Thermodynamic Constraints in Dynamic Random-Access Memory Cells: Experimental Verification of Energy Efficiency Limits in Information Erasure

Abstract

We measured the energy efficiency of information erasure using silicon DRAM cells capable of counting charges on capacitors at the single-electron level. Our measurements revealed that the efficiency decreased as the erasure error probability decreased, and notably, the Landauer limit was not achieved even under effectively infinite-time bit erasure. By comparing the measured efficiency with the Landauer limit, we identified a thermodynamic constraint that prevents DRAM from reaching this limit: the inability to prepare the initial state in thermal equilibrium, which in turn prohibits quasistatic operations. This finding has broad implications for DRAM cells and for many electronic circuits sharing similar structures. Furthermore, it validates our experimental approach to discovering thermodynamic constraints that impose tighter, practically relevant limits, opening a new direction in information thermodynamics research.

Figures (7)

• Figure 1: Experimental scheme. (a) Circuit diagram of a DRAM cell. (b) Conceptual diagram for the erasure of a 1-bit memory. (c) Operational sequence of $V_{\mathrm{BL}}$ used in experiments. (d) Calculated $p_n$ and $\Psi_n$ during the erasure process, with parameters $E_{\rm c}=8.2\ {\rm meV}$, $T=300\ {\rm K}$, and $\Delta n_{\rm BL}=2.5$.
• Figure 2: Experimental setup and characterization. (a) Scanning electron micrograph of a device with measurement setup. (b) The sensor transistor current ($I_{\rm d}$) under equilibrium conditions. (c) $p_n$ at $n_{\rm BL}=0$, with a Gaussian fit (red line). (d) The mean value of $n$ ($n_{\rm mean}$) obtained from Gaussian fit of the distribution of $n$ at various $V_{\rm BL}$. The error bars for $n_{\rm mean}$ indicate the standard error of the mean.
• Figure 3: Erasure process at $\Delta n_{\rm BL}= 3.7$. (a) $p_n$ before (dark blue) and after (light blue) erasure, with logical-state occupations. (b) Top: $\left <n \right >$ during discharge. The green dashed and purple solid lines represent cases starting immediately after the initial state preparation with the quench from $V_\mathrm{BL}=V_\mathrm{i} \mp \Delta V_\mathrm{BL}$, respectively. The grayscale background indicates $p_n$. Bottom: Ensemble-averaged cumulative heat dissipation $-Q_\mathrm{cum}$ during discharge. (c) Top: $p_n$ during charging, with $\langle n\rangle$ (blue) and $n_\mathrm{BL}$ (red). Bottom: $-Q_\mathrm{cum}$ during charging.
• Figure 4: Erasure experiment results. Time evolution data are in the SM SM. (a) $-\Delta S$ versus $\Delta n_{\mathrm{BL}}$. (b) $-Q$ versus $\Delta n_{\mathrm{BL}}$. (c) $-Q$ versus $-\Delta S$. Blue line: The Landauer limit ($Q/k_{\rm B}T=\Delta S$). (d) Efficiency $\eta$ versus erasure error probability $\varepsilon_\mathrm{erasure}$. Black solid lines: theoretical calculations. Error bars: standard error of the mean for $Q$.
• Figure S1: Circuit diagram for the general calculation.