TCAD Modeling of Resistive-Switching of HfO2 Memristors: Efficient Device-Circuit Co-Design for Neuromorphic Systems

Abstract

In neuromorphic computing, memristors (or “memory resistors”) have been primarily studied as key elements in artificial synapse implementations, where the memristor provides a variable weight with intrinsic long-term memory capabilities, based on its modifiable resistive-switching characteristics. Here, we demonstrate an efficient methodology for simulating resistive-switching of HfO2 memristors within Synopsys TCAD Sentaurus—a well established, versatile framework for electronic device simulation, visualization and modeling. Kinetic Monte Carlo is used to model the temporal dynamics of filament formation and rupture wherein additional band-to-trap electronic transitions are included to account for polaronic effects due to strong electron-lattice coupling in HfO2. The conductive filament is modeled as oxygen vacancies which behave as electron traps as opposed to ionized donors, consistent with recent experimental data showing p-type conductivity in HfOx films having high oxygen vacancy concentrations and ab-initio calculations showing the increased thermodynamic stability of neutral and charged oxygen vacancies under conditions of electron injection. Pulsed IV characteristics are obtained by inputting the dynamic state of the system—which consists of oxygen ions, unoccupied oxygen vacancies, and occupied oxygen vacancies at various positions—into Synopsis TCAD Sentaurus for quasi-static simulations. This allows direct visualization of filament electrostatics as well as the implementation of a nonlocal, trap-assisted-tunneling model to estimate current-voltage characteristics during switching. The model utilizes effective masses and work functions of the top and bottom electrodes as additional parameters influencing filament dynamics. Together, this approach can be used to provide valuable device- and circuit-level insight, such as forming voltage, resistance levels and success rates of programming operations, as we demonstrate.

Memristor Compact Model with Oxygen-Vacancy Concentration as State Variable

“…For 2D or 3D modeling, in which spatiallydependent features are integral, a quantum approach may be desired for its improved accuracy. A complete derivation of both is provided in the supplementary material of our previous work [37] and elsewhere [42,43] as implemented in standard device simulators [44].…”

“…The shift from a tunnel gap to a concentration state variable may be more physically appropriate, given that the formation of a one-dimensional defect chain is statistically unlikely considering other competing factors such as vacancy diffusion, thermophoresis [24] and the increased thermodynamic stability of defect clusters [35] expected to lead to additional conduction pathways. These, along with the presence of grain-boundaries and other imperfections which may reduce the zero-field formation enthalpy of oxygen vacancies suggest a variety of filament shapes with varying connectivity as seen in comprehensive modeling approaches [31,36,37] and experimental observations [38].…”

“…In our model, the oxygen vacancy concentration is split into two state variables to allow the electron-occupancy of the vacancies to vary between occupied and unoccupied depending on electron capture and emission processes. This is based on recent KMC modeling approaches [37] and reflects ab-initio calculations showing increased thermodynamic stability of negatively-charged oxygen vacancies under conditions of electron-injection [35] as well as experimental observations of a negative-space charge associated with suspected filament regions [38]. This has immediate implications on retention, since a larger thermal emission barrier would result in a more stable low resistance state and therefore, longer retention time as we show by comparison to experimental data of memristors having different electrode materials.…”

“…This has immediate implications on retention, since a larger thermal emission barrier would result in a more stable low resistance state and therefore, longer retention time as we show by comparison to experimental data of memristors having different electrode materials. The compact model is implemented in Verilog-A, using simplifying assumptions made to our previous model [37]. In particular, a key approximation is that the field-dependence of the microstate transitions is approximated using the average electric field as opposed to the local electric field.…”

“…Together, Equations 9, 11 and 12 define a dynamic relationship between atomic and electronic processes, which we have evaluated numerically in a recent manuscript in two dimensions, taking into account diffusion, Frenkel pair generation and recombination, electron capture and emission [37]. For simplicity, the compact model developed here does not consider diffusion; diffusion of charged point-defects would produce a spatially and time-dependent electric field which would complicate compact model development.…”