362
P. Huang et al.
instance, even if a universal compact model covered all the features of Ox-RRAM is
still not available, many models have been proposed with various degrees of accuracy,
different features, and mixed results.
The first model of RRAM is the memristor model proposed by Chua [49]. Strukov
et al. presented a physical model of a two-terminal electrical device that behaves like
a perfect memristor for a certain restricted range of the state variable w [50]. The
model provides a simplified explanation for the reports of current–voltage anomalies,
including switching and hysteretic conductance, multiple conductance states and
apparent negative differential resistance. Guan et al. presented a compact model by
considering the generation/migration of V O /oxygen ion [51]. The proposed model
is implemented in Ngspice as a macrocircuit. P. Huang et al. proposed a physical
electro-thermal model by modelling the length and width of filament [25, 40]. The
model can be implemented into HSPICE for the simulation of large-scale RRAM
based circuit by Verilog-A [52]. By modelling the local electrochemical reduction
and redox, a self-consistent physical model for SET/RESET operations is built for
unipolar RRAM by Bocquet et al. [53]. By gathering local electrochemical reactions
and heat equation in a single master equation, M. Bocquet et al. proposed a robust
compact model for simultaneously describing Forming, SET, and RESET operations
of bipolar RRAM [54]. A self-accelerated thermal dissolution model for RESET
operation of unipolar RRAM is proposed by Russo et al. via accurately modelling
the joule heat and temperature [55, 56]. Larentis et al. presented a numerical RESET
model based on temperature/field-driven ion migration in bipolar RRAM devices
[28]. A brief summary of the presented models is listed in Table 1. Three typical
compact models of Ox-RRAM will be discussed in detail in this section.
7 Linear Ion Drift
In 2008, RRAM devices were linked with memristor and a couple variable-resistor
model is proposed to understand the hysteretic I-V relation by HP Labs [50]. RRAM
device is modelled as two films sandwiched between two electrodes as shown in
Fig. 18a. The total resistance of the device is determined by two variable resistor
connected in series. The doped film with thickness D has a low resistance R on . And
the resistance of the other undoped film is relatively high, called as R off . The boundary
of this two films will move caused by the drift of dopants when an external bias v(t)
is applied. The relation between the external applied voltage v(t) and the current
through the device i(t) owing to Ohmic electronic conductance and linear ionic drift
in a uniform field with average ion mobility is given by:
v(t) =
R on
w(t)
D
+ R off
1 −
w(t)
D
i(t)
(13)
The state variable of above equation is the w(t) and can be expressed as:
P. Huang et al.
instance, even if a universal compact model covered all the features of Ox-RRAM is
still not available, many models have been proposed with various degrees of accuracy,
different features, and mixed results.
The first model of RRAM is the memristor model proposed by Chua [49]. Strukov
et al. presented a physical model of a two-terminal electrical device that behaves like
a perfect memristor for a certain restricted range of the state variable w [50]. The
model provides a simplified explanation for the reports of current–voltage anomalies,
including switching and hysteretic conductance, multiple conductance states and
apparent negative differential resistance. Guan et al. presented a compact model by
considering the generation/migration of V O /oxygen ion [51]. The proposed model
is implemented in Ngspice as a macrocircuit. P. Huang et al. proposed a physical
electro-thermal model by modelling the length and width of filament [25, 40]. The
model can be implemented into HSPICE for the simulation of large-scale RRAM
based circuit by Verilog-A [52]. By modelling the local electrochemical reduction
and redox, a self-consistent physical model for SET/RESET operations is built for
unipolar RRAM by Bocquet et al. [53]. By gathering local electrochemical reactions
and heat equation in a single master equation, M. Bocquet et al. proposed a robust
compact model for simultaneously describing Forming, SET, and RESET operations
of bipolar RRAM [54]. A self-accelerated thermal dissolution model for RESET
operation of unipolar RRAM is proposed by Russo et al. via accurately modelling
the joule heat and temperature [55, 56]. Larentis et al. presented a numerical RESET
model based on temperature/field-driven ion migration in bipolar RRAM devices
[28]. A brief summary of the presented models is listed in Table 1. Three typical
compact models of Ox-RRAM will be discussed in detail in this section.
7 Linear Ion Drift
In 2008, RRAM devices were linked with memristor and a couple variable-resistor
model is proposed to understand the hysteretic I-V relation by HP Labs [50]. RRAM
device is modelled as two films sandwiched between two electrodes as shown in
Fig. 18a. The total resistance of the device is determined by two variable resistor
connected in series. The doped film with thickness D has a low resistance R on . And
the resistance of the other undoped film is relatively high, called as R off . The boundary
of this two films will move caused by the drift of dopants when an external bias v(t)
is applied. The relation between the external applied voltage v(t) and the current
through the device i(t) owing to Ohmic electronic conductance and linear ionic drift
in a uniform field with average ion mobility is given by:
v(t) =
R on
w(t)
D
+ R off
1 −
w(t)
D
i(t)
(13)
The state variable of above equation is the w(t) and can be expressed as: