Stochastic Analysis of Retention Time of Coupled Memory Topology

TL;DR

This paper introduces a physics-inspired mathematical framework to analyze retention times in coupled memory topologies, providing analytical tools to predict performance and material effects without extensive experiments.

Contribution

It presents a novel, generic analytical framework based on Glauber dynamics for evaluating retention times in coupled memory systems, validated by matching simulations.

Findings

Closed-form expressions for retention times in various topologies

Framework accurately predicts retention times matching simulations

Provides insights into material and topology impacts on retention

Abstract

Recently, it has been experimentally demonstrated that individual memory units coupled in certain topology can provide the intended performance. However, experimental or simulation based evaluation of different coupled memory topologies and materials are costly and time consuming. In this paper, inspired by Glauber dynamics models in non-equilibrium statistical mechanics, we propose a physically accurate generic mathematical framework for analyzing retention times of various coupled memory topologies and materials. We demonstrate efficacy of the proposed framework by deriving closed form expressions for a few popular coupled and uncoupled memory topologies, which match simulations. Our analysis also offers analytical insights helping us estimate the impact of materials and topologies on retention time.