10
Macromolecular Memory

Benjamin F. Bory and Stefan C.J. Meskers

Eindhoven University of Technology, The Netherlands

10.1 Chapter Overview

Macromolecular materials, such as polymers, can be used to make electronic memory cells. This chapter focuses on data storage based on resistive switching in diodes incorporating macromolecules. The organization of the chapter is as follows. We start with a brief introduction into the chemical structure and properties of macromolecules. We then sketch the phenomenology of electronic memory effects involving macromolecules and review the current state of the art in polymer memory technology. The subsequent sections are devoted to the electrical and semi-(conducting) properties of polymers and macromolecules and physical–chemical mechanisms of the electronic memory effects. Finally we classify different types of macromolecular memory based on the physical–chemical characteristics of the material involved.

10.2 Macromolecules

10.2.1 Chemical Structure

Macromolecules can be defined as large molecules built up of more than, say, 102 atoms. The class of macromolecules includes synthetic and biological polymers, polyelectrolytes and also encompasses frameworks such as carbon nanotubes and graphene. The backbone of these macromolecules often consists mainly of carbon atoms, sometimes silicon. Two carbon atoms in the chain can be linked via either a single, double or triple bond depending on the number of electron pairs that are shared between the two atoms. Hydrogen and hetero atoms such as oxygen, nitrogen, sulfur can also be incorporated in the chain in various ways and this makes the possible variation in chemical structure almost endless. Compared to other solids, polymers can be characterized as “soft” condensed matter. The solid state structure of a polymer is usually disordered and has considerable internal free volume. The free volume leaves room for motion of the chains in the solid, which in turn allows for migration and diffusion of small molecules and ions and for rearrangements of intermolecular and intramolecular ordering. Furthermore, because of the large size of the molecules, relaxation times to reach thermodynamic equilibrium are often very long. As a consequence, macromolecular materials commonly occur in long-lived, metastable thermodynamic states and might not even reach thermodynamic equilibrium in a time span of years.

10.2.2 Memristive Effects in Macromolecular Materials

The free volume and internal motion allow macromolecules to adapt their structure and conformation in response to external stimuli and perturbations. This also extends to the electrical properties of macromolecules. In the past decade it has been shown that using a macromolecular material as insulator in a Metal–Insulator–Metal (MIM) structure, one can realize diodes whose electrical resistance can be modified by application of electrical bias voltage. Table 10.1 gives an overview of review articles that describe progress and achievements in this field.

Table 10.1 Reviews on diodes incorporating organic materials showing electronic memory effects in their electrical resistivity

Title of review Reference details Description
Electrical switching and bistability in organic/polymeric thin films and memory devices [1] Adv. Funct. Mater. vol. 16, pp. 1001–1014, 2006. Resistive switching in π-conjugated polymers
Nonvolatile memory elements based on organic materials [2] Adv. Mater. vol. 19, pp. 1452–1463, 2007. Classification of electrical characteristics and minimal performance specifications
Nanoionics-based resistive switching memories [3] Nat. Mater. vol. 6, pp. 833–840, 2007. Redox process involving metal ions; growth/dissolution of filaments
Polymer electronic memories: materials, devices and mechanisms [4] Prog. Polym. Sci. vol. 33, pp. 917–978, 2008. Mechanism in relation to chemical structure of polymers
Polymer and organic nonvolatile memory devices [5] Chem. Mater. vol. 23, pp. 341–358, 2011. Principles of operation and feasibility
Recent results on organic-based molecular memories [6] Curr. Appl. Phys. vol. 11, pp. e49–e57, 2011. Molecular aspects of organic memory
Progress in nonvolatile memory devices based on nanostructured materials and nanofabrication [7] J. Mater. Chem. vol. 21, pp. 14 907–14 112, 2011. Fabrication and integration of organic memory and device architecture
Donor–acceptor polymers for advanced memory device applications [8] Polym. Chem. vol 2, pp. 2169–2174, 2011. Polyimide polymers
Organic resistive memory devices: performance enhancement, integration, and advanced architectures [9] Adv. Funct. Mater. vol 21, pp. 2806–2829, 2011. Architecture, operation and integration of polymer memory; inventory of the different mechanisms and the integration into electronics
Organic resistive nonvolatile memory materials [10] MRS Bull. vol. 37, pp. 144–149, 2012. Performance and requirements; integrated circuit architectures
Advanced polyimide materials: syntheses, physical properties and applications [11] Prog. Polym. Sci. vol. 37, pp. 907–974, 2012. Synthesis and properties of polyimide materials; functionalized polyimids for resistive memory
Polyimide memory: a pithy guideline for future applications [12] Polym. Chem. vol. 4, pp. 16–30, 2013. Classification of memory effects in polyimides; electronic structures of polyimide materials in relation to memory

The change in resistance may be transient and disappear when short-circuiting the diode (volatile memory) or could be semi-permanent under short-circuit conditions (nonvolatile memory). For the latter memristive devices, one can differentiate between write once read many (WORM, W) and rewriteable memory cells. The rewriteable cells can be further subdivided into cells that require write and erase voltages of opposite polarity (Bipolar, B) and cells that can be operated using write and erase voltages of the same polarity (Unipolar, U).

Attractive features of macromolecular memory include the possibility to use solution-based deposition methods such as printing and casting of the active layers. In addition, flexible, lightweight, and disposable substrates may be used. Furthermore because macromolecular memory is essentially a thin film technology and one can make economic use of raw materials (Figure 10.1).

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Figure 10.1 Macromolecular memory: flexible substrates (left, [60]) and 3-D integration (right, a–c, [26]. Copyright: Wiley VCH

10.2.3 Current State of Macromolecular Memory

In the last decade enormous progress has been made in the realization of macromolecular memory. Resistive switching has been shown to occur locally and downscaling to nm lengths is feasible. Projected retention times on the order of 10 years have been realized and switching is possible using short voltage pulses (submicrosecond). Integration into arrays has been demonstrated. So far, a complete device technology seems not to have been disclosed. A main challenge for macromolecular memory is still to understand and control the resistive switching. As will become clear, macromolecular memory operates close to the threshold for electrical breakdown. Reproducibility of the switching characteristics is often an issue. In view of the very stringent requirements regarding uniformity, cycle endurance, and bit error rate for application as NAND flash, variability in the characteristic of cells may be an issue.

10.3 Elementary Physical Chemistry of Macromolecular Memory

10.3.1 Required Activation Barrier between Stable States

For a rewriteable, nonvolatile memory, one would like to have a molecular system that is bistable, having two distinct stable states (“ON” and “OFF”) separated by a barrier in energy (see Figure 10.2). For electronic memory applications, the ON and OFF states should differ in charge transport related properties, namely delocalization length of charge carriers and energies of the electron and holes states on the polymer. The transition between the ON and OFF states is in essence a monomolecular chemical reaction. The transition state theory developed by Eyring describes the rate of chemical reactions and allows one to estimate the rate of interconversion between ON and OFF state, kON/OFF in s−1, as a function of the height of the energy barrier separating the two minima [13]. To warrant a lifetime of at least 10 years for the ON and OFF state, the barrier in between the two states should have a height of at least 1.25 eV of Gibbs free energy.

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Figure 10.2 Gibbs Free energy ΔG as function of a generalized configurational coordinate for a bistable molecule. The rate of spontaneous interconversion between ON and OFF states, kON/OFF, is determined by the height of the barrier (ΔG‡) in between the two stable states and temperature. For a lifetime of ON and OFF states of 10 years at room temperature, a minimal barrier height of ΔG‡ = 1.25 eV is required according to molecular transition state theory

The barrier should have sufficient width to suppress quantum mechanical tunneling between the states. Application of a potential difference over the memory cell should lead to rapid conversion between the ON and OFF states. From the estimated barrier height it then follows that the minimal voltages needed to switch the cell will exceed 1.25 V.

Furthermore, memory cells relying on trapping of charges can most likely not be realized with semiconducting materials with a bandgap smaller than 1.25 eV.

One might argue that small molecules are inherently less stable and more prone to thermodynamical and quantum mechanical fluctuations than bulk phases in large crystals. So is there any experimental evidence for small bistable molecular systems with lifetime of the individual states exceeding 10 years? Amino acids are small molecules with fewer than 12 carbon atoms, that serve as monomeric units of proteins and polypeptides. Amino acids can exist in two mirror image related stable configurations labeled L and D. Even though the two forms have identical energies, in living plants and animals only the L form is produced and biochemically active. Analysis of fossils has shown that interconversion of the L into the D forms takes place on a time scale of 103 years [14]. This shows that bistable molecular systems with interconversion sufficiently slow for electronic memory applications indeed exist.

10.3.2 Electronic Structure of Macromolecules: Insulators, Semiconductors, Conductors

Depending on the type of connection between the carbon atoms, macromolecules behave electrically as either insulators, semiconductors or conductors. The origin of the diversity lies in the different possible types of coordination of substituents around the carbon atom. Two neighboring carbon atoms can form a chemical bond by sharing two valence electrons between them, with each atom donating one electron. The two electrons forming the bond must have antiparallel spin. Because carbon has four valence electrons it can bind to maximally four other atoms. Electrostatic repulsion between the electron pairs forming the bonds is minimized when the four carbon atoms binding to the central one are arranged in the form of a tetrahedron. Hybridization of the hydrogen like 2s and three 2p orbitals around the carbon nucleus into four equivalent sp3 orbitals facilitates the formation of these four bonds. The resulting atomic arrangement is that of diamond, a material that can be characterized as a wide (5.4 eV) indirect bandgap semiconductor.

Within the diamond lattice, electrons and holes have high and almost equal mobility (2 × 103 cm2/Vs).

In another allotrope of carbon, graphite, each carbon atom is bound to only three neighboring atoms and one valence electron per atom is delocalized over the honeycomb hexagonal sheet of carbon atoms. In this case, repulsion between electron pairs forming the bonds results in a planar triangular arrangement of the three substituents. Hybridization of the carbon 2s with two 2p orbitals to sp2 orbitals can facilitate this bonding. This leaves one 2p orbital unhybridized containing one electron. Overlap between unhybridized 2p orbitals on neighboring sp2 hybridized carbon atoms allows for quantum mechanical delocalization of these electrons and gives rise to (semi-)conducting properties of the molecular material. The delocalization of the electrons in the 2p atomic orbitals contributes to the bonding between two neighboring carbon atoms (now sharing a double bond) and the two atoms are said to be π-conjugated. A single layer of graphite, graphene, contains delocalized electrons and may be classified as a zero bandgap semiconductor. Electron and hole mobilities are exceptionally high (estimated > 2 × 104 cm2/Vs [15]) and relate, from a chemical point of view, to the stability of the two-dimensional hexagonal lattice against distortion.

Replacing two of the coordinating carbon atoms by hydrogen, a polymeric structure may be obtained (polyacetylene, see Figure 10.3). In this macromolecule, or π-conjugated polymer (named after the double or π-bond) one electron per carbon atom is still delocalized. Due to pairing of neighboring carbon atoms in the chain (Peierls distortion), a band gap opens (1.5 eV) and the resulting chain is alternating longer, singly bonded carbon atom pairs and shorter doubly bonded pairs. Because of the presence of double or π-bonds, polyacetylene is a π-conjugated polymer. The mobilities of charge carriers along the chain are reduced because of polaron formation and bulk mobilities are severely limited by poor intermolecular transport of carriers and trapping on impurities and defects. Carrier mobilities in purified molecular materials rarely exceed 1 cm2/Vs and for π-conjugated polymers usually fall in the range 10−3–10−7 cm2/Vs. π-Conjugated polymers can be made conductive by oxidative or reductive doping. In the case of polyacetylene, doping with molecular iodine (I2) results in a hole conducting material with conductivity approaching that of metals. By introducing dopants which themselves are macromolecules, diffusion, sublimation, and electromigration of the dopants can be suppressed and stable molecular conductors can be obtained. A well known example is poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate), or PEDOT:PSS, where positive charge carriers on the π-conjugated EDOT polymer are stabilized by the deprotonated and negatively charged polystyrene sulfonate polymer (PSS).

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Figure 10.3 Left: Diamond lattice and polyethene with sp3 hybridized carbon atoms and saturated bonds. Middle: Graphene sheet. Right: Polyacetylene polymer with two overlapping atomic 2pz orbitals on two neighboring sp2 hybridized carbon atoms forming a double bond

10.3.3 Inducing Changes by Application of Bias Voltage: Electrochemistry

As mentioned above, bias voltages ≥1.25 V will be needed for switching between bistable states of macromolecular memory. Currently in NAND flash technology, voltages up to 20 V are used to program the floating gate transistor. The question arises: which chemical changes might one expect to be induced by applying voltages in the range 1–101 volt? From physical chemistry, the energies needed to break a chemical bond are well known. For a carbon–carbon single bond, 3.6 eV is required to break the bond. To split the strongest homodimeric bond known in organic chemistry, the nitrogen–nitrogen triple bond NimgN, 9.8 eV is required. Taking into account that macromolecular memory is a thin film technology and that the bias voltage applied often results in a potential drop localized over only a narrow spatial region in the organic materials, programming voltages up to 10 V could well lead to charge carriers with up to 10 eV of kinetic energy. In principle, the 10 eV energy of the electron suffices to break any chemical bond in a molecule. We remark that, in electrochemistry, energies needed for a chemical reaction can be measured quantitatively, using polar solvents and adding salt ions (electrolyte) to localize the electric field strength in a small region close to an electrode. From electrochemistry, it is well known that within a voltage range up to a few volts, almost any chemical conversion can be driven, including oxidation and reduction of all metals. This simple line of argument illustrates the tremendous difficulties that one may face when trying to unravel mechanistic aspects of memristive effects in organic molecular materials: with programming voltages typically in the range 2–8 V a multitude of chemical processes is likely to be induced.

10.3.4 Filamentation

As mentioned above, by applying potential differences on the order of 10 V over a thin organic layer, one can drive a molecular material very far out of thermodynamic equilibrium. Note that the low mobility of charge carriers contributes to localizing the electric field strength to narrow regions. In soft condensed matter, the behavior of molecular systems far away from equilibrium has been studied in considerable detail in the last half century. One of the striking outcomes is that when a system is driven far out of equilibrium, spontaneous self-organization into patterns and structures is possible. In contrast, under near equilibrium conditions, such self-organization processes would not be favorable because of the reduction of entropy associated with the emergence of organization, patterns and structures [16]. One of the self-organization processes studied in detail is filamentation, which occurs for instance in the transmission of light when the strength of the optical electric field becomes so high that the refractive index of the material changes. The light can then focus itself into small filaments [17]. Other examples of filamentation are the formation of plasma arcs [18]. Filamentation of electrical current in planar organic memory diodes is often observed and should most likely be considered as an integral part of the response of the materials to the large thermodynamic driving force applied.

10.4 Classes of Macromolecular Memory Materials and Their Performance

In this section we give an overview of recent reports on macromolecular memory (see Table 10.2). Because the mechanism of switching is often unclear we classify the memory diodes according to the type of macromolecular material used.

Table 10.2 Memory performance characteristics for macromolecular memory

Material MIM architecture Type Von Voff On/Off Retention (s) Endurance
PEO-AgClO4 [19] Pt//Ag B 1 −1 105 105 10
π-Conjugated polyelectolyte [20] Ag//p+-Si B 3 −2 104 105 nd
Donor–acceptor polyimide [21] ITO//Al B 2.7 −1.5 104 104 nd
Donor–acceptor polyimide ITO//Al U 2.2 1 104 104 nd
Donor–acceptor polyimide ITO//Al W 2
PEDOT:PSS [22] Al//Al B −2.5 1.2 105 105 10
PEDOT:PSS [23] Au//Au U 4 1 102 104 nd
PEDOT:PSS [24] Al//Cu B 1 −0.8 104 104 nd
Fullerene [25] ITO//Al U 4 2 105 104 101
Fullerene [26] Al//Al U 5 10 103 107 102
Carbon nanotube [27] Al//Al B −2 2 102 105 102
Diamond-like carbon [28] W//Pt U 1.2 0.4 300 103 103
Diamond-like carbon [29] Ti//Pt U 1.4 −1.5 10 104 nd
Amorphous Carbon [30] Ag//Ag B 6 −7 30 106 30
Graphite [31] U 3 6 106 106 106
Graphene [32] ITO/PMMA//PMMA/Al B 3.5 −4 106 105 105
B: bipolar; U: unipolar; W: WORM; nd: not determined.

10.4.1 Saturated Macromolecules

Polymers that do not contain any double bonds are insulators and charge carrier injection via a metal contact into these materials is practically impossible. However these polymers may still be used as host materials in memory applications, when combined with additives that can take care of carrier transport. For instance, polyethylene oxide (PEO) is a polymer that can solvate ions. PEO combined with the silver salt AgClO4 can be used to realize memory cells. In AgClO4-PEO cells, electrochemical conversion of silver ions into metallic silver gives rise to the formation and dissolution of metal filaments, leading to resistive switching [19]. A disadvantage of these electrochemical cells is that the amount of charge needed to switch the diode depends on the history of the diode. The amount of current needed to switch the diode is only minimal close to the percolation threshold via the metallic filament. Some saturated polymers containing fluor substituents are ferroelectric and can be used to make a capacitive memory. When blended with semiconducting polymer resistive switching diodes have been accomplished [33]. For further information, we refer the reader to the discussion of ferroelectric memories in Chapters 6 and 9.

10.4.2 Macromolecules with π-Conjugation

10.4.2.1 Dynamic Doping

Organic molecules containing double bonds (π-conjugation) usually have semiconducting properties. The presence of charged dopants in these materials can change barriers for charge injection and the charge carrier density. Migration of charged dopants under the influence of applied bias leads to memristive effects [34]. The memory functionality of the macromolecular material can be enhanced further by doping with metal ions that can also be reduced electrochemically to metal filaments.

10.4.2.2 Donor–Acceptor Polymers

A large research effort has focused on polyimide polymers functionalized with π-conjugated moieties that have pronounced electron donating and electron accepting properties [8,11,12]. These materials often show volatile resistive switching, but nonvolatile behavior has also been observed, including both WORM and rewritable characteristics. The volatile behavior has been related to the presence of an ionized electronic state of the donor acceptor polymer (charge transfer state) in which the electron donating unit has transferred an electron to the electron accepting moieties.

10.4.2.3 Conducting Polymers

Conducting polymers such as PEDOT:PSS have been used as WORM, relying on destructive processes induced at high current densities [35,36]. However also rewritable memory cells have been realized with PEDOT:PSS and a number of studies indicate the importance of the interface between polymer and metal contact in the switching and indicate an active role of native oxides [37–39].

10.4.2.4 Carbon Allotropes

Fullerenes are spheroidal π-conjugated molecules that in comparison with π-conjugated polymers show high electron and hole mobilities. When mixed with a host polymer, a solution processable material is obtained that shows rewriteable memory effects after optimization of the mixing ratio characteristic [40–42]. Very promising memory characteristics have been reported and integration of cells into 2-D [43,44] and 3-D [26] has been achieved. A number of studies have indicated the importance of an interfacial oxide layer in the resistive switching process [26,43–46]. Carbon nanotubes can also be applied in memories and also here indications for the involvement of an interfacial oxide layer in the switching have been obtained (Al2O3 [27,47], SiO2 [48]). Graphene can give rise to bipolar switching [49] and sometimes WORM [50] memory effects. Graphene oxide functionalized with polymer chains gives a solution processable macromolecular material, displaying memory effects in combination with ITO and Al electrodes [51–53]. Finally, amorphous carbon and diamond-like carbon are amorphous carbon allotropes that show electronic memory effects in MIM devices. Amorphous carbon contains both sp3 and sp2 hybridized carbon atoms. Variation in the ratio and distribution of the semi-conducting (sp2) and insulating (sp3) varieties induced by the application of electrical stress has been suggested to lead to memory effects [54,55].

10.4.2.5 Hybrid Diodes Involving a Dedicated Inorganic Switching Layer

A number of studies have been devoted to MIM structures incorporating a (macro-)molecular layer in combination with a dedicated inorganic switching layer consisting of metal oxide [56,57] or metal halide [58]. Similar to metal oxide memory cells, these hybrid devices require an electroforming step before resistive memory effects become apparent. The electroforming process is induced by bias voltage stress and can be subdivided into different stages. The early stages involve charge trapping at the interface between the macromolecular semiconductor and the metal oxide [59]. The final step of electroforming involves soft breakdown of the inorganic insulator and is related to hole injection [58].

10.5 Perspectives

Memory cells using macromolecular materials that rely on resistive switching show excellent memory characteristics when operated as isolated cells under single write/read/erase events. Large-scale integration does not seem to have been realized, and therefore performance as integrated memory is currently difficult to estimate. The occurrence of a so-called dead time in repeated switching could be a major hurdle. Key opportunities of macromolecular memory include the low cost of raw materials and deposition methods, for example, printing and coating. Furthermore, memory cells incorporating environmentally friendly materials can be realized. This provides applications in low-end, disposable electronics on, for example, flexible substrates such as paper or plastic.

Summary of macromolecular memory parameters:
Cell size Demonstrated 130 nm
Projected 10 nm
Density Demonstrated Not known
Projected Comparable to ferroelectric and phase change
Device speed (switching speed for logic devices; reading/writing speed for memory devices Demonstrated 15 ns
Projected <10 ns
Circuit speed Demonstrated Not known
Projected Depends on “dead-time”
Operation voltages Demonstrated <6 V
Projected Not known
Switching energy Demonstrated 5E-11 Joule/bit
Projected Not known
Endurance Demonstrated >1E5
Projected Not known
Retention (for memory) Demonstrated ∼1 yr
Projected
Binary throughput Demonstrated Not known
Projected Not known

10.6 Summary

Macromolecular materials can give rise to a wide variety of electronic memory effects. Although impressive memory characteristics have been obtained, lack of understanding and control over the switching mechanisms is still a major issue.

Acknowledgments

The work of BBF forms part of research programme of the Dutch Polymer Institute (DPI 704). We thank D.M. De Leeuw and H.L. Gomes for stimulating discussion.

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