Finite-time erasure cost of a DRAM cell with discrete stored charge

Abstract

Erasing a bit in a dynamic random-access memory (DRAM) cell with discrete stored charge costs more heat than the Landauer bound even in the quasistatic limit, and for the quasistatic protocol studied so far the efficiency rises with the ratio κ of the single-electron charging energy to the thermal energy. We optimize the bitline and wordline protocols of cyclic erasure in the stochastic model of such a cell at fixed error probability and finite operation time, for κ from 0.05 to 8, and evaluate their heat exactly in the master equation. The efficiency of the optimized protocols increases with κ at every operation time tested; the relative cost of finite time falls as for a continuous charge whose relaxation rate grows with κ, and it stops falling where the charge becomes discrete. In cyclic operation each erasure starts from the mixture of states that the previous erasures left, so its heat depends on their final mean charge through a boundary term. This term explains why a linear ramp exceeds its slow-driving cost, and it lets protocols that end below the equilibrium mean dissipate less than the quasistatic discharge-then-charge protocol, already in the infinite-time limit; the gain is up to 1.8% with Fermi hopping rates and depends strongly on the rate law, reaching 7.0% with Metropolis rates. Protocols designed with a mean-field surrogate of the charge dynamics come within 2.5% of the optimized protocols at κ ≤ 0.1 and dissipate up to 13.5% more heat for 1 ≤ κ ≤ 4 and up to 62.5% more at κ = 8. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, is responsible for its content.