Resonant tunneling transport

The ratio Vo/B determines the transition from coherent diffusive propagation of wavefunctions (delocalized states) to the trapping of wavefunctions in random potential fluctuations (localized states). If I > Vo, then the electronic states are extended with large mean free path. By tuning the ratio Vq/B, it is possible to have a continuous transition from extended to localized states in 3D systems, with a critical value for Vq/B. Above this critical value, wave-functions fall off exponentially from site to site and the delocalized states cannot exist any more in the system. The states in band tails are the first to get localized, since these rapidly lose the ability for resonant tunnel transport as the randomness of the disorder potential increases. If Vq/B is just below the critical value, then delocalized states at the band center and localized states in the band tails could coexist. 

It is thus desirable to examine the resonant tunneling in a Luttinger liquid in a broad range of temperature down to T = 0 and for various parameters of the barriers. Our purpose in this paper is to analyze transport through a double barrier of arbitrary strength, strong or weak, symmetric or asymmetric, within a general analytical method applicable to all these situations. 

Let us come back to our favorite problem - transport through a quantum system. There is one case (called sequential tunneling), when the simple formulas discussed above can be applied even in the case of resonant tunneling... 

Fig. 27 Processes involved in the transport characteristics in figure 26. ei = ei,CT, 62 = 62,(7, The red line indicates electron resonant-tunnelling, a) The first conductance peak, b) The second conductance peak, c) The pseudo-peak of conductance, d) The first current maximum, and the red line indicates resonant tunnelling of electrons, e) The second current maximum for electron resonant tunnelling, f) The dip of conductance.

A.-P. Jauho, N.S. Wingreen, Y. Meir, Time-Dependent Transport in Interacting and Noninteracting Resonant Tunneling Systems, Phys. Rev. B 50 (1994) 5528-5544. 

Both the absorption and the resonant tunneling experiments find quantization effects for layer thicknesses of 50 A or less. It is, however, not immediately obvious why the quantum states should be observed even in these thin layers. The discussion of the transport in Chapter 7 concludes that the inelastic mean free path length is about 10-15 A at the mobility edge. The rapid loss of phase coherence of the wavefunction should prevent the observation of quantum states even in a 50 A well, but there are some factors that may explain the observations. The mean free path increases at energies above the... 

THE EQUIVALENT CIRCUIT OF SPIN-DEPENDANT TRANSPORT IN DOUBLE-BARRIER RESONANT TUNNELING... 

An equivalent circuit of resonant-tunneling nanostructures taking into account spin-polarized transport of charge carriers is proposed. It is based on the approximation of I-V characteristics and represents spin shifted energy levels in the quantum well. 

B. Gelmont, D. Woolard, W. Zhang and T. Globus, Electron Transport within Resonant Tunneling Diodes with Staggered-Bandgap Heterostmctures, Solid State Electronics 46, 1513-1518 (2002). 

Jauho A, Wingreen N, Meir Y (1994) Time-dependent transport in interacting and noninteracting resonant-tunneling systems. Phys Rev B 50(8) 5528... 

The quantum cascade laser is very different from the conventional semiconductor laser that has been described in this article, and is based on the intersubband transitions between the excited states of coupled quantum wells, or superlattice structures, and on the resonant tunneling between the wells as the pumping mechanism. This means that lasing action takes place between energy levels within the conduction band (not between the conduction and valance bands). More importantly, since the electron is still in the conduction band, novel bandgap engineering can provide for a transport mechanism that allows for this electron to be reinjected into another set of coupled quantum wells, and is therefore reused. As a result, one injected... 

Under appropriate conditions, the faradaic current may be used to form images of the electrochemical reactivity of a surface. This is known as scanning electrochemical microscopy (SECM), where the transport and heterogeneous redox activity of species within the junction mediate the tip-substrate interaction. This subject has been thoroughly reviewed [43,44], and an excellent paper demonstrating the transition from STM to SECM is available [45]. The possible contribution of confined redox species to resonant tunneling has also been examined [19,46,47]. 

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