Nonequilibrium Population Research Articles

Bipolar Spin Switch

A thin ferromagnetic film can be used to polarize the spin axes of the electrons carrying an electric current in a manner loosely analogous with a light polarizer. When such a film is fabricated on a gold film, a nonequilibrium population of spin-polarized electrons is built up in the gold causing a "spin bottleneck" effect. The addition of a second ferromagnetic film results in a device whose output voltage depends on the orientation of the spins.

Role of interface optical phonons in cooling hot carriers in GaAs-AlAs quantum wells.

We present an experimental study of the nonequilibrium phonon population generated by the relaxation of hot carriers photoexcited in GaAs-AlAs quantum wells. The optical phonon population is measured by anti-Stokes Raman scattering performed in the plane of the layers. The measured occupation numbers suggest that interface phonon modes contribute significantly to the relaxation dynamics over the lifetime of an electron-hole pair. These results are explained on the basis of the interplay between emission and reabsorption of hot phonons, which leads to a large population of interface phonons under steady-state conditions.

Study of electron-phonon interaction in quantum wells using optically excited nonequilibrium population of phonons

It is well known that nonequilibrium populations of phonons can be generated in bulk semiconductors by the relaxation of photoexcited hot electrons. In this paper we demonstrate that nonequilibrium phonons can also be generated in quantum wells by picosecond lasers and then probed by time-resolved Raman scattering. Using this method we have studied the interaction between hot electrons and interface and confined LO phonons in GaAs/AlAs quantum wells for well widths varying between 2 to 6 nm. The results are compared quantitatively with three macroscopic models of electron-LO phonon interaction. Only the model proposed by Huang and Zhu agrees both qualitatively and quantitatively with experimental results.

Isolation by Distance in Equilibrium and Non-Equilibrium Populations

Isolation by Distance in Equilibrium and Non-Equilibrium Populations

ISOLATION BY DISTANCE IN EQUILIBRIUM AND NON-EQUILIBRIUM POPULATIONS.

It is shown that for allele frequency data a useful measure of the extent of gene flow between a pair of populations is M∘=(1/FST-1)/4, which is the estimated level of gene flow in an island model at equilibrium. For DNA sequence data, the same formula can be used if FST is replaced by NST . In a population with restricted dispersal, analytic theory shows that there is a simple relationship between M̂ and geographic distance in both equilibrium and non-equilibrium populations and that this relationship is approximately independent of mutation rate when the mutation rate is small. Simulation results show that with reasonable sample sizes, isolation by distance can indeed be detected and that, at least in some cases, non-equilibrium patterns can be distinguished. This approach to analyzing isolation by distance is used for two allozyme data sets, one from gulls and one from pocket gophers.

Nonequilibrium edge-state transport resolved by far-infrared microscopy.

Subwavelength focusing of far-infrared light (\ensuremath{\lambda}=392 \ensuremath{\mu}m) is introduced to resolve spatially the photoconductivity of a two-dimensional electron gas. An increased cyclotron resonance amplitude is observed at one of the sample edges which proves that it is at the edge where states with nonequilibrium population can exist.

Electron-longitudinal-optical-phonon coupling and intersubband scattering in modulation-doped quantum wells under high-electric-field transport conditions.

The electron--longitudinal-optical-phonon coupling in GaAs/${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As modulation-doped quantum wells is studied under the conditions of steady-state high-field transport from theoretical and experimental points of view. The calculations are based on the Lei-Ting approach of high-field transport in a two-subband system. A common hot-electron temperature is assumed for both subbands but the Fermi levels are allowed to split off because of the weakness of the intersubband Coulomb interaction against the impurity and LO-phonon intersubband scatterings. The agreement with experiments requires a phonon lifetime of about 5 ps and a nonequilibrium hot-phonon population drifting with the electron gas. Moreover, we show that the temperature versus power-loss diagrams do not fully characterize the electron--LO-phonon coupling since this coupling increases with the drift velocity through the Doppler shift of the LO-phonon frequency. Finally, for a vanishing electric field, the low-temperature mobility is shown theoretically to be mainly reduced at the onset of the second subband by intrasubband scattering. It is argued that the high-mobility electrons lying at the Fermi level of the ground subband are efficiently scattered within their subband by the low-mobility carriers of the upper subband through the electron-electron Coulomb interaction.

Hot-electron transport in GaAs/Ga1-xAlxAs quantum-well structures.

We present a review of the experimental results of the steady-state hot-electron energy and momentum relaxation for longitudinal transport in GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells. The results of the current work and the work reported in the literature indicate that the nonequilibrium population of LO phonons, contrary to the assumptions made in conventional theories, is randomized in K space. Therefore, the production of hot phonons not only reduces the energy relaxation rate but also enhances the momentum relaxation rate. The latter reduces the drift velocity at high fields and hence inhibits negative differential conductivity via real-space transfer or intervalley transfer. The results are compared with a comprehensive theoretical model involving nondrifting hot phonons and scattering from remote impurities and interface roughness. It is shown that hot-phonon effects increase with increasing three-dimensional carrier concentration and the agreement between the theory and the experiments carried out by three independent research groups is excellent.

Theory of thermal unimolecular reactions at low pressures. III. Superposition of weak and strong collisions

Biexponential models for collisional energy transfer are formulated representing superimposed weak and strong collisions. Analytical solutions of the master equation for low pressure thermal unimolecular reactions at steady state are derived for such models. Nonequilibrium populations of excited states as well as collision efficiencies βc in the low pressure rate constant differ considerably from the corresponding quantities for simple exponential collision models. The results are analyzed in terms of general expressions of the collision efficiency βc as a function of the average energy transfer quantities 〈ΔE〉 and 〈ΔE2〉.

Inter-edge-state scattering and nonlinear effects in a two-dimensional electron gas at high magnetic fields.

Charge-carrier transport in the presence of a nonequilibrium population of edge states is studied both theoretically and experimentally. The attention is focused on the temperature dependence of the inter-edge-state (IES) electron scattering and on nonlinear effects of the edge-state transport, both in the integer-quantum-Hall-effect regime. First, a theoretical analysis of the IES transition is developed, which explicitly considers the Fermi distribution function of electrons in edge states and takes account of both a long-range impurity scattering and the acoustical-phonon scattering. The analysis explains well the observed temperature dependence of the IES equilibration length in high-mobility GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure devices when a smooth parabolic edge potential is assumed. Second, analysis of nonlinear transport across a potential barrier predicts an inverted population of electrons in edge states, which explains asymmetric energy dissipation around the barrier recently observed by other authors. Furthermore, the analysis predicts a nonlinear two-terminal resistance of the potential barrier, which provides a reasonable account for the experimentally observed resistance. Third, nonlinear effects are reported in which the edge states reorganize themselves in the presence of a nonequilibrium population of electrons. This leads to a population-dependent IES equilibration length, which accounts for an observed nonlinear Hall resistance which is asymmetric about I=0. The onset of the IES spontaneous acoustic-phonon emission is observed when the amplitude of the unequal population between relevant edge states exceeds a threshold. Finally, experimental evidence is presented to show that the maximum amplitude to which adjacent edge states can be unequally populated is limited to one-half the value of the Landau-level-energy spacing \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$.

Nonequilibrium Population Structure in Forked Fungus Beetles: Extinction, Colonization, and the Genetic Variance Among Populations

Local extinction and recolonization play a significant role in determining the amount of genetic variance among populations of Bolitotherus cornutus, the forked fungus beetle. Several demographic parameters are known to be important to genetic differentiation; the local population size distribution, migration rate, extinction rate, colonization number, and the probability of common origin of colonists were measured for forked fungus beetles. An artificial colonization site experiment demonstrated that the numbers of colonists and migrants per generation are approximately equal. These observations, interpreted with previous theoretical analyses, predict that the genetic variance among populations is increased in Bolitotherus relative to the case of long-lasting populations at an equilibrium between drift and migration. An electrophoretic comparison of populations of different ages supports this prediction. Young populations are more differentiated than older populations; the effect of the extinction/recolonization process in this species is to increase the genetic variance among populations. This study provides a methodology based on recent theory that can be applied to the study of the effects of local extinction and recolonization in other species.

Subpicosecond real-space charge transfer in GaAs/AlAs type II superlattices

The authors report time-resolved anti-Stokes Raman scattering measurements of short-period GaAs/AlAs type II superlattices which reveal directly that q approximately 0 confined and interface optical phonons are emitted by electrons when they transfer from the Gamma valley in the GaAs layers to the Xz valley in the AlAs layers in structures where the Gamma -Xz separation is greater than the optical phonon energy. The transfer time is estimated from the risetime of the non-equilibrium phonon population to be approximately=1 ps.

Hot-electron transport in GaAs quantum wells: effect of non-drifting hot phonons and interface roughness

The influence of a non-equilibrium population of LO phonons (hot phonons) on hot-electron energy and momentum relaxation in modulation-doped GaAs quantum wells are studied both experimentally and theoretically. The experimental results on high-field parallel transport indicate strongly that: (i) non-equilibrium phonons in GaAs quantum wells, contrary to the assumptions made in the conventional theories, are non-drifting; (ii) therefore, the production of hot phonons not only reduces the energy relaxation rate but also enhances the momentum relaxation rate; (iii) the enhancement of the momentum relaxation at high fields inhibits negative differential conductivity via real space transfer or intervalley transfer; (iv) the enhancement of the momentum relaxation rate also reduces the drift velocity at high fields, which is detrimental to the speed of the hot electron devices; (v) hot phonon effects increases with increasing 3D carrier concentration. The results are compared with a comprehensive theoretical model involving non-drifting hot phonons and scattering from remote impurities and interface roughness. The agreement between the theory and the experiments is excellent.

Characterization of the B̃←X̃ transition of the chlorobenzene cation prepared in non-equilibrium rotational population distributions by resonance-enhanced multiphoton ionization

The technique of resonance-enhanced multiphoton ionization has been used to prepare the chlorobenzene cation in a series of different non-equilibrium rotational population distributions in its ground state. The ion is probed by a second laser leading to dissociation into fragments detected mass spectrometrically. The varied rotational contours resulting from this experiment provide valuable extra information for characterization of the ion transition.

A log-linear modeling framework for selective mixing

Nonrandom mixing can significantly alter the diffusion path of an infectious disease such as AIDS that requires intimate contact. Recent attempts to model this effect have sought a general framework capable of representing both simple and arbitrarily complicated mixing structures, and of solving the balancing problem in a nonequilibrium multigroup population. Log-linear models are proposed here as a general framework for solving the first problem. This approach offers several additional benefits: The parameters used to govern the mixing have a simple, intuitive interpretation, the framework provides a statistically sound basis for the estimation of these parameters from mixing-matrix data, and the resulting estimates are easily integrated into compartmental models for diffusion. A modified selection model is proposed to solve the second problem of generalizing the selection process to nonequilibrium populations. The distribution of contacts under this model is derived and is found to satisfy the assumptions of statistical inference for log-linear models. Together these techniques provide an integrated and flexible framework for modeling the role of selective mixing in the spread of disease.

Electron-optical-phonon interactions in ultrathin GaAs/AlAs multiple quantum wells.

Nonequilibrium populations of both confined and interface phonons generated by picosecond laser pulses in a series of GaAs/AlAs quantum wells have been studied by time-resolved picosecond Raman scattering as a function of well width. The dependence of the nonequilibrium phonon populations on well width is found to be sensitive to the theoretical model which is used to describe the electron-phonon interaction. Our data disagree with the macroscopic model of electron-phonon interaction, but they are in excellent agreement with the microscopic model proposed recently by Huang and Zhu.

Anharmonic decay time, isotopic scattering time, and inhomogeneous line broadening of optical phonons in 70Ge, 76Ge, and natural Ge crystals.

High-accuracy (0.02-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) first-order Raman spectra of two different isotopically enriched Ge crystals (95.9% $^{70}\mathrm{Ge}$ and 86.0% $^{76}\mathrm{Ge}$) and a Ge crystal of natural isotopic composition as well as time-resolved picosecond Raman spectra of the isotopically enriched $^{70}\mathrm{Ge}$ and natural Ge were measured and compared with theoretical calculations using the self-consistent Born approximation and the coherent-potential approximation. The broadening of the Raman line in the frequency domain was found to be predominantly caused by the anharmonic decay of optical phonons into lower-energy acoustic phonons, resulting in a line broadening that is inversely proportional to the average isotopic mass m\ifmmode\bar\else\textasciimacron\fi{}. Isotopic disorder contributes only a little to the line broadening and depends on the isotopic composition of the material. From the phonon linewidths the anharmonic decay time of optical phonons in Ge at 80 K was determined to be m\ifmmode\bar\else\textasciimacron\fi{}(8.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ ps (m\ifmmode\bar\else\textasciimacron\fi{} is the average isotopic mass in atomic-mass units). The isotopic (elastic) scattering time of optical phonons depends strongly on the isotopic composition and is two orders of magnitude longer than the decay time in all samples. The asymmetry observed in the Raman lines is explained in terms of the opacity of the material and the asymmetric phonon self-energies (due to isotopic disorder). The decay time of the time-resolved incoherent anti-Stokes Raman signal is 8\ifmmode\pm\else\textpm\fi{}1 ps for both the isotopically enriched and the natural Ge. It is suggested that the discrepancy between the phonon decay time (determined from the frequency-domain measurements) and the nonequilibrium phonon population decay time (determined from the time-domain measurements) is due to effects related to the phonon-generation process in the transient experiment.

Effect of valence-subband structure on the energy relaxation dynamics of electrons in GaAs quantum wells grown on Si.

Different electron energy relaxation dynamics are observed in narrow and wide modulation Be-doped GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells grown on Si substrates (GaAs QW's/Si) arising from different valence-subband structure. The combination of built-in biaxial stress and spatial hole confinement results in a reversal of light- and heavy-hole subbands in narrow GaAs QW's/Si structures. For narrow (wide) quantum-well structures of 40 (188) \AA{} at 4.3 K in which there is a two-dimensional light- (heavy-) hole gas, the energy-loss process of photoexcited hot electrons is extremely rapid (slow) due to strong (weak) energy exchange with the cool light (heavy) holes. The nonequilibrium phonon population was found to build up from the relaxation of hot electrons in the 188-\AA{} wells but not in the 40-\AA{} wells.

Spectral and temporal dynamics of nonequilibrium phonons in LaF3:Pr3+

Defect-induced one-phonon absorption is used to generate high-occupation-number narrow-band nonequilibrium phonon populations at a range of frequencies in ${\mathrm{LaF}}_{3}$:${\mathrm{Pr}}^{3+}$. The spectral and temporal dynamics associated with the return to equilibrium of these phonons is observed. Processes that dominate the spectral evolution are shown to be narrow-band phonon confluence, anharmonic decay, and the broadband confluence of anharmonic decay products. The experimental data are shown to be in good agreement with a phonon-occupation-number rate-equation analysis that incudes the above processes.

Correlation of hot-phonon and hot-carrier kinetics in Ge on a picosecond time scale.

We report room-temperature measurements of time-resolved reflectivity from intrinsic crystalline Ge induced and probed by \ensuremath{\lambda}=0.575 \ensuremath{\mu}m, 2-ps pulses and for photogenerated carrier densities up to \ensuremath{\sim}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. These data are used together with our earlier picosecond-time-resolved Raman-scattering data at 77 and 300 K to self-consistently determine transient nonequilibrium carrier and phonon effects. The combined data sets are modeled with a Boltzmann transport description of coupled electron and phonon kinetics to understand the temporal and spatial evolution of carrier density and temperature and the generation and decay of Raman-active phonons. Using known material parameters in the model, we can account for the magnitude and temporal evolution of the electron, hole, and phonon thermodynamic parameters. In particular, the model accounts for the relative delay between the peak of the pulse and the nonequilibrium phonon population, the number of nonequilibrium phonons generated, and the initially rapid diffusion of hot carriers away from the sample surface on a 5-ps time scale.