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

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

Nontrivial capacitance behavior, including a negative capacitance (NC) effect, observed in a variety of semiconductor devices, is discussed emphasizing the physical mechanism and the theoretical interpretation of experimental data. The correct interpretation of NC can be based on the analysis of the time-domain transient current in response to a small voltage step or impulse, involving a self-consistent treatment of all relevant physical effects (carrier transport, injection, recharging, etc.). NC appears in the case of the nonmonotonic or positive-valued behavior of the time-derivative of the transient current in response to a small voltage step. The time-domain transient current approach is illustrated by simulation results and experimental studies of quantum well infrared photodetectors (QWIPs). The NC effect in QWIPs has been predicted theoretically and confirmed experimentally. The huge NC phenomenon in QWIP's is due to the nonequilibrium transient injection from the emitter caused by the properties of the injection barrier and the inertia of the QW recharging.

Negative capacitance effect in semiconductor devices

Nontrivial capacitance behavior, including a negative capacitance (NC) effect, observed in a variety of semiconductor devices, is discussed emphasizing the physical mechanism and the theoretical interpretation of experimental data. The correct interpretation of NC can be based on the analysis of the time-domain transient current in response to a small voltage step or impulse, involving a self-consistent treatment of all relevant physical effects (carrier transport, injection, recharging etc.). NC appears in the case of the non-monotonic or positive-valued behavior of the time-derivative of the transient current in response to a small voltage step. The time-domain transient current approach is illustrated by simulation results and experimental studies of quantum well infrared photodetectors (QWIPs). The NC effect in QWIPs has been predicted theoretically and confirmed experimentally. The huge NC phenomenon in QWIPs is due to the non-equilibrium transient injection from the emitter caused by the properties of the injection barrier and the inertia of the QW recharging.

The properties of hot electrons in systems where electrons and phonons experience quantum confinement are reviewed. The modifications to the behaviour of electrons and phonons brought about by confinement are described, particularly with reference to the principal scattering mechanism. The latter include the interaction with longitudinal optical phonons and plasmons, along with carrier-carrier effects. Some conflict in the literature concerning Fuchs-Kliewer polaritons is discussed. Low-temperature interactions with acoustic phonons are described. A central topic is that of energy relaxation, and the experimental and theoretical data relating to this form a large part of the review. Energy relaxation mechanisms in the femtosecond to nanosecond regimes, including intersubband and well-capture processes, are eventually summarized. An equally large section deals with hot-electron transport; in which negative differential resistance and other instabilities associated with parallel transport are discussed before turning to ballistic transport and impact ionization.

https://iopscience.iop.org/article/10.1088/0034-4885/54/2/001/pdf

Hot electrons in low-dimensional structures

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

Preliminary results are presented for a 3-terminal device fabricated by incorporating a narrow quantum well into the collector barrier of a unipolar hot electron transistor. The structure allows unique studies of the mechanism of resonant tunneling in which the carrier injection energy and the bias across the double barrier can be independently varied. The transistor clearly shows an additional current collection threshold representing as much as 10% of the injected current attributable to tunneling via the single subband in the quantum well. This interpretation is confirmed by measurements in perpendicular and parallel magnetic fields despite the fact that theoretical estimates of the resonant tunneling current without scattering are many orders of magnitude smaller, and there are strong indications that elastic scattering in the well is responsible for the enormous discrepancy. The data tend to support proposals (Gueret, 1989a, 1989b; Wolak, 1988) that elastic scattering is responsible for the large valley currents in resonant tunneling diodes, and it appears that the tunnel process may not be completely incoherent as has frequently been assumed up to now.

A study of resonant tunneling in a 3-terminal ballistic device

Quasiclassical behavior of ballistic electrons in a perpendicular magnetic field.

A striking effect of illumination on the vertical nonequilibrium electron transport has been observed in the GaAs‐based tunneling hot electron transfer amplifier (THETA). Weak illumination can considerably increase the transparency of a THETA structure for quasiballistic electrons if the photon energy exceeds the GaAs band gap. The temperature and illumination intensity dependencies indicate that the effect is caused by photoneutralization of ionized impurities which are a major source of hot electron scattering.

Optical suppression of ionized impurity scattering in vertical hot‐electron transport

Bleaching effect of illumination on the vertical hot-electron transport

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