Preface
xxi
fashioned name “condenser”—instead of capacitor—in his 1963 classic, “The
Feynman Lectures on Physics,” when he wrote on pages 6–12, vol. II, “The
coefficient of proportionality is called the Capacity, and such a system of two
conductors is called a Condenser” [27]. Electronic circuit theory is concerned
only with the prediction of the voltage v(t) and current i(t) associated with the
external terminals sticking out of an enclosing cocoon (henceforth called a black
box) whose interior may contain some newly minted nonlinear electronic device or
an interconnection of various electronic devices, batteries, and so on. And thus,
basic nonlinear circuit elements must be defined from a black-box perspective,
independent of their internal composition, material, geometry, and architecture.
From the circuit-theoretic point of view, the three basic two-terminal circuit
elements are defined in terms of a relationship between two of the four fundamental
circuit variables, namely, the current i, the voltage v, the charge q, and the flux
ϕ. Out of the six possible combinations of these four variables, five have led
to well-known relationships [23]. Two of these relationships are already given
by q(t) =
t
−∞ i(τ )dτ and ϕ(t) =
t
−∞ v(τ )dτ . Three other relationships
are given, respectively, by the axiomatic definition of the three classical circuit
elements, namely, the resistor (defined by a relationship between v and i), the
inductor (defined by a relationship between ϕ and i), and the capacitor (defined
by a relationship between q and v). Only one relationship remains undefined: the
relationship between ϕ and q. From the logical as well as axiomatic points of view,
it is necessary for the sake of completeness to postulate the existence of a fourth
basic two-terminal circuit element, which is characterized by a ϕ − q relationship
(see [21, Fig. 1(a)]). This element is christened the memristor because it behaves
like a nonlinear resistor with memory, remembering things past.
As a proof of principle, three memristors were built in 1969 using operational
amplifiers and off-the-shelf electronic components. They demonstrated three distinct ϕ − q curves on a bespoke memristor curve tracer that I had designed for this
purpose [4]. However, the challenge of fabricating a passive monolithic memristor
remained unfulfilled for 37 years until a team of scientists from the HP lab, under
the leadership of Dr. R. Stanley Williams, reported in May 1, 2008, issue of Nature
the world’s first operational memristor made by sandwiching a thin film of titanium
dioxide between platinum electrodes [5, 28]. The pinched hysteresis loop fingerprint
of this seminal HP memristor is reproduced below the four-element quartet in [21,
Fig. 1(a)]. It is truly remarkable that the pinched hysteresis loop is in fact an
endearing signature that nature endowed upon all basic nonlinear circuit elements
[29, 30] capable of remembering their past, including the memcapacitor and the
meminductor that I identified to be lossless at the opening lecture of the first UC
Berkeley Memristor and Memristive Systems Symposium in November 2008 [31].
Prior to Dr. Williams’s Nature paper, no one understood how certain experimental two-terminal solid-state devices could remember and switch between two or
more values of resistance without a power supply. The seminal Nature publication
has provided a unifying foundation for all nonvolatile memory devices, which go by
such names as ReRAM, PCRAM, STT-RAM, RRAM, MRAM, FRAM, PCM, and
the Atomic Switch [32], where the device’s high and low resistance states are used
xxi
fashioned name “condenser”—instead of capacitor—in his 1963 classic, “The
Feynman Lectures on Physics,” when he wrote on pages 6–12, vol. II, “The
coefficient of proportionality is called the Capacity, and such a system of two
conductors is called a Condenser” [27]. Electronic circuit theory is concerned
only with the prediction of the voltage v(t) and current i(t) associated with the
external terminals sticking out of an enclosing cocoon (henceforth called a black
box) whose interior may contain some newly minted nonlinear electronic device or
an interconnection of various electronic devices, batteries, and so on. And thus,
basic nonlinear circuit elements must be defined from a black-box perspective,
independent of their internal composition, material, geometry, and architecture.
From the circuit-theoretic point of view, the three basic two-terminal circuit
elements are defined in terms of a relationship between two of the four fundamental
circuit variables, namely, the current i, the voltage v, the charge q, and the flux
ϕ. Out of the six possible combinations of these four variables, five have led
to well-known relationships [23]. Two of these relationships are already given
by q(t) =
t
−∞ i(τ )dτ and ϕ(t) =
t
−∞ v(τ )dτ . Three other relationships
are given, respectively, by the axiomatic definition of the three classical circuit
elements, namely, the resistor (defined by a relationship between v and i), the
inductor (defined by a relationship between ϕ and i), and the capacitor (defined
by a relationship between q and v). Only one relationship remains undefined: the
relationship between ϕ and q. From the logical as well as axiomatic points of view,
it is necessary for the sake of completeness to postulate the existence of a fourth
basic two-terminal circuit element, which is characterized by a ϕ − q relationship
(see [21, Fig. 1(a)]). This element is christened the memristor because it behaves
like a nonlinear resistor with memory, remembering things past.
As a proof of principle, three memristors were built in 1969 using operational
amplifiers and off-the-shelf electronic components. They demonstrated three distinct ϕ − q curves on a bespoke memristor curve tracer that I had designed for this
purpose [4]. However, the challenge of fabricating a passive monolithic memristor
remained unfulfilled for 37 years until a team of scientists from the HP lab, under
the leadership of Dr. R. Stanley Williams, reported in May 1, 2008, issue of Nature
the world’s first operational memristor made by sandwiching a thin film of titanium
dioxide between platinum electrodes [5, 28]. The pinched hysteresis loop fingerprint
of this seminal HP memristor is reproduced below the four-element quartet in [21,
Fig. 1(a)]. It is truly remarkable that the pinched hysteresis loop is in fact an
endearing signature that nature endowed upon all basic nonlinear circuit elements
[29, 30] capable of remembering their past, including the memcapacitor and the
meminductor that I identified to be lossless at the opening lecture of the first UC
Berkeley Memristor and Memristive Systems Symposium in November 2008 [31].
Prior to Dr. Williams’s Nature paper, no one understood how certain experimental two-terminal solid-state devices could remember and switch between two or
more values of resistance without a power supply. The seminal Nature publication
has provided a unifying foundation for all nonvolatile memory devices, which go by
such names as ReRAM, PCRAM, STT-RAM, RRAM, MRAM, FRAM, PCM, and
the Atomic Switch [32], where the device’s high and low resistance states are used