Rectangular potential barrier

Abstract: A formula is derived for the electric tunnel effect through a potential barrier of arbitrary shape existing in a thin insulating film. The formula is applied to a rectangular barrier with and without image forces. In the image force problem, the true image potential is considered and compared to the approximate parabolic solution derived by Holm and Kirschstein. The anomalies associated with Holm's expression for the intermediate voltage characteristic are resolved. The effect of the dielectric constant of the insulating film is discussed in detail, and it is shown that this constant affects the temperature dependence of the J‐V characteristic of a tunnel junction.

Abstract: We present first-principles based calculations of the tunneling conductance and magnetoconductance of epitaxial $\mathrm{Fe}(100)|\mathrm{MgO}(100)|\mathrm{Fe}(100)$ sandwiches. Our results indicate that tunneling is much more interesting and complicated than the simple barrier model used previously. We obtain the following general results: (1) Tunneling conductance depends strongly on the symmetry of the Bloch states in the electrodes and of the evanescent states in the barrier layer. (2) Bloch states of different symmetry decay at different rates within the barrier. The decay rate is determined by the complex energy bands of the same symmetry in the barrier. (3) There may be quantum interference between the decaying states in the barrier. This leads to an oscillatory dependence of the tunneling current on ${k}_{\ensuremath{\Vert}}$ and a damped oscillatory dependence on barrier thickness. (4) Interfacial resonance states can allow particular Bloch states to tunnel efficiently through the barrier. For $\mathrm{Fe}(100)|\mathrm{MgO}(100)|\mathrm{Fe}(100)$ our calculations indicate that quite different tunneling mechanisms dominate the conductance in the two spin channels. In the majority channel the conductance is primarily via Bloch electrons with small transverse momentum. One particular state with ${\ensuremath{\Delta}}_{1}$ symmetry is able to effectively couple from the Fe into the MgO. In the minority channel the conductance is primarily through interface resonance states especially for thinner layers. We predict a large magnetoresistance that increases with barrier thickness.

Abstract: We present a new analytical potential fluctuations model for the interpretation of current/voltage and capacitance/voltage measurements on spatially inhomogeneous Schottky contacts. A new evaluation schema of current and capacitance barriers permits a quantitative analysis of spatially distributed Schottky barriers. In addition, our analysis shows also that the ideality coefficient n of abrupt Schottky contacts reflects the deformation of the barrier distribution under applied bias; a general temperature dependence for the ideality n is predicted. Our model offers a solution for the so‐called T0 problem. Not only our own measurements on PtSi/Si diodes, but also previously published ideality data for Schottky diodes on Si, GaAs, and InP agree with our theory.

Abstract: The dependence of the barrier height of metal-semiconductor systems upon the metal work function is derived based on the following assumptions: (1) the contact between the metal and the semiconductor has an interfacial layer of the order of atomic dimensions; it is further assumed that this layer is transparent to electrons with energy greater than the potential barrier but can withstand potential across it. (2) The surface state density (per unit area per electron volt) at the interface is a property only of the semiconductor surface and is independent of the metal. The barrier height φВn is defined here as the energy needed by an electron at the Fermi level in the metal to enter the conduction band of the semiconductor.