Patent Publication Number: US-8975610-B1

Title: Silicon based selector element

Description:
FIELD OF THE DISCLOSURE 
     This invention relates generally to nonvolatile memory elements, and more particularly, to methods for forming selector elements used in nonvolatile memory devices. 
     BACKGROUND 
     Nonvolatile memory elements are used in systems in which persistent storage is required. For example, digital cameras use nonvolatile memory cards to store images and digital music players use nonvolatile memory to store audio data. Nonvolatile memory is also used to persistently store data in computer environments. Nonvolatile memory is often formed using electrically-erasable programmable read only memory (EPROM) technology. This type of nonvolatile memory contains floating gate transistors that can be selectively programmed or erased by application of suitable voltages to their terminals. 
     As fabrication techniques improve, it is becoming possible to fabricate nonvolatile memory elements with increasingly smaller dimensions. However, as device dimensions shrink, scaling issues are posing challenges for traditional nonvolatile memory technology. This has led to the investigation of alternative nonvolatile memory technologies, including magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), spin transfer torque random access memory (STT-RAM), and resistive random access memory (ReRAM), among others. 
     Resistive memory devices are formed using memory elements that have two or more stable states with different resistances. Bistable memory has two stable states. A bistable memory element can be placed in a high resistance state or a low resistance state by application of suitable voltages or currents. Voltage pulses are typically used to switch the memory element from one resistance state to the other. Nondestructive read operations can be performed to ascertain the value of a data bit that is stored in a memory cell. 
     Resistive switching based on transition metal oxide switching elements formed of metal oxide films has been demonstrated. Although metal oxide films such as these exhibit bistability, the resistance of these films and the ratio of the high-to-low resistance states are often insufficient to be of use within a practical nonvolatile memory device. For instance, the resistance states of the metal oxide film should preferably be significant as compared to that of the system (e.g., the memory device and associated circuitry) so that any change in the resistance state change is perceptible. The variation of the difference in resistive states is related to the resistance of the resistive switching layer. Therefore, a low resistance metal oxide film may not form a reliable nonvolatile memory device. For example, in a nonvolatile memory that has conductive lines formed of a relatively high resistance metal such as tungsten, the resistance of the conductive lines may overwhelm the resistance of the metal oxide resistive switching element. Therefore, the state of the bistable metal oxide resistive switching element may be difficult or impossible to sense. Furthermore, the parasitic resistance (or the parasitic impedance, in the actual case of time-dependent operation), (e.g. due to sneak current paths that exist in the system), may depend on the state of the system, such as the data stored in other memory cells. It is often preferable that the possible variations of the parasitic impedance be unsubstantial compared to the difference in the values of the high and low resistance of a memory cell. 
     Similar issues can arise from integration of the resistive switching memory element with current selector elements (also known as current limiter or current steering elements), such as diodes and/or transistors. Control elements (e.g. selector devices) in nonvolatile memory structures can screen the memory elements from sneak current paths to ensure that only the selected bits are read or programmed. Schottky diode can be used as a selector device, which can include p-n junction diode or metal-semiconductor diode, however, this requires high thermal budget that may not be acceptable for 3-dimensional (3D) memory application. Metal-Insulator-Metal Capacitor (MIMCAP) tunneling diodes may have a challenge of providing controllable low barrier height and low series resistance. In some embodiments, the control element can also function as a current limiter or control element. In some embodiments, a control element can suppress large currents without affecting acceptable operation currents in a memory device. For example, a control element can be used with the purpose of increasing the ratio of the measured resistances in the high and low resistance state, further making the non-volatile memory device less susceptible to the noise due to parasitic impedances in the system. Note that the terms “control element”, “current selector”, “current limiter”, and “steering element” may often times be substituted for each other, due to a substantial overlap in the functional utility of the elements they may describe. Such a substitution does not affect the scope of this description, which is limited only by the claims. 
     Therefore, there is a need for a control element that can meet the design criteria for advanced memory devices. 
     SUMMARY 
     The following summary of the disclosure is included in order to provide a basic understanding of some aspects and features of the invention. This summary is not an extensive overview of the invention and as such it is not intended to particularly identify key or critical elements of the invention or to delineate the scope of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description that is presented below. 
     In some embodiments, control elements that can be suitable for nonvolatile memory device applications are disclosed. The control element can have low leakage currents at low voltages to reduce sneak current paths for non selected devices, and high leakage currents at high voltages to minimize voltage drops during device switching. The control element can be based on multilayer dielectric stacks. The control element can include a titanium oxide-silicon-titanium oxide multilayer stack. Electrode materials may include one of ruthenium, titanium nitride, or carbon. The control element can include a silicon nitride-silicon-silicon nitride multilayer stack. Electrode materials may include titanium nitride. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. The drawings are not to scale and the relative dimensions of various elements in the drawings are depicted schematically and not necessarily to scale. 
       The techniques of the present invention can readily be understood by considering the following detailed description in conjunction with the accompanying drawings, in which: 
         FIGS. 1A-1C  illustrate a schematic representation of a ReRAM operation according to some embodiments. 
         FIG. 2A  illustrates a plot of a current passing through a unipolar ReRAM cell as a function of a voltage applied to the ReRAM cell, in accordance with some embodiments.  FIG. 2B  illustrates the same type of a plot for a bipolar ReRAM cell, in accordance with some embodiments. 
         FIG. 3  illustrates a memory array of resistive switching memory elements according to some embodiments. 
         FIG. 4  illustrates sneak path currents in a cross point memory array according to some embodiments. 
         FIG. 5  illustrates sneak path currents in a cross point memory array according to some embodiments. 
         FIGS. 6A-6B  illustrate examples of I-V response for a control element according to some embodiments. 
         FIG. 7  illustrates a cross point memory array according to some embodiments. 
         FIGS. 8A-8B  illustrate examples of I-V response for a control element according to some embodiments. 
         FIG. 9  illustrates an example of a band gap diagram according to some embodiments. 
         FIG. 10  presents data for leakage current density versus titanium oxide thickness measured at 0.75V according to some embodiments. 
         FIG. 11  presents data for leakage current density versus titanium oxide thickness measured at 3.5V according to some embodiments. 
         FIG. 12  presents data for leakage current density versus voltage for different MIIIM stacks according to some embodiments. 
         FIG. 13  presents data for leakage current density versus silicon nitride thickness measured at 0.75V according to some embodiments. 
         FIG. 14  presents data for leakage current density versus voltage for different MIIIM stacks according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     A detailed description of one or more embodiments is provided below along with accompanying figures. The detailed description is provided in connection with such embodiments, but is not limited to any particular example. The scope is limited only by the claims and numerous alternatives, modifications, and equivalents are encompassed. Numerous specific details are set forth in the following description in order to provide a thorough understanding. These details are provided for the purpose of example and the described techniques may be practiced according to the claims without some or all of these specific details. For the purpose of clarity, technical material that is known in the technical fields related to the embodiments has not been described in detail to avoid unnecessarily obscuring the description. 
     Before various embodiments are described in detail, it is to be understood that unless otherwise indicated, this invention is not limited to specific layer compositions or surface treatments. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of the present invention. 
     It must be noted that as used herein and in the claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a layer” includes two or more layers, and so forth. 
     Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit unless the context clearly dictates otherwise, between the upper and lower limit of that range, and any other stated or intervening value in that stated range, is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges, and are also encompassed within the invention, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the invention. The term “about” generally refers to ±10% of a stated value. 
     The term “substrate” as used herein may refer to any workpiece on which formation or treatment of material layers is desired. Substrates may include, without limitation, float glass, low-iron glass, borosilicate glass, display glass, alkaline earth boro-aluminosilicate glass, fusion drawn glass, flexible glass, specialty glass for high temperature processing, polyimide, plastics, polyethylene terephthalate (PET), etc. for either applications requiring transparent or non-transparent substrate functionality. 
     The term “horizontal” as used herein will be understood to be defined as a plane parallel to the plane or surface of the substrate, regardless of the orientation of the substrate. The term “vertical” will refer to a direction perpendicular to the horizontal as previously defined. Terms such as “above”, “below”, “bottom”, “top”, “side” (e.g. sidewall), “higher”, “lower”, “upper”, “over”, and “under”, are defined with respect to the horizontal plane. The term “on” means there is direct contact between the elements. The term “above” will allow for intervening elements. 
     As used herein, a material (e.g. a dielectric material or an electrode material) will be considered to be “crystalline” if it exhibits greater than or equal to 30% crystallinity as measured by a technique such as x-ray diffraction (XRD). 
     As used herein, the notation “Ni—Ti—Nb—O” and “NiTiNbO” and “NiTiNbO x ” will be understood to be equivalent and will be used interchangeably and will be understood to include a material containing these elements in any ratio. Where a specific composition is discussed, the atomic concentrations (or ranges) will be provided. The notation is extendable to other materials and other elemental combinations discussed herein. 
     As used herein, the terms “film” and “layer” will be understood to represent a portion of a stack. They will be understood to cover both a single layer as well as a multilayered structure (i.e. a nanolaminate). As used herein, these terms will be used synonymously and will be considered equivalent. 
     As used herein, elements described or labeled by the phrases “control element”, “selector”, “current limiter”, and “current steering device” will be understood to be equivalent and will be used interchangeably. 
     As used herein, the phrase “sneak current” and “sneak-through current” will be understood to be equivalent and will be used interchangeably and will be understood to refer to current flowing through non-selected memory cells during a read operation. 
     A cross-bar architecture is promising for future non-volatile memories such as phase change memory (PCM) or resistive random access memory (ReRAM) because of the small cell size of 4F 2  achievable with each cell at the intersections of perpendicular word lines and bit lines, and the potential to stack multiple layers to achieve very high memory density. Two key challenges for the cross bar architecture are the possibility of current sneak-through paths (e.g., when trying to read a cell in a high resistance state adjacent to cells in a low resistance state) and the need to avoid unselected cell modification when half of the switching voltage is applied to the selected cell 
     In some embodiments, current selectors are provided with a non-linear current-voltage (I-V) behavior, including low current at low voltages and high current at higher voltages. Unipolar selectors can be appropriate for a unipolar memory such as PCM whereas bipolar selectors can be more appropriate for a bipolar memory such as ReRAM and spin transfer torque random access memory (STT-RAM). The unipolar selector can have high resistance in reverse polarity. Both the unipolar and the bipolar selectors can have high resistance at low voltages. These selectors can prevent sneak-through current, even when adjacent memory elements are in low-resistance state. Furthermore, the non-linear I-V can also provide the current selector with low resistance at higher voltages so that there is no significant voltage drop across the current selector during switching. 
     In some embodiments, current selectors requiring low temperature processing (e.g., &lt;650 C) are provided, which can be suitable for emerging non-volatile memory architectures such as ReRAM, PCM and STT-RAM. In addition, the current selectors can include fab-friendly materials and can exhibit desired device performance. 
     In some embodiments, electrode-dielectric-electrode and/or electrode-semiconductor-electrode stacks are provided as bipolar current selectors with low leakage at low voltages and high leakage at high voltages. For example, the dielectric layer can have a graded band gap, (e.g., a band gap having graded electron energy level), so that at low applied voltages, the effective thickness of the dielectric layer, accounted for the band bending effect due to the applied voltage, can remain large enough to prevent high tunneling or thermionic current. The graded band gap can be further configured so that at low applied voltages, the effective thickness of the dielectric layer can be adequate to allow high tunneling or thermionic current. 
     In some embodiments, symmetrical current control elements can be provided as bipolar current steering elements. For example, in asymmetrical control elements, one electrode interface can have a high barrier height (e.g., TiN—ZrO 2  or Pt—TiO 2 ) and the other electrode interface can be ohmic. Alternatively, asymmetrical control elements can include addition of bulk or interfacial defects which can allow tunneling through the Schottky barrier. 
     A ReRAM cell exhibiting resistive switching characteristics generally includes multiple layers formed into a stack. The structure of this stack is sometimes described as a Metal-Insulator-Metal (MIM) structure. Specifically, the stack includes two conductive layers operating as electrodes. These layers may include metals and/or other conductive materials. The stack also includes an insulator layer disposed in between the electrode. The insulator layer exhibits resistive switching properties characterized by different resistive states of the material forming this layer. As such, this insulator layer is often referred to as a resistive switching layer. These resistive states may be used to represent one or more bits of information. The resistance switching properties of the insulator layer are believed to depend on various defects&#39; presence and distribution inside this layer. For example, different distributions of oxygen vacancies in the layer may reflect different resistance states of the layer, and these states may be sufficiently stable for memory application. 
     To achieve a certain concentration of defects in the resistance switching layer, the layer has been conventionally deposited with defects already present in the layer, (i.e., with preformed defects). In other words, defects are introduced into the layer during its formation. For example, tightly controlled Atomic Layer Deposition (ALD), Physical Vapor Deposition (PVD), or some other low-temperature process to remain within a Back End of Line (BEOL) thermal budget may be used to deposit the insulator layer of the stack. It may be difficult to precisely and repeatedly control formation of these defects, particularly in very thin resistance switching layers (e.g., less than 100 Angstroms). For example, when ALD is used to form resistance switching layers, some unreacted precursors may leave carbon-containing residues that impact resistance characteristics of the deposition layers and ReRAM cells including these layers. Furthermore, achieving precise partial saturation repeatedly may be very difficult if possible at all. In the case of PVD, sputtering targets tend to wear out influencing the deposition rates and creating variation in resulting resistance switching layers. 
     The resistive switching layer changes its resistive state when a certain switching voltage (e.g., a set voltage or a reset voltage) is applied to this layer as further explained below. The applied voltage causes localized heating within the layer and/or at one or both of its interfaces with other components. Without being restricted to any particular theory, it is believed that a combination of the electrical field and localized heating (both created by the applied voltage) causes formation and breakage of various conductive paths within the resistive switching layer and/or at its interfaces. These conductive paths may be established and broken by moving defects (e.g., oxygen vacancies) within the resistive switching layer and through one or more interfaces that the resistive switching layer forms with adjacent layers. 
     The interfaces can be inert interfaces or reactive interfaces. The inert interface generally does not have any substantial defect transfer through this interface. While the defects may be present within one or both layers forming this interface, these defects are not exchanged through the inert interface when switching, reading, or other types of voltages are applied to the ReRAM cell. The reactive interface generally experiences a transfer of defects through this interface. When a resistive switching layer includes an oxygen containing material, such as metal oxides, the reactive interface is formed by an oxygen reactive material, such as titanium. The inert interface may be formed by a material that is not oxygen reactive, which may be a part of an electrode or a diffusion barrier layer. In some embodiments, the flux of defects through the reactive interface is at two or more orders of magnitude greater than the flux of defects through the inert interface. As such, the “inert” and “reactive” naming convention is relative. 
     The inert interface provides a control for the resistive switching layer while defects are moved in and out of the resistive switching layer through the reactive interface. For example, when a switching voltage is applied to the resistive switching layer in order to reduce its resistance, the reactive interface allows defects to flow into the layer. The defects are typically driven by the electrical potential applied to the layer and form conductive paths through the layer. The direction of this flow may be determined by the polarity of the switching voltage and/or by the electrical charge of the defects (e.g., positive charged oxygen vacancies). At the same time, the second inert interface prevents defects from escaping the layer despite the driving potential. If both interfaces are reactive and allow defects to pass through, then the resistive switching layer may gain defects at one interface and loose at another. In this situation, the layer may never be able to gain enough defects to form conductive paths. 
     The above scenario is applicable in a very similar manner to a resetting operation during which the resistive switching layer is brought to its high resistance state. When a switching voltage is applied to the layer in order to increase its resistance of the layer, the reactive interface allows defects to flow out of the layer. The defects may also be driven by the electrical potential applied to the layer as described above. The loss of defects may eventually break conductive paths in the layer. At the same time, the second inert interface prevents defects from entering the layer despite the driving potential. If both interfaces are reactive and allow defects to pass through during the resetting operation, then the resistive switching layer may gain defects at one interface and loose at another. In this situation, the layer may never be able to lose enough defects in order to break it conductive paths. It should be noted that defects are often mobile in many times of resistive switching materials. 
     The ability of an interface to block defects (as in the inert interface) or to allow defects to diffuse through the interface (as in the reactive interface) depends on properties of a layer forming this interface together with the resistive switching layer. Often conductive electrodes are used to form both reactive and inert interfaces. These electrodes may be referred to as reactive and inert electrodes and materials used to form these electrodes may be referred to as reactive and inert materials. It should be noted that this terminology (i.e., reactive and inert) refers to primarily to defect mobility properties of the interfaces. Some examples of inert electrode materials include doped polysilicon, platinum, ruthenium, ruthenium oxide, gold, iridium, copper, silver, tantalum, and tungsten. Examples of reactive electrode materials include titanium. Furthermore, some materials may be defined as semi-inert including tantalum nitride, tantalum silicon nitride, and tungsten silicon nitride. In the context of oxygen containing resistive switching materials, such as metal oxides, reactive materials may be also referred to as oxygen reaction materials since oxygen or oxygen vacancies are exchanged through the reactive interface. Titanium is one example of an oxygen reactive material, however other examples may be used as well. 
     A brief description of ReRAM cells and their switching mechanisms are provided for better understanding of various features and structures associated with methods of forming nonvolatile memory elements further described below. ReRAM is a non-volatile memory type that includes dielectric material exhibiting resistive switching characteristics. A dielectric, which is normally insulating, can be made to conduct through one or more filaments or conduction paths formed after application of a sufficiently high voltage. The conduction path formation can arise from different mechanisms, including defects, metal migration, and other mechanisms further described below. Once the one or more filaments or conduction paths are formed in the dielectric component of a memory device, these filaments or conduction paths may be reset (or broken resulting in a high resistance) or set (or re-formed resulting in a lower resistance) by applying certain voltages. Without being restricted to any particular theory, it is believed that resistive switching corresponds to migration of defects within the resistive switching layer and, in some embodiments, across one interface formed by the resistive switching voltage, when a switching voltage is applied to the layer. 
       FIGS. 1A-1C  illustrate a schematic representation of a ReRAM operation according to some embodiments. A basic building unit of a memory device is a stack having a capacitor like structure. A ReRAM cell includes two electrodes and a dielectric positioned in between these two electrodes.  FIG. 1A  illustrates a schematic representation of ReRAM cell  100  including top electrode  102 , bottom electrode  106 , and resistance switching layer  104  provided in between top electrode  102  and bottom electrode  106 . It should be noted that the “top” and “bottom” references for electrodes  102  and  106  are used solely for differentiation and not to imply any particular spatial orientation of these electrodes. Often other references, such as “first formed” and “second formed” electrodes or simply “first” and “second”, are used identify the two electrodes. ReRAM cell  100  may also include other components, such as an embedded resistor, diode, and other components. ReRAM cell  100  is sometimes referred to as a memory element or a memory unit. 
     Top electrode  102  and bottom electrode  106  may be used as conductive lines within a memory array or other types of devices integrated with the ReRAM. As such, electrode  102  and  106  are generally formed from conductive materials. As stated above, one of the electrodes may be a reactive electrode and act as a source and as a reservoir of defects for the resistive switching layer. That is, defects may travel through an interface formed by this electrode with the resistive switching layer (i.e., the reactive interface). The other interface of the resistive switching layer may be inert and may be formed with an inert electrode or a diffusion barrier layer. 
     Resistance switching layer  104  which may be initially formed from a dielectric material and later can be made to conduct through one or more conductive paths formed within the layer by first applying a forming voltage and then applying a switching voltage. To provide this resistive switching functionality, resistance switching layer  104  includes a concentration of electrically active defects  108 , which may be at least partially provided into the layer during its fabrication. For example, some atoms may be absent from their native structures (i.e., creating vacancies) and/or additional atoms may be inserted into the native structures (i.e., creating interstitial defects). 
     In some embodiments, these defects may be utilized for ReRAM cells operating according to a valence change mechanism, which may occur in specific transition metal oxides, nitrides, and oxy-nitrides. For example, defects may be oxygen vacancies triggered by migration of oxygen anions. Migrations of oxygen anions correspond to the motion of corresponding oxygen vacancies that are used to create and break conductive paths. A subsequent change of the stoichiometry in the transition metal oxides leads to a redox reaction expressed by a valence change of the cation sublattice and a change in the electrical conductivity. In this example, the polarity of the pulse used to perform this change determines the direction of the change, (i.e., reduction or oxidation). Other resistive switching mechanisms include bipolar electrochemical metallization mechanisms and thermochemical mechanisms, which leads to a change of the stoichiometry due to a current-induced increase of the temperature. Some of these mechanisms will be further described below with reference to  FIGS. 1A-1C . In the described examples, top electrode  102  is reactive, while bottom electrode  106  is inert or is separated from resistive switching layer  104  by a diffusion barrier layer (not shown). One having ordinary skills in the art would understand that other arrangements are possible as well and within the scope of this disclosure. 
     Specifically,  FIG. 1A  is a schematic representation of ReRAM cell  100  prior to initial formation of conductive paths, in accordance with some embodiments. Resistive switching layer  104  may include some defects  108 . Additional defects  108  may be provided within top electrode  102  and may be later transferred to resistive switching layer  104  during the formation operation. In some embodiments, the resistive switching layer  104  has substantially no defects prior to the forming operation and all defects are provided from top electrode  102  during forming. Bottom electrode  106  may or may not have any defects. It should be noted that regardless of the presence or absence of defects in bottom electrode  106 , substantially no defects are exchanged between bottom electrode  106  and resistive switching layer  104  during forming and/or switching operations. 
     During the forming operation, ReRAM cell  100  can change its structure from the one shown in  FIG. 1A  to the one shown in  FIG. 1B . This change corresponds to defects  108  being arranged into one or more continuous paths within resistive switching layer  104  as, for example, schematically illustrated in  FIG. 1B . Without being restricted to any particular theory, it is believed that defects  108  can be reoriented within resistance switching layer  104  to form these conductive paths  110  as schematically shown in  FIG. 1B . Furthermore, some or all defects  108  forming the conductive paths may enter resistive switching layer  104  from top electrode  102 . For simplicity, all these phenomena are collectively referred to as reorientation of defects within ReRAM cell  100 . This reorientation of defects  108  occurs when a certain forming voltage  104  is applied to electrodes  102  and  106 . In some embodiments, the forming operation is also conducted at elevated temperatures to enhanced the mobility of the defects within ReRAM cell  100 . In general, the forming operation is considered to be a part of the fabrication of ReRAM cell  100 , while subsequent resistive switching is considered to be a part of operation of ReRAM cell. 
     Resistive switching involves breaking and reforming conductive paths through resistive switching layer  104 , for example switching between the state schematically illustrated in  FIG. 1B  and the state schematically illustrated in  FIG. 1C . The resistive switching is performed by applying switching voltages to electrodes  102  and  106 . Depending on magnitude and polarity of these voltages, conductive path  110  may be broken or re-formed. These voltages may be substantially lower than forming voltages (i.e., voltages used in the forming operation) since much less mobility of defects is needed during switching operations. 
     The state of resistive switching layer  104  illustrated in  FIG. 1B  is referred to as a low resistance state (LRS), while the state illustrated in  FIG. 1C  is referred to as a high resistance state (HRS). The resistance difference between the LRS and HRS is due to the different number and/or conductivity of conductive paths that exists in these states, (i.e., resistive switching layer  104  has more conductive paths and/or less resistive conductive paths when it is in the LRS than when it is in the HRS). It should be noted that resistive switching layer  104  may still have some conductive paths while it is in the HRS, but these conductive paths are fewer and/or more resistive than the ones corresponding to the LRS. 
     When switching from its LRS to HRS, which is often referred to as a reset operation, resistive switching layer  104  may release some defects into top electrode  102 . Furthermore, there may be some mobility of defects within resistive switching layer  104 . This may lead to thinning and, in some embodiments, breakages of conductive paths as shown in  FIG. 1C . Depending on mobility within resistive switching layer  104  and diffusion through the interface formed by resistive switching layer  104  and top electrode  102 , the conductive paths may break closer to the interface with bottom electrode  106 , somewhere within resistive switching layer  104 , or at the interface with top electrode  102 . This breakage generally does not correspond to complete dispersion of defects forming these conductive paths and may be a self-limiting process, (i.e., the process may stop after some initial breakage occurs). 
     When switching from its HRS to LRS, which is often referred to as a set operation, resistive switching layer  104  may receive some defects from top electrode  102 . Similar to the reset operation described above, there may be some mobility of defects within resistive switching layer  104 . This may lead to thickening and, in some embodiments, reforming of conductive paths as shown in  FIG. 1B . In some embodiments, a voltage applied to electrodes  102  and  104  during the set operation has the same polarity as a voltage applied during the reset operation. This type of switching is referred to as unipolar switching. Some examples of cells that exhibit unipolar switching behavior include resistive switching layers formed from most metal oxide materials and having inert electrodes at both sides, (e.g., Pt/MeO x /Pt where “MeOx” represents a generic metal oxide material). Alternatively, a voltage applied to electrodes  102  and  104  during the set operation may have different polarity as a voltage applied during the reset operation. This type of switching is referred to as bipolar switching. Some examples of cells that exhibit bipolar switching behavior include resistive switching layers formed from metal oxide materials and having one inert electrode and one reactive electrode, (e.g., TiN/MeOx/Pt and TiN/MeOx/poly-Si). Setting and resetting operations may be repeated multiple times as will now be described with reference to  FIGS. 2A and 2B . 
       FIG. 2A  illustrates a plot of a current passing through a unipolar ReRAM cell as a function of a voltage applied to the ReRAM cell, in accordance with some embodiments.  FIG. 2B  illustrates the same type of a plot for a bipolar ReRAM cell, in accordance with some embodiments. The HRS is defined by line  122 , while the LRS is defined by  124  in  FIG. 2A  and by lines  222  and  224  respectively in  FIG. 2B . Each of these states is used to represent a different logic state, (e.g., the HRS may represent logic one (“1”) and LRS representing logic zero (“0”) or vice versa). Therefore, each ReRAM cell that has two resistance states may be used to store one bit of data. It should be noted that some ReRAM cells may have three and even more resistance states allowing multi-bit storage in the same cell. 
     The overall operation of the ReRAM cell may be divided into a read operation, set operation (i.e., turning the cell “ON” by changing from its HRS to LRS), and reset operation (i.e., turning the cell “OFF” by changing from its LRS to HRS). During the read operation, the state of the ReRAM cell or, more specifically, the resistive state of its resistance switching layer can be sensed by applying a sensing voltage to its electrodes. The sensing voltage is sometimes referred to as a “READ” voltage or simply a reading voltage and indicated as V READ  in  FIGS. 2A and 2B . If the ReRAM cell is in its HRS (represented by lines  122  and  222  in  FIGS. 2A and 2B ), the external read and write circuitry connected to the electrodes will sense the resulting “OFF” current (I OFF ) that flows through the ReRAM cell. As discussed previously, this read operation may be performed multiple times without changing the resistive state (i.e., switching the cell between its HRS and LRS). In the above example, the ReRAM cell should continue to output the “OFF” current (I OFF ) when the read voltage (V READ ) is applied to the electrodes for the second time, third time, and so on. 
     Continuing with the above example, when it is desired to turn “ON” the cell that is currently in the HRS switch, a set operation is performed. This operation may use the same read and write circuitry to apply a set voltage (V SET ) to the electrodes. Applying the set voltage forms one or more conductive paths in the resistance switching layer as described above with reference to  FIGS. 1B and 1C . The switching from the HRS to LRS is indicated by dashed lines  126  and  226  in  FIGS. 2A and 2B . The resistance characteristics of the ReRAM cell in its LRS are represented by lines  124  and  224  respectively. When the read voltage (V READ ) is applied to the electrodes of the cell in this state, the external read and write circuitry will sense the resulting “ON” current (I ON ) that flows through the ReRAM cell. Again, this read operation may be performed multiple times without switching the state of the ReRAM cell. 
     At some point, it may be desirable to turn “OFF” the ReRAM cell by changing its state from the LRS to HRS. This operation is referred to as a reset operation and should be distinguished from set operation during which the ReRAM cell is switched from its HRS to LRS. During the reset operation, a reset voltage (V RESET ) is applied to the ReRAM cell to break the previously formed conductive paths in the resistance switching layer. Switching from a LRS to HRS is indicated by dashed line  128  in  FIG. 2A  and line  228  in  FIG. 2B . Detecting the state of the ReRAM cell while it is in its HRS is described above. 
     It should be noted that polarity of the reset voltage and the set voltage may be the same as shown in  FIG. 2A  or different as shown in  FIG. 2B . The cells that have the same polarity of set and reset voltages are referred to as unipolar cells, while the cells that have different polarities of set and reset voltages are referred to as bipolar cells. Without being restricted to any particular theory, it is believed that unipolar switching occurs due to metallic filament formation and destruction caused by resistive heating and application of electrical field. Bipolar switching is believed to be based on filaments formed from oxygen vacancies. The formation and rupture of the filaments is accomplished by oxygen vacancy movement. The switching voltages of unipolar and bipolar switching are typically comparable. However, the endurance of bipolar devices is generally better than that of unipolar devices. 
     Overall, the ReRAM cell may be switched back and forth between its LRS and HRS many times. Read operations may be performed in each of these states (between the switching operations) one or more times or not performed at all. It should be noted that application of set and reset voltages to change resistance states of the ReRAM cell involves complex mechanisms that are believed to involve localized resistive heating as well as mobility of defects impacted by both temperature and applied potential. 
     In some embodiments, the set voltage (V SET ) is between about 100 mV and 12V or, more specifically, between about 500 mV and 5V. In some embodiments, the read voltage (V READ ) may be between about 0.1 and 0.5 of the write voltage (V SET ). In some embodiments, the read currents (I ON  and I OFF ) are greater than about 1 mA or, more specifically, is greater than about 5 mA to allow for a fast detection of the state by reasonably small sense amplifiers 
     In some embodiments, the same ReRAM cell may include two or more resistance switching layers interconnected in series. Adjacent resistance switching layers may directly interface each other or be separated by an intermediate layer. 
     The ReRAM cells can be configured in a cross point memory array. The cross point memory arrays can include horizontal word lines that cross vertical bit lines. Memory cells can be located at the cross points of the word lines and the bit lines. The memory cells can function as the storage elements of a memory array. 
       FIG. 3  illustrates a memory array of resistive switching memory elements according to some embodiments. Memory array  300  may be part of a memory device or other integrated circuit. Memory array  300  is an example of potential memory configurations; it is understood that several other configurations are possible. 
     Read and write circuitry may be connected to memory elements  302  using signal lines  304  and orthogonal signal lines  306 . Signal lines such as signal lines  304  and signal lines  306  are sometimes referred to as word lines and bit lines and are used to read and write data into the elements  302  of array  300 . Individual memory elements  302  or groups of memory elements  302  can be addressed using appropriate sets of signal lines  304  and  306 . Memory element  302  may be formed from one or more layers  308  of materials, as is described in further detail below, and may include additional elements such as those described below, including selection or control elements. 
     One having ordinary skills in the art would understand that other arrangements of memory cells are possible; in particular, a memory array can be a 3-D memory array. For example, several 2-D memory arrays (as shown in  FIG. 3 ) can be stacked in a vertical fashion to make multi-layer 3-D memory arrays. As another example, one set of signal lines can be composed of vertical lines, and the other set of signal lines can be a composed of one or more subsets of horizontal lines, the subsets (if applicable) being positioned at an angle (e.g. orthogonally) to each other, and the memory devices can be formed as substantially concentric cylindrical layers around the vertical lines. 
     Any suitable read and write circuitry and array layout scheme may be used to construct a non-volatile memory device from resistive switching memory elements such as element  302 . For example, horizontal and vertical lines  304  and  306  may be connected directly to the terminals of resistive switching memory elements  302 . This is merely illustrative. 
     During the operation of the cross point memory array, such as a read operation, the state of a memory element  302  can be sensed by applying a sensing voltage (i.e., a “read” voltage) to an appropriate set of signal lines  304  and  306 . Depending on its history, a memory element that is addressed in this way may be in either a high resistance state or a low resistance state. The resistance of the memory element therefore determines what digital data is being stored by the memory element. If the memory element has a low resistance, for example, the memory element may be said to contain a logic one (i.e., a “1” bit). If, on the other hand, the memory element has a high resistance, the memory element may be said to contain a logic zero (i.e., a “0” bit). During a write operation, the state of a memory element can be changed by application of suitable write signals to an appropriate set of signal lines  304  and  306 . 
     Ideally, only the selected memory cell, (e.g., during a read operation), can allow a current to flow. However, currents, (often referred as sneak path currents), can flow through unselected memory elements during the read operation. The sensing of the resistance state of a single memory cell can be unreliable. For example, all memory cells in the array are coupled together through many parallel paths. The resistance measured at one cross point can include the resistance of the memory cell at that cross point in parallel with resistances of the memory cells in the other rows and columns. 
       FIG. 4  illustrates sneak path currents in a cross point memory array according to some embodiments. Sneak path currents can exist concurrently with operating current when a voltage is applied to the cross point memory array. A memory cell  410  can be selected, for example, for a read operation, by applying a voltage to signal line  430 , and grounding signal line  440 . A sensing current  415  can flow through the memory cell  410 . However, parallel current paths, (e.g., sneak path current), can exist, for example, represented by a series of memory cells  420 A,  420 B, and  420 C. The applied voltage (signal line  430 ) can generate a current  425  through memory cells  420 A- 420 C, and return to ground (signal line  440 ). The sneak path current  425  can be particularly large, (e.g., larger than the sensing current  415 ), when the selected cell  410  is in a high resistance state and the neighboring cells (e.g.  420 A- 420 C) are in a low resistance state. 
     There can be multiple sneak path currents  425 , and the resistances of the series memory cells  420 A- 420 C can be smaller than that of the selected memory cell  410 , this can obscure the sense current  415  through the selected memory cell  410  during a read operation. 
     To reduce or eliminate the sneak path occurrence, a control device, (e.g., a selector), can be used in the cross point memory array. For example, a diode can be located in each memory cell. The control device can isolate the selected memory cell from unselected memory cells by breaking parallel connections of the memory cells. 
     The sneak path current  425  can include currents in an opposite direction as compared to the sensing current. For example, as seen in  FIG. 4 , sneak path current  425  passes through memory device  420 B in an opposite direction, (e.g., upward), as compared to the sensing current  415  passing through the selected memory cell  410 . Thus a one-way electrical device, such as a diode, can be used to block the sneak current path  425 . For example, a diode can be added to each memory device, (e.g., memory devices  410 , and  420 A- 420 C), thus allowing currents to pass only in one direction. As an example, the diodes can be incorporated into the memory devices so that the current can only pass in a downward direction in  FIG. 4 . With the incorporation of diodes, the sneak path current can be blocked, for example, at memory device  420 B. 
     In some embodiments, control elements for lower current values through a memory element, for example, during a read operation or a set or reset operation, are provided. The current for the memory element can be reduced at lower than the operating voltages, such as a read voltage, while still maintaining appropriate current at the operating voltages to avoid interfering with the memory device operation. In some embodiments, the current density can be small, (e.g., &lt;10 −3  A/cm 2 ), at half of the operating voltage (V s /2) to prevent modification to the memory array. The low current at half the operating voltage can ensure that when V s /2 is applied to selected cell, (e.g., V s /2 is applied to a selected row and −V s /2 is applied to a selected column), the other cells on the selected row and column are not programmed or disturbed. The current selector thus should have high resistance at V s /2. In some embodiments, the current density can be large, (e.g., ˜10 6 -10 8  A/cm 2 ), at the operating voltage, (e.g., set or reset voltage) to allow switching of the memory cells. In other words, the current selector can have very low resistance at V s  to ensure that the voltage drop across the current selector can be minimal during the memory cell programming. 
     In some embodiments, control elements for a non-linear current response of a memory element are provided. At low voltages, (e.g., lower than the operating voltages or at half an operating voltage), the current can be significantly reduced, while the current can remain the same or can be controlled to ensure proper operation of the memory devices. The lower current values at low voltages can also reduce power consumption and thus improve the power efficiency of the memory array. 
     In some embodiments, selector elements for resistive-switching memory elements and cross point memory arrays are provided. The selector device can be constructed using familiar and available materials currently used in semiconductor fabrication facilities. 
       FIG. 5  schematically illustrates sneak path currents in a cross point memory array according to some embodiments. A memory cell  522  can be selected, for example, for a read operation, by applying a voltage to signal line  530 , and grounding signal line  540 . A current can flow through the memory cell  522 . However, parallel current paths, (e.g., sneak path current), can exist, for example, represented by a series of memory cells  524 ,  526 , and  528 . The applied voltage (signal line  530 ) can generate a current  514  through memory cell  524 , passing through memory cell  526 , and returning to the ground (signal line  540 ) through memory cell  528 . 
     There are multiple sneak path currents, and the resistances of the series memory cells can be smaller than that of the selected memory cell. This can obscure the sense current through the selected memory cell during a read operation. 
     To reduce or eliminate the sneak path occurrence, a control element, (e.g., a selector), can be used in the cross point memory array. For example, a series transistor or a diode can be located in a memory cell. The control device can isolate the selected memory cell from unselected memory cells by breaking parallel connections of the memory cells. 
     A resistive memory element can require a minimum set current to cause the memory element to switch from a high resistance state, (e.g., “0” state), to a low resistance state, (e.g., “1” state). In practice, the difference between the applied set current and the minimum set current is much larger than necessary to cause the device to reliably switch to the logic “1” state, (e.g., low resistance state). Further, it has been found that the magnitude of the current required to switch the memory element to a high resistance state from a low resistance state can be dependent on the magnitude of the current used to set the device in the low resistance state. If a high set current is used, then a higher “reset” current is required to achieve a desirable high resistance state. In other words, the difference between the applied reset current and the minimum reset current also needs to be larger than necessary to cause the device to switch from the “1” to the “0” state if the magnitude of the prior applied set current is too far from the minimum set current. 
     The larger than necessary swings in the current used to switch between the “1” and “0” states can damage the materials and components in the switching memory device, thus affecting the memory element&#39;s lifetime and reliability. 
     In some embodiments, the control element can be provided so that its impedance can limit the current through the memory element to a value that is just greater than the minimum set current, and still allow the “1” logic state to be reliably set by the applied V SET  voltage. It is believed that the control element can also help reduce the apparent minimum set current, since the control element impedance can reduce the swing in current between the set and reset switching currents at the same fixed applied voltage, thus affecting the density and movement of the traps in the variable resistance layer. Not intending to be bound by theory, but it is believed that when a smaller “1” state switching current is applied to a device that the formed filaments, or aligned traps, in the variable resistance layer will be smaller in size than if a higher “1” current is applied, thus making the filaments easier to alter during the reset phase of the resistive switching process. 
     In some embodiments, control elements for lower current values through a memory element, (e.g. during a read operation or a set or reset operation), are provided. The current for the memory element can be reduced at lower than the operating voltages, (e.g. such as a read voltage), while still maintaining appropriate current at the operating voltages to avoid interfering with the memory device operations. A control element can be optimized for one or more operations (e.g. such as read, set, and/or reset) that is performed at a specific operating voltage (V s ), but can be compatible with other operations. In some embodiments, the current can be small, (e.g., between 10 −10  and 10 −6  A/cm 2 ), at half of the operating voltage (V s /2) to prevent modification to the memory array. For high density memory devices, higher leakage currents can be acceptable, (e.g. such as less than 10 3  A/cm 2 ) for less than 10 micron size devices. The low current at half the operating voltage can ensure that when V s  is applied to a selected cell, and smaller voltages are applied to other cells in the same row or column, the other cells are not accidentally programmed and/or disturbed. Further, the state of the other cells does not substantially affect the desired operation on the selected cell (such as the value of the sensed current during a read operation). For example, one way to perform an operation (such as a read operation) can be by applying V s /2 to a selected row and −V s /2 to a selected column, and grounding other rows and columns, so that the full operating voltage V s  is applied to the selected cell, and a smaller voltage V s /2 is applied to other cells on the selected row and column. Other methods of applying V s  to the selected cell (e.g. during a read operation) may be preferred, but in general they all may potentially subject a large number of cells, or even the majority the cells in the array, to non-zero voltages no larger than V s /2. The current selector thus can have high resistance at and below V s /2 but much smaller resistance at the operating voltage V s  and above. 
     In some embodiments, the current can be large, (e.g., between 10 −3  and 10 3  A/cm 2 , or between 10 1  and 10 3  A/cm 2 ), at voltages equal to (or higher than) the operating voltage. For high density memory devices, higher currents can be achieved, such as between 10 6  and 10 7  A/cm 2  for less than 10 micron size devices. For example, to allow switching of the memory cells, the currents should reach these values when sufficient voltages are applied to the switching layer. The voltage applied to the switching layer can be different (e.g., much larger) than the voltage that falls across the control element. Because the control element can be electrically in series with the switching layer, these high currents can flow through the control element, and thus, the portion of the voltage that falls across the control element during set and/or reset operation can be substantially higher than V s /2, for example, it can be around or slightly above the operating voltage V s . If a much larger voltage falls across the control element while high currents are flowing through it, the Joule heating can lead to unintended thermal damage. In other words, the control element can have very low resistance at V s  to ensure that the voltage drop across the control element can be minimal during the memory cell programming despite the high current levels. 
       FIGS. 6A-6B  illustrate examples of I-V response for a control element according to some embodiments. These plots are given as an illustration and are not assuming any particular scale of the axes. In  FIG. 6A , a current voltage response, (e.g., I-V curve), for a control element employed in a unipolar device is shown. The current can start from low current (substantially zero current) at zero voltage, and can increase until the on-state voltage V on-state  (e.g., the operating voltage V s ), which can be as high as the read voltage V READ  or even higher. The current will continue to increase up to the highest voltage used for any operation, such as V SET . The current can slowly increase for low voltages that are less than V off-state , (e.g., less than V s /2), and then rapidly increase toward the on-state voltage V on-state . The low current at the vicinity of zero voltage can reduce the leakage current. For example, the current  630  at half the operating voltage can be less than about 10 −6  A/cm 2 , such as between 10 −10  A/cm 2 , and 10 −6  A/cm 2 , to prevent accidental changes to the memory cells. At high voltages, such as at the operating voltage V s , the current can be very high to prevent any interference with the operation of the memory devices. For example, the current  620  at the operating voltage can be higher than about 10 −3  A/cm 2 , such as between 10 −3  A/cm 2 , and 10 3  A/cm 2 , or higher than about 10 1  A/cm 2 , such as between 10 1  and 10 3  A/cm 2 , so that the voltage drop across the control element is small. At opposite polarity voltages, the current  640  can be small, (e.g., negligible), to be used as a diode for unipolar memory cells. The current values can be dependent on memory density, for example, for memory sizes of a few hundred microns. For smaller memory sizes, such as less than 10 microns, higher leakage values (e.g., 10 3  A/cm 2 ) at low voltages can be allowed, and higher current values (e.g., 10 6-7  A/cm 2 ) at high voltages can be required. Note that the specific target current densities may depend on the dimensions of the device and the material used in the switching element; the above numbers are cited as examples and are not intended to be limiting. 
       FIG. 6B  shows a current response for a control element that can be used for bipolar memory cells, (Note: the absolute value of current is shown, regardless of the current direction). The current response curve can be similar in both positive and negative polarities. For example, for the positive voltages, the current can be small  630  at V off-state , and very large  620  at V on-state . For the negative voltages, the current behavior can be similar, (e.g., small  635  at V off-state1 , and large  625  at V on-state1 ). As shown, both curves are plotted on the upper half of an I-V coordinate, but in general, the left half can be plotted on an (−I)-(V) axis while the right half can be plotted on I-V axis. This approach can account for a linear-log plot, for example, with the voltage axis being linear and the current axis being logarithm. 
     In some embodiments, the curves can be symmetrical, (e.g., V off-state =V off-state1  and V on-state =V on-state1 ). For example, in a bipolar memory cell, the set voltage V set  and reset voltage V reset  can have a same magnitude with opposite polarities. In some embodiments, the curves can be asymmetrical, (e.g., V on-state ≠V on-state1 ). 
     In some embodiments, designs for control elements for resistive memory devices are provided. A control element can be based on tunneling and/or thermionic conduction in the on-state, with minimum leakage in the off-state. At low voltages, (e.g., lower than the operating voltages or at half an operating voltage), the current can be significantly reduced, while the current can remain the same or can be controlled to ensure proper operation of the memory devices. The lower current values at low voltages can also reduce power consumption and thus improve the power efficiency of the memory arrays. In some embodiments, the ratio of on-current to off-currents can be large (e.g., &gt;10 4 ) with a high on-current (e.g., greater than 10 1  A/cm 2  for large area memory devices and greater than 10 3  or 10 6  A/cm 2  for small area memory devices). 
     In some embodiments, the memory device including a memory element and a control element can be used in a memory array, such as a cross point memory array. For example, the control element can be fabricated on the memory element, forming a columnar memory device, which can be placed at the cross points of the word lines and bit lines.  FIG. 7  illustrates a cross point memory array according to some embodiments. A switching memory device can include a memory element  720  and a control element  725 , which are both disposed between the electrodes  730  and  740 . The control element  725  can be an intervening electrical component, disposed between electrode  730  and memory element  720 , or between the electrode  740  and memory element  720 . In some embodiments, the control element  25  may include one or more additional layers of materials. 
     Leakage current in dielectric materials can be due to Schottky emission, Frenkel-Poole defects (e.g. oxygen vacancies (V ox ) or grain boundaries), or Fowler-Nordheim tunneling. Schottky emission, also called thermionic emission, is a common mechanism and is the thermally activated flow of charge over an energy barrier whereby the effective barrier height of a MIM capacitor controls leakage current. The nominal barrier height is a function of the difference between the work function of the electrode and the electron affinity of the dielectric. The electron affinity of a dielectric is closely related to the conduction band offset of the dielectric. The Schottky emission behavior of a dielectric layer is generally determined by the properties of the dielectric/electrode interface. Frenkel-Poole emission allows the conduction of charges through a dielectric layer through the interaction with defect sites such as vacancies, grain boundaries, and the like. As such, the Frenkel-Poole emission behavior of a dielectric layer is generally determined by the dielectric layer&#39;s bulk properties. Fowler-Nordheim emission allows the conduction of charges through a dielectric layer through direct tunneling without any intermediary interaction with defects. As such, the Fowler-Nordheim emission behavior of a dielectric layer is generally determined by the physical thickness of the dielectric layer. 
     In some embodiments, a control element for a cross point memory array is provided, wherein the cross point memory array includes one of magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), or resistive random access memory (ReRAM). In some embodiments, the control element includes one of a metal-insulator-metal (MIM), metal-insulator-insulator-insulator-metal (MIIIM), metal-semiconductor-metal (MSM), metal-semiconductor-semiconductor-semiconductor-metal configuration (MSSSM), or metal-insulator-semiconductor-insulator-metal (MISIM) (e.g. stacks of layers). The control element is designed to exhibit substantially symmetric I-V behavior (e.g. bipolar behavior as discussed previously). In some embodiments, the operating voltage (e.g. V s ) of the cross point memory array is between about 3V and about 5V (or between −3V and −5V for the negative polarities). In some embodiments, the operating voltage of the cross point memory array is about 4V. The control element is designed to have leakage current density values between about 10 6  A/cm 2  and 10 8  A/cm 2  over these voltage ranges. The control element is designed to have leakage current density values that are lower at voltages that are less than about half of the operating voltage (e.g. V s /2). Advantageously, the ratio of the leakage current density at the operating voltage (e.g. J at V s ) to the leakage current density at half of the operating voltage (e.g. J at V s /2) is on the order of 10 6 -10 8 . These design criteria give a non-linearity factor of about 4 decades/volt over the voltage range between V s /2 and V s . The control element is designed so that the stack does not exhibit irreversible breakdown behavior when stressed by voltages up to and slightly greater than V s . 
     The previous discussion has described the use of the non-linearity of the various leakage mechanisms through dielectric materials to form control elements for use in non-volatile memory arrays. There are other materials and leakage mechanisms that can be exploited to form control elements for use in non-volatile memory arrays. 
     The leakage current through semiconductor materials may also exhibit non-linear behavior. Therefore, a metal-semiconductor-metal (MSM) control element (or MSSSM or MISIM) may be formed within each memory cell of a cross-bar memory array (e.g. similar to the MIM control elements discussed previously). The leakage current is low or increases slowly for voltages below a threshold voltage (V Threshold ). In this voltage range, the control element has a high resistance and the leakage current is low, or increases only slowly. Above the threshold voltage, the resistivity of the control element decreases and the control element may exhibit snapback, wherein the voltage across the control element decreases to a lower value (e.g. V Hold ) because the resistance of the control element suddenly decreases. The mechanisms involved in snapback behavior are not well understood. As discussed with respect to  FIG. 7 , the control element and the memory element are arranged in series within each memory cell. At voltages greater than the threshold voltage, the control element passes most of the current through to the memory element. This behavior allows higher voltages such as V set  and V reset  to be applied to the memory element (e.g. a MRAM element, FRAM element, PCM element, STT-RAM element, ReRAM element, or others) to change the state of the memory element. 
       FIGS. 8A-8B  illustrate examples of I-V response for a control element according to some embodiments. These plots are given as an illustration and are not assuming any particular scale of the axes. In  FIG. 8A , a current voltage response, (e.g., I-V curve), for a control element employed in a unipolar device is shown. The current can start from low current (substantially zero current) at zero voltage, and can increase until the threshold voltage V Threshold  is reached along line  820 . As discussed previously, when the threshold voltage is reached, the semiconductor material exhibits snapback and the voltage across the control element decreases as illustrated by line  830 . As the voltage continues to increase, the current will continue to rise (not shown) as dictated by the resistance of the memory element with only a small influence by the control element. 
       FIG. 8B  shows a current response for a control element that can be used for bipolar memory cells, (Note: the absolute value of current is shown, regardless of the current direction). The current response curve can be similar in both positive and negative polarities. The current can start from low current (substantially zero current) at zero voltage, and can increase until the threshold voltage V Threshold  is reached along line  820  (or line  822  for negative voltages). As discussed previously, when the threshold voltage is reached, the semiconductor material exhibits snapback and the voltage across the control element decreases as illustrated by line  830  (or line  832  for negative voltages). As the voltage continues to increase, the current will continue to rise (not shown) as dictated by the resistance of the memory element with only a small influence by the control element. As shown, both curves are plotted on the upper half of an I-V coordinate, but in general, the left half can be plotted on an (−I)-(V) axis while the right half can be plotted on I-V axis. This approach can account for a linear-log plot, for example, with the voltage axis being linear and the current axis being logarithm. In some embodiments, the curves can be symmetrical, (e.g., V Threshold =V Threshold-1  and V Hold =V Hold-1 ). 
     In some embodiments, the dielectric layer in the MISIM stack includes a multilayer of titanium oxide-silicon-titanium oxide (e.g. the titanium oxide acts as an insulator and silicon acts as a semiconductor). The electrode layers may be one of ruthenium, titanium nitride, or carbon. Titanium oxide has a high k-value (e.g. between about 40 to above about 80, with a band gap of about 3 eV, depending on the crystal orientation and the deposition and processing parameters). Other high-k dielectric metal oxide materials can be substituted for the titanium oxide in the MISIM stack. Examples of other high-k dielectric metal oxide materials include hafnium oxide, aluminum oxide, magnesium oxide, and the lanthanide oxides. Silicon is selected because it has a band gap of about 1 eV. The multilayer stack is deposited thick enough to suppress direct tunneling (e.g. Fowler-Nordheim mechanisms) at voltages lower than about V s /2. In some embodiments, the thickness of the silicon layer is less than about 30 nm. In some embodiments, the thickness of the titanium oxide layers (or other metal oxide layers) is less than about 2 nm. Electrode materials with high work function values are used to suppress thermionic emission (e.g. Schottky emission mechanisms) at lower voltages. Advantageously, the two metal electrodes include the same material. The electrode layers may be one of ruthenium, titanium nitride, or carbon. The symmetry of the stack results in symmetric I-V behavior under bipolar operation. However, electrodes with different work function values can be selected to distort the symmetry of the I-V behavior if so desired. 
       FIG. 9  illustrates a band gap diagram according to some embodiments. The two titanium oxide layers (or other metal oxide layers) of the MISIM dielectric stack are indicated by elements  902  and  904 . As illustrated, the titanium oxide has a higher band gap. The central silicon layer of the MISIM dielectric stack is indicated by element  906 . As illustrated, the silicon has a lower band gap. 
     Between 0 V and about V s/2 , the leakage current density is primarily determined by the two titanium oxide layers (or other metal oxide layers). The leakage current density can be adjusted by varying the thickness of the two titanium oxide layers and/or introducing defects into the two titanium oxide layers.  FIG. 10  presents data for leakage current density (J) versus the thickness of each of the two titanium oxide layers, measured at 0.75 V. The data indicate that including as little as 0.5 nm (5 Å) of titanium oxide is sufficient to lower the leakage current density by between 6 and 8 orders of magnitude. Within this voltage range, the leakage current density is determined by a combination of Schottky emission mechanisms and Frenkel-Poole mechanisms. Those skilled in the art will understand that each of these mechanisms is non-linear as a function of applied voltage and therefore, the leakage current density will increase in a non-linear fashion within this voltage range. 
     At higher voltages (e.g. between V s/2  and V s ), a number of mechanisms contribute to the leakage current through the device. As the voltage increases, the Schottky emission mechanism increases through the two titanium oxide layers.  FIG. 11  presents data for leakage current density (J) versus the thickness of each of the two titanium oxide layers, measured at 3.5 V (e.g. close to V s ). The data indicate that the leakage current density can be lowered by increasing the thickness of each of the titanium oxide layers. Those skilled in the art will understand that the leakage current density measured at 3.5 V, as presented in  FIG. 11 , is higher than the leakage current density measured at 0.75 V, as presented in  FIG. 10 . As the voltage increases, the two titanium oxide layers may undergo a soft breakdown and the leakage current will increase. At the higher voltages, the silicon layer may exhibit snapback behavior as discussed with respect to  FIGS. 8A and 8B . 
       FIG. 12  presents data for leakage current density (J) versus for several MISIM stacks. The data for curve  1202  presents data for a ruthenium-silicon-ruthenium (e.g. MSM) stack wherein the silicon layer has a thickness of about 10 nm. The data indicate that this stack exhibits a hard breakdown at voltages in excess of about +/−0.5 V. The data for curve  1204  presents data for a ruthenium-titanium oxide-silicon-titanium oxide-ruthenium (e.g. MISIM) stack wherein the silicon layer has a thickness of about 10 nm, and each of the two titanium oxide layers has a thickness of about 1 nm. The data indicate that this stack does not exhibit a hard breakdown at voltages up to about +/−4.0 V. The data for curve  1206  presents data for a ruthenium-titanium oxide-silicon-titanium oxide-ruthenium (e.g. MISIM) stack wherein the silicon layer has a thickness of about 30 nm, and each of the two titanium oxide layers has a thickness of about 1 nm. The data indicate that this stack does not exhibit a hard breakdown at voltages up to about +/−4.0 V. Curves  1104  and  1106  exhibit the same behavior and lie on top of one another in the graph, indicating that the leakage current density is not influenced by the thickness of the central silicon layer. In some embodiments, the titanium oxide is replaced by at least one of zirconium oxide, hafnium oxide, aluminum oxide, magnesium oxide, or the lanthanide oxides. 
     In some embodiments, the dielectric layer in the MISIM stack includes a multilayer of metal-silicon nitride-silicon-silicon nitride-metal. The electrode layers may be one of ruthenium, titanium nitride, or carbon. Silicon nitride is selected as the insulator since it has a high k-value (e.g. about 7.5, with a band gap of about 5 eV, depending on the deposition and processing parameters). Silicon is selected as the semiconductor because it has a band gap of about 1 eV. The multilayer stack is deposited thick enough to suppress direct tunneling (e.g. Fowler-Nordheim mechanisms) at voltages lower than about V s /2. In some embodiments, the thickness of the silicon layer is less than about 30 nm. In some embodiments, the thickness of the silicon nitride layers is less than about 2 nm. Electrode materials with high work function values are used to suppress thermionic emission (e.g. Schottky emission mechanisms) at lower voltages. Advantageously, the two metal electrodes include the same material. The electrode layers may be one of ruthenium, titanium nitride, or carbon. The symmetry of the stack results in symmetric I-V behavior under bipolar operation. However, electrodes with different work function values can be selected to distort the symmetry of the I-V behavior if so desired. 
       FIG. 9  illustrates a band gap diagram according to some embodiments. The two silicon nitride layers of the MISIM dielectric stack are indicated by elements  902  and  904 . As illustrated, the silicon nitride has a higher band gap. The central silicon layer of the MIIIM dielectric stack is indicated by element  806 . As illustrated, the silicon has a lower band gap. 
     Between 0 V and about V s/2 , the leakage current density is primarily determined by the two silicon nitride layers. The leakage current density can be adjusted by varying the thickness of the two silicon nitride layers and/or introducing defects into the two silicon nitride layers.  FIG. 13  presents data for leakage current density (J) versus the thickness of each of the two silicon nitride layers, measured at 0.75 V. The data indicate that including as little as 2 nm of silicon nitride is sufficient to lower the leakage current density by between 3 and 5 orders of magnitude. Within this voltage range, the leakage current density is determined by a combination of Schottky emission mechanisms and Frenkel-Poole mechanisms. Those skilled in the art will understand that each of these mechanisms is non-linear as a function of applied voltage and therefore, the leakage current density will increase in a non-linear fashion within this voltage range. At the higher voltages, the silicon layer may exhibit snapback behavior as discussed with respect to  FIGS. 8A and 8B . 
     At higher voltages (e.g. between V s/2  and V s ), a number of mechanisms contribute to the leakage current through the device. As the voltage increases, the Schottky emission mechanism increases through the two silicon nitride layers. As the voltage increases, the two silicon nitride layers may undergo a soft breakdown and the leakage current will increase. 
       FIG. 14  presents data for leakage current density (J) versus for several MISIM stacks. The data for curve  1402  presents data for a ruthenium-silicon-ruthenium (e.g. MSM) stack wherein the silicon layer has a thickness of about 10 nm. The data indicate that this stack exhibits a hard breakdown at voltages in excess of about +/−0.5 V. The data for curve  1404  presents data for a ruthenium-silicon nitride-silicon-silicon nitride-ruthenium (e.g. MISIM) stack wherein the silicon layer has a thickness of about 10 nm, and each of the two silicon nitride layers has a thickness of about 2 nm. The data indicate that this stack does not exhibit a hard breakdown at voltages up to about +/−4.0 V. In some embodiments, the silicon nitride is replaced by at least one of titanium oxide, zirconium oxide, hafnium oxide, aluminum oxide, magnesium oxide, or the lanthanide oxides. 
     Although the foregoing examples have been described in some detail for purposes of clarity of understanding, the invention is not limited to the details provided. There are many alternative ways of implementing the invention. The disclosed examples are illustrative and not restrictive.