Reduced master equation analysis of multiple–tunnel junction single-electron memory device

Abstract

We employ a master equation (ME) approach in the charge transport analysis across a uniform multiple–tunnel junction (MTJ) memory trap, using a much-reduced state list derived from circuit symmetry, and previous assumptions by Jensen and Martinis. This enables all significant single tunneling and higher-order cotunneling sequences to be accounted for, while avoiding the computational cost of the full ME method. The reduced ME method is conceptually simpler and yields greater accuracy, compared with previous approximations based on tunneling probabilities. For an MTJ trap with zero stray capacitance C0, the results obtained are found to agree very closely with the full ME results up to a temperature of T≈3T0/10, where T0=e2/kBC, whereas previous methods break down at T≈T0/10. Furthermore, unlike the earlier methods, the reduced ME approach can be applied to the realistic but less symmetric case of a trap with finite C0, and remains valid up to the trap’s maximum operating temperature of T≈T0/100. Finally, our reduced ME results are in close agreement with available experimental data at T<T0/200.