Tunneling direct

Finally, we show that the second-order coupling between direct tunneling transitions is subdominant to the already computed quantities. Consider an interaction of the form yy l,-2 )(2,l + H.C. If one repeats simple-mindedly the steps leading to Eq. (75), one obtains the following simple expression for the free energy correction due to interaction between the underlying structural transitions ... 

The rapid course of the normal electrodeless titration of Fe2+ with Ce4+ also proves the occurrence of the direct "tunnelling of the electron between the ions, notwithstanding the simultaneous hydration rearrangement, viz.,... 

Beebe JM, Kim B-S, Gadzuk JW, Frisbie CD, Kushmerick JG (2006) Transition from direct tunneling to field emission in metal-molecule-metal junctions. Phys Rev Lett 97 026801... 

Fig. 8-38. Redox electron transfer at film-covered metal electrodes (a) transfer of redox electionB across a thin semiconductor film (direct tunneling transfer of electrons), (b) transfer of redox elections throu a thidc semiconductor film (indirect transfer of elections through electron levels in a thick film).

For metal electrodes covered with a superficial thin film, electron transfer proceeds by direct tunneling between the electrode metal and the redox particles the film influences only the barrier to the electron transfer. Usually, the transfer current of cathodic electrons, ile), is given by Eqn. 8-84 ... 

FIG. 3. Schematic presentation of an immersed tunnel junction where in addition to direct tunneling between the tip and substrate there is also the possibility of electrochemical reactions occurring at the tip and substrate. The broken arrow indicates the possibility of coupling between the electrochemical reactions occurring at the tip and substrate, which is the basis of SECM. (From Ref. 26.)... 

The direct tunneling current is assumed to be proportional to the exponential decay of the wave function, J exp[—icrfl, where = 4ti U is the barrier... 

Electronic conduction in crystalline semiconductors (except for the case of extremely high doping levels or very low temperatures) invariably involves motion in extended states. However, because of the high densities of defect centers, the possibility exists for transport by direct tunneling between localized states. 

From eqn. (27) it is seen that the effective initial concentration of donors nt,f (v) = (0) exp[ - (4/3)7i/ dAT determined formally by extrapolating the dependence In n(t) to t = 0 is lower than the real one by the number (per unit volume) of the donors which were located initially in the sphere of radius Rn near the acceptor and which had decayed via direct tunneling for the time t since the begining of the reaction. From eqn. (27) it also follows that, by straightening the kinetic curve in the coordinates ln[n(0/rc(0)] vs. t, one can obtain the values of RZ) and D from the segment cut off on the ordinate axis and the tangent of the slope angle. 

Secondly, the model of thermal diffusion does not allow one to explain the independence of the reaction rate on temperature observed for many low-temperature electron transfer processes. Indeed, the thermal diffusion of molecules in liquids and solids is known to be an activated process and its rate must be dependent on temperature. True, at low temperatures when activated processes are very slow, diffusion itself can be assumed to become a non-activated process going on via a mechanism of nuclear tunneling, i.e. by tunneling transitions of atoms over very short (less than 1 A) distances. A sequence of such transitions can, in principle, result in a diffusional approach of reagents in the matrix. Direct tunneling of the electron, whose mass is less than that of an atom by a factor of 10 or 104, can, however, be expected to proceed much faster. 

Thus, the total sum of the experimental data obtained in studying low-temperature electron transfer reactions as well as the results of theoretical analysis indicate that these reactions proceed via direct tunneling rather than via thermal diffusion or stepwise tunneling. 

Note that this characteristic of direct tunneling is valid for the low bias regime (see Eq. 3.3a). 

Fig. 40. Electron transfer from redox systems within the electrolyte across a semiconducting passive layer (n-type) (1) direct tunnelling to CB (2) tunnelling through space charge layer (3) transfer via surface states (4) hopping mechanism via interband states (5) transfer via sub-band and (6) transfer via valence band.

The imaging of anodic oxides raises the question about the necessary electron transfer. A thin film of less than 1 nm permits direct tunnelling from the tip to the substrate metal. However, if the film thickness exceeds ca. 1 nm, then tunnelling should not be possible according to relation 35 for the tunnel probability, which contains the energy AE and the width x for the barrier of the tunnel process and the effective mass of the electron m. If the oxide layer is thicker than 1 nm, then the electrons have to... 

Simmons21 has shown that the current I, as a function of applied voltage V, that traverses a molecule considered simply as a rectangular barrier of energy B and width d, in the direct tunneling regime V < B e X [12,13] is given by... 

Non-radiative transitions invariably involve the conversion of excitation energy into phonons. Thermalization involves many inelastic transitions between states in the band or band tails. Three mechanisms of thermalization apply to a-Si H. Carriers in extended states lose energy by the emission of single phonons as they scatter from one state to another. Transitions between localized states occur either by direct tunneling or by the multiple trapping mechanism in which the carrier is excited to the mobility edge and recaptured by a different tail state. 

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