The old question of "How long does it take to tunnel through a barrier?" has acquired new urgency with the advent of techniques for the fabrication of semiconductor structures in the nanometer range. For the restricted problem of tunneling in a scattering configuration, a coherent picture is now emerging. The dwell time ${\ensuremath{\tau}}_{D}$ has the status of an exact statement of the time spent in a region of space, averaged over all incoming particles. The phase times ${\ensuremath{\tau}}_{T}^{\ensuremath{\phi}}$ and ${\ensuremath{\tau}}_{R}^{\ensuremath{\phi}}$ are defined separately for transmitted and reflected particles. They are asymptotic statements on completed scattering events and include self-interference delays as well as the time spent in the barrier. Consequently, neither the dwell time nor the phase times can answer the question of how much time a transmitted (alternatively, reflected) particle spent in the barrier region. Our discussion of this question relies on a few simple criteria: (1) The average duration of a physical process must be real. (2) Since transmission and reflection are mutually exclusive events, the times ${\ensuremath{\tau}}_{T}$ and ${\ensuremath{\tau}}_{R}$ spent in the barrier region are, if they exist, conditional averages. Consequently, they must obey the identity ${\ensuremath{\tau}}_{D}=T{\ensuremath{\tau}}_{T}+R{\ensuremath{\tau}}_{R}$, where $T$ and $R$ are the transmission and reflection probabilities, respectively. The existence of this identity distinguishes tunneling in a scattering configuration from tunneling out of a metastable state. (3) Any proposed ${\ensuremath{\tau}}_{T}$ and ${\ensuremath{\tau}}_{R}$ must meet every requirement that can be constructed from ${\ensuremath{\tau}}_{D}$. On the basis of (2), the naively extrapolated phase times, as well as the B\"uttiker-Landauer time, must be rejected. The local Larmor times, as introduced by Baz', satisfy (2), but not every criterion of type (3). The local Larmor clock is therefore unreliable. The asymptotic Larmor clock shows the phase times, as it should. Finally, the inverse characteristic frequency of an oscillating barrier cannot always be defined. It is shown not to represent the duration of the tunneling process. This leaves the dwell time and the phase times as the only well-established times in this context. It also leaves open the question of the length of time a transmitted particle spends in the barrier region. It is not clear that a generally valid answer to this question exists.

Tunneling times: a critical review

important corrections are presented. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ‘‘mesoscopic’’ level and is derived from the ‘‘microscopic’’ wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. This approach is extended to mesoscopic correlations between multiple scattered intensities that arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to microwaves, sound waves, and noninteracting electrons. [S0034-6861(99)00601-7]

/pdf/multiple-scattering-of-classical-waves-microscopy-mesoscopy-3cjkvpzjmd.pdf

Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion

Over sixty years ago, it was suggested that there is a time associated with the passage of a particle under a tunneling barrier. The existence of such a time is now well accepted; in fact the time has been measured experimentally. There is no clear consensus, however, about the existence of a simple expression for this time, and the exact nature of that expression. The proposed expressions fall into three main classes. The authors argue that expressions based on following a feature of a wave packet through the barrier have little physical significance. A second class tries to identify a set of classical paths associated with the quantum-mechanical motion and then tries to average over these. This class is too diverse to permit assessment as a single entity. The third class invokes a physical clock involving degrees of freedom in addition to that involved in tunneling. This not only is a prescription for the derivation of expressions for the traversal time but also leads to a direct relationship to experiment.

Barrier interaction time in tunneling

Respiratory sounds : Advances beyond the stethoscope

Multiple ionization of neon, argon and xenon in a high-intensity Ti:Sapphire laser field has been studied Ion yield curves of xenon versus laser intensity have been obtained for the first six charges Curves of charges 2+ to 6+ present obvious structures which can be attributed to the occurrence of non-sequential ionization processes Also, comparison of the ion yields of the first three charges of Ar with previously obtained results inside a different laser field (Nd:Glass laser , ) indicates that non-sequential ionization is strongly wavelength dependent

Non-sequential multiple ionization of rare gas atoms in a Ti:Sapphire laser field

Tunneling in low‐barrier GaAs/AlxGa1−xAs/GaAs heterostructures has been systematically investigated over a wide range of barrier heights and thicknesses. Measured conductance data have been compared with tunnel conductances calculated with and without the image potential correction. Experimental evidence is found for the validity of the static image correction in the limit of large tunneling times, and for the occurrence of dynamic effects in the limit of short tunneling times.

Experimental observation of the dynamical image potential in extremely low GaAs/AlxGa1−xAs/GaAs tunnel barriers

Investigation of possible dynamic polarization effects on the transmission probability of n-GaAs/AlxGa1−xAs/n-GaAs tunnel barriers

We present data obtained on a set of symmetric GaAs/AlGaAs double‐barrier quantum‐well structures in which the thickness of the AlGaAs barriers has been systematically varied from 31 to 7.5 nm. Low‐temperature I(V ) characteristics, temperature dependencies, and magnetotunneling have been investigated. Our data suggest a dominance of sequential tunneling processes in the range investigated and point to interface roughness in the well as the possible cause for the large valley currents. Our best devices exhibit a current peak‐to‐valley ratio of about 20.

Investigations on resonant tunneling in III‐V heterostructures

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Experimental observation of the dynamical image potential in extremely low GaAs/AlxGa1−xAs/GaAs tunnel barriers

Investigation of possible dynamic polarization effects on the transmission probability of n-GaAs/AlxGa1−xAs/n-GaAs tunnel barriers

Investigations on resonant tunneling in III‐V heterostructures