Every software package contains a full set of examples suitable for that version and are installed with the software. If you see examples here that are not in your installation you should consider updating to a later version of the software. These examples can be used by beginners and advanced users for product evaluation, teaching purposes, and self-training.
Required Modules
Victory Mesh
- 3D Meshing
Victory Device
- 3D Simulator
- 3D Chemistry
- 3D Giga
- 3D MixedMode
This example is related to the SISPAD publication [1] and to the Silvaco Simulation Standard 2017 article [2], and demonstrates how to simulate the I(V) characteristics of an HfO2-based ReRAM using Victory Device. The simulated device is based on 1T1R memory cell with a compliance transistor for the current limitation. The effect of the transistor is taken into account within a mixed-mode simulation. The circuit including the compliance transistor as well as the operation of the 1T1R memory cell is specified within a SPICE-like section. This section is located between the .BEGIN and the .END statement of the file ReRAM_ex01.in and changes depending on the particular device operation. The ReRAM itself is described in the file RERAM_AUX.in, which is included int the ReRAM_ex01.in using the SOURCE statement. The file ReRAM_AUX.in contains the following information:
1) The filament formation and rupture is described by the two chemical reactions
REACTION formula= “SiOx + 2e- <=> Vo + Ox- ” forward.rate=2.5e-13 forward.ea=2 reverse.rate=1e-11 reverse.ea=0.5 dipole.moment=8e-8 dipole.orientation=(0.0,-1.0,0.0) dipole.fraction=0.5 dipole.permittivity=21
REACTION formula= “IfOx + 2e- <=> If + Ox- ” forward.rate=6.6e-13 forward.ea=2 reverse.rate=3e-11 reverse.ea=1.15 dipole.moment=7e-8 dipole.orientation=(0.0,+1.0,0.0) dipole.fraction=0.5 dipole.permittivity=21
with the involved species defined on the following SPECIES statements:
SPECIES formula= “Si:Ox ” charge=+0 name= “SiOx “
SPECIES formula= “Si ” charge=+0 name= “Vo “
SPECIES formula= “Ox ” charge=-2 name= “Ox- “
SPECIES formula= “Ti ” charge=+0 name= “If “
SPECIES formula= “Ti:Ox ” charge=-0 name= “IfOx “
The first reaction describes the decay of the weak spots (SiOx) into oxygen vacancies (Vo) and oxygen interstitials (Ox-) upon the application of an electric field. The Vo remain fixed due to their negligible diffusion constant but they can carry a trap-to-trap tunneling current. The Ox- can drift to the active top electrode, where they can undergo a reaction with interfacial defects (If) and become IfOx according to the second reaction. The initial profile of the chemical species are given by the DOPING or the INTERFACE statements. The SiOx concentration is assumed to peak at the center of the device cell, which is the location where the conductive filament forms or disolves during the SET/RESET operation. The If and IfOx sites represent the active electrode and therefore are defined at the top interface while they are absent at the bottom electrode.
2) The initial conductivity of the oxide is specified on the MOBILITY statement by using the C-Interpreter function in the file functions.c
MOBILITY region=1 F.CONMUN=functions.c
with its parameters given by the OPTION statements:
OPTIONS cint.param=MUN_X0 cint.double=1e-3
OPTIONS cint.param=MUN_DX cint.double=1e-4
OPTIONS cint.param=MUN_YMIN cint.double=2.0e+2
OPTIONS cint.param=MUN_YMAX cint.double=5.0e+5
This conductivity accounts for pre-existing defects, which can carry a small current through the oxide and thereby heats up te device. They are located close to the region where the conductive filament will form and disrupt during the hysteresis cycle. The conductance of the conductive filament itself is represented by the bridging mobility model, where the mobility depends on the concentration of the oxygen vacancies.
MOBILITY material=silicon bridging.species= “Vo ” \
bridging.conductivity=3.0e5 \
bridging.min.fraction=0.40 \
bridging.delta = 0.11
3) The thermal effects play a key role in ReRAM devices and, therefore, the lattice heatflow equation is enabled by setting the flag LAT.TEMP on the MODELS statement. The top and the bottom electrode are connected to thermal contacts as defined on the THERMCONTACT statements. The heating due to the trap-assisted tunneling current through the oxide is considered by joule heating by setting the flag JOULE.HEAT on the MODELS statement. The heat flow also considers a temperature dependent thermal conductivity, which is defined by a C-Interpreter function on the MATERIAL statement, and an interfacial heat transfer conductance on the INTERFACE statement:
MATERIAL material=silicon F.TCOND=functions.c
INTERFACE r1number=1 r2number=2 ihtc.rounded ihtc.t.low=600 ihtc.h.low=1e+4 ihtc.t.high=1200 ihtc.h.high=8e6
INTERFACE r1number=1 r2number=3 ihtc.rounded ihtc.t.low=600 ihtc.h.low=1e+4 ihtc.t.high=1200 ihtc.h.high=8e6
The full simulation is in the file ReRAM_ex01.in and consists of four parts:
1) Structure generation:
The radially symmetric ReRAM structure consists of an HfO2 oxide which lies inbetween the active and inactive electrodes. The generated mesh is refined around the filament located in the middle of the radial structure. It is noted that the oxide (region 1) is defined as a semiconductor but with a large bandgap in order to emulate an insulator in the simulation.
2) Equilibration phase:
An equilibration step is carried out in order to balance all chemical reactions. This is achieved by a transient simulation, in which no bias is applied to the device terminals and the temperature are set to a high value of 600K for a fast equilibration. The simulation of the 1T1R ReRAM cell is based on a mixed-mode simulation, where the actual ReRAM is in series with the compliance transistor. The source and the bulk contacts of the compliance transistor are grounded while a bias of 1V is applied to the gate contact. The drain contact is connected to the bottom electrode of the ReRAM and the bias ‘va’ is applied to the top electrode. During the equilibration step, the bias at this node remains constant at 0V during the whole time interval from 0s to 1s. While the details of the circuit simulation are given in the file ReRAM_ex01.in, the physical description of the ReRAM is included from the file RERAM_AUX.in using the SOURCE statement. At the end of the equilibration step, the solution is saved in the file ReRAM_ex01_equilibrium_aR.str, which will be taken as a starting point for the subsequent simulations of the current hysteresis and the current run-away.
3) Current hysteresis:
In the hysteresis simulation, the I(V) characteristics are calculated using a transient simulation where the applied bias is swept between -1.5V and +1.5V. So, the bias is first ramped up to 1.5V during the first 15s (SET forward) and goes back to 0V after the next 15s (SET reverse). Then, the bias is ramped down to -1.5V during the next 15s (RESET forward) and goes back to 0V after the next 15s (RESET backward). In the inputdeck, this zigzag curve is defined as a piecewise linear function for the contact ‘va’. The simulated hysteresis curve is plotted using Victory Visual and shows the expected current hysteresis for the SET and the RESET phase.
4) Current run-away:
This simulation should demonstrate that a compliance transistor is required to prevent the current run-away. For this purpose, the effect of the compliance transistor is removed by increasing the conductance of the transistor. The run-away simulation covers only the SET forward phase and is stopped when the given compliance temperature is exeeded. The simulation result is overlaid to the hysteresis curve and demonstrates the current run-away without the current compliance.
[1] Y. Hirchaou et al., “Advanced TCAD Modeling of HfO2-based ReRAM: Coupling Redox Reactions and Thermal Effects, ” SISPAD 2023, Kobe, Japan, 2023, pp. 333-336, doi: 10.23919/SISPAD57422.2023.10319635.
[2] Silvaco Simulation Standard 2024 article “Advanced TCAD Modeling of HfO2-based ReRAM: Coupling Redox Reactions and Thermal Effects “.
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