Operating regimes for multivalued single-electron tunneling phase logic

Abstract

The dc bias range and the logic-state lifetime for multivalued single-electron tunneling phase logic are examined in computer simulations. Results for quaternary operation, which is of particular interest for compact logic circuitry, are compared with those for ternary and binary logic. Quaternary logic is shown to exhibit a rotation rule similar to binary and ternary logic and to have an optimized dc bias range of 14%, compared with 20 and 37 % for ternary and binary logic, respectively. The effects of shot noise and Nyquist noise on the logic-state lifetime are strongly influenced by the number of logic states. The ratio of tunnel resistance to series resistance required to suppress the effects of shot noise below those of Nyquist noise depends on the number of logic states. To obtain a lifetime equal to 1000 phase-locked cycles together with a maximum dc bias operating range, the ratio of Coulomb energy to thermal energy Ec/kBT must be 400, 1650, and 2830 for two, three, and four states, respectively. This corresponds to a rapid drop in the maximum operating temperature with the number of states, which can be related to an exponential dependence of lifetime on the activation energy for a thermally activated escape process. The implications of these results on the trade-offs between the operating regimes for dc bias, temperature, and junction size are discussed.