Quantum Mechanical Transmission Coefficient Research Articles

Suppressed pair creation due to electron-positron attraction

We propose a coupled Dirac sea approach to examine numerically the electron-positron pair creation process with interfermionic interactions in a supercritical background field. In this approach the Hilbert space is doubled, leading to two separate Dirac equations for the dynamics of the electrons and the positrons. It permits us to remove the unphysical self-repulsion while the internal electric fields that couple different fermions are determined from the Maxwell equations. The time evolution of the yield and the spatial distribution, as well as the energy spectra of the particles, show that the attractive force between the created particles decreases the pair creation probability, independent of the spatial characteristics of the force-intermediating internal fields. This decrease is accompanied by shifts in the kinetic energy spectrum of the emitted particles. These findings are supported by an independent model that predicts the creation rate based on the quantum mechanical transmission coefficient.

Conductive-AFM topography and current maps simulator for the study of polycrystalline high-k dielectrics

In this work, a simulator of conductive atomic force microscopy (C-AFM) was developed to reproduce topography and current maps. In order to test the results, the authors used the simulator to investigate the influence of the C-AFM tip on topography measurements of polycrystalline high-k dielectrics, and compared the results with experimental data. The results show that this tool can produce topography images with the same morphological characteristics as the experimental samples under study. Additionally, the current at each location of the dielectric stack was calculated. The quantum mechanical transmission coefficient and tunneling current were obtained from the band diagram by applying the Airy wavefunction approach. Good agreement between experimental and simulation results indicates that the tool can be very useful for evaluating how the experimental parameters influence C-AFM measurements.

Pair creation rates for one-dimensional fermionic and bosonic vacua

We compare the creation rates for particle-antiparticle pairs produced by a supercritical force field for fermionic and bosonic model systems. The rates obtained from the Dirac and Klein-Gordon equations can be computed directly from the quantum-mechanical transmission coefficients describing the scattering of an incoming particle with the supercritical potential barrier. We provide a unified framework that shows that the bosonic rates can exceed the fermionic ones, as one could expect from the Pauli-exclusion principle for the fermion system. This imbalance for small but supercritical forces is associated with the occurrence of negative bosonic transmission coefficients of arbitrary size for the Klein-Gordon system, while the Dirac coefficient is positive and bound by unity. We confirm the transmission coefficients with time-dependent scattering simulations. For large forces, however, the fermionic and bosonic pair-creation rates are surprisingly close to each other. The predicted pair creation rates also match the slopes of the time-dependent particle probabilities obtained from large-scale ab initio numerical simulations based on quantum field theory.

Quantum mechanical electron transmission coefficient at interfaces and ballistic electron emission microscopy

We derive the quantum mechanical transmission coefficient for the electron transport across a plane interface of a metal/semiconductor or semiconductor/semiconductor heterostructure. An effective mass model is used for the conduction band in each layer of the system. Non-diagonal mass tensors and indirect band minima are covered by the model. The quantum effects for the electron transmission are investigated for the system Au(111)/Si(111) as a test case. We find sizeable corrections originating from quantum effects.

A Numerical Method for the Calculation of Transmission Coefficient11The project supported by National Natural Science Foundation of China under grant 19104010 and by the China Center for Advanced Science and Technology (CCAST)

A numerical method is presented for calculating the quantum-mechanical transmission coefficient of one-dimensional problems with potentials of arbitrary shapes. The method is demonstrated to give very accurate results on two solvable examples. The numerical error in the calculated transmission coefficient is proportional to the second power of integration step size for potentials without discontinuities; for potentials with discontinuities, the dependence is linear.

Rectification Properties of Asymmetrical Superlattices

A rectifying superlattice which can be used for detecting THz waves is proposed. The device is created by using an effective-mass superlattice in which the superlattice cycle is gradually changed. The operating principle is based on the fact that the quantum mechanical transmission coefficient with asymmetrical geometry is asymmetrical with respect to the applied voltage. The forward current is several orders in magnitude greater than the reverse current at a relatively low applied voltage. This feature is potentially useful for detecting and mixing small signals at THz frequencies.

Exact solution of the Schrodinger equation across an arbitrary one-dimensional piecewise-linear potential barrier

A simple yet exact method of solving the Schrodinger equation across an arbitrary one-dimensional piecewise-linear potential is described. It is based on the analytical solution of the Schrodinger equation across a linear potential, where the solution can be expressed as a linear combination of the Airy functions. Proper boundary conditions are imposed at the interface between adjacent linear intervals of the potential, and a transfer-matrix procedure is utilized in the derivation. The quantum mechanical transmission coefficient across a potential barrier and eigenenergies of a potential well can also be easily calculated using this method.

Electron Transport across a Semiconductor Heterojunction

An electron-transport theory is presented for an isotype semiconductor heterojunction diode with energy-band and effective-mass discontinuities. During an interface electron transfer, the electron total energy and transverse momentum are assumed to be conserved. After the quantum-mechanical transmission coefficient is determined with a tight-binding connection of the electron wave functions, the boundary conditions for the momentum distribution function are obtained, assuming a conservation of electron flux. These conditions are applied to quasi-Fermi energy formulation in an approximate way. Numerical examples in an AlxGa1-xAs/GaAs junction indicate that due considerations concerning interface electron-transfer effects are necessary for the design and simulation of longitudinal-type heterojunction devices.

Analytical calculation of the quantum-mechanical transmission coefficient for a triangular, planar-doped potential barrier

The thermionic emission limit for current transport in planar-doped triangular barrier devices is determined by the quantum-mechanical reflection of the charge carriers at the barrier. In this paper we present an analytical calculation for the quantum-mechanical transmission and reflection coefficients for such a barrier.

Interface resistance

Interface resistance is studied by using the Landauer formula which relates the resistance to the quantum mechanical transmission coefficient. A simple rederivation of the Landauer formula is given. Using a step-like potential barrier as a model for the metal-semiconductor contact an analytical expression for the effective Richardson constant is derived. As an other application the grain boundary resistance in polycrystalline semiconductors is studied. The short-range potential fluctuation associated with the grain boundary is described by a rectangular potential barrier. The results for the grain boundary limited mobility cover both the strong and weak scattering regimes.

Calculation of the transmission coefficient of low-energy (

A simple approximation method is developed for calculating the quantum-mechanical transmission coefficient T( E) of a slow electron (in the energy range E < 20 eV) for the case of a one-dimensional surface potential barrier model which simulates most closely the real shape of the potential acting on an electron at a metal-vacuum interface. Although this method is developed for this particular case, it should permit, in principle, the direct investigation of arbitrary potential-energy functions.

Carrier transport across heterojunction interfaces

A general theory is presented to describe the carrier transport across heterojunction interfaces. In matching the boundary conditions at the interface, the conservation of total energy and perpendicular momentum is assumed and the difference of effective masses on two sides of the junction is taken into account. The quantum mechanical transmission coefficient is calculated by a combined numerical and WKB method. Application of the present model to an Al xGa 1−xAsGaAs N- n heterojunction is performed and it gives rise to rectifying characteristics together with non-saturated reverse current. Comparison with the classical thermionic emission model is made to show the significance of tunneling and effect of quantum mechanical reflection.

Internal photoemission and quantum-mechanical transmission coefficient

The effect of the quantum-mechanical transmission coefficient on the photoemissive quantum yield in sandwich structures with thin insulators is investigated for the trapezoidal barrier and for the barrier with a parabolic top. The transmission coefficient evaluated in an explicit form from the exact solution of the Schrodinger equation is compared with that obtained from the modified WKB approximation and its applicability to real barriers is discussed. The resulting Fowler plots (square root of the quantum yield plotted against photon energy) deviate from the straight line in the low-energy region; this deviation corresponds in its magnitude and shape to the so-called low-energy tail known from experiment. Moreover, the Fowler plots obtained using the transmission coefficient evaluated exactly from the Schrodinger equation show weak superimposed oscillations; this effect results from the oscillations in the transmission coefficient which have their origin in the interference of electron waves within the insulator. Es wird der Einflus des quantenmechanischen Transmissionskoeffizienten auf die Quantenausbeute der Photoemission in Sandwichstrukturen mit dunnen Isolatoren fur die trapezformige Barriere und fur die Barriere mit parabolischem Gipfel untersucht. Der in expliziter Form aus der exakten Losung der Schrodingergleichung berechnete Transmissionskoeffizient wird mit dem aus der modifizierten WKB-Naherung verglichen und seine Anwendung auf reale Barrieren diskutiert. Die resultierenden Fowler-Kurven (Quadratwurzel der Quantenausbeute uber der Photonenenergie) weichen im niederenergetischen Bereich von der Geraden ab; diese Abweichung entspricht in Grose und Form dem niederenergetischen Teil, wie er experimentell bekannt ist. Daruberhinaus zeigen die Fowler-Kurven, die mit dem aus der Schrodingergleichung exakt berechneten Transmissionskoeffizienten erhalten wurden, schwache uberlagerte Oszillationen; dieser Effekt ruhrt von Oszillationen im Transmissionskoeffizienten her, die ihren Ursprung in der Interferenz der Elektronenwellen innerhalb des Isolators haben.

Proton Tunneling in the Hydrogen-Evolution Reaction

The quantum-mechanical theory of tunneling was applied to the proton-discharge step of the hydrogen-evolution reaction. An unsymmetric Eckart barrier with allowance for zero-point energies was employed. The quantum-mechanical rate iq was calculated by integration with a digital computer for a large number of combinations of barrier width, barrier heights, heats of reaction, and temperatures over a large potential range for protium, deuterium, and tritium. From these results the quantum-mechanical transmission coefficient τ and the quantum-mechanical correction Γ to the separation factor, Tafel slopes, and activation energies were calculated. By comparison to observed values of SH,T, and SH,T as a function of temperature and potential the most probable barrier parameters were obtained. These values were tested by comparison of calculated and observed activation energy, Tafel slopes, SH,D as a function of potential, and the rate of protium evolution at high cathodic overpotentials as a function of temperature. The degree of proton tunneling was found to be significant being 69% at a cathodic overpotential of 1 V for Hg in acid solution.

The Transmission Coefficient in the Theory of Absolute Reaction Rates

The activated complex theory of reaction rates is discussed critically. The transmission coefficients for a number of idealized energy surfaces have been computed quantum mechanically. It appears that curvature of the reaction path may introduce activation energy in addition to that caused by constriction and elevation of the energy valley. Except at low temperatures, this additional activation energy is almost negligible. However, it may contribute to the separation of isotopes, where small differences in activation energy are important. For systems in thermal equilibrium at room temperatures and above, the average quantum mechanical transmission coefficient is found to differ insignificantly from that calculated by classical mechanics.