Energy-dependent Transmission Research Articles

Space charge in nanostructure resonances

In quantum ballistic propagation of electrons through a variety of nanostructures, resonance in the energy-dependent transmission and reflection probabilities generically is associated with (1) a quasi-level with a decay lifetime, and (2) a bulge in electron density within the structure. It can be shown that, to a good approximation, a simple formula in all cases connects the density of states for the latter to the energy dependence of the phase angles of the eigen values of the S-matrix governing the propagation. For both the Lorentzian resonances (normal or inverted) and for the Fano-type resonances, as a consequence of this eigen value formula, the space charge due to filled states over the energy range of a resonance is just equal (for each spin state) to one electron charge. The Coulomb interaction within this space charge is known to ‘distort’ the electrical characteristics of resonant nanostructures. In these systems, however, the exchange effect should effectively cancel the interaction between states with parallel spins, leaving only the anti-parallel spin contribution.

The energy-dependent transmission coefficient and the energy distribution of classical particles escaping from a metastable well

We investigate the distribution of energies of thermally activated particles escaping from a metastable well. This energy distribution is connected by detailed balance to the energy-dependent transmission coefficient, the probability that a particle injected into a well will stick. Theoretical expressions for the energy-dependent transmission coefficient show good agreement with simulation results for a one-dimensional reaction coordinate coupled to a frictional bath. Slight deviations from theoretical predictions based on turnover theory [E. Pollak, H. Grabert, and P. Hänggi, J. Chem. Phys. 91, 4073 (1989)] are understood in light of the assumptions of turnover theory. Furthermore, the theoretical expressions for energy distributions also provide good fits for fully three-dimensional simulations of sticking and desorption of Ar and Xe on Pt(111) [J. C. Tully, Surf. Sci. 111, 461 (1981)]. Finally, we compare the theoretical efficiencies of several reactive flux sampling schemes, including a scheme designed to be optimal.

Hot electron transport in SiO2 probed with a scanning tunnel microscope

Hot electrons injected with a scanning tunnel microscope (STM) tip into Pt/SiO2/Si(100) structures were detected as a collector current in the Si by using a STM configuration known as ballistic electron emission microscopy. The collector current, observed for STM tip potentials ≳4 V and for oxide biases ≥0 V, is direct evidence for electron transmission through the conduction band of the SiO2. Negative oxide biases delayed the onset of current to correspondingly higher tip potentials. A simple model was used to extract the energy and bias dependent transmission probabilities from the experimental data for a 62 Å SiO2 layer. The results are compared with Monte Carlo calculations.

Scattering and spectral shape in ballistic-electron-emission microscopy of NiSi2-Si(111) and Au-Si samples.

The ballistic-electron-emission microscopy (BEEM) tip voltage versus collector current spectral shape is used as a tool to study Au-Si and ${\mathrm{NiSi}}_{2}$-Si samples on a nanometer scale. A method is outlined for the extraction of an energy-dependent transmission factor from the BEEM spectra. Results for Au-Si samples compare favorably with theoretical interface transmission calculations. Data from both systems suggest that the shape of the spectra is influenced by scattering. The influence of scattering induced broadening of the injected electron transverse momentum distribution is considered.

Ballistic electron emission spectroscopy of noble metal–GaP(110) interfaces

Ballistic electron emission microscopy (BEEM) was used in an UHV environment to investigate the current–voltage spectra of Cu, Ag, and Au films on cleaved n-type GaP(110). Current thresholds, which occur when the applied tip-to-metal bias exceeds the Schottky barrier height, were remarkably uniform to within ±0.02 V for any particular metal–GaP interface, but varied for interfaces with different metals. The fitted threshold voltage Vo depends on the model used for the interface current transport. Its value varies by ∼0.05 V between a prior model that predicts a (V−Vo)2 dependence near threshold and a new (V−Vo)5/2 dependence proposed here. The latter includes an energy dependent transmission coefficient for transport across the metal–semiconductor interface. Significant BEEM current variations and fluctuations were observed, which are associated with topographic gradients of the metal surface and sudden changes in the tunneling geometry during the experiment. The transport model is further developed to include average angles of incidence of the injected electrons that are off-normal at the metal–semiconductor interface, a condition that occurs when the tunneling tip is scanning over nonplanar surface features. Model predicted current variations are consistent with the range of surface gradients observed in the topographic images of the noble metal films on GaP.

Quasi-ballistic resonant tunneling of minority electrons into the excited states of a quantum well

Observation of energy-dependent transmission of nonequilibrium minority electrons through a symmetric double-barrier (DB) quantum well heterostructure is reported. The DB is placed in the base of a GaInAs/AlInAs bipolar transistor. The electrons are launched into the DB with variable kinetic energies using a tunnel barrier in the emitter and varying the emitter-base voltage. The resulting peak in the collector current provides for the first time evidence of quasi-ballistic resonant tunneling of minority carriers into the eigenstates of a quantum well. The small peak-to-valley ratio and the broad peak also demonstrate the importance of scattering and of the anisotropy in momentum space of the incident distribution function in the region between the ballistic electron launcher and the DB.

On the interpretation of current images in scanning tunneling spectroscopy of Si(111)7×7

During scanning of Si(111)7×7 the tunneling current has been determined at every tip position as a function of bias voltage keeping the distance between tip and sample at a constant value by stabilization of the tunneling current for only a small time interval. For positive (2 V) and negative (−2 V) stabilization voltage we have obtained two sets of current images. Our results show that the hitherto neglected energy-dependent transmission probability on the tunneling current and the intimate relation between electronic and topographic properties prevent a simple determination of the local density of states.

Time-dependent tunneling of wave-packets through heterostructures in an applied field

We investigate time-dependent tunneling of wave-packets through heterostructures by numerically solving the time-dependent effective mass Schrödinger equation. In particular, we analyze the effect of the form of the initial wave-packet on the energy-dependent transmission coefficient, discuss various time-scales related to resonant tunneling, and study effects of applied fields.

Determination of ion temperatures in the edge plasma from ion flux transmission of apertures

The flow of ions through an aperture perpendicular to a strong magnetic field has been calculated for a Maxwellian velocity distribution. The results obtained are needed for the interpretation of time resolved analysis of fluxes using the collecting probe technique and also for in situ mass, energy, and charge state analysis with spectrometers. Moreover, the energy dependent transmission of the aperture can be used to determine ion temperatures. Deuterium, carbon and metal impurity ion temperatures in the limiter shadow plasma of TFR 600 have been evaluated from measured ion flux transmission. For deuterium a temperature of 100 eV was found on the electron side of the collector. At the ion side the temperatures are higher by a factor of two. Impurity ion temperatures are ambiguous to the extent of the knowledge on the charge state. Assuming singly charged ions for Ni + a temperature of 10 eV on the ion side and 4 eV on the electron side was found during high density discharges with an Inconel limiter. In case of a carbon limiter the C + ion temperature on the ion side was about 35 eV.

Energy-dependent transmission and reflection in thin slabs

Abstract The energy- and angle-dependent reflection and transmission distributions for the slab albedo problem are obtained for scattering described by a separable kernel. These solutions follow by relating the solution of the nonlinear, invariant imbedding integral equations to the endpoint values of an inhomogeneous, linear, Fredholm integral equation. Use of a stochastic description also permits determination of the mean number of collisions suffered by a particle before it emerges from a face of the slab. Numerical results are obtained for neutrons incident upon a free gas.

Neutron Transmission Properties of Cd and B Filters in Moderating Media and Its Application in the Determination of 1/E-Spectrum

The energy dependent neutron transmission function of the Cd-filter covering a cylindrical 1/ν-detector was calculated with consideration given to the perturbation effect in the surrounding medium. The results were found to agree well with experiments using lead slowing-down time spectrometer.The effective Cd cut-off energy for 1mm thick Cd was calculated from the above transmission function, and found to be about 50% larger than the reported values.The validity of the assumption of 1/E1+β spectrum in a graphite moderator is discussed, and the β-value determined with an accuracy of 0.01 from the reaction rate ratio of BF3-counters covered with the different thicknesses of Cd- and B-filters. The region of the 1/E-spectrum neutron field in the graphite standard pile was determined by using this technique.