Non-adiabatic effects in electron tunneling

The adiabatic approximation is one of the keystones on which the theory of electron tunneling is based (see Sect. 2). In particular, the matrix element for the transition between the initial and the final electron states contain the adiabatic wave functions of the donor and acceptor. Adiabatic approximation is known [25] to have a very high degree of accuracy. Because of this the non-adiabatic effects have been neglected until recently in the theory of electron tunneling without detailed analysis of whether this can actually be done. In the present section we shall try to fill in this blank and to discuss to what extent the non-adiabatic effects can influence the process of electron tunneling. 

The following ideas have been used in these studies. If the electron is located near the donor (say at a distance less than rQ = 15 A from it), then the wave function of the system comprising the core of the donor + electron is described with good accuracy in terms of the adiabatic approximation 

The energy of the donor state described by the wave function Fl (q) is IA + n wd, where Id is the ionization energy of the donor (Fig. 6). The total energy of the system the core of the donor + electron as has been noted above, is nu)d. Thus, the energy with which the electron leaves the donor is equal to ruod — (Id + n tod) and the coefficient ynn has the form 

the damping of the electron wave function on its removal from the donor depends on the vibrational state in which nuclei of the donor remain. 

This statement is the evident consequence of the energy conservation law. 

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