Energy Relaxation Rate Research Articles

Effects of vibrational energy relaxation and reverse reaction on electron transfer kinetics and fluorescence line shapes in solution

The existing theoretical formulations of electron transfer reactions (ETR) neglect the effects of vibrational energy relaxation (VER) and do not include higher vibrational states in both the reactant and the product surfaces. Both of these aspects can be important for photo-induced electron transfer reactions, particularly for those which are in the Marcus inverted regime. In this article, a theoretical formulation is presented which describes the two aspects. The formalism requires an extension of the hybrid model introduced earlier by Barbara et al. [Science 256, 975 (1992)]. We model a general electron transfer as a two-surface reaction where overlap between the vibrational levels of the two surfaces create multiple, broad reaction windows. The strength and the accessibility of each window is determined by many factors. We find that when VER and reverse transfer are present, the time dependence of the survival probability of the reactant differs significantly (from the case when they are assumed to be absent) for a large range of values of the solvent reorganization energy (λX), quantum mode reorganization energy (λq), electronic coupling constant (Vel) and vibrational energy relaxation rate (kVER). Several interesting results, such as a transient rise in the population of the zeroth vibrational level of the reactant surface, a Kramers (or Grote–Hynes) type recrossing due to back reaction and a pronounced role of the initial Gaussian component of the solvation time correlation function in the dynamics of electron transfer reaction, are observed. Significant dependence of the electron transfer rate on the ultrafast Gaussian component of solvation dynamics is predicted for a range of values of Vel, although dependence on average solvation time can be weak. Another result is that, although VER alters relaxation dynamics in both the product and the reactant surfaces noticeably, the average rate of electron transfer is found to be weakly dependent on kVER for a range of values of Vel; this independence breaks down only at very small values of Vel. In addition, the hybrid model is employed to study the time resolved fluorescence line shape for the electron transfer reactions. It is found that VER can have a significant influence on the fluorescence spectrum. The possibility of vibrational state resolved spectra is investigated.

Results on the energy-relaxation rates of dense two-temperature aluminum, carbon, and silicon plasmas close to liquid-metal conditions.

We present results for the electron-ion energy relaxation coupling constants g(ei)(T(e),T(i),kappa) for aluminum, carbon, and silicon plasmas at several electron and ion temperatures T(i), T(e) of experimental interest. The calculations use the Fermi golden rule and the Landau-Spitzer model valid at weak electron-ion coupling, as well as the coupled-mode approach suitable for strong coupling. A physically motivated simple derivation of the coupled-mode energy relaxation formula for two-component charged fluids is presented. While the commonly used weak-coupling theories predict relaxation constants relatively independent of the ion temperature, the strong-coupling theory predicts energy relaxation constants that become smaller by an order of magnitude as the ion temperature is lowered.

Calculating Vibrational Energy Relaxation Rates from Classical Molecular Dynamics Simulations: Quantum Correction Factors for Processes Involving Vibration−Vibration Energy Transfer

A convenient starting point for calculating vibrational energy relaxation rate constants is Fermi's golden rule, which relates the rate constant to the Fourier transform of a certain quantum-mechanical force−force time-correlation function. Often, researchers replace this Fourier transform by the Fourier transform of the analogous classical time-correlation function multiplied by a quantum correction factor. This approach has the great advantage that the classical time-correlation function and its Fourier transform can be calculated easily from a classical molecular dynamics simulation. The disadvantage is that it is often unclear what form one should take for the quantum correction factor. In this paper we suggest several possible forms for this factor for vibrational energy relaxation processes involving intermolecular vibration−vibration energy transfer. We apply our results to vibrational energy relaxation in the B state of carbonmonoxy-myoglobin.

Interacting random Dirac fermions in superconducting cuprates.

We study the effects of quasiparticle interactions on disorder-induced localization of Dirac-like nodal excitations in superconducting high- Tc cuprates. As suggested by the experimental angle-resolved photoemission spectroscopy and terahertz conductivity data in Bi2Sr2CaCu2O(8+delta), we focus on the interactions mediated by the order parameter fluctuations near an incipient second pairing transition d --> d + is(id'). We find interaction corrections to the density of states, specific heat, and conductivity as well as phase and energy relaxation rates and assess the applicability of the recent localization scenarios for noninteracting random Dirac fermions to the cuprates.

The stochastic properties of a molecular-dynamical Lennard-Jones system in equilibrium and nonequilibrium states

The K-entropy and the tm time of dynamical memory (the time of forgetting initial conditions during numerical integration) of a classical system of particles whose interactions are governed by the Lennard-Jones potential were calculated by the method of molecular dynamics. The K value was a characteristic of a system of many particles, and the tm value proved to increase logarithmically as fluctuations of the total energy of the system decreased; that is, as the accuracy of numerical integration increased. Two different K-entropy values corresponding to the same total energy of the system were found to exist, namely, Ke for the equilibrium and Kn for the nonequilibrium state. The rate of kinetic energy relaxation (tr−1) was shown to equal Kn, and the Kn value was found to be a more fundamental characteristic than (tr−). The density dependences of Ke (monotonic) and Kn (nonmonotonic) were calculated. The transition from dynamical (Newtonian) correlations to stochastic for the velocity autocorrelation function was considered. The reasons for the finiteness of dynamical memory in physical processes are discussed. The duration of dynamical correlations in real systems is limited by quantum uncertainty and is of the order of picoseconds.

Exciton energy relaxation on acoustic phonons in double-quantum-well structures

The paper analyzes the rate of energy relaxation involving acoustic phonon emission between exciton states in a double quantum well. A theoretical study is made of the part played by two mechanisms, one of which is a one-step transition with emission of an acoustic phonon and the other is a two-step transition, which includes elastic exciton scattering from interface nonuniformities followed by energy relaxation within an exciton subband. The rate of the two-step transition in real double quantum wells is shown to be higher than that of the one-step transition. As follows from calculations, the fast energy relaxation between exciton states is determined by the elastic scattering of phonons from the interface.

Photovoltage effects in photoemission from thin GaAs layers

A set of thin GaAs p-type negative electron affinity (NEA) photocathodes have been used to measure the yield of photoemitted electrons at high intensity excitation. The active layer thickness is 100 nm and the p-type doping ranges from 5×10 18 to 5×10 19 cm −3 for a set of four samples. The results show that the surface escape probability is a linear function of the NEA energy. The surface photovoltage effect on photoemission is found to diminish to zero at a doping level of 5×10 19 cm −3. The experimental results are shown to be in good agreement with calculations using a charge limit model based on surface photovoltage kinetics that assume a constant electron energy relaxation rate in the band bending region.

Phonon emission and absorption in the fractional quantum Hall effect

We investigate the time dependent thermal relaxation of a two-dimensional electron system (2DES) in the fractional quantum Hall regime, where ballistic phonons are used to heat up the system to a non-equilibrium temperature. The thermal relaxation of a 2DES at ν=1/2 can be described in terms of a broad band emission of phonons, with a temperature dependence proportional to T4. In contrast, the relaxation at fractional filling ν=2/3 is characterized by phonon emission around a single energy, the magneto-roton gap. This leads to a strongly reduced energy relaxation rate compared to ν=1/2 with only a weak temperature dependence for temperatures 150mK<T<400mK.

Extracting rates of vibrational energy relaxation from centroid molecular dynamics

We investigate the ability of centroid molecular dynamics (CMD) to determine quantum correlation functions pertinent to the bath force correlation function, appearing in the rate expression for vibrational energy relaxation. We consider a one-dimensional model consisting of two or three Helium atoms. As expected, it is found that CMD performs best when the dominant bath coupling is linear in the bath coordinates, but it also performs well in determining the high frequency components of the force correlation functions. It is suggested that CMD should be used instead of classical dynamics when studying vibrational energy relaxation in cases where quantum effects are expected to be significant.

Ultrafast electron relaxation via breathing vibration of gold nanocrystals embedded in a dielectric medium

Relaxation dynamics of electrons in gold nanocrystals with diameters of 3.0--17.5 nm embedded in ${\mathrm{SiO}}_{2},$ ${\mathrm{Al}}_{2}{\mathrm{O}}_{3},$ and ${\mathrm{TiO}}_{2}$ matrices have been investigated by means of femtosecond pump and probe spectroscopy. The experiments show that the energy relaxation rates depend on both the nanocrystal size and the matrix material. A model taking account of electron-breathing mode interaction, electron-bulk phonon interaction, and thermal diffusion through the interface can explain well the observed results. The breathing mode damping in the medium on a time scale of a few picoseconds plays an important role in the electron-energy dissipation process of the nanoscale composite system.

Energy relaxation by hot electrons in n-GaN epilayers

The energy relaxation rate for hot electrons in n-type GaN epilayers has been measured over the temperature range 1.5–300 K. Several samples grown by molecular-beam epitaxy and having different electron concentrations have been studied. At low electron temperatures (Te&amp;lt;20 K), the energy relaxation is via acoustic phonon emission. The magnitude and temperature dependence of the energy relaxation are found to be in good agreement with theoretical calculations using appropriate values of the deformation potential and piezoelectric coupling constants and ignoring screening. For Te⩾70 K, the dominant mechanism of energy loss is optic phonon emission. For the several samples studied, consistent values of the optic phonon energy and electron-optic phonon relaxation time, 90±4 meV and 5–10 fs, respectively, are measured. The energy agrees well with values obtained by other methods and the relaxation time is consistent with theoretical calculations of the Fröhlich interaction and indicate that hot phonon effects are absent up to 10−8 W/electron dissipation.

Energy transfer in collisions of oxygen atoms in the terrestrial atmosphere

The total and differential cross sections of elastic O(3P) + O(3P) collisions have been obtained from quantal calculations, and the rate of energy relaxation of fast oxygen atoms in atmospheric oxygen gas has been evaluated using realistic differential cross sections of oxygen‐oxygen collisions. All the electronic energy curves of O2 separating to the atomic ground states have been incorporated in calculations of the scattering phase shifts. The total and differential cross sections averaged over a statistical population of O(3P) fine structure levels have been used for calculations of the self‐diffusion coefficient, the viscosity and thermal conductivity of oxygen gas. The kernel of the Boltzmann equation for the energy relaxation process has been determined. The rate of energy losses of energetic oxygen atoms in the upper terrestrial atmosphere are calculated for typical thermospheric conditions. The energy distribution function of the recoil oxygen atoms is constructed using the computed energy relaxation kernel.

Noninertial mechanism for electronic energy relaxation in nanocrystals

The low-frequency vibrational spectrum of an isolated nanometer-scale solid differs dramatically from that of a bulk crystal, causing the decay of a localized electronic state by phonon emission to be inhibited. We show, however, that an electron can also interact with the rigid translational motion of a nanocrystal. The form of the coupling is dictated by the equivalence principle and is independent of the ordinary electron-phonon interaction. We calculate the rate of nonradiative energy relaxation provided by this mechanism and establish its experimental observability.

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

A model for the electron-vibration energy exchange in nitrogen based on a Landau-Teller-type rate equation is presented. Analytical expressions of relaxation times are derived for cutoff harmonic oscillator and Morse oscillator approximations, assuming that the relaxation proceeds by way of a continuous series of Boltzmann distributions over the vibrational states. Comparisons with the direct numerical integration of the master equation have shown that the use of a a two-temperature relaxation time allows accurate modeling of the nitrogen vibrational energy relaxation rate for various conditions encountered in high-enthalpy flows with electron and vibrational temperatures up to 40,000 K.

Heat generation approximation in modulation-doped field-effect transistors by the energy relaxation between carriers and phonons

A combination of the nonlinear charge-control model, rate balance equations, and electron-phonon scattering is used to simulate the hot-electron transport and heat generation problem of modulation-doped field-effect transistors. Based on the present model, the trend of high-field transport can be well demonstrated. In addition, the heat generation inside the channel can also be estimated by the energy flux balance equation with the energy relaxation rate formulated by polar-optical phonon scattering mechanism. Scaling down the gate length to submicron range, more heat power is generated inside the channel. However, the heat generation ratio reveals that hot electrons carry over half of the energy density gained from the applied electric field directly into drain region. For 0.1 μm gate length, more than 90% energy density is achieved. By reducing the gate length into the deep submicron range, the thermal impact on the drain side becomes more serious and complicated than the one found inside the channel.

Quasi-Particle Properties of a One-Dimensional Electron System Interacting with a Short-Range Potential

We study the quasi-particle properties of a one-dimensional electron gas interacting via a short-range electron–electron interaction. The electron self-energy is calculated using the leading-order dynamical-screening approximation with (GWΓ approximation) and without the vertex corrections (GW approximation). We test the reliability of the plasmon-pole approximation against the full self-energy calculations. Energy relaxation rate via longitudinal optical (LO)-phonon emission is also examined to explore the effects of short-range potential. Our results for the quasi-particle properties indicate that an effective short-range interaction can be used as a qualitative model to understand various quantities in a realistic quantum wire with long-range Coulomb interactions.

Quasi-Particle Properties of a One-Dimensional Electron System Interacting with a Short-Range Potential

We study the quasi-particle properties of a one-dimensional electron gas interacting via a short-range electron–electron interaction. The electron self-energy is calculated using the leading-order dynamical-screening approximation with (GWΓ approximation) and without the vertex corrections (GW approximation). We test the reliability of the plasmon-pole approximation against the full self-energy calculations. Energy relaxation rate via longitudinal optical (LO)-phonon emission is also examined to explore the effects of short-range potential. Our results for the quasi-particle properties indicate that an effective short-range interaction can be used as a qualitative model to understand various quantities in a realistic quantum wire with long-range Coulomb interactions.

Ultrafast electron relaxation measurements on α-SiO2 using high-order harmonics generation

Time-resolved photoemission spectroscopy, using high order harmonics, is used to measure the energy relaxation rate of hot electrons in α-SiO2 with sub-picosecond time resolution. Our results indicate that electrons of 30 eV kinetic energy in the conduction band relax at a rate which is at least two orders of magnitude lower than the one of photo-excited carriers of a few eV. As a result, we give insight in the relaxation process of hot electrons and show that impact ionization probability per unit time is only of the order of 1/40 ps−1, in very strong contrast with the much higher value generally assumed in models of optical breakdown.

Energy losses of 2D electron gas due to near-surface acoustic phonon scattering

We have shown that for quantum wells placed close to the stress-free surface of the semiconductor heterostructure, the energy relaxation rate of two-dimensional electrons interacting with acoustic phonons at low temperatures (Bloch–Grüneisen regime) is changed considerably in comparison with that of a two-dimensional electron gas placed in a bulk of semiconductor. The relaxation rate is enhanced in the case of a semiconductor–vacuum system and is suppressed in the case of the surface covered by a thin metal film. The enhanced energy loss is caused by additional scattering at localized and reflected acoustic waves, and the decrease appears due to suppression of piezoelectric scattering in the vicinity of the metal.

Nonlinear optical dynamics of semiconductor nanostructures:: feasibility of the photonic quantum gate

This paper is related to the modern branch of the nonlinear optics which is a search for and design of new media appropriate for the photonic information devices. We have studied experimentally a resonant nonlinear photoresponse of semiconductor nanostructure with GaAs/AlGaAs superlattice and determined the energy and phase relaxation rates of the free excitons in this structure. Theoretical analysis of resonant interaction of the coherent light pulses with quasi-two-dimensional nanostructure allowed us to conclude that such structures can be used for the fabrication of the photonic gates for quantum computer.