Wentzel-Kramer-Brillouin tunneling

The process of formation of a bubble having a critical radius, can be computed using a semiclassical approximation. The procedure is rather straightforward. First one computes, using the well known Wentzel-Kramers-Brillouin (WKB) approximation, the ground state energy Eq and the oscillation frequency //() of the virtual QM drop in the potential well U JV). Then it is possible to calculate in a relativistic framework the probability of tunneling as (Iida Sato 1997)... 

Field emission is a tunneling phenomenon in solids and is quantitatively explained by quantum mechanics. Also, field emission is often used as an auxiliary technique in STM experiments (see Part II). Furthermore, field-emission spectroscopy, as a vacuum-tunneling spectroscopy method (Plummer et al., 1975a), provides information about the electronic states of the tunneling tip. Details will be discussed in Chapter 4. For an understanding of the field-emission phenomenon, the article of Good and Muller (1956) in Handhuch der Physik is still useful. The following is a simplified analysis of the field-emission phenomenon based on a semiclassical method, or the Wentzel-Kramers-Brillouin (WKB) approximation (see Landau and Lifshitz, 1977). 

Wentzel Kramer-Brillouin approximation, tunneling, 1492 Whewefi, Reverend, 1050 Whiskers, 1327, 1336 White, and organic adsorption. 979 Wieckowski, A., 1146 Will, 1205... 

This is supported by computed rate constants with tunneling contributions using the semiclassical Wentzel-Kramers-Brillouin (WKB) theory. The WKB procedure requires a carefully described intrinsic reaction path, and... 

The calculation of the electronic-transmission factor currently involves three different methods, viz. the Landau-Zener formula, Fermi s golden mle [35], and electron tunneling formalism such as the Wentzel-Kramer-Brillouin method [36]. We used the Landau-Zener formula [37,38] to calculate it ... 

If on the other hand AFJ is much smaller than Ipv, the eigenstates 1), 12) essentially coincide with the handed states L), /2). In that case the absolute value of the difference E2 — 1] between the eigenstates is approximately 2 V v - We can estimate the size of the tunneling splitting for typical chiral molecules for instance within the Wentzel-Kramers-Brillouin approximation. If we assume a quartic double well potential with a barrier height of 200 kJ mol a barrier Avidth of 200 pm and a tunneling mass... 

At t=T the escape rate begins to depart from the above reported law, tending to a temperature-independent quantum transition rate (Fig. G.l), which has the same form, in the usual WKB (Wentzel-Kramers-Brillouin) approximation for quantum tunneling, as in the case of switching of magnetization via thermal activation ... 

From a simple Wentzel-Kramers-Brillouin (WKB) approach [2], the tunneling current increases exponentially as the thickness of the Si02 decreases. MOSFET is the capacitance-operated device. The source-drain current of the MOSFET depends on the gate capacitance ... 

For a proper interpretation of STM, it is essential to understand how the tunneling current works. Figure 7.1b shows a simple model of a tunneling junction consisting of a metal (tip)-vacuum-metal (surface) in which the tunnehng current can be derived bythe Fermi golden rule and Wentzel-Kramers-Brillouin (WKB) approximation. The tunneling current is then expressed by ... 

This expression is the Wentzel-Kramer-Brillouin (WKB) tunneling probability for a parabolic barrier and n E) dE is the Matthews and Khan modified form of the expression for available electrons. The complete photocurrent must include contributions for tunneling, as well as over-the-barrier currents. 

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