Ballistic Motion Of Electrons Research Articles

Electrical Conduction Through Small Contact Spots

Earlier literature has reported that the voltage-temperature (V-T) relation for electrical contacts, and classical electrical contact theory in general, are invalid where the a-spots are on the order of nanometers. This paper reviews earlier literature dealing with the breakdown of the V-T relation and presents quantitative arguments to propose that this breakdown stems from the ballistic motion of electrons through nanometer-sized constrictions. Earlier literature also suggested that the breakdown of classical theory stems in part from thermal losses from a-spots to contaminant layers in an electrical interface. Through the use of a simple a-spot model, this paper shows that this cooling mechanism is not sufficiently important to affect the validity of the classical V-T relation and classical electrical contact theory in general

Ballistic electron transport in Au films

Femtosecond transient reflectivity measurements on gold films revealed damped oscillations, which are attributed to anisotropic ballistic electron motion and reflection at the film boundaries. A theoretical model based on a modified Fermi-liquid theory can explain the observed oscillation periods as a result of ballistic transport in directions determined by the actual shape of the Fermi surface of Au.

Ballistic electron motion in a random magnetic field

Using a new scheme of the derivation of the non-linear $\sigma$-model we consider the electron motion in a random magnetic field (RMF) in two dimensions. The derivation is based on writing quasiclassical equations and representing their solutions in terms of a functional integral over supermatrices $Q$ with the constraint $Q^2=1$. Contrary to the standard scheme, neither singling out slow modes nor saddle-point approximation are used. The $\sigma$-model obtained is applicable at the length scale down to the electron wavelength. We show that this model differs from the model with a random potential (RP).However, after averaging over fluctuations in the Lyapunov region the standard $\sigma$-model is obtained leading to the conventional localization behavior.

Carbon Nanotubes for Cold Electron Sources

AbstractTechnological advances in the field of microelectronic fabrication techniques have triggered a great interest in vacuum microelectronics. In contrast to solid‐state microelectronics, which entails scattering‐dominated electron transport in semiconducting solids, vacuum microelectronics relies on the scattering‐free, ballistic motion of electrons in vacuum. Since the first international conference on vacuum microelectronics substantial progress in this field has been made. The first technological devices using micrometer‐sized electron emitting structures are currently being commercialized. Field‐emission flat‐panel displays (FED) seem to be an especially promising competitor to LCD displays. Today there is only one mature technology for producing micro‐gated field‐emission arrays: the Spindt metal‐tip process. The drawbacks of this technology are expensive production, critical lifetime in vacuum, and high operating voltage. Carbon nanotubes (CNT) can be regarded as the potential second‐generation technology to the Spindt metal micro‐tip. In this review we show that the field emission (FE) behavior of CNT can be accurately described by Fowler–Nordheim tunneling and that the field‐enhancement factor β is the most prominent factor. Therefore the FE properties of a CNT thin film can be understood in terms of local field enhancement β(x,y), which can be determined with scanning anode field emission microscopy (SAFEM). To characterize the FE properties of an ensemble of electron emitters we used a statistical approach (as for thin film emitters), where f(β)dβ gives the number of emitters on a unit area with field‐enhancement factors within the interval [β,β + dβ]. We show that the field‐enhancement distribution function f(β) gives an almost complete characterization of the FE properties.

The break-up of heavy electrons at a quantum critical point

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study on the heavy-electron material YbRh2Si2 found that near a field-induced QCP electrons move ever more slowly and scatter off one another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and scattering cross-section. But these studies could not shed light on whether these properties were an artefact of the applied field, or a more general feature of field-free QCPs. Here we report that, when germanium-doped YbRh2Si2 is tuned away from a chemically induced QCP by magnetic fields, there is a universal behaviour in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current-carrying motions of the electron fluid.

Terahertz Generation Due to Streaming Plasma Instability in n+-n--n-n+ InN Submicron Structure

Streaming plasma instability at near ballistic electron motion in InN n+–n––n–n+ structures is theoretically investigated by the Monte Carlo particle technique at low lattice temperatures (T < 140 K), when dominating scattering mechanism is the optical phonon emission. It is shown that the electron transport through the structure of certain geometry can be essentially nonstationary in some bias range. The simulation of the steady state transport and microwave power generation in InN n+–n––n–n+ structures, connected with an external parallel resonant circuit, demonstrates that up to 50 μW of the microwave power can be delivered by the structure in the 1.1 to 1.2 THz frequency range at liquid nitrogen temperature.

InN Submicron Structure for Generation at Terahertz Frequencies

Streaming plasma instability at near ballistic electron motion in InN n + n - nn + structures is theoretically investigated. At low lattice temperatures (T < 140 K), when dominating scattering mechanism in InN is the opticall phonon emission the electron transport through the structure of certain geometry can be essentially nonstationary in some bias range. By Monte Carlo particle technique the steady state transport and microwave power generation in InN n + n - nn + structures connected with external parallel resonant circuit are simulated. It is demonstrated that over hundred microwatt of the microwave power can be delivered by the structure in 1.1 ∼ 1.2 THz frequency range at liquid nitrogen temperature.

Nonlinear electrodynamics of electrons in a quasi-one-dimensional ballistic ring

We consider ballistic electron motion in a quasi-one-dimensional ring under the uniform high-frequency electric field induced by an electromagnetic field. The electron satisfies a nonlinear equation of motion which is formally identical to that for a pendulum with a vibrating suspension point. The averaging method of Kapitza is used. The electromagnetic emission spectrum is calculated. The spectrum consists of low-frequency radiation, scattered radiation at the incident radiation frequency and combination scattered radiation; the intensities and frequencies of all components depend nonlinearly on the incident radiation frequency. At a certain value of that intensity the spontaneous symmetry breakdown occurs. As a result, the system acquires some static electric dipole moment.

Numerical simulation of the tunneling current and ballistic electron effects in field emission devices

Using a two-dimensional model, we have considered the effects of spatially changing fields and potentials, stochastic electron emission, and ballistic electron motion on the anode current and on the width of the electron beam in field emission displays. We have solved the electrostatic problem using the boundary element method. Our electron emission model evaluates the current density at the cathode surface from the tunneling transmission coefficient, which is calculated from the solution of the one-dimensional Schrödinger equation using a potential barrier which includes the effect of image charges and nonuniform electric field. The current density is used to calculate the rate of electron emission for each segment of the emitter’s surface. The emission time is assumed to follow a Poisson distribution. The electron’s velocity magnitude and angle with the normal to the surface are also stochastically generated following the probability distribution of field emitted electrons. Ballistic transport is used to propagate electrons through the device. For very sharp tips the electric field changes from its surface value over a very short distance away from the surface, which can be comparable to the tunneling distance. We found that the resulting current density is considerably lower for the calculated barrier profile than for the triangular one, especially at low values of the electric field. We have also shown that the effect of the lateral kinetic energy and emission angle distribution on the electron beam width at the anode is negligible for sharp emitters, where the angular spread is dominated by the curvature of the emitting surface.

Electron and lattice dynamics following optical excitation of metals

New results about relaxation dynamics of optically excited electrons in metals, mostly gold and nickel films, are presented. Emphasis is on electron temperature near the surface as well as on the range of energy transport by ballistic and diffusive electron motion in comparison to the optical penetration depth. The experiments focus on the interval between creation of an electron temperature and the time at which thermal equilibrium between electrons and lattice is reached. Results were obtained by time-resolved linear and second-harmonic reflectivity measurements carried out in pump-probe mode. It is shown that the two-temperature model is well suited to describe hot electron diffusion in metals and to extract electron–phonon coupling constants from experimental data, provided corrections for ballistic electron motion are incorporated. The electron–phonon coupling constant of gold was found to be independent of film thickness down to 10 nm. For noble metals, probe reflectivities near the interband transition were related to electron temperatures by a proper model for the dielectric function. For transition metals such relation between reflectivity and electron temperature is more difficult. A new pump-pump-probe technique was introduced which allows to study hot electron relaxation by probing the reflectivity in thermal equilibrium between electrons and lattice. Also these results can be well described by the two-temperature model. Finally, the interface sensitivity of the second harmonic was utilized to detect vibrational motion and thermal expansion of ultrathin nickel films on Cu(001).

Persistent current in a mesoscopic ring with diffuse surface scattering

The persistent current in a clean mesoscopic ring with ballistic electron motion is calculated. The particle dynamics inside a ring is assumed to be chaotic due to scattering at the surface irregularities of atomic size. This allows one to use the so-called ``ballistic'' supersymmetric \sigma model for calculation of the two-level correlation function in the presence of a nonzero magnetic flux.

Internal magnetic focusing in an array of ballistic cavities

We study the ballistic motion of electrons in an array of submicron circular cavities, fabricated by electron beam lithography and dry etching techniques. Pronounced magnetoresistance oscillations are observed that can be understood in terms of internal magnetic focusing or commensurability between the electron trajectories and the geometry of the cavities. The depletion distance in the two-dimensional electron gas caused by the dry etching process can be deduced by analysis of the resonance peak positions within a simple magnetic focusing picture.

Internal Magnetic Focusing in an Array of Open Quantum Dots

The ballistic motion of electrons is studied in an array of open quantum dots. The submicron dots are fabricated by electron beam lithography and dry etching techniques. Pronounced oscillations are observed in the magnetoresistance which can be understood in terms of the commensurability effect between the ballistic trajectories and the geometry of the circular cavity or the internal magnetic focusing. By breaking the symmetry of the entrance/exit openings, or by inducing a large antidot at the center of the cavity, the commensurability effect disappears.

Magnetic localization of classical electrons in 2D disordered lattice

The classical ballistic motion of 2D electrons interacting with a disordered system of round scatterers is studied in a magnetic field. Besides the usual percolational phase transition related to geometrical connectedness, the magnetic percolation threshold was found, separating the infinite motion for high cyclotron radius r c and total localization of electrons for small r c. The components of the conductivity tensor are studied far and near the pecolation threshold. Nonlinear conductivity of the insulating magnetic phase is obtained.

Symmetry-breaking and chaos in electron transport in semiconductor superlattices

We study the motion of ballistic electrons in a single miniband of a semiconductor superlattice (SSL) driven by a terahertz laser polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behavior and symmetry-breaking. Finally, we estimate the magnitude of the DC current and voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of real SSLs.

Hall magnetometer in the ballistic regime

A Monte Carlo simulation of the ballistic motion of electrons in a mesoscopic Hall bar containing a local inhomogeneous magnetic field profile is presented. We find that in the regime of low magnetic fields, the Hall resistance is determined by the average magnetic field in the cross junction and is independent of the shape and position of this profile in the junction. Information on the size of the local magnetic field profile can also be obtained from the Hall measurement. The bend resistance, on the other hand, is much more precise on the exact details of the local magnetic field in the cross junction.

Magnetoresistance oscillations induced by periodically arranged micromagnets (invited)

Probing magnetic fields can be done, e.g., by employing the well established Hall effect. Alternatively, we make use of the ballistic motion of electrons in high mobility two-dimensional electron systems (2DES) to probe electrically the stray field of periodically arranged micomagnets. We investigate the magnetoresistance of the 2DES underneath arrays of magnetic strips and magnetic dots having periods between 500 nm and 1 μm. The periodic stray field gives rise to pronounced oscillations of the resistivity as a function of a homogeneous (weak) magnetic field. The magnetization orientation of the dots and strips can be aligned in different directions with respect to the current flow through the device. The observed magnetoresistance depends characteristically on the magnetization direction and can be understood in terms of the stray field pattern probed by the electrons.

Long-mean-free-path ballistic hot electrons in high-purity GaAs.

The mean free path (mfp) of hot ballistic electrons, injected into high-purity GaAs, was measured and found to be several micrometers long. The hot electrons were injected at energies just below the LO-phonon emission threshold and their mfp was measured by two techniques: first, by comparing different devices with different layer thickness; and second, in a single device, utilizing the cyclotron motion of ballistic electrons in tilted magnetic fields. We find the mfp scales roughly inversely with impurity concentration. We suggest that the dominant scattering is due to impact ionization of neutral impurities.

Dissipative chaos in semiconductor superlattices.

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.

Cyclotron oscillations in a tilted magnetic field: A tool to measure the mean free path of ballistic electrons in high purity GaAs

The mean free path (mfp) of ballistic electrons in high purity GaAs was measured using a novel effect due to the cyclotron motion of ballistic electrons in tilted magnetic fields. Whenever the cyclotron orbit is commensurate with the device length an increase in the collected current is observed, leading to pronounced oscillations. We utilize the fact that the total path length varies as we change the angle of the magnetic field to extract the mfp using a single device. For high purity GaAs with an impurity concentration N a+ N d≈6 × 10 14 cm −3 we measure an mfp of ≈4 μm for electrons below the optical phonon energy. We suggest that the observed mfp is primarily due to impact ionization of neutral donors by the ballistic electrons. The large contrast of the oscillations proves that both injection and collection give preference to the direction normal to the layers and thus, that the momentum component parallel to the layers is conserved during transmission over the barrier.