  With the advent of the Internet of Things, nanoelectronic devices or
memristors have been the subject of significant interest for use as new
hardware security primitives. Among the several available memristors, BiFe$\rm
O_{3}$ (BFO)-based electroforming-free memristors have attracted considerable
attention due to their excellent properties, such as long retention time,
self-rectification, intrinsic stochasticity, and fast switching. They have been
actively investigated for use in physical unclonable function (PUF) key storage
modules, artificial synapses in neural networks, nonvolatile resistive
switches, and reconfigurable logic applications. In this work, we present a
physics-inspired 1D compact model of a BFO memristor to understand its
implementation for such applications (mainly PUFs) and perform circuit
simulations. The resistive switching based on electric field-driven vacancy
migration and intrinsic stochastic behaviour of the BFO memristor are modelled
using the cloud-in-a-cell scheme. The experimental current-voltage
characteristics of the BFO memristor are successfully reproduced. The response
of the BFO memristor to changes in electrical properties, environmental
properties (such as temperature) and stress are analyzed and consistent with
experimental results.
