Electron-phonon Relaxation Time Research Articles

Ultrafast photoresponse in microbridges and pulse propagation in transmission lines made from high-T/sub c/ superconducting Y-Ba-Cu-O thin films

We report our femtosecond time-resolved measurements of the photoresponse of microbridges in YBa/sub 2/Cu/sub 3/O/sub 7-x/ (YBCO) thin films, performed using an electrooptic sampling technique. Our test structures consisted of 5-/spl mu/m-wide, 7-/spl mu/m-long microbridges, incorporated in 4-mm-long coplanar waveguides, fabricated in 100-nm-thick, high-quality epitaxial YBCO films grown on LaAlO/sub 3/ substrates by laser deposition. When varying the biasing conditions between the superconducting and switched states, we observed transients of single-picosecond duration that corresponded to the nonequilibrium kinetic-inductance and the electron-heating response mechanisms, respectively. In both cases, experimental waveforms could be accurately simulated using a nonequilibrium (two-temperature) electron-heating model. From the fits, the YBCO intrinsic temporal parameters associated with the nonequilibrium conditions were extracted. The electron thermalization time was found to be 0.56 ps in the state above the material's critical temperature (T/sub c/=89 K) and 0.9/spl plusmn/0.1 ps in the superconducting state at temperatures ranging from 20 to 80 K. The electron-phonon energy relaxation time was found to be 1.1 ps. The single-picosecond pulse distortion due to propagation on a YBCO coplanar waveguide was also studied. Our results show that a YBCO microbridge can intrinsically operate as a photodetector at rates exceeding 100 Gb/s, making it useful as an optical-to-electrical transducer for optoelectronic interfaces in YBCO digital electronics. Simultaneously, YBCO mixers, based on hot-electron effects, should exhibit an intrinsic bandwidth exceeding 100 GHz.

Aluminium electron-phonon relaxation-time measurement from subpicosecond nonlinear single-photon photoelectric emission at 248 nm

The sensitivity of photoelectric emission of polycrystalline aluminium, produced by 248 nm laser pulses with p-polarization and 450 fs duration, under incidence anglesθ = 74–86°, has been measured. A nonlinear increase of photoemission efficiency, as a function of the incident laser peak intensity in the range of 1–50 GW/cm2, was displayed, which confirms earlier observations with gold and tungsten. This nonlinearity is consecutive to the non-thermal distribution of electron gas of laser-heated metal on the time scale of the electron-phonon relaxation time. Analysis of experimental data, using the model previously developed by us [1], gives a value of electron-phonon relaxation time ≈0.55 ± 0.11 ps.

Aluminium electron-phonon relaxation-time measurement from subpicosecond nonlinear single-photon photoelectric emission at 248 nm

Aluminium electron-phonon relaxation-time measurement from subpicosecond nonlinear single-photon photoelectric emission at 248 nm

Heating and failure of niobium tip cathodes due to a high-density pulsed field electron emission currenta)

This article presents the investigative results of pulsed threshold current densities of niobium tip cathodes at temperatures ranging from 4.2 to 300 K. It has been shown that the superconducting-to-normal phase state transition of the cathode has no effect on pulsed threshold current densities. Estimations have been made for the factors limiting the current from a superconducting emitter. The experiments have shown that the cooling of the cathode from 300 to 4.2 K changes the dynamics of cathode heating considerably and leads to a steady increase in the threshold current densities with the delay time range of 10−9–10−6 s. Numerical analysis of thermal processes in the emitter has shown that the above effects are not due to the difference between the electron and the phonon temperatures (the electron–phonon relaxation time does not exceed 10−9 s), but to the more intense heat transfer processes and the reduction of Joule heating, with the cooling of the cathode. It has been shown that the space charge of emitted electrons produces a considerable effect on the temperature and current density distribution in the tip apex. Investigations have shown that the mechanism of the tip cathode failure depends on the delay time range. The simple relationship for estimation of average pulsed threshold emission current density of the tip cathode for a delay time range of 10−9–10−7 s is presented.

Low-temperature electronic transport properties in thin films of Pd and PdH0.3.

Low-temperature magnetoresistance measurements have been used to determine various electron scattering times in pure Pd and ${\mathrm{PdH}}_{0.3}$ thin films with different thicknesses, which have been prepared by electron-gun evaporation. From low-field magnetoresistance measurements, using localization theory, the spin-flip, electron-electron, and electron-phonon relaxation times can be deduced and they are found to depend on the electronic structure of both systems. It is also found that the increase of the disorder of the systems enhances the spin-orbit coupling, which is larger in ${\mathrm{PdH}}_{0.3}$ than in Pd. On the other hand, the high-field magnetoresistance allows the determination of both the Coulomb screening factor F and the Land\'e factor g for both systems. It is found that the F factor depends on the band structure and takes the mean values 0.63 and 0.53 for pure Pd and ${\mathrm{PdH}}_{0.3}$, respectively, while the g factor depends on the degree of disorder.

Theoretical analysis of the thermal conductivity of high-temperature superconductors

The thermal conductivity of YBa2Cu3O7−δ high-T c superconductor is analysed self-consistently on both normal and superconducting states on the base of the Bardeen-Rickayzen-Tewordt extended theory to take into account the effects of magnetic field and superconducting fluctuations. It is shown that experimental data are in a quantitative agreement with theory even if the number and variation intervals of adjustable parameters are substantially reduced in comparison with previous works. Phonon relaxation rates due to different mechanisms of phonon scattering as well as the parameters of electron-phonon interaction are estimated. It is shown that thermal conductivity in YBa2Cu3O7−δ is consistent with the BCS model with intermediate electron-phonon coupling λ=1–3 the phonon-electron and electron-phonon relaxation times near critical temperature are evaluated to be 10−10s and 10−12s, respectively.

The electron-phonon interaction and melting of metals

The minimum uncertainty product form of Heisenberg's Uncertainty Principle is applied to the electron-phonon interaction in metals in the free-electron and Debye approximations. Twice the Debye frequency follows as an upper limit to the electron-phonon scattering rate. This is an extension of an earlier application to the 3-phonon anharmonic scattering rate, and Lindemann's law of melting follows in both cases. Corrections and clarifications of the earlier work are included. It is shown that the electron-phonon relaxation time, the Debye zoneboundary phonon relaxation time, the ion-ion collision time on the liquid side of melting, and the inverse of twice the Debye frequency are all approximately equal at the melting point.

Interference of impurity and phonon scattering in the magneto-transport of two-dimensional electron systems

A calculation of the electron-LA phonon relaxation time of a two dimensional electron gas under the action of a strong magnetic field is performed using a memory function formalism. It is well known that the inverse of the transport relaxation time is the sum of the contributions arising from electron-phonon enteraction and from impurity elastic scattering. In this work we are dealing with the electron-LA phonon scattering contribution, which is the important phonon scattering mechanism at low temperatures. We take into account, through vertex corrections in the diffusive pole approximation, the effect on phonon scattering due to the presence of impurities in the material, which renormalizes the polarization function. The effect of temperature on the renormalized electron-phonon relaxation time is discussed and we show that it yields a non-zero resistivity in the phonon channel scattering at zero temperature.

Mechanism of picosecond response of granular YBaCuO films to electromagnetic radiation

Ultrafast mechanisms of radiation detection in granular YBaCuO films are studied in the wide wavelength range from millimeter waves to near infrared. With an increase in radiation frequency, the Josephson detection at the grain-boundary weak links is replaced by electron heating into the grains. This change occurs in the submillimeter wavelength range. The electron-phonon relaxation time tau /sub eph/ is determined from direct measurements, quasi-stationary electron heating measurements, and the frequency dependence of the current at which maximum voltage shift is observed. The temperature dependence of tau /sub eph/ at T<or=40 K was found to be tau /sub eph/ approximately T/sup -1/. The results show that detectors with a response time of a few picoseconds at nitrogen temperature are attainable.

Mechanism of picosecond response of granular YBaCuO films to electromagnetic radiation

The ultrafast mechanisms of radiation detection in granular YBaCuO films are studied in the wide wavelength range from millimeter to near infrared. With the rise of radiation frequency the Josephson detection at the grain boundary weak links is replaced by electron heating into the grains. This change occurs in the submillimeter wavelength range. Electron-phonon relaxation time τeph is determined by direct measurements and analyses quasistationary electron heating. Temperature dependence of τeph at T ≤ 40 K was found to be τeph ∼ T−1. The results show that detectors with the response time of few picoseconds at nitrogen temperature are attainable.

Femtosecond thermal modulation measurements of electron-phonon relaxation in niobium

Thermal modulation measurements using 120 fs/620 nm laser pulses were performed on niobium films. The electron-phonon relaxation time was found to be ultrafast and measured to be 360 fs, and the electron-phonon coupling constant was estimated to be (17±3)×1017 W m−3 K−1.

Ultrafast relaxation of electrons probed by surface plasmons at a thin silver film.

We present a novel subpicosecond optical transient-reflection method, which employs the surface-plasmon resonance of a thin silver film as a very sensitive probe to study small transients of the effective electron and lattice temperature. By measuring under surface-plasmon resonant and nonresonant conditions, we can discriminate between lattice and electron heating. We find a change of the lattice and electron temperature of respectively, \ensuremath{\Delta}${T}_{l}$=0.10(5) K and \ensuremath{\Delta}${T}_{e}$=30--90 K for an intensity of 180 W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ and an electron-phonon energy relaxation time of 670(70) fs.

Nonlinear dc conductivity in disordered metals near the metal-insulator transition.

A detailed study of the nonlinear dc conductivity of two disordered alloys, ${\mathrm{Ge}}_{\mathrm{x}}$${\mathrm{Au}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ and ${\mathrm{C}}_{\mathrm{x}}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$, is carried out near their metal-insulator transition for electric fields up to 500 V/m at 1.3 K &lt;T&lt;4.2 K and, for ${\mathrm{C}}_{\mathrm{x}}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$, down to 15 mK. Analysis of the \ensuremath{\sigma}(E) data in the context of an electron-gas-heating model yields unexpectedly long electron-phonon relaxation times. Above 1 K the hot-electron model is not sufficient to explain these results. We propose that the electric field also acts directly on the localizing electrons, which leads to an ${E}^{1/3}$ dependence of the conductivity.

Phonon-drag effect in TiSe2-xSx mixed compounds.

Thermoelectric power (TEP) measurements of ${\mathrm{TiSe}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{S}}_{\mathrm{x}}$ solid solutions have been performed in the temperature range 10--315 K for 0\ensuremath{\lesssim}x&lt;2. A phonon-drag effect is identified around 25 K. Its contribution to the TEP has been analyzed as a function of x. An estimate of the electron-phonon relaxation time ${\ensuremath{\tau}}_{e\mathrm{\ensuremath{-}}\mathrm{ph}}$ is derived from this analysis. This estimate is found to be in accordance with the value of ${\ensuremath{\tau}}_{e\mathrm{\ensuremath{-}}\mathrm{ph}}$ obtained from theoretical predictions.

Electron-phonon relaxation in5D4 of Tb3+ in yttrium aluminium garnet

The electron-phonon relaxation times of the crystal-field levels of the metastable state5D4 of Tb3+ were measured between 2 and 4.2K. The relaxation of the lowest pseudodoublet (ΔE=1.25 cm−1) shows an Orbach process via higher crystal-field levels. The other levels show direct relaxation on a nanosecond time scale. The higher crystal-field levels were used to look for propagation of high-energy (ν≦4THz) nonequilibrium phonons by phonon-induced fluorescence. No ballistic propagation of high-energy phonons could be found.

Femtosecond Laser Interaction with Metallic Tungsten and Nonequilibrium Electron and Lattice Temperatures

High-intensity, 75-fs optical pulses have been applied to observe multiphoton and thermally enhanced photoemission from a tungsten metal surface. Experimental results suggest the presence of anomalous heating, a transient nonequilibrium temperature difference between the electrons and lattice. Pump-probe measurements indicate an electron-phonon energy relaxation time of several hundred femtoseconds.

Phenomenological model for pisosecond-pulse laser annealing of semiconductors

A system of three coupled diffusion equations describing the equilibration process in the premelt phase of laser annealing is solved and analyzed for a short pulse—20,30 psec—on a thin (d=150 Å) and thick Si,Ge slabs. We find the carrier temperature to be a very sensitive gauge for the electron-phonon relaxation time constant τ0. The existing data (Si, λL =0.533 μm and EL =0.25 J/cm2) are consistent with τ0≂0.4–1.0 psec, and the carrier peak temperature is predicted to be in the range 2000–4300 °K.

Importance of electron-phonon processes in the inelastic lifetime of conduction electrons

The temperature of conduction electrons can be raised above the lattice temperature by a high electric current density. The achieved temperature difference is proportional to the electron-phonon relaxation time. Weak localization yields information about the electron temperature and allows the conclusion that electron-phonon processes are an essential determinant for the inelastic lifetime of the conduction electrons.

Investigation of electric field penetration into superconducting tantalum near a normal-superconducting interface

The temperature dependence of the excess resistance of Ta-Cu-Ta sandwiches was investigated. The samples were prepared by the mutual rolling of the bulk materials, with the thickness of the superconducting plates (⋍0.1 cm) much greater than the penetration length of the electric field into the superconductorlE up to temperatures very close toTc. The penetration of the electric field through the clean NS interface into a superconductor with a relatively long electronic mean path (1⋍ξ0) was studied. We used an rf SQUID voltmeter to measure the resistance, ∼10−9 Ω, at currents not exceeding 1 mA. The experimental data were compared with the Artemenko-Volkov and Hsiang-Clarke theories. The electron-phonon relaxation time τɛ for our tantalum sample was estimated to be ∼1×10−10 sec.

The frequency dependence of phonon interactions at Terahertz-frequencies studied by time-resolved phonon spectroscopy

Phonon properties concerning propagation, frequency spectrum and lifetime in the Terahertz range have been investigated. The phonons have been produced by square wave Joule heating of thin constantan films evaporated onto a strongly doped ruby. Cross sections for phonon scattering at the Cr3+ impurity ions of the ruby were determined as a function of frequency. The theoretical estimate for mass defect scattering given by Klemens [9] is found to agree reasonably with the experimental results. Lifetime measurements indicate that phonons in ruby preferentially propagate in the transversal mode. Phonon frequency spectra in the constantan films were measured under experimental conditions, where the strength of electron phonon coupling is significant; thus electron-phonon relaxation times could be obtained as a function of frequency.