Diffusive tunneling

If the interface has roughness of the order of the mean free path, the tunneling electrons are scattered at the interface (diffusive tunneling), and the resultant tuimeling spectrum is momentum-averaged, approximately equivalent to the density of states N(E). It seems that most of the tunneling processes through planar-type jimctions on HTSC are close to the diffusive limit, so that anisotropy in the excitation spectrum can hardly be detected. 

Kitamura N, Lagally M G and Webb M B 1993 Real-time observations of vacancy diffusion on Si(001)-(2 1) by scanning tunnelling microscopy Rhys. Rev. Lett. 71 2082... 

Jaklevic R C and Elie L 1988 Scanning-tunnelling-microscope observation of surface diffusion on an atomic scale Au on Au(111) Rhys. Rev. Lett. 60 120... 

As time progresses, charge is generated by photon currents, semiconductor dark currents, diffusion, depletion, surface, avalanche, and tunneling. The time required to fill the well by dark currents is the storage time, given by the following. 

Under Httle or no illumination,/ must be minimized for optimum performance. The factor B is 1.0 for pure diffusion current and approaches 2.0 as depletion and surface-mode currents become important. Generally, high crystal quality for long minority carrier lifetime and low surface-state density reduce the dark current density which is the sum of the diffusion, depletion, tunneling, and surface currents. The ZM product is typically measured at zero bias and is expressed as RM. The ideal photodiode noise current can be expressed as follows ... 

Note in passing that the common model in the theory of diffusion of impurities in 3D Debye crystals is the so-called deformational potential approximation with C a>)ccco,p co)ccco and J o ) oc co, which, for a strictly symmetric potential, displays weakly damped oscillations and does not have a well defined rate constant. If the system permits definition of the rate constant at T = 0, the latter is proportional to the square of the tunneling matrix element times the Franck-Condon factor, whereas accurate determination of the prefactor requires specifying the particular spectrum of the bath. 

Difoggio and Corner [1982] and Wang and Comer [1985] have discovered tunneling diffusion of H and D atoms on the (110) face of tungsten. They saw that the Arrhenius dependence of the diffusion coefficient D sharpy levels-off to the low-temperature limit (D = D ) at 130-140 K (fig. 47) the values of depend but slightly on the mass of the tunneling particle for the D and... 

The diffusion coefficient corresponding to the measured values of /ch (D = kn/4nRn, is the reaction diameter, supposed to be equal to 2 A) equals 2.7 x 10 cm s at 4.2K and 1.9K. The self-diffusion in H2 crystals at 11-14 K is thermally activated with = 0.4 kcal/mol [Weinhaus and Meyer 1972]. At T < 11 K self-diffusion in the H2 crystal involves tunneling of a molecule from the lattice node to the vacancy, formation of the latter requiring 0.22 kcal/mol [Silvera 1980], so that the Arrhenius behavior is preserved. Were the mechanism of diffusion of the H atom the same, the diffusion coefficient at 1.9 K would be ten orders smaller than that at 4.2 K, while the measured values coincide. The diffusion coefficient of the D atoms in the D2 crystal is also the same for 1.9 and 4.2 K. It is 4 orders of magnitude smaller (3 x 10 cm /s) than the diffusion coefficient for H in H2 [Lee et al. 1987]. 

This slow diffusion of a crucial new technique can be compared with the invention of the scanning tunnelling microscope (STM) by Binnig and Rohrer, first made public in 1983, like X-ray diffraction rewarded with the Nobel Prize 3 years later, but unlike X-ray diffraction quickly adopted throughout the world. That invention, of comparable importance to the discoveries of 1912,now(2 decades later) has sprouted numerous variants and has virtually created a new branch of surface science. With it, investigators can not only see individual surface atoms but they can also manipulate atoms singly (Eigler and Schweitzer 1990). This rapid adoption of... 

Valette-Hamelin approach,67 and other similar methods 24,63,74,218,225 (2) mass transfer under diffusion control with an assumption of homogeneous current distribution73 226 (3) adsorption of radioactive organic compounds or of H, O, or metal monolayers73,142,227 231 (4) voltammetry232,233 and (5) microscopy [optical, electron, scanning tunneling microscopy (STM), and atomic force microscopy (AFM)]234"236 as well as a number of ex situ methods.237 246... 

The effects of transfer of atoms by tunneling may play an essential role in a number of phenomena involving the transfer of atoms and atomic groups in the condensed phase. One may expect that these effects may exist not only in the proton transfer reactions considered above but also in such processes as the diffusion of hydrogen atoms and other light ions (e.g., Li+) in liquids, tunnel inversion and isomerization in some molecules, quantum diffusion of defects and light atoms in the electrode at cathodic incorporation of the ions, ion transfer across the liquid/solid interface, and low-temperature chemical reactions. 

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