Trajectory Representations, Fluctuations, and Stability of Granular Electronic Devices

Summary

Granular nanoelectronics or single-electronics is concerned with the development of device technologies which approach the information theoretic limit of one bit on one electron. Only recently, with the demonstration of a single-electron shift register device based on correlated single electron tunneling in coupled metal-insulator-metal capacitors, has a serious candidate emerged which has the appropriate device and system properties. These system properties are shown here to include: pronounced fault tolerance to variations in capacitor parameters but sensitivity to cross-talk. The regimes of logic stability are described. Simple global clocking schemes are shown to lead to incoherence and synchronization failure unless precautions are taken. The analysis is based on the Fokker-Planck projection of the density matrix in the charge diagonal representation and by Monte Carlo and linear programming solutions to the coupled circuit equations. Transfer of these circuit concepts to semiconductor configurations based on strongly confined squeezed two-dimensional electron gas (2DEG) channels is discussed. Finally, the Bohm-de Broglie pilot field model of quantum mechanics is examined as a useful interpretive and computational aid to understanding the granular electronic regime. Apparent contradictions with conventional quantum transport formalisms are resolved and the connection with conventional Wigner distributions is established.