Landauer-Buttiker formula for time-dependent transport through resonant-tunneling structures: A nonequilibrium Green's function approach

A nonequilibrium Green's-function formalism is employed to study the time-dependent transport through resonant-tunneling structures. With this formalism, we derive a time-dependent Landauer-Buttiker formula that guarantees current conservation and gauge invariance. Furthermore, we apply the formula to calculate the response behaviors of the resonant-tunneling structures in the presence of rectangular-pulse and harmonic-modulation fields. The results show that the displacement current plays the role of retarding the tunneling current.

TUNNELING ESCAPE TIME OF ELECTRONS THROUGH DOUBLE-BARRIER RESONANT-TUNNELING STRUCTURES

Tunneling escape of electrons from quantum wells (QWs) has systematically been studied in an arbitrarily multilayered heterostructures, both theoretically and experimentally. A wave packet method is developed to calculate the bias dependence of tunneling escape time (TET) in a three-barrier, two-well structure. Moreover, by considering the time variation of the band-edge profile in the escape transient, arising from the decay of injected electrons in QWs, we demonstrate that the actual escape time of certain amount of charge from QWs, instead of single electron, could be much longer than that for a single electron, say, by two orders of magnitude at resonance. The broadening of resonance may also be expected from the same mechanism before invoking various inhomogeneous and homogeneous broadening. To perform a close comparison between theory and experiment, we have developed a new method to measure TET by monitoring transient current response (TCR), stemming from tunneling escape of electrons out of QWs in a similar heterostructure. The time resolution achieved by this new method reaches to several tens ns, nearly three orders of magnitude faster than that by previous transient-capacitance spectroscopy (TCS). The measured TET shows an U-shaped, nonmonotonic dependence on bias, unambiguously indicating resonant tunneling escape of electrons from an emitter well through the DBRTS in the down-stream direction. The minimum value of TET obtained at resonance is accordance with charging effect and its time variation of injected electrons. A close comparison with the theory has been made to imply that the dynamic build-up of electrons in DBRTS might play an important role for a greatly suppressed tunneling escape rate in the vicinity of resonance.

GIANT CAPACITANCE OSCILLATIONS RELATED TO THE QUANTUM CAPACITANCE IN GAAS ALAS SUPERLATTICES

We have observed periodic current and capacitance oscillations with increasing bias on doped GaAs/AlAs superlattices at a temperature of 77 K. The maximum of the observed capacitance is larger than usual geometric capacitances in superlattices, being comparable to the quantum capacitance of the two-dimensional (2D) electron system proposed by Luryi. A model based on well-to-well sequential resonant tunneling due to the movement of the boundary between the electric field domains in superlattice was proposed to explain the origin of the giant capacitance oscillations. It was demonstrated that the capacitance at the peaks of capacitance-voltage (C-V) characteristics reflects the quantum capacitance of the space-charge region at the boundary between the domains (a novel 2D electron system).

Electron tunneling through a planar single barrier in HgTe quantum wells with inverted band structures

We present a theoretical study on the electron tunneling through a single barrier created in a two-dimensional electron gas (2DEG) and quantum spin Hall (QSH) bar in a HgTe/CdTe quantum well with inverted band structures. For the 2DEG, the transmission shows the Fabry-Perot resonances for the interband tunneling process and is blocked when the incident energy lies in the bulk gap of the barrier region. For the QSH bar, the transmission gap is reduced to the edge gap caused by the finite size effect. Instead, transmission dips appear due to the interference between the edge states and the bound states originated from the bulk states. Such a Fano-like resonance leads to a sharp dip in the transmission which can be observed experimentally.

Tunneling magnetoresistance in (Ga,Mn)As/Al-O/CoFeB hybrid structures

Tunneling magnetoresistance (TMR) in Ga(0.9)2Mn(0.08)As/Al-O/Co40Fe40B20 trilayer hybrid structure as a function of temperature from 10 to 50 K with magnetic field vertical bar H vertical bar <= 2000 Oe has been studied. TMR ratio of 1.6% at low fields at 10 K was achieved with the applied current of 1 mu A. The behavior of junction resistance was well explained by the tunneling resistance across the barrier. Strong bias dependences of magnetoresistance and junction resistance were presented. (C) 2009 American Institute of Physics. [DOI 10.1063/1.3068418]

Resonant tunneling theory of planar quantum dot structures

The ballistic transport in the semiconductor, planar, circular quantum dot structures is studied theoretically. The transmission probabilities show apparent resonant tunneling peaks, which correspond to energies of bound states in the dot. By use of structures with different angles between the inject and exit channels, the resonant peaks can be identified very effectively. The perpendicular magnetic field has obvious effect on the energies of bound states in the quantum dot, and thus the resonant peaks. The treatment of the boundary conditions simplifies the problem to the solution of a set of linear algebraic equations. The theoretical results in this paper can be used to design planar resonant tunneling devices, whose resonant peaks are adjustable by the angle between the inject and exit channels and the applied magnetic field. The resonant tunneling in the circular dot structures can also be used to study the bound states in the absence and presence of magnetic field.

Resonant tunneling of holes in GaMnAs-related double- barrier structures

Using the multiband quantum transmitting boundary method (MQTBM), hole resonant tunneling through AlGaAs/GaMnAs junctions is investigated theoretically. Because of band-edge splitting in the DMS layer, the current for holes with different spins are tuned in resonance at different biases. The bound levels of the "light" hole in the quantum well region turned out to be dominant in the tunneling channel for both "heavy" and "light" holes. The resonant tunneling structure can be used as a spin filter for holes for adjusting the Fermi energy and the thickness of the junctions.

Tunneling magnetoresistance in (Ga,Mn)As/Al-O/CoFeB hybrid structures

Tunneling magnetoresistance (TMR) in Ga(0.9)2Mn(0.08)As/Al-O/Co40Fe40B20 trilayer hybrid structure as a function of temperature from 10 to 50 K with magnetic field vertical bar H vertical bar <= 2000 Oe has been studied. TMR ratio of 1.6% at low fields at 10 K was achieved with the applied current of 1 mu A. The behavior of junction resistance was well explained by the tunneling resistance across the barrier. Strong bias dependences of magnetoresistance and junction resistance were presented. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3068418]

SELF-CONSISTENT TREATMENT OF 3-DIMENSIONAL - 2-DIMENSIONAL AND 2-DIMENSIONAL - 2-DIMENSIONAL RESONANT-TUNNELING IN DOUBLE-BARRIER STRUCTURES

By using a transfer-matrix method on the basis of two-dimensional (2D) Bloch sums in accordance with a tight-binding scheme, a self-consistent calculation on the resonant tunneling in asymmetric double-barrier structures is presented, in which contributions to resonant tunneling from both three-dimensional (3D) electrons in the contacts and 2D electrons in the spacer or accumulation layers are considered simultaneously. The charge buildup effect on the current versus voltage (I-V) curves is evaluated systematically, showing quantitatively how it results in the I-V bistability and enhanced differences between I-V curves for positive and negative bias in an asymmetric double-barrier structure. Special attention is focused on the interaction between 3D-2D and 2D-2D resonant-tunneling processes, including the suppression of 2D-2D resonant tunneling by the charge buildup in the well accompanying the 3D-2D resonant tunneling. The effects of the emitter doping condition (doping concentration, spacer thickness) on the presence of two types of quasi-2D levels in the emitter accumulation layers, and on the formation of a potential bulge in the emitter region, are discussed in detail in relation to the tunneling process.

SCATTERING AND RESONANT-TUNNELING THEORY FOR A CYLINDRICAL WELL IN PLANAR STRUCTURES

A two-dimensional atomic scattering theory is developed for scattering of electrons by a circularly symmetric quantum structure in the two-dimensional electron gas. It is found that the scattering cross section oscillates as a function of ka where k is the electron wave vector and a is the radius of the cylindrical potential barrier. If there is a quantum well inside the potential barrier, there appears a series of sharp resonant-tunneling peaks superposed on the original scattering-cross-section curves. The width of the resonant-tunneling peak depends sensitively on the thickness, the height of the potential barrier, and the electron energy.

LO-PHONON-ASSISTED TUNNELING IN ASYMMETRIC DOUBLE-WELL STRUCTURES WITH THICK BARRIERS

Nonresonant electron tunneling between asymmetric double quantum wells in AlxGa1-xAs/GaAs systems has been investigated by using steady-state and time-resolved photoluminescence spectra. Experimental evidence of LO-phonon-assisted tunneling through thick barriers has been obtained by enhancing excitation power densities or applying electric fields perpendicular to the well plane. LO-phonon-assisted tunneling times have also been estimated from the variation of the decay time of the narrow-well photoluminescence with applied electric fields. Our findings suggest that LO phonons in the barriers play an important role in the tunneling transfer.

RESONANT TUNNELING, EIGENVALUE AND ENERGY-BAND CALCULATION FOR POTENTIAL AND PERIODIC POTENTIAL STRUCTURES

Recursion formulae for the reflection and the transmission probability amplitudes and the eigenvalue equation for multistep potential structures are derived. Using the recursion relations, a dispersion equation for periodic potential structures is presented. Some numerical results for the transmission probability of a double barrier structure with scattering centers, the lifetime of the quasi-bound state in a single quantum well with an applied field, and the miniband of a periodic potential structure are presented.

Resonant tunneling of holes in GaMnAs-related double- barrier structures

Using the multiband quantum transmitting boundary method (MQTBM), hole resonant tunneling through AlGaAs/GaMnAs junctions is investigated theoretically. Because of band-edge splitting in the DMS layer, the current for holes with different spins are tuned in resonance at different biases. The bound levels of the "light" hole in the quantum well region turned out to be dominant in the tunneling channel for both "heavy" and "light" holes. The resonant tunneling structure can be used as a spin filter for holes for adjusting the Fermi energy and the thickness of the junctions.