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P. Huang et al.
and electrical filed/temperature. Hence the SET process is usually abrupt [21]. As
more V O generated in the insulator layer, a conductive filament consisting of V O will
connect the two electrodes, which results in the cell switching from HRS to LRS.
The generation probability (P g ) of V O under electric field during dt is governed by
the following equation [22]:
P g (E, T, dt) = f dt exp
−
E a − α a ZeE
k B T
(1)
where E is the electric field, T is the local temperature, f is the vibration frequency
of oxygen atom, E a is the average active energy of V O , α a is the enhancement factor
of the electric field for the lowering of E a , Z = 2 is the charge number of oxygen ion,
e is the unit charge and k B is the Boltzmann constant. The hopping probability (P h )
of the dissociated O
2− under the electric field during dt can be described as [23]:
P h (E, T, dt) = f dt exp
−
E h − α h ZeE
k B T
(2)
E h is the hopping barrier of O
2− and α h is the enhancement factor of the electric field
for the lowering of E h .
During RESET process, the O
2− stored in top electrode will be released and then
hop in the oxide layer. The release probability (P m ) of an O
2− is governed by the
equation [24]:
P m (V, T, dt) = f dt exp
−
E i − γ ZeV
k B T
(3)
V is the external voltage, E i is the energy barrier between the electrode and oxide,
γ is the enhancement factor of the external voltage during the O
2− release process.
The dissociated O
2− can recombine with V O , which can be modeled as an energy
relaxation process and governed by the following equation [22]:
P r (T, dt) = f dt exp
−
E r
k B T
(4)
Pr (T, dt) is the probability of the recombination between V O and O
2− during dt,
ΔE r is the relaxation energy during the recombination process. The recombination
between the O
2− and V O will lead to the rupture of conductive filament and a gap
region forms between the CF and top electrode. So the current decreases and the
device switches from LRS to HRS. As V O recombined with O
2− , the electrical
filed in the gap region and temperature will decrease and the hopping of O
2− and
recombination will become slow. It means that there is a negative feedback between
the rupture of conductive filament and the decrease of electrical field and temperature.
Therefore, the RESET process is usually gradual and more than hundreds of states
can be achieved under proper voltage pulses during the RESET process [21, 25].
P. Huang et al.
and electrical filed/temperature. Hence the SET process is usually abrupt [21]. As
more V O generated in the insulator layer, a conductive filament consisting of V O will
connect the two electrodes, which results in the cell switching from HRS to LRS.
The generation probability (P g ) of V O under electric field during dt is governed by
the following equation [22]:
P g (E, T, dt) = f dt exp
−
E a − α a ZeE
k B T
(1)
where E is the electric field, T is the local temperature, f is the vibration frequency
of oxygen atom, E a is the average active energy of V O , α a is the enhancement factor
of the electric field for the lowering of E a , Z = 2 is the charge number of oxygen ion,
e is the unit charge and k B is the Boltzmann constant. The hopping probability (P h )
of the dissociated O
2− under the electric field during dt can be described as [23]:
P h (E, T, dt) = f dt exp
−
E h − α h ZeE
k B T
(2)
E h is the hopping barrier of O
2− and α h is the enhancement factor of the electric field
for the lowering of E h .
During RESET process, the O
2− stored in top electrode will be released and then
hop in the oxide layer. The release probability (P m ) of an O
2− is governed by the
equation [24]:
P m (V, T, dt) = f dt exp
−
E i − γ ZeV
k B T
(3)
V is the external voltage, E i is the energy barrier between the electrode and oxide,
γ is the enhancement factor of the external voltage during the O
2− release process.
The dissociated O
2− can recombine with V O , which can be modeled as an energy
relaxation process and governed by the following equation [22]:
P r (T, dt) = f dt exp
−
E r
k B T
(4)
Pr (T, dt) is the probability of the recombination between V O and O
2− during dt,
ΔE r is the relaxation energy during the recombination process. The recombination
between the O
2− and V O will lead to the rupture of conductive filament and a gap
region forms between the CF and top electrode. So the current decreases and the
device switches from LRS to HRS. As V O recombined with O
2− , the electrical
filed in the gap region and temperature will decrease and the hopping of O
2− and
recombination will become slow. It means that there is a negative feedback between
the rupture of conductive filament and the decrease of electrical field and temperature.
Therefore, the RESET process is usually gradual and more than hundreds of states
can be achieved under proper voltage pulses during the RESET process [21, 25].