Comparison of the lifetime of excited electrons in noble metals

Keyling, Robert; Schöne, Wolf-Dieter; Ekardt, W.

doi:10.1103/physrevb.61.1670

Cited by 58 publications

(69 citation statements)

References 23 publications

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“…A comparison between the theoretical and experimental data reveals good agreement for band energies above 2 eV but it shows a huge discrepancy for energies below 2 eV. 7,8 Alike results have been found by similar calculations. 9 This shows that the GW approximation does not contain enough physics to explain the lifetime of hot electrons in Cu.…”

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confidence: 70%

Transient excitonic states in noble metals and Al

Schöne

Ekardt

2002

Phys. Rev. B

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Bound states between electrons and holes, so-called excitons, are an ubiquitous feature in the spectra of excited states of molecules, clusters, and in a variety of solids such as semiconductors or ionic solids. It is common wisdom that excitons do not exist in metals because the attractive, long-range particle-hole interaction which is needed for the formation of an exciton does not exist in metals due to almost complete screening. We showed in a previous publication that excitons in metals can exist as transient states right after the creation of the electron-hole pair which explained in a natural way the up to then not understood transitions seen in Cu in the experimental spectra of time-resolved two-photon photoemission spectroscopy. In this paper we report about transient excitonic states in Ag and Au. We explain why these states have not yet been detected in Ag but we predict their existence. We show furthermore why transient excitonic states cannot be built up in Al. DOI: 10.1103/PhysRevB.65.113112 PACS number͑s͒: 78.47.ϩp, 72.15.Lh, 71.10.Ϫw, 71.20.Gj With the advent of modern femtosecond laser technology it has become possible to measure ultrafast relaxation processes of excited electrons in metals. [1][2][3] Whereas in most cases the experimentally observed states can be identified as single-particle band states there are other cases where the experimental results cannot be explained on the basis of a single-particle band structure. Most prominent are the measurements of the lifetime of excited electrons using timeresolved two-photon photoemission ͑TR-2PPE͒ spectroscopy performed on single crystals of Cu ͑Refs. 1,2,4͒ and Au. 5 They show data for states in the ͑100͒ and ͑111͒ direction in an energy range between 1 and 4 eV. We are not aware of any such data for Ag. These two directions are of special interest since the band structures for all three noble metals do not show single-particle states in these directions for the energy range under consideration ͑1-4 eV͒. 6 There is a second observation; Ogawa et al. 1 also measured the lifetime of excited electrons in the Cu͑110͒ direction. Since this direction shows a single-electron band the lifetime of electrons in this band has been calculated using a state-of-the-art ab initio many-body calculation within the GW approximation. A comparison between the theoretical and experimental data reveals good agreement for band energies above 2 eV but it shows a huge discrepancy for energies below 2 eV. 7,8 Alike results have been found by similar calculations. 9 This shows that the GW approximation does not contain enough physics to explain the lifetime of hot electrons in Cu. This is noteworthy because calculations utilizing the GW approximation typically lead to very good agreement with experimental data, a fact that laid the foundation for its big success. 10 It was speculated that the observed states are caused by an attractive interaction between the photoelectron and its localized hole in the d bands. 4 In a recent paper 11 we presented a model which sub...

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confidence: 70%

Transient excitonic states in noble metals and Al

Schöne

Ekardt

2002

Phys. Rev. B

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“…Further, an energy-dependent correlation decreases the Hartree-Fock band gap by raising the valence-band energy and lowering the conduction-band energy. There is some empirical evidence that supports the idea that even in the first iteration (that is, using just the noninteracting Green's function G 0 ) one obtains quite accurate results for oneelectron properties such as the excitation energy Louie, 1985, 1986;Godby et al, 1986Godby et al, , 1987Godby et al, , 1988Aryasetiawan and Gunnarsson, 1998) and the quasiparticle lifetime (Campillo et al, 1999;Schö ne et al, 1999;Echenique et al, 2000;Campillo, Silkin, et al, 2000;Keyling et al, 2000;Silkin et al, 2001;Spataru et al, 2001). This is important for practical applications of the GW approach since, despite its formal simplicity, the practical solution of the self-consistent GW equations is a formidable task, which has been carried out only recently: self-consistent calculations were performed for the homogeneous electron gas (Holm and von Barth, 1998;Holm and Aryasetiawan, 2000;García-Gonzá lez and Godby, 2001), simple semiconductors, and metals (Shirley, 1996; Schö ne and Eguiluz, 1998).…”

Section: First Iteration Step: the Gw Approximationmentioning

confidence: 95%

Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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“…In metals, the scattering rate of an impact electron ͑⌫ =1/ ͒ is usually obtained with many-body theory from the imaginary part of the electron self-energy. 2,7,8,10 The rate ⌫ n,k is a product of the Fourier transform of the screened Coulomb interaction and of the expansion coefficients of the electron wave functions sampled in the irreducible part of the Brillouin zone. 2,7 This rate depends on the wave vector k and the energy band n. Therefore, it has to be summed over all k and n available at the same ͑impact͒ energy in the Brillouin zone in order to obtain the average value ⌫͑E͒ as a function of the impact energy.…”

Section: B Impact Ionization Rate ⌫"E… At Low Energiesmentioning

confidence: 99%

“…Both experimental data and first-principles calculations at low impact energies are available for these metals. 7,9,10,32 Coefficients a and b appearing in Eq. ͑6͒ were estimated by fitting to the electron mean free paths obtained with Eq.…”

Section: Mean Free Path Fittedmentioning

confidence: 99%

“…5,6 At very low energies around E F , they are calculated either with experimental data on electron lifetimes or with first-principles calculations. 2,[7][8][9][10][11][12][13][14][15][16][17][18][19][20] In the low-energy region electron mean free paths have been extensively studied, especially in semiconductors, where they are needed to understand the properties of semiconductor devices under high electric fields ͑see, e.g., Ref. 14͒.…”

Section: Introductionmentioning

confidence: 99%

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Ionization by impact electrons in solids: Electron mean free path fitted over a wide energy range

Ziaja

London

Hajdu

2006

Journal of Applied Physics

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We propose a simple formula for fitting the electron ionization mean free paths in solids both at high and at low electron energies. The free-electron-gas approximation used for predicting electron mean free paths is no longer valid at low impact energies ͓͑E − E F ͒ Ͻ 50 eV͔, as the band structure effects become significant at those energies. Therefore, we include the results of band structure calculations in our fit. Finally, we apply the fit to nine elements and two compounds.

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Comparison of the lifetime of excited electrons in noble metals

Cited by 58 publications

References 23 publications

Transient excitonic states in noble metals and Al

Transient excitonic states in noble metals and Al

Electronic excitations: density-functional versus many-body Green’s-function approaches

Ionization by impact electrons in solids: Electron mean free path fitted over a wide energy range

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