Tunneling processes

This relation may be interpreted as the mean-square amplitude of a quantum harmonic oscillator 3 o ) = 2mco) h coth( /iLorentzian distribution of the system s normal modes. In the absence of friction (2.27) describes thermally activated as well as tunneling processes when < 1, or fhcoo > 1, respectively. At first glance it may seem surprising... 

The instanton action behaves in accord with the scaling predictions and is independent of coq. Loosely speaking, the frequency ojq is replaced by the friction coefficient rj. Grabert et al. [1984b] have studied the energy loss A [Pg.84]

As seen from this table, the WKB approximation is reasonably accurate even for very shallow potentials. At 7 = 0 the hindered rotation is a coherent tunneling process like that studied in section 2.3 for the double well. If, for instance, the system is initially prepared in one of the wells, say, with cp = 0, then the probability to find it in one of the other wells is P( jn, t) = 5sin (2Ar), while the survival probability equals 1 — sin ( Ar). The transition amplitude A t), defined as P( + t) = A t), is connected with the tunneling frequency by... 

Electron-tunneling Model. Several models based on quantum mechanics have been introduced. One describes how an electron of the conducting band tunnels to the leaving atom, or vice versa. The probability of tunneling depends on the ionization potential of the sputtered element, the velocity of the atom (time available for the tunneling process) and on the work function of the metal (adiabatic surface ionization, Schroeer model [3.46]). 

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

Ion neutralization (or Ion survival) can dominate this technique. A number of theories have arisen to account for this phenomenon, but all seem to Include both Auger transitions and resonance tunneling processes as the dominant means of Ion neutralization.(4,5) For very slow Ions, as In LEISS, Auger... 

Soon after the invention of the STM as a tool for imaging surfaces in real space, it was discovered that the microscope could also be used (or misused) for surface manipulations, that is, for nano structuring of surfaces [5]. The extremely close vicinity of the STM tip and the sample surface required by the tunnel process... 

In impure metals, dislocation motion ocures in a stick-slip mode. Between impurities (or other point defects) slip occurs, that is, fast motion limited only by viscous drag. At impurities, which are usually bound internally and to the surrounding matrix by covalent bonds, dislocations get stuck. At low temperatures, they can only become freed by a quantum mechanical tunneling process driven by stress. Thus this part of the process is mechanically, not thermally, driven. The description of the tunneling rate has the form of Equation (4.3). Overall, the motion has two parts the viscous part and the tunneling part. 

The development of an ab initio quantum molecular dynamics method is guided by the need to overcome two main obstacles. First, one needs to develop an efficient, yet accurate, method for solving the electronic Schrodinger equation for both ground and excited electronic states. Second, the quantum mechanical character of the nuclear dynamics must be addressed. (This is necessary for the description of photochemical and tunneling processes.) This section provides a detailed discussion of the approaches we have taken to solve these two problems. 

Fig. 3 Energy diagram for an M-A-M diode showing elastic and inelastic tunneling processes (top). The HOMO (n) and LUMO (71 ) orbital energies and a few vibrational levels are indicated. Applied bias energy (eV) is just sufficient to allow inelastic tunneling with excitation of the first vibrational level, eV = hv. Also shown (bottom) are the I(V) curve, conductance- / curve, and the IETS spectrum that would result from both elastic processes and the first inelastic channel. (Reproduced by permission of the American Chemical Society from [19])...

A different view of the OMT process is that the molecule, M, is fully reduced, M , or oxidized, M+, during the tunneling process [25, 26, 92-95]. In this picture a fully relaxed ion is formed in the junction. The absorption of a phonon (the creation of a vibrational excitation) then induces the ion to decay back to the neutral molecule with emission (or absorption) of an electron - which then completes tunneling through the barrier. For simplicity, the reduction case will be discussed in detail however, the oxidation arguments are similar. A transition of the type M + e —> M is conventionally described as formation of an electron affinity level. The most commonly used measure of condensed-phase electron affinity is the halfwave reduction potential measured in non-aqueous solvents, Ey2. Often these values are tabulated relative to the saturated calomel electrode (SCE). In order to correlate OMTS data with electrochemical potentials, we need them referenced to an electron in the vacuum state. That is, we need the potential for the half reaction ... 

Berry, R.S., Correlation of rates of intramolecular tunneling processes with application to some Group V compounds, /. Chem. Phys., 32, 933, 1960. 

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