Organic Ferroelectric Polymer Memory (PVDF and P(VDF-TrFE))

1. Theory

Definition: Organic ferroelectric polymer memory uses a ferroelectric polymer, usually PVDF or its copolymer P(VDF-TrFE), as the storage layer in a capacitor, a transistor or a diode.
Origin of polarization: Aligned dipoles of the $C H_{2}$ - $C F_{2}$ units in the polar all-trans crystal phase; switching rotates the chains inside the crystallites.
Remanent polarization: Ideal crystal value about $10$ to $13 μ C/c m^{2}$ (estimates differ with the dipole moment used), but films reach a few to about $10 μ C/c m^{2}$ because only part of the film is crystalline and oriented.
Coercive field: About 50 MV/m, scaling only as $d^{- 2/3}$ with film thickness (Kay-Dunn), so thinning lowers the voltage slowly.
Low-temperature processing: Spin coating at low temperature allows memory on flexible plastic substrates.
Three device forms: Capacitor (read by switched charge), organic ferroelectric FET (read by threshold shift) and ferroelectric diode (read as current).

2. Working Principle

Write: A voltage above the coercive voltage (about 5 V for 100 nm) aligns the polymer dipoles up or down.
Capacitor read: Destructive switched-charge sensing, $2 P_{r} A$ , as in FeRAM.
Transistor read: The polarization shifts the threshold of an organic semiconductor channel, read non-destructively.
Diode read: In a ferroelectric-semiconductor polymer blend, polarization raises or lowers the injection barrier, switching the current on or off.
Switching energy: About $2 P_{r} V_{c}$ per area (about 0.8 pJ for a $1 μ m^{2}$ cell with illustrative values).
Annealing: Annealing above the Curie temperature raises crystallinity and polarization.

3. Applications

Current status: Mainly research, with limited commercial use.
Printed memory labels: Low-bit-count rewritable memory printed on plastic for tags, labels and toys.
Flexible electronics (target): Non-volatile memory for wearable sensors and flexible circuits.

Name	Formula	Related Formulae	Variables/Constants
Polarization of a polar polymer crystal	$P_{cr y s t} = \frac{n _{d} μ _{d}}{V _{u}}$	$P_{r} \approx x_{c} x_{o} P_{cr y s t}$	$P_{cr y s t} : p o l a r i z a t i o n o f a p er f ec tl y a l i g n e d cr y s t a l o f t h e p o l a r p ha se (t h e b e t a p ha se o f P V D F an d i t s co p o l y m er w i t h t r i f l u or oe t h y l e n e)$ $n_{d} : n u mb er o f m o n o m er d i p o l es in t h e u ni t ce l l$ $μ_{d} : d i p o l e m o m e n t o f o n e m o n o m er u ni t (t h e C H_{2} - C F_{2} g r o u p)$ $V_{u} : v o l u m e o f t h e cr y s t a l u ni t ce l l$ $P_{r} : r e man e n t p o l a r i z a t i o n o f t h e f i l m$ $x_{c} : cr y s t a l l in e f r a c t i o n o f t h e f i l m$ $x_{o} : or i e n t a t i o n f a c t or o f t h e cr y s t a l l i t es, e q u a l t o o n e w h e n a l l t h e c hain s a r e a l i g n e d w i t h t h e f i e l d d i r ec t i o n (t h e f i l m p o l a r i z a t i o n i s l o w er t han t h e cr y s t a l v a l u e b ec a u se o f t h e am or p h o u s f r a c t i o n an d t h e or i e n t a t i o n)$
Thickness dependence of the coercive field (Kay-Dunn)	$E_{c} (d) = E_{c 0} (\frac{d _{0}}{d})^{2/3}$	$V_{c} = E_{c} d = E_{c 0} d_{0}^{2/3} d^{1/3}$	$E_{c} (d) : coer c i v e f i e l d o f a f i l m o f t hi c k n ess d$ $E_{c 0} : coer c i v e f i e l d a t t h e r e f er e n ce t hi c k n ess d_{0}$ $d, d_{0} : f i l m t hi c k n ess an d r e f er e n ce t hi c k n ess$ $V_{c} : coer c i v e v o l t a g e a cr oss t h e f i l m (i t r i ses s l o w l y w i t h t h e t hi c k n ess, so a t hin f i l m l o w er s t h e o p er a t in g v o l t a g e)$ $(t h e e m p i r i c a l sc a l in g w a s f o u n d f or f er r oe l ec t r i c cr y s t a l s an d i s u se d f or t hi c k er p o l y m er f i l m s; v er y t hin L an g m u i r - B l o d g e tt f i l m s ha v e b ee n r e p or t e d t o s h o w a coer c i v e f i e l d in d e p e n d e n t o f t h e t hi c k n ess, so t h e sc a l in g s h o u l d n o t b e e x t e n d e d t o a f e w nan o m e t r es)$
Switching charge and energy of a capacitor cell	$Q_{s w} = 2 P_{r} A$	$W_{s w} \approx 2 P_{r} V_{c} A$ $W_{l oo p} \approx 4 P_{r} E_{c} A d$	$Q_{s w} : c ha r g e r e l e a se d w h e n t h e p o l a r i z a t i o n o f a c a p a c i t or ce l l o f a r e a A i s r e v er se d$ $P_{r} : r e man e n t p o l a r i z a t i o n$ $A : e l ec t r o d e a r e a$ $W_{s w} : e n er g y n ee d e d t o r e v er se t h e p o l a r i z a t i o n o n ce, f or a r ec t an g u l a r h y s t er es i s l oo p$ $V_{c}, E_{c} : coer c i v e v o l t a g e an d coer c i v e f i e l d$ $W_{l oo p} : e n er g y d i ss i p a t e d in o n e f u l l cy c l e o f t h e h y s t er es i s l oo p (t h e a r e a o f t h e l oo p t im es t h e v o l u m e A d)$ $d : f i l m t hi c k n ess$ $(t h e r e a d i s d es t r u c t i v e, a s in t h e f er r oe l ec t r i c c a p a c i t or o f t h e F e R A M p a g e)$
Ferroelectric diode: barrier modulation by the polarization	$Δ V_{P} = \frac{P t _{i}}{ε _{0} ε _{i}}$	$Δ φ_{B} \approx 2Δ V_{P}$ $\frac{J _{O N}}{J _{O F F}} \approx exp (\frac{q Δ φ _{B}}{k _{B} T})$	$Δ V_{P} : p o t e n t ia l d r o p a cr oss an in t er f a c ia l l a y er p r o d u ce d b y t h e p o l a r i z a t i o n c ha r g e t ha t i s n o t scr ee n e d b y t h e e l ec t r o d e$ $P : p o l a r i z a t i o n o f t h e f er r oe l ec t r i c p o l y m er$ $t_{i}, ε_{i} : t hi c k n ess an d r e l a t i v e p er mi tt i v i t y o f t h e in t er f a c ia l l a y er (t h e se mi co n d u c t in g p o l y m er or an in s u l a t in g l a y er)$ $Δ φ_{B} : c han g e o f t h e inj ec t i o n ba r r i er h e i g h t b e tw ee n t h e tw o p o l a r i z a t i o n d i r ec t i o n s : t h e d r o p i s + Δ V_{P} f or + P an d - Δ V_{P} f or - P, so t h e d i f f er e n ce i s 2Δ V_{P} (an u pp er b o u n d)$ $J_{O N}, J_{O F F} : inj ec t i o n - l imi t e d c u r r e n t d e n s i t i es o f t h e tw o s t a t es f or t h er mi o ni c e mi ss i o n$ $q, k_{B}, T : e l e m e n t a r y c ha r g e, B o l t z mann co n s t an t an d t e m p er a t u r e$ $(a cr u d e es t ima t e : t h e ba r r i er m o d u l a t i o n i s scr ee n e d b y t h e c ha r g es in t h e se mi co n d u c t or, so i t i s s ma l l er t han t h e u n scr ee n e d v a l u e; t hi s r o w i s a s im pl e e l ec t r os t a t i c co n s t r u c t i o n an d n o t t h e m o d e l o f a p a r t i c u l a r p a p er)$

Important Questions

Ques: What is a ferroelectric polymer memory?

It is a ferroelectric memory in which the ferroelectric layer is a polymer, usually poly(vinylidene fluoride) (PVDF) or its copolymer with trifluoroethylene, P(VDF-TrFE). The polarization comes from the aligned dipoles of the CH $_{2}$ -CF $_{2}$ units in the polar crystalline phase, and it switches by the rotation of the chains in the crystallites. The devices are the capacitor (read by the switched charge), the ferroelectric field-effect transistor with an organic semiconductor channel (read by the threshold shift) and the ferroelectric diode (read as the current). The layer is deposited by spin coating at a low temperature, so the memory can be made on flexible substrates. Reference: A.J. Lovinger, “Ferroelectric polymers,” Science 220, 1115 (1983); T. Furukawa, “Ferroelectric properties of vinylidene fluoride copolymers,” Phase Transitions 18, 143 (1989).

Ques: How large is the polarization, and why is it lower than the ideal crystal value?

The ideal polarization of the all-trans polar crystal follows from the dipole density, $P_{cr y s t} = n_{d} μ_{d} / V_{u}$ , and is of the order of 0.1 to 0.13 C/m $^{2}$ (10 to 13 $μ$ C/cm $^{2}$ ) for PVDF. The remanent polarization of a film is lower because only the crystalline fraction $x_{c}$ is ferroelectric and the crystallites are only partly oriented ( $x_{o}$ ), and values of the order of a few $μ$ C/cm $^{2}$ to about 10 $μ$ C/cm $^{2}$ are reported for P(VDF-TrFE) films. Annealing above the Curie temperature raises the crystallinity and the polarization. Reference: T. Furukawa, Phase Transitions 18, 143 (1989); A.J. Lovinger, Science 220, 1115 (1983).

Ques: What determines the operating voltage, and how much energy does a switch take?

The coercive field of P(VDF-TrFE) is of the order of 50 MV/m, so a film 100 nm thick has a coercive voltage of about 5 V, and the voltage falls as the film is made thinner, but only as $d^{1/3}$ (the Kay-Dunn scaling), so a thinner film does not lower the voltage in proportion. With $P_{r} = 8 μ$ C/cm $^{2}$ (0.08 C/m $^{2}$ ) and $V_{c} = 5$ V, the energy of one reversal per unit area is $2 P_{r} V_{c} = 0.8$ J/m $^{2}$ , that is about 0.8 pJ for a 1 $μ$ m $^{2}$ cell. These are illustrative numbers, and the practical voltage is higher than the coercive voltage because the switching is faster at a higher field. Reference: W.J. Merz, “Domain formation and domain wall motions in ferroelectric BaTiO $_{3}$ single crystals,” Phys. Rev. 95, 690 (1954); H.F. Kay and J.W. Dunn, “Thickness dependence of the nucleation field of triglycine sulphate,” Philos. Mag. 7, 2027 (1962); S. Ducharme et al., “Intrinsic ferroelectric coercive field,” Phys. Rev. Lett. 84, 175 (2000).

Ques: How does a ferroelectric polymer diode work?

A ferroelectric polymer is blended with a semiconducting polymer, and the film is placed between two electrodes. The polarization of the ferroelectric phase produces a field at the interface that adds to or subtracts from the injection barrier, and the current is high for one polarization direction and low for the other. The barrier change is crudely twice the potential drop in the interfacial layer, since the drop reverses with the polarization (the row of the diode), but it is partly screened by the charge in the semiconductor, so the effective change is smaller, and the on/off ratio follows the exponential of the barrier change. The device is a two-terminal memory that is read non-destructively. Reference: K. Asadi, D.M. de Leeuw, B. de Boer and P.W.M. Blom, “Organic non-volatile memories from ferroelectric phase-separated blends,” Nat. Mater. 7, 547 (2008); R.C.G. Naber et al., “High-performance solution-processed polymer ferroelectric field-effect transistors,” Nat. Mater. 4, 243 (2005).

Quartz 5

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