2.2 Ideal Memristors and Non-volatile Memories
47
pulses. A nano-scale device with resistance which can be modulated electronically
would permit denser analogue circuits, multi-state memory and large-scale, solidstate artificial neural networks, where it would be crucial in implementing neuron
synapses and learning [10–12].
2.2.3 Ideal Memristor as Discrete Memory Memristor
In digital computer applications, to be used as a nonvolatile binary memory, a fluxcontrolled memristor should exhibit only two sufficiently distinct memductances.
Example 2.12 Consider a memristor with the piecewise linear CR in Fig. 2.19a,
thus q = ˆ
q(ϕ) has a zero slope segment for |ϕ| ≤ 2.5 Wb and two straight lines with
slope 800 nS when |ϕ| > 2.5 Wb. Such a memristor exhibits just two memory states
corresponding to the two different values 0 nS and 800 nS of memconductance. Let
us perform an experiment where the initial memristor flux ϕ(0) = 0 and we apply a
square voltage waveform as in the upper part of Fig. 2.19b. The result is a triangular
waveform for ϕ (middle part of Fig. 2.19b) while the memductance W (t) displays a
square waveform switching between the two levels 0 nS and 800 nS (lower part of
Fig. 2.19b).
If a flux-controlled or charge-controlled ideal memristor is defined by a piecewise
linear CR with multiple slopes, then it acts as a discrete memory memristor, that is
there exist multiple memory states corresponding to the memristance/memductance
values specified by the slopes. Each memory state can be programmed by suitable
input pulses.
To summarize, an ideal flux-controlled (resp., charge-controlled) memristor has
a continuum of equilibrium states, i.e., it can memorize in a nonvolatile way
infinitely many values of the flux (resp., of the charge) as stable EPs. The corresponding memorized conductances (resp., memristances) may assume a continuum
of values or a discrete set of values.
At any EP we have v = 0 and i = 0, i.e., the memristor current, voltage, and
absorbed power are zero. It is important to observe that if one opens or short-circuits
a memristor having a given memductance (resp., memristance) at t 0 , the memristor
does not lose the value of memductance (resp., memristance) because both voltage
and current become zero at the instant when the power is switched off, but rather
holds the value unchanged thereafter! Because memristors remember their state
even when the power is turned off, it is (ideally) possible to store data indefinitely,
using energy only when the state of a memristor is toggled or read. We stress that is
basically different from capacitors in conventional dynamic RAM (DRAM), which
in practice will quickly lose their stored charge, if the power to the chip is turned
off, due to leakage currents.
47
pulses. A nano-scale device with resistance which can be modulated electronically
would permit denser analogue circuits, multi-state memory and large-scale, solidstate artificial neural networks, where it would be crucial in implementing neuron
synapses and learning [10–12].
2.2.3 Ideal Memristor as Discrete Memory Memristor
In digital computer applications, to be used as a nonvolatile binary memory, a fluxcontrolled memristor should exhibit only two sufficiently distinct memductances.
Example 2.12 Consider a memristor with the piecewise linear CR in Fig. 2.19a,
thus q = ˆ
q(ϕ) has a zero slope segment for |ϕ| ≤ 2.5 Wb and two straight lines with
slope 800 nS when |ϕ| > 2.5 Wb. Such a memristor exhibits just two memory states
corresponding to the two different values 0 nS and 800 nS of memconductance. Let
us perform an experiment where the initial memristor flux ϕ(0) = 0 and we apply a
square voltage waveform as in the upper part of Fig. 2.19b. The result is a triangular
waveform for ϕ (middle part of Fig. 2.19b) while the memductance W (t) displays a
square waveform switching between the two levels 0 nS and 800 nS (lower part of
Fig. 2.19b).
If a flux-controlled or charge-controlled ideal memristor is defined by a piecewise
linear CR with multiple slopes, then it acts as a discrete memory memristor, that is
there exist multiple memory states corresponding to the memristance/memductance
values specified by the slopes. Each memory state can be programmed by suitable
input pulses.
To summarize, an ideal flux-controlled (resp., charge-controlled) memristor has
a continuum of equilibrium states, i.e., it can memorize in a nonvolatile way
infinitely many values of the flux (resp., of the charge) as stable EPs. The corresponding memorized conductances (resp., memristances) may assume a continuum
of values or a discrete set of values.
At any EP we have v = 0 and i = 0, i.e., the memristor current, voltage, and
absorbed power are zero. It is important to observe that if one opens or short-circuits
a memristor having a given memductance (resp., memristance) at t 0 , the memristor
does not lose the value of memductance (resp., memristance) because both voltage
and current become zero at the instant when the power is switched off, but rather
holds the value unchanged thereafter! Because memristors remember their state
even when the power is turned off, it is (ideally) possible to store data indefinitely,
using energy only when the state of a memristor is toggled or read. We stress that is
basically different from capacitors in conventional dynamic RAM (DRAM), which
in practice will quickly lose their stored charge, if the power to the chip is turned
off, due to leakage currents.