370
P. Huang et al.
the array is more significant during RESET than during SET, since the initial larger
current flow in RC network leads to a larger latency feedback. The power dissipation during the operation can also be investigated by the compact model as shown
in Fig. 23d. The average power dissipation decreases with the array size due to the
decrease of the V GS and I max of the selected cell, which is caused by the increased
voltage drop along the signal lines. However, the power dissipation increases with
the array size resulting from the increase of sneak current path.
9 Marc-Bocquet Model
Based on the creation and destruction of CF assisted by the joule heat and the electrical
field, Marc-Bocquet presented the models for the bipolar and unipolar RRAM [53,
54]. The models discussed above regard to the bipolar RRAM, so here we only focus
on the compact for the unipolar RRAM. As shown in Fig. 24, the CF connecting
two electrodes will grow and rupture, which depends on the applied voltage. The
temperature of the cell will increase due to the joule heat. In one dimension geometry,
the heat equation can be simply written as:
σ CF (x) · ξ(x)
2
= −K th CF
∂
2 T CF
∂ x 2 + h
T CF (x) − T ox
t ox
(23)
where σ CF is the CF conductivity, T CF (x) is the CF temperature, T ox is the oxide
temperature, K thCF is the CF thermal conductivity, t ox is the oxide thickness, and h is
the heat transfer coefficient between CF and surrounding oxide. The CF is assumed
to be metallic with a high conductivity σ CF . In contrast, the resistance of the oxide
gap is higher. The analytical expression of the electric field ξ can be derived:
ξ(x) = I 0 · R(x)
(24)
Fig. 24 Schematic representation of a formed and dissolved conductive filament resulting from
SET and RESET operations, respectively, in MIM structure. During RESET, the inner temperature is raised by Joule effect and leads to the destruction of the CF. In contrast, during SET, an
electrochemical local reduction process enables restoring CF. Reprinted from [53]
P. Huang et al.
the array is more significant during RESET than during SET, since the initial larger
current flow in RC network leads to a larger latency feedback. The power dissipation during the operation can also be investigated by the compact model as shown
in Fig. 23d. The average power dissipation decreases with the array size due to the
decrease of the V GS and I max of the selected cell, which is caused by the increased
voltage drop along the signal lines. However, the power dissipation increases with
the array size resulting from the increase of sneak current path.
9 Marc-Bocquet Model
Based on the creation and destruction of CF assisted by the joule heat and the electrical
field, Marc-Bocquet presented the models for the bipolar and unipolar RRAM [53,
54]. The models discussed above regard to the bipolar RRAM, so here we only focus
on the compact for the unipolar RRAM. As shown in Fig. 24, the CF connecting
two electrodes will grow and rupture, which depends on the applied voltage. The
temperature of the cell will increase due to the joule heat. In one dimension geometry,
the heat equation can be simply written as:
σ CF (x) · ξ(x)
2
= −K th CF
∂
2 T CF
∂ x 2 + h
T CF (x) − T ox
t ox
(23)
where σ CF is the CF conductivity, T CF (x) is the CF temperature, T ox is the oxide
temperature, K thCF is the CF thermal conductivity, t ox is the oxide thickness, and h is
the heat transfer coefficient between CF and surrounding oxide. The CF is assumed
to be metallic with a high conductivity σ CF . In contrast, the resistance of the oxide
gap is higher. The analytical expression of the electric field ξ can be derived:
ξ(x) = I 0 · R(x)
(24)
Fig. 24 Schematic representation of a formed and dissolved conductive filament resulting from
SET and RESET operations, respectively, in MIM structure. During RESET, the inner temperature is raised by Joule effect and leads to the destruction of the CF. In contrast, during SET, an
electrochemical local reduction process enables restoring CF. Reprinted from [53]