Modelling the Multiplicity of Conductance Structures in Clusters of Silicon Quantum Dots
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tunnelling creates a conductive path that selects only a few of
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the many possible microcrystallite sizes available in a given Al device. Since only a few nanoscale particles are involved in the resonant tunnelling, different groups of particles can cause different peaks, rather than acting to smear a given peak. This Figure 1. Cross section of the leads to a simple model based on a few parallel particles of resonant tunnelling structure. different sizes, as shown in Fig. 2. In the conventional double barrier structure utilizing n+ contacts and an n+ substrate, virtually all the applied voltage appears across the double barrier structure and any potential drop across the heavily doped substrate can be neglected. Accordingly, the energy levels at the measured current peaks can be related directly to the voltage applied across the device, and the magnitude of the current is determined mainly by transmission through the double barrier structure. In our devices, the substrate is only doped to 3.5 x 1016 cm- 3 , and resonant tunnelling is observed when the substrate is negatively biased into deep depletion. In this case, the applied voltage divides between the thin oxide layer containing the quantum dots and the substrate depletion layer. The series resistance of the substrate depletion layer and corresponding potential drop can no longer be neglected as in the case of an n+ substrate, and act to reduce the potential that appears across the oxide layer containing the quantum dots, as illustrated in Fig. 3. This series resistance would also ordinarily be expected to reduce any observed current jumps caused by electrons tunnelling through the quantum dot into the substrate. However, for a high enough applied voltage, this is no longer the case. The injection of electrons into a deeply depleted substrate results in carrier multiplication when the avalanche regime is reached. Since a small resonant tunnelling current begets a large increase in device current, a single dot can control a considerable current. This 569
Mat. Res. Soc. Symp. Proc. Vol. 358 01995 Materials Research Society
mechanism, together with multiple parallel current paths through parallel particles, allows a fair quantitative fit to the measured I-V characteristics.
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Before positive bias electrical EIC • (b) forming 2 ,3 the samples are highly resistive and demonstrate no resonant tunnelling. The electrical forming process eliminates the high resistive amorphous tissue regions surrounding the microcrystallites, as illustrated in Fig. 4. The forming current does not flow uniformly over the entire device area; rather, it follows a local path of least resistance, where the oxide is thinner or less resistive. Thus only a small discrete set of particles, those in the forming path, (c) will be electrically connected to the front and back contacts. The selection of particles is likely to consist of particles of different No ' sizes, hence with different
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