Electron Tunneling Time Research Articles

A novel energy filter using semiconductor superlattices and its application to tunneling time calculations

An artificial quantum-mechanical filter using superlattice structures is proposed in this paper. By gradually changing the barrier widths of a superlattice according to a Gaussian function, a broad-band and almost zero sidelobe transmission profile can be obtained. The WKB approximation is applied to demonstrate the phenomena of abrupt change of transmission profile. The proposed structure allows the incident electrons to be nearly totally transmitted when the impinging electron energy is in the passband. On the other hand, a complete reflection occurs when the impinging energy is in the stopband. By adjusting the structure parameters, the desired passband and stopband of such a filter can be obtained. Time evolution of an electron wavepacket moving through the structure is calculated by numerically solving the time-dependent Schrodinger equation. Numerical results clearly demonstrate the characteristics of total transmission and reflection. By simulating the movement of a totally transmitted wavepacket, ambiguity results from the nature of the wavepacket in the determination of electron tunneling time can be avoided. The generalized concept of matched quantum-mechanical wave impedance (QMWI) analogous to transmission line theory is presented to explain the occurrence of total transmission of the proposed structure. The tunneling time (/spl tau//sub QMWI/) calculated based on the concept of QMWI is compared with the accurate tunneling time obtained by our simulation.

The stationary traversal time for tunnelling

A conceptual experiment is proposed which allows to define the time taken for a particle to traverse a region with arbitrary potential profile under quasi-stationary conditions. Its mathematical representation is used to examine the electron tunnelling time through a rectangular potential barrier. In particular, it is found that in the transparent-barrier limit the electron traverses the barrier quasi-ballistically, whereas in the opaque-barrier limit the tunneling time rises exponentially with the barrier width.

Carrier escape tunnelling out of shallow multiple quantum wells studied by transient four-wave mixing

We demonstrate that transient optical dephasing experiments on electrically biased, shallow multiple quantum wells offer the unique possibility of studying the first step in carrier sweep-out, namely the escape tunnelling out of the individual quantum wells. We perform transient four-wave mixing experiments on two shallow GaAs/AlxGa1-xAs multiple quantum well samples with x=0.04 and x=0.06. We find that the electron tunnelling times out of the quasibound n=1 quantum well states into the continuum states decrease with increasing electric field, and lie in the subpicosecond regime at high fields. In addition, for the x=0.06 sample, the experimentally determined escape rate is resonantly enhanced when the quasibound n=1 quantum well state couples to the n=2 state embedded in the continuum above the second-nearest-neighbour well.

Dependence of resonant electron and hole tunnelling times between quantum wells on barrier thickness

We investigated resonant tunnelling of electrons and holes between coupled quantum wells using time-resolved luminescence spectroscopy. Exponential dependence of tunnelling times on barrier width is observed for electrons but not for holes. The tunnelling times of electrons are correctly described by a model which takes into account inhomogeneous broadening.

Study of tunneling time in tunneling BI‐quantum‐well and resonant tuneling barrier structures

AbstractWe studied the electron tunneling time in tunneling bi‐quantum‐well and resonant tunneling burrier structures with a pump‐probe photo‐luminescence system using optical mixing. The tunneling time decreased as the temperature increased, which is attributed to electrons in an exciton state thermalizing into free electrons having a faster tunneling time. © 1994 John Wiley & Sons, Inc.

Electron tunneling time through a heterostructure potential barrier

The phase time of an electron tunneling through a heterostructure potential barrier is derived, including the position-dependent effective-mass effect. The usual phase time of the tunneling derived assuming a homogeneous effective mass deviates from this result by -15% ∼ -28%.

Escape tunneling out of shallow multiple quantum wells studied by transient four-wave mixing

We demonstrate that transient optical dephasing experiments on electrically biased, shallow multiple quantum wells offer the unique possibility of studying the first step in carrier sweep-out, namely, the tunneling escape out of the individual quantum wells. We find that the electron tunneling times out of the quasibound n=1 quantum well states into the continuum states lie in the subpicosecond regime at high electric fields. In addition, the experimentally determined escape rate is resonantly enhanced when the quasibound n=1 quantum well state couples with the resonant n=2 continuum state originating from the second-nearest neighbor well.

Differences in Tunneling Time between 77 K and Room Temperature for Tunneling Biquantum Wells

We measured the recovery time from excitonic absorption bleaching in tunneling biquantum wells at 77 K and room temperature. The absorption recovery time corresponds to the tunneling time of electrons from narrow to wide wells. We have found that tunneling at 77 K is about 2.5 times slower than at room temperature.

Field Ionization of Shallow Donors in Germanium

Transient currents due to field ionization of shallow donors are investigated in thin germanium samples by transient tunneling spectroscopy. In particular, the electron tunneling time from antimony atoms to the conduction band is measured as a function of electric field strength, lattice temperature, and electric field direction. The results are compared with a simple hydrogenic model. Various factors which may influence the TTS spectra, such as impurity impact ionization, doping inhomogeneity, etc., are discussed. It is concluded that pure electron tunneling from the ground 1 s state of antimony atoms takes place at lattice temperatures smaller than 7 K. [Russian text ignoured]

Tunneling through Single AlGaAs Barriers

AbstractTunneling transfer through Al0.35Ga0.65As barriers is studied in asymmetric double quantum well structures by time‐resolved photoluminescence measurements in the pico‐ and femtosecond regime. A large variety of electron and hole resonances is detected when electric fields of both signs are externally applied. The ground state resonance shifts, when the electrons tunnel in the reverse direction, revealing the importance of excitonic effects. Longitudinal optical phonon assisted tunneling plays a minor role for narrow quantum wells in comparison to impurity or interface roughness assisted transfer. Resonant electron tunneling times depend exponentially on the integrated square root of the tunneling barrier height and are an order of magnitude faster than resonant hole tunneling times. The n = 2 to n = 1 electronic intersubband scattering time in a 10 nm quantum well is determined to be 550 fs measuring the transfer time through a thin barrier.

Effect of Γ–X mixing on electron tunneling times in GaAs/AlAs double barrier heterostructures

The effect of Γ–X mixing on electron tunneling time in GaAs/AlAs symmetric double barrier heterostructures is studied theoretically using an empirical tight-binding band structure model. It is found that the Γ quasibound state tunneling times can be shortened or lengthened by Γ–X mixing, depending on whether the AlAs barriers consist of an even or odd number of monolayers. This is attributed to the interference between the Γ and X conduction channels in the AlAs barriers.

Tunnelling of electrons and holes in asymmetric double quantum well structures

Simultaneous measurements of electron and hole tunnelling times, and the exciton formation rate in asymmetric double well structures are achieved by the nonlinear double-pulse photoluminescence cross-correlation technique.

Resonances in tunnelling between quantum wells

Time-resolved photoluminescence measurements in the picosecond regime on GaAs/Al0.35Ga0.65As asymmetric double quantum well structures with perpendicular electric fields applied in both directions are reported. A large number of electron and hole resonances are detected. A splitting of the ground state resonances reveals the importance of excitonic effects. Longitudinal optical phonon assisted tunnelling plays a minor role for narrow quantum wells in comparison with impurity or interface roughness assisted transfer. Resonant electron tunnelling times depend exponentially on the square root of the effective barrier height and are an order of magnitude shorter than resonant hole tunnelling times.

Effect of band mixing on hole-tunneling times in GaAs/AlAs double-barrier heterostructures.

We examine the influence of band mixing on hole-tunneling times in GaAs/AlAs double-barrier heterostructures using the eight-band effective bond-orbital model. We find that mixing of heavy-hole and light-hole states in the valence subbands can substantially reduce hole-tunneling times from the values predicted by the Kronig-Penney model, which does not account for band mixing. These results are in agreement with the experimental measurements of Jackson et al. [Appl. Phys. Lett. 54, 552 (1989)], indicating that hole-tunneling times are much shorter than predicted by the Kronig-Penney model, and comparable in fact to electron-tunneling times. We also compare our calculation with an earlier phenomenological model for incorporating band-mixing effects in the calculation of hole-tunneling times.

Direct determination of the electron-tunneling escape time from a GaAs/AlxGa1-xAs quantum well by transient-capacitance spectroscopy.

Direct determination of the electron-tunneling escape time from a GaAs/AlxGa1-xAs quantum well by transient-capacitance spectroscopy.

Tunnel ionization of donors in pure germanium

Abstract Transient currents due to field ionization of shallow donors at the liquid helium temperature are investigated in thin germanium samples by transient tunneling spectroscopy (TTS). The electron tunneling time from the antimony atoms to the conduction band has been measured as a function of electric field strength and compared with a simple scaled hydrogenic model.

Longitudinal-optical-phonon assisted tunneling in tunneling bi-quantum well structures

We discuss the electron tunneling time observed in a new AlGaAs/GaAs superlattice structure, the tunneling bi-quantum well (TBQ). To calculate the nonresonant tunneling time, we made experiments on resonant tunneling to confirm that the 60% rule of conduction-band discontinuity accurately evaluates the free tunneling probability of electrons. We found that the observed recovery time agrees quite well with the calculated longitudinal optical phonon emission tunneling time for thin (≤ 10 monolayers) barriers.

Search for long-range Coulomb interaction in disordered metals

The theory of disordered electron systems predicts that the dynamical Coulomb interaction (ω > 0) is strongly enhanced and in particular long ranged. This modification of the Coulomb interaction has many important consequences on the behavior of disordered electron systems. However, its effect has only been observed indirectly. Therefore we have looked for a direct observation of this long-ranged character. We used a sandwich of two disordered metal films separated by an insulating layer. For a long-range Coulomb interaction the two films should assist each other in screening. The In( T) dependence of the resistance, i.e., the Coulomb anomaly, is used to determine the strength of the Coulomb interaction. The coupled two films represent a tunneling junction with a tunneling resistance of a few μΩ. The electronic properties of the junction, in particular, the tunneling time, are measured by means of weak localization. The thickness of the tunneling barrier is chosen so that the tunneling time of the conduction electrons is larger than the thermal coherence time ℏ / k B T. Our measurements do not support the current theory of the long-range character of the dynamical Coulomb interaction and represent a challenge to our present understanding of the Coulomb effect in disordered electron systems.

Electron and hole tunneling times in GaAs/AlGaAs asymmetric double quantum well heterostructures

We present CW and time-resolved photoluminescence measurements on GaAs/AlGaAs asymmetric double quantum well heterostructures. Several samples (eight) have been considered in order to study the influence, on the carrier tunneling process, of both barrier thickness and energy separation between the levels in the different wells. A comparison between photoluminescence decay time of excitonic recombinations in the narrow well and wide well, under resonant and non resonant excitation, allows us to determine both the electron and hole tunneling times. Evidence of non resonant and LO phonon-assisted electron tunneling, resonant and near-resonant hole tunneling is found and discussed.

Time-Resolved Optical Investigation of Tunneling of Carriers Through Single AlxGa1-xAs Barriers

An asymmetric double quantum well structure consisting of a wide and a narrow quantum well separated by AlxGa1-xAs barriers of various thicknesses is used to investigate resonant and nonresonant tunneling of electrons as well as holes through a single barrier. The carrier transfer times are obtained by tracing the luminescence decay of the two quantum wells with picosecond time resolution as a function of an applied electric field. For the first time, resonant and nonresonant electron and hole tunneling times in one single structure are reported. Our results are compared with those of other groups. Idealized theoretical models cannot explain the experimental values.