358
P. Huang et al.
RESET
SET
Fig. 11 Simulated CF geometry evolution behaviors during a RESET and b SET processes in
HfO X -based RRAM. Reprinted from [40]
∂n(r, t)
∂t
= ∇[D∇n(r, t) − V ion n(r, t)] + G
(11)
where n is the O
2− concentration, D is the diffusivity, V ion is the ion velocity, and G
is the net ion generation, which is equal to generation of V O . and
V ion = a f exp
−
E m
k B T
sinh
ea E
2k B T
(12)
Accurate field and temperature distributions are also crucial for evaluating the
hopping rates. For the sake of simplicity, only the movement to the nearest neighbor
positions is considered.
Simulated Results
The simulated CF geometry evolution during RESET and SET processes in HfO X -
based RRAM is shown in Fig. 11. Corresponding to the same resistance level, the
evolutions of filament geometry during SET are quite different from RESET. For
RESET, the whole filament firstly disconnects at the top electrode and then extends
to the interior as the sweeping voltage increases. For SET, a fine filament forms
firstly in the rupture region and then gradually extends along the radius direction as
current increases [36]. The corresponding simulated I-V characteristic is shown in
Fig. 12. It can be found that the gradual RESET and abrupt SET are reproduced by
the proposed model.
3D simulation can also be performed to reproduce the resistive switching characteristics of RRAM. As an example, a 3D volume of SiO X -RRAM has been simulated,
by investigating an oxide thickness of 15 nm and a simulated contact area of 30 nm
long and 30 nm wide [45]. Figure 13 shows the vacancy generation process. The initial
structure includes defect/Si-rich areas in the form of a pillar as shown in Fig. 13a.
At low biases, few vacancies are created. At round 5 V, filament seeds appear and
P. Huang et al.
RESET
SET
Fig. 11 Simulated CF geometry evolution behaviors during a RESET and b SET processes in
HfO X -based RRAM. Reprinted from [40]
∂n(r, t)
∂t
= ∇[D∇n(r, t) − V ion n(r, t)] + G
(11)
where n is the O
2− concentration, D is the diffusivity, V ion is the ion velocity, and G
is the net ion generation, which is equal to generation of V O . and
V ion = a f exp
−
E m
k B T
sinh
ea E
2k B T
(12)
Accurate field and temperature distributions are also crucial for evaluating the
hopping rates. For the sake of simplicity, only the movement to the nearest neighbor
positions is considered.
Simulated Results
The simulated CF geometry evolution during RESET and SET processes in HfO X -
based RRAM is shown in Fig. 11. Corresponding to the same resistance level, the
evolutions of filament geometry during SET are quite different from RESET. For
RESET, the whole filament firstly disconnects at the top electrode and then extends
to the interior as the sweeping voltage increases. For SET, a fine filament forms
firstly in the rupture region and then gradually extends along the radius direction as
current increases [36]. The corresponding simulated I-V characteristic is shown in
Fig. 12. It can be found that the gradual RESET and abrupt SET are reproduced by
the proposed model.
3D simulation can also be performed to reproduce the resistive switching characteristics of RRAM. As an example, a 3D volume of SiO X -RRAM has been simulated,
by investigating an oxide thickness of 15 nm and a simulated contact area of 30 nm
long and 30 nm wide [45]. Figure 13 shows the vacancy generation process. The initial
structure includes defect/Si-rich areas in the form of a pillar as shown in Fig. 13a.
At low biases, few vacancies are created. At round 5 V, filament seeds appear and