Polaron tunneling

Santos-Lemus and Hirsch (1986) measured hole mobilities of NIPC doped PC. Over a range of concentrations, fields, and temperatures, the transport was nondispersive. The field and temperature dependencies followed logn / El/2 and -(T0IT)2 relationships. For concentrations of less than 40%, a power-law concentration dependence was reported. The concentration dependence was described by a wavefunction decay constant of 1.6 A. To explain a mobility that shows features expected for trap-free transport with a field dependence predicted from the Poole-Frenkel effect, the authors proposed a model based on field-enhanced polaron tunneling. The model is based on an earlier argument of Mott (1971). 

In all cases, ac conductivity for hopping mechanisms follows a law dependent on frequency o-ac = < > (with. v 1) (Austin and Mott f79J) this law agrees also with polaronic tunneling considered sometimes (see p. 346 of Ref. 69). Moreover [26,27], as a function of temperature, this law is either thermally activated (conduction process in band tails) or linear (conduction in levels near Ey). 

Small polarons are mobile electrons (or holes) of a mixed-valence configuration that either tunnel or hop firom site to site (e.g. Fe + Fe " Fe " + Fe ) in a time T, > cor ... 

The experiments just discussed made it clear that the motion of the hole on the series of As represents a different mechanism of transport than tunneling. Giese [13] and Bixon and Jortner [18] suggested that this mechanism is incoherent hopping of the hole between neighboring bases. This means that the hole wavefunction is Hmited to one base. The wavefunctions of the remaining electrons on that base would of course be distorted by the presence of the hole. Thus in this view of the transport process the base on which the hole sits could be called a molecular polaron, or a small polaron because it is limited to one site. 

In some of the metal-insulator transitions discussed here the use of classical percolation theory has been used to describe the results. This will be valid if the carrier cannot tunnel through the potential barriers produced by the random internal field. This may be so for very heavy particles, such as dielectric or spin polarons. A review of percolation theory is given by Kirkpatrick (1973). One expects a conductivity behaving like... 

In Kemeny and Rosenberg s model to explain the compensation rule (Kemeny and Rosenberg, 1970a, b) the tunnelling of small polarons (effective mass < I00me, where me is the free electron mass) is considered leading to a relationship between T0 and the Debye temperature. 

Now let us consider the polaron transformation (146)-(147) applied to the tunneling Hamiltonian... 

When the system is weakly coupled to the leads, the polaron representation (154), (162) is a convenient starting point. Here we consider how the sequential tunneling is modified by vibrons. 

The result of the calculation is shown in Fig. 14, it is clear seen that the tunneling from the state 0,0) to the charged state and from the state 1,0) to the neutral state is exponentially suppressed in comparison with the bare tunneling rate F at large values of the electron-vibron interaction constant A. This polaron memory effect can be used to create nano-memory and nanoswitches. At finite voltage the switching between two states is easy accessible through the excited vibron states. It can be used to switch between memory states [112]. 

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