetectors (QWIPs) fabricated with various material systems, and the effects of barrier material properties on the device characteristics through detailed ensemble Monte Carlo simulations. When the energy spacing between the central and satellite valleys is increased, the improvement in the excited electron lifetime is found to be much stronger than that in the average electron velocity in the device. According to our results, relatively high gain observed in InP/In0.53Ga0.47As QWIPs under large bias is not due to the higher mobility in InP as suggested earlier; it can mainly be attributed to higher excited electron lifetime as a result of relatively large Γ–L energy spacing. We discuss the details of the fast part of the Al0.3Ga0.7As/GaAs QWIP transient photoresponse, which exhibits three regions with different decay characteristics under a short pulse of radiation. The duration of the final region, during which the electrons excited near the emitter are extracted from the collector, is observed to be considerably long due to the dispersion of the photoelectrons. The photoresponse time rapidly decreases with increasing bias under low bias, and nearly saturates at ∼10ps under large bias being ∼40% larger than the average transit time estimated by dividing the device length to the average steady-state electron velocity in device. We also investigate the effects of the interface reflections on the photoresponse time.

First-principles multiple scattering theory of quasiparticle lifetimes in ferromagnetic materials

We develop a first-principles approach for evaluating the lifetimes of excited electrons in Fe and Ni based on the self-energy formalism of many-body theory. The GW approximation is applied for the lowest self-energy term whereas the high-order terms are evaluated within T-matrix approach. Both for Ni and Fe we find important contributions of the T-matrix self-energy terms corresponding to the excited electron scattering from spin waves.

ONE- AND TWO-PARTICLE PHENOMENA IN THE ELECTRONIC LIFETIMES IN METALS: QUASIPARTICLES AND TRANSIENT EXCITONS

The experimental and theoretical investigation of the lifetime of excited electrons is of great importance for a variety of different fields in condensed matter physics. In this review two distinct classes of processes are discussed, which determine the lifetime of excited electrons in crystalline systems. One class is single-particle processes, which in many cases is able to describe the decay of excited electrons. For systems with weakly correlated electrons the state-of-the-art method is the solution of the Dyson equation using the GW approximation for the electronic self-energy. If applicable this approach leads to very good results. However, many of the experimental studies about the lifetime of excited electrons have been done using time-resolved two-photon photoemission spectroscopy utilizing ultrashort laser pulses. This technique, applied to materials with localized d electrons, can lead to the creation of bound, excitonic-like states in metals on a very short time scale, which are beyond the physics described in the single-particle approach. In this review the experimental evidence for both mechanisms is given and the theoretical tools to describe them are discussed. Furthermore, theoretical results are presented and compared to experimentally available data.

Lifetime of excited electrons in transition metals

We present ab initio calculations for the lifetime of excited electrons in transition metals. The computations were done using a pseudopotential approach in connection with a plane-wave expansion of the wave functions. The lifetimes for each element are resolved for various bands and with respect to certain directions of the crystal momentum. Our results reveal rather different trends for different transition metals showing the impossibility to work with simple models, thus emphasizing the need for first-principles calculations.

Watching the life of electrons at surfaces with two-photon photoemission

An electron put on a metal surface is attracted by the image force. A Rydberg-like series of image-potential states is formed which describes loosely bound electrons which can move freely parallel to the surface. With time-resolved two-photon photoemission spectroscopy the electronic band structure and the femtosecond dynamics of these states are studied in the energy- and time-domain. The decay of the image-potential-state population is attributed to electron–electron interaction with metal electrons, which constitutes an inelastic scattering process. Defects (or phonons) may lead to elastic scattering which changes the phase of the electronic wave function without changing the population. With time-resolved two-photon photoemission inelastic and elastic scattering processes can be separated. From these experiments we can extract information on the lifetime of excited electrons at surfaces in excellent agreement with theoretical calculations by Echenique and co-workers. The interaction of image-potential states with adsorbates or steps gives insight into the inelastic and elastic scattering by the various surface defects which are not accessible by any other technique.

Lifetime of surface states in optically excited Al, Cu, and Ag

In this Letter we report about ab initio calculations of the lifetime of excited electrons in surface states of Al, Cu, and Ag. We show that at the ab initio level the decay of surface states is very much similar to that of bulk states, because in both cases it is the density of the final bulk states which matters. This shows by way of example that most probably the popular jellium-like models will fail in predicting accurate lifetimes and that the ab initio treatment of surface states is a must.

Relaxation rate of excited electrons in metals: A nonperturbative calculation based on kinetic theory

By using an effective independent-particle model for an interacting electron gas, the relaxation rate of excited electrons close enough to the Fermi surface is calculated. The theoretical description is based on a binary collision treatment, implemented by an approximate nonlinear characterization of the residual screened interactions and exact phase-shift calculations. The important constituents of a consistent attempt are discussed. The results obtained are analyzed and compared to those based on perturbative linear-screening predictions. Reductions in the lifetime of excited electrons are found. Comparisons with experimental data from different sources are made.

Time-dependent screening of a positive charge distribution in metals: Excitons on an ultrashort time scale

Experiments determining the lifetime of excited electrons in crystalline copper reveal states which cannot be interpreted as Bloch states [S. Ogawa {\it et al.}, Phys. Rev. B {\bf 55}, 10869 (1997)]. In this article we propose a model which explains these states as transient excitonic states in metals. The physical background of transient excitons is the finite time a system needs to react to an external perturbation, in other words, the time which is needed to build up a polarization cloud. This process can be probed with modern ultra-short laser pulses. We calculate the time-dependent density-response function within the jellium model and for real Cu. From this knowledge it is possible within linear response theory to calculate the time needed to screen a positive charge distribution and -- on top of this -- to determine excitonic binding energies. Our results lead to the interpretation of the experimentally detected states as transient excitonic states.

Influence of excited electron lifetimes on the electronic structure of carbon nanotubes

We have studied the dynamics of electrons in single-wall carbon nanotube (bucky paper) samples using femtosecond time-resolved photoemission. The lifetime of electrons excited to the π ∗ bands is found to decrease continuously from 130 fs at 0.2 eV down to less than 20 fs at energies above 1.5 eV with respect to the Fermi level. This should lead to a significant lifetime-induced broadening of the characteristic van Hove singularities in the nanotube density of states.

Comparison of the lifetime of excited electrons in noble metals

We present results for the lifetimes of hot electrons in the noble metals Cu, Ag, and Au obtained by ab initio calculations within the framework of the GW approximation. Our results show an overall good agreement with the available experimental data, especially for Ag. In Cu and Au the experimental lifetimes reveal a sudden increase at low frequencies which cannot be explained within the GW approximation. For frequencies larger than 2 eV the calculated lifetimes are in good agreement with experiment. We also perform a detailed comparison of our calculation with so-called ``mass-shell'' calculations.

Inelastic Lifetimes of Hot Electrons in Real Metals

We report a first-principles description of inelastic lifetimes of excited electrons in real Cu and Al, which we compute, within the GW approximation of many-body theory, from the knowledge of the self-energy of the excited quasiparticle. Our full band-structure calculations indicate that actual lifetimes are the result of a delicate balance between localization, density of states, screening, and Fermi-surface topology. A major contribution from $d$-electrons participating in the screening of electron-electron interactions yields lifetimes of excited electrons in copper that are larger than those of electrons in a free-electron gas with the electron density equal to that of valence ($4s^1$) electrons. In aluminum, a simple metal with no $d$-bands, splitting of the band structure over the Fermi level results in electron lifetimes that are smaller than those of electrons in a free-electron gas.

Shaping of the shock pulse transmitted by a high quality quantum well

For recently available low-dimensional semiconductor structures of high quality, the radiative decay is an important mechanism which determines the lifetime of electronic excitations. We develop the microscopic theory of the linear response of a semiconductor quantum well to pulsed laser excitation under the condition that the homogeneous broadening of the exciton is dominated by radiative recombination. A strong time-domain sharpening of the transmitted pulse and a high reflection are predicted for strongly asymmetrical incident pulses with a sharp front.

Femtosecond dynamics of electrons on surfaces and at interfaces.

Two-photon photoemission is a promising new technique that has been developed for the study of electron dynamics at interfaces. A femtosecond laser is used to both create an excited electronic distribution at the surface and eject the distribution for subsequent energy analysis. Time- and momentum-resolved two-photon photoemission spectra as a function of layer thickness fully determine the conduction band dynamics at the interface. Earlier clean surface studies showed how excited electron lifetimes are affected by the crystal band structure and vacuum image potential. Recent studies of various insulator/metal interfaces show that the dynamics of excess electrons are largely determined by the electron affinity of the adsorbate. In general, electron dynamics at the interface are influenced by the substrate and adlayer band structures, dielectric screening, and polaron formation in the two-dimensional overlayer lattice.