Electronic Transmission Coefficient Research Articles

Carrier transport coefficients across GaAs–GaAlAs (100) interfaces

We present calculations of reflection and transmission coefficients for electrons and holes at (100) interfaces for the GaAs–Ga1–xAlxAs system. We consider semi-infinite crystals of the two semiconductors joined at an abrupt or compositionally graded interface. The calculations are performed using the empirical tight binding approximation. The transport coefficients were computed as a function of the components of the incident carrier wavevector normal and parallel to the interface. We have investigated the transport coefficients for incident states near various band minima into different final state channels. The transmission into states with qualitatively similar character to the incident state is found to be much greater than transmission into states of different character. For example, an electron near the X minimum normal to the interface in Ga1–xAlxAs transmits into the X valley of GaAs with much greater probability than it transmits into the Γ minimum of GaAs. We have investigated the dependence of the transport coefficients on alloy composition. The effect of compositional grading of the interface on the transport coefficients has also been investigated.

Single-reflection layer-scattering theory of low energy electron diffraction spectra

A simple general method for computing medium and low energy electron diffraction (LEED) spectra of layered materials has been developed for application to transition metal dichalcogenides. Electron transmission and reflection coefficients for each individual sheet of atoms are computed; the separate sheets are grouped into sandwiches which are stacked upon one another to form the crystal; the intersheet scattering is treated with the single-reflection approximation. For an unrelaxed lattice whose sandwiches are separated by the distance b and whose intrasandwich layers are separated by a, the scattered electron intensity is ‖ f (a) ‖ 2 S (b), where f (a) is the single-sandwich form factor for the outermost sandwich. Lattice relaxation of the surface sandwich slightly modifies this result. The static structure factor S (b), which is a spiked function of energy and contains mainly bulk structural information, produces the principal peaks in the intensity versus energy spectrum, but the surface sandwich reflectivity ‖ f (a) ‖ 2 smoothly modulates the peak intensities and contains most of the surface structure information. This method of fitting ‖ f (a) ‖ 2 should be contrasted with most LEED analyses that concentrate on fitting peaks [which are related to S (b) and actually contain little surface structure information]. This simple single-reflection analysis of the surface structure is confirmed by a complete multiple scattering calculation.

Statistical model of electrical conduction in polycrystalline metals

A new statistical model for the effect of grain boundaries on electrical conduction is proposed. The electronic transmission coefficient t is given as an exponential function of the electron path assuming that t ≈ 1. A mean free path related to grain boundary effects is then derived; the Boltzmann equation is solved using the assumption that background scattering and grain boundary scattering operate independently. The analytical expression of the total conductivity obtained in this way agrees with the Mayadas-Shatzkes equations.

Transmission and reflection coefficients of carriers at an abrupt GaAs-GaAlAs (100) interface

We present calculations of reflection and transmission coefficients for electrons and holes at an abrupt (100) interface for the GaAs-${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ system. We consider semi-infinite crystals of the two semiconductors joined at a perfect atomically abrupt interface. The calculations are performed using the empirical tight-binding approximation. The transport coefficients were computed as a function of the components of the incident carrier wave vector normal and parallel to the interface. We have investigated the transport coefficients for incident states near various band minima into different final-state channels. The transmission into states with qualitatively similar character to the incident state is found to be much greater than transmission into states of different character. For example, an electron near the $X$ minimum normal to the interface in ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ transmits into the $X$ valley of GaAs with much greater probability than it transmits into the $\ensuremath{\Gamma}$ minimum of GaAs. The dependence of the transport coefficients on the alloy composition has also been investigated.

Electrical Properties of Epitaxial Aluminium Films

The resistivity of monocrystalline Al films was measured and compared with the resistivity calculated in terms of the function which takes into account both the external and the internal size effects. A comparison of the theoretical and experimental curves shows that the specular reflection coefficient (p) is small, while the coefficient of electron transmission through the grain boundary (r) increases with increasing film thickness.

A comment on photoemission from negative-electron-affinity GaAsP with a direct or an indirect band-gap

The transmission coefficients are calculated for Gamma and L conduction band electrons incident on GaP(111)B negative-electron-affinity surfaces within the abrupt-step model. For large band-bending, the transmission coefficient for Gamma electrons is found to be 0.83 compared with 0.22 for L electrons. These results provide an explanation for the lower quantum yields observed by Escher and Antypas (Appl. Phys. Lett., vol.30, p.314 (1977)) for negative-electron-affinity photocathodes using indirect-gap GaAsP compared with those observed using direct-gap GaAsP.

The contribution of once scattered electrons to the transmission coefficient of hot electrons in tunnel triodes

physica status solidi (a)Volume 43, Issue 1 p. K77-K80 Short Note The contribution of once scattered electrons to the transmission coefficient of hot electrons in tunnel triodes G. U. Reinsperger, G. U. Reinsperger Zentralinstitut für Elektronenphysik der Akademie der Wissenschaften der DDR, BerlinSearch for more papers by this authorW. Ludwig, W. Ludwig Zentralinstitut für Elektronenphysik der Akademie der Wissenschaften der DDR, BerlinSearch for more papers by this author G. U. Reinsperger, G. U. Reinsperger Zentralinstitut für Elektronenphysik der Akademie der Wissenschaften der DDR, BerlinSearch for more papers by this authorW. Ludwig, W. Ludwig Zentralinstitut für Elektronenphysik der Akademie der Wissenschaften der DDR, BerlinSearch for more papers by this author First published: 16 September 1977 https://doi.org/10.1002/pssa.2210430161AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume43, Issue116 September 1977Pages K77-K80 RelatedInformation

An empirical relation for the transmission coefficient of electrons under oblique incidence

An empirical relation for the transmission coefficient of electrons impinging on aluminum absorbers is given as a function of absorber thickness x, incident energy T 0, and angle of incidence θ. It has been formulated by incorporating the dependence upon θ in the empirical equation for the case of normal incidence reported previously by the present authors. Numerical constants in the relation have been determined through least-squares fit to the data for T 0 = 0.5−10 MeV generated by the Monte Carlo code of Berger and Seltzer. The rms absolute deviation, evaluated over θ = 0°−75°, of the relation from the Monte Carlo data is about 0.03 in the entire energy region considered.

Energy- and angular-dependent secondary-electron emission from a silicon (111) 7 × 7 surface. Emission from bulk states

Energy- and angular-dependent secondary-electron emission (EADSEE) spectra from a silicon (111) 7 \ifmmode\times\else\texttimes\fi{} 7 reconstructed surface are reported. Only spectra which consist of electrons that have emerged from bulk states are considered here. The spectra are interpreted in terms of the conventional three-step model, in which electrons are excited into high-lying conduction states, move to the surface, and emerge into the vacuum. Microscopic models are considered for the processes that contribute to each of the three steps. The processes which are important in determining the shape of these EADSEE spectra have been identified by comparing the predictions of the models with the observed spectra. The shape of the EADSEE spectra between 6 and 40 eV is determined mostly by the incoherent scattering that occurs as the electrons cross the reconstructed layer. This scattering obliterates the structure in the internal hot-electron distribution, structure which is observed in the spectra of electrons which emerge from a (111) 1 \ifmmode\times\else\texttimes\fi{} 1 unreconstructed surface. For emergence energies below 6 eV there is evidence for a number of processes. It is found that the spectral shape of the internal flux is dominated by structure in the density of conduction states, as first described by Kane. This shape is modified somewhat by energy-dependent transport losses. Most of the observed low-energy ( 6 eV) electrons have emerged coherently through the surface. The energy and angular structure in the low-energy secondary flux is affected in a number of ways in this emergence process. Evidence is seen for diffraction, refraction, and reflection of the emerging electrons. Diffraction at the surface causes peaks in the internal electron distribution to appear at angles of emergence not otherwise expected. Refraction of the outgoing waves leads to a cosine dependence of the angular plot of the secondary current for fixed energies. Reflection of the outgoing electrons at the surface barrier causes a decrease in the number of secondaries. With certain assumptions the reflection (transmission) coefficient of electrons at the barrier, and the wave-vector dependence of this coefficient, can be deduced from the data.

A generalized empirical equation for the transmission coefficient of electrons

An empirical equation for the transmission coefficient of mono-energetic electrons normally incident on the absorber has been formulated by modifying the expression proposed by Rao. It utilizes a semiempirical equation recently developed for the extrapolated range of electrons, and the dependence of a single remaining parameter upon the incident energy T 0 and the atomic number Z of the absorber has been determined by using a total of 79 experimental transmission curves for T 0 = 8 keV-30 MeV and for Z = 4–82. The rms absolute error of the equation is about 0.03 in most cases.

High-power electromagnetic transmission characteristics of a diffusing reentry plasma

Antenna voltage breakdown arising from the transmission of high-power microwave radiation may be suppressed on a reentry vehicle by injecting electrophilic chemicals into the flow field. This paper describes numerical procedures for calculating the amount of high-power microwave radiation that can be transmitted through a plasma chemically seeded with an electron-attaching substance. The power incident on a reentry plasma slab may be sufficient to induce electron temperature changes, resulting in variations in time of the electron density and effective collision frequency. The plasma properties are determined as a function of time by numerically integrating the two continuity equations for the electron and positive-ion densities. The processes of electron impact ionization, electron attachment, detachment, and recombination are taken into consideration. The diffusion of the electrons and positive ions in the ambipolar limit is influenced by the presence of negative ions. Runge-Kutta numerical integration of Maxwell's equations together with the above set of plasma transport equations yield the time-dependent plane-wave transmission and reflection coefficients as a function of incident power level for a very wide range of reentry plasma conditions. For one particular set of reentry conditions, graphs are presented of the electron density profile, reflection coefficient, and transmission coefficient as functions of time.

Electron transmission through ultra-thin insulating barriers

We propose a model to explain the exponential dependence of the electron transmission coefficient through ultra-thin (4–12 Å average thickness) evaporated films of Al 2O 3. The mechanism involves molecular pinholes in the Al 2O 3 rather than tunneling.

Mechanism of noise formation in electric conduction in thin metal films

On the basis of an experimental study of the effect of ion absorption on the electrical conduction in thin metallic films, a theory is developed to explain current noise in metal films with a granular structure. According to these experiments, trapping of electrons in the substrate surface modulates the transmission coefficient of electrons in the intergrain tunnelling process which is responsible for the electric conduction in these films. The power spectrum of the noise is calculated and compared with the experimental results.

A model calculation of field emission from 3d bands in nickel

Field emission from narrow, 3d bands of ferromagnetic nickel is discussed. A one-dimensional model, with a triangular surface barrier, is used to calculate the ratio of the transmission coefficient of an electron in a tight-binding, 3d band to that of a free electron of the same energy. The results indicate that, depending on the interatomic crystal spacing chosen, the free electron transmission coefficient is roughly 1 or 2 orders of magnitude greater than the 3d transmission coefficient. In disagreement with previous work, this ratio is independent of the applied electric field at all electron energies.

Response of silicon detectors to monoenergetic electrons with energies between 0.15 and 5.0 MeV

By means of measurements as well as Monte Carlo calculations response functions have been obtained which describe the pulse-height distributions produced by monoenergetic electrons incident perpendicularly on silicon detectors. Generally good agreement has been found between experimental and Monte Carlo results at energies of 0.25, 0.50, 0.75 and 1.00 MeV for detectors with thicknesses of 0.061, 0.105, 0.191, 0.530, 1.0 and 3.0 mm. Additional calculated results have been obtained as follows: (1) response functions at fifteen energies between 0.15 and 5.0 MeV for detectors with ten thicknesses between 0.05 and 10.0 mm; (2) response functions for arrangements in which the silicon detector is shielded partially or completely by other detectors operating in anticoincidence; (3) reflection, transmission and absorption coefficients of electrons for plane-parallel silicon targets.

Investigations of the Proximity Effect by Electron Tunneling

We have investigated the proximity effect in the Ag-Pb, Cu-Pb, and Sn-Pb systems by electron tunneling. A well-defined gap structure is induced in the normal metals by contact with the superconductor and, in tin below its transition temperature, the gap is augmented by the proximity of the lead. The results are in reasonable agreement with a theory of McMillan's and indicate electron transmission coefficients at the Ag-Pb, Cu-Pb, and Sn-Pb interfaces of about 0.1, 0.1, and 0.5, respectively.

Double Barrier in Thin-Film Triodes

The electron transmission coefficient for an asymmetric double barrier model of a thin-film triode is discussed. Two resonant terms appear in the transmission expression, one of which depends on the relative properties of the barriers and the other on the thickness of the base or control film. The results of a detailed calculation for a simplified model are given.