Barrier height, tunneling, determination

When the current in molecular junctions is dominated by electron tunnelling (Fig. 2b), it can be described as a first approximation by Simmons s theory [40,41]. In this model, the current depends on (1) the height O of the potential barrier, which is determined by the interactions of the electron with the medium and (2) the thickness d of the barrier (Fig. 3). 

The significant variation of the barrier height observed for immersed junctions reflects the experimental difficulties associated with determining the tunneling constant, k. Two key issues are contamination of the junction and uncertainty as to the structural and electronic character of the tip [104], Recent data clearly reveal a dependence of the apparent barrier height on tip-substrate separation [7,92-94,104]. Specifically, the effective barrier is observed to diminish for resistance values below <10 Q as shown in Fig. 

In Eq. 73, T is a pre-factor close to unity, which depends weakly on the effective barrier height Vac — E x). The distance dependence of the tunneling probability is determined by... 

Peyghambarian et al. modeled the dependence of the current flow and the efficiency of devices on various device parameters as the (balance of the) charge carrier mobility and the barrier height at the interfaces for devices, where the current flow is determined by Fowler-Nordheim tunneling (see Fig. 9-24) [83]. In this case, the current flow through the LEDs is injection limited and dominated by Fowler-Nordheim tunneling and the following characteristics are observed [83] ... 

The resistivity and breakdown field of the wet thermal oxide on SiC have been measured to be comparable to those of thermal Si02 on Si, about 1016 Q cm [26,37,40] and as high as 8xl06Vcm [41], respectively. From analysis of Fowler-Nordheim tunnelling currents in the I-V characteristics of 3C-SiC MOS capacitors, the barrier height between thermal oxide and 3C-SiC has been determined as about 3.1 eV [37,40,41],... 

The above representation of the transmission coefficient is appropriate for the description of overlapping resonances situated below the barrier heights of multibarrier tunneling structures [55, 62, 63]. It is worth stressing that there are not free parameters here. All the quantities above depend on the values of fhe complex poles and fhese are determined by the potential parameters. 

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