Zener tunnelling

Figure 7. Detail of the energy level diagram near an avoided level crossing, m and m are the quantum numbers of the energy level. Pm m- is the Landau-Zener tunnel probability when sweeping the applied field from the left to the right over the anticrossing. The greater the gap A and the slower the sweeping rate, the higher is the tunnel rate, Eq. (2).

The eharge transfer meehanism aeross the interfaee barrier layer is different for lowly doped and heavily doped p-type silieon. For lowly doped p-type siheon the proeess is by thermal emission of holes to go over the barrier layer whereas it is by Zener tunneling for heavily doped materials. For n-Si the eonduetion band proeesses depend on doping density and on illumination intensity. For heavily doped n-Si it is by Zener tunneling and the i-V eurve is identical to that forp-Si. For moderately or lowly doped -Si in the dark the reaetion is limited by the minority holes, which are required to initiate the dissolution proeess. Significant dissolution of n-Si can proceed when a large number of holes are generated by illumination. 

ID PCs PSi-based ID photonic superlattices have allowed the demonstration of interesting optical analogs of electronic phenomena, such as photonic Bloch oscillations, Zener tunneling, Anderson localization, and optical switch (Sapienza et al. 2003 Agarwal et al. 2004 Octavio Estevez et al. 2012 Ghulinyan et al. 2005 Bertolotti et al. 2005 Barthelemy et al. 2007). Besides... 

Ghulinyan M, Oton CJ, Gaburro Z, Pavesi L (2005) Zener tunneling of light waves in an optical superlattice. Phys Rev Lett 94 127401... 

The problem of nonadiabatic tunneling in the Landau-Zener approximation has been solved by Ovchinnikova [1965]. For further refinements of the theory beyond this approximation see Laing et al. [1977], Holstein [1978], Coveney et al. [1985], Nakamura [1987]. The nonadiabatic transition probability for a more general case of dissipative tunneling is derived in appendix B. We quote here only the result for the dissipationless case obtained in the Landau-Zener limit. When < F (Xe), the total transition probability is the product of the adiabatic tunneling rate, calculated in the previous sections, and the Landau-Zener-Stueckelberg-like factor... 

Figure A.l. Schematic adiabatic potentials and various parameters used in the ZN formulas, (a) Landau-Zener type, (b) Nonadiabatic tunneling type. Taken from Ref. [9].

On the basis of a Landau-Zener curve crossing formalism, Borgis and Hynes derived the nonadiabatic rate constant k, which is similar to that expressed by the DKL model but where the tunneling term Cnm found in Eq. (4) is significantly modified due to the influence of the low-frequency promoting mode Q, with a frequency 0)q, on the tunneling rate. The dependence of Cnm on Q is given by [13]... 

In the case of semiconductors, the idea of electron tunneling has been used by Zener [42] to describe the so-called interband tunneling. Such tunneling represents one of the possible mechanisms of semiconductor breakdown. To understand the nature of interband tunneling, we shall first follow Ziman [43] and consider the one-dimensional motion of an electron in a separate band under the influence of an electric field. If we use the scheme of repeated bands, then the electron motion in momentum space is an up and down motion along the OABC periodic curve (Fig. 16). In the coordinate space, the electron, starting from point O, accelerates then slows down as it approaches point A here, the direction of the motion is changed to the... 

In order to apply quantitatively the Landau-Zener formula Eq. (2), we first saturated the crystal of Fes clusters in a field of Hz = -1.4 T, yielding an initial magnetization Min = -Ms. Then, we swept the applied field at a constant rate over one of the resonance transitions and measured the fraction of molecules which reversed their spin. This procedure yields the tunneling rate P 1010 and thus the tunnel splitting A 1010 , Eq. (2), with n = 0, 1, 2,. 

An applied field in the xy-plane can tune the tunnel splittings Amm. via the Sx and Sy spin operators of the Zeeman terms that do not commute with the spin Hamiltonian. This effect can be demonstrated by using the Landau-Zener method (Section 3.1). Fig. 8 presents a detailed study of the tunnel splitting A 10 at the tunnel transition between m - +10, as a function of transverse fields applied at different angles (p, defined as the azimuth angle between the anisotropy hard axis and the transverse field (Fig. 4). 

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