  Resistance-change random access memory (RRAM) devices are nanoscale
metal-insulator-metal structures that can store information in their resistance
states, namely the high resistance (HRS) and low resistance (LRS) states. They
are a potential candidate for a universal memory as these non-volatile memory
elements can offer fast-switching, long retention and switching cycles, and
additionally, are also suitable for direct applications in neuromorphic
computing. In this study, we first present a model to analyze different
resistance states of RRAM devices or so-called "atomristors" that utilize novel
2D materials as the switching materials instead of insulators. The developed
model is then used to study the electrical characteristics of a single defect
monolayer MoS$_{2}$ memristor. The change in the device resistance between the
HRS and LRS is associated to the change in the tunneling probability when the
vacancy defects in the 2D material are substituted by the metal atoms from the
electrodes. The distortion due to defects and substituted metal atom is
captured in the 1D potential energy profile by averaging the effect along the
transverse direction. This simplification enables us to model single defect
memristors with a less extensive quantum transport model while taking into
account the presence of defects.
