Organic and Molecular Resistive Memory

1. Theory

Definition: Organic and molecular resistive memories are two-terminal devices whose active layer is a polymer, a small-molecule film or a single molecule, and whose state is stored as a resistance change.
Organic thin-film cell: A metal / organic layer / metal sandwich.
Molecular junction: A molecule or a monolayer between two electrodes.
Filament switching: Metal (Al, Cu, Ag) from an electrode forms a conductive filament through the organic layer.
Charge-trap switching: Traps (often nanoparticles or donor-acceptor units) capture charge and change the space-charge-limited current.
Charge-transfer complexes: Materials such as Cu-TCNQ switch between two electronic states.
Molecular switching: Molecules such as rotaxanes and catenanes change conformation or redox state, altering junction conductance.

2. Working Principle

Space-charge-limited conduction: A trap-free layer follows $J = \frac{9}{8} ε μ V^{2} / d^{3}$ ; traps lower the current until they fill at the trap-filled-limit voltage.
States from traps: Empty traps give the high-resistance state and filled traps the low-resistance state; the log-log I-V slope ( $1$ , then $2$ or $l + 1$ , a steep rise at $V_{T F L}$ , then $2$ ) identifies the mechanism.
Hopping transport: Conduction in disordered films is thermally activated variable-range hopping.
Molecular tunnelling: Off-resonance conductance falls exponentially with molecular length; bringing a level near the Fermi level raises transmission (Landauer formula).
Field-assisted switching: An applied field lowers the conformational energy barrier, setting the switching rate.
Limitations: Film variability, low mobility, sensitivity to oxygen and moisture, and limited endurance and retention.

3. Applications

Current status: Research devices; not in commercial products.
Flexible and printed electronics (target): Low-cost, solution-processed memory on plastic substrates, where density and speed matter less than cost and flexibility.

Name	Formula	Related Formulae	Variables/Constants
Space-charge-limited current (trap-free)	$J = \frac{9}{8} ε μ \frac{V ^{2}}{d ^{3}}$	$V_{T F L} = \frac{q N _{t} d ^{2}}{2 ε}$	$J : c u r r e n t d e n s i t y o f a t r a p - f r ee in s u l a t or w i t h an o hmi c inj ec t in g co n t a c t (M o tt - G u r n ey l a w)$ $ε : p er mi tt i v i t y o f t h e or g ani c l a y er$ $μ : c a r r i er m o bi l i t y in t h e or g ani c l a y er$ $V : a ppl i e d v o l t a g e$ $d : t hi c k n ess o f t h e l a y er$ $V_{T F L} : t r a p - f i l l e d - l imi t v o l t a g e, a t w hi c h t h e inj ec t e d c ha r g e f i l l s t h e t r a p s an d t h e c u r r e n t r i ses s t ee pl y t o w a r d t h e t r a p - f r ee l a w$ $q : e l e m e n t a r y c ha r g e$ $N_{t} : d e n s i t y o f t h e t r a p s (a s in g l e t r a p l e v e l i s t ak e n f or t h e V_{T F L} e x p r ess i o n)$
Trap-limited space-charge current	$J \propto \frac{V ^{l + 1}}{d ^{2 l + 1}}$	$l = \frac{T _{t}}{T}$ $J = θ \frac{9}{8} ε μ \frac{V ^{2}}{d ^{3}} (s ha l l o w t r a p s)$	$J : c u r r e n t d e n s i t y w i t h an e x p o n e n t ia l d i s t r ib u t i o n o f t r a p s b e l o w t h e t r an s p or t l e v e l$ $V, d : v o l t a g e an d l a y er t hi c k n ess$ $l : e x p o n e n t o f t h e c u r r e n t - v o l t a g e l a w, g r e a t er t han o n e f or a t r a p d i s t r ib u t i o n$ $T_{t} : c ha r a c t er i s t i c t e m p er a t u r e o f t h e e x p o n e n t ia l t r a p d i s t r ib u t i o n$ $T : t e m p er a t u r e$ $θ : r a t i o o f t h e f r ee c ha r g e t o t h e t o t a l inj ec t e d c ha r g e f or s ha l l o w t r a p s$ $ε, μ : p er mi tt i v i t y an d m o bi l i t y (t h e f i l l in g o f t h e t r a p s s w i t c h es t h e ce l l f r o m t h e t r a p - l imi t e d t o t h e t r a p - f r ee l a w, w hi c h i s t h e m ec hani s m f or t h e l o w - r es i s t an ce s t a t e in t r a p - ba se d ce l l s)$
Variable-range hopping	$σ = σ_{0} exp [- (\frac{T _{0}}{T})^{1/4}]$	$T_{0} = \frac{β _{M}}{k _{B} g ( E _{F} ) ξ ^{3}}$	$σ : co n d u c t i v i t y o f a d i sor d er e d or g ani c f i l m b y h o pp in g b e tw ee n l oc a l i z e d s t a t es (M o tt l a w in t h r ee d im e n s i o n s)$ $σ_{0} : p r e f a c t or$ $T_{0} : c ha r a c t er i s t i c t e m p er a t u r e$ $T : t e m p er a t u r e$ $β_{M} : n u m er i c a l co n s t an t o f t h e p er co l a t i o n a r g u m e n t, ab o u t 18 t o 21 d e p e n d in g o n t h e d er i v a t i o n (S hk l o v s k ii an d E f r os g i v e ab o u t 21)$ $k_{B} : B o l t z mann co n s t an t$ $g (E_{F}) : d e n s i t y o f l oc a l i z e d s t a t es a t t h e F er mi l e v e l$ $ξ : l oc a l i z a t i o n l e n g t h o f t h e s t a t es$
Molecular junction: non-resonant and resonant transport	$G = G_{c} exp (- β_{N} N)$	$T (E) = \frac{4 Γ _{L} Γ _{R}}{( E - ε _{0} ) ^{2} + ( Γ _{L} + Γ _{R} ) ^{2}}$ $I = \frac{2 q}{h} \int T (E) [f_{L} (E) - f_{R} (E)] d E$	$G : co n d u c t an ce o f a m o l ec u l a r w i r e b e tw ee n tw o e l ec t r o d es in t h e n o n - r eso nan t (t u nn e l l in g) r e g im e$ $G_{c} : co n t a c t - l imi t e d co n d u c t an ce f or z er o l e n g t h$ $β_{N} : d ec a y co n s t an t p er r e p e a t u ni t o f t h e m o l ec u l e$ $N : n u mb er o f r e p e a t u ni t s in t h e m o l ec u l a r w i r e$ $T (E) : t r an s mi ss i o n o f a s in g l e m o l ec u l a r l e v e l a t e n er g y E (B r e i t - W i g n er f or m)$ $ε_{0} : e n er g y o f t h e m o l ec u l a r l e v e l$ $Γ_{L}, Γ_{R} : b r o a d e nin g o f t h e l e v e l b y t h e co u pl in g t o t h e l e f t an d t h e r i g h t e l ec t r o d e, a s ha l f - w i d t h s : t h e p e ak ha s a ha l f w i d t h a t ha l f ma x im u m Γ_{L} + Γ_{R} an d a h e i g h t 4 Γ_{L} Γ_{R} / (Γ_{L} + Γ_{R})^{2} \leq 1 (w i t h f u l l w i d t h s γ_{i} = 2 Γ_{i} t h e s am e p e ak r e a d s γ_{L} γ_{R} / [(E - ε_{0})^{2} + (γ_{L} + γ_{R})^{2} /4])$ $I : c u r r e n t f r o m t h e L an d a u er f or m u l a (s p in d e g e n er a cy in c l u d e d)$ $f_{L}, f_{R} : F er mi f u n c t i o n s o f t h e tw o e l ec t r o d es$ $q, h : e l e m e n t a r y c ha r g e an d P l an c k co n s t an t$
Field-assisted conformational switching rate	$k_{s} = ν exp (- \frac{E _{b} - Δ p _{∥} E}{k _{B} T})$	$\frac{k _{s} ( E )}{k _{s} ( 0 )} = exp (\frac{Δ p _{∥} E}{k _{B} T})$	$k_{s} : r a t e o f t h e t r an s i t i o n o f a m o l ec u l e b e tw ee n tw o co n f or ma t i o n s or r e d o x s t a t es$ $ν : a tt e m pt f r e q u e n cy$ $E_{b} : e n er g y ba r r i er o f t h e t r an s i t i o n a t z er o f i e l d$ $Δ p_{∥} : co m p o n e n t a l o n g t h e f i e l d o f t h e d i p o l e m o m e n t c han g e b e tw ee n t h e ini t ia l s t a t e an d t h e t r an s i t i o n s t a t e (t h e f i e l d l o w er s t h e ba r r i er w h e n i t i s p os i t i v e)$ $E : e l ec t r i c f i e l d a t t h e m o l ec u l e$ $k_{B}, T : B o l t z mann co n s t an t an d t e m p er a t u r e$ $(a g e n er i c A r r h e ni u s r a t e w i t h a l in e a r, B e l l - t y p e l o w er in g o f t h e ba r r i er b y t h e f i e l d; n o t f r o m a s p ec i f i c m o d e l o f a p a r t i c u l a r m o l ec u l e)$

Important Questions

Ques: What kinds of switching are found in organic and molecular memory?

Four mechanisms are reported. In the first, a metal (Al, Cu, Ag) from an electrode forms a filament through the polymer or small-molecule layer, as in an electrochemical metallization cell. In the second, charge is trapped in the layer, often in embedded metal nanoparticles or in donor-acceptor units, and the space-charge-limited current changes between a trap-limited and a trap-free law (the two space-charge rows). In the third, a charge-transfer complex such as Cu-TCNQ switches between two electronic states. In the fourth, individual molecules (rotaxanes, catenanes) change conformation or redox state, which changes the conductance of a molecular junction. In many reports the mechanism was inferred from the current-voltage curve and not demonstrated. Reference: J.C. Scott and L.D. Bozano, “Nonvolatile memory elements based on organic materials,” Adv. Mater. 19, 1452 (2007); Q.-D. Ling et al., “Polymer electronic memories: materials, devices and mechanisms,” Prog. Polym. Sci. 33, 917 (2008).

Ques: How does the space-charge-limited current show the switching state?

With an ohmic contact the current of a trap-free layer follows the Mott-Gurney law $J = \frac{9}{8} ε μ V^{2} / d^{3}$ . Traps capture the injected carriers and the current is lower and rises with a higher power of the voltage, $J \propto V^{l + 1}$ , until the traps are filled at $V_{T F L} = q N_{t} d^{2} /2 ε$ , above which the current rises steeply to the trap-free law. The high-resistance state is the empty-trap state, the low-resistance state is the filled-trap state, and the analysis of the slope of the log-log current-voltage curve (slope 1, then 2 for a shallow single level or $l + 1$ for an exponential distribution, a steep rise at $V_{T F L}$ , then 2) is the standard test of the mechanism. A cell with a filament does not show this scaling with $1/ d^{3}$ and with area. Reference: M.A. Lampert and P. Mark, Current Injection in Solids, Academic Press, 1970; J.C. Scott and L.D. Bozano, Adv. Mater. 19, 1452 (2007).

Ques: What does the molecular junction add to the picture?

In a molecular junction the molecule is the active element, and the current is a coherent tunnelling current through the molecular levels. For a molecule that is off resonance the conductance falls exponentially with the length, $G = G_{c} exp (- β_{N} N)$ ; when a level is brought near the Fermi level the transmission is a Breit-Wigner peak $T (E)$ and the current is given by the Landauer formula. A change of conformation or redox state moves the level and changes the conductance by orders of magnitude in principle. The practical problems are the variability of the contact, the small number of molecules, and the stability of the molecule in the solid-state device. Reference: A. Nitzan and M.A. Ratner, “Electron transport in molecular wire junctions,” Science 300, 1384 (2003); C.P. Collier et al., “A [2]catenane-based solid state electronically reconfigurable switch,” Science 289, 1172 (2000).

Ques: Why are organic memories studied, and what limits them?

The organic layers can be deposited by solution or printing at low temperature on flexible substrates, and they allow chemical design of the energy levels. The limits are the variability of the film, the low mobility and the sensitivity to oxygen and moisture, the low endurance and retention, and the lack of a switching model that predicts the behaviour; the reliability numbers are covered on the reliability pages. The devices are mostly studied for flexible and low-cost applications, not for density or speed. Reference: Q.-D. Ling et al., Prog. Polym. Sci. 33, 917 (2008); R.S. Potember, T.O. Poehler and D.O. Cowan, “Electrical switching and memory phenomena in Cu-TCNQ thin films,” Appl. Phys. Lett. 34, 405 (1979).

Quartz 5

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