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2 Fundamental Properties of Mem-Elements
The prophecy has come true 37 years later when, in 2008, the team at HP
laboratories led by S. Williams published a paper entitled “The missing memristor
found” [28] where, in their words, they present “the logical and scientific basis
for the existence of a new two-terminal circuit element called the memristor
(contraction for memory resistor) which has every right to be as basic as the three
classical circuit elements already in existence, namely, the resistor, inductor, and
capacitor.” In that paper it is also shown, “using a simple analytical example, that
memristance arises naturally in nanoscale systems in which solid-state electronic
and ionic transport are coupled under an external bias voltage.”
The HP memristor [28] is a capacitor-like Metal-Insulator-Metal (MIM) structure
consisting of a thin titanium oxide TiO 2 film (50 nm) sandwiched between two
metal (platinum) contacts (Fig. 2.24). Actually, TiO 2 is split into two chemically
different layers. Stoichiometric TiO 2 (the ratio of oxygen to titanium was perfect,
exactly 2 to 1) and closer to the top platinum electrode, the titanium dioxide is
missing a tiny amount of its oxygen, between 2 and 3 %, called oxygen-deficient
titanium dioxide TiO 2−x , where x is about 0.05 %. The TiO 2 is electrically
insulating (actually a semiconductor), but the TiO 2−x is conductive, because its
oxygen vacancies are donors of electrons, which makes the vacancies themselves
positively charged. Then, the semiconductor film has a region with a low resistance
R on , while the remaining part has a much higher resistance R off . The total resistance
of the device is thus determined by two variable resistors connected in series
(Fig. 2.24). The resistive state of the HP memristor is modulated by the bias voltage
applied across the electrodes because the electric field is capable of shifting the
interface between TiO 2 and TiO 2−x due to the migration of oxygen vacancies.
As remarked in [28], “vacancies . . . can be pushed up and down at will in the
titanium dioxide material because they are electrically charged.” In fact, if a positive
voltage is applied to the top electrode of the device, it will repel the (also positive)
oxygen vacancies in the TiO 2−x layer down into the pure TiO 2 layer. That turns
the TiO 2 layer into TiO 2−x and makes it more conductive. A negative voltage has
the opposite effect: the vacancies are attracted upward and back out of the TiO 2 ,
and thus the thickness of the TiO 2 layer increases and the device becomes less
conductive. In [28] it is also stressed that the “resistance of these devices stayed
constant whether we turned off the voltage or just read their states (interrogating
them with a voltage so small it left the resistance unchanged). The oxygen vacancies
didn’t roam around; they remained absolutely immobile until we again applied
a positive or negative voltage. That’s memristance: the devices remembered their
current history. We had coaxed Chua’s mythical memristor off the page and into
being.”
Both fields, resistive switching and memristor theory, share a similar goal,
namely, describing and controlling the process of storing information in the resistive
state of an electronic device. Initiated around the same time and in parallel, both
have been largely ignored because of the lack of an immediate practical application
and because CMOS technology was already performing similar tasks at reduced
cost.
2 Fundamental Properties of Mem-Elements
The prophecy has come true 37 years later when, in 2008, the team at HP
laboratories led by S. Williams published a paper entitled “The missing memristor
found” [28] where, in their words, they present “the logical and scientific basis
for the existence of a new two-terminal circuit element called the memristor
(contraction for memory resistor) which has every right to be as basic as the three
classical circuit elements already in existence, namely, the resistor, inductor, and
capacitor.” In that paper it is also shown, “using a simple analytical example, that
memristance arises naturally in nanoscale systems in which solid-state electronic
and ionic transport are coupled under an external bias voltage.”
The HP memristor [28] is a capacitor-like Metal-Insulator-Metal (MIM) structure
consisting of a thin titanium oxide TiO 2 film (50 nm) sandwiched between two
metal (platinum) contacts (Fig. 2.24). Actually, TiO 2 is split into two chemically
different layers. Stoichiometric TiO 2 (the ratio of oxygen to titanium was perfect,
exactly 2 to 1) and closer to the top platinum electrode, the titanium dioxide is
missing a tiny amount of its oxygen, between 2 and 3 %, called oxygen-deficient
titanium dioxide TiO 2−x , where x is about 0.05 %. The TiO 2 is electrically
insulating (actually a semiconductor), but the TiO 2−x is conductive, because its
oxygen vacancies are donors of electrons, which makes the vacancies themselves
positively charged. Then, the semiconductor film has a region with a low resistance
R on , while the remaining part has a much higher resistance R off . The total resistance
of the device is thus determined by two variable resistors connected in series
(Fig. 2.24). The resistive state of the HP memristor is modulated by the bias voltage
applied across the electrodes because the electric field is capable of shifting the
interface between TiO 2 and TiO 2−x due to the migration of oxygen vacancies.
As remarked in [28], “vacancies . . . can be pushed up and down at will in the
titanium dioxide material because they are electrically charged.” In fact, if a positive
voltage is applied to the top electrode of the device, it will repel the (also positive)
oxygen vacancies in the TiO 2−x layer down into the pure TiO 2 layer. That turns
the TiO 2 layer into TiO 2−x and makes it more conductive. A negative voltage has
the opposite effect: the vacancies are attracted upward and back out of the TiO 2 ,
and thus the thickness of the TiO 2 layer increases and the device becomes less
conductive. In [28] it is also stressed that the “resistance of these devices stayed
constant whether we turned off the voltage or just read their states (interrogating
them with a voltage so small it left the resistance unchanged). The oxygen vacancies
didn’t roam around; they remained absolutely immobile until we again applied
a positive or negative voltage. That’s memristance: the devices remembered their
current history. We had coaxed Chua’s mythical memristor off the page and into
being.”
Both fields, resistive switching and memristor theory, share a similar goal,
namely, describing and controlling the process of storing information in the resistive
state of an electronic device. Initiated around the same time and in parallel, both
have been largely ignored because of the lack of an immediate practical application
and because CMOS technology was already performing similar tasks at reduced
cost.