Capacitance in Single Electron Tunneling
The charging energy for single electron tunneling (SET) in mesoscopic semiconductor heterostructures is typically parameterized in terms of a single number C, the system “capacitance”, as e 2/2C.This number, which is sensitively measured by spacings in the current versus gate-voltage oscillations, has not been independently computed, but is rather estimated from the simple geometric capacitances of the charge elements of the structure. We present a systematic study for the computation of the charging energy and capacitances in SET devices at various levels of approximation. First, assuming the capacitive elements of the structure to be perfect conductors and assuming constant contact voltages, we compute the charging energy and activation energy for SET. We show that the former energy is determined by the dot to gate capacity and the latter by the dot self-capacity. We calculate the screening effect of the contacts by Thomas-Fermi approximation. We generalize the notion of capacitance in order to treat the case of semiconductors and we use a self-consistent electronic structure calculation to investigate the “local capacities” of the quantum dot. Finally, we use the self-consistent energies from this calculation along with computed energy-dependent tunneling rates to compute the current-gate voltage characteristics of a realistic device. We compare the resonance spacings and activation energy with that determined from the simpler theory, as well as with that determined by experiment.
KeywordsGate Voltage Charge Energy Resonance Spacing Capacitive Element Single Electron Tunneling
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