RRAM Device Characterizations and Modelling
355
sample surface in physical contact. A. Ranjan et al. investigate the RTN performance
on ultra-thin HfO 2 dielectric films using conductive AFM (CAFM) at a spatial resolution of 10–20 nm. Figure 8b illustrates the spatial inhomogeneity of the defect density
distribution, and it may need different measurement patterns of CAFM. Based on
the precision detection of CAFM, the metastable V O defect state and the clustering
model at nanoscale level are verified by the experiment [39].
4 Monte Carlo Dynamic Simulation of Resistive Switching
Behavior
The Monte Carlo technique is an ideal tool to study the atomic-scale evolution of
a system. For RRAM, the Monte Carlo simulation method can be used to selfconsistently simulate the microscopic process of the generation and recombination
of vacancies and the transport of interstitial oxygen ions under the external electric
field and influenced by the local temperature [40]. This benefits to deeply understand
the underlying physics of resistive switching behaviors and processes. The simulation
algorithm flow is shown in Fig. 9. Take 2D simulation as an example, the simulation is
performed on an atomic matrix with a size of m*n, where m and n depend on the fabricated device structure and size. Usually as the inputs of the simulation, the intrinsic
defects are introduced and randomly generated when initializing simulation. After
that, the potential and current distributions in the resistive switching layer are solved
by the Poisson’s equations or resistor network, and then the local temperature distribution is calculated. Following these, the probabilities of the physical effects during
resistive switching are calculated respectively. By precisely assigning different activation energies (E a ) to particles according to their local structure, the probabilities
of the physical processes can be calculated by Eqs. 1–4. The values of these activation energies can be obtained through ab-initio calculations [41] and can also be
determined as experimental parameters [42]. After obtaining the probabilities, which
physical process occurs can be decided by using Monte Carlo method by comparing
the probabilities with the random numbers uniformly distributed between [0 1]. The
time and particle distributions have to be updated in every time step. The field and
temperature distributions are updated regularly, and are in turn used to update the
vacancy/ion configurations. For each time step, all the main physical processes are
reevaluated to decide the next move. The above calculations will be repeated as the
sweeping voltage changes.
5 Simulation Method
There are two popular methods to calculate the electric field, solving the Poisson’s
equation and using the resistor network. By applying the boundary condition, the
355
sample surface in physical contact. A. Ranjan et al. investigate the RTN performance
on ultra-thin HfO 2 dielectric films using conductive AFM (CAFM) at a spatial resolution of 10–20 nm. Figure 8b illustrates the spatial inhomogeneity of the defect density
distribution, and it may need different measurement patterns of CAFM. Based on
the precision detection of CAFM, the metastable V O defect state and the clustering
model at nanoscale level are verified by the experiment [39].
4 Monte Carlo Dynamic Simulation of Resistive Switching
Behavior
The Monte Carlo technique is an ideal tool to study the atomic-scale evolution of
a system. For RRAM, the Monte Carlo simulation method can be used to selfconsistently simulate the microscopic process of the generation and recombination
of vacancies and the transport of interstitial oxygen ions under the external electric
field and influenced by the local temperature [40]. This benefits to deeply understand
the underlying physics of resistive switching behaviors and processes. The simulation
algorithm flow is shown in Fig. 9. Take 2D simulation as an example, the simulation is
performed on an atomic matrix with a size of m*n, where m and n depend on the fabricated device structure and size. Usually as the inputs of the simulation, the intrinsic
defects are introduced and randomly generated when initializing simulation. After
that, the potential and current distributions in the resistive switching layer are solved
by the Poisson’s equations or resistor network, and then the local temperature distribution is calculated. Following these, the probabilities of the physical effects during
resistive switching are calculated respectively. By precisely assigning different activation energies (E a ) to particles according to their local structure, the probabilities
of the physical processes can be calculated by Eqs. 1–4. The values of these activation energies can be obtained through ab-initio calculations [41] and can also be
determined as experimental parameters [42]. After obtaining the probabilities, which
physical process occurs can be decided by using Monte Carlo method by comparing
the probabilities with the random numbers uniformly distributed between [0 1]. The
time and particle distributions have to be updated in every time step. The field and
temperature distributions are updated regularly, and are in turn used to update the
vacancy/ion configurations. For each time step, all the main physical processes are
reevaluated to decide the next move. The above calculations will be repeated as the
sweeping voltage changes.
5 Simulation Method
There are two popular methods to calculate the electric field, solving the Poisson’s
equation and using the resistor network. By applying the boundary condition, the