H.Q. Nguyen

Use of a scanning tunneling microscope to rectify optical frequencies and measure an operational tunneling time

This paper elaborates on the idea, recently advanced by the authors, of using the scanning tunneling microscope (STM) in new experiments on laser frequency synthesis and laser rectification at optical frequencies. We first introduce the subject of harmonic generation and mixing of laser beams by the related tunneling device called ‘‘point contact diode.’’ Then, we present new quasistatic current–voltage characteristics of several STM junctions, emphasizing their nonlinear and rectifying aspects. The physical origin of the observed asymmetrical I–V curves is discussed. Finally, we describe the proposed rectification experiment which should result in an operationally meaningful definition of a tunneling time for electrons crossing an STM junction and we present some very preliminary results.

Study of metal surfaces by scanning tunneling microscopy with field ion microscopy

The reconstruction of Au and Ni surfaces has been studied by scanning tunneling microscopy (STM). The correlation between the tunneling tip geometry, observed by field ion microscopy, and the resultant STM image leads to an operational definition of STM resolution. New structural models for Ni(110)–H and Ni(110)–Au surfaces are proposed.

Model studies of tunneling time

The precise definition and physical interpretation of a tunneling time is a fundamental problem in quantum mechanics. The lack of a well‐defined time operator in quantum theory precludes the calculation of time in terms of an expectation value. Consequently, model calculations and simulation studies have been proposed and used to determine the time for a particle to traverse a quantum‐mechanical barrier. The results offer both qualitatively and quantitatively, disparate predictions. One of the more commonly used approaches is the phase method, which we have applied to several one‐dimensional model potentials to show that the tunneling time is characterized by the ratio of the typical decay length in the barrier to the incident velocity, τ∼(1/κ)/v0. We also show that the phase and the spin precession methods are equivalent when the magnetic field is applied throughout the space containing the particle wave function and the tunneling barrier. In principle, the spin precession method can be regarded as an op...

Computer simulation of a wave packet tunneling through a square barrier

It is shown that, for energies E<or=V/sub 0/, the barrier height, the typical tunneling time is on the order of 10/sup -15/ s. The traversal time as a function of kinetic energy is locally symmetric near E=V/sub 0/. The tunneling time depends on the shape of the wave packet. The tunneling time is linearly dependent on barrier thickness for a wave packet with finite width. These conclusions are compared with the results obtained from other methods for estimating tunneling times.

An analytical solution for the WKB transmission coefficient for potential functions up to quartic order: Application to tunneling in metal-vacuum-metal junctions

A technique is described for obtaining an analytical solution to the WKB integral in which the integrand consists of a rational function of x and P(x) , where P(x) is a polynomial of order four or less. For this class of potentials, the integral can be evaluated in terms of elliptic integrals. As a prototype of this technique, the WKB transmission coefficient for the Simmons approximation to the multiple image interactions in an MVM planar tunneling junction is calculated. This transmission coefficient is used to calculate the J-V characteristics for a planar W-W junction as a function of temperature for different electrode separations. Comparison of the J-V characteristics with those obtained from a numerical evaluation of the same WKB transmission coefficient showed good to excellent agreement with the analytical solution for barrier thickness ranging from 1–3 nm. An important advantage of the analytical solution is that the algorithm for it is about 1–2 orders of magnitude faster than the numerical algorithm.