Charge discreteness and the energy efficiency of information erasure in dynamic random-access memory cells

A dynamic random-access memory (DRAM) cell stores information as an integer number of electrons on a capacitor, and whether this discreteness is thermodynamically relevant depends on the competition between the charging energy and thermal fluctuations. This competition is quantified by the ratio $\kappa$ of the single-electron charging energy to the thermal energy, and here we investigate how $\kappa$ affects the energy efficiency of information erasure in a DRAM cell. Using a stochastic-thermodynamic model of a DRAM cell, we show that the nonquasistatic heat released during the discharge step is suppressed as $\kappa$ increases, whereas the quasistatic heat of the charge step approaches the Landauer cost. As a result, the energy efficiency increases monotonically with $\kappa$ and approaches the Landauer limit where the effect of charge discreteness is maximal and the cell is effectively reduced to two charge states. The parameter $\kappa$ thus connects two thermodynamic regimes: a multilevel single-well memory, whose nonequilibrium initial state prevents quasistatic erasure, and an effective two-level memory that can attain the Landauer limit. These results identify $\kappa$ as the parameter that controls the fundamental efficiency ceiling of transistor--capacitor memory circuits.