Alberto Rubio

Decay widths for double‐barrier resonant tunneling

Calculations of the decay width and the partial decay widths for double‐barrier resonant tunneling structures are discussed using a description of resonances in terms of the complex energy poles of the transmission amplitude of the system and comparing it with the corresponding Wentzel–Kramers–Brillouin approximations. The effect of the asymmetry of the potential profile is emphasized.

An expansion of continuum wave functions in terms of resonant states: (II). Solvable models

Abstract This paper applies the formalism developed in part I which provides a purely discrete expansion for a continuum wave solution of the Schrodinger equation in terms of resonant states along the interior region of a finite range interaction. We consider two exactly solvable models for several values of the distance and momenta on and off resonance. Our results are compared with a recent approach by Bang and collaborators which involves subtraction terms. It is found that along the internal region the subtraction terms are not in general negligible. Our work substantiates an expression for the continuum wave function near resonance. We also obtain an equation for time delay in terms of resonant states.

Percolation in 2-D random systems: From isotropic to directed

A computer simulation method is used to study percolation for two-dimensional random systems. Percolation is analyzed as it changes from the isotropic to the directed regime. A parameter that measures the degree of anisotropy is introduced and for a set of values that range between the two regimes we calculate the percolation radius, the critical exponents and the fractal dimension of critical clusters. The results obtained for the isotropic limit are consistent with well known values. The new results for the directed limit and intermediate cases are compared with those obtained from other models and may be used in the description of various physical problems.

On the transit time of electrons in resonant structures

A resonance formalism based on the notions of partial decay widths and resonance energy [1] is used to compare the transmission phase time, the dwell time and the Larmor time near resonance energy for coherent processes in one dimension. It turns out that except for the case of full transmission, i.e., the transmission coefficient equal to unity, the above notions do not yield an appropriate definition for the transit time of an electron through the system. On the other hand, the resonance formalism is used to support an alternative definition of the transit time given by τtr = 14(h/Γ0n + h/ΓLn) where Γ0n and ΓLn stand for the two partial decay widths associated to the corresponding two channels in a one-dimensional system [2]. For a double-barrier structure the time scale provided by τtr turns out to be inversely proportional to the tunneling current integrated across the resonance width.

Transit time for resonant tunneling in semiconductor heterostructures

We consider a resonance formalism to obtain an expression for the transit time in double‐barrier resonant structures in terms of the partial decay widths Γ0n and ΓLn as τtr = (ℏ/Γ0n + ℏ/ΓLn)/4. We demonstrate that the time scale associated to the tunneling current density integrated across a sharp resonance is inversely proportional to τtr. We also show that the dwell time, the transmission phase time, and the Larmor traversal time are not appropriate notions for the transit time except when the partial decay widths are equal as is the case for a symmetric potential profile.