The present invention relates to memristive devices, and more particularly, to techniques for using field effects to reduce a threshold voltage of memristive devices via an applied gate voltage.
Resistive memory devices (termed ‘memristive’ devices) store information based on the resistance of an active region of the device. Phase change materials are an ideal candidate for use as the active region since they can encode information based on the phase configuration, and hence resistance, of the material.
A key parameter governing the implementation of memristive memory devices is the threshold voltage. Namely, in modern multi-level memristive memory devices and analog computational memory devices, threshold voltages are non-trivial owing to the choice and large volumes of the phase change materials employed. However, large threshold voltages undesirably increase the overall power dissipation of the device.
Further, multiple access transistors, attached in series, are often required to access memristive memory devices, where the voltage distribution between the transistors ensures that no access transistor is over-driven in the state of high field and potential breakdown. However, the use of multiple access transistors increases the areal complexity (i.e., inefficiencies) of the device architecture.
Therefore, techniques that efficiently and effectively reduce the threshold voltage of phase change material-based devices such as memristive memory devices would be desirable.
The present invention provides techniques for using field effects to reduce a threshold voltage of memristive devices via an applied gate voltage. In one aspect of the invention, a memristive device is provided. The memristive device includes: a memristive material; multiple electrodes directly contacting the memristive material; and a gate terminal separated from the memristive material by an electrical insulator.
In another aspect of the invention, a system is provided. The system includes: a unit cell having multiple memristive devices, wherein each of the multiple memristive devices includes a memristive material, multiple electrodes directly contacting the memristive material, and a gate terminal separated from the memristive material by an electrical insulator; and a gate word line connected to the gate terminal of each of the multiple memristive devices in the unit cell.
In yet another aspect of the invention, a method for operating a memristive device is provided. The method includes: applying a gate voltage to the memristive device, where the memristive device includes a memristive material, multiple electrodes directly contacting the memristive material, and a gate terminal separated from the memristive material by an electrical insulator, and where the gate voltage is applied to the gate terminal to build up charge in the memristive material, thereby lowering a threshold voltage of the memristive material via field effects.
A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings.
As described above, the threshold voltage in conventional memristive memory architectures is non-trivial, undesirably leading to increased power dissipation and area complexity tradeoffs. Advantageously, provided herein is a device-level approach to easily and effectively reduce the threshold voltage or VTH of memristive memory devices and selector cells.
As will be described in detail below, the present devices uniquely employ a separate gate terminal offset from a memristive material by an insulator (e.g., an oxide or ferroelectric material) that, via field effects, reduces the VTH of the devices. Namely, an external electric field applied to the gate terminal is used to build up charge in the memristive material, thereby modulating the Fermi level of the memristive material to alter the activation energy. The use of a ferroelectric insulator provides the added benefit of non-volatility. Namely, the gate terminal electric field will switch the ferroelectric material in a non-volatile way such that, even when voltage to the gate terminal is removed, that field will be maintained in the ferroelectric material.
Embodiments will be presented below where this unique gated design is implemented in memristive memory devices to lower their VTH. These memristive memory devices can be included in circuit designs employing access transistors (in varying arrangements—see below) or, alternatively, in conjunction with (e.g., chalcogenide) selector cells. Like with the memristive memory devices, such selector cells too can benefit from a lowered VTH if gated in the same manner.
The present threshold voltage tuning mechanism is attributable to an electrothermal model where the field and temperature dependent electrical conductivity of memristive materials such as chalcogenide phase change materials are coupled to a feedback mechanism. Namely, an increase in conductivity from an applied electric field induces a rise in lattice temperature. The increase in lattice temperature in turn increases the conductivity further. A key parameter governing these dynamics is the material dependent activation energy (Ea). Specifically, the exponential field dependence of conductivity a can be expressed as:
with self-heating T included as:
where e is electronic charge, K is a constant, μ0 is the band mobility, Ea is activation energy for conduction, F=V/ua is electric field on the memristive material with effective thickness ua whereby a is a (unphysical) fit parameter, Tamb is ambient temperature, and Rth is effective thermal resistance.
Electron instability from the applied electric field is the foundation for the electrothermal feedback mechanism. Under an applied input voltage, e.g., across source-drain terminals, the potential landscape of the memristive material is modified such that the Ea for charge transport is minimized. Beyond a certain input voltage value (called the VTH) the lattice temperature increase induces a snap back where a significant amount of current flows through the memristive material. However, with conventional device designs, this VTH value is high.
Advantageously, the present techniques offer another knob to regulate Ea using what is referred to herein as a gate energy parameter EG. Here, EG is realized using an additional terminal in the device, i.e., the gate terminal (GT), and an applied gate voltage or VG which provides modulation of the Fermi level from gate induced changes in the carrier density in the memristive materials, and through that a decrease the Ea.
Doing so leverages the field effect in memristive materials. Specifically, applying VG to the gate terminal causes charge to build up in the memristive material. The carrier density in the subthreshold regime of the memristive material can be determined as:
This charge build up changes the Fermi level of the memristive material, and thereby reducing the VTH. For instance, Ea can be expressed as a function of a conductance band edge (Ec) and fermi level (EF) of the memristive material and gate voltage (VG), i.e.,
Thus, with a gate voltage VG applied, EF can be altered. As a result, Ea will be decreased. Consequently, the self-heating in the device increases from the increased flow of current, which results in a decrease in the VTH.
Given the above overview, an exemplary configuration of a memristive device 100 in accordance with the present techniques is shown illustrated in
Notably, due to the presence of the electrically insulating gate dielectric 110 between the gate terminal 112 and the memristive material 102, during operation no current will pass from the gate terminal 112 to the memristive material 102. Thus, a first voltage VG applied to gate terminal 112 and the top electrodes, i.e., second electrode 106 and third electrode 108, will result in no current passing through the memristive material 102. It is this first voltage VG that will be used to decrease the VTH of the memristive material 102 via the above-described field effects. By contrast, applying a second voltage to first (bottom) electrode 104 will cause current to pass through the memristive material 102 between the first (bottom) electrode 104 and the top electrodes, i.e., second electrode 106 and third electrode 108, since there is no insulator present between either the top or bottom electrodes and the memristive material 102.
For instance, referring to the example depicted in
The term ‘memristive material’ refers to any material whose resistance can be programmed in order to store information, such as by switching the memristive material or a portion thereof from a high resistance state to a low resistance state, and vice versa. Notably, the present techniques generally apply to the use of any memristive materials where the switching mechanism thereof can have a thermal dependence, such that the increased conductivity via a gate field allows for improved power dissipation (i.e., heating) which, in turn, accelerates the switching (see above). Thus, a wide variety of materials can be employed as memristive material 102 in accordance with the present techniques. For instance, according to an exemplary embodiment, memristive material 102 is a phase change material. In the sense that it can exist in amorphous and crystalline form almost any material is a phase change material, such as metals, semiconductors or insulators. However, only a small group of materials has the properties that makes them technologically useful phase change materials, with high on/off resistance ratio, fast switching times and good data retention. Many technologically relevant phase change materials are chalcogenides, i.e., they contain one or more chalcogenide elements. These are Group 16 in the periodic table, e.g., sulfur (S), selenium (Se) and/or tellurium (Te). According to one exemplary embodiment, the phase change material is a chalcogenide alloy that includes the chalcogenide element Te, in addition to other elements such as antimony (Sb) and/or germanium (Ge), forming the alloys Sb2Te3, GeTe, and Ge2Sb2Te5 (GST 225). Other technologically relevant phase change materials that are not chalcogenides include III-V semiconductor materials (such as gallium antimonide (GaSb)) or Ge—Sb based alloys. Often additional elements such as silver (Ag), indium (In), nitrogen (N) or bismuth (Bi) are added to the phase change alloys to optimize their properties.
A phase change material can be switched between two states, poly-crystalline (or single-crystal) and amorphous. In the poly-crystalline state, each grain of the phase change material is a perfect crystal and the phase change material is conductive (almost metallic). It is notable however that each of the grains is randomly oriented with respect to the other grains resulting in an overall poly-crystalline material. In the amorphous state, there is no order in the material and the phase change material is highly resistive. These two states make phase change materials particularly well-suited for storing data.
According to another exemplary embodiment, memristive material 102 is an organic semiconductor and/or a two-dimensional (2D) semiconductor material. Suitable organic semiconductors include, but are not limited to, organic polymers such as Tris-(8-hydroxyquinoline)aluminum, poly(3-hexylthiophene-2,5-diyl) (or P3HT), polyaniline (or PANI), poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene], phthalocyanine, polyphenylene vinylene (or PPV), polyvinylphenol (or PVP), polyvinyl alcohols. pentacene, polypyrrole and/or polycarbazole and/or organic-inorganic hybrid materials such as organic-inorganic perovskite materials. Suitable 2D semiconductor materials include, but are not limited to, nanowires and/or graphene. Notably, the switching mechanism in such materials can have a thermal dependence, just like phase change materials. As such, these organic and 2D semiconductor materials can also benefit from the increased conductivity and improved power dissipation (i.e., heating) from a gate field which, in turn, accelerates their switching.
The first electrode 104, second electrode 106 and third electrode 108 can each be formed from a material or a combination of materials. For instance, suitable materials for the first electrode 104, second electrode 106 and third electrode 108 include, but are not limited to, metals such as copper (Cu), nickel (Ni), platinum (Pt), titanium (Ti), tungsten (W), cobalt (Co), ruthenium (Ru), aluminum (Al), tantalum (Ta), titanium nitride (TiN), tantalum nitride (TaN), aluminum-containing alloys such as titanium aluminide (TiAl), titanium aluminum nitride (TiAlN), titanium aluminum carbide (TiAlC), tantalum aluminide (TaAl), tantalum aluminum nitride (TaAlN), tantalum aluminum carbide (TaAlC), titanium-containing alloys such as titanium carbide (TiC), tantalum titanium (TaTi), and any combinations thereof.
The gate dielectric 110 is an electrical insulator meaning, as highlighted above, that it will prevent current flow between the gate terminal 112 and the top electrodes, i.e., second electrode 106 and third electrode 108. According to an exemplary embodiment, the gate dielectric 110 is an oxide dielectric material. Suitable oxide dielectric materials include, but are not limited to, silicon oxide (SiOx) and/or high-κ dielectric materials such as hafnium oxide (HfO2), lanthanum oxide (La2O3), hafnium-lanthanum oxide (HfLaO2), hafnium zirconium oxide (HfZrO2), hafnium aluminum oxide (HfAlO2), titanium oxide (TiO2) and/or zirconium oxide (ZrO2). The term “high-κ,” as used herein, refers to a material having a relative dielectric constant x which is much higher than that of silicon dioxide (e.g., a dielectric constant κ=25 for HfO2 rather than 4 for SiO2). In one exemplary embodiment, gate dielectric 110 has a thickness of from about 1 nanometer (nm) to about 5 nm.
The gate terminal 112 can be configured similar to the first electrode 104, second electrode 106 and third electrode 108. For instance, according to an exemplary embodiment, the gate terminal 112 is formed from a metal(s) such as Cu, Ni, Pt, Ti, W, Co, Ru, Al, Ta, TiN, TaN, aluminum-containing alloys such as TiAl, TiAlN, TiAlC, TaAl, TaAlN, TaAlC, titanium-containing alloys such as TiC, TaTi, and any combinations thereof.
An exemplary methodology 200 for fabricating memristive device 100 is now described by way of reference to
A metallization process such as a damascene approach or other suitable technique is then used to form the first (bottom) electrode 104 in substrate 101. As provided above, suitable materials for the first (bottom) electrode 104 include, but are not limited to, metal(s) such as Cu, Ni, Pt, Ti, W, Co, Ru, Al, Ta, TiN, TaN, aluminum-containing alloys such as TiAl, TiAlN, TiAlC, TaAl, TaAlN, TaAlC, titanium-containing alloys such as TiC, TaTi, and any combinations thereof, which can be deposited using a process or combination of processes including, but not limited to, chemical vapor deposition (CVD), atomic layer deposition (ALD), physical vapor deposition (PVD), sputtering, plating, evaporation, ion beam deposition, electron beam deposition, laser assisted deposition, chemical solution deposition, etc. According to an exemplary embodiment, the metal overburden is removed, e.g., using an etching process like chemical-mechanical planarization (CMP), such that a topmost surface of the first (bottom) electrode 104 is coplanar with a topmost surface of the substrate 101, as shown in
In step 204, the memristive material 102 is deposited onto the substrate 101 over the first (bottom) electrode 104 such that the memristive material 102 directly contacts the first (bottom) electrode 104. As provided above, suitable memristive materials 102 include, but are not limited to, phase change materials such as chalcogenide alloys that include Te, in addition to other elements such as Sb and/or Ge, forming alloys such as Sb2Te3, GeTe, and Ge2Sb2Te5 (GST 225) and/or non-chalcogenides such as III-V semiconductor materials, e.g., GaSb, or Ge—Sb based alloys, any of which can optionally contain additional elements such as Ag, In, N or Bi, organic semiconductors such as organic polymers like Tris-(8-hydroxyquinoline)aluminum, poly(3-hexylthiophene-2,5-diyl) (or P3HT). polyaniline (or PAN I), poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene], phthalocyanine, polyphenylene vinylene (or PPV), polyvinylphenol (or PVP), polyvinyl alcohols, pentacene, polypyrrole and/or polycarbazole and/or organic-inorganic hybrid materials such as organic-inorganic perovskite materials and/or 2D semiconductor materials such as nanowires and/or graphene. According to an exemplary embodiment, the memristive material 102 is a phase change material deposited using a process such as PVD or CVD. The specific targets (PVD) or precursors (CVD) for the deposition process depend of course on the particular phase change material being formed. For example, when physical vapor deposition (PVD) is used to deposit Ge2Sb2Te5 the most common source is a Ge2Sb2Te5 target. Separate elemental Ge, Sb and Te targets can also be used by adjusting the flux from each target to obtain the desired composition. In another example, molecular beam epitaxy (MBE) can also be used to deposit Ge2Sb2Te5. When MBE is used the sources are usually individual Knudsen effusion cells. Each cell contains one of the alloy elements (Ge, Sb or Te), and the flux of each element is controlled by the effusion cell temperature. According to an exemplary embodiment, the deposition of the phase change material is performed at a high substrate temperature, for example, at a substrate temperature of from about 150 degrees Celsius (° C.) to about 300° C. For example, for Ge2Sb2Te5 the preferred temperature range is from about 175° C. to about 200° C. The result is formation of a crystalline phase change material. A room temperature deposition would typically yield amorphous material when Ge2Sb2Te5 is deposited. However, some phase change materials such as Sb2Te3 would be crystalline even at deposition temperatures below 100° C. Alternatively, when the memristive material 102 is an organic or 2D semiconductor, a process such as molecular layer deposition (MLD) or atomic layer deposition (ALD) can be employed to deposit the organic semiconductor as the memristive material 102 onto the substrate 101, while a casting process such as spin-coating or spraying can be used to deposit 2D semiconductors as the memristive material 102 onto the substrate 101.
In step 206, the memristive material 102 is patterned, and the top electrodes, i.e., second electrode 106 and third electrode 108, are formed on substrate 101 directly contacting opposite sides of the memristive material 102. Standard lithography and etching techniques can be employed to pattern the memristive material 102. As provided above, suitable materials for the second electrode 106 and third electrode 108 include, but are not limited to, metal(s) such as Cu, Ni, Pt, Ti, W, Co, Ru, Al, Ta, TiN, TaN, aluminum-containing alloys such as TiAl, TiAlN, TiAlC, TaAl, TaAlN, TaAlC, titanium-containing alloys such as TiC, TaTi, and any combinations thereof, which can be deposited using a process or combination of processes including, but not limited to, CVD, atomic layer ALD, PVD, sputtering, plating, evaporation, ion beam deposition, electron beam deposition, laser assisted deposition, chemical solution deposition, etc. The metal overburden can then be removed using a process such as CMP.
In step 208, the gate dielectric 110 is deposited onto the substrate 101, memristive material 102, and second electrode 106 and third electrode 108, and the gate terminal 112 is formed on the gate dielectric 110. As provided above, suitable materials for the gate dielectric 110 include, but are not limited to, oxide dielectric materials such as SiOx, HfO2, La2O3, HfLaO2, HfZrO2, HfAlO2, TiO2 and/or ZrO2, which can be deposited using a process such as CVD, ALD or PVD. Embodiments will be presented below where a ferroelectric insulator is employed, rather than an oxide material. In that case, deposition processes such as thermal evaporation or sputtering may be preferred. As provided above, suitable materials for the gate terminal 112 include, but are not limited to, metal(s) such as Cu, Ni, Pt, Ti, W, Co, Ru, Al, Ta, TiN, TaN, aluminum-containing alloys such as TiAl, TiAlN, TiAlC, TaAl, TaAlN, TaAlC, titanium-containing alloys such as TiC, TaTi, and any combinations thereof, which can be deposited using a process or combination of processes including, but not limited to, CVD, atomic layer ALD, PVD, sputtering, plating, evaporation, ion beam deposition, electron beam deposition, laser assisted deposition, chemical solution deposition, etc.
In step 210, standard lithography and etching techniques are used to pattern the gate dielectric 110 and gate terminal 112. Following patterning, the gate dielectric 110 and gate terminal 112 are present over only the memristive material 102, and thus no longer cover the substrate 101 nor the second electrode 106 or third electrode 108, as shown in
Several different derivations of the present design are contemplated herein. For instance, referring to
Namely, as shown in
As highlighted above, the present gated designs can also leverage the non-volatility of a ferroelectric material. Like the above gate dielectric, ferroelectric materials are electrical insulators, and thus too can serve as a barrier to current flow. For instance, referring to
As shown in
Advantageously, the direction of the polarization of these ferroelectric domains can be modified by an applied electric field.
Suitable ferroelectric materials include, but are not limited to, potassium sodium tartrate (KNaC4H4O6·4H2O), bismuth titanate (Bi4Ti3O2), barium titanate (BaTiO3), barium strontium titanate (Ba0.73Sr0.27TiO3), lead zirconate titanate (PbZr1-xTixO3), lead titanate (PbTiO3), lead zirconate (PbZrO3), lithium niobate (LiNbO3), potassium niobate (KNbO3), lead bismuth niobate (PbBi2Nb2O9), potassium dihydrogen phosphate (KH2PO4), guanidine aluminum sulfate hexahydrate (C(NH2)3Al(SO4)2·6H2O), strontium bismuth tantalate (SrBi2Ta2O9), and any combinations thereof. In one exemplary embodiment, the ferroelectric material 402 has a thickness of from about 1 nanometer (nm) to about 5 nm.
Thus, in the same manner as described above, during operation a first voltage VG (applied via the (first word line WLG and BL to the gate terminal 112 and top electrodes, i.e., second electrode 106 and third electrode 108, respectively) is used to lower the VT based on field effects in the memristive material 102, while a second voltage (applied via the SL to the first (bottom) electrode 104) through access transistor 114, which is controlled via the second word line WLT, is used to program the resistance of the memristive material 102. Additionally, in this example, by enabling the WLG, a perpendicular gate field can be applied to the memristive material 102 in a non-volatile manner by switching the polarization of the ferroelectric domains. As such, the field does not collapse when WLG is turned off (as is the case when a non-ferroelectric oxide dielectric material as in the previous embodiment is employed) thereby storing the gate voltage VG history, i.e., the polarity of the last applied VG which changes the direction of the polarization state of the ferroelectric domains and thus is stored in the ferroelectric material 402.
Referring to memristive device 500 of
Namely, as shown in
Further in regard to the use of ferroelectric materials in the present memristive device design, embodiments are also contemplated herein where the polarization of the ferroelectric domains within the ferroelectric material 402 are pre-aligned during manufacturing. In that case, the first word line WLG can be removed from memristive device 500. See, for example, memristive device 600 shown in
Each of the designs described thus far has been a four-terminal device, i.e., having a first electrode, a second electrode and a third electrode, and a gate terminal. However, other configurations are also contemplated herein. For instance, by way of example only, by connecting the BL to an electrode on only one side of the memristive material 102 (referred to herein as a source electrode 702), and connecting the access transistor 114 to an electrode on only an opposite side of the memristive material 102 (referred to herein as a drain electrode 704), then the need for a bottom electrode is eliminated, resulting in a three-terminal device. See, for example, memristive device 700 shown in
The terms ‘source’ and ‘drain’ are used to distinguish the terminal for the BL from the terminal for the access transistor 114, and vice versa, as opposed to the symmetric (second/third) top electrodes in the previous designs. However, the source electrode 702 and the drain electrode 704 can be configured similar to the top electrodes. For instance, according to an exemplary embodiment, the source electrode 702 and the drain electrode 704 are each formed from a material or a combination of materials including metals such as Cu, Ni, Pt, Ti, W, Co, Ru, Al, Ta, TiN, TaN, aluminum-containing alloys such as TiAl, TiAlN, TiAlC, TaAl, TaAlN, TaAlC, titanium-containing alloys such as TiC, TaTi, and any combinations thereof.
Further, while memristive device 700 shown in
In the preceding examples, an access transistor 114 is used as the memristive selector. However, embodiments are also contemplated herein where (e.g., chalcogenide) selector cells are instead used in this capacity. Advantageously, in the present selector-based designs the above-described field effect can also be leveraged to modulate the threshold voltages of the selector cells. As will be described in detail below, this can be done by modulating both the memristive device and the associated selector cell through a shared electrical connection, or through distinct connections.
For instance, in one exemplary embodiment, a gate dielectric and gate terminal are shared across a memristive device 800 and adjacent selector cell 802. See
It is notable that, while the electrical insulator in between the gate terminal 112′ and the memristive material 102 is in this example an oxide material, embodiments are contemplated herein where a ferroelectric material is employed instead of the gate dielectric 110′. See, e.g.,
The selector cell 802 includes a selector material 804, the (shared) gate terminal 112′ separated from the selector material 804 by the (shared) electrically insulating gate dielectric 110′, and a selector source electrode 806 and a selector drain electrode 808 each directly contacting opposite sides of the selector material 804. Like the access transistor 114 in the previous examples, the role of selector cell 802 is to enable access to particular memristive devices in an array (see below), and suppress unwanted current flow in unselected devices. An added advantage is that selector cell 802 can also benefit from the present gated designs to build up charge in the selector material 804, thereby modulating the Fermi level in the selector material 804 and reducing the threshold voltage of the selector cell 802. In this particular embodiment, this threshold voltage adjustment is achieved via the gate terminal 112′ and the gate dielectric 110′ which are both shared across the memristive material 102 and the selector material 804. Namely, as shown in
During operation, selector cell 802 undergoes a transition between a low conducting state and a high conducting state through a region of negative differential resistance, exhibiting a non-linear conduction. A threshold current is needed to keep the selector cell 802 in a high conducting state. According to an exemplary embodiment, selector material 804 is a chalcogenide material such as germanium selenium (GeSe), silicon tellurium (SiTe), silicon selenide (SiSe), and combinations thereof.
As shown in
As highlighted above, this shared gate configuration can also be implemented with a shared ferroelectric material (which for ease and clarity of depiction is given the reference numeral 402′) rather than an oxide material to remember the applied gate field history. See, for example,
Alternatively, the memristive device 800 and selector cell 802 can be separately gated. See, for example,
Further, while
Systems including at least one of the present memristive devices are also contemplated herein. For instance,
As shown in
A derivation of this unit cell design is also contemplated herein where the gate terminals 112A and 112B of the memristive devices 700A and 700B, respectively, and the gate nodes of the access transistors 114A and 114B are controlled by the same signal driver. See, for example, unit cell 1202 in
As highlighted above, crossbar layouts of the present memristive device unit cells may be implemented. See, for example, crossbar array 1300 shown in
A similar crossbar layout can also be implemented using the present memristive devices having selector cells. See, for example, crossbar array 1400 shown in
In step 1502, a first voltage (also referred to herein as a gate voltage or VG) is applied to the gate terminal 112. As described in detail above, the gate terminal 112 is separated from the memristive material 102 by an electrical insulator, which prevents current flow through the memristive material 102 from the applied VG. This electrical insulator can be a gate dielectric 110 such as an oxide material, or alternatively a ferroelectric material such as ferroelectric material 402 (see, e.g.,
As described in detail above, applying the first voltage (i.e., gate voltage) to the gate terminal 112 serves to build up charge in the memristive material 102. Doing so lowers a threshold voltage (VTH) of the memristive material via field effects. Namely, the VTH of the memristive material 102 with applied VG is lower than what the VTH of the memristive material 102 would be without the applied VG.
In step 1504, a second voltage is applied to one of the electrodes to program a resistance of the memristive material 102. Being that the electrodes are in direct contact with the memristive material 102, application of the second voltage will result in a current flow through the memristive material 102. For example, applying the second voltage to the second electrode 106 and third electrode 108 will result in a current flow between the second electrode 106/third electrode 108 and the first (bottom) electrode 104. Similarly, applying the second voltage to the source electrode 702 (see, e.g.,
Although illustrative embodiments of the present invention have been described herein, it is to be understood that the invention is not limited to those precise embodiments, and that various other changes and modifications may be made by one skilled in the art without departing from the scope of the invention.